Lessons on ISM
modelling
from kiloparsec
scale simulations
Adrianne Slyz
University of Oxford
Zurich, September 18th 2007
What physical processes regulate …
log Σ SFR (Msol yr-1 kpc-2)
Kennicutt (1998)
starbursts
centers of
normal disks
normal disks
SFR
Area
~
∑gas1.4
log Σ gas(Msol pc-2)
the rate at which gas turns into stars?
Zurich, September 18th 2007
Link between density structure
& star formation ?
Zurich, September 18th 2007
Key insights from periodic box simulations in the 90’s:
1. Density structure of isothermal medium structured by
supersonic, compressible turbulence is well described
by a log-normal distribution whose dispersion reflects
the Mach number of the medium (Vazquez-Semadeni
1994, Padoan, Nordlund & Jones 1997, Nordlund & Padoan 1999)
2. Isothermal and adiabatic turbulence decays quickly
(within a sound crossing time) whether the medium
is magnetized or not (Stone et al. 1998, Maclow et al. 1998,
Padoan & Nordlund 1999)
Zurich, September 18th 2007
Initial conditions
Homogeneous gas
ρ = 1 at/cm3
1.28 kpc
T = 105 K
Turbulent velocity
field imposed on
large scales
P(k) ∝ k-4
1.28 kpc
1.28 kpc
Periodic boundary conditions
Zurich, September 18th 2007
Initial conditions
Homogeneous gas
ρ = 1 at/cm3
1.28 kpc
T = 105 K
Turbulent velocity
field imposed on
large scales
P(k) ∝ k-4
1.28 kpc
1.28 kpc
Periodic boundary conditions
Zurich, September 18th 2007
Radiative cooling
log10(T) ergs cm3/s
-21
-22
-23
-24
-25
-26
3
4
5 6 7
T (Kelvin)
8
White and Sarazin (1987),
Rosen and Bregman (1995)
Zurich, September 18th 2007
log10(normalized PDF)
log10gas - <log10gas>
PDF =
with
σ = ln
1___
(2 π)1/2 σ
[ 1 + (M
rms
exp
/2)2
]
(
- (ln ρ - < ln ρ >) 2
2σ 2
(Padoan &
2002)
)
Nordlund
Zurich, September 18th 2007
log10(normalized PDF)
log10gas - <log10gas>
PDF =
with
σ = ln
1___
(2 π)1/2 σ
[ 1 + (M
rms
exp
/2)2
]
(
- (ln ρ - < ln ρ >) 2
2σ 2
(Padoan &
2002)
)
Nordlund
Zurich, September 18th 2007
log10(normalized PDF)
log10gas - <log10gas>
PDF =
with
σ = ln
1___
(2 π)1/2 σ
[ 1 + (M
rms
exp
/2)2
]
(
- (ln ρ - < ln ρ >) 2
2σ 2
(Padoan &
2002)
)
Nordlund
Zurich, September 18th 2007
log10(normalized PDF)
log10gas - <log10gas>
PDF =
with
σ = ln
1___
(2 π)1/2 σ
[ 1 + (M
rms
exp
/2)2
]
(
- (ln ρ - < ln ρ >) 2
2σ 2
(Padoan &
2002)
)
Nordlund
Zurich, September 18th 2007
log10(normalized PDF)
log10gas - <log10gas>
PDF =
with
σ = ln
1___
(2 π)1/2 σ
[ 1 + (M
rms
exp
/2)2
]
(
- (ln ρ - < ln ρ >) 2
2σ 2
(Padoan &
2002)
)
Nordlund
Zurich, September 18th 2007
Open questions
fc = ∫
Universal PDF?
∞
ρ PDF d ρ
ρth
fraction of
mass above th
∞
∫0
ρ PDF d ρ
(Elmegreen 2002
Krumholz & McKee 2005
Wada & Norman 2007)
Is there a
clear density
threshold for
star formation?
Zurich, September 18th 2007
log10(normalized PDF)
Log-normal fit to high density
end of run with stars, self-gravity, fbk
PDF =
2
1___
(ln
ρ
<
ln
ρ
>)
(
)
exp
1/2
(2 π) σ
2σ 2
< ln ρ > = 3.9
⇒ ρpeak ≈ 50 at cm-3
σ = 1.22
log10gas (at/cm3)
⇒M
rms
= 3.1
Zurich, September 18th 2007
PDF for SN driven stratified segment of a disk
1 X 1 X 20 kpc
density Probability
Distribution Function (PDF)
10
8
6
4
x-y plane
2
1
0
-0.5
-1
-2
PDF
Z (kpc)
0.5
-4
-6
-8
-10
Avillez & Breitschwerdt 2005
n (cm3)
Zurich, September 18th 2007
PDFs in different subbox sizes for
SN driven stratified segment of a disk
0.5 X 0.5 X 10 kpc disk segment
PDFs for gas near midplane
125 pc subbox
4 pc subbox
Joung & MacLow 2006
Zurich, September 18th 2007
3D isolated disks,
25-50 pc resolution
stars
New generation of ISM simulations
temperature
pressure
face-on view
density
log Temp
edge-on view
2.5
PDF
7.5
Tasker & Bryan 2006
0.001
1.0
1000
 (Msol pc3)
Zurich, September 18th 2007
Different philosophies for adding
supernovae explosions in ISM models
A
Model star formation
m* =  ρgasVcell ∆t/tdyn
+
Stellar Initial Mass Function
B
Model observed supernovae
rates & mimic their distribution
(e.g. isolated, clustered)
e.g.
