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Enrique Vázquez-Semadeni
Adriana Gazol
CRyA UNAM, México
Collaborators:
Thierry Passot (OCA)
Jongsoo Kim (KASI)
Dongsu Ryu (Chungnam U.)
Ricardo González (CRyA UNAM)
1
Contents
1.
2.
–
–
Introduction
“Classical” ISM models vs. turbulence:
•
Equilibrium vs. out-of-equilibrium
Turbulence in thermally bistable media
Effects of net cooling
•
•
Effective thermodynamic behavior
Dependence of probability distributions on turbulent
parameters
3.
Magnetic field correlations with density and
pressure
4.
Thin CNM sheet formation
5.
Small-scale structures in simulations
2
I. INTRODUCTION
• Classic theories of ISM: Based on
pressure balance and equilibrium states.
– ISM theories: multiphase:
• Field, Goldsmith & Habing (1969): “two-phase” model:
dense, cool (100 K) clouds in thermal-pressure
equilibrium with surrounding warm (104 K), diffuse
medium.
• McKee & Ostriker (1977): “three-phase model”:
supernova-dominated ISM, with shell fragmentation
into cold clouds and warm medium. Hot gas in interiors
of SN remnants. All 3 phases in rough pressure
equilibrium.
3
– Caveat: left out advection (transport by
gas motions), self-gravity, magnetic
fields, rotation,... (see Elmegreen 1991, 1994
for linear instability analysis).
• Eturb , Emag, Ecr > Eth in ISM (Boulares & Cox 1990)
• Eturb  advection (transport) and inertia (not just an
additional pressure) (Ballesteros-Paredes, VázquezSemadeni & Scalo 1999).
– The ISM is turbulent:
• WNM is transonic (Kulkarni & Heiles 1987)
• CNM (e.g., Heiles & Troland 2003) and molecular gas
(e.g., Zuckerman & Palmer 1974) are supersonic.
4
• Turbulent flows are characterized by
strong nonlinear fluctuations of the physical
variables about their mean values.
• The fluctuations (tails of the probability
distributions)
– are transient and locally out of equilibrium.
– are responsible for important phenomena. E.g.:
• Star formation
• TSAS?
5
II. TURBULENCE IN THERMALLY BISTABLE
MEDIA
1. Effects of net cooling (heating G + cooling L):
1.1 Net cooling determines the compressibility of
the gas (Tohline et al. 1987).
• If heating and cooling laws are power laws, the gas
response to compressions can be described by a
polytropic law P ~ rgeff and effective polytropic exponent
geff (Elmegreen 1991; Vázquez-Semadeni et al 1996, 2003):
geff
Thermal-equilibrium
(TE, G=nL) value gTE
Adiabatic value g
for tcool << tcros
for tcool >> tcros
6
adiabatic
(fast)
isobaric
TE (slow)
log n (cm-3)
7
1.2. In the presence of externally-driven velocity fluctuations,
density field is expected to include a roughly stationary
population of zones at “unstable” values, made up of fluid
parcels traversing this regime from one phase to another.
Because of the dynamic nature of the process, thermal
pressure is expected to deviate from TE at transitional
densities.
DPinstab
gTE~0.7
gTE~ -0.7
gTE~0.7
gTE~0
8
• Indeed, a parametric study (Gazol, VS & Kim 2005,
ApJ) of randomly-driven turbulence shows:
9
Effect of the driving scale lfor,
M=1 (w.r.t. diffuse gas @ 7000K)
Simulations in 100-pc boxes, 5122
resolution, random Fourier driving
lfor = 50pc
lfor = 25pc
2D histograms in P-r space
lfor = 12.5pc
Slope = geff
lfor = 6.25pc
As lfor decreases, tcros decreases, geff approaches g of the gas.
10
Effect of the Mach number
M (w.r.t. the WNM)
M=0.5
M=1
M=1.25
lfor =50pc
lfor =6.25pc
The dynamic range of P and n, and the mean
slope of the distribution increase with M
11
Fits to the points in P-r diagram give:
g is always >0
and
increases with M
and 1/lfor
= 1/lfor
As either M increases or lfor decreases, tcros/tcool decreases
the gas behaves farther from thermal equilibrium and closer to
adiabatic
12
Implications: thermally unstable gas should be present in the ISM...
