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Extraction d’étoiles standard pour l’étalonnage en flux
de l’instrument SNIFS dans l’expérience Nearby
Supernova Factory
Nathalie Blanc
To cite this version:
Nathalie Blanc. Extraction d’étoiles standard pour l’étalonnage en flux de l’instrument SNIFS dans
l’expérience Nearby Supernova Factory. Astrophysique [astro-ph]. Université Claude Bernard - Lyon
I, 2006. Français. �tel-00136871�
HAL Id: tel-00136871
https://tel.archives-ouvertes.fr/tel-00136871
Submitted on 15 Mar 2007
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No d’ordre 167-2006
LYCEN – T 2006-26
Thèse
présentée devant
l’Université Claude Bernard Lyon-I
pour l’obtention du
DIPLOME de DOCTORAT
Spécialité : Physique et Astrophysique
(arrêté du 25 avril 2002)
par
Nathalie BLANC
Extraction d’étoile standard pour l’étalonnage en flux
de l’instrument SNIFS dans l’expérience
Nearby Supernova Factory
Soutenue le 27 septembre 2006
devant la Commission d’Examen
Jury : Mme
M.
M
M.
M.
A.
P.
F.
G.
E.
Ealet
Astier
Hammer
Smadja
Gangler
Rapporteur
Rapporteur et Président du jury
Directeur de thèse
No d’ordre 167-2006
LYCEN – T 2006-26
Thèse
présentée devant
l’Université Claude Bernard Lyon-I
pour l’obtention du
DIPLOME de DOCTORAT
Spécialité : Physique et Astrophysique
(arrêté du 25 avril 2002)
par
Nathalie BLANC
Extraction d’étoile standard pour l’étalonnage en flux
de l’instrument SNIFS dans l’expérience
Nearby Supernova Factory
Soutenue le 27 septembre 2006
devant la Commission d’Examen
Jury : Mme
M.
M
M.
M.
A.
P.
F.
G.
E.
Ealet
Astier
Hammer
Smadja
Gangler
Rapporteur
Rapporteur et Président du jury
Directeur de thèse
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c0a*mn8tDdAuh8nb{rla-n8d‰sŒƒOnbhAgd
c0a*mn8tDdGn s±0x sn8tDyzaOclnŠƒf}n °¨Ž†gcld&aO‡cz‡rzƒ„g—hA‡c2st&gh saO‡c
H(t) =
WV
l0
u0gd‰§¨yŽ¨s‡saO{Irln
c0a*mn8tDdŒI§¨c†gyaO{r0nbnAdvs£l‡2clh—gyn8c0xŠsj‡rIs£c0gsjrltDn8ƒOƒ„n8yn8csŒŽ†gtƒ„n8d4x8{Ir0gsaO‡2cld
f/ÌGaOcld‰sn8aOc7n sbƒOnŽlt&aOclh8aOŽ’nh8‡d&yz‡ƒO‡€aO{r0nu0n s
‡ ¥ƒ„nŽ-‡2aOc2s
l
k = −1
yz‡rImnAyn8c2sŒn8d‰sŒn8cy‡A§n8c0clnbh8n8ƒOr0a†0ž“‚wƒf}n °¨Ž0gc0d&aO‡clnbƒf õ
ln8de€2gƒ„g°¨aOnAdq,‚›ƒf}aOc0d‰sjgc2s
ln›ƒf õ
ulƒf}n °lŽ0gcld&aO‡c¥d&n8t&g|aOc¨p†claOndDa
c+hA‡cld&aOlkAtDn£gƒO‡tDd5st&‡aOd¶s®§lŽ-n8deln4û0r0aOln8dAuln8r¨°¢vh8ƒ„gd&d&aO{r0n8d‰¤4n sGrlcw¢vcl‡2rImnAgr¨¤›Á
ƒOn8dû0rlaO0n8dhA‡yŽ’‡d&x8dln™Ž†gtvsaOhArlƒOn8dc0‡cI®tDn8ƒ„gsja*m¨aOd‰sn8d“Ž-‡r0tʃOnAdD{Irln8ƒOd“‡c
ŽltDnAdDd&aO‡c¥n8d‰s
crlƒOƒ„nl©Íg|lnAcld&a*sx
ρ
Ž’n8rIs¯h8‡cld&aOlxAtDn8t{r0nƒ„g
0r“û†rlaO0n—n8d‰sbgƒO‡tDdŠŽltDaOc0h8aOŽ0gƒOn8yn8csŠd&‡c¥x8c0n8tD€aOn0n—yÊgd&dDn20³›f}n8d‰s
ƒOn£hAgde0n£ƒ„g—yÊgsaOk8t&n£~0gt‰§‡claO{Irln£‡t&laOc0gaOtDnun s±cl‡rldGŽ†gtDƒOn8t&‡cldG0gcldGhAn£hAgdGlnŠyzgsaOkAtDn2©Íg—yÊgsaOk8t&n
cl‡aOt&nul{r0nc0‡rldŠx m‡{Irln8t&‡cldŠŽ0gtŠƒ„g|d&r0a*snuld&nhAƒ„gd&dDnwl‡c0hx8€2gƒOn8yn8cs
·
†gcldŠh8n s&snhAgsx8€‡t&aOn
dWerd ­ gs]ZcWt(u cwvfhx8ysfhz{f}|N_~c
q
q
ƒOn8d4û0r0aOln8dŒh8‡yŽ’‡d&x8dŒln›Ž0gt‰saOh8r0ƒOn8d4t&n8ƒ„gsa*m¨aOd‰sjn8d£g8mn8h—rlcln›Žlt&n8d&dDa„‡c
p ' ρ/3
x8cln8t&€aOn-³›f}n8d‰sbƒOnhAgdŠ0r¥t&g8§‡clc0n8yn8cs”
rlc1cl‡rImnAgrsv§¨Ž-n±0nGû0r0aOln±0‡c2s5ƒ„g
lnAcld&a*sx
ρ
al
‡2~-n8t‰sd&‡cI
Î
ρ
n8d‰s£ƒ„g1lnAcld&a*sx›n8c
n8d‰s5aOclhA‡clcr0n”`bp0c0n±tDn8c0ltDn±hA‡yŽ¨sn±lnƒ„gŠh8‡2cld‰sjgc2sjn
h8‡d&y‡ƒO‡2€aO{rln2u0cl‡rldŠh8‡2cld&aOlk8t&n8tD‡c0d£aOhAarlc¥û0rlaO0nl‡2c2s
ÌecrIsjaOƒOaOdgc2sŒƒ„gwyzx stDaO{Irlnbln
WV
‡
ƒ„gln8c0d&a*sx
ρ
c0n›m2gtDaOnŽ†gd
H
g8mn8hwƒOn›sjn8yŽ0d ”
gƒOÈn8t±Ž’‡rlttDx8d&‡rl0tDnbƒOn8dx8{r†gsaO‡c0df/ÌGaOcld‰snAaOcʎ’‡rltrlcÊû0rla„ln
Ž0gtD–ga*s”u!ª0tDaOn8lyÊgclcn sw©•n8yzg½OsjtDn+Ž0gtvm¨aOn8c0cln8cs‚ƒf}x8{r†gsaO‡c˜dDr0a*mgcsnu!gŽlŽ’n8ƒOx8n+x8{r†gsaO‡c0n+ª0tDaOn80yzgc0c
(S QQ^U q›Á
o#m‡aOtŠŽ0gtŠn °¨n8yzŽlƒOnÄlgcl†g€n
2
ȧ
8πG
k
Λ
=
ρ− 2 +
a
3
a
3
Ìec7h8‡cld&aO0x8t&gc2sbƒOn8dŒst&‡aOdŒs®§¨Ž-nAd£0n—û0r0aOlnuln s
o Q ¿öq
f/gŽ0tDk8dŠƒ„g|0x p0claMsaO‡c¥0r“sjgr¨°¯f}n °lŽ0gc0dDaO‡2cËox8{Ir0gsaO‡2c
Q /µ2q
‡c¥Ž’n8r¨sŠxAh8tDaOtDnzÁ
H 2 (t) =
WV
‡
i
c
k
Λ
8πG X
ρi − 2 +
3
a
3
o Q /·2q
i
t&n8h8n8cld&nbƒOn8d4la !x8tDn8c2sjdGsv§¨Ž-n8d4ln
‡r¥c0‡cËoyzgsaOkAtDnulc0‡sx8nb¢ ¦
û†rlaO0n8dh8‡c0crldAulnbŽ0gtvsaOh8r0ƒOn8d4tDn8ƒ„gsa*mlaOd‰sn8d—ot&g8§‡clc0n8yn8cs”ucl‡sjx4¢ Î
¤‰q 0ÌGc¥la*mlaOd&gc2s
ƒOnAdŠln8r¨°¯ynAy1~ltDnAd£Ž†gt
H2
¤vq
u0‡c¥‡~¨saOn8c2s1Á
Š
8πG X
k
Λ
−
=1
ρi +
3H 2
3H 2 a2 H 2
o Q  q
i
c7lx p0c0a*sbgƒO‡tDdÁ

§k
8πG
ρi
3H 2
k
Ωk = − 2 2
a H
Λ
ΩΛ =
3H 2
X
8πG X
Λ
Ω =
Ωi + Ω Λ =
ρi +
2
3H
3H 2
o Q  2q
Ωi =
i
o Q ÿ q
o Q  QAú q
o Q  QQ q
i
³4n™d&‡c2s¯ln8d“ln8cld&a*sjx8dtDx80rla*sn8d“d&gcld0aOyn8c0dDa„‡culx8Ž’n8cl†gc2sn8d0rÏsnAyŽldA4©Gf}x8{r0gsaO‡c
d8f/x8h8tDa*s›gƒO‡tDd
lnª0tDaOn80yzgc0c
ln–)g«A‡c“sjtDk8dŠd&aOyŽ0ƒOaMp0x8nzÁ
n s+ƒf}‡cËm‡a*s|aOh8a±{r0nʃ„g7lnAcld&a*sx

n ’n s”u-ƒOn1d&aO€c0n0n
€x8‡yzx stDaOnÊ0nʃf õ
Ωk
Ω
Ž-nAtDyn s+0nÊtDn8yz‡c2sn8t1laOtDnAh sn8yzn8c2s|‚7ƒ„g€x8‡yzx stDaOnlnʃf õ
x sjgc2s—‡Ž0Ž-‡d&x+‚zh8nAƒOrla¶ln
cla*mn8tDdÁ•Ž0ƒ„gs+d&a
Ω=1
k
u†ƒ„gÊhA‡yŽ0gt&gaOd&‡c™ln
u͇rImn8t‰s+dDa
Ω<1
lnh8‡2cld‰sjgc2sjnh8‡d&yz‡ƒO‡€aO{r0nwn8ƒOƒOn—pl°¨nƒOnwln mnAclaOt£0nƒf õ
oœ4aO€Ê³4t&rlclhji-q uln sbd&a
Ω<1
o Q  Q ùq
Ω = 1 − Ωk
dD‡2c¥n °¨Ž†gcld&aO‡c7n8d‰s
aOclp0claOn2
Ω
n s+–#n8t&yxÊd&a
c0a*mn8tDdwÁ0dDa
Ω>1
g8mn8h
Q
Ω>1
cla*mn8t&d85Ìec
Ž’n8tDyn s›ln1h8‡c0c0g½OsjtDnƒ„g
¶¬›nʎ0ƒOrldAuÍn8cˆƒf/g~ld&n8c0h8n
a„ƒh8‡c0c0g½Ostg|rlc0ntDn8h8‡cst&gh sjaO‡c
‚€ 1ƒ^„h\†‡ƒ^„ˆ5‰ˆŠŒ‹^iƒ†h\ŽŒ>ŽWh‹H†h\ŠŒ‘Z’‹^‡“a‘1ˆ„•”–ƒ‡‡—8Š˜‘Z~™š‹H†hˆ‹“‚ h‘1Š›‹œiƒa”ƒ^Š˜ƒ^ž^Ž˜‘^Ÿ}‹H„ha‚ŽF‹‰h‰W‘ ŠŒ¡
>‹“kŽ›ŠF’ƒ^†^™šŽ˜‘ †^™k„ˆ†‡‘
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ò Ú
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c
õ
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ò å ò ß!Ù àÍÜIÚã†à
>b àÍáÝ
à5Ù
c0a*mn8tDdgr‘v‡2rltD•f}irlaen sx mnAc2srlnAƒOƒOn8yn8csŽltDx80aOtDndD‡2cÅx m‡ƒOr¨saO‡cŖ#r¨srlt&nu!ƒ„g
yn8d&rlt&nln8dw0a ’x8tDnAc2sn8dw0n8cld&a*sxAdwtDx8lr0a*sn8dwn8d‰s1h8tDrlhAa„gƒOnÍ¬bnzcl‡y+~ltDn8r0d&n8dwn °¨Ž’x8tDaOn8c0h8n8dwd&‡c2s1lx8la„x8n8d‚¯ƒ„g
c
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rlclnwŽltDn8yzaOk8tDna„lx8n
œ4aOn8c¥d&žltŠln8dŠyn8d&r0tDn8dŠlaOtDn8h sn8dŠd&‡c2s
claO{r0nu¨{Irln—c0‡rld£h8‡2clc0gaOd&d&‡c0d£~laOn8c¥n s
Ž’‡d&d&aO~lƒOn8dŠŽ-‡2rlt£ƒOn8dŠlnAcld&a*sx8dŠlntgla„gsa„‡c¥n s
0nyzgsaOk8tDn~†gtv§‡
dg8m‡cldŠ‡~ld&n8t‰mn8t80Æ5gt£yÊgsaOk8t&n—~†gtv§‡c0aO{rln2u¨‡c¥n8c2snAcl¯ƒ„g|yÊgsaOk8t&n
h8‡clcIrlnu4Žlt&aOclh8aOŽ†gƒOn8yzn8c2s¥h8‡c0dvsja*srlx8n•f}i2§¨0tD‡€k8c0nn s¥f}i0x8ƒOaOrly7u4n s¥tDx8Ž0gt‰saOnŽlt&aOclh8aOŽ†gƒOn8yzn8c2s¥n8c2st&nƒOn8d
x s‡aOƒOnAdn s+ƒOnʀgŸÊaOc2snAtDd‰sn8ƒOƒ„gaOt&n¶©Íg7ynAdDr0tDnz0aOtDn8h snÊln
d&nʖ)ga*s+n8cYgc0gƒ*§ldgc2s+ƒf/g~0d&‡tDŽIsjaO‡cˆlnʃ„g7ƒOr¨
Ωb
yaOk8t&n+d&rlt›ƒOn8d—ƒOaO€clnAd›0nm¨aOd&x8n+Ž’‡rlt›lnAd›‡~l‘vn sd—ƒO‡aOc2sjgaOcld|Á’‡c0x sn8t&yaOc0n+gaOc0d&a5ƒf/g~-‡c00gc0h8n+f}xAƒOx8ynAc2sd
ƒOx8€n8tDdh8‡yyzn+ƒOn+lnArIsx8t&aOrly
ƒf õ
Ž†gt›t&gŽlŽ’‡tvsw‚ƒ„g“{r0gc2sa*sx+•f}i2§¨0tD‡€k8c0n+n s‡c˜‡~IsaOnAc2sƒ„gh8‡2yŽ-‡2dDa*sjaO‡c0n
claMmn8tDdƒO‡tDdÊ0n7ƒ„gËcr0h8ƒOx8‡d‰§¨csilk8d&nŽltDaOyz‡tD0a„gƒOnu±h8n8dÊxAƒOx8yn8csd™o¬+u
7 ©•au 3
!
¥
n”qcf}x sjgc2s“Ž0gdʎ0tD‡0rla*sd
Ž0gt›ƒOn8d›tDx”gh saO‡c0d›ln+–#rld&aO‡ccr0h8ƒOxAgaOt&n+grh wrltb0n8d›x s‡a„ƒOn8dAu0§™x sjgc2s—Ž0ƒOrIs s—h8‡c0dDr0yx8dA!©nAd›y‡Ilk8ƒOn8d›0n
crlh8ƒ„x8‡d‰§¨c2si0k8d&n
Žlt&aOy‡tD0a„gƒOn
sS Q ù U
clnwyn8d&rlt&ntDx8h8nAc2sn
õ
Ž’n8tDyzn sDsnAc2sŒgƒO‡tDd0n
l‡clc0n
lx80rlaOtDn
0n
h8n8d4g~’‡cl†gclh8nAd±tDnAƒ„gsa*mn8dƒ„gmgƒOnArlt±0n
Ωb h2 = 0.0214 ± 0.0020 (±9.3%)
u†g8mn8h
h = H0 /100


Ωb
©•n8d,Žlil‡s‡cld,dD‡2c2seln8d,Ž0gtvsaOh8r0ƒOn8d5t&n8ƒ„gsa*mlaOdvsjn8dAun seŽ0gt‰saOh8aOŽ’n8c2sel‡c0hŒgr¢vtg8§‡clc0n8yn8csD¤l‡cseƒ„gbln8c0dDa*sjx
n8d‰s
ΩR
c
0­®ƒOdŠm¨aOn8clc0n8c2sbŽ0tDaOclhAaOŽ0gƒOn8yzn8c2s›lr7–#‡2cl70a ’rld
§Î
ƒ„gwtDn8h8‡2y1~laOc†gaOd&‡c Šn s4{rla-n8d‰sr0cÊh8‡t&Žld±c0‡aOt±Žlt&n8d&{rln
h8‡d&yz‡ƒO‡€aO{r0nu†t&g8§‡c0cln8yzn8c2sbxAyaOdbgry‡yzn8c2sb0n
Ž†gtD–)ga*sŒ‚wƒÀg—sn8yzŽ-x8t&gsrltDn
ln
2.48 × 10−5
u’d&‡a*s—rlc0n1lnAcld&a*sx10n
ln8dŠx s‡2aOƒOn8doa„cl–#x8tDa„n8rltDn‚
Žli0‡s‡c0d8}hAy
ülQQ
Žli0‡s‡c•}h8y
Q
−3
n SQ µ U 
2.728 ± 0.004
Ωγ h 2 =
©•g¯ƒ„‡aelnÊÄsn8–)gcŎ’n8tDyzn s1gƒO‡tDdw0n|t&n stD‡r¨mn8tƒ„g¯0n8cld&a*sx0nt&g8§‡clc0n8ynAc2sŽ’‡rlth8n8dwŽli0‡s‡c0dÁ
−3 u-ƒ„gtD€n8yzn8c2sdDr0Ž-x8t&aOn8rlt&n+‚Êh8nAƒOƒOn10n8d›Žlil‡s‡cld›aOd&d&rld
c
q l`br¨stDnh8‡2yŽ-‡2d&gc2snwlr¥t&g8§‡2clcln8yzn8c2sulƒOn–)‡cl¥0a ’r0d£0ncln8r¨
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c
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Ων h2 = 1.15 × 10−5
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QQ ù|clnArIstDaOc0‡dA}h8y
−3
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Tν
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n
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ln“ƒ„g™yzgsaOkAtDn“dDr‘vn sDsjn“‚aOcsn8t&gh saO‡c
€t&g8m¨a*s gsaO‡c0cln8ƒOƒOn+n8c™x sjrlla„gc2s—ƒ„gÊh8‡tDt&x8ƒ„gsaO‡2c™lnAdb€2gƒ„g°¨aOn8dA-­vƒOd›Ž-n8tDyzn sDsjn8c2s—gaOcld&a¶ln1yzn8d&rltDnAt
saOn8c0cln8c2s
Sk U
Á
ΩM h ≈ 0.20
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³
œ
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Ž’‡rlt£³Œ‡d&yaOh
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rl~0~lƒOn
gaOcld&a
WV
la !rld¯h8‡d&y‡2ƒO‡€aO{r0nÂo‡r¾t&g8§‡c0cln8yzn8c2s7‚
h = H0 /100
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c
n s1lnÊyÊgsaOk8t&nz~†gtv§‡c0aO{r0n
l
S· U  
ΩM
•©•n8dwlnAtDclaOn8t&dtDxAdDr0ƒ*sjgsdw0n
H0
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h = 0.73−0.03
n s
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nAclh8‡t&n
u¶gaOc0dDa±{Irlnʎ-‡r0twƒ„g7h8‡c0d‰sjgc2snÊ0n
Ωb
+0.007 u
ΩM h2 = 0.127−0.013
Ωb h2 = 0.0223+0.0007
−0.0009
cËn8cË0x8lr0a*s1Ž-‡2rlt
rlcln|mgƒOn8rltgŽlŽlt&‡A°¨aOyzgsa*mnz0n ú ¿ùµ k¨u
ΩM
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l‡c0cln8c2s
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QAÿ
yzgaOdGƒOn8deŽlt&n8yaOkAtDn8de‡~ld&n8t‰mgsaO‡2cldetDxAgƒOaOdDxAn8dehA‡clh8n8t&c0gaOn8csGr0claO{r0n8ynAc2sGlnAde€2gƒ„g°¨aOnAdŠohAnŒd&‡c2s±ƒOn8de‡2~¨‘vn sdGƒOn8d
ŽlƒOrld—~ltDaOƒOƒ„gc2sdAu’l‡clh+ƒOn8d—ŽlƒOrld
mlaOdDaO~0ƒOn8d—‚€tgcl0n1laOd‰sjgclh8n”q u-n sƒOn8d—yn8d&rlt&n8d—gaOcld&a5tDxAgƒOaOd&x8nAd›c•f}x sjgaOnAc2s—Ž†gd
dDrl´zdgyzyn8cswŽltDx8hAaOdDnAd—Ž’‡r0t›Ž’‡rIm‡2aOt—h8‡c0h8ƒOrlt&n©Gf}x m‡ƒOr¨saO‡cÅln8d€2gƒ„g°laOn8dclnŽ-n8t&yn swŽ0gd—0n|h8‡yzŽ0gtDnAt
âS}ù Fú U ¶­®ƒ4–)gr¨s|l‡2clhÊstD‡r¨mn8t10n8d
c
ln“–)g«8‡cYp†g~0ƒOn“ƒOn8d+‡~0dDnAtvmgsjaO‡cld|tDxAgƒOaOd&x8n8d‚0n8d+laOd‰s gclh8n8d|la ’x8t&n8c2snAd
¢vhji0gclln8ƒ„ƒOn8d1d‰sjgcl†gtDld‰¤ju͇~¨‘vn sjd1{rlacf}x m‡ƒOr0n8c2s|Ž0gd+grYh8‡r0tDd1lrËsn8yzŽldAuÍl‡c0hÊl‡2c2s+ƒ„gƒOrlyzaOcl‡d&a*sxn8d‰s
s‡r‘‰‡rltDdŠaO0n8c2sjaO{rln†©Gf}aOlx8nw•f}rIsaOƒOaOd&n8tŠ0n8dŠd&rlŽ-nAtDcl‡Am2þ¾0n›s®§¨Ž’n­vgŽ’‡rlt£hAn8ƒ„gzgx sxŽ0tD‡Ž’‡d&x8nŽ†gtb²—‡‡~0gt
sS}ù ^Q U uaOlxAnŠ{Irla†gw0‡clc0xŠc0ga„dDdgc0h8nb‚wƒf}n °¨Ž’x8tDaOn8c0h8n›ÄIrlŽ’n8tDc0‡Amg³Œ‡dDyz‡ƒO‡€§Æet&‡‘vn8h s”u
n sŒÆ¶n8t&ƒOy1rIs&sn8t±n8c
QAÿÿ ö
ln8d‰saOc0x8n£‚—ƒ„g›0x8h8‡r¨mn8tvsnŒ0nŒd&rlŽ’n8tDc0‡Amþ
ƒO‡aOcsjgaOclnAd8uƒOnAdedDr0Ž-n8t&cl‡Amþ
hA‡clcr0n8decf}x sjgc2sgƒO‡tDdeŽ†gded&r¨´zdgcsn8d
S}ùù U †Ä¨a!ƒOnAd£Ž0tDn8yzaOk8tDn8dŠdDr0Ž-n8t&cl‡Amþ¾ƒO‡a„c2sjgaOc0n8dŠlx8h8‡r¨mn8tvsjn8d£c•f}‡c2s Ž†gd£d&r¨´
n8ƒOƒOn8d1c0‡cˆŽlƒOr0d+‚7h8‡c2stgaOcl0tDnʃOn8d1yz‡lk8ƒ„n8dã/S ùµ¨u5ù üWU uÍ0k8d1{rlnʃOn8r0tcl‡2y1~lt&ng7x sxÊd&r¨´Êdgc2s+ƒOn8d+y‡0k8ƒOn8d
f õ c0a*mn8tDd£‚1hA‡cld‰sjgcsn›h8‡d&yz‡ƒO‡€aO{r0n›cIrlƒOƒOn›‡2c2s£x sx—x8hAgtvsjx8dwS Q ¨
u Q k U I`›r‘v‡r0tDf}iIrla!g8mn8h—ƒOn8dŒ‡~0dDnAtvmgsaO‡2cld
Ž-‡r0tŒhA‡c2st&gaOcllt&n—ƒ„n8dŠy‡0k8ƒOn8d
dDŽ†gsa„gƒOnAd+ƒOn8d+yzn8d&rltDn8d+d&‡c2slnŽ0ƒOrld+n8cYŽ0ƒOrld+c0‡y1~lt&n8rld&n8d+n sŽltDx8h8a„dDnAd1n s|ƒOn8d+yzn8d&rltDnAd1t&xAgƒOaOd&x8n8d|g8mn8h“ƒOn
¥
sx8ƒOn8d&h8‡Ž’n›d&Ž0gsja„gƒ
IS}ùö¨ulù· U
r0~l~lƒOn
cla*mn8tDd£d&rlŽ0Ž-‡d&xŽlƒ„gs”0©Íg1p†€rlt&n
õ
0‡clc0n8c2sÁ
Ž-‡r0teƒOn8dG0a*mn8tDd,sv§¨Ž-nAdGf}n °lŽ-x8tDaOnAclh8n8dG†gcldGƒOnŠŽlƒ„gc
ƒOn8d£stD‡aOd
n s
h8‡c2s‡2rltDd
ΩΛ ≈ 0.7
l‡c0clx8n8d
`
ΩΛ − Ω M

+#
<; <;®ä
ØGܝÝ
#
u
Ω ≈ 1 ΩM ≈ 0.3
Í©•n8ds‡r¨sn8dw0n8tDc0aOk8tDn8dyn8d&rlt&n8dwn !n8h sr0x8n8d€t&h8nÊ‚Ä b©¶Ät&n8h8n8cld&n8cs1lnzŽlƒOr0dwcl‡2y1~ltDnArld&n8d
h8‡yzŽ0gsaO~0ƒOn8d
g8mnAhƒOnAdŠyn8d&rlt&n8dŠŽltDx8hAx8ln8csn8d
clxAh8n8d&dgaOtDn0ntDn mn8c0aOt£d&r0t£ƒ„g|cl‡saO‡c7ln0x8hAgƒ„g€n—mn8tDd
?%@Âë5E-íA tvAkå @ô• @†é([email protected]Ïéê¶ì*å@Í@lèGtvA
2ã†å#ãlß-Ü
yD BA [email protected]Í@-ç
ë4î è ÍçGí
S}ù U 
d‰sjgcl†gtDldŠŽ’n8tDyzn sbf}‡~Isjn8claOtŠh8nAdŠtDxAdDr0ƒ*
ƒOntD‡r0€nuldg|t&n8ƒ„gsaO‡cg8mnAhƒ„g|0aOd‰sjgclhAn
gr0d&dDaÍg8mn8hwƒ„g|ƒOr0yaOc0‡d&a*sx0n8dŠ‡~¨‘vn sdŠ‡~ld&n8t‰mx8dAulh8nw{rlnwcl‡rldŠ–#nAtD‡cldŠ†gcldŠƒOnŽ†gt&g€tgŽli0n
ï :ï
Ž-‡2rlt4rlc
Á2hji0g{r0n£n °lŽ-x8tDa„n8clh8nŠlx8ƒOaOyza*snŠrlchA‡c2s‡r0ten s
p†c7lnwh8‡yŽ0tDn8c0ltDnwh8‡yyzn8c2sbƒf}‡~0d&n8tvmgsjaO‡c7lnwhji†gcl0n8ƒOƒOn8d
yzgaOd
ΩΛ = 0.75+0.06 ± 0.04
d&nt&n8h8‡r¨m¨tDn8c2sbŽ’‡rltŠ–#‡tDyzn8tŠrlc7Ž’n sa*sbl‡yzgaOclngr¨s‡rltŠln8d£mgƒOnArltDd
‚€t&gcl7lx8h”gƒ„g€n—mn8tDdŠƒOnwtD‡r0€nn sbtDn8d‰sn8cs
sjgsdAulaOƒ•n8d‰s
n s
ΩM = 0.25+0.07 ± 0.04
~lƒOnln8d£hA‡c2st&gaOc2sn8dŠh8‡c0crl−0.07
n8d ‚+ƒf}i0n8rltDnwgh sjrln8ƒOƒOn
Q ¿ù+tDnAŽltDx8d&n8csnƒf}n8cld&n8y+−0.06
Q  Q ¿ù¨
D C :ê tê¨å5î[email protected]
í¨ê
ÜáÚzå#Üá ò àÍ߆Ü