SN frequency Milky Way
Galaxy:1/330 yr-1 for Type I and
1/44 yr-1 for Type II (Tammann et al. 1994)
Scale heights: Type I :325 pc (Heiles 1987)
Type II :90 pc
Calculate energy and mass
returned to interstellar medium
via supernovae and stellar winds
Power law distribution of superbubbles:
dNB ~ n*-2dn*
(Kennicutt et al. 1989, McKee & Williams 1997)
Zurich, September 18th 2007
B
Supernovae feedback in Joung & Maclow 2006
1.) Identify supernovae site (stick to the observations)
2.) Grow a sphere at that site until it encloses 60 Msun.
Radius of this sphere Rexp ~ 7 pc to 50 pc
Rexp
Mexp =
60 Msun
3.) Redistribute mass in that sphere so that it has uniform
density  = 3Mexp/(4  Rexp3)
4.) Inject thermal energy ESN = 1051 ergs evenly into the sphere
NO mass ever removed to form a star
Zurich, September 18th 2007
Compare estimated SFR to input SN rates
SFRs derived from input SN rates
Identify Jeans unstable
boxes Mbox/MJ > 1
where MJ = <J3
 = avg density in box
=1
 = 0.3
~ 1 order of
magnitude
predictions
J = (/G<)1/2 tot
tot = (<cs>2 + 1/3<2)1/2
(Chandrasekhar 1951)
SFR = Mbox/tff where  = 0.3 or 1
(2 input supernovae rates:
assuming 130 and 200 Msol
required per SN)
Joung & MacLow 2006
Zurich, September 18th 2007
Is that because they ignore self-gravity in their model?
no fbk,
with s-g
Gotoh & Kraichnan (1993)
found power law PDFs for 1D
sims of Burgers flows ⇒ infinitely
compressible flows
Mrms=11.8
Mrms=5.1
Mrms=5.2
Mrms=5.8
(Slyz et al. 2005)
Zurich, September 18th 2007
Heyer et al. 1998
A
First make stars . . .
(FCRAO CO survey)
m = ε ρgasVcell ∆t/tdyn
if the gas satifies:
Cen &
Ostriker
1992
*
> thresh -> dense
T < T thresh -> cold
 v < 0
-> contracting
t cool < t dyn
-> cooling rapidly
Zurich, September 18th 2007
Then do stellar feedback . . .
Cen & Ostriker 1992
DmSF (t) = m*(t-t*)/т2 exp [-(t-t*)/τ]


1.28 kpc
Calculate a time dependent SFR:
where τ = max(tdyn, 10 Myr)
Stellar winds: f ∆mSF
returned to gas
Supernovae:  ∆mSF c2
injected as thermal
energy
100 pc @ 10 Myr
if v=10 km/s
f, determined by IMF
Zurich, September 18th 2007
Non-instantaneous feedback
4.5 Myr
density
temp
pressure
22 Myr
41 Myr
Slyz, Devriendt,
Bryan, Silk (2005)
Zurich, September 18th 2007
Instantaneous feedback
4.5 Myr
density
temp
pressure
22 Myr
41 Myr
Slyz, Devriendt,
Bryan, Silk (2005)
Zurich, September 18th 2007
Is this the same old story . . . ?
When put supernova thermal energy ESN = 1051 ergs
in dense regions most of the energy is quickly radiated away?