Density PDF
Simulations of warm and
cold media, with ionization
heating only.
(VS, Gazol & Scalo 2000 ApJ)
Temperature PDFs: ~ 50% of the
mass at “unstable” temperatures.
Cumulative
Qualitatively consistent
with observations: Dickey
et al. 1979; Heiles 2001;
Kanekar et al. 2003.
PDF
(Gazol, VS, Sánchez-Salcedo & Scalo 2001 ApJL)
(see also Wada & Norman 2001; de
Avillez & Breitschwerdt 2004; Mac Low
13
et al. 2005; Audit & Hennebelle 2005)
... and also large pressure fluctuations:
Numerical simulations
with SN driving, no B
N(P) ~ P-5/2
de Avillez & Breitschwerdt 2004
14
2. Dependence of PDFs on turbulent parameters
– Functional form of density PDF depends on geff
1998).
(Passot & VS
• Due to variation of sound speed with density c ~ r(g-1)/2, so
effective Mach number of a compression depends on local
density.
– Width of PDF (standard deviation) depends on Mrms.
Isothermal case: lognormal
(molecular clouds)
General polytropic case:
power law tails (~atomic ISM)
g = 0.3
g = 1.7
Passot & Vázquez-Semadeni 1998
15
– Apparently similar behavior for pressure PDF:
Gazol et al. 2005
lfor = 50 pc
•
The high-P wing approaches
a power law for high M.
•Low-g–like behavior
M = 0.5
M=1
M = 1.25
lfor = 6.25 pc
•
The high-P wing drops rapidly,
and its slope is independent of M
•High-g–like behavior
16
Comparison with observations should constrain geff
Observations of CI pressure PDF
Jenkins 2004
•
Also column density PDF? (VS & García 2001)
17
III. B-r, P correlations
Numerical simulations of ideal MHD interstellar
turbulence (without AD) show little correlation
of magnetic pressure (B2) with density.
Passot, VS & Pouquet 1995
(multi-temperature)
Padoan & Nordlund 1999
(isothermal)
See also Hennebelle & Pérault 2000
(multi-temperature)
Ostriker, Stone & Gammie
2001 (isothermal)
18
• de Avillez & Breitschwerdt (2004) (multi-temperature)
• Similarly for observations of B in atomic ISM
Crutcher et al. 2003; Heiles & Troland 2005)
(e.g.,
19
•
Interpretation (Passot & VS 2003): Analytical+numerical
study of magnetic pressure in driven MHD
turbulence.
Found different asymptotic B2-r scaling for different
modes of nonlinear MHD (“simple”) waves:
•
B2 ~ r2
Fast wave
B2 ~ c1 – c2r
Slow wave
B2 ~ r1/2—2
Alfvén wave
Fast mode domination
Slow mode domination
log B2
log B2
•
log r
log r
20
Alfvén mode, low Ma
Alfvén mode, high Ma
r2
r1/2
 In a turbulent medium with superpositions of waves: Value
of B at a given position and time is not a function of local
r, but of the history of wave passages at that position.
 B2 not characterized by a single response to compressions;
randomizes the behavior of the restoring force.
21
•
•
•
Thermal-magnetic pressure correlation:
Generally uncorrelated...,
2005; Mac Low et al. 2005)
(see also de Avillez & Breitschwerdt
except at high densities, where Pth is high and Pmag is
medium-to-high.
•
Cold gas can have high or low Pth. In latter case, Pmag
makes up for low Pth (see also Inutsuka’s poster).
Sorted by temperature
Sorted by density
Dense gas
Diffuse cold gas
104 K < T
6100 < T < 104 K
310 < T < 6100 K
140 < T < 140 K
45 < T < 140 K
Gazol, Luis & Kim 2006
T < 45 K
n < 0.1 cm-3
0.1 < n < 0.6 cm-3
0.6 < n < 3.2 cm-3
3.2 < n < 7.0 cm-3
-3
7.0 < n < 80 cm
22
80 cm-3 < n
IV.Thin CNM sheet formation
Passot, González & Gazol 2006 ApJ)
–
(VS, Ryu,
Fortuitous finding while investigating molecular cloud
formation by colliding WNM streams.