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lnƒf}‡c0lntDnA«8rlnƒO‡t&dD{Irlnƒf}xAyn sDsjn8rlt+n s|ƒOntDxAh8n8ŽIsjn8rlt1d&‡c2s|nAcYy‡2rImn8yzn8c2s|ƒf}r0cYŽ0gt+t&gŽlŽ’‡tvs‚ƒf/gr¨stDn
³›f}n8d‰s£h8n›{Irla’Ž-nAtDyn sŒc0‡sjgyzyn8c2s£0n›lx snAtDyaOc0n8t4ƒOn8dm¨a*sn8d&d&n8dŒln›tD‡s gsaO‡c¯ln8dŒx s‡aOƒOnAd4†gcldŒrlc0nb€gƒ„g°¨aOn|Á
ƒOn›d&Ž-nAh stDn—ln8dŒx sj‡aOƒOn8dŒ{Irla’d&n—t&gŽlŽ0tD‡hji0n8c2s£0n›ƒf}‡~0dDnAtvmgsjn8rltŒn8d‰s£0x8hAgƒOxbmn8tDdŒƒOn—~lƒOn8rsjgcllaOdŒ{Irln›h8nAƒOrla’0n8d
x s‡aOƒOnAd4{r0a-dAf}x8ƒ„‡aO€cln8cs£n8d‰sŒ0x8hAgƒOx
mnAtDd4ƒOn›tD‡r0€n¨ÌGc“tDn8h8‡c0c0gaOd&dgc2s£lnAd4t&gaOn8dŒŽ0gtvsaOh8r0ƒOaOk8tDn8dAuIŽ0gt4n °ln8yŽ0ƒOn
ƒOn8dzt&gaOn8dzf/g~0d&‡tDŽIsjaO‡cÏln¥ƒf}i2§¨0tD‡€k8c0n¥ln8dÊgsyz‡d&ŽlilkAtDn8dd‰snAƒOƒ„gaOtDn8dAuen sÊnAcÏh8‡yŽ†gt&gcszƒOnArltDdzŽ-‡d&a*saO‡2cld
tDn8d&Ž-nAh sa*mn8d0gc0d±ƒOn8d±d&Ž-nAh stDn8d±‡cʎ’n8rIs4lx snAtDyaOc0n8tGƒ„g—m¨a*snAdDd&n
tDn8ƒ„gsja*mn
h8ƒ„gd&d&aO{rln2u†ƒOn1lx8h”gƒ„g€n1n8d‰s—laOtDn8h sn8yzn8c2s›Ž0tD‡Ž’‡tvsaO‡2clcln8ƒ5‚zƒÀg|m¨aMsn8d&d&n
t&gŽlŽ’‡tvs›‚|ƒf}‡~ld&n8t‰mgsn8r0t£Ž†gt£ƒ„gtDn8ƒ„gsjaO‡cÅÁ
z=
WV
‡
n s
n8d‰sŠƒ„g+ƒO‡2cl€rlnArltŒf/‡clln—xAyaOd&nu
c
nAc7gcl€2ƒ„gaOdjq4n s
Ž-nArIs
v
ƒf}‡~¨‘‰n s‡2~ld&n8tvmx2ÌGcÊyx8hAgclaO{r0n
0nlxAŽlƒ„gh8nAyn8c2s—0nƒ„gÊd&‡rltDh8n1Ž0gt
∆λ
v
=
λe
c
o Q  Q µ2q
ƒ„g+0a ’x8tDnAclh8n—n8cstDn—ƒO‡c0€rln8r0tDd£f}‡c0ln—tDn8«Arln—n sŠxAyaOd&n
λe
∆λ
ƒ„g¯mla*sn8d&d&nÊlnʃf}‡cl0noŽ-‡r0twc0‡rldAu•ƒ„g¥m¨a*sn8d&d&nÊlnʃ„g7ƒOrlyzaOk8tDn”q
c
otDn80dDi0aO–„s
ln
‹ stDnwclxA€2gsaO–5dDa•x8yn s&sn8r0t£n s
QAú

z
λr − λ e
n8d‰s|gŽ0Ž-n8ƒOxÊ0x8hAgƒ„g€nzmn8tDd1ƒOnÊtD‡rl€n
tDxAh8n8ŽIsjn8rlt£d&nwt&gŽlŽ0tD‡hji0n8c2s1o
λr < λ e
q 
u
dWerd ­ gs]ZcWt(u cwvfhx8ysfhz{f}|N_~c
×œØ®Ù©Ú Q ¿ù ÉJ½JǑ·Èà ÆнÇ<¼ºÀ©Ã ¾¿Ç<»(¼ºÏÒÏÒ¼ºÀ©À‘» ·©ÏÒ¼ºÀ>ŏÃd·Èà Ù-Ø¿Ç<·‘¼ÊÀ5¾¿ÉJÀ<Ù-ÉJϊÉÎJÆйi» ¼ÊÀ>Á\à ½(À©ÏŠ¼%ŏÏÐà ½
ÅÉJ» ·5Ç<·‘ÉJÆÐÀÇyÓBżºÀ
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Ž0gc0dDaO‡2cln+ƒf õ

c0a*mn8tDdAu’ƒf/gŽ0ŽltD‡Ihjiln+h8ƒ„gd&d&aO{r0n+cf}n8d‰sŽlƒ„rld›Ž’n8tvsaOc0n8c2sn+n saOƒ5c0‡rld—–)grIs€x8c0x8t&gƒOaOd&n8t—h8n sn ’n s
‚ƒf}x8hji0n8ƒOƒOn¥h8‡2dDyz‡ƒO‡€aO{IrlnGÆ5‡rlth8n8ƒ„glu,‡cÏh8‡c0d&aOlk8t&n¯ƒ„g™st&g‘‰n8h s‡aOt&n¯•f}rlcώlil‡s‡c†gcldƒ„g˜yzx stDaO{Irln¯0n
al
‡~-n8t‰sd&‡cI
Î

gƒOÈn8tA£³4n s&sn™st&g‘vnAh s‡aOtDn˜dAf}n !n8h sr0nƒOn˜ƒO‡c0€Âf}rlc0n€x8‡Ilx8d&aO{r0nu4n s¥‡c
f/gŽ0tDk8dŠƒf}x8{r†gsaO‡c
Q ¿ù¯Á
dr2
1 − kr 2
dt2 = a2
t£ƒOnwŽli0‡s‡c7dDnwt&gŽ0ŽltD‡h ilnlnwƒf}‡~ld&n8tvm2gsn8r0t8ul0‡clh‡2c¥Ž-nArIs

ÄI‡a*s”u0Ž-‡r0t£rlc7Žlil‡sj‡c¥x8yzaOd
‚
t1
ln
tDn8«Ar7‚
t0
t1
dτ 2 = 0
uŒd&‡a*s”u
o Q  Q8ü q
x8hAtDaOtDnÁ
dt
dr
= −√
a(t)
1 − kr 2
n s
r1
Z
g
o Q  Q öq
Á
t0
Z r1
dt
dr
√
=
a(t)
1 − kr 2
0
QQ
o Q  Q ·2q
XZY\[^]\_a`abHcdWeQX*fhg5`ic!jk`ic
Ì5sulŽ-‡2rlt£r0c7grIst&nŽli0‡s‡c7x8yaOdŠ0nƒ„gy‹8yznd&‡rltDhAnw‚
Z
t0 +δt0
¬V
¬1f}‡ ulnAc¥Ž’‡dgc2s
n s
a0 = a(t0 )
Z
t0 +δt0
t1 +δt1
ultDn8«Ar7‚
dr
√
=
1 − kr 2
Z
δt0
δt1
dt
'
−
+
a(t)
a(t0 ) a(t1 )
Z
dt
=
a(t)
t1 +δt1
tÁ

Z
t1 + δt1
a1 = a(t1 )
r1
0
Á
t0
t1
t0
t1
t0 + δt0
Á
dt
a(t)
o Q  Q q
k
dt
a(t)
o Q  Q 2q
δt1
δt0
=
a0
a1
Ì5suld&aƒf}‡c7hjil‡2aOdDa*sbh8‡2yynwn8d&Ž0gh8nAyn8c2s
WV
‡
δt1
o Q  QAÿ q
ƒ„gŽ-xAtDaO‡lnwlnƒf}‡c0lnwx8yaOd&n
T1
a1
δt1
T1
ν0
λ1
=
=
=
=
a0
δt0
T0
ν1
λ0
ν
lxAdDa„€clnbƒ„g1–#tDxA{rln8c0h8nbln›ƒf}‡cl0nbn s
mn8tDdrlclnyzx st&aO{rlnzŽlƒ„gsn2 Î
λ
dg1ƒO‡cl€r0n8rlt4f}‡c0ln 
gŽ0Ž-n8ƒO‡2cldw{r0nuŽ’‡rltwrlc
õ
z=
δt0 = T0
n sÁ
o Q ¿ù ú q

c¯gnAcn ’n s
cla*mn8t&dwn8cËn °¨Ž†gcld&aO‡cu
~laOn8crlc|0x8hAgƒ„g€n4mn8t&deƒOnŒtD‡2rl€nŒ†gcldeƒOn£d&Ž-n8h sjtDnŒln8de‡~l‘vn sdeƒO‡2aOc2sjgaOc0d8 
–)g«8‡c7{r0n0gc0d£ƒ„nhAgdŠhAƒ„gd&dDaO{Irlnwlnƒf/x8{r0gsjaO‡c
ul‡cgrlt&g
ƒO‡t&dD{Irlnbƒf}‡2czsjn8cl
λ = c/ν
u0‡clhz‡cˇ~ld&n8tvmn
a1
a0 > 1
clx p†cla*sGh8n£lx8hAgƒ„g€nŒ0nŒƒ„g—y‹8yzn
Q  Q µ¨u0h8n{Irla–)ga*sÁ
λ0 − λ 1
λ0
a0
∆λ
=
=
−1=
−1
λ1
λ1
λ1
a1
n s¯ƒOn™lx8h”gƒ„g€n7mnAtDdƒOn™t&‡rl€n™n8d‰s¯laOtDnAh sn8yzn8c2s¯tDn8ƒOaOx˜gr
o Q ¿ù Q q
©#b‡rld“Ž-‡2rIm‡c0dtDn8yÊgtD{r0n8t
–)gh sn8r0tf}x8h iln8ƒOƒOn
{rf/ga„cld&au’ƒOn+lx8hAgƒ„g€nmn8t&d›ƒOn+t&‡rl€n+Ž’n8rIsŽltDn8c0ltDn+ln8dbmgƒOn8r0tDd›d&r0Ž-x8t&aOn8rltDnAd—‚rlcdgcld—Ž-‡r0t›grIs gc2saOy|
ŽlƒOaO{r0n8t4r0cln£¢:m¨a*sjn8d&d&n ¤bln›ƒ„g+d&‡rltDhAn›{rla!dDn8tga*s£d&r0Ž-x8t&aOn8rltDn—‚1hAn8ƒOƒOn›0n›ƒ„g1ƒOr0yaOk8t&n Î
n8yÊgtD{r0‡cldŒx8€2gƒOn8yzn8c2s
{rlnh8nÊhAgƒOh8rlƒclnʖ)ga*s+aOcsn8tvmn8claOt1{rf}r0c¢v0x8Žlƒ„ghAn8yn8csD¤zƒOaOx“grY–)gh snArlt•f}x8hjiln8ƒOƒOn2u¶n s+{r•f/‚7h8nAƒOrla*:hAa±Ž-n8r¨s

d8f¿g‘v‡rIsjn8trlcyz‡rImn8yn8cs4Ž0tD‡Ž0tDnblnbƒf}‡~l‘vn s”utg‘v‡rIs gc2sŒr0cn ’n sŠ¬b‡Ž0ŽlƒOn8tAI©nAdGm¨aMsn8d&d&n8dŽ†gtvsaOhArlƒOaOk8t&n8d0n8d
€2gƒ„g°¨aOnAdx sjgcs1lnzƒf}‡t&ltDnz0nzƒ„g¥h8n8csjgaOclnÊlnzÈaOƒO‡2yk st&n8dŽ0gtwd&n8hA‡clln2ud&aGƒf}‡2~¨‘vn s+‡~ld&n8tvmxzn8d‰s1d&r¨´zdgy|
yn8csx8ƒ„‡aO€clx¥o Q
²—Ž’h+Ž†gt—n °¨n8yzŽlƒOn”qbdgÊm¨a*sn8d&d&n|Žlt&‡ŽltDn|d&n8t&g“clx8€ƒOa„€nAg~lƒOnln m2gc2sd&‡c˜xAƒO‡aO€cln8yzn8c2sw0žÅ‚
ƒf}n °¨Ž†gcld&aO‡clnwƒf õ
cla*mnAtDdA 
m¨r¥†gcldŠƒ„g|d&n8h saO‡c
Q  Q  Q 
:h
cla*s—gƒO‡tDd
ØGãˆÝ5Ù#Ú Û”ã ó ܝÝÍܘå#à YÙ óÍò ڔÙÀÛ
{Irlnwƒf}‡cd&nwd&a*sr0nw†gcld
q¥
ƒOnû†‡sb0n
rl~0~lƒOnu†h8‡yyznwcl‡2rld
³4‡c0dDaO0x8tD‡c0d+yzgaOcsn8c0gc2s”u¶Ž-‡r0t1rlcY‡~l‘vn s|l‡2c2s|ƒ„gƒOrlyzaOcl‡d&a*sjxaOc2stDaOc0d&k8{rlnnAdvs
!
ƒf}‡~ld&n8tvm2gsn8r0t80¬—gc0dŠh8n{r0ad&rla*sul‡c¥r¨saOƒOaOd&n8t&gŽlƒOr¨s s
n8d‰s
n s
u̓Onû0rI°ˆtDnA«8rYŽ0gt
o Q ¿ùùq
ƒOn—tg8§‡clc0n8yn8csŠn8d‰sŠd&r0ŽlŽ-‡2dDxaOd&‡stD‡Ž’nu¨n8d‰s
Î
al
‡2~-n8tvsjdD‡2cI
ƒ„g|d&rltD–gh8nlnƒ„g|dDŽ0ilk8tDnn8d‰s
lx8hAgƒ„g€n›mnAtDdŠƒOntD‡2rl€nu0{rlat&x8lr0a*s
ln8dŠŽ0il‡s‡2cldŠn8d‰s
χ
L
lx p†claOnhA‡yyznÁ
rlclaO–)‡tDyxAyn8c2s
laOd‰st&aO~lrlxdDr0t
€2gtD0gc2sƒOn8dÊcl‡sjgsaO‡cldʎltDx8hAx8ln8csn8dAuGd&a£ƒ„gÅ0aOdvs gclh8n7n8cstDn7ƒ„gÅd&‡rltDhAn7n sʃ¡f}‡~ld&n8tvm2gsn8r0t
u-†gcld›ƒ„gÊyx st&aO{rln10n
χ1
d = a 0 χ1
ƒ„gh8‡‡2tDl‡c0clx8nhA‡y‡~0aOƒOn
dr
dχ = √
1 − kr 2
©•g|ƒOrlyzaOcl‡d&a*sxlnƒf}‡~¨‘vn su¨0‡c2s
rlcln7d&Žli0k8tDn±Ìec
ƒf/g8m‡cld
ln
gƒOÈn8tbƒ„gÊ0aOdvs gclh8n1Ž0tD‡Žlt&n+gr™y‡yzn8c2s—ln1ƒf}‡~0d&n8tvmgsaO‡c™d&n8tg
4π(a0 χ1 )2
0©•n—û0rI°¯lnƒ„g|d&‡rltDhAn—n8d‰s
ƒf}x8clnAtD€aOnwln8dŠŽli0‡s‡c0d£f/rlc¥–)gh sn8r0t
ν1
ν0
lnŽlƒOr0d£y‡IlaMp0xŽ0gt£ƒOn
=1+z
0©•n›sjgrI°¯•f}x8yaOd&d&aO‡c
x8€gƒOn8ynAc2sbhji0gc0€xhAgt£ƒf}x8hji0n8ƒOƒOnw0n›sn8yzŽldŠcf}nAdvsbŽlƒOr0dŠƒ„g|yz‹8ynzÁ δt
0
=1+
Ž0gtŠd&n8h8‡c0ln”q4t&n8«8r¥Ž†gt£ƒ¡f}‡~ld&n8tvm2gsn8r0t£dAf}x8h8tDa*s p0c†gδt
ƒOn81ynAc2sÁ
ox8clnAtD€aOnwŽ0gt£r0cla*sxwlnd&rlt&–)gh8nn s
f=
L
4π(a0 χ1 )2 (1 + z)2
Q ù
z
uln sbƒOnû0rI°
o Q ¿ùµ2q
dWerd ­ gs]ZcWt(u cwvfhx8ysfhz{f}|N_~c
³4‡yyznƒ„gz0aOdvs gclh8nŽ0tD‡Žlt&nwc•f}n8d‰s›Ž0gdbrlc0nwyzn8d&rltDn1ghAh8n8d&d&aO~lƒOnŽ†gt
lnƒOr0yaOcl‡2dDa*sjx
ƒf}‡~ld&n8tvm2gsaO‡c•u†‡c0x p0c0a*sbƒ„gz0aOd‰sjgclhAn
dL
h8‡yzynƒOnwt&g8§‡2c7gŽ0Ž0gtDnAc2sb‚Ž0gtvsjaOt£lnwh8n—û0r¨°˜Á
dL ≡
s
L
= a0 χ1 (1 + z)
4πf
o Q ¿ù ü q
ctDn8yzgtD{r0nwaOh8a̓„gztDn8ƒ„gsaO‡cd&aOyŽlƒ„nwnAc2stDnlaOd‰sjgclh8nŽltD‡Ž0tDnwn sb0aOdvs gclh8nlnƒOrlyzaOcl‡d&a*sjxzÁ

#
‡s‡2cld,0n4Ž0ƒOrld,{IrlnuŽ-‡2rlt,rlc|Žlil‡s‡cuƒ„g
ŽltD‡Ž0tDndAf}x8h8t&a*s
d = a 0 χ1
WV
st&g‘‰n8h s‡aOt&nŒd&rla*sGƒ„g›€x8‡0x8d&aO{rlnun s
u0f}‡
d = a0
t8u†h8‡yzynwc0‡rld

ƒf¿g8m‡cldŠm¨r™grlŽ0gt&g8mgcs+ot&n8ƒ„gsaO‡c
lx8hAgƒ„g€nbmnAtDd£ƒOn—tD‡2rl€n 
dL
ΩR
n8d‰s
t0
t1
dt
a(t)
Q ¿ù Q q u†ƒOn–)gh snArlt
dL = d(1 + z)
dt  
aOhAac0x8€ƒOaO€x”q—Á
t1 a(t)
o Q ¿ùöq
f}x8hji0n8ƒOƒOnn8d‰sb0aOtDn8h snAyn8csbtDnAƒOaOxgr
!ª5aOc0gƒOn8yn8cszocl‡r0d›cf}nAc2stDn8t&‡cld›Ž†gd›aOhAa¶†gcld›ƒ„n+lx sjgaOƒ¶0n8d›hAgƒ„h8rlƒOdjq u’‡c
z
dL
n8c¯–#‡clh saO‡c¯lr“0x8hAgƒ„g€nbmnAtDdŒƒOn›tD‡r0€n›n sŠln8dŒŽ0gt&gyk stDn8d
n s
ΩM
p Z z
− 1 0
1+z
0 2
0
0
0
2
p S
dz
dL =
|κ|
(1 + z ) (1 + z ΩM ) − z (2 + z )ΩΛ
H0 |κ|
0
ΩΛ
o Q ¿ù·2q
-S/ù ^Q U u0‡WVÅÁ
aOh8a†gcldŠƒ„gcl‡sjgsaO‡c7rIsaOƒOaOd&x8nwŽ0gtb²—‡‡~0gt£n s›Æ¶n8t&ƒOy1rIs&sn8t

 sin(x)
sinh(x)
S(x) =

x
ƶ‡r0t,hji0g{IrlnŒh8‡2rlŽlƒOn
(ΩM , ΩΛ )
n s
n s
n s
d&a
κ = 1 − Ω M − ΩΛ
κ = 1 − Ω M − ΩΛ
κ=1
d&a
d&a
ΩM + Ω Λ > 1
ΩM + Ω Λ < 1
Ω M + ΩΛ = 1
u‡c|Ž’n8rIsGl‡c0hŒŽltDxAlaOtDnŒƒOn4û†rI°+tDn8«8r|•f}rlc0n4d&‡r0tDh8nŒ0‡c2sGƒOn4û0r¨°+aOc2stDa„cld&k8{r0n
n8d‰s›h8‡clcIr7ƒO‡2tDd&{rlnƒf}‡c™h8‡clc†g½Os›x8€2gƒOnAyn8c2s›d&‡c0x8hAgƒ„g€nmn8tDdbƒOntD‡r0€n†­®ƒÍcl‡r0d
¢vhji0gclln8ƒ„ƒOn8d5d‰sjgc00gtD0d‰¤u‡2~¨‘vn sd,l‡cs,ƒ„gbƒOr0yaOcl‡2dDa*sjx4aOc2stDa„cld&k8{r0n
L
–)grIs›h8n8Ž-nAcl0gc2sba„h8a•0n8d
n8d‰seh8‡c0crln4n secf}x m‡ƒOrln4•f/grlh8r0cln4–)g«8‡c
grh8‡r0tDd›0r7sjn8yŽ0d|ohf}nAdvsw‚la„tDn|g8mn8h+ƒOn+0x8hAgƒ„g€2nmn8tDd—ƒOn+tD‡rl€2n”q ’`br¨stDn8yzn8c2sla*su-d&a5Ž-‡2rlt›rlcln+d&‡rltDhAn
L
n8c
n s
z
d&‡c2szhA‡clcr0dAu,‡cώ-n8r¨szn8cÏlx80rlaOtDn¯ƒOn¯û†rI°
!
t&n8«8rŽ†gt|ƒ¡f}‡~ld&n8tvm2gsn8r0t8eÌGc
gd‰stD‡c0‡yaOnue‡cÏrIsaOƒOaOd&n
€2x8clx8tgƒ4ƒ„gyzg€2cla*sr0ln˜o)m‡aOtgclc0n °¨n“`qŽ0ƒOrIs sz{r0n“ƒOn“û0rI°u5hf}n8d‰szŽ-‡r0tD{r0‡a4‡cŽ0gt&ƒOn“0n¢vt&n8ƒ„gsaO‡c
yzg€c0a*srl0n :tDnAld&ilaO–„s&¤“Ž’‡rltƒOn8dzhji0gc0ln8ƒOƒOn8dzd‰sjgc00gtD0dAG³Œn sDsn¥tDn8ƒ„gsaO‡c
«¥
st&gh8nAt1ƒOn“la„g€t&gyyn“ln
dDr0Ž-nAtDcl‡Amþ
WV
o)m‡aOtx8{Ir0gsaO‡c
rl~0~lƒOnu5‡ Yƒ„g™yzg€c0a*srl0n“gŽ0Ž0gtDn8csnogrYyzg°¨aOy1r0y
`1 ÿ q+Ž’n8tDyn sz0n
ln“ƒOrlyzaOcl‡d&a*sxu5hAgt+ƒOn8d
lns®§lŽ-n­vgˆd&‡cs¯0n8d“‡2~¨‘vn sd¯l‡cs¯ƒ„gYƒOr0yaOcl‡2dDa*sjxmgtDa„n™tgŽlaOlnAyn8cs˜Á4hf}n8d‰s¥ƒ„gYƒOr0yaOcl‡2dDa*sjx
yzg°¨a„yzgƒOnŠ{r0alŽ’n8rIs‹ stDnŠh8‡yzŽ0gt&x8n£•f}rlclnŠd&rlŽ’n8tDcl‡Am2g‚ƒf/grIsjtDn”q,n8d‰s±t&n8ŽltDxAdDnAc2sx8nŠn8cz–#‡c0h saO‡czlrzlxAhAgƒ„g€n
¦
mn8tDd,ƒOn4tD‡rl€n4Ž’‡rltÍs‡r¨sn8d5ƒOnAd5d&rlŽ’n8tDcl‡Am2þˆ0nGsv§¨Ž-n4­vgbh8‡c0crln8degr‘v‡r0tDf}iIrla¬ba ’x8tDn8csd5yz‡0k8ƒOn8d5•f õ
oh8‡r0ŽlƒOn8d
(ΩM , ΩΛ )
cla*mn8tDd
q±d&‡cs£t&n8ŽltDxAdDnAc2sx8dŒd&r0t4ƒOn—y‹Ayn›0a„g€t&gyyn—Ž†gt4ƒ„n8rltŒtDn8ƒ„gsa„‡cz¢vyÊg€cla*sjrlln :tDn80dDi0aO–„sD¤
n s±ƒf}‡czŽ-n8r¨sGn8c0x8lr0aOtDn£ln8dGh8‡c2sjt&ga*sn8dGd&rlteƒOn8dGŽ0gtgyk sjtDn8dGh8‡d&y‡ƒO‡2€aO{rlnAd8©Ígbp†€rlt&n
_¥brl~l~0ƒOnŒh8‡c0d‰stDrlaMsg8mn8h£ƒOn8dGŽlt&n8yaOk8t&n8de0‡clc0x8n8de0n
Q /µ—n8d‰s±rlcn °ln8yŽ0ƒOn
æS Q U `›r+m¨rln£ƒf}x8{Ir0gsaO‡2c
ln£la„g€t&gyyzn£ln
Äl³ŒÆ
n s—0n1h8n1laÀg€t&gyzynu-‡2c™tDn8yÊgtD{Irln1{r0n1Ž-‡r0tbƒOn8d›–)gaO~0ƒOn8d›lx8hAgƒ„g€n8d
mnAtDd›ƒOn1tD‡2rl€n1ƒ„gtDn8ƒ„gsjaO‡c™c•f}n8d‰s—{r0n
ƒOaOclxAga„tDnwn8c
z
n sbc0nwlx8Ž’n8cl7Ž0gdŠ0n8dŠŽ†gt&gyzk stDnAdŠh8‡2dDyz‡ƒO‡€aO{Irln8dÁ0h8ncf}n8d‰sb{IrlnwŽ-‡r0tŠln8d
ƒOnŠt&‡rl€nbgr¨:lnAƒ„‚0n
f õ
ú ¿ö{r0nŠƒf}‡2cʎ-n8r¨s‡~0dDnAtvmn8t±ƒ„gwƒOn mx8n
d
ln
0x8€x8clxAtDn8d&h8n8c0h8nŠnAc2stDn
c
Q ¿ù·
lx8hAgƒ„g€n8d£mn8tDd
ƒOn8dla ’x8t&n8c2sdy‡0k8ƒOn8d
c0a*mn8tDdhjil‡aOd&aOdaOh8aG³›f}n8d‰szŽ’‡rltD{Irl‡a4ƒOnAd|ynAdDr0tDn8d|n ’n8h sr0x8n8ddDr0t+ƒOn8dhji0gc0ln8ƒOƒOnAd|d‰sjgc00gtD0d|cf}‡csŽ0r
‹ stDnbh8‡c0h8ƒOr0gcsn8d{r0n
ƒO‡tDd&{r0n
ƒOnAdŽlt&n8yaOk8t&n8dh8aO~lƒOnAdƒO‡aOc2sjgaOcln8d4‡c2s4Ž0rʋ sjtDn
‡2~ld&n8tvmxAn8dA ¦
gaOdcl‡r0dGmn8tDtD‡2cld
Ž0gtwƒ„g¥dDr0a*snz{rlnzƒf}‡~0d&n8tvmgsjaO‡cËlnzhji0gc0ln8ƒOƒOnAdwd‰sjgc00gt&ldwŽlt&‡hjilnAdwcf}n8d‰s1Ž0gdlx8cr0x8n•f}aOc2sxAtD‹ s”u•~laOn8cˆgr
h8‡c2stgaOtDn
+#
©•n8dŒtDxAdDr0ƒ*sjgsd£ƒOn8dŒŽ0ƒOrldŒtDxAh8n8c2sdAu¨‡~Isjn8crld£Ž0gtŒƒf}n °¨Ž’x8tDaOn8c0h8nÄ b©¶Ä’u¨dD‡csŠtDn8Žlt&x8d&n8c2sx8d4p†€rltDn
ƒf}‡cwh8‡c0dDaO0k8tDnGrlc
õ

t,ƒ„gb0aOd‰sjgclhAn
c¯Ž-nArIsŠl‡c0h—lx80rlaOtDn—lnbsj‡rIsŠhAn8h8a!rlc0n—tDn8ƒ„gsaO‡c¯nAc2stDn—0aOd‰sjgclhAn—ln—ƒOr0yaOcl‡2dDa*sjx
n slx8hAgƒ„g€nmn8tDd—ƒOn+tD‡2rl€n
Ž-n8r¨s£x8h8tDaOt&n›rlc0n›n °¨Ž0tDn8d&d&aO‡c“0n
o
Z
χ1 =
R t0
Q ü
S}ù U lĨa
cla*mn8tDd•Ž0ƒ„gs”uAi2§¨Ž’‡si0k8d&ne{rlnGcl‡2rld•d&rl€€2k8tDn8c2s¶–#‡t‰sn8ynAc2s̓„n8dÍgrIsjtDn8d!s®§lŽ-n8d͍f}n °¨Ž’x8tDaOnAclh8n8d
dDr0t•ƒOnAd͎†gt&gyk stDn8dÍhA‡dDyz‡ƒO‡€aO{Irln8d4o#m‡aOtÍd&n8h saO‡c
Q  Q  Q q ugƒO‡t&d
Q µ
ΩΛ
cln±Ž’n8rIs5‹ stDn±cr0ƒuAh8n±yz‡lk8ƒOn±x s gc2s5n °¨h8ƒOr
XZY\[^]\_a`abHcdWeQX*fhg5`ic!jk`ic
זØ~Ù©Ú
Ž0gt
ƒOn8d
Q /µ
qsç ÆÐÃdηÈà هÙ-¼XÁ ¼Xæ>»(â(â\ÏÒ¼/Å\·‘ÉBÁ\»(ƧǩÃ×˼ʾ/ÏÒ¼ºÀ'Å(·‘¼ºÙ3ÆÒØ×·‘¼ÊÀ'À‘» Å$¼×·<½ ÉÊËÌøÏÒÉJÆÒ½JÇäà ÆÒ½ ¼ÊÀçÉâÀƒ¼×·ƒËJ¸×¼ºÀ'ŏÃd· à Û éTÚ
0‡clc0x8n8dA†©Gf/g‘vr0dvsjn8yn8csbŽ’‡rlt
rlc
õ
cla*mn8tDd
Ž0ƒ„gsb0‡clc0ngƒO‡t&d
ƒOnh8‡rlŽ0ƒOn
sx8ƒOn8d&h8‡2Ž-nÅd&Ž0gsja„gƒU¥ r0~l~lƒOn2uŒ{r0a
S
µ Q U u!~laOn8c˜{r0n+ƒOn8dln8r¨°™n °¨Ž’x8tDaOnAclh8n8dgclcl‡c0h8n8c2swlnAd—aOclh8nAtvsa*sr0ln8d
) = (0.29, 0.71)
³4n8d7tDx8d&rlƒ*s gsd¥d&n8y+~lƒOn8csh8‡yŽ†gsaO~0ƒOn8d7gAmn8hŃOn8d7ln8t&claOn8tDd7tDx8d&rlƒ*s gsd7lr
‡~IsaOnAclclnAc2s
(ΩM , ΩΛ
cln0x8Ž0gd&dgc2sbŽ0gd
<; <;M
(ΩM , ΩΛ ) = (0.26, 0.74)