Get neither thermal or dynamical heating (Katz 1992)
Fixes: 1)artificial time delay in cooling (Gerritsen 1997;
Thacker & Couchman 2001; Governato et al. 2006)
2)assign explosion energy to fluid parcels
as pure kinetic energy (Navarro & White 1993)
3)introduce a thermalization efficiency whereby assign
some fraction of supernova energy as kinetic and some
as thermal (Navarro & White 1993, Hernquist & Mihos 1995)
4)sub-grid models of multi-phase ISM (Yepes et al. 1999,
Springel & Hernquist 2003)
Zurich, September 18th 2007
Time evolution of density PDF
green: inst fbk, black: non-inst fbk
Zurich, September 18th 2007
Time evolution of energy spectra
no s-g
no fbk
s-g
no fbk
no s-g
fbk
s-g
fbk
compressible
∇ ✘ vcom= 0
solenoidal
∇ ⋅ vsol = 0
ratio
Zurich, September 18th 2007
Time evolution of energy spectra
no s-g
no fbk
Instantaneous
s-g
no s-g
feedback
no fbk
fbk
s-g
fbk
compressible
∇ ✘ vcom= 0
solenoidal
∇ ⋅ vsol = 0
ratio
Zurich, September 18th 2007
Comparison of inputs into Silk prescription
Q = SFR G-1/2 ρgas-3/2 (σgas / σf ) -2.72
0.2
0.0
5
4
3
2
1
Porosity
(km/s)
with instantaneous fbk,
with gravity
0.4
-1.5
-2.0
(Msun/pc3)
with non-instantaneous fbk,
with gravity
log10<ρ>
with non-instantaneous fbk,
no gravity
0.6
(Msun/yr)
SFR
no fbk,
with gravity
<σ>MW
Different physics
no fbk,
no gravity
0.8
-2.5
-3.0
40
30
20
10
0
0
100 200 300
time (Myr)
Zurich, September 18th 2007
Effect on star
formation rate
4.5 Myr
density
temp
pressure
non-instantaneous feedback
density
22 Myr
41 Myr
0.6
0.4
instantaneous
feedback
SFR (Msun/yr)
0.8
temp
pressure
0.2
0
100
200
300
time (Myr)
Slyz, Devriendt, Bryan, Silk (2005)
Zurich, September 18th 2007
Time evolution of density PDF
green: inst fbk, black: non-inst fbk
Zurich, September 18th 2007
How to erase a thermal instability…
log (number of cells)
1 kpc2 box
P(k) ∝ k-4
Large scale forcing
vs
Small scale forcing
> thresh
 v < 0
log 
Vazquez-Semadeni,
Gazol, Scalo 2000
heat for
6 X 106 yrs
to mimic
« photoionization »
Zurich, September 18th 2007
Time evolution of density PDF
non-instantaneous feedback run
Zurich, September 18th 2007
Time evolution of density PDF
non-instantaneous feedback run
~85 Myr
Time →
Zurich, September 18th 2007
Time evolution of density PDF
non-instantaneous feedback run
Zurich, September 18th 2007
Time evolution of density PDF
green: inst fbk, black: non-inst fbk
Zurich, September 18th 2007
Time evolution of thermal phase diagrams
Initial
conditions
Zurich, September 18th 2007
Time evolution of thermal phase diagrams
Initial
conditions
Zurich, September 18th 2007
Thermally unstable regime
Zurich, September 18th 2007
Lines of
constant
pressure
(kB-1 cm-3 K)
Zurich, September 18th 2007
1D cut
Accretion shock!
Density,
pressure
2D pressure map
X (kpc)
Zurich, September 18th 2007
Different philosophies for adding
supernovae explosions in ISM models
A
Model star formation
m* =  ρgasVcell ∆t/tdyn
+
Stellar Initial Mass Function
B
Model observed supernovae
rates & mimic their distribution
(e.g. isolated, clustered)
e.g.
SN frequency Milky Way
Galaxy:1/330 yr-1 for Type I and
1/44 yr-1 for Type II (Tammann et al. 1994)
Scale heights: Type I :325 pc (Heiles 1987)
Type II :90 pc
Calculate energy and mass
returned to interstellar medium
via supernovae and stellar winds
Power law distribution of superbubbles:
dNB ~ n*-2dn*
(Kennicutt et al. 1989, McKee & Williams 1997)
Zurich, September 18th 2007
HORIZON
Marenostrum Simulation
~ 1 billion
DM particles
~1 billion cell
root grid
(3 -6 AMR levels)
50h-1 Mpc
How can we begin to capture the complicated
gas physics in a cosmological simulation?
~ 1.5 kpc
physical
resolution
Zurich, September 18th 2007
How to make progress?
1
Run many local models at high resolution
and use them to construct subgrid-models
e.g. For a given star formation rate do a high res
simulation of a stratified disk to measure the
efficiency of the energy transfer of a superwind,
then use result as a subgrid model in a cosmological
simulation.
Enourmous parameter space!
How many boxes do you have to simulate to capture
conditions of ISM in different environments, at different
redshifts, with different IMFs etc.
Zurich, September 18th 2007
128 root grid,
3 nested grids
11-15 AMR refinement levels
3 h-1 Mpc
spatial resolution
~ 1 pc (physical) on finest level
Slyz & Devriendt (in prep)
9 h-1 Mpc
2
AMR « resimulations » …
Zurich, September 18th 2007
No single density threshold
th for gravitational collapse?
large subbox
~ 32 pc
small subbox
~ 4 pc
th depends
on scale on which
collapse occurs
Joung & Maclow 2006
Zurich, September 18th 2007
Zurich, September 18th 2007