Physical setup: (see also
n, T, P, v1
n, T, P, -v1
Hennebelle & Pérault 1999; Koyama &
Inutsuka 2000, 2002; Audit &
Hennebelle 2005; Heitsch et al. 2005)
• WNM inflow:
–
–
–
–
n = 0.34 cm-3
T = 7100 K
P = 2400 K cm-3
Mach number in WNM: M = v1/cWNM (control parameter)
23
• Analytical model for early stages:
– Ingredients:
• Adiabatic shock.
• Quasi-stationary state after ~ cooling time (shocked layer
thickness ~ 2 cooling lengths lc).
• Phase transition through TI to cold phase after cooling
length.
• DP/lc ~ momentum flux drop across lc.
Predictions: Conditions in dense layer
as function of M.
~ lc
24
• Excellent agreement with 1D simulations:
Simulation with L = 64 pc, M = 1.03, resol. = 4000
• Cold dense layer has properties comparable to Heiles &
Troland’s (2003) thin cold neutral medium sheets:
–
–
–
–
–
N ~ 2.5 x 1019 cm-2 (after 1 Myr)
T ~ 25 K
n ~ 250 cm-3
vf ~ 0.015 pc Myr-1
P ~ 7000 K cm-3  Note higher-than-mean ISM PT because of
dynamical origin. In pressure balance 25
with
inflow’s total (ram + thermal) pressure.
• Linewidth ~ 1 km s-1
v
0
-v
r
• A signature of the inflow gas velocity, not of the
internal turbulence.
– Does not imply excessively short (104 yr) lifetimes.
– N at t ~ 1 Myr comparable to observed value.
26
• Late stages (3D runs @ 2003):
– Turbulence apparently develops by NTSI-like instability in
cooling gas:
16 pc
64 pc
• Shocked warm gas is everywhere subsonic, but large density
contrast provided by phase transition.
• Time for turbulence development depends on inflow Mach
number M:
– ~ 10 Myr for M ~ 2.5
– ~ 50 Myr for M ~ 1.
r
P
M = 1.03, Dt = 80 Myr
M = 2.4, Dt = 26.7 Myr
27
M = 1.03, Dt = 80 Myr
M = 2.4, Dt = 26.7 Myr
Thin CNM sheets may be the “little sisters” (low-M
collisions) of molecular clouds
28
V. Small-scale structure
(Gazol, VS & Kim, in prep.)
–
Ongoing analysis of small-scale structures in highresolution simulations of atomic ISM turbulence.
–
20482 simulation of randomly-driven turbulence at
Mrms~1 in WNM (see also P. Hennebelle’s talk)
29
Density field.
Lbox = 100 pc
resol. = 20482
Dx = 0.05 pc
Large-scale
driving.
30
–
Formation of sheets and cometary cloudlets.
–
Steady overdense (n > 100 cm-3) and over-pressured (P >
4000 K cm-3) mass fraction ~ 5-10% (compare to 2-4%
reported by Stanimirovic & Heiles 2005).
–
Relatively common excursions to n > 1000 cm-3, P > 104 K
cm-3, occasionally to n ~ 3000 cm-3, P ~ 3x104 K cm-3.
(cooling function implies
a transition to ~ isothermal
~
regime at 10 K at n > 2000 cm-3.)
31
VI. Summary
• ISM in statistical equilibrium, but not necessarily in local
thermal and pressure equilibria.
• Structure and star formation provided by the fluctuations.
 Theories must discuss variances as well as mean values.
•
r, Pth and Pmag all expected to fluctuate significantly in
transonic, thermally bistable media such as atomic ISM.
– Thermally unstable gas AND overdense,
cloudlets are NON-equilibrium structures .
overpressured
• Pth for intermediate-density gas fluctuates because of competition
between approach to thermal equilibrium and turbulent crossing
time.
• Pmag fluctuates because different trends for different MHD waves.
• Overdense, overpressured cloudlets are created by transient rampressure compressions.
32
• Thin CNM sheets can be transiently formed by transonic
collisions of WNM streams, with lifetimes ~ 1 Myr.
•
Structure down to the smallest resolved scales (a few x 0.1
pc), with high densities (n > 1000 cm-3) and pressures (P > 104
K cm-3).
– Sufficient to account for observed frequency of TSAS?
33
The End
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