ú  ú ö|d&rltŠh8n8dŠŽ0gt&gyk stDn8dA
è @Dì±é @Dë[email protected]êéŒì'pUë5AÍçDt>[email protected]?Yç @†é(D
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aOh8aƒOn8d
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n
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dD‡2c2s5n ’n8h sjrlx8n8d¶n8caOc2sxA€t&gc2s5r0clnGŽ†gtvsa„n±lnGƒOnArltÍdDŽ’n8h sjtDn±dDr0t•r0cw0‡yzgaOc0n±lnGƒO‡2cl€r0n8rlt͍f}‡c0ln±l‡c0clxÆGƒOrld
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c
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ŽlƒOrldbƒO‡aOc2sjgaOcld
–ga*s›{rlnŽ-‡r0tŠƒOny‹Aynwp0ƒ*st&nwr¨saOƒOaOd&xŽ0gt
aOc2sx8€2tDx8n0­®ƒ–)grIs
0‡clhwgŽ0ŽlƒOaO{r0n8tŠln8dŠh8‡tDt&n8h saO‡2cld
ƒf}‡~ld&n8t‰mgsnArlt8u†rlcln1grIst&nwŽ†gtvsaOnlrd&Ž-nAh stDnn8d‰s
gr¥p0ƒ*stDnwrIsa„ƒOaOdDx2uln s”u0ƒO‡tDd&{r0nƒOnwlx8hAgƒÀg€n—mn8tDdŠƒOnwtD‡rl€2n
n8d‰s+aOyŽ’‡tvsjgcs”u•r¨saOƒOaOd&n8t0n8dwp†ƒ*stDn8d1ŽlƒOr0dtD‡2rl€n8dA¶Æ,gtn °¨nAyŽlƒOnŽ-‡r0twr0cˆlx8hAgƒ„g€n
¨
z = 0.5
u̓„nzp0ƒ*st&n7f Î
otD‡r0€n”qŠd‰sjgc00gtD™h8‡ ¡clh8a„ln1{r†gd&aOyn8c2sgAmn8h1h8n1{Irlnwmn8t&t&ga*s—ƒOnp†ƒ*stDnf/œ›f5o~lƒOn8r-q£Ž’‡rltbƒOn1yz‹8yn1‡~l‘vn s—c0n
f
(S µ2ù U 0©Íg+p†€rltDn
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n
107
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a„cln8tvsjnf/ilx8ƒOaOr0y
grIs‡2rlt10rl{Irln8ƒƒ¡f}i2§¨lt&‡€k8c0n“h8‡c2saM
crln¥‚–)rld&aO‡clc0n8t|n8cÏh8‡rlhji0n¯x8Ž†gaOd&dDn2e©n¥cl‡A§grύf}i0x8ƒOaOrly7u,aOd&‡silnAtDynu,d&n¥h8‡c2stgh sn¯0‡rlh8nAyn8cszn szd&n8d
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h r0t±f}ilxAƒOaOrly
d&n
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P = ρ5/3
q u¨{rla!cf/n8d‰s
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108
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12
6
16
8
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XZY\[^]\_a`abHcdWeQX*fhg5`ic!jk`ic
n s—‡A°§¨€kAcln+gr™h8n8c2sjtDn1lnƒ„gʀ2xAgc2sn2u†Ž0rlaOdbnAchA‡{r0aOƒOƒOn1grIs‡r0t
grÂs‡s gƒŠn8c2m¨a„tD‡c
rlc
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-S µ k U
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t&g8§‡c¥n8d‰s
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ρ = 4 × 109
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u2sn8yzŽ-x8t&gsrltDnb‚ƒ„g{r0n8ƒOƒOnbƒf}ilx8ƒOa„rly
lnyÊgd&d&n1gs‡2yaO{r0n
A
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u-‡c™gÊn8c™y‡A§n8clcln
A/2
107
n
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c0‡A§grŽltDxAdDnAc2s
x8ƒOn8h stD‡c0d+oc0‡stDnx sj‡aOƒOn1cln1h8‡c2sjaOn8c2s—ŽlƒOrld›f}i2§¨0tD‡€kAcln”q u
l‡c0hƒOnc0‡y1~lt&nf}xAƒOn8h stD‡2cldŠ0gcldŠƒf}x s‡aOƒOnd8f}xAh8tDa*s1Á
WV
‡
Ne =
mH
o Q ¿ù q
n8d‰s—ƒ„gzyÊgd&dDn1lr™ŽltD‡sj‡c-©•‡tDd&{r0nƒOn8dbxAƒOn8h st&‡cldbd&‡c2s—lx8€2x8clx8t&x8dAu†aOƒOdb‡Ih8h8rlŽ’n8c2s
ƒf}n8d&Ž0gh8nwln8d
aOyŽlr0ƒOd&aO‡clde‘vr0dD{Irf/‚|ƒf}aOyzŽlr0ƒOdDaO‡2c¥0nwª0n8tDyza
dD‡2a*s”uln8c7rIsjaOƒOaOdgc2sbƒ„g|tDn8ƒ„gsaO‡c
Q ¿ù
Ne =
2
h3
Z
`•mn8h˜ƒ„gˆmgƒOnArlts®§¨Žla„{rln˜ln
ρ
pF
uln s
Bk
3h3
16πmH
31
o Q ¿ù 2q
o Q ¿ù ÿ q
1
ρ3
n °¨Ž0tDaOyxAnŽ0ƒOrld¯i†grIs”uŒ‡c¾‡~IsjaOn8c2s7l‡c0hŽ’‡rlt¯ƒOn8d¥x8ƒOn8h st&‡cldÅÁ
Ȁl}y7}d
−1 ulmgƒOn8r0tŠd&rlŽ’x8tDaOn8r0tDn‚ƒ¡f}x8cln8t&€aOnlnwyÊgd&d&nw0nwh8nAdŠyz‹8ynAd
10−22
Ȁ0}y¥}d
−1 0©•n8dŠx8ƒOn8h stD‡c0d£d&‡cs
€2gŸ•f}x8ƒOn8h sjtD‡cld
s‡2rldbƒOn8dbx sjgsdb0n
‡cg¯Á
2 4
π (pF (e))3
h3 3
d3 p =
pF (e) =
3.5 ×
10−22
ρ
2mH
l‡clht&n8ƒ„gsa*mlaOdvsjn8dA 
lx8€x8c0x8tDx8dwÁ
2
Pe = 3
h
¬›gcldŠƒ„gƒOaOya*snwrlƒ*stg:tDnAƒ„gsa*m¨aOd‰snzÁ
~v =
dD‡2a*sÁ
hc
Pe =
8mH
Z
1
p~ · ~v d3 p
3
1
3
4
pF (e) =
me c = 2.7 ×
c7Ž-n8r¨sŠyÊgaOc2snAc0gc2sbhAgƒOh8r0ƒOn8t£ƒ„g|Ž0tDn8d&d&aO‡c¥0n—hAn
o Q /µ ú q
2cπ
c p~
⇒ Pe = 3 (pF )4
p
3h
3
16πmH
x8ƒOn8h sjtD‡cldÁ
ρ 3 = 3.10 × 1022
o Q /µ Q q
Æ5g
o Q /µ2ùq
‘ ƒŠ˜‘ Ž›Š ÖhŠŒƒH“‚a¦}„¬« „h†‡‘žH“‚‹H†hh‘ „‡“k‘8~™QŽŒ†hˆŽŒ’¡>‘¿‹>¯‘ Z’‘¿~»h”*ÇWƒ^ŠŒ‘HŸ‡‘ Š›Š˜‘“a‘>‰h“a¡ Á
Ë5†m‹H®™a“aƒ†‡ƒ^”©Ž˜‘^ŸhŠ˜‘¿~»h”*ÇWƒ^ŠŒ‘ “a‘>‰W¡ ®‘ †^™‚‘†‡ƒH™a“a
®‘ †^™‚‘¿hƒ^†hŠ›‹–¯‹HŠŒ‘ „‡“Q‡‘*ŠŒ‹žH“‚‹H†ˆ‡‘ „‡“¨’ƒH“a“a‘8®‰Wƒ^†hˆ‹H†^™a‘¿h‹^†h¨Š˜‘*>‹H¨h„ƒŠ˜‘ Ž›ŠLŸˆaƒ^Ž ™ ŸFŽŒ>ŽLŸFŠŒ‹©”©‹Haa‘¿aƒ^ŠŒ‹^Ž˜“a‘H°
ù ú
dWeŒþ ÿ z{[bc}v>Y\cbHv>Y5c-u cwv Y5[hg\u¾czrz{cx•x}`i[ˆg\u [hb^uNx
Ì5s,ƒf}‡c+tDn st&‡rImnƒf}x8{r†gsaO‡c+f}x s gs,f}rlc1Ž’‡ƒ*§st&‡Ž-nŽ-‡r0t̓OnA{rln8ƒ
‡c7grlt&ga*s1Á
~v =
dD‡2a*sÁ
aOh8ar0c1Ž-‡ƒ*§IstD‡Ž’n±Ž-‡2rlt̓On8{r0n8ƒ
¬—gcld5ƒ„g
ƒOaOya*sjncl‡c1tDn8ƒÀgsa*m¨aOd‰snu
8π
p~
⇒ Pe =
(pF )5
me
15me h3
h2
Pe =
40me mH
n s5‡2c1g
P ∝ ρ4/3
3
2πmH
P ∝ ρ5/3
2
3
o Q /µµ2q
5
ρ 3 = 3.15 × 1022
©Íg£mgƒOn8r0tÍ0n±ƒ„g
Æ5g
o Q /µ ü q
ŽltDnAdDd&aO‡c1n8d‰s50ryz‹8yn‡tD0tDn±ln€t&gclln8r0t
{rln0gc0d¶ƒOnhAgd5rlƒ*sjt&g:tDnAƒ„gsa*m¨aOd‰sn2©•nhAgƒOh8r0ƒlnƒ„g£sn8yŽ’x8t&gsjrltDnln4ª0n8tDya0n8d¶x8ƒOn8h sjtD‡cldŒo
WV
‡
EF
n8d‰sbƒf}x8clnAtD€aOngd&d&‡h8aOx8n‚
pF
TF (e) =
qŒcl‡r0d£0‡clc0nÁ
1 p
pF (e)2 c2 + m2e c2 − me c2 = 3.7 × 109
k
Ì5s›‡ctDn stD‡r¨mnw~0aOn8crlc0n—sn8yzŽ-x8tgsrlt&nwln1ª0n8tDyza•Ž’‡rltŠƒOnAd
lrÂyaOƒOaOn8r•u,l‡clh¯r0c
n
u
o Q /µ2öq
~laOnAc7d&r0Ž-x8t&aOn8rltDn1‚zƒ„g+snAyŽ-xAt&gsr0tDn
€gŸ¯f}x8ƒOn8h stD‡c0d|lxA€x8clx8t&x8dA,©•n8dy‹8yzn8d|hAgƒOh8rlƒOdŽ-‡r0t+ƒOn8dcl‡A§gr¨°¾ol‡2c2szh8n8tvsjgaOcld
dD‡2c2sŠ0n8dŒ–)n8tDya„‡cldAu¨hA‡yyzn—Ž0gtŒn °¨n8yzŽlƒOn
mN c = 7.0 × 10−18
x8ƒOnAh stD‡c0d
kTF = EF −mc2
Ȁl}y7}d
−1
13 ³£q4cl‡rld£l‡2clclnAc2s
pF (N ) = 1.8 × 10−22
o‡2c¥g|h8‡cld&aO0x8tDxaOh8a!r0c¯cIrlyxAtD‡gs‡2yaO{r0n—y‡A§n8c¥ln
Ȁ0}y¥}d
dD‡2c2s›0‡clhŽ†gdbtDn8ƒ„gsja*m¨aOd‰sn8dA’¬bn1y‹8yznu†ƒOnArlt£sjn8yŽ’x8t&gsjrltDnln+ªlnAtDya¶x sjgc2s—lnƒf}‡t&ltDn1ln
stDk8dŠaOcl–#xAtDaOn8rlt&nw‚|ƒ„g1sn8yzŽ-x8tgsrlt&n—0r¥yaOƒOaOnAruln s
Ž0gtwƒOn8dwc0‡A§gr¨°Åd8f}xAh8tDa*s1l‡c0h¥Á
x8ƒOn8h sjtD‡cld›lx8€xAclx8tDxAd8 
ƒOn8dŠc0‡A§grI°¯c0nd&‡c2s
PN = nN kT = 2.3 × 1019
−1 gƒO‡tDd£{r0n
Q8ü q 0©nAdŒc0‡A§gr¨°“c0n
104
n
u-n8ƒOƒOn1n8d‰s
Ž†gd£0x8€x8c0x8tDx8dA0©•gŽltDn8d&d&aO‡c¥–#‡2rltDc0aOn
Æ,g¥n sn8d‰swstDkAdwaOcl–)x8tDaOn8r0tDnʂ¯ƒ„g¥Ž0tDn8d&d&aO‡cÅ0n8d
cŽ’n8rIs—x8€2gƒOnAyn8c2shAgƒOh8rlƒ„n8tbƒ„gʎltDnAdDd&aO‡c™0rtg8§‡clc0n8yn8cs|o¡g8mn8h1ƒ„gʃO‡a¶0n|Äsn8–gc
Ž-‡r0tƒOn—h8‡tDŽ0d4cl‡2aOtq±n s£‡c“‡~¨saOn8csŒr0cln›ŽltDnAdDd&aO‡c
ŽltDn8d&d&aO‡c7ln8dŠx8ƒ„n8h stD‡2cldA
Pr
ln›ƒf}‡2tDltDn›0n
Æ,g¨uIn8ƒOƒOngrld&d&a0sjtDk8dŒaOcl–#x8t&aOn8rlt&n›‚1ƒ„g
1012

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n8d‰s¶l‡c0hGh8n8ƒOƒOnG0nGd&n8dÍx8ƒOn8h sjtD‡cldÍlxA€x8clxAtDx8dAuAn s¶ƒOn8dÍh8‡c0d&aOlx8tDnAt•h8‡yzynGr0cw€2gŸGŽ†gtD–)ga*s5lnG–#n8tDyzaO‡cldÍlxA€x8clxAtDx8d
n8d‰s¥rlc0nstDk8d¯~’‡clc0ngŽlŽlt&‡A°¨aOyzgsjaO‡c
Ž’‡rlt“ƒ„n8d¯x s‡aOƒOnAd¯lnh8n™s®§¨Ž’n
y‡0k8ƒOn0n8d+h8‡t&tDn8h saO‡2cld+lnÊs®§¨Ž’n8d+x8ƒOn8h stD‡d‰sjgsjaO{rln˜ogsDsjt&gh sa„‡c
ln8d4xAƒOn8h st&‡cldŒŽ0gt4ƒOn8dŒcl‡A§gr¨°!u¨grld&d&a!gŽlŽ’n8ƒOx8n›tDxAgh saO‡c
yzgaOdŠ0‡c2s
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g8mn8hфgÂyzx8hAgc0aO{rlnÅ{Ir0gc2sjaO{rlnÅn s7ƒ„gÏd‰sjgsaOd‰saO{IrlnÅln˪0n8tDyza*®¬›aOt&gh2Š©nAd¥‡~0d&n8tvmgsjaO‡cld7lnˆÄIa„tDaOrldœ
n8c
ðS}µ ˆÿ U u’{r0a,g8mgaOnAc2sŽ’n8tDyzaOd›0n1hA‡clc0g½OstDn+dgzsnAyŽ’x8t&gsr0tDnu’n swg8mn8h|n8ƒOƒOn+d&‡c˜t&g8§‡cn sdgln8c0dDaMsx¯odg
QAÿ¨Q ö
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g8mn8h±r0cln±ln8c0dDaMsx4ù úúú
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}
lnÊh8n sDsnÊyzgdDd&n5³—f}n8d‰s|ªl‡ bƒOn8t{rlauÍn8c
QAÿ ù·lu͎ltD‡Ž’‡d&nz•f/gŽlŽ0ƒOaO{rlnAtgr¨°ÅxAƒOn8h stD‡2cld0n8dc0gaOcln8d~0ƒ„gclhji0n8d
tDx8h8nAc2sdAul0nƒ„g|yzx8hAgc0aO{rln{Ir0gc2sjaO{rlnsS ü2úˆU Á5º ò ¸ –
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ƒOn8dŠtDx8d&r0ƒ*sjgsdAu0gƒO‡t&dŒs‡r¨s
(S ülQ^U 
ŽltD‡r¨mnƒf}n °laOd‰sn8clhAn•f}rlclnyÊgd&d&nyzg°¨aOy1r0yÓgŽ0Ž-n8ƒ„x8nln8Ž0rlaOd¢vyÊgd&d&nln1³4i0gc0lt&gd&n8ÈIi0gtv¤
šUã†ÚAÚ8ܙÝÍÜ K
ñ E
ã ó ÝÍáã†Ú8Ü
ã0á
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
yzgaOcsaOn8clc0n8c2srlc0nŽltDnAdDd&aO‡c
d&r¨´zdgcsnŽ’‡rlt1x m¨a*sn8t+ƒf}n ’‡2cllt&n8yn8cs|€tg8m¨a*sjgsjaO‡clc0n8ƒ
lx p†claOd&dgc2s|rlc0n|¢vŽ0tDn8d&d&aO‡cY€t&gAm¨a*sjgsaO‡2clclnAƒOƒOn ¤
h8‡tDŽ0d“0nyzgd&d&n
M
n s¥0nt&g8§‡2c
S µ k U
€t&g8m¨a*s gsaO‡c0cln8ƒOƒOnwdAf}x8h8t&a*s
Á
R
PG
c
Ž-n8r¨s|l‡2clhu¶n8c

‚Ž0gtvsaOt10nƒf}x8clnAtD€aOn“Ž-‡snAc2saOn8ƒOƒOn“€t&g8mla*sjgsaO‡c0cln8ƒOƒ„n0r
u4x8h8tDa„tDnƒ„gYt&n8ƒ„gsaO‡c¾f}xA{rlaOƒOaO~0tDn
PG ' −
ù Q
G M2
4π R4
Á
PG + Pe = 0


t“ƒ„g
ŽltDn8d&d&aO‡c
o Q /µ·2q
XZY\[^]\_a`abHcdWeQX*fhg5`ic!jk`ic
n s”u͎’‡rltƒOnÊhAgd1cl‡cˆt&n8ƒ„gsa*mlaOdvsjnÊh8‡yzynʎ’‡rltƒOnÊhAgd1rlƒ*sjt&g:t&n8ƒ„gsa*m¨a„dvsjnu̓Onʀ2gŸÊ•f}x8ƒOn8h sjtD‡cld1d&nÊh8‡yzŽ-‡tvsjn
h8‡yyzn
rlcʎ’‡ƒ*§st&‡Ž-n2u2h2f}n8d‰sŒ‚wlaOtDnb{rln
ln—Ž0rlaOd&dgclh8n
Pe ∝ ργ
x m¨aO0n8yyzn8c2s
WV
ul‡
γ
dgwŽltDnAdDd&aO‡cn8d‰s4laOtDnAh sn8yzn8c2s4tDnAƒOaOx8nb‚wdgw0n8cld&a*sx
Ž0gtrlcln
nAdvsbgŽ0Ž-n8ƒOxaOclln °“Ž’‡ƒ*§stD‡2ŽlaO{r0no‡r¥n °¨Ž’‡dgc2sbgla„g~†gsaO{r0n”q  
tDnAƒ„gsaO‡c
c¥Ž-n8r¨sŠ~laOn8c
tDxAx8h8tDaOt&nh8n s&snt&n8ƒ„gsaO‡c7n8c7–#‡clh saO‡c7lnƒ„gyzgd&d&nn sblr¥tg8§‡cu0h8nw{rlac0‡rldŠl‡2clclnzÁ
ÄI‡a*sbrlc¥t&gŽlŽ-‡2tvs
n8cstDnƒOn8d
(
Mγ
R3γ
Pe ∝
o Q /µ q
ln8rI°¥ŽltDnAdDd&aO‡c0dwÁ
k
PG
∝ M 2−γ R3γ−4
Pe
¬›gcld
ƒOnwhAgd
M 1/3 R
cl‡c¨:tDn8ƒ„gsja*m¨aOd‰snu
ox8{r†gsaO‡c
γ = 5/3
o Q /µ 2q
Q /µ ü qŒn sbƒ„nwt&gŽlŽ’‡tvsblnAdŠŽlt&n8d&dDaO‡2cld
n8d‰sbŽltD‡Ž’‡tvsjaO‡clclnAƒ•‚
Æ5‡rltrlcln|yÊgd&dDnl‡c0clx8nu!d&a,ƒOnt&g8§‡cËgrl€yzn8c2sn2ugƒO‡tDdƒ„g¯ŽltDnAdDd&aO‡cŀt&g8m¨a*sjgsaO‡clc0n8ƒOƒOnd&n8t&g“Ž0ƒOrld
aOyŽ’‡tvsjgcsn—n s
WV
–#n8t&g+t&n :la„yaOcr0n8tŒƒOnt&g8§‡cÅÁ¨ƒf}x sj‡aOƒOnn8d‰sŠd‰sjg~lƒOn2lÌGƒOƒOn›mx8tDaMp†n—rlc0n—tDn8ƒ„gsjaO‡c¥yzgd&d&n :t&g8§‡c¯‡
o
3γ−4
M ∝ R−3 M ∝ R γ−2
g8mn8h
γ = 5/3
q  ¦
gaOd±Ž’‡rltG{r0nŠƒf}i2§lŽ-‡si0k8d&nŠcl‡c¨:tDn8ƒ„gsa*m¨aOd‰sn
dD‡2a*sGmxAtDaMp0xAnu2aOƒ0–grIs
clx8h8nAdDdgaOt&n8yn8csoŽ0gtwlx p†cla*saO‡c-q›{Irlnzƒf}aOyŽ0rlƒOd&aO‡cËlnʪ0n8tDyzaed&‡a*s1–)gaO~0ƒOnzln m2gc2sƒ¡f}x8cln8t&€aOnzlnzyzgd&d&n0n8d
x8ƒOn8h sjtD‡cld
Á
pF m e c
u2n s4l‡clh2u2f/gŽ0tDk8dGƒ„gwtDn8ƒ„gsjaO‡c
Q ¼ù ÿ u2{IrlnŠƒ„glnAcld&a*sxŠlnŠƒ„gwc0gaOc0nŠ~lƒ„gc0hjilnŠd&‡a*s–gaO~lƒOn
¬V
ƶ‡r0teƒOn8dGc†gaOclnAde~lƒÀgclhji0n8dGln£i†grIsn£0n8cld&a*sxu2‡czgs&sn8aOc2sƒOn£hAgdGƒOaOyaMsn£r0ƒ*st&g®tDn8ƒ„gsaMm¨aOd‰snu‡
γ = 4/3
2¬—gc0d
h8nbhAgd8uIƒOnbt&gŽlŽ-‡2tvsŒln8d4Ž0tDn8d&d&aO‡cld4cln›lx8Ž’n8clŽ0ƒOrld4lrtg8§‡cuIn sŒƒf}xA{rlaOƒOaO~0tDnbc0nbŽ’n8rIsŒ‹ st&nbtDxAgƒOaOdDx›{r0nbŽ-‡r0t
rlcln1yzgd&d&n1l‡c0clx8nu’gŽlŽ’n8ƒOx8n1yzgd&d&n1ln+³Œi0gc0lt&gd&n8ÈIi0gt8!³4n s&sn1yzgd&d&nn8d‰s—lr™y‹Ayn‡2tDltDn10n€t&gclln8r0t
{rln›ƒ„g1yzgd&d&n›dD‡2ƒ„gaOtDn+Á
MCh = 2.86 × 1030
Ȁ
= 1.44 M
lÄIa!gr“lx8Ž0gtvsŒƒ„g1yÊgd&dDn›n8d‰s£aOcl–#x8t&aOn8rlt&n›‚1h8n sDsjn
yzgd&d&nʃOaOya*sn2uÍhf}n8d‰s+ƒ„g7Ž0tDn8d&d&aO‡cˆln8d1x8ƒOn8h sjtD‡cld1{r0a±ƒf}n8yŽ’‡tvsn2u•n s+ƒf}x s‡aOƒOnÊd&r0~la*s+rlc0nzn °lŽ0gc0dDaO‡2c7‘vrld&{r•f/‚
h8n1{r0n1ƒ„gln8c0dDa*sjx1laOyzaOcrln+dDrl´zdgyzyn8c2sŽ-‡r0tbtDn mn8c0aOt›grhAgd›c0‡cI:t&n8ƒ„gsa*mlaOdvsjn!ÄIa5Ž0gtbhA‡c2st&n1ƒ„gÊyÊgd&d&n
lx8Ž†gd&dDnwƒ„g|yzgdDd&nƒOaOyza*snu0ƒ„g|Ž0tDn8d&d&aO‡c¥€2t&g8m¨a*sjgsaO‡clc0n8ƒOƒOnwƒf}n8yŽ’‡tvsjnuln s
ƒ¡f}x s‡aOƒOnwd&rl~0a*s
rlc0nh8‡c2stgh saO‡c7{r0n
tDaOn8c7cf}n8yzŽ-‹8hji0n0©Íg|yÊgd&d&nln1³4i0gc0lt&gd&n8ÈIi0gt£nAdvsbl‡c0hrlc0nyzgd&d&nƒOaOyza*snwlnwdvs g~laOƒOa*sx2
<;~äZ;M
è E†í$A•çîyD [email protected]"Dë3=œ@+ps©tê:Dîê¶ç sŒê DBDîF>[email protected]
ï
ƶ‡2rltz‡~¨sn8c0aOtzrlcln7d&rlŽ’n8tDc0‡Amg˜0n¯s®§¨Ž-n7­vgluGaOƒŠ–)grIs0‡clh7rlc0n¥c†gaOcln7~0ƒ„gclhji0n7{rla
ƒOaOya*snbln—³4i0gc0lt&gd&n8ÈIi0gt8I©nbdDh8xAc0gtDaO‡1d‰sjgc00gtDʖga*s4aOcsn8tvmnAclaOt±r0cln
dv§ld‰sk8ynz~laOc0ga„tDnn s+gh8h8tDk sjn0nƒ„g¯yÊgsaOk8t&nlnzdD‡2cÅh8‡yzŽ0g€c0‡c ¦
gsDsn8a„c2sn+Ž’‡rlt—rlcln|ln8c0dDa*sjx
lr
ρ = 2.7 × 1013
Ȁ0}y
hAgt&~-‡c0nu5{r0a4n8d‰sln“ƒf}‡2tDltDn¯ln“{Irln8ƒO{r0n8d
8
~lƒ„gc0hjiln
~0ƒ„gclhji0n
gsDsjn8aOc2sƒ„gÅyÊgd&d&n
{r0a†–)ga*sŒŽ0gtvsjaOn
f}r0c
gaOdwƒ„g¥yzgd&d&n0nʳ4i0gc0lt&gdDnAÈi0gtwn8d‰s
−3 u!d&rlŽ-xAtDaOn8r0tDn|grd&n8r0aOƒ5ln|ƒ„g–)rld&aO‡c™siln8t&y‡cr0h8ƒOxAgaOt&n
ÈI€l}y
,©Íg™–#rld&aO‡cÂlr
−3
1012
q
g8mgc2sf/gsDsn8aOc0ltDnƒf}aOc0d‰sjg~laOƒOa*sjx“tDn8ƒ„gsa*mlaOd‰snoŽ-‡r0t
M . MCh
cf}n8d‰sŽ0ƒOrldh8‡c2st ƒOx8nun s4ƒ„gwc0gaOcln
c†gaOcln
hAgtD~-‡c0n“n8d‰s0‡clh¯gyz‡tDh8x8n
5©n“yaOƒOa„n8rYx s gc2s|0x8€x8c0x8tDxu¶ƒ„g™ŽltDnAdDd&aO‡c
n8d‰sn8csaOk8tDnAyn8cs0x stDr0a*snŠŽ†gtGr0clnŠn °¨ŽlƒO‡d&aO‡csi0n8tDyz‡crlhAƒOxAgaOtDn
³4nd&h8xAc0gtDaO‡zn °¨Ž0ƒOaO{rlnwŽlƒOr0dDaOnArltDdŠlnAd£h”gt&gh sjx8tDaOd‰saO{r0n8dŠŽlt&‡ŽltDnAdŠgrI°¯d&rlŽ’n8tDc0‡Amþ¾0n›s®§¨Ž’n­vg¯Á
q
q
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q
ƒ„g+ŽltDx8d&n8c0h8n›0n›h8nAdŒd&rlŽ-nAtDcl‡Am2þ
q
lxAŽ-‡r0tvm¨r0n8d
0gcldŒƒOn8dŒ€gƒ„g°¨aOn8d£n8ƒOƒOaOŽ¨saO{r0n8d—Á¨ƒf}x s‡2aOƒOn—cln—l‡a*sŠŽ0gd£clx8h8n8d&dgaOt&n8yn8cs
‹ stDnwyzgd&d&a*mn
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t&gaOn8d
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‘vrld&{r•f/‚wƒ„gwd‰§¨c2sjilk8d&n
0rÊclaOhjÈnAƒ†0gcld±ƒOnAd
#
56 a
28
56 ³Œ‡
27
0.7 M
→56
27
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MB – 5 log(h/65)
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-18
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-16
Calan/Tololo SNe Ia
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40
60
days
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light-curve timescale
“stretch-factor” corrected
MB – 5 log(h/65)
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0
20
40
days
60
Kim, et al. (1997)
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2
Entries
8400896
Mean
4.319e+04
RMS
1860
1800
1600
1400
1200
1000
800
600
400
200
0
10000
20000
30000
40000
50000
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2
Entries
Mean
RMS
1400
DiffØrence hypothŁse linØaire-rØalitØ (ADU), chip 01
diff
4167666
0.5164
3.381
1600
x10
2
Entries
Mean
RMS
diff
4167666
0.4262
4.78
1400
1200
1200
1000
1000
800
800
600
600
400
400
200
200
0
lnwƒ„g|p†€rltDnµl¿ùIu0Ž-‡2rltŠhji0ghArlc70n8dŠhji0aOŽld
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DiffØrence hypothŁse linØaire-rØalitØ (ADU), chip 00
x10
õ
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-10
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0
5
10
0
15
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-15
-10
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0
5
10
15
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Profile difference vs ADU (1H), chip 00
Profile x600 vs ADU (1H), chip 00
ADUprof
Entries 4167666
Mean
15.15
RMS
5.517
12
10
x600prof
Entries 4167666
Mean
15.15
RMS
5.517
30
25
8
6
20
4
15
2
10
0
5
-2
-4
0
-6
-8
m¨aOd&aO~lƒOn¥†gcldƒ„n¯€tgŽli0n
-5
0
20
40
60
80
100
120
x0 vs. x3600, chip 00
140
0
40
60
80
100
120
x0 vs. x600, chip 00
x0/x3600
Entries 4167666
Mean
15.48
RMS
5.134
3
20
140
x0/x600
Entries 4167666
Mean
2.351
RMS
2.998
5
4
2
3
1
2
1
0
0
-1
-1
-2
-2
0
לخٝÚ
20
40
60
80
100
120
0
20
40
60
80
100
120
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x600 vs. x3600, chip 00
histo des valeurs de x0, chip 00
x102
2_x600/x3600
Entries 4167666
Mean x
15.48
Mean y
2.346
RMS x
5.12
RMS y
2.937
30
25
20
x0
4167666
0.338
1.982
3000
2500
15
10
2000
5
0
1500
-5
1000
-10
500
-15
-20
Entries
Mean
RMS
3500
0
20
40
60
80
100
histo des valeurs de x600, chip 00
x102
0
-20
120
2200
-10
-5
0
5
10
histo des valeurs de x3600, chip 00
x102
x600
Entries 4167666
Mean
2.346
RMS
2.936
2400
-15
15
20
x3600
Entries 4167666
Mean
15.46
RMS
5.009
2500
2000
1800
2000
1600
1400
1500
1200
1000
1000
800
600
500
400
200
0
-20
לخ٩Ú
ê,ë_ì_í
-15
-10
-5
0
5
10
15
0
-40
20
-30
-20
-10
0
10
20
30
40
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Valeurs de l’Øclairement moyen, chip 01
Meanlight
Entries
0
Mean
6.737
RMS
4.162
0.006
Meanlight
Entries
0
Mean
6.708
RMS
4.16
0.007
0.006
0.005
0.005
0.004
0.004
0.003
0.003
0.002
0.002
0.001
0.001
0
0
2
4
6
8
10
12
Rapport des Øclairements moyens des deux chips: chip01/chip00
0
0
14
2
4
6
8
10
12
14
Rapport
Entries
16
Mean
6.982
RMS
4.022
1.2
1
0.8
0.6
0.4
0.2
0
0
2
4
6
8
10
12
14
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Valeurs de l’Øclairement moyen pour 24 poses
42800
42600
42400
42200
42000
Meanlight
Entries
0
Mean
12.56
RMS
6.631
41800
41600
2
4
6
8
10
12
14
16
18
20
22
24
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Valeurs de l’Øclairement moyen pour 24 poses, chip 01
Valeurs de l’Øclairement moyen pour 24 poses, chip 00
47200
49000
47000
48800
46800
48600
46600
46400
46200
Meanlight
Entries
0
Mean
12.55
RMS
6.631
48400
Meanlight
Entries
0
Mean
12.56
RMS
6.631
48200
46000
2
4
6
8
10
12
14
16
18
20
22
24
2
4
6
8
10
12
14
16
18
20
22
24
Rapport
Entries
26
Mean
12.49
RMS
6.634
Rapport des Øclairements moyens des deux chips: chip01/chip00
1.045
1.044
1.043
1.042
1.041
1.04
2
4
6
8
10
12
14
16
18
20
22
24
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Valeurs de l’Øclairement moyen, chip 00
Valeurs de l’Øclairement moyen, chip 01
2390
2480
2385
2475
2380
2470
2375
2370
2465
Meanlight
Entries
0
Mean
17.55
RMS
10.11
2365
2360
Meanlight
Entries
0
Mean
17.53
RMS
10.11
2460
2455
2355
2350
0
5
10
15
20
25
30
Rapport des Øclairements moyens des deux chips: chip01/chip00
2450
0
35
5
10
15
20
25
30
35
Rapport
Entries
52
Mean
17.49
RMS
10.1
1.042
1.0415
1.041
1.0405
1.04
1.0395
1.039
1.0385
1.038
0
5
10
15
20
25
30
35
×œØ®Ù©Ú µ¨§k q ò ¾×Ïcà Ɗ·‘¼ÊÙ-¼º½JÇ'Ù-ÉÊÓJ¼º½qÅÉJ» ·ç¾äå\à ¾×»\½Á ¼ºÀç¾Èå\ƊÅ\À Ý ¼Ê½qåÃd» Ç ß Á ¼©ÅÉJÀƒ¼ºÀdô,õ ë À‘»(¾º¾¿¼ºÀ‘À<ƧËJ¼ºÀçÁ ¼>Ç<¼ºÙ3Å\ÀNÁ ¼©Å$ÉÀ‘¼
Á(Ɗõ$¸×·‘¼º½JÇ<ÀºÕ(ƒ
ÉÊ˼º·<À‘¾ºÃ ½K¼¿Çâ\Æcà ÆÒÀÀƒÉJ»(ÀƒÇ<·Èà ƧÇÈÀ Þ ½âÃ ÀºÕ ·ÈÃdÅ\ÅÉ·ƒÇ'¼Ê½Ç<·‘¼XÏÒ¼ºÀÁ ¼º» ÑKå(ÆÒÀƒÇ<É Î·Èà هÙ-¼ºÀ/Ü\¾Èå(ÆÒÅ á ¾Èå(ÆÒÅ áá
Ú
ï6÷
Ú
Rapport aux voisins
10
7
10
6
10
5
10
4
10
3
10
2
rapportot
Entries
Mean
Rapport aux voisins
1.678949e+07
1
RMS
10
0.009788
rapportot
7
Entries
1.678949e+07
Mean
10
1
0
1
2
3
4
5
6
7
10
6
10
5
10
4
10
3
10
2
1
RMS
χ 2 / ndf
Constant
Mean
Sigma
0.9
0.95
1
1.05
0.00758
1.449e+04 / 22
7.566e+06 ± 2293
1 ± 1.822e-06
0.007458 ± 1.338e-06
1.1
ÄL‹ Æ5ú ‹‰h‰WƒH“®™1¬« „ˆ†3‰FŽ ­‡‘ ŠNª©®ƒ^†3¯^ƒ^Ž›aŽ›†
ÄLÇ Æ û ¨®„h®™a‘8”–‘ †^™Qˆ„3‰FŽŒ‰h“‚Ž›†h>Ž˜‰ˆ‹^Š
×œØ®Ù©Ú µ¨ ÿ Îià »(¾äå ¼ÕË Ã ÏÒ¼º» ·<ÀÁ\»_·ÈÃdÅ\ÅÉ·ƒÇ|Á(»8À‘ÆÒνÃ ÏBÁ+ »(½%Å\Æ§Ñ ¼ºÏ Ã×ËJ¼º¾N¾×¼ºÏÒ»\ÆBÁ ¼çÀƒÉJ½_ËÉJÆÐÀ‘Æн Á(·‘ÉJƧÇ<¼Õ Ý ·<ÉÀ<À‘ÆÐÀ‘À‘¼ºÙ-¼º½JÇ
À‘» ·5ϊ¼XÅ\Æо/q”Å(·<ü Æн(¾×ÆÒŏà Ï|Ü 0.9 < x < 1.1 Ú ½°Ãdêu»\ÀuÇ<¼ºÙ-¼Ê½ÇÎiÃd»\À‘À<Ɗ¼º½K¼ºÀƒÇ¼×õ¼º¾äÇÈ» ¸_À<» ·¾×¼/ŏÆÒ¾ Õ\Ú Åü Ãd·Èà Ù-¸¿Ç<·<ÆÐÀƒ¸XÁ ¼_ÏcÃ-ÀƒÉ·ƒÇ<¼3Ü
Ú
)
(
f (x) = Constant × e
Ú
−0.5×
M;~äZ;„L
ñK‚
õ
2
î1è2ì±ë@Ïë[email protected]>=„ê"•
ò
@ é(Dí$A•ç
†
à¶á¯åÀܙáÜߒÙ)Ú ÛAáܝÚdáÙÀÜ
7^`\YBaˎ’n8tDyzn sf¿g8m‡aOt|rlc0n“ŽltDnAyaOk8tDn¯aOlx8n¯ln“ƒ„g
c0n“x sr0ln“0n“ƒf}‡AmnAtDd&hAgcŽ’‡rlt+ƒOn8d|Ž’‡d&n8d|lns®§¨Ž-n
©&ŠÌŠ!©ÍgÊp†€rltDnµ¨ªç ú
³
x−M ean
Sigma
tDn8Žlt&x8d&n8c2sn+ƒOn|ŽltD‡p†ƒ5il‡t&aOŸ8‡c2sjgƒ50n+ƒf}‡Amn8tDd&hAgc˜d&x8tDaOn¯Á’Ž’‡rlt
ö
x
ç
hA‡yŽlt&aOd—n8c2st&n
ú ù
XY5[^]\_a`‚bcGe * t g¾_iLhc[¾t(uktâX X 1
ç
n s
ú ö·¨u¨‡c“t&n8ŽltDxAdDnAc2sn›ƒ„g+yz‡A§n8clc0n›ln—ƒ„gwm2gƒOn8r0t4lr“û0r¨°tDn8«8rÅon8c¯`›¬
qd&rlt±s‡2rIsn8dŒƒOnAdŒƒOaO€clnAd8l©Íg1Ž’‡d&n
õ
q^$`(Y a0nù ú d&n8h8‡2clln8dx m‡I{rlx8nAdŽlƒOrldi0gr¨s”u•h8‡2tDtDaO€x8nÊrlc0aO{rlnAyn8c2s10n
oh8‡tDtDnAh saO‡cˎ0gaOtv®aOyŽ0gaOtn s‡B’
 d&n s q •©•nŽlt&‡p0ƒen8d‰s1g‘‰rld‰sxŽ0gtrlc0n|n °¨Ž-‡c0n8c2sjaOn8ƒOƒOnz‚¯Ž0gtvsaOt0r
rIsaOƒOaOd&x8nÊaOh8aGnAdvs+rlclnz0n8d+ù ü
ƒf}‡Amn8tDd&hAgc
Ž’‡d&n8d
stD‡aOd&aOk8yznŽ0a*°¨n8ƒ
Overscan en profil horizontal
Overscan en profil horizontal
zoomov
Entries
0
Mean
1030
RMS
3.625
zoomov
Entries
0
Mean
1030
RMS
3.516
50
40
40
30
30
20
20
10
10
0
0
1030
זØ~Ù©Ú

ln˜ù ú
ªç
µl
1035
1040
1045
1050
1055
1030
1035
1040
1045
1050
1055
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ú
c
-^$`(Y a
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d&n8h8‡c0ln8d˜oƒ„gˆd&x8t&aOn™rIsa„ƒOaOdDxAn™n8d‰s¯ƒ„gYy‹8yzn™{r0n™Ž-‡2rltƒf}x sr0ln™0n™ƒf}x8h8ƒÀgaOtDn8yzn8c2s¥y‡A§n8c

n ’nAh srlxAn
ªç,çue†gcldƒ„g{Irln8ƒOƒOnÅÁen8cÏi†grIs‚0tD‡a*sjn¯nAdvsÊtDnAŽltDx8d&n8csx
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n8ci†grIsw‚€2grlhji0n
ŽlƒOrldzi0grIs q 

c
g˜Ž-‡r0t|h8nAh8aŒt&xAgƒOaOd&x¥ƒ„gp0€r0tDn7µ¨
c
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ù ü
/
Ž-‡d&n8d 5nAc
~0gd‚™€2gr0hjiln“n8d‰stDn8Ž0tDx8d&n8c2sjxu5n8c
ƒf}‡Amn8tDd&hAgc•u¨ƒOn—tgŽlŽ’‡tvsŠln—hAn8ƒOrlaeo
ƒ„g¥mgƒOnArlt
x0
xi
qlr¯Ž0a*°¨n8ƒ
ln“ƒf}x8h8ƒ„gaOt&n8yn8cs|0rYln8t&claOn8t1Ž0a*°¨n8ƒ4g8m2gc2sƒf}‡Amn8tDd&hAgc
oy‹Ayncrlyzx8tD‡s gsaO‡c{IrlnŽ-‡r0t
ƒ„gp0€r0tDn1µ¨/·2q  õ
x sjgc2s›gc†gƒO‡€rlnAdŠŽ-‡r0t£ƒOn8dŠ0n8rI°¯hji0aOŽldA

i
–#‡c0h saO‡cÂln“ƒf}x8h8ƒ„gaOtDn8ynAc2s
ln—ƒf}‡AmnAtDd&hAgc¯n sŠln
x0
0rY0n8tDclaOnAt+Žla*°¨n8ƒŒg8m2gc2s
¨n8c¯~†x0
gd£‚+0tD‡a*snn8d‰sŠtDn8Žlt&x8d&n8c2sxAn
n8cY–)‡clh sjaO‡cY0rYcrlyzx8tD‡™0nƒ„gŽ’‡dDn
cd&n8rlƒÍln8dblnArI°7hjilaOŽ0d
n8d‰s›aOh8aÍhA‡cld&aOlxAtDxu†ƒOn8dbtDx8d&rlƒ*s gsd
©&ŠÌŠuÍga„cld&aG{rlnzƒ¡f}x srl0nzlnzd&‡cˆh8‡yŽ’‡tvsnAyn8c2s1n8cˆ–#‡clh sjaO‡cË0r
cˆŽltD‡Ž’‡d&nzn8cld&rlaMsnzrlcËhAgƒOhArlƒG0n³
©&
ªç
sn8yzŽldŠlnwŽ’‡d&nzo)p†€rltDnµ¨ ”ùq 0©Ígʳ
Ì
”çö+Ž0tDn8yzaOn8tDd
aOh8a•hAgƒOhArlƒOx8nwn8d‰sbƒOnwt&gŽ0Ž-‡t‰s
Žla*°¨nAƒOd¶f}‡Amn8tDd&hAgc1nAcŽ0tD‡p†ƒi0‡tDaOŸ8‡csjgƒn s,ƒ„g
n8c2st&nƒf/aOc2sx8€tgƒOnwd&rltŠƒOn8d
d&‡yyzn±0n±hAn sDsnaOc2sxA€t&gƒOnn s,0n±ƒ„g£m2gƒOn8rlt
x0
lr1ln8t&claOn8t¶Žla*°¨nAƒ
x8h8ƒ„gaOt&x•©nAdŽ-‡d&n8daOhAa,h8‡2cld&aOlx8t&x8n8dd&‡c2slnAdyx80a„gclnAdhAgƒOh8r0ƒOx8n8d‚“Ž0gtvsaOtlnŽlƒOr0dDaOnArltDdŽ’‡d&n8dlny‹8yzn
§k
lrlt&x8n“oaOƒ¶dAf/g€a*sln1ƒ„gÊy‹Ayn1d&x8tDaOn10nŽ’‡d&n8d›{rln1Ž’‡rltbƒ„gzp†€rltDn+µ¨ 2qbgrI°l{rln8ƒOƒOnAdbƒOn+h8‡rltgc2s—f}‡~0d&h8rltDa*sjx
gÊx sx+d&‡rld‰stga*s”-ý
€2grlhji0n1d&‡c2s›s‡r¨s—f/g~-‡tDtDn8Žlt&x8d&n8c2sxAdbƒOn8d—t&gŽlŽ’‡tvsd
‡2~Isn8cIrld›Ž-‡r0tbh8n8d›Ž-‡2dDnAd
^`(Y a1yzx8la„gcln8dA2©•n8d,mgƒOn8r0tDdGn8cÊg~ld&h8aOd&d&n£tDnAŽltDx8d&n8csn8c2s±ƒOnŠcr0yx8tD‡wln£ƒ„gŽ-‡xi/x0
d&nÁ ú Ž-‡2rlt—ç£d&n8h8‡2cllnŠln£Ž’‡d&nu
痎-‡r0t£ù+dDn8hA‡cl0n8dAulù1Ž’‡r0t ü d&n8hA‡cllnAd8ulµ|Ž-‡r0t/+
k d&n8hA‡cl0n8dAu ü Ž’‡rltŒç”ù1d&n8hA‡cl0n8d8u0ö1Ž’‡rltŒçA·|dDnAh8‡cl0n8dAul·
Ž-‡r0tù ú d&n8h8‡c0ln8dAu’n sn8c¨p†cÊ
Ž’‡rltwù ü d&n8h8‡c0ln8dA³4nAh8a5Ž’‡rlt›ƒOn|hjilaOŽ úú n8c˜i0gr¨sn sŽ’‡rlt›ƒOn|hjilaOŽ ú ç+n8c
~0gdA†`
lt&‡a*sn1n8d‰s›tDnAŽltDx8d&n8csxƒOn1hAgƒOh8r0ƒÍ0n+³©& Ì
Ž-‡2rlt h8nAdby‹8yzn8dbŽ-‡2dDnAd8u-hjilaOŽ úú n8c™i0grIs—n s—ƒOnhji0aOŽ ú ç
n8c¥~0gdA# ‡s‡cldŠ{rlnƒOnwh8‡rltgc2s f}‡~0d&h8rltDa*sjxrIsaOƒOaOd&xaOh8aGodD‡2rld‰st&ga*sb‚|h i0g{r0nŽ-‡d&n”qŒg|x sx‡2~Isn8cIr7‚|Ž0gtvsjaOt
ln8d±Ž’‡d&n8d5W$Y Z(|
[ ln ƒ„gwy‹AynŠd&x8t&aOnu€t&h8nb‚wrlc0nŠh8‡y+~laOc0gaOdD‡2cʃOaOclxAgaOt&nŠ0rzû0rI°zf}‡~0d&h8rltDa*sjxŠf}r0cln dDnAh8‡cl0n
g8mn8hwh8n8ƒOr0af}r0clnyzaOcrIsjnu0gp0c7lnwyaOn8r¨°¯y‡Ilx8ƒOaOd&n8tŠƒOn~0a„gaOdŠaOc2sjtD‡lr0a*s
©&
©Íg1³
̈d&n8ƒO‡cƒOn
tDnA€aOd‰stDn
d&x8tDa„n
n8d‰s4l‡2clh£stDkAd±~’‡clc0nuln
ªç
ƒf}‡t&ltDn
0n
Ž0gt£ƒOn›sjn8yŽ0d£0nŽ-‡2dDn2
1 − 10−6
ÌGƒOƒOn
c0n
lx8Ž’n8clʎ0gd±0r
sn8yzŽld›ln+Ž-‡d&nu’h8‡yzyn+‡cŽ-n8r¨s—ƒOn+h8‡cld‰sjgsjn8tbp0€rlt&n+µ¨ Aµ¨Ä¨rlt›h8n sDsn1p0€2rltDn1nAdvstDnAŽltDx8d&n8csx8nu!‚Ê€2gr0hjilnu
c
rlcln+n8d‰saOyzgsaO‡c™0n1ƒ„ghji0gt&€n10a ’x8tDxAn1‡~¨sn8cr0n1n8c™d&‡r0d‰st&g8§gcs—ƒ„gzmgƒOnArltbn8c`›¬
Þç
õ
lr™Ž0tD‡p†ƒ¶il‡tDa„Ÿ8‡c2sjgƒ
f}rlc0nzh8‡ƒO‡c0clnzcˆ‚7h8n8ƒOƒOnz0nzƒ„g¥h8‡2ƒO‡clclnzc¨ 7Á•n8cYg~ld&h8aOd&d&nu•ƒOnzcIrlyxAtD‡7lnzƒ„g¥hA‡ƒO‡clc0nzf}‡Amn8tDd&hAgc
Œçu‡c|g›d&‡rld‰stga*seƒ„g›h8‡ƒO‡2clclnŒç
ƒf/g~ld&h8aOd&d&n
c
ú ù ÿ
8ç
‚›ƒ„g›h8‡ƒO‡c0cln
Bk
n8c|ƒ„g—la*m¨aOdgc2s±Ž0gteƒ„g›0a ’x8tDn8c0h8nŒhA‡ƒO‡clc0nŒx8h8ƒÀgaOtDx8n4•Žlt&n8yaOk8t&nŒh8‡ƒO‡c0clnŒ•f}‡Amn8tDd&hAgc 
Bk
ö
c
oŽ-‡r0t
ú ù 2q un sGn8c|‡tDl‡2clclxAn4ƒ„g›la ’x8t&n8clh8nŒcl‡t&yzgƒOaOd&x8n
c|tDn8yÊgtD{r0nŒrlcŽltD‡p†ƒ
G eŒþJåwt¬[email protected]Ö¥t¬cx8h`!tu
horizontal profile of the overscan, chip 01
Entries
Mean
RMS
χ2 / ndf
p0
p1
50
40
cx•xhtˆb¹u¾cx–]ZfˆxcHx¹u ¢ h`i[hz{fˆg¾g5[}|¾c
values of the slope for the overscan profile, chip 01
zoomov
0
1030
3.874
2.81 / 25
319.1 ± 2.008
-0.3073± 0.001945
1.8
24
Mean
-0.3159
RMS
0.01939
1.6
1.4
1.2
30
1
0.8
20
0.6
10
0.4
0.2
0
1030
1035
1040
1045
1050
0
-0.37
1055
xi/x0 vs. x0, chip 01
-0.36
-0.35
-0.34
-0.33
-0.32
-0.31
-0.3
-0.29
values of x0 vs. time, chip 01
49400
1.2
49200
hrapp
1
0.8
Entries
696
Mean x
Mean y
4.882e+04
0.1024
RMS x
RMS y
0.6
49000
340.2
0.2289
48800
0.4
Entries
48600
0.2
Mean x
Mean y
48400
0
-0.2
hvars
Entries
2
htime
696
12
4.884e+04
RMS x
6.633
RMS y
318.8
48200
48200
זØ~Ù©Ú
48400
48600
ªç3ç q ò
µ¨
n °¨Ž’‡cln8csaOn8ƒl‡2c2s
48800
49000
49200
49400
2
4
6
8
10
12
14
16
18
20
22
24
ÇÈ»\Á ¼XÁ(¼XÏ ɍ˼׷<À<¾ºÃ ½KÀ‘¸×·<ÆÒ¼/ÅÉJ» ·Wó Å ÉJÀ‘¼ºÀæô3õ ë Á ¼ýó á À‘¼º¾¿ÉJ½(Á(¼ºÀ'¾×ÉJ½(Àƒ¸Ê¾×»BÇÈƧËJ¼ºÀ
ö
Ú
‡c7g|t&xAgƒOaOd&xƒf/g‘vr0d‰sn8yzn8c2s”0ýUltD‡a*sjnulƒOnƒO‡€2gtDa*silyzn0x8h8aOyÊgƒlnƒ„g–#t&gh sjaO‡c¥lnhji†gtD€n
†øç›dDr0t4h8‡ƒO‡c0cln›cI7ç”qGnAc“–#‡clh saO‡c“ln›ƒf}x8hAƒ„gaOtDn8yzn8c2sŠy‡A§n8c¯ln›ƒ„g1Ž’‡dDn›n8c“ƒO‡2€2gtDa*si0yn›lxAh8aOyzgƒ
oh8‡ƒO‡c0cln›c
x8€2gƒOn8yzn8c2s”0`br0h8rlc0nh8‡tDtDxAƒ„gsaO‡c7c•f}n8d‰s
‡~ld&n8t‰mx8n
©Így‹8yznx sjrlln“gx sjx–)ga*sjnŽ-‡r0t1ƒOn8d+h8‡ƒO‡c0cln8d¯otDnA€aOd‰stDnŽ0gt&gƒOƒOk8ƒOn”q u¶n8c
rIsaOƒOa„d&gcs|ƒOnŽlt&‡p0ƒGmnAtvsaOhAgƒ
ogc0gƒO‡€rln—lr“Ž0tD‡p0ƒ’i0‡tDaOŸ8‡2c2sjgƒÀqn s£n8c¯ƒOrla!gŽ0ŽlƒOaO{r†gc2s£ƒOnAd4yz‹8ynAd4yzx si0‡ln8dA¨©•n›tDx8d&r0ƒ*sjgs£h8‡2tDtDn8d&Ž’‡cl0gc2s
ªç
ªç
‚¯h8n8ƒOr0aelnzƒ„g“p†€rltDnʵ¨ ”ù¯n8d‰stDnAŽltDx8d&n8csx|p0€r0tDnzµ¨
ü ­®hAaen8cËtDn mgclhjiln2uƒ„g¯h8‡2rlŽlr0tDnzgrË{rlaOc0Ÿ8aOk8ynzŽla*°ln8ƒ
+#
ln—ƒf}‡Amn8tDd&hAgc¥Ž-‡2rlt4ƒOn—hAgƒOhArlƒ!ln—ƒf}aOc2sxA€t&gƒOn—Ž†gt&g½OsŠy‡aOc0d5‘vr0d‰saMp0x—{rln—†gcldŒƒOn—hAgd£lr“t&n8€aOd‰stDn—d&x8tDaOn2
‡d
la*mn8t&dDnAd1‡~ld&n8t‰mgsaO‡2cld1c0‡rld1‡cs+yz‡c2st&xÊ{r•f}aOƒ±x s ga*s|laM´Êh8aOƒOnlnlx sjn8tDya„cln8t1‚Ž0gt‰saOt1lnÊ{Irln8ƒŽla*°ln8ƒ±‡c
Ž-‡r¨mga*sh8‡cld&aO0x8tDn8t±g8m‡aOt±gsDsjn8aOc2sƒOnŠŸ8x8tD‡lu2h8nŠ{rla0d&n8y1~lƒOn
gc0‡tDyÊgƒln s±c0‡rld±gh8‡cl0rla*sd±‚ynAcln8ter0clnŠx sr0ln
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sn8yzŽldŒln›Ž’‡d&n
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h8‡cld&aO0x8tDx8n8dŠd&‡cs
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XY5[^]\_a`‚bcGe * t g¾_iLhc[¾t(uktâX X 1
xi/x0 (pourmille) vs. nb, chip 00
CTE (pourmille) vs. nb, chip00
hrapp0
Entries
232
Mean x
3.5
Mean y 0.09704
RMS x
2.291
RMS y
0.2113
1
hcte0
Entries
8
Mean
3.543
RMS
2.276
3
2.5
0.8
2
0.6
1.5
0.4
1
0.2
0.5
0
0
1
2
3
4
5
6
xi/x0 (pourmille) vs. nb, chip 01
0
7
1
2
3
4
5
6
CTE (pourmille) vs. nb, chip01
hrapp1
Entries
232
Mean x
3.5
Mean y
0.1078
RMS x
2.291
RMS y
0.2766
2
0
7
hcte1
Entries
8
Mean
3.322
RMS
2.326
3.5
3
1.5
2.5
2
1
1.5
0.5
1
0.5
0
0
1
3
ªç
µ¨ ”ù
4
5
6
0
7
0.001
Constant
Slope
0.0008
-7.69 ± 0.0227
-0.475 ± 0.00808
0.0006
0.0004
3
4
5
6
Á ¼_Á(Ɗõ¸º·‘¼º½ÇÈÀçÇ<¼ºÙ-Å\ÀÁ ¼/Å$ÉÀ‘¼
7
Ú
-2.5
-2.6
-2.7
-2.8
-2.9
-3.2
-3.3
0
5
10
15
20
25
Column
3
Är‹ Æ<¢ ha ‹H“ažH‘¿hŽŒºW¡>“a¡>‘
`
2
-3.1
0
ªç
ë
1
-3
0.0002
זØ~Ù©Ú
0
qâÛ ÃdÏо׻(ÏÁ(¼ Û Û Þ Àƒ¸º·<Ɗ¼XÅÉJ» ·Á ¼ÊÀæô,õ
Charge fraction (log10)
Charge fraction
זØ~Ù©Ú
2
µ¨ Aµ
3.2
3.4
3.6
3.8
4
4.2
4.4
4.6
4.8
5
Mean electrons (log10)
ÄLÇ ¯ƒ^ŠŒ„‡™‚ŽŒƒ^†â‡‘ Š›‹I¶·“‚‹Hi™‚ŽŒƒ^†âh‘-ah‹“ažH‘ hŽŒºW¡>“a¡>‘
‹ ¯^‘Æ}þ ŠŒ‘Z™‚‘ ”‰ˆ¨h‘‰Wƒ^®‘
q™ò ÇÈ»(Á ¼_Á ¼_ÏÐÃ-¾äå\Ãd·‘μXÁ\Ɗõ¸×·<¸×¼/¼×Ç5Á ¼_ÀƒÉJ½¸¿ËJÉJÏÒ» Ç<ÆÒÉJ½Ã×˼ʾ/ÏÒ¼©Ç<¼ÊÙ-Å\À'Á ¼XÅÉJÀƒ¼XÅÉJ» ·ÏÒ¼/·‘¼ºÎJÆÒÀuÇ<·‘¼XÀ‘¸×·<ÆÒ¼ Ú
p†c¯0n—dAf/gd&d&rltDnAtŒ{r0n—ƒOn8dŠla*mn8tDd&n8d£h8‡t&tDn8h sjaO‡cldwodD‡2rld‰st&gh saO‡c¥f}‡AmnAtDd&hAgculln~la„gaOdAuOOO¿qŒ‡c2s


x sxn ’n8h
srlx8nAdh8‡tDt&n8h sn8yzn8c2su!r0clndDxAtDaOn|0n+sn8d‰sdwg¯x sjx|n !n8h sr0x8ndDr0t—ƒOnAdŽlt&‡p0ƒOdi0‡tDaOŸ8‡2c2sjgr¨°˜n s—mnAtvsaOhAgrI°˜Ž-‡r0t
7^`\YBaY‚lac!x8tDn8csd|d‰sjgln8dAG³4n8d+sn8d‰sdd&n¯d&‡c2sztDx mx8ƒOx8dd&gsaOd&–)gaOdgc2sdAu
ƒOn8d|Ž’‡d&n8df}x s gƒO‡clc†g€n¯n szƒ„gŽ’‡d&n
ªç
h8‡yyznƒOn1y‡c2sjtDnƒf}n °ln8yŽ0ƒOntDn8Ž0tDx8d&n8c2sxp0€r0tDn1µ¨ A·¨-­®h8aÍd&‡cs›tDn8Ž0tDx8d&n8c2sxAd
ƒOn8dbŽ0tD‡p†ƒOd
i0‡tDaOŸ8‡2c2sjgr¨°7Ž-‡r0t
^`\YBa¥~ltDr¨snu†ƒ„gʎ-‡d&n^$`(YBa¥‡Amn8tDd&hAgcd&‡r0d‰st&ga*s”u-lnƒ„g
Ž-‡d&n^`\YBa¯~la„gaOdbd&‡rld‰st&ga*s|o~la„gaOdbclnŽlt&n8c0gcsbŽ†gd n8ch8‡2yŽIsjnwƒOnsnAyŽldblnŽ-‡d&n”q u†0nwƒ„gzŽ’‡dDn^`\YB¯
a ~laÀgaOd
oln0tD‡a*sn+‚z€2grlhjiln1n s›0ni†grIs›n8c™~0gdjqÁ-ƒ„gzŽ’‡d&n
· ú
G eŒþJåwt¬[email protected]Ö¥t¬cx8h`!tu
yi/y0 (pourmille) vs. nb, chip 00
cx•xhtˆb¹u¾cx–]ZfˆxcHx¹u ¢ h`i[hz{fˆg¾g5[}|¾c
CTE pour y (pourmille) vs. nb, chip00
hrappy0
Entries
208
Mean x
3.5
Mean y
0.246
RMS x
2.291
RMS y
0.4046
3
2.5
16
14
12
2
10
1.5
8
1
6
4
0.5
0
hctey0
Entries
8
Mean
1.84
RMS
2.064
2
0
1
2
3
4
5
6
yi/y0 (pourmille) vs. nb, chip 01
0
7
2
1
2
3
4
5
6
7
CTE pour y (pourmille) vs. nb, chip01
hrappy1
Entries
208
Mean x
3.5
Mean y
0.2205
RMS x
2.291
RMS y
0.3434
2.5
0
hctey1
Entries
8
Mean
1.802
RMS
2.026
14
12
10
1.5
8
1
6
0.5
4
2
0
0
1
זØ~Ù©Ú
2
ªç
µl
ü
3
4
5
6
0
7
qÑÛ Ã ÏÒ¾º»(ÏÁ ¼ Û Û Þ ÅÃd·Èà ÏÒÏÒغϊ¼XÅÉJ» ·5Á ¼ºÀ
Overscan Strip
Entries
Mean
RMS
χ2 / ndf
p0
1400
1
ô,õ ë
2
3
4
5
6
7
Á ¼_Á(ÆÒõ¸×·‘¼º½JÇÈÀNÇ<¼ºÙ3Å\À'Á ¼XÅÉJÀƒ¼
Ú
Valeurs de la marche de l’overscan, chip 00
ovscprfl
45408
4064
36.95
23.99 / 22
1389 ± 0.2938
10
8
6
1390
1380
1370
4
Entries
Mean
RMS
2
χ / ndf
p0
p1
0
Marche_0
2
0
2
4
6
8
10
12
14
16
18
0
13.6
5.549
5.658 / 5
0.2117 ± 0.1044
0.5304 ± 0.009063
20
Valeurs de la marche de l’overscan, chip 01
1360
10
1350
8
6
1340
2
4020
4040
4060
4080
4100
4120
Marche_1
Entries
Mean
RMS
χ2 / ndf
p0
p1
4
1330
1320
4000
0
0
13.52
5.592
11.26 / 5
0.1198 ± 0.1608
0.4682 ± 0.01432
0
0
2
4
6
8
10
12
14
16
18
20
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×œØ®Ù©Ú µ¨ªç”ö Þ Ñ(ÆÒÀƒÇ‘¼Ê½(¾¿¼Á+ »\½-É õ+Àƒ¼¿Ç ÁÃd½\À|ÏcÃ>âà ½(Á ¼Á+ ÉÊËJ¼×·<À‘¾ÊÃd½-¼¿Ç ¸¿ËJÉJÏÒ»BÇÈÆÒɽUÃ×˼º¾'ÏÒ¼çÇ<¼ºÙ-ŏÀ|Á ¼'ÅÉJÀ‘¼ç¼Ê½8¸Ê¾×ÏÐà ÆÒ·‘¼ºÙ-¼Ê½Ç
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d
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tDn sjtD‡rImnË~laOn8c•u£Ž’‡rlt¥ƒ„gώ-‡2dDnË~ltDr¨snu£ƒf}n ’n s™Ž0ga„tv:aOyzŽ0gaOt8uŠh8‡tDtDaO€x˃O‡2tDd7ln˃„gÂd&‡r0dvsjt&gh sjaO‡c
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ƒf}‡Amn8tDd&hAgc•G©Gf}x s gƒO‡clc†g€n¥c0n¥d&‡r ’t&n
B
n8ƒOƒOn+cf}aOcstD‡0rla*s—{Irf}rlc‡ ’d&n sh8‡c0dvs gc2sd&rltŠsj‡rIsƒOn1h”gŽIsn8r0t8u-Ž’‡rltDtgʋ st&n1aOc0h8ƒOrln+0gc0d›ƒOn+–#‡cld&‡rld‰st&ga*s
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§ç
·
XY5[^]\_a`‚bcGe * t g¾_iLhc[¾t(uktâX X 1
Horizontal Profile
horiprfl
Entries
Mean
RMS
1450
Horizontal Profile
4330633
1042
8.363
Entries
Mean
RMS
50
1440
40
1430
30
1420
20
HoriPrflTot
4322929
1042
8.367
10
1410
0
1400
1030
1035
1040
1045
1050
Horizontal Profile
1055
Entries
Mean
RMS
50
1030
horiprfl
1035
1040
1045
1050
Horizontal Profile
4327678
1042
8.363
50
40
40
30
30
20
20
10
10
0
1055
HoriPrflHori
Entries
4295655
Mean
1042
RMS
8.367
0
1030
1035
1040
1045
1050
Horizontal Profile
1055
Entries
Mean
RMS
0.5
0.4
1030
1035
1040
1045
1050
Horizontal Profile
HoriPrflTot
4322929
1042
8.367
1055
Entries
Mean
RMS
0.01
HoriPrflTot
4359168
1042
8.367
0.008
0.3
0.006
0.2
0.1
0.004
-0
0.002
-0.1
0
-0.2
-0.3
-0.002
-0.4
-0.5
1030
זØ~Ù©Ú
1035
1040
1045
1050
-0.004
1055
1030
1035
1040
1045
1050
1055
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chanel 00
Charge fraction
0.005
0.0045
0.004
0.0035
0.003
0.0025
0.002
0.0015
0.001
0.0005
0
200
400
600
800
1000
Column
200
400
600
800
1000
Column
chanel 01
Charge fraction
0.005
0.0045
0.004
0.0035
0.003
0.0025
0.002
0.0015
0.001
0.0005
0
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Entries
Mean
RMS
χ 2 / ndf
p0
p1
p2
1408
1406
1404
1402
Vertical Profile for standard columns, chip 01
stdprof
2500
4116
7.211
18.82 / 22
818.9 ± 0.2149
-0.1989 ± 5.235e-05
1390 ± 0.06324
1406
1404
1402
1400
1400
1398
1398
1396
1396
1394
1394
1392
1392
1390
4105
4110
4115
4120
Vertical Profile for hot columns
Entries
Mean
RMS
χ 2 / ndf
p0
p1
p2
1500
1480
1460
Entries
Mean
RMS
χ2 / ndf
p0
p1
p2
1408
1390
4125
4105
4110
4115
4120
Vertical Profile for hot columns, chip 01
hotprof
600
4116
7.211
27.56 / 22
816.8 ± 0.2374
-0.198 ± 5.78e-05
1393 ± 0.1633
Entries
Mean
RMS
χ2 / ndf
p0
p1
p2
1500
1480
1460
1440
1440
1420
1420
1400
stdprof1
2500
4116
7.211
22.22 / 22
817.5 ± 0.3096
-0.1986 ± 7.544e-05
1392 ± 0.09208
4125
hotprof1
500
4116
7.211
14.39 / 22
819.4 ± 0.3319
-0.1987 ± 8.082e-05
1394 ± 0.2661
1400
4105
4110
4115
4120
4125
4105
4110
4115
4120
4125
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3.4
3.6
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4.4
4.6
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Values of alphax for Hiltner600, 06 014 067
1.4
3
χ2 / ndf
p0
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48.7 / 52
3.866 ± 0.098
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45.4 / 98
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3500
4000
4500
5000
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5500 6000 6500 7000 7500 8000 8500 9000 9500
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Values of alphay for Hiltner600, 06 014 067
1.4
1.6
1.3
1.2
1.4
1.1
1.2
1
1
χ 2 / ndf
p0
p1
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34.77 / 52
1.751 ± 0.096
4.545e-05 ± 4.550e-05
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4000
4500
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Results.y_0:Results.x_0 {Results.lambda>5500 && Results.lambda<9000}
y (arcsec)
y (arcsec)
Results.y_0:Results.x_0 {Results.lambda>3500 && Results.lambda<5000}
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y = 0.12922 - 0.539857*x
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y = 0.188272 + -0.4349*x
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x (arcsec)
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x (arcsec)
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Values of position along x axis for Hiltner600, 06 014 067
0.6
0
0.5
-0.2
0.4
-0.4
0.3
-0.6
133.7 / 99
χ2 / ndf
60.49 / 53
0.2
Position at Lref -0.3518 ± 0.0006
-0.1152 ± 0.0004
f(P)
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2
χ / ndf
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3500
4000
4500
Position at Lref
f(P)
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5000
5500
Wavelength (Angstroms)
š*cȊ—
ŠE:¤$Œn—n’
0.42 ± 0.00
-0.1384 ± 0.0005
5500 6000 6500 7000 7500 8000 8500 9000 9500
Wavelength (Angstroms)
x
Values of position along y axis for Hiltner600, 06 014 067
0.6
0.12
2
χ / ndf
Position at Lref 0.3214 ± 0.0006
-0.1137 ± 0.0006
f(P)
0.5
0.4
χ2 / ndf
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152.6 / 53
104.3 / 99
Position at Lref
0.08
0.005993 ± 0.000284
-0.1378 ± 0.0011
f(P)
0.06
0.04
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Wavelength (Angstroms)
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5500 6000 6500 7000 7500 8000 8500 9000 9500
Wavelength (Angstroms)
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5500 6000 6500 7000 7500 8000 8500 9000 9500
Wavelength (Angstroms)
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Values of chi2/ndf obtained for Hiltner600 (06 014 067)
8
14
7
12
6
10
5
8
4
6
3
4
2
2
1
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5000
5500
Wavelength (Angstroms)
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Slices at 5544 and 5547 A for Hiltner600, 06 014 067
slice at 5544 A
18000
slice at 5547 A
16000
14000
12000
10000
8000
6000
4000
2000
0
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1.002
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Spectra obtained with a simple fit for Hiltner600 (06 014 067)
3
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1800
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1200
146 fits failed out of 1705
300
1000
800
200
600
400
100
200
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1
1.01
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0.994
0.992
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5500 6000 6500 7000 7500 8000 8500 9000 9500
Wavelength (Angstroms)
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Blue channel
106
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105
3000
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Flux
Sky spectrum from an exposure of Hiltner600, 06 014 067
2000
Blue channel
Red channel
1500
1000
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0
3000
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Error spectrum from an exposure of Hiltner600, 06 014 067
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4
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103
3000
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1
0.99
0.99
0.98
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0.97
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0.96
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0.94
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0.93
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Wavelength (Angstroms)
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Wavelength (Angstroms)
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m¯ikZQShRQSL hCd‚PJZdCQScLO[\XMZd‚hCd‚hRLOTUwȘP~ZdRQScOLO[xX¹€m¯i|e‡°dRNXzLOTLO[xXegdCQqeUwXX>LO[RhReg[RcOL vVNqZdRNYȗLONYX>UWTVLOQmW]OµÁOQqLOTLO[xX
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cOZTP€egQqegUWNqZ[hCLON‹legmWLdCQSNP~Z\dCQ mWLªcOdR}~LªL^X!NqZ[pCZTVZmWZµdCL QSLOcOZ\[CNYX>QSdRUwX±sLO[+[CZ\UWQO{K©e§cOZdRQS}~LªLO[QSZdCµ\L
QSLOPCQq]ONqLO[\X>L‹m¯i|egmWmWdRQSL‹hCdANqUWµ[€egmtegfR[§hCLyQqLOP~]QSLOQ»mWLON[ dCTV]OQSZNhCLyTVUWcOQSZ‡È—mWL[\X>UWmWmWLONcOZQqQSLONqP~Z\[ChReg[xX’egd4rA}JZQShCN
hCL»m„e’X>QqeTL{x²M[PJLOd4XŠegUW[CNqUCcOZ\[CNYXzeŒX>LQ:“4dCL»mWLONhCU‘`J]QSLO[CcLONILO[xX>QSL»hCZ[R[C]OLNIL^XžTZ4hCÁOmWL»NqZ[\XžPRmWdCN³´egUW}CmWLONPReQ
0.4
10000
0.2
5000
Flux
(real - reconstructed)/real slice
Slice at 7000 A, Hiltner600 expo 06 014 067
0
0
-0.2
-5000
-0.4
-10000
-0.6
20
40
60
80
100
120
140
160 180 200 220
Microlens number
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ów4ö 3W÷õYñMð»ô\ý û˜þ-Œùxöó QqegPCPJZQX‹egdÔNqUWµ[Regm:P~ZdRQMmWLONNqPReŒrCLOmWNPCQqZ czpCLONhRdŽcOLO[\X>QqL!hRL!m„e NqZdCQqcOLsbemWZQSN“ dtikLOmWmWLONPJLOd4lxL[\X‹eŒXSX>LUW[ChCQqL
5 * hCdVNqUWµ[Regm€P~ZdRQmWLONž}~ZQqhCNhRL(m„eMX>Q>egTL{x©ey“4dRegmWUwXz](hC]OcOLaleg[\XzL(hCL(m¯ikL^r4X>Qqegc^XzUWZ[VNqLOQ>egUwXŠhRZ[Cc(hRdCLvydR[CL
TVegd legUWNqL‹LONYX>UWTVeŒXzUWZ[§hCd§³ºZ[RhAhRLycUWLOm¯sRL^X’eg`JLOc^X>LQqehCZ[RcyPRQS]O³º]OQqLO[\X>UWLmWmWLOTLO[xXm„LON(PJZNqLON(mWLONPCmWdRN(cOZdCQYX>LONs
cOZ[\X>L[Reg[\X PJLOdÔhCL³ºZ[Cht7{ 6Z\dCNyQSL^lCUWLO[ChRQSZ[CNyNqdCQymWLONyPRQSZ}CmWÁTLONyhRdCN‹egdŽX>LOTPRNyhCL PJZNqL h€eg[CNym„e_NqLOc^X>UWZ[
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hCZ[R[C]OLONUWhC]emWLON{x¿ikLONYXždC[PRQSLOTVUWLOQuX>LNXŠP~ZdRQulx]OQSU‘f€LOQIm„eycOZpC]QSLO[CcL»hCdPRQSZ cO]hC]{\©eMf€µdCQSL H{ GQSLPCQS]ONqLO[xX>L
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d4X>UWmWUWNqLªdR[CL «Š¬ ­/hCU‘`J]QSLO[\XzLªP~ZdRQ m„e§NqUWTdRm„eŒX>UWZ[+LaX!m¯i|e‡°dRNXzLOTLO[xXƒ¹LO[+Lar X>QqeR e[\X eOlxLcªdC[RLª³ºZ[CcaX>UWZ[+hRL
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ePRQSLOTVUWNAhCLŽlx]OQSU‘f€LOQAm„ecZQSQS]Om„e‡X>UWZ[/LO[xX>QSLmWLONAP€egQqegTVÁ^X>QSLONAhRLÔ³ºZ\QSTL L^X s‰“4dCU®°YdCNYX>U‘fRLmWLNSLcOZ[Ch
e‡°dCNYX>LTLO[\XhCLy«Š¬C­v β f r ]\U{ 6Z\dCN»P~Zd lxZ[RN‰LO[ALa`JLaX‰lxZU„Q‰NqdCQ»m„ef€µdCQqL α W{ VmWLβQq]ONqdCmwXzeŒXhCLym¯i|e‡°dCNYX>LTLO[xX
UW[\X>LOQqT]OhRU„egUWQSLhCd_PRegQqeTÁ^X>QqL β Z}4XzLO[ d_LO[_L^r X>Qqe R eg[\XeOlxLOcdC[RLM³ºZ[Rc^X>UWZ[_hR#L SoZg`beŒX(cOUWQScOdRm„egUWQSLmWLNqP~LOc^XzQSL
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Values of beta for an elliptic Moffat simulation, circular extraction
3.15
8.957 / 49
2.578 ± 0.238
0.0001962 ± 0.0001120
-2.489e-08 ± 1.303e-08
2
χ / ndf
p0
p1
p2
3.05
3.1
3.05
3
3
2.95
2.95
2.9
2.85
2.9
2.8
2.75
2.85
2
χ / ndf
p0
p1
p2
2.629 / 95
1.968 ± 0.145
0.0002788 ± 0.0000399
-1.944e-08 ± 2.712e-09
2.7
3500
4000
4500
5000
5500
Wavelength (Angstroms)
5500 6000 6500 7000 7500 8000 8500 9000 9500
Wavelength (Angstroms)
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P~ZdRQXzeg[xXcZ[CNqUWhC]OQq]OL‹cOZTVTL‹m„ePRmWdCNQSZ}CdRNYX>L»°dCNq“ dti|vPCQS]ONqLO[xX ¹€mWLONhCLOQS[RUWÁOQSLON’egT]Om„UWZQqeŒX>UWZ\[CNNqdCQ(mWLONPRe‡È
QqegTÁaX>QSLON hRLV³ºZQqTLVZ\[\XPJLOQSTVUWN dC[CLªPCQS]cOUWNqUWZ[6NqdCÃVN>eg[\XzLVP~ZdRQ‹TVL^XSX>QSLªLO[+eOl\eg[\X!cOLVPRQSZ}RmWÁOTLªQS]ONqUWhCdRLOm
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ÝxÞ98;:~ÜzäÚ¯äå Ü ãaàŒÖ=<^ÛzÜzâJãOÜ
Flux
(real - reconstructed)/real slice
Slice at 4000 A, elliptic simulated cube, elliptic extracted
30000
0.02
20000
0.01
10000
0
-0
-10000
-0.01
-20000
-0.02
-30000
-40000
-0.03
20
40
60
80
100
120
140
160 180 200 220
Microlens number
éžê£ë‰ì 1{ n
í ~õYöù\Qü ðªÿ b oc ò4÷Œýõ ó ðVü>ý 4ðVûþ ñ’ý\óÒpú ,ðzùö xûü>þwû˜û—ð " ó ðVùgý\ñú>õ˜÷Aô\ðVû—ò4öaïgðzó " ü xö +gýðªó -þ ŒùðVðzû¨ø
ù‡ý\ñú>õ˜÷øú>ð‹ó ýxùðöOò\õ/.zûó öýgøõ˜ðq2€ðzù_÷±õô÷Œù\ùúzð " ówöô\þ104úzõ˜ðzù\ü>ðyðzùŒøõ˜ð‹ô\÷Œù\ùú>ð^û»õú>ðzówóÒðzû(ðqøõðzüq÷Œù\û—ø˜õYý\þ|øðzûù÷±õñyöówþ û˜ú>ð
ò öOõó ð»û1þ Œùxöó îù!õ˜÷Œý ±ð " ó öó ówýõ˜ð(ô\ý û˜-þ Œùxöó cOZ[CcLOQS[Reg[xX(m„e!PJZNqUwX>UWZ[j{RÄiÒegd4X>QSLN»]^X>dChRLON‰NqZ[xX(hCZ[Rc[C]OcLONqNqeUWQSLON»P~ZdRQ‰TUWLd4rƒcOZTVPCQSL[ChCQqLMmWLycOZTVP~ZQXzL^È
TLO[xXhCL‹m¯i|e‡°dCNYX>LTLO[\X’NqdCQ»hRLON(cOdC}JLON(NSUWT!dCmW]ONs€eg}~ZQqhC]MX^egQShCUwlxLTLO[xXhReg[RN»[RZ‡X>QSL eg[Re\m R NqL{
¿®ZTVTLZ[ÔPJLOd4X‹NikLO[hCZd X>LOQOsbm¯i|eg°dCNYX>LOTVLO[\X hjikdC[RL ³ºZ[CcaX>UWZ[cOUWQScOdRm„egUWQSLPRegQdR[CL ³ºZ[Rc^X>UWZ[LOmWmWUWP4XzUW“ dCL
[CLŽPJZNqLŽPRegN_hRLŽPCQSZ\}CmWÁOTVLŽPRegQYX>UWcOdRmWUWLOQŽ¹®m„e³ºZ[Rc^X>UWZ[ Z}4XzLO[ dCLÔPRegQƒm¯iÒe‡°dCNYX>LOTVLO[\X§QSL^X>QqZd4lxLÔmWLON_TOTVLON
legmWLOdRQSN»P~Z\dCQ α L^X(PJZdRQ α ·´fRµdRQSL {|¸\¼^U{ 6’Z‡X>Z[RN»]Oµ\egmWLTLO[\XNqdCQ»cOL^XSXzLMfRµdRQSLmWLy}JZ[_cOZ\TP~Z\QX>LOTVLO[\X(hRL
x
y
Values of alphax and alphay for a circular Moffat simulation, elliptic extraction
0.6
0.6
2
χ / ndf
p0
p1
p2
0.55
0.08058 / 54
0.8841 ± 0.0380
-0.000121 ± 0.000018
8.341e-09 ± 2.141e-09
0.58
2
χ / ndf
p0
p1
p2
0.56
0.54
0.09436 / 54
0.884 ± 0.038
-0.000121 ± 0.000018
8.348e-09 ± 2.126e-09
0.52
0.5
0.5
0.48
0.46
0.45
0.44
0.42
0.4
3500
4000
4500
5000
5500
Wavelength (Angstroms)
3500
4000
4500
5000
5500
Wavelength (Angstroms)
éžê£ë‰ì {|¸ íTXZ¨ýxû¨øðzñMð^ù±ø:þ ùŒø˜ðzõñMúzôxþwöþ õ˜ðŠôð ð>øuô\ð ô öOùxûKó ðŠüzöûuô ý\ù\ðžðqïgøõYöüSøYþÒ÷Œùyò4öOõuý\ùðr3‘÷ŒùxüSøYþÒ÷Œù‹ðzó ówþÒò\øYþ-+‡ý\ð
ò4÷Œýõý\ù ü>ý ð»ûþ ñ’ý\óÒúöJ)±ð^ü‰ýxùð3‘÷Œù\üSøYþ ÷±ù ü>þ αõü>ýxówöþÒõð α
x
y
m¯i|e‡°dCNYX>LTLO[\X hCLNyPRegQqegTVÁ^X>QqLON α P€egQdR[ÔPJZm\R [Us\TL hRdÔNqLOcOZ[RhÔhRLOµQS]VegmWZQSN‹“ dCLm„eƒNqUWTdRm„eŒX>UWZ[6e_d4X>UWmWU„NS]
dC[CLymWZUjhCLyPCdCU„NSN>eg[RcOLPJZdCQ»TZ4hC]OmWUWNqLOQ»m¯ik]^lxZmWd X>UWZ[§hCLym„e!m„egQqµLOdCQ(v TUwȘpRegd X>LOdCQ(eOlxLOcym„e mWZ[Cµ\dCLOdRQ‰htikZ[ChRL{
¿®LOcOU:cOZ[ f€QSTL!hRZ[Cc m„e Nqd êNqe[CcOL!hRdŽTZ4hCÁOmWL!“4dCL![RZdCNyeOlxZ[RNczpCZU„NSU:P~ZdRQMm¯i|e‡°dRNXzLOTLO[xXyUW[\X>LQST]OhRU„egUWQSL
hCLON(PReQqegTÁaX>QSLON(hRLy³ºZQSTVLyLO[§³ºZ[Rc^X>UWZ[§hCLym„emWZ[Cµ\dCLOdRQ»hjikZ[RhCL{
©tL PCQSUW[RcOUWP~L TTL hCL m„e‚NqUWTdRm„eŒX>UWZ[PJLOQSTVL^XSXze[\X!hRL cOZTP€egQSLOQmWL NqP~Lc^X>QSL d4XzUWmWUWNq] P~ZdRQ cOZ[RNXzQSdCUWQqL
mWLÔcOdC}JLÔNqUWTdCmW]L^X§cOLOm„dCUUWNqNqd hCLÔm¯ikLar X>QqegcaX>UWZ[js»[CZdRNAeOlxZ[RNAQSLOPRQS]ONqLO[\Xz]ŽfRµdCQqL { mWLONAQ>egPCPJZQX>NALO[\X>QqL
NSPJLOc^XzQSL’L^r XzQqegUwX‰LaX‰NqP~LOcaX>QSL’NqUWTdRmW]’PJZdCQ®mWLON®hCU‘`J]QSLO[\X>N®c±egN{4čeg[CN®mWLMcegN®hCLMm¯ikL^r XzQqegc^X>UWZ\[ P€egQŠdR[CL’³ºZ[Rc^X>UWZ[
cOUWQScOdRm„egUWQSLMhjikdR[CL’³´Z[Cc^X>UWZ\[ NqUWTdRmW]OLMLOmWmWUWP4XzUW“ dCL ·£cOZdRQS}JLONŠ}RmWLOdCLN>¼as Z[ƒNi|eŒXSX>LO[RhƒvZ}CNqLOQl LOQŠhRLON®]OceQX>N®hCdRN‰v
m¯ikUW[ReghR]O“ d€eŒX>UWZ[!hCL®m„e³´ZQSTL®hCL‰«ž¬C­§czpCZUWNqUWL®P~Z\dCQKm¯i|eg°dCNYX>LOTVLO[\X±{g©tLONu]OcegQYX>NuLO[!La`JLaX:PJZdCQKcOLaXSX>L®L^r X>Q>egc^X>UWZ[
Ñ5
ÕuÖJ×aØJÙ¯Ú¨ÛzÜ ÝxÞa`IÜ^ÛS߯àŒÛSáƒ×ŒâJãaÜ^äåJæ ãaà4å Ü å:ç ÜqèbÚ¨Ûz×\ã±Ú¯Ùºà‡â
Ratio circular extracted / circular simulated
1.01
1.008
1.004
1.006
1.002
1.004
1.002
1
1
0.998
0.998
0.996
0.996
0.994
0.992
3500
4000
4500
5000
5500
Wavelength (Angstroms)
Ratio elliptic extracted / circular simulated
1.01
1.008
6500
7000
7500
8000
8500
9000
9500
Wavelength (Angstroms)
5500
6000
6500
7000
7500
8000
8500
9000
9500
Wavelength (Angstroms)
5500
6000
6500
7000
7500
8000
8500
9000
9500
Wavelength (Angstroms)
5500
6000
6500
7000
7500
8000
8500
9000
9500
Wavelength (Angstroms)
1.004
1
1.004
1.002
0.998
1
0.996
0.998
0.994
0.996
0.994
0.992
3500
4000
4500
5000
5500
Wavelength (Angstroms)
Ratio circular extracted / elliptic simulated
1.02
1.06
1.01
1
1.04
0.99
1.02
0.98
1
0.97
0.98
0.96
0.96
0.95
0.94
0.93
6000
1.002
1.006
0.992
5500
0.94
3500
4000
4500
5000
5500
Wavelength (Angstroms)
Ratio elliptic extracted / elliptic simulated
1.012
1.006
1.01
1.008
1.004
1.006
1.004
1.002
1.002
1
1
0.998
0.996
0.998
0.994
0.992
0.996
3500
4000
4500
5000
5500
Wavelength (Angstroms)
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Jö )±ð^ü ý\ùðh3‘÷ŒùxüSøYþÒ÷Œù§ô\ðjLV÷ 0CöaøMü>þ õü>ý\ó‘öþÒõ˜ðq2Jðzù§ôðzûû—÷Œý\û " ðqï‡øõYöüqøþ ÷Œù‚öJ)±ð^ü‹ýxùðh3‘÷ŒùxüSøYþÒ÷ŒùAðzówó þ òøYþ-+gýð!ô ý\ùðh3W÷Œù\üSøYþÒ÷Œù
ü>þÒõüzý\ówöþ õ˜ðq2Rðzùƒô\ðzû˜û˜÷Œý\û " ðqï‡øõYöüSøYþ ÷Œù_öJ)±ð^üý\ù\ðd3‘÷ŒùxüSøYþÒ÷ŒùƒüzþÒõü>ýxówöþ õ˜ðyô ýxùðd3W÷Œù\üSøYþÒ÷Œùƒðzó ówþÒò\øþ\+‡ý\ðq2Rðzù öû " ðqï‡øõYöüSøYþ ÷Œù
ðqø®ûþ ñ’ý\ówöaøYþ ÷±ùªöJ)Œðzüý\ùð 3‘÷ŒùxüSøYþÒ÷ŒùVôð L÷ 0CöaøŠðzówó þ òøYþ-+gýð vu öùxûžüQxö +‡ýðMüzöû " ó ðü>ý 4ðwxó ðzýðzû¨ø‰ÿd‡öOýxüððqø‰óÒð’ü>ý4ð
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QSLONYXzeg[xXªLONYXªmWUW]§vdC[CLAhR]OP~LO[RhReg[RcOL§eOlxLOcAm„emWZ[Cµ\dCLOdCQVhjikZ[RhCL{Äeg[CNVcOLONVNqUWT!dCm„eŒX>UWZ\[CNsIm„eoXzQqeg[CNqTVUWNSNqUWZ[
hCL§m¯ikUW[CNYX>QSdRTLO[xXª[ti|eÔP€egNV]^X>]§PCQqUWNqLALO[ cOZ\TP4XzL¹m„ehC]OPJLO[Ch€eg[CcOL§LO[ mWZ[CµdRLOdCQVhjikZ[RhCL§[jikLONYX hCZ[RcAmWUW]OL
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NSPJLOc^XzQSL mWdRUwȗTVOTL{²[P~ZdRQSQqegUwX LO[\lCUWNqeµLOQyhCLcZ[CNqUWhC]OQqLOQymWLcOdR}~LLO[PCmWdRNSU„LOdCQSN‹hCZTVeUW[CLON‹hCLmWZ[Cµ\dCLOdRQ
hjikZ[RhCL P~Z\dCQ³´egUWQqL [CZN‹e‡°YdCNYX>LOTVLO[\X>NsbTªegUWNyUWm:³´edChCQ>egUwX egmWZQSN‹PCQS]^l ZUWQmWLONyhRU‘ÃVcOdRmwX>]ONyhCLTLONqdCQqL P~ZdRQmWLON
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x
ratio fitted/simulated law for alpha_x vs. lambda
(0.89111+-0.000124232*x+(8.71502e-09)*x^2)/(15*pow(x,-0.4)/1.01965)
1.012
1.01
1.008
1.006
1.004
1.002
1
3500
4000
4500
5000
5500
6000
Wavelength (Angstroms)
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αx
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corr
0.4zε(λ)
corr
ratio of two spectra of Hiltner600, night 06 014
1.2
1.2
1.15
1.15
1.1
1.1
1.05
1.05
1
1
0.95
0.95
0.9
0.9
0.85
0.85
0.8
0.8
0.75
3500
4000
4500
5000
5500
Wavelength (Angstroms)
0.75
5500
6000
6500
7000
7500
8000
8500 9000 9500
Wavelength (Angstroms)
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L^X cL[RZ‡XzegTVTLO[\XPRegQqcOL“4dCLVmWLON‹NqdCPJLOQS[CZl ©¥NqZ[\XhCLN‹NqZdCQScOLN v_³£egUW}CmWL¶Rd rԓ dRUI[C]cOLONqNqUwX>LO[\XhCLON‹PJZNqLON
mWZ[CµdRLON(“ dRLym¯ikZ[§[CL‹P~LOd XPRegN‰X>Zd°ZdCQqN»PRQSLO[RhCQSLyh€eg[CN(mWLON(TVLOUWmWmWLOdRQSLON(cOZ\[ChCUwXzUWZ[CN{
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hjikdC[RLVP~ZNqLVhCŽL G AN PCQSUWNqLªvAdR[CLVTªegNqNSLVhti|egUWQ‹hRL Ñ4{ {©v st[RZ‡X>QSL XzZd4XPRQSLOTUWLQ e‡°dCNYX>LTLO[\XNqZdC`JQSLVhRL
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m„e_TVegd legUWNqLcOZ[\l LOQSµLO[RcOLhRL m¯i|eg°dCNYX>LOTVLO[\X hRLV«ž¬C­†egmWZ\QSN‹“ dCL!X>ZdRNymWLON‹P€egQqegTVÁ^X>QSLON‹NqZ[\X m„egUWNqNq]ON‹mWUW}CQSLNOs
cOZTTVLmWL’TZ[xX>QSL’m„eyf€µdCQqL { Gª¹ hCL[RZT}RQSLOd4rªP~ZUW[xX>NŠTVe[C“ d€eg[\X>NŠPJLOd4lxLO[xX®³´egdRNSNqLOQŠm¯i|e‡°dRNYX>LOTL[\X®hRL β s
NSdRQX>Zd XUWcOUuhReg[RNMmWL!cOdC}JL}CmWLdj¤{ SŽegUWNMcOL!PCQqLOTUWLQMe‡°dRNXzLOTLO[xXL^Xym„eªf rCeŒXzUWZ[ŽhCL β PJLOQSTVL^XyegdŽhCLOd r UWÁOTVL
Values of beta for G191B2B, night 06 014
7
2
χ / ndf
p0
p1
p2
6
5
7
55.12 / 22
-5.691 ± 1.094
0.004467 ± 0.000531
-5.684e-07 ± 6.388e-08
χ2 / ndf
p0
p1
p2
6
5
34.82 / 72
4.845 ± 0.406
-0.0006224 ± 0.0001150
4.557e-08 ± 8.061e-09
4
4
3
3
2
2
1
1
3500
4000
4500
5000
5500
Wavelength (Angstroms)
5500
6000 6500 7000 7500 8000 8500 9000 9500
Wavelength (Angstroms)
éžê£ë‰ì { G n
í XZ¨ý\û—øðzñMðzùŒøþ ùŒøð>õñMú^ô\þwöþ õ˜ðªôð β ò4÷Œý\õ ý\ùðVò ÷±û˜ðªóÒ÷ŒùŒýð
‡†[ˆK‰ˆ ò\õYþ û˜ð»ó‘öMù‡ý\þÒø „ b ${® û&‹ÿ±õYöù\ô\ðVñ‹öû˜û—ðªô öþÒõ
hCLcOZ[\l LOQSµLOQs cOZTTVLZ[_P~LOd X»mWL’l ZUWQ‰UWcOUjeOlxLOcyP~ZdRQ®L^rCLOTPRmWLm¯i|e‡°dRNXzLOTLO[xX»hRL
αy
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Values of alphay for G191B2B, night 06 014
2.2
1.75
2
1.7
1.8
1.65
1.6
1.6
1.4
χ2 / ndf
p0
p1
p2
1.2
1
1.55
20.07 / 58
-1.4 ± 0.1
0.00187 ± 0.00006
-2.565e-07 ± 6.926e-09
1.5
1.45
0.8
3500
4000
4500
5000
5500
Wavelength (Angstroms)
éžê£ë‰ì { V °í XZ¨ýxû¨øðzñMð^ù±øyþwù±øð>õñúzô\þ‘öþÒõ˜ð ô\ð
‡†[ˆK‰ˆ ò\õYþ û˜ð»ó‘öMù‡ý\þÒø „ b 36.02 / 117
χ2 / ndf
2.845 ± 0.049
p0
-0.0003368 ± 0.0000137
p1
2.067e-08 ± 9.473e-10
p2
αy
5500
6000 6500 7000 7500 8000 8500 9000 9500
Wavelength (Angstroms)
ò ÷±ý\õýxùð!ò4÷Œû˜ð óÒ÷ŒùŒý\ð
û ’ÿ ±õYöù\ô\ð ñyöû˜û˜ð!ô öþ õ
${® & Ž
$?‰\ &!,
mWLON XzQqeg[CczpRLONAhCd cOdR}~LÔQS]^ȗ]czpReg[\XzUWmWmWZ[C[R]ÔZ[\X§}CUWL[ cOZ[\lxLQSµ]ÔL^X§NqZ[xX§PCQS]ONqLO[xX>LONAP~ZdRQƒmWLNAe‡°dRNXzLOTL[\X>N
UW[\X>LOQqT]OhRU„egUWQSLON{76Z‡XzZ[CN‹egdÔPRegNqN>egµL m„e_µQqeg[ChRL cOZdCQq}CdCQqL!Z}4XzLO[ dRL!h€eg[CNmneƒmWZU:hCLlegQqU„eŒX>UWZ[hCL α eOlxLOc
m„e‚mWZ[Cµ\dCLOdRQhjikZ[RhCLsKL^X NqdCQYX>Zd4X mWL cOZTVP~ZQYX>LOTVLO[\X P~ZdRQmWLON!mWZ[CµdRLOdCQqNhji|Z[ChCL NqdCPJ]OQSUWLOdRQSLON v 5 ˜!{
¿®L’cOZTVP~ZQYX>LOTL[\X±s PCQq]ONqLO[\X‰P~Z\dCQX>ZdRNŠmWLON‰e‡°dRNYX>LOTL[\X>N®UW[\X>LOQSTV]OhCUnegUWQSLON®hCL’cOLMcOdC}JLsxNqL’QqL^X>QSZd lxL’hReg[RNŠhRL
[CZT}RQSLOdRNSLN:P~ZNqLON:L^XNqZdCmWUWµ\[CL‰mWL‰³´egUwX“ dCLsgP~ZdRQucLON:mWZ[RµdCLOdRQSN:hjikZ\[ChCL‰L^r X>QqOTLONsgm„efCrCeŒX>UWZ\[ czpCZUWNqUWL‰P~ZdRQ
mWLONPRegQ>egTÁ^XzQSLONhCLPJZNqUwX>UWZ[ L^XKhRL³ºZQqTLPJLOd4XSȘ^X>QSL[R]O³´egNYX>Lžv(m„e»}JZ[C[RLL^r X>Q>egc^X>UWZ[ hCd NSPJLOc^X>QqL{ 6]e[CTZ\UW[CNs
Z[AP~LOd X(hRUWQSLy“ dCLym¯ikL^r XzQqegc^X>U„Z[AhCLyPJZNSLN»mWZ[Cµ\dCLONv µQqeg[ChRLTªegNqNqLON»hti|egUWQ»LONYXµmWZ}RegmWLTLO[xXN>eŒX>UWNq³´egUWN>eg[\XzL¹
LO[La`JL^XVNSU®mWLƒPRQSLOTU„LOQ e‡°dRNXzLOTLO[xX hRL_«ž¬C­EQqLY°L^XSXzL dR[[CZT!}CQSLƒQSLOm„e‡X>UwlxLOTVLO[\XUWTVP~ZQYXzeg[\XhRLVXzQqeg[CczpRLONs
mWLONe‡°YdCNYX>LOTVLO[\X>NUW[\X>LQST]OhRU„egUWQSLONhCLONPRegQqegTVÁ^X>QqLON hRLV³ºZQqTLs[RZ‡XzegTVTLO[\X!hCL β sPJLOQSTVL^XSX>L[\X!egd+hRLOQS[RUWLOQ
e‡°dCNYX>LTLO[\XKhRLIcOZ\[CNqUWhC]OQqLOQbX>Zd4XzLONtmWLONjX>Qqeg[RczpCLONN>eg[CNegdRcOdC[‹]OczpRLOc{Œ¿MikLNXKm„e»Q>egUWNqZ[‹PCQqUW[CcOUWP€egmWLP~ZdRQjm„eg“4dCLOmWmWL
[CZdRNªeOlxZ[CNªczpCZUWNqU(hCL_X>Q>egUwX>LOQVmWL§cOZTPJZQX>LTLO[xXªhCd P€egQqegTÁaX>QSL β eOl LOc§m„emWZ[CµdRLOdCQVhjikZ\[ChCL§hCL§³´e –OZ[
NS]PRegQS]Ls€LaXMNqdRQX>Zd XMhCLQSLO³´eUWQSLdC[Že‡°dCNYX>LTLO[\XhCL!«Š¬ ­ eOlxLc β f r ]{J©teªcZQSQS]Om„e‡X>UWZ[oLO[\XzQSLmWLON’hRU‘`J]OQSLO[xX>N
PRegQqeTÁ^X>QqLONVhCL§³´ZQSTL§[CZ\dCNªP~LOQSTVL^XªhRL§cOZQSQqUWµLOQVLO[ PReQX>UWL§hjik]alxLO[\X>dRLOmWmWLONªLOQSQSLdCQSNªNSdRQm¨ikLONYX>UWTVeŒXzUWZ[ hRL
cOLŽP€egQqegTVÁ^X>QSLÔL^X‚egUW[CNqUhjikZ}4XzLO[CUWQ_dC[CL«Š¬ ­ cOLOQYX>LON_UWTVPRegQS³£egUwX>Ls‰TVegUWNANqd ÃVN>eg[xX>LŽPJZdCQAegUWhCLOQ_hCLÔ³´e –OZ[
G
y
xÝ ÞH—˜:~ÜzäÚ¯äå ÜMÛzàv™CægäژÜzäqä^Ü
NSU„µ[CU‘fRc±eŒX>UwlxLAvÔm„eŽcOZ[\l LOQSµLO[RcOL_hCL_m¯i|e‡°YdCNYX>LOTVLO[\X±{I©tLON!X>LNXzN hCL_cOZ\pC]OQSL[CcOL·ºl ZUWQ!fRµ\dCQSL { 5 ¼!NqdCQ cOL^XSXzL
TOTVLyP~Z\NSL‹Z[\XTVZ[\X>Qq]ydR[CLyQSLcOZ[CNYX>QqdCc^X>UWZ\[_f€eg}RmWL‹egd§P~ZdRQScOLO[xXPCQSÁN»LO[§µ]O[R]OQqegm¯{
sum(reconstructed)/sum(cube)
sum(reconstructed)/sum(cube)
Consistency of the extraction for G191B2B, night 06 014
1.02
1
0.98
0.96
0.94
1.02
1
0.98
0.96
0.94
0.92
0.92
3400 3600
3800
4000
4200
4400 4600 4800 5000
Wavelength (Angstroms)
5500 6000 6500 7000 7500 8000 8500 9000 9500
Wavelength (Angstroms)
éžê£ë‰ì { 5íTtŠöOò\ò4÷±õ—øuð^ù±øõ˜ð®ô÷Œù\ù\ú>ðzûKõ˜ðzü>÷±ùxû¨øõý\þÒøðzû:ÿ»ò öOõ—øYþÒõ:ôð®ó öN¨ýxû¨øðzñðzù±øuðqøIô÷Œù\ùúzðzû}\õýø˜ð^ûò4÷Œý\õuó‘ö»ò4÷Œû—ð®ô\ð
‡†[ˆK‰ˆ ò\õYþ û˜ð»ó‘öMù‡ý\þÒø „ b ”:•{>u•?> ±MEt¢F€rC£™€˜²‰¡*
Àf€[ŽhRL X>LONYXzLOQMm¯ikL^r XzQqegc^XzUWZ[ÔP~ZdRQMhCL ³´egUW}CmWLNM¶Rd rbsJdR[CL!Nq]OQSUWL hRL!P~Z\NSLNMNqZdRNYȗL^r PJZNq]OLONyeƒ]^X>]!PRQSUWNqL egd
cOZdCQqNhtikdC[CL [4dCUwX PCpRZ‡X>ZTV]^X>QSUW“4dCL{u«uLO[Ch€eg[\X mWLN[4dCUwX>NiÐ VoL^XTг Ð suhCLOd4r+[ dRUwX>N!PCpCZgX>ZT]aX>QSUW“ dRLONs
m¯ik]^X>ZUWmWLª­RLOUWµL 5 Чe_]^X>]PCQqUWNqLvAhCU‘`J]OQqLO[\X>NX>LOTVPCNyhRLP~Z\NSL\sbhRL voG_NqLOcOZ[RhCLONsjPJZdCQyhCLON‹TVegNqNqLON‹hji|eUWQ
PCQSZ4czpCLON hCL {:©ik]^X>dChRLƒhCLƒm„eŽcOZpC]QSLO[CcLÔ·£QqegPRP~ZQYX L[\X>QSLƒ¶Rd4r6X>ZgXzegm®QSLcOZ[CNYX>QqdCUwXL^X¶Rd4r6XzZ‡Xzegm®hRdcOdC}JL
hCLhCZ[R[C]OLN>¼MTZ[xX>QSLdC[6egcOcZQSh6v_dC[ZdhCLd4rÔP~ZdRQScOLO[xX>NyPCQqÁONyLO[\XzQSLhCZ[R[C]OLON‹L^X QSLOcOZ[RNYX>QSdCcaX>UWZ[P~ZdRQ
hCLONMX>LOTPRNhRL!PJZNqL edŽTVZUW[CNy]Oµ\egd rÔ;v V 5 NqLOcZ[ChRLON·ºXzLOTPRNhCL P~Z\NSL hRUWNSPJZ[CUW}RmWLON ´¹ V 5 s 5 s 5 s ¸ ƒLaX
GNqLOcZ[ChRLONz¼^{€«uZdCQ(hRLON»X>LOTVPCNhCL‹PJZNqL‹hCL L^Xy
Ñ NqLOcOZ[RhCLONsRZ\[§cOZ[RNYXzeŒX>L‹dR[§hC]NqecOcOZQSh‚hCL 5 v k
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NSLcOZ[ChRL{ ©i|e‡°dRNYX>LOTL[\X»LNX(hRLMPCmWdRN‰LO[_PCmWdCN‰m„eg}JZQSUWLOd r mWZ\QSNq“ dCLmWL’X>LOTPRN‰hCLMPJZNqLMhRUWTUW[4dCLs4cZTTVLM[RZdCN
m¯i|eOlxZ[CN»l d‚egd§czpRegPRUwX>QSL ¸Z I§dC[ALar LOTPRmWL‹hCLycLON(P~Z\NSLN(NSZ\dCNYȗL^r PJZNq]OLONe]^X>]‹PCQqUWN(P~ZdRQ»TVZ[\X>QqLOQ»m¯ikd X>UWmWUwX>]
hCdQSLY°L^XžhCLONIPJZUW[\XzNITVegQSµ\UW[Regd4r mWZQqNIhCLONeg°dCNYX>LOTVLO[\X>NIUW[xX>LOQSTV]OhCU„eUWQSLON(·£fRµdCQqL»¸ { ¼a{©eMfRµdCQqL { ЍTVZ[\X>QqL
mWLONQqegPCPJZQX>NLO[\X>QqLVNqPJLOc^X>QqLON L^r XzQqegUwX>NQqegTVLO[C]Nv§dC[RLVTªegNqNqLVhti|egUWQ hRL L^XvAdR[X>LOTVPCN hRLVPJZNqLªhjikdR[CL
NSLcOZ[ChRLPJZdCQMhCUwl LOQSNXzLOTPRNMhCL!P~ZNqLsbeOlxLc!P~ZdRQ’TVOTL!QS]O³´]OQSLO[RcOL!dC[CL!P~Z\NSL!hCiL G N{b©e cOZTP€egQqegUWNqZ[
LO[\X>QqL(mWLONŠNqP~Lc^X>QSLONŠUWNSNqdRNžhRL(PJZNqLONžhRL 5 L^gX G‹NM·£LO[ªpRegd X^¼:TVZ[\X>QqLdC[ª}~Z[ egcOcZQSho·£ZNqcOUWmWmneŒX>UWZ[CN®egd X>ZdRQ
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fRµdRQSL { 4sjQSLOPRQS]ONqLO[\Xze[\X‹m„eƒcZTP€egQqegUWNqZ[LO[\X>QSLQSLOcOZ[RNXzQSdCc^XzUWZ[ÔL^X‹hRZ[C[R]OLONyP~ZdRQm„eƒP~Z\NSL hRTL G_NhRL
­CLUWµL 5 Ѓ[RZdCNye R4eg[\X‹NqLOQlCUuhRL!Qq]O³º]OQSL[CcOL{bӘcU¯sJNqU:mWLONyhCU‘`b]OQSLO[RcOLONyeŒXqX>LOUWµ[RLO[\X»°dCNq“4dji|vAÑ k)hRdŽNqUWµ[€egm:P~ZdRQ
cOLOQX^egUW[CNNqP€eŒr LOmWNsKLOmWmWL [ji|LONYX!P€egNN R NYX>]OTªeŒX>UW“ dRLOTL[\X PCmWdCNU„TP~Z\QXzeg[\XzLªPJZdCQmWLON!NSP€eŒr LOm„NhCd}~ZQqh+hRLªm„e
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cegQmWL!X>LOTVPCNyhCL PJZNqL LONYX czpCZUWNqU:L[Ô³ºZ[Rc^X>UWZ[hCLm„eƒNqZdCQqcOL Z}RNSLQlx]OLsjcOL “4dCU:PJLOQSTLaX‹hjikZ} X>LO[CUWQyhReg[RNm„e
PCmWdCP€egQX»hCLON‰cegN‰dC[ ¶Rd4r Nqd êNqe[\X‰PJZdCQ®m¯ikL^r4X>QqegcaX>UWZ[ƒcOZQqQSLOc^X>LMhRd NqPJLOc^X>QSL\{4©eQSZ}RdCNYX>LONqNqL’hRL’m¯ikLar X>Qqec^X>UWZ[
P~ZdRQ‰mWLN»³´egUW}RmWLON»¶Rd rƒLNXhRZ[CcyN>eŒX>UWNq³´egUWN>eg[\XzL{CӘmjQSLONYX>L‹v [RZ‡X>LOQ»mWLycOZTVP~ZQYX>LOTVLO[\XhCLym¯i|e‡°dRNXzLOTL[\X’eOlxLOc‹mWL
G
ÕuÖJ×aØJÙ¯Ú¨ÛzÜ ÝxÞa`IÜ^ÛS߯àŒÛSáƒ×ŒâJãaÜ^äåJæ ãaà4å Ü å:ç ÜqèbÚ¨Ûz×\ã±Ú¯Ùºà‡â
Ratio of spectra of Feige56, night 06 096 (brought to airmass 1, 1s): 150s / 300s
1.04
1.04
1.02
1.02
1
1
0.98
0.98
0.96
0.96
0.94
0.94
3400
3600
3800
4000
4200
4400
4600 4800 5000
Wavelength (Angstroms)
5500
6000
6500
7000
7500
8000
8500 9000 9500
Wavelength (Angstroms)
5500
6000
6500
7000
7500
8000
8500 9000 9500
Wavelength (Angstroms)
5500
6000
6500
7000
7500
8000
8500 9000 9500
Wavelength (Angstroms)
Ratio of spectra of Feige56, night 06 096 (brought to airmass 1, 1s): 50s / 300s
1.02
1.02
1
1
0.98
0.98
0.96
0.96
0.94
0.94
0.92
0.92
0.9
3400
3600
3800
4000
4200
4400
4600 4800 5000 5200
Wavelength (Angstroms)
0.9
Ratio of spectra of Feige56, night 06 096 (brought to airmass 1, 1s): 20s / 300s
1
1
0.98
0.98
0.96
0.96
0.94
0.94
0.92
0.92
0.9
0.9
0.88
0.88
0.86
0.86
0.84
0.84
0.82
3400
3600
3800
4000
4200
4400 4600 4800 5000
Wavelength (Angstroms)
0.82
éžê£ë‰ì { Ð oí tŠöOò\ò4÷±õ—øYûžðzù±øõ˜ðMû—ò4ðzüSøõ˜ð^ûžô\ð Œxðzþ-±ð ž „‹þ û˜ûý\ûŠô\ðò4÷Œû—ðzû®ôð’ôxýõ˜ú>ðzû®ô\þ104úzõ˜ðzù±øðzûŠò\õYþ û—ð^ûžò4ðzùxôxöù±ø‰ó‘öyùgý\þÒø
ò÷ø÷ŒñMúqøõþ\+‡ý\ð „ _† „ µ ð^ûIû—ò4ðzüqø˜õðzû:÷Œù±øò\õ˜ú^öó‘öxóÒð^ñMðzùŒøIú>ø˜ú»õYöñMðzùú^ûÿ’ýxùð»ñyöûû—ð»ô öþÒõôð ðqøžÿMý\ùø˜ð^ñMòxûIô\ð
ò4÷Œû—ðMô ý\ùðMû˜ðzüq÷Œù\ô\ð vµ ðMû—ò4ðzüSøõ˜ðMýgøYþwó þwû—úMüq÷ŒñyñMðõ˜ú‡3‘ú>õ˜ð^ù\üqðw)\þÒðzùŒø»ô ý\ùð’ò4÷Œû—ðMô\ð ® û vµ ý\þJû˜÷Œù±ø‰üq÷Œñò öOõ˜ú>ðzû ,4ð^ù
xöýgø " ý\ùð(ò4÷Œû—ðôð Nž û " öý üqð^ù±øõ˜ð " ýxùð(ò4÷Œû—ð(ô\ð ž û " ðqøžðzùi öû " ý\ù\ð»ò ÷±û˜ð(ôð ‰ û ¶u öù\ûžü ö +‡ýðü^öOû " óÒðü>ý4ð
xóÒð^ýð^û¨øŠÿ ‡öý\ü \ð‰ðqøžó ð(ü>
ý 4ð»õ˜÷Œý ±ð(ÿMôõ÷±þÒøð QqegPCPJZQXžNqUWµ[Rem NqdRQI}CQSdCU‘X±sghRZ[\Xžm¯ik]^X>dRhCL»PJLOd4Xž^X>QSL(egPRPCQSZ³´Z[ChCU„L‰P€egQIL^r LOTVPCmWL»LO[QS]±egmWUWN>eg[\XžhRLONINqUWTdRm„eŒX>UWZ[RN
hCLycOdR}~LON(}RQSdCUwXz]ON{
”:{• >u{• z ±›Kœž¤¥¤ž™7šR¢£=™ CB¢ A~‰›gŸEtœŸ
6Z‡XzQSLªP~ZNqLªhC;
L UWmwXz[CLOQqÐ §PCQSUWNqLªm„e§[ dRUw]X \˜Ð V‚cOZ[xX>UWLO[\X!dR[6³´Z[Ch+hCLªcOUWLOmŠeNSNqLO UWTP~Z\QXzeg[xXcegQ m„e
©jdR[CLM]^X^egUwX»PCmWLUW[CLMcOLaXSX>LM[ dRUwXSȗm„v s4“4dC#L UWmwXz[CLOQqÐ [tikLO[ƒ]^XzegU‘X»“ dji|vÑ 4{ 5 ƒ¯s4L^X»“4djikUWmJNi|egµUWNqN>egUwX(hjikdR[CLMP~Z\NSLMhRL
¸ ‹NOsxhCZ[CcQSLOm„eŒXzUwlxLOTL[\X®mWZ[CµdRL{ ²[VNqL(PRQSZPJZNqL(cOLOPJLO[ChRe[\XŠhRe[CNžcOL(P€egQqegµQqePCpCL\sxe‡fR[ªhCLcOZ[ f€QSTLOQžcOLON
QS]ONqdCmwX^eŒX>NsRhCL‹PRQSLO[RhCQSL‹]Oµ\egmWLTLO[\XMP~ZdRQ(L^r LOTVPCmWL‹m„LONQS]ONqdCmwX^eŒX>NZ}4X>LO[4dCNP~ZdRQ(dC[‚egd X>QSL‹L^rCLOTPRmWL‹hCL‹PJZNqL
G\Ñ
ÝxÞH—˜:~ÜzäÚ¯äå ÜMÛzàv™CægäژÜzäqä^Ü
Flux
(real - reconstructed)/real slice
Slice at 4000 A, Feige56, 300s, 06 096 049
10000
0.2
5000
0
-0
-5000
-0.2
-10000
-15000
-0.4
-20000
-0.6
-25000
20
40
60
80
100
120
140
160 180 200 220
Microlens number
éžê£ë‰ì { ³í ~õYöù\ü \ð‹]ÿ b ic ò4÷Œýõówö!ò4÷Œû—ð‹ôð ® û(ô!ð Œxðz1þ ±ð ž „ " ùgý\þÒø „ _† „;,€ðzùAö xû˜üzþ û˜û˜ð " ó ð‹ù‡ý\ñú>õ˜÷ô\ð
—û ò öaïðzó " üQxö +‡ý\ð ówþ1Œù\ð‹ðzû—øMù‡ý\ñú>õ˜÷øú>ð ó ýxùðöOò\õ·.zûó öOýøõ˜ðq2€ðzùA÷±õô÷Œù\ù\ú>ð $ ðzù§ù÷ŒþÒõQ& " ówöôxþ104úzõ˜ðzù\üqð ð^ù±øõ˜ð ô\÷±ùxùú>ðzû
õ˜ú>ðzówóÒðzûIðqøõðzüq÷Œù\û—ø˜õYý\þ|øðzûù÷±õñyöówþ û˜ú>ð‰ò öOõó ð(û˜þ1Œù öOó µ öMüq÷Œýõ·4ð‰õ˜÷Œý±ð»õ˜ð>ò\õ˜ú^û—ðzùŒø˜ð(ówö43W÷±õñMð»ô\ý û˜þ-Œùxöó mWZ[CµdRLMPCQqUWNSLdC[CLM[4dCUwX»hCLPCmWLOUW[RL©tdC[CL!¹ ©(¯¯ V s [ dCUwXw 5 ÑgÐV PCpCZ‡XzZT]^XzQSUW“ dRL{ ©te!PCQSLTUWÁOQSLMczpRZNqLM“ dRL
[CZdRNIPJZd4l Z[CNcOZ[RNX^eŒX>LOQNSdRQIcOL^XqX>L»PJZNqL»hCL(Ð NLONYXŠ“ dCL»m¯ikU„TP~Z\QXzeg[RcOL»hRd³ºZ[RhhCL(cOUWLOmR[jikLONYXžP€egN[C]O³´eNXzL
P~ZdRQm„eocOZ[\l LOQSµLO[RcOLƒhCLƒm¯i|e‡°dCNYX>LTLO[\XhRLƒ«Š¬ ­®suTOTVL mWZQqN!hCLƒm„eoPCQSLTUWÁOQSLƒ]^XzegPJLs:egmWZQSN “ dCLªX>ZdRN!mWLON
PRegQqeTÁ^X>QqLONžNqZ[\X®m„egUWNqNq]ONžmWUW}CQqLON{ ¿Mi|LONX®L[ X>Z\dCNžcegNŠcOL(“4dCL(m¯i|Z[VPJLOd XlxZUWQfRµdRQSL { ¸ sxZ IVNqZ[xXŠQqLOPCQS]NSL[\X>]ON
mWLONŠe‡°dRNYX>LOTL[\X>NžhCdªPReQqegTÁaX>QSL β PJZdCQcL^XSX>LP~Z\NSL ¹\PJLOdVhRL(P~Z\UW[\X>NžZ\[\XŠ]^Xz](]cegQX>]ONŠNqdCUwX>L’vydR[CL(Tªegd4l\egUWNqL
cOZ[\lxLQSµLO[RcOLyhR!L SoUW[ dCUwX±{
Values of beta for LTT9491, night 05 264
12
12
χ 2 / ndf
p0
p1
p2
10
8
39.35 / 55
2.474 ± 1.199
0.00012 ± 0.00058
2.516e-08 ± 7.020e-08
10
8
6
6
4
4
2
2
3500
4000
4500
5000
5500
Wavelength (Angstroms)
χ2 / ndf
p0
p1
p2
223.9 / 113
9.899 ± 0.781
-0.001951 ± 0.000223
1.516e-07 ± 1.581e-08
5500 6000 6500 7000 7500 8000 8500 9000 9500
Wavelength (Angstroms)
éžê£ë‰ì { ¸ íYXq—ý\û¨øð^ñMðzùŒøŠþ ùŒøð>õñMú^ô\þwöþ õ˜ðôð ò4÷ŒýõŠó ðzûžô\ðzýgïü>ý4ðzû $ xóÒð^ýVÿ#‡öOýxüð " õ˜÷Œý ð’ÿyôõ˜÷ŒþÒøðN&Iôðówöò ÷±û˜ð
ôð µ K † b † ò\õþwû—ð(ówöMùgý\þ|ø mž4‰ „b $ ò4÷Œû—ð»ù¶¸ b βž" ñyöû˜û˜ð»ô öþÒõô\ð ‰" „ û& ½ [ hRLOd4rCUWÁOTLMeNSPJLOc^X‰“4dCL’[CZdRNŠPJZd4l Z[CN®L^r PRmWZQSLOQŠLONYX‰mWLMQqegPRP~ZQX‰LO[xX>QSL’cOdR}~L’QSLcOZ[CNYX>QqdCUwX»v PReQX>UWQŠhRL
m¯i|e‡°dCNYX>LTLO[\X»L^X‰cOdC}JL’hCL’hCZ[R[C]OLNO{4©e‹fRµ\dCQSL { ± TZ[xX>QSL’“ dRLs P~ZdRQŠmWL’cOdC}JL’}CmWLOdts mWL’QqegPCPJZQX‰LO[xX>QSL¶Rd r
Z}CNqLOQl ](L^XŠQSLOcOZ[RNYX>QSdCU‘XžLNXŠcZ[CNYXzeg[xXM·£mWL(PRUWc(v 5 Ñd†LNXŠha¹ªegd4r ¶RdRc^X>d€eŒX>UWZ[RNhCL(m„eymnegTL(hRUWczpCQSZgƗ“ dCLŒ¼uLaX
“ dCLm¯ikZ[_NqZdRNÈ˜LONYX>UWTLmWLM¶Rd4rƒhCL‹Ñ k LO[\lCUWQSZ[t{C¿®LaXSX>LNqZdCNYȗLONYX>UWTªeŒX>UWZ[_PJLOd X»^X>QSLcOZ\QSQSUWµ]OLNqUbm¯ikZ[_QSL^XzQSZd4l L
}CUWLO[ªcOL^XSXzL(NYXzeg}RUWmWUwX>]P~ZdRQhCU‘`J]QSLO[\XzLONžP~ZNqLON{xčeg[RNžmWL(QqZdCµLLO[VQqL^leg[RczpCLs\Z\[VQSLaX>QSZd lxL(m„e‹NqZdCNYȗLONYX>UWTªeŒX>UWZ[
hCLƒÑ k_sKv‚m„eg“ dCLmWmWLªNi|e‡°YZd4X>LO[xX!hRLON ¶RdRc^X>dRe‡X>UWZ[CNUWTVP~ZQX^eg[\X>LONƒ·¨Ñ k¼yh€eg[CNmWLONÂZ[CLONcOZ\QSQSLONqPJZ[ChRe[\X egd r
QqegUWLONKhjik]OTVUWNqNqUWZ[eŒX>TVZNqPCpC]QSUW“ dRLONhCL®d² s±PCdRUWNm¯ik]OceQX‰·£NqZdCNYȗLNXzUWTVeŒXzUWZ[€¼jL^XumWLON¶RdRc^X>dRe‡X>UWZ[CNKNOiÒegcOcOLO[xX>dCLO[xX
GG
uÕ ÖJ×aØJÙ¯Ú¨ÛzÜ ÝxÞa`IÜ^ÛS߯àŒÛSáƒ×ŒâJãaÜ^äåJæ ãaà4å Ü å:ç ÜqèbÚ¨Ûz×\ã±Ú¯Ùºà‡â
P~ZdRQŠmWLONŠmWZ\[CµdRLOdCQSN®hjikZ\[ChCL’NqdCPJ]OQSUWLOdRQSLON®v j!s QS]ONqdCmwX^eŒX‰“ dCL’[RZdCN‰eOl UWZ[CN®hR]Y°Yv PRdªcZ[CNYXzeŒXzLOQŠP~Z\dCQŠmWLON
egd4X>QqLONMPJZNSLNO{b©i|egNqP~LOcaX’X>QqÁONMUW[CNYXzeg}RmWL!hCLcL^XSX>L!T]ONqLONYX>UWTªeŒX>UWZ[ÔhCd‚¶€d4rom„eªQqLO[ChŽhCU‘êcOUWmWLOTL[\XycOZQSQSUWµ\UW}CmWLs
L^XUWmtLONYX[C]cOLONqN>egUWQSLyhti|egPCPRQSZ³ºZ[RhCUWQ»cL^XSX>L‹]^X>dRhCLyhRLON(³ºZ[ChRN»UWTVP~ZQYXzeg[\XzNO{
sum(reconstructed)/sum(cube)
sum(reconstructed)/sum(cube)
1
1
0.98
0.98
0.96
0.96
0.94
0.94
0.92
0.92
0.9
0.9
0.88
0.88
0.86
0.86
0.84
0.84
0.82
0.82
3400 3600 3800 4000 4200 4400 4600 4800 5000 5200
5500 6000 6500 7000 7500 8000 8500 9000 9500
Wavelength (Angstroms)
éžê£ë‰ì { yíTtŠöOò\ò4÷±õ—øuð^ù±øõ˜ð®ô÷Œù\ù\ú>ðzûKõ˜ðzü>÷±ùxû¨øõý\þÒøðzû:ÿ»ò öOõ—øYþÒõ:ôð®ó öN¨ýxû¨øðzñðzù±øuðqøIô÷Œù\ùúzðzû}\õýø˜ð^ûò4÷Œý\õuó‘ö»ò4÷Œû—ð®ô\ð
ò\õþwû—ð(ówöMùgý\þ|ø mž#‰ „Nb X‡öOýxü ð»ò4÷ŒýõžóÒð»üzý 4ð xó ðzýð>øŠÿMôõ˜÷ŒþÒø˜ð»ò4÷Œýõó ð»üzý 4ð‰õ÷±ý ±ð µ K † b †
© e!czp4d4X>LyhCdAQqegPCPJZQX(PJZdCQ»mWLON»mWZ[RµdCLdCQSN»hji|Z[ChCLyNqdCP~]QSUWLOdCQqLON(v ] cOZ[CfRQSTVLmWLy³´egUwX“ dCLym¯i|e‡°dRNYÈ
X>LOTVLO[\X[jikLNXyPRegNMcOZ\QSQSLOc^Xm„ZQSNq“ dCL!mWLQ>egPCPJZQXNqUWµ[RegmuNSdRQ’}CQqdCUwXhCLal UWLO[\XMX>QSZPŽ³´egUW}CmWL\s~TVeUWNMedCNqNqUK“ dCLhRLON
UWTPJLOQS³ºLOcaX>UWZ[CN®PJLOd4lxLO[xX‰^X>QSLMegPRP~ZQYX>]OLON®PReQŠm„e‹f rReŒX>UWZ[ hRLON®PRegQqeTÁ^X>QqLON®hCL’³ºZQqTL’hCL’mne«Š¬ ­NqdRUwleg[\X‰hRLON
mWZUWNI“ dRU [CL‰NqZ[\XIl QqeUWTLO[\XIlx]OQSU‘f€]OLONI“4dCL‰P~Z\dCQ:mWLONImWZ[RµdCLOdRQSNIhjikZ[RhCL‰cOL[\X>QqegmWLNIhCLONIcOdR}~LON{gӘmCLONYX]Oµ\egmWLOTVLO[\X
UW[\X>]OQqLONqNqe[\XhCLyQSLOTªegQS“4dCLOQ»“ dCL\s PJZdCQ»mWLON(mWZ[RµdCLOdRQSN»htikZ[ChRLNqdRP~]OQqUWLOdCQSLN(%v 5 i!s m„eNXzQSdCc^XzdCQSLyhCdAQqegP È
P~ZQYX®L[\X>QSL’cdC}~L’QSLcOZ[CNYX>QqdCUwX‰L^X‰cOdR}~L’hCL’hRZ[C[C]LONŠQSLPCQSLO[Rh L^rCegc^XzLOTLO[xX‰m„e NYX>QSdRc^X>dRQSLhRd NSPJLOc^XzQSL’hCL’cOUWLOmbv
cOLON(mWZ[Cµ\dCLOdCQqN»htikZ[ChRLsCcOZTTVLyZ[APJLOd4XmWLMl ZUWQ»NqdCQ»mWLyµQ>egPCpRLQqLOPCQq]ONqLO[\X>]fRµ\dCQSL {ÒÑ CsCZ IAm¨ikZ[§e La`bLOc^X>dR]
dC[ŽÂOZ4ZT;NqdCQMm„eƒÂOZ[CL ¸xÑ ŒÈ Ñ ; hCdŽNqP~Lc^X>QSL!hRL!m„eªfRµdRQSL!PRQS]OcO]OhRLO[\X>L_·¯LO[Ž[CZUWQz¼^{b«uZdCQMcZTP€egQqegUWNqZ[js
m„e ³´ZQSTL hCdÔNqP~Lc^X>QSL!hRL!cOUWLmuPJZdRQMcOL^X‹UW[\X>LQlegmWmWL hCL mWZ[RµdCLOdRQMhtikZ[ChRL!LONYX‹QSLOPCQq]ONqLO[\X>] LO[ÔQSZdCµLA·£]czpCLOmWmWL
[CZ[§QSLONqP~LOcaX>]OL±¼a{
sum(reconstructed)/sum(cube)
1
0.98
0.96
sky spectrum shape
0.94
0.92
0.9
8200
8400
8600
8800
9000
9200
Wavelength (Angstroms)
éžê£ë‰ì {ÒÑ í º4÷g÷ŒñÅôð ów%ö »Œýõ˜ð!ò\õ˜úzüqú^ôðzùŒø˜ð ûýõó þwù±øð>õ/)öówóÒð Ÿ_‰N ¼F†_‰ Žc½$ ðzù‚ù÷Œþ õQ& îù§õ˜÷Œý ð " ówöŽ3W÷õYñMð!ôxý
û—ò4ðzüqø˜õð»ô úzñþwû˜ûþÒ÷Œù!ôxý!ü>þ ðzóCò4÷Œý\õüqðqøžþwù±øð>õ )±öówóÒð $ úzü\ðzó ó ð(ù÷Œùõðzû—ò4ð^üSøú>ðN& M² [LO[hC]OhRdCUwX “ dRLªm¯i|eg°dCNYX>LOTVLO[\X NqLOT!}CmWL TVUWLOd4r+QSLcOZ[CNYX>QqdCUWQSL mWL R¶ d4rX>Z‡X^egmŠmWZQSNq“ dRL Wm L ³ºZ[RhhCL Oc UWLOm
LONYXUWTPJZQX^eg[\X±stcOLª“ dCUNqLOT!}CmWLVLO[egcOcOZ\QSh+eOlxLcVcOLª“ dCLV[RZdCNeOl UWZ[RN PC6d cZ[CNYXzeŒXzLOQ‹hRe[CN „m eANqLOc^X>U„Z[ { s
GV
xÝ ÞH—˜:~ÜzäÚ¯äå ÜMÛzàv™CægäژÜzäqä^Ü
NSZ\UwX dC[³ºZ[Rh+hRL cOUWLOmŠNqdCQSLONYX>U„T] mWZQSNq“ dRLªcOLmWdCUwȗcUžLNX ³£egUW}CmWL{u©e§fRµdRQSL {ÒÑ X>L[Che‚cOZ[ f€QSTLOQcOL ³£egUwX_¹
m„eªX>Q>eg[CczpRLv_¸\¸GYsjNSUwXzdC]OLNqdCQdC[RL QqegUWLhjik]TUWNqNqUWZ[hCdcOUWLOm¯sjLONYX‹TU„LOd4rÔQSLOcOZ[RNYX>QSdRUwX>L “ dRL NqZ[ÔpRZTZgÈ
mWZµdCLAv¾³!suNqU‰m¯ikZ[7cOZTP€egQSL_m„eŽhCUWNYX>QSU„}Cd4XzUWZ[hRLON hCU‘`J]QSLO[CcLON LO[xX>QSLªl\egmWLOdRQ!QS]LOmWmWL_L^XVQSLOcOZ\[CNYX>QSdRUwX>L
[CZQSTªegmWUWNq]OLONPRegQ m„e‚legm„LOdCQ QS]OLOmWm„LƒPJZdRQ!czpRe“ dCL_NqPReŒr Lm¯{I²[7P~Ld4XPJLO[CNqLOQegdl d7hCL_cOL^XSXzLAeg[Reg\m RCNSL_“ dRL
1000
0.5
0
0
-0.5
-1000
-1
-2000
-1.5
-3000
-2
-4000
-2.5
20
40
60
80
100
120
140
160 180 200 220
Microlens number
0.6
1000
Flux
1
(real - reconstructed)/real slice
Slice at 8830 A, LTT9491, 05 264 045
2000
Flux
(real - reconstructed)/real slice
Slice at 7000 A, LTT9491, 05 264 045
0.4
500
0.2
0
0
-0.2
-500
-0.4
-1000
-0.6
20
40
60
80
100
120
140
160 180 200 220
Microlens number
éžê£ë‰ì {ÒÑ »í u ð^ýgïMøõYöù\üQðzûKô\þ-04ú>õ˜ð^ù±øðzûò4÷Œý\õKó‘ö‰ò4÷Œû—ðŠôð µ K † b † " ù‡ýxþ|ø _žw‰ „b!,±øõYöù\ü\ð®ÿw c ÿŒöýxüð " ðqø
ø˜õSöOùxüð(ÿ Ÿ Ÿ ® 4c ÿ’ôõ˜÷Œþ|øð îù õ÷±ý ±ð " ýxùð®õð>ò\õ˜úzû˜ðzù±øSöaøYþÒ÷Œù!ôð‰ó‘ö 3‘÷±õñð‰ôðzû:ô\÷Œù\ùú>ð^û:û˜ý\õIówöø˜õSöOùxüð $ ú^üð^ó ó ð‰ù\÷Œù
õ˜ðzû—ò ðzüSøú>Nð & µ öøõYöù\ü\ð(ÿ Ÿ Ÿ ® #c" û˜þÒøYýú>ð(û˜ý\õý\ùð»õYöþÒð(ô úzñþwû˜ûþÒ÷Œù!ôxý!ü>þ ðzó " ðzû¨øMŒó ÷ öóÒð^ñMðzùŒøžñþÒð^ýgïõ˜ðzüq÷Œù\û—ø˜õYý\þ|øð m¯i|e‡°dCNYX>LTLO[\X LONYX NSL[CNqUW}CmWLƒegd+}RQSdCU‘X!“ dRUžhCL^lCUWLO[\X UWTPJZQXzeg[xX!PJZdCQ mWLN‹X>QSÁON!³´egUW}CmWLON¶Rd r6mWZQSNq“ dRLªmWL ³ºZ[Rh
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cOZTP€egQqegUWNqZ[AeOlxLOcm„e!P~ZNqLMhRLMQS]O³º]QSLO[CcLMhCL^lCUWLO[\X(pRegN>egQShRLOdCNqL{ ©tLPCQSZ}RmWÁOTLhCLM³ºZ[RhƒUWTVP~ZQYXzeg[\X»LNX(hCZ[Rc
PCQSZPRQSLVegd4rÔZ}RNqLOQle‡X>UWZ[CN‹hCLNqdCPJLOQS[RZl © eOlxLOcVmWLOdCQyµ\egm„e‡r UWLap s‡X>L§·£“ dRU:cZ[CNYX>UwX>dRLdC[³ºZ[RhNYX>QSdRc^X>dCQq]±¼’LaX
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m„e P~L^X>U‘X>LMXzegUWmWmWLyhRdAczpRegTVP_hR]^l UW]MlxLQSN»mWLyNqPJLOc^X>QSZµ\QqegPCpRLsCcOLOcOUjPJLOd4XLO[\X>Qqme ^n[CLOQ»hRLON»PJLOQX>LN»hCL¶Rd rƒPRmWdCN»Zd
TZUW[RN(UWTPJZQX^eg[\X>LON={ Å i|eUjczpRZUWNqUtUWcOUjdR[CL‹P~ZNqL‹PRegQXzUWcOdCmWUWÁOQqLOTLO[xX’PReŒX>pRZmWZµUW“ dRL‹P~ZdRQ®X>LNXzLOQ»mWLN(mWUWTUwXzLON(hRL
m¯ikL^r X>Q>egc^X>UWZ[+hCLVNSPJLOc^XzQSLP€egQ‹m¯i|e‡°dCNYX>LTLO[\XhRLV«Š¬ ­®{tӘmINi|egµ\UwXhjikdR[CLVP~ZNqLhR%L Mǐ¸Ð GV§PRQSUWNqLPJLO[Ch€eg[\X m„e
[ dCUwX’PRpCZ‡XzZT]^XzQSUW“ dChL 5 mÑ VV‚·¯P~ZNqL‹=[ ƒZÐÐ\¼^s~egmWZQSN“4djikLOmWmWL ]^XzegUwXvdC[CL‹TªegNqNqL‹hji|egUWQhCjL G { {J¿®ZTVTL‹[RZdCN
m¯i|eOlxZ[CN‹l djstmWLVPJZUW[\X>]VPJZdCQ‹mWLON ]^XzZUWmWLON }CQqUWmWm„eg[\X>LN‹hRLVcOL /X R PJLVLONYXhCU‘`J]QSLO[\XhRd6P~ZUW[xX>]Vd4X>U„mWUWNS]ªLO[ÔX>LOTVPCN
[CZQSTªegmLaXP~Ld4XLO[RµLO[ChRQSLOQ‹hRLON LOQSQqLOdCQSNstNqdCQYX>Zd4X vAµQ>eg[ChRLVTVegNqNqLªhji|egUWQO{ӘcOUžm¯ik]^X>ZUWmWLªLNX X>Zd4X vA³´eUwX!egd
G5
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}~ZQqh hCdczp€egTPL^X±s\eOlxLOc»m„eQS]O³ºQqec^X>UWZ[VeŒX>TVZNqPCpR]OQSUW“ dRL‰hRU‘`J]OQSL[\X>UWLOmWmWL\sgNqZ[cOL[\X>QSL»LONYXL[ hRLOpCZQSNIhRd czp€egTP
P~ZdRQ»cOLOQYXzegUW[CLN»mWZ\[CµdCLdCQSN(htikZ[ChRLsCcOZTVTL‹mWLyTZ\[\X>QSL‹m„e!f€µdCQSL {ÒÑÑ4{
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ÆÈß É¤Ê(ËBLJÌ_Í/Î ÏQÐqÑràNÔ‡Ô‡Ô ÕáJÔNÔ‡Ô Õ_âNÔ‡Ô‡Ô Õ_Ï·ØDãԇԇԇÔgÙ°Æ9Ú ÏKÛNÇNÜ_Í Î ÏMÑgÚ ËFÝNÞWØFÏ[É
éžê£ë‰ì {ÒÑÑ Tí ŠJ÷Œýõ:ý\ùðŠò4÷Œû—ðžðqï\üqðzùŒø˜õú>ð®ô×ð ×t Ÿ „ ® bò\õþwû—ðŠó‘ö(ù‡ýxþ|ø mžw‰ b b " ôxHþ )Œð>õû˜ðzûø˜õYöùxü ð^ûðzù‹ó ÷Œù Œýð^ýõuô ÷Œù\ô\wð ,
Òó ðzûuðJ04ð>øûuô\ð®ó‘ö»õ˜ú‡3‘õYöüSøYþ ÷±ù!ö^øYñ÷Œû—ò\ú>õþ-+gýð®ô\þ-04ú>õ˜ðzùŒøYþÒðzówóÒð®ò4÷Œýxû˜û—ð^ù±øIóÒð‰üqðzùŒø˜õ˜ð‰ôð®ó‘öû—÷Œýõüqðg÷±õûuô\ýüxöñò‹ò ÷±ý\õ:óÒðzû
±õYöù\ôðzûóÒ÷ŒùŒýð^ýõûô ÷Œù\ôð $ ñyöû˜û˜ð‰ô öþ õ, ®\ & Ç(LOµ\egQqhCZ[CN‰X>Z\d4Xhti|eg}~ZQqhAmWLON(QS]NSdRmwXzeŒX>N(Z} X>LO[ dRN»PJZdCQ»mWL‹cOdC}JLy}CmWLOdt{R«KZdRQ»mWLON‰XzQqeg[CczpRLON(hCLymWZ[RµdCLOdRQSN
hjikZ[RhCL UW[C³º]OQqUWLOdCQSLN’v 54 %¥LO[xl UWQSZ[ts€mWL PCQSLOTVUWLOQ’e‡°dCNYX>LOTVLO[\XMcOZ[xlxLOQSµL N>eg[RNhCU‘êcOdCmwXz] L^XMm¯i|e‡°dCNYXzLOTLO[xX
hCd6PRegQqeTÁ^X>QqL β st“ dRUILONYXQSLONYX>QSLUW[\XedhRZTVegU„[CL%G 5 ŒÈ 5 ostP~LOd XeOlxZUWQ‹mWU„LOd6Nqe[CN‹LO[RcOZT}RQSL§·£fRµdRQSL
{ÒÑ G\¼^{KÄMLVTOTVLVP~ZdRQymWLN e‡°dRNYX>LOTL[\X>N NqdCUwleg[xX>N “ dCUžeg}~Z\d4X>UWNqNqLO[\X!vAdR[CLVL^r X>Q>egc^X>UWZ[+hCLVNqP~LOcaX>QSLªvAPCQqL^È
Values of beta for HR8634, off-centered exposure 05 244 066
5
Values of beta for HR8634, centered exposure 05 244 052
5
4.5
2
χ / ndf
p0
p1
p2
4
215.1 / 54
4.385 ± 0.644
-0.0001098 ± 0.0002954
-4.796e-08 ± 3.376e-08
4.5
4
3.5
3.5
3
3
2.5
2.5
2
2
1.5
1.5
1
3500
4000
4500
5000
5500
Wavelength (Angstroms)
1
3500
4000
éžê£ë‰ì {ÒÑ G íoXZ¨ý\û—ø˜ð^ñMðzùŒøŠôxý ò4öOõYöñ4.qøõ˜ð ò ÷±ý\õŠý\ù\ð(ò4÷Œû˜ð(ðqï\üqðzùŒø˜õú>ðô\ðw×t
xþÒð^ù!ü>ðzù±øõ˜ú>ð»ò\õþwû—ð(ówöñ4Ozñð‰ùgý\þÒøò÷ø÷ŒñMú>βø˜õþ\+‡ý\ð $ ÿ’ô\õ˜÷Œþ|øðN& 97.99 / 59
6.535 ± 0.271
-0.00164 ± 0.00012
1.83e-07 ± 1.39e-08
2
χ / ndf
p0
p1
p2
4500
5000
5500
Wavelength (Angstroms)
ÿ Œöýxüð&uð>øŠò4÷ŒýõŠýxùð(ò ÷±û˜ð
Ÿ „ ® b $ #
TUWÁOQqLl dCLªcZQSQSLOcaX>L{}6’ZdCNP~Z\d4lxZ[RN TªegUW[\X>L[Reg[\X cOZTP€egQSLOQ m„LªQS]ONqdRmwXzeŒX!Z} X>LO[ dv‚dC[egd X>QSLªNqPJLOc^X>QSLªhRL
’ǐ¸
Ð GVZ}CNqLOQlx]’m„e‹TOTVL[ dCU‘X®PCpCZ‡XzZT]^XzQSUW“ dRLP~ZdRQhR]^X>LOc^XzLOQžmWLONŠPCQSZ}RmWÁOTLNžQSL[CcOZ[xX>QS]ON{ ©eyfRµ\dCQSL {ÒÑmV
GÐ
xÝ ÞH—˜:~ÜzäÚ¯äå ÜMÛzàv™CægäژÜzäqä^Ü
QSLOPCQq]ONqLO[\X>L hCZ[RcsRPJZdCQm„e lxZUWL }CmWLOdRLsRmWLNhRLOd4rANqPJLOc^X>QqLONhCLh’ǐ¸ÐGVªZ}RNSLQlx]ON’cOL^XSX>L [ dRUwXSȗm„v s€QqegTVLO[C]ONMv
dC[CLTVegNqNqLhji|egUWQ‰hCL L^XvdR[ªX>LTPCN‰hRLMPJZNqLMUWhRLO[\X>UW“4dCLsCegUW[CNqUb“ dCLmWLQqegPRP~ZQX(LO[\X>QqLMcLON‰hCLOd r NqPJLOc^X>QSLNO{
Flux
Two spectra of HR8634 (Airmass 1, 1s)
7
10
Ratio of the two spectra of HR8634 (Airmass 1, 1s)
1.3
exposure 05 244 052
exposure 05 244 066, off-centered
1.2
1.1
106
1
0.9
105
3500
4000
4500
5000
5500
Wavelength (Angstroms)
3500
4000
4500
5000
5500
Wavelength (Angstroms)
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±÷Œþ ðgxó e ðzýð " üq÷ŒñMò öOõ˜úzð»öý!û—ò4ðzüqø˜õ˜ð‰÷ øðzùgýò öOõIó‘öò4÷Œû˜ð mž ‰ ôð»ó‘ö’ñ4O^ñMð‰ùgý\þ|ø " ñþ ðzýgïüqð^ù±øõ˜ú>ð " ñ‹öû˜û—ð»ô öþÒõ W®h$ ð^ù
ù÷ŒþÒõQ& ôõ˜÷ŒþÒøð#,\õYöOò\ò4÷±õ—øðzù±øõ˜ð(óÒð^ûIô\ðzýgï!û—ò4ð^üSøõ˜ðzû " ò4÷Œû˜ð‰ðqï\üqðzù±øõ˜úzð»ûýõIò4÷Œû—ð(üqðzùŒø˜õú>ð )
M² [ cOZ[CNYXzeŒXzL®dC[CL®mW]µÁOQSL®hRU‘`J]OQSL[CcOL®LO[xX>QSL®mWLNuhRLOd4rNqP~Lc^X>QSLONs‡mWL®NqP~Lc^X>QSL®Z} X>LO[ d eOlxLc®m„e’PJZNqL®L^r cLO[\X>QS]L
]^Xzeg[\XIUW[C³´]OQSUWLOdRQKhjikL[\l UWQSZ\[ 5 k%egd!NqP~LOcaX>QSL®UWNSNqd!hCL®m„ePJZNqLŠcOLO[xX>QS]OL‰eOleg[\XKV sŒPRdCUWNuNqdCPJ]OQSUWLOdRQKhjikLO[xl UWQSZ[
5 k LO[xX>QSL VxÑL^X 5 j!{4¿‰LOcOU~PJLOd4XŠlxLO[CUWQŠhtikdC[RLmW]µÁOQSL’TV]ONqLONYX>UWTVeŒXzUWZ[ hCdª¶€d4rªP~LOQqhCd hCL’m¯ik]^X>Z\UWmWLs TªegUWN
egdCNqNqU~hRd ³£egUwX»“ dCLs e R eg[\X(PCmWdCN®hRL’NqP€eŒr LOmWN‰hCLM³ºZ[ChƒhCLMcOUWLOm¨s cOLmWdCUwȗcU~PRdCUWNqNqL’^XzQSL’TVUWLOd rªLONYX>UWTV]MhReg[CN‰mWLMcegN
L^r cOLO[xX>QS]{xÀ’d4ȘhCLOm„vyhCL 5 !s\mWLONžNYX>QSdRc^X>dCQqLONZ}RNqLOQlx]OLNNqZ[\X®hCdRLONžegd r ¶RdRc^X>d€eŒX>UWZ[CNžhRLONPRQSZPRQSUW]^X>]ONžhCL(m„e
m„egTL®hRUWczpCQSZgƗ“ dCL\{g²[QqLOTVegQq“ dCL®]Oµ\emWLOTLO[xXIhCLON:PCUWcON:ed[RUwlxLegd!hRLONuQ>egUWLON:hCL®m¯ik]^X>ZUWmWL‰“ dCU4P~LOd lxLO[\XIPRQSZlxLO[RUWQ
hjikdC[ƒPCQSZ}RmWÁOTVL’P~Z[Rc^X>dCLm~hjik]^XzemWZ[C[ReµL’L[ mWZ[RµdCLOdRQŠhjikZ[RhCL{ ©teTVegNqNqL’hti|egUWQŠPJZdCQŠm„eP~Z\NSL’Lar cOLO[xX>QS]OLMLONYX
LO[oLa`JL^XMX>QSÁONMUWTPJZQXzeg[xX>LƒF· G { ¼^s~L^Xm¯ikZ}RNSLQleŒX>UWZ\[oNqUKPCQSÁN’hCLm¯ikpRZQSUWÂOZ\[ŽeªPCdoPCQqZlxZ “ dRLOQ’hCLN¶€L^r UWZ[RN’“ dRL
m¯ik]^XzegmWZ\[C[Regµ\L‹LO[AmWZ[RµdCLOdRQ»htikZ[ChRLy[jiÒe PCd§cOZQSQqUWµLOQ(LO[\X>UWÁQSLOTL[\X±{RÀf€[AhCLlx]OQSU‘f€LOQ»NikUWmtNi|egµUwX’Zd§[CZ[§hjikdR[
PCQSZ}RmWÁOTLhji|LONYX>UWTVeŒXzUWZ[ªhRdV³´Z[Chjsx[CZ\dCNŠeOlxZ[RNŠ]^X>dChRUW]m„eX>Qqeg[RczpCL’!v V 5 ! hRL(c^pRegcOdR[ªhCLONŠcOdC}JLONsgX>Q>eg[CczpRL
P~ZdRQIm„eg“ dRLOmWmWL(m„ehRU‘`J]OQSL[CcOL(LO[\X>QqL»mWLONžhCLOd4rNqP~LOc^XzQSLONžeŒXSXzLOUW[\X 5 kƒ{x©eMfRµ\dCQSL {ÒÑ 5 QSLOPRQS]ONqLO[\XzL»P~ZdRQIczp€egcOdC[RL
10000
0.2
0
0
-0.2
-10000
-0.4
-20000
-0.6
-0.8
20
40
60
80
100
120
140
-30000
160 180 200 220
Microlens number
6000
0.4
4000
0.2
2000
0
0
-2000
-0.2
-4000
-0.4
-6000
-0.6
-0.8
Flux
0.4
(real - reconstructed)/real slice
Slice at 4750 A, HR8634 expo 05 244 066
Flux
(real - reconstructed)/real slice
Slice at 4750 A, HR8634 expo 05 244 052
-8000
20
40
60
80
100
120
140
160 180 200 220
Microlens number
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Flux (/arcsec^2)
Flux (/arcsec^2)
Sky spectrum from HR718, 05 249 052
3
10
2
10
2
10
10
10
3400 3600 3800 4000 4200 4400 4600 4800 5000 5200
Wavelength (Angstroms)
1
5500 6000 6500 7000 7500 8000 8500 9000 9500
Wavelength (Angstroms)
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cegQX>LNeOl LOc!cOZ[xX>ZdCQqNegUW[RNqUu“ dCL!m¯ikpRUWNYX>ZµQqegTVTL hCLON’legmWLOdRQSNhCdo¶Rd roP~ZdRQ’czp€eg“ dRL!NqPReŒr LOm¨{b©te ³´ZQSTL!hRL
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]OcegQXzNyZ}RNSLQlx]ONyPJZdCQymWLON‹PRegQqeTÁ^X>xQqLONyhCL³ºZQqTL{jÀf€[ÔhRL cZTPCQqLO[ChRQSL m„e l\egQSU„eŒX>U„Z[hCLm¯ikLONYX>UWTVe‡X>UWZ[hRd
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hCL m„eƒQqegUWLYv G sbZ IÔmWLONyhCU‘`J]QSLO[CcOLNZ} X>LO[ dRLONPJZdCQm¯i|e‡°dCNYX>LTLO[\X hCL x NqZ[\X‹UWTPJZQXzeg[xX>LONsbmWL PCQSZgf€m
hCLON!hCZ[C[R]OLON{u©te§f€µdCQSL {ÒÑ QqLOPCQS]NSL[\X>LsKP~ZdRQ mWLON X>Q>eg[CczpCLN!v G Ð 5 L^Xv G \oÑ !sKmWLON‹l\egmWLOdCQqNhCd+¶Rd r
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Values of beta for HR718, 05 249 052
4
2
796.5 / 617
8.264 ± 0.169
-0.00275 ± 0.00008
3.217e-07 ± 9.151e-09
χ / ndf
p0
p1
p2
3.5
3
2.5
2
1.5
1
3400
3600 3800
4000 4200
4400
4600 4800 5000 5200
Wavelength (Angstroms)
χ2 / ndf
2041 / 557
4.587 ± 0.022
p0
-0.001812 ± 0.000010
p1
2.063e-07 ± 1.226e-09
p2
0.9
alphay
alphax
Values of alpha for HR718, 05 249 052
1
0.8
0.7
0.8
χ2 / ndf
p0
p1
p2
168.6 / 557
2.357 ± 0.015
-0.0008546 ± 0.0000069
9.736e-08 ± 8.044e-10
0.6
0.7
0.5
0.6
0.4
0.5
0.4
0.3
3400
3600 3800 4000 4200 4400 4600 4800 5000 5200
Wavelength (Angstroms)
3400 3600 3800 4000 4200 4400 4600 4800 5000 5200
Wavelength (Angstroms)
y
x
Values of position for HR718, 05 249 052
-0.7
0.75
χ2 / ndf
-0.8
Position at Lref
f(P)
4163 / 558
-1.017 ± 0.000
-0.08776 ± 0.00097
0.7
0.65
0.6
-0.9
0.55
-1
0.5
0.45
-1.1
0.4
0.35
3400
3600 3800 4000 4200 4400 4600 4800 5000 5200
Wavelength (Angstroms)
χ2 / ndf
804.3 / 558
Position at Lref 0.5542 ± 0.0001
-0.1176 ± 0.0003
f(P)
3400 3600 3800 4000 4200 4400 4600 4800 5000 5200
Wavelength (Angstroms)
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slice at 4200 A
4
10
slice at 4100 A
103
2
10
10
1
20
40
60
80
100
120
140
160 180 200 220
Microlens number
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35000
slice at 3965 A
30000
slice at 3972 A
25000
20000
15000
10000
5000
0
-3
ÿ
-2
-1
0
1
2
3
x (arcsec)
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1
10000
0.5
0
0
-0.5
-10000
-1
-1.5
-20000
-2
-30000
-2.5
20
40
60
80
100
120
140
160 180 200 220
Microlens number
1
Flux
1.5
(real - reconstructed)/real slice
Slice at 4200 A, HR718 expo 05 249 052
20000
Flux
(real - reconstructed)/real slice
Slice at 4100 A, HR718 expo 05 249 052
40000
0.5
20000
0
0
-20000
-0.5
-40000
-1
-60000
-1.5
20
40
60
80
100
120
140
160 180 200 220
Microlens number
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Ratio of ’quick’- and ’PSF’-obtained spectra for G191B2B, night 06 014
1.2
1.3
1.1
1.2
1
1.1
0.9
1
0.8
0.9
0.7
0.8
0.6
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3400 3600 3800 4000 4200 4400 4600 4800 5000 5200
Wavelength (Angstroms)
5500 6000 6500 7000 7500 8000 8500 9000 9500
Wavelength (Angstroms)
0/ 121
43 65 1
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’quick’ spectrum for G191B2B, night 06 014
60000
’PSF fit’ spectrum for the same exposure
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40000
30000
20000
10000
6600
6800
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Wavelength (Angstroms)
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Ratio of ’quick’ and ’PSF’ spectra for HR3454, 06 014 092
1.08
1.08
1.06
1.06
1.04
1.04
1.02
1.02
1
1
0.98
0.98
0.96
0.96
0.94
0.94
0.92
0.92
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0.88
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Wavelength (Angstroms)
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Wavelength (Angstroms)
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800
600
400
200
3500
4000
4500
5000
5500
Wavelength (Angstroms)
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ratio of two spectra of Hiltner600, night 06 014, quick-script
1.2
1.15
1.2
1.15
1.1
1.1
1.05
1.05
1
1
0.95
0.95
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0.85
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0.8
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0.75
0.75
3500
4000
4500
5000
5500
Wavelength (Angstroms)
5500
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6500
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Wavelength (Angstroms)
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Ratio of ’quick’ spectra of Feige56, 150s/300s
1.04
1.04
1.02
1.02
1
1
0.98
0.98
0.96
0.96
3400
3600 3800
4000
4200 4400 4600 4800 5000 5200
Wavelength (Angstroms)
5500 6000 6500 7000 7500 8000 8500 9000 9500
Wavelength (Angstroms)
Ratio of ’quick’ spectra of Feige56, 50s/300s
1.02
1.02
1
1
0.98
0.98
0.96
0.96
0.94
0.94
0.92
0.92
0.9
3400
3600 3800
4000 4200
4400 4600 4800 5000 5200
Wavelength (Angstroms)
Ratio of ’quick’ spectra of Feige56, 20s/300s
1.1
0.9
1.1
1.05
1.05
1
1
0.95
0.95
0.9
0.9
0.85
0.85
0.8
0.8
0.75
3400
3600 3800 4000 4200 4400 4600 4800 5000 5200
Wavelength (Angstroms)
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Wavelength (Angstroms)
0.75
5500 6000 6500 7000 7500 8000 8500 9000 9500
Wavelength (Angstroms)
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’quick’ extraction
’PSF fit’ extraction
103
Flux /arcsec^2
Flux /arcsec^2
Sky spectrum from HR718, 05 249 052
103
’quick’ extraction
’PSF fit’ extraction
2
10
2
10
10
3400 3600 3800 4000 4200 4400 4600 4800 5000 5200
Wavelength (Angstroms)
5500 6000 6500 7000 7500 8000 8500 9000 9500
Wavelength (Angstroms)
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“ dCLsjNqUIm¯ikL^r4X>Qqegc^XzUWZ[6egc^XzdCLOmWmWLV]OPCQqZd4lxL!X>Zd°ZdRQSNyhRLONyhRU‘ÃVcOdRmwX>]ON v_LONYX>UWTLQycOZQSQSLc^X>LOTVLO[\X mWL³ºZ[RhhCLcOUWLOm
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NSU„TPCmWL‹hCZ\[\XZ\[AhRUWNSPJZN>egUwXMegdCP€egQqeOle[\X±{~²M[§P~LOd X]Oµ\egmWLTLO[\XMQSLOTVeQS“ dCLQ»PJZdCQ»m„ePJZNqLyhChL x y Ñ y “ dRL
mWLONNqP~LOcaX>QSLONL^r X>QqeUwX>N’eOlxLOc‹mneT]^XzpCZ hRL 灓 dRUWcz¾ èyNqZ[\XX>QSÁON}CQSdRUwX>]ON ¹RP~ZdRQ(mWLONP~ZNqLONmWZ[RµdCLONsRm¯ikLar X>Qqec^X>UWZ[
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cOZTTVLy[CZdRN»m¯i|eOlxZ[RN®lCd§egdAcOZdCQqN»hCLym„e NqLOc^XzUWZ[ {ÒÑ4sCcOLyNqZ[xX(m„LON»]^XzZUWmWLON(NX^eg[Ch€egQShCN(³´egUW}CmWLON(“ dRUbNi|eOlxÁQSLO[\X
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[CZdRN‹UWTPJZQX>LVP~LdU„cOU¯stcOZ[CNqUWNYXzegUwX!vA³£egUWQSLVmWLVQqegPCPJZQXLO[xX>QSLVmWLNqPJLOc^X>QqLLar X>QqegUwX!egdR“ dCLmIZ[+e§e‡°Zd X>] ÑÑ 5
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vƒe‡°Zd X>LOQX>Z\d4X>LONmWLON’legmWLdCQSNhCLONNqPReŒrCLOmWNP~ZdRQ’c^pReg“ dRL X>Qqeg[RczpCLŒ¼^{b¿‰L X>LONYXyLa`bLOc^X>dR] v m¯ik]OPJZ “ dRL e hCZ[R[C]
hCLON’NqP~LOcaX>QSLON’cOZTVPCQqLO[Reg[\XhCLON’PCUWcN’ed‚[CUwl Legd‚hRLON’QqegUWLONMhCLON’]^X>ZUWm„LONs€cOZTVTLmWL TVZ[\X>QqL m¯ikL^r LOTVPCmWLhCL m„e
fRµdRQSL H{ G ·£dR[CL»LOQSQqLOdCQINik]^XzegUwXŠµmWUWNqNS]L»hReg[RNIcLŠXzLONYXžL^XžmWLON:legmWLOdRQSNLO[ZQShCZ\[C[C]OL»NqZ[xXžLOQSQSZ[R[C]OLN>¼a{\¿‰LONIPRUWcON
NSZ\[\XhCdRN(v dC[AmW]OµLOQ(hC]O³´ed4XhCLym¯ik]^XzemWZ[C[ReµLyLO[AmWZ[RµdCLOdRQ»hjikZ[RhCLy“ dCUjLONYXhC]cegmW]yhjikdR[ANSPJLOc^X>QqLyv m¯i|egd X>QSLs
54
ÕuÖJ×aØJÙ¯Ú¨ÛzÜ ÝxÞa`IÜ^ÛS߯àŒÛSáƒ×ŒâJãaÜ^äåJæ ãaà4å Ü å:ç ÜqèbÚ¨Ûz×\ã±Ú¯Ùºà‡â
’quick’ extraction
’PSF fit’ extraction
5000
4000
1500
Flux /arcsec^2
Flux /arcsec^2
Sky spectrum from G191B2B, 06 014
’quick’ extraction
’PSF fit’ extraction
1000
3000
500
2000
1000
0
0
-1000
3500
4000
4500
5000
5500
Wavelength (Angstroms)
-500
5500 6000 6500 7000 7500 8000 8500 9000 9500
Wavelength (Angstroms)
Flux /arcsec^2
’quick’ extraction
’PSF fit’ extraction
2000
Flux /arcsec^2
Sky spectrum from HR3454, 06 014 092
2500
’quick’ extraction
’PSF fit’ extraction
800
600
1500
400
1000
200
500
0
0
3400 3600 3800 4000 4200 4400 4600 4800 5000 5200
Wavelength (Angstroms)
5500 6000 6500 7000 7500 8000 8500 9000 9500
Wavelength (Angstroms)
éžê£ë‰ì H{ G¸ Yí ‹gò4ðzüSøõ˜ðzûIô\ð3‘÷Œùxô!ôð»üzþÒðzóC÷ øðzùgý\ûÿ’ò4öaõ˜øþ õôðzûIò4÷Œû—ðzûIô\ðw ‡†[ˆK‰ˆ $ ðzù] öýgøœ&ð>øM×t ® b ž b $ ð^ùh öû&
ò\õþwû—ðzûuówö(ù‡ýxþ|ø „ b " ò4÷Œýõuü öü>ý\ùð®ôðzûuñMúqø\÷gô\ðzûKô ðqï‡øõYöüSøYþ ÷ŒùT,6>B+‡ý\þwüC?PAžðzù ù÷ŒþÒõKð>øKò öOõ:ý\ù ö¨ý\û—øðzñMðzùŒøuôðrŠ}‹Œ
ðzù!ü>÷±ýxóÒðzý\õ (spec + 225*bkg - sum(cube))/sum(cube)
0.5
(spec + 225*bkg - sum(cube))/sum(cube)
Red part, obtained from HR7596, night 05 114, exposure 027
Blue part, obtained from HR7596, night 05 114, exposure 027
1.5
0.4
1
0.3
0.2
0.5
0.1
0
0
-0.1
-0.5
3600
3800
4000
4200
4400
u7 23
Æ9ÇÉ ´Ü ßÏ*ß HÏQÜ
4600
4800
5000
Wavelength (Angstroms)
5500
6000
6500
7000
u7
7500
8000
8500 9000 9500
Wavelength (Angstroms)
ÆÈßÉ ¤Ü_ßÏKËFÝNÜ ÛNÏ
éžê£ë‰ì H{ G Aí ~ðzû¨øMJð 04ð^üSøYýúûýõMý\ùðò4÷Œû—ðô\hð ×t× ž † „ òxõþ û˜ðówöVùgý\þÒø mž b $ ò4÷Œû—ð m‰ &#,bóÒð^ûòxþwü>ûöOò öOõYöþ ûûöùŒø
ö ýù\þ1)±ð^öý!ô\ðzûuõSöOþ ðzûIôð‰ó úqø÷Œþ ó ð‰ô\úzù÷Œù\ü>ðzù±øýxùô\ú[3„öýgøô öù\û:ó úqøSöOó ÷Œù\ùxö±ð‰ðzù!óÒ÷ŒùŒýð^ýõIô ÷Œùxôð µ ðzûK\þwû¨ø÷ ±õYöññMð^û
õ˜ð>ò\õ˜ú^û—ðzùŒøðzù±øó ðõYöOòxò4÷±õ—ø»ð^ù±øõ˜ðyô ýxùðò4öOõ—øóÒð‹û—ò4ð^üSøõ˜ððqï‡øõYöþÒø’öN¨÷Œýgøú‹öýƒû˜ò4ðzüSøõ˜ð‹ôðd3W÷Œù\ôƒñ’ý\óÒøþ òxówþÒúyò öOõ ‰ ‰ ž" ðqø
ô öýgøõ˜ð‰ò öOõ—øžó‘öMû—÷Œññð‰ô\ð®ø÷Œý\ûIó ðzûû—ò4ð^üSøõ˜ðzûIô\ý ü>ý 4ð»ô\ð»ô÷Œùxùú>ðzû cOLª“ dRU³´eUwX!“ dCLªh€eg[CN dR[CLªTTLX>Qqeg[RczpCLªhRd+cOdC}JLVZ} X>LO[ dtsbXzZdCNmWLONNSP€eŒr LOmWN[CLªNqZ[\X PRegN LarCegc^XzLOTLO[xX
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PCQSZ}RmWÁOTL e hRLOPCdRUWN(]^X>]ycZQSQSUWµ]\sCL^X’mWLyTVOTLX>LONYX’La`JLOc^XzdC]‹NSdRQ»mWLON(TVOTLN(P~ZNqLONe R e[\X’NqdC}CUjdR[A[CZ\d4lxLegd
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(spec + nspec*bkg - sum(cube))/sum(cube)
(spec + nspec*bkg - sum(cube))/sum(cube)
0.12
0.1
0.1
0.05
0
0.08
-0.05
0.06
-0.1
0.04
HR7596, night 05 114 expo 027
0.02
HR7596, night 05 114 expo 027
-0.2
0
-0.02
-0.15
-0.25
3600
3800
4000
4200
4400
u7 23
4600
4800
5000
Wavelength (Angtroms)
Æ9ÇÉ ´Ü ßÏ*ß HÏQÜ
5500
6000
6500
7000
u7
7500
8000 8500 9000 9500
Wavelength (Angtroms)
ÆÈßÉ ¤Ü_ßÏKËFÝNÜ ÛNÏ
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hCL ¬U6Ó­I¬ƒPRQS]ONqLO[\XzLyhCLON(hR]O³´egd4XzN»PJZdCQ(cOLOQX^egUW[CLON(mWZ[RµdCLOdRQSN(hji|Z[ChCL\{€¿®Ly³£egUwXLONYXMeOlx]OQS]\sCTªegUWN(cOLy“4dCUjPJZNqL
PCQSZ}RmWÁOTL®egd°ZdCQShtikp dRUxLONYX:“ dCLŠmWLONKmWZ[RµdCLOdRQSNKhtikZ[ChCLŠhCLNKhC]O³´ed4X>NKLO[“ dRLONYX>UWZ[‹legQqUWLO[\XIegdcOZdCQqNKhCd‹X>LOTVPCN{
ӘmjNqLOT}Cm„L4RAeOlxZUWQ(dC[RLhR]OP~LO[RhReg[RcOLyLO[AmWUWLO[‚eOlxLOcymWLXzegd4r_htikp dCTVUWhCUwXz]sCTVegUWN(Z[§e]Oµ\egmWLOTVLO[\X’Z}CNqLOQl ]hRLON
hC]Ocem„egµLON»UWTPJZQXzeg[xX>N‰LO[_P~LdƒhCL’X>LOTVPCNs4htikdC[CLP~Z\NSLyv!m¯i|egd4X>QqLMP€egQ®Lar LOTVPCmWL{R¿®LON®legQSU„eŒXzUWZ[CN»LOTPJOczpCL[\X
m¯ik]^XzegmWZ\[C[Regµ\L NqP~LOcaX>QSZ‡È—NqP€eŒX>U„egm:hCL cOZQSQqUWµLOQcOZQqQSLOc^X>LTLO[xXymWLNhC]O³£egd4X>NyhCL m„eƒm„egTL\{j½[CL cOZQqQSLOc^X>UWZ\[ŽLNX‹LO[
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Ratio of two spectra of HR7596, night 05 114 (Airmass 1, 1s)
2
1.3
1.8
1.2
1.6
1.1
1.4
1
1.2
0.9
1
3500
4000
4500
Š‰
5000
5500
Wavelength (Angstroms)
1 98:‹ =Œ
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P1
5500 6000 6500 7000 7500 8000 8500 9000 9500
Wavelength (Angstroms)
WY/ Ž
·ØBËBÞ Ü ÏÆ9ÔNÓ ã‡ã·Ö ÉBÕ ÝNÐFÏKÍ·ÝNÜ_Ë?ØFÏÆ
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Ratio of two spectra of Feige56, night 06 096 (Airmass 1, 1s)
1.12
1.1
1.1
1.05
1.08
1
1.06
0.95
1.04
0.9
1.02
0.85
1
0.8
0.98
0.75
0.96
0.7
0.65
0.94
3500
4000
4500
5000
5500
Wavelength (Angstroms)
0‰ 1 98:‹ Œ
Æ\ß É Ü_Þ Ø mΠ݇ØFÝ
Ž P1 43
5500 6000 6500 7000 7500 8000 8500 9000 9500
Wavelength (Angstroms)
W
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Reference spectrum
0.8
Blue spectrum from HR3454, night 06 014, exposures 070 and 092
Red spectrum from HR3454, same exposures
0.6
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Atmospheric extinction
Reference spectrum
0.8
Hiltner600, 06 014 067-080
HR3454, 06 014 070-086
HR3454, 06 014 070-092
0.6
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HR8634, 05 226 053-071
0.4
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Ã<ÆPË0Ìw¾mÀ½»¼¿ÌÃ<Í<Ë}ÀʇÜ)νΏÍϹÌÆg‡ÄW¼'À Á}Á‡Î À½Í Â}Ë}ÆPÆg̹WÍ4¼'»½Á À Æ'Ù »ÌwÙÀ½Â}Í4¼'ȇÂ}ÀÞÃÓ»½Æ½¼¿Ç\Í<¼'Í<Á}À½ÃÓ»Ì»¹W¼'ʇÁm¼'¹ÑÀÃ<¹ÌU¹WÀ6»6Ám¹Ë‡È!Í<Å=ÆgÀ6Â&Á}ÌwÆg¼‡Á¿ÈEÌUΏÌÀ6ÆgÁmÄW¼'»½Á}¼'Á‡¾mÀ½Ë&ÍÌwÄWÀ:À{ÌwÃÏÀ½Ë0¾SÀ½Ë‡»Ìwà ÍÏȇÀÉÀÞȇË0À ¼'’ÃÏÀÞÇ ÀÌUÀÐ ×Ìw¹W¹WÁ}Ã<ÃÏ»ÂaÌw¹W¼'È}Á À
@?v6 BAC?
9?U6 BAC?
\R Us
6
D
9E
WV F
)
(T (λ))−1
:
0
5+* _6
) 0
*
+
"
] wGV 5 V
HR3454 (1s, secz=1.06) *8.0 AA
10-9
10-10
10-11
8
HR3454 (1s, secz=1.05) *8.0 AA
10-10
autofcalibNrebinspece3d_TC06_014_070_001_17_B.fits
HR3454.fits
Flux [ergs/cm2/s/A]
Flux [ergs/cm2/s/A]
5 WV * ¤6
) G
autofcalibNrebinspece3d_TC06_014_070_001_17_R.fits
HR3454.fits
10-11
Flux calibration: fluxNrebinspece3d_TC06_014_070_001_17_B.fits (1s, secz=1.06)
Flux calibration: fluxNrebinspece3d_TC06_014_070_001_17_R.fits (1s, secz=1.05)
10
Relative error [%]
Relative error [%]
6
4
2
0
-2
-4
-6
Error: 0.05 +/- 1.57%
-8
3000
3500
4000
4500
5000
Wavelength [AA]
5500
6000
5
0
-5
-10
0.5
Error: 0.58 +/- 1.96%
0.6
0.7
0.8
Wavelength [AA]
0.9
1.0
x1e4
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