adrianne slyz
DESCRIPTION
Lessons on ISM modelling from kiloparsec scale simulations. Adrianne Slyz. University of Oxford. Zurich, September 18 th 2007. What physical processes regulate …. Kennicutt (1998). starbursts. - PowerPoint PPT PresentationTRANSCRIPT
Zurich, September 18th 2007
Adrianne Slyz University of Oxford
Lessons on ISM modellingfrom kiloparsec scale simulations
Zurich, September 18th 2007
What physical processes regulate …
the rate at which gas turns into stars?
starbursts
centers of normal disks
normal disks
Kennicutt (1998)
SFR Area
~ ∑gaslog Σ
SFR
(M
sol y
r-1 k
pc-
2)
log Σ gas(Msol pc-2)
1.4
Zurich, September 18th 2007
Link between density structure & star formation ?
Zurich, September 18th 2007
Key insights from periodic box simulations in the 90’s:
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)
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)
Zurich, September 18th 2007
1.28 kpc
Initial conditions
ρ= 1 at/cm3
T = 105 K
Turbulent velocityfield imposed on large scales
P(k) ∝ k-4
Homogeneous gas
Periodic boundary conditions
1.28 kpc1.28 kpc
Zurich, September 18th 2007
1.28 kpc
Initial conditions
ρ= 1 at/cm3
T = 105 K
Turbulent velocityfield imposed on large scales
P(k) ∝ k-4
Homogeneous gas
Periodic boundary conditions
1.28 kpc1.28 kpc
Zurich, September 18th 2007
Radiative cooling
White and Sarazin (1987), Rosen and Bregman (1995)
3 4 5 6 7 8T (Kelvin)
-21
-22
-23
-24
-25
-26log
10
(T)
erg
s cm
3/s
Zurich, September 18th 2007
PDF = 1___
(2 π)1/2 σexp - (ln ρ- < ln ρ>) 2
2σ2
with σ = ln 1 + (Mrms/2)2 (Padoan & Nordlund 2002)[ ]
(
)
log
10(n
orm
aliz
ed
PD
F)
log10gas - <log10gas>
Zurich, September 18th 2007
PDF = 1___
(2 π)1/2 σexp - (ln ρ- < ln ρ>) 2
2σ2
with σ = ln 1 + (Mrms/2)2 (Padoan & Nordlund 2002)[ ]
(
)
log
10(n
orm
aliz
ed
PD
F)
log10gas - <log10gas>
Zurich, September 18th 2007
PDF = 1___
(2 π)1/2 σexp - (ln ρ- < ln ρ>) 2
2σ2
with σ = ln 1 + (Mrms/2)2 (Padoan & Nordlund 2002)[ ]
(
)
log
10(n
orm
aliz
ed
PD
F)
log10gas - <log10gas>
Zurich, September 18th 2007
PDF = 1___
(2 π)1/2 σexp - (ln ρ- < ln ρ>) 2
2σ2
with σ = ln 1 + (Mrms/2)2 (Padoan & Nordlund 2002)[ ]
(
)
log
10(n
orm
aliz
ed
PD
F)
log10gas - <log10gas>
Zurich, September 18th 2007
PDF = 1___
(2 π)1/2 σexp - (ln ρ- < ln ρ>) 2
2σ2
with σ = ln 1 + (Mrms/2)2 (Padoan & Nordlund 2002)[ ]
(
)
log
10(n
orm
aliz
ed
PD
F)
log10gas - <log10gas>
Zurich, September 18th 2007
∞fc =∫
ρ PDF d ρ
ρ PDF d ρ∫
ρth
0
∞ fraction of mass above th
Universal PDF?
Is there aclear densitythreshold forstar formation?
(Elmegreen 2002Krumholz & McKee 2005Wada & Norman 2007)
Open questions
Zurich, September 18th 2007
Log-normal fit to high density end of run with stars, self-gravity, fbk
⇒ρpeak ≈ 50 at cm-
3
< ln ρ> = 3.9
σ= 1.22
⇒Mrms = 3.1
PDF = 1___ (2 π)1/2 σ
exp - (ln ρ - < ln ρ >) 2
2σ 2
( )
log10gas (at/cm3)
log
10(n
orm
aliz
ed
PD
F)
Zurich, September 18th 2007
Avillez & Breitschwerdt 2005
PDF for SN driven stratified segment of a disk1 X 1 X 20 kpc
x-y plane
density ProbabilityDistribution Function (PDF)
n (cm3)
PD
F
10
8
6
4
2
1
0.5
0
-0.5
-1
-2
-4
-6
-8
-10
Z (
kpc)
Zurich, September 18th 2007
Joung & MacLow 2006
PDFs for gas near midplane
4 pc subbox
125 pc subbox
PDFs in different subbox sizes for SN driven stratified segment of a disk
0.5 X 0.5 X 10 kpc disk segment
Zurich, September 18th 2007
New generation of ISM simulationsdensity temperature pressure stars
0.001 1.0 1000 (Msol pc3)
PD
F
7.5
2.5
log
Tem
p
edge-on view
face
-on
vie
w3D isolated disks, 25-50 pc resolution
Tasker & Bryan 2006
Zurich, September 18th 2007
Different philosophies for adding supernovae explosions in ISM models
m* = ρgasVcell ∆t/tdyn
+Stellar Initial Mass Function
Calculate energy and massreturned to interstellar mediumvia supernovae and stellar winds
Model star formation Model observed supernovaerates & mimic their distribution(e.g. isolated, clustered)
e.g. SN frequency Milky WayGalaxy:1/330 yr-1 for Type I and1/44 yr-1 for Type II (Tammann et al. 1994)
Scale heights: Type I :325 pc (Heiles 1987) Type II :90 pc
Power law distribution of superbubbles: dNB ~ n*
-2dn*
(Kennicutt et al. 1989, McKee & Williams 1997)
A B
Zurich, September 18th 2007
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
3.) Redistribute mass in that sphere so that it has uniformdensity = 3Mexp/(4 Rexp
3)
4.) Inject thermal energy ESN = 1051 ergs evenly into the sphere
Mexp =60 Msun
Rexp
NO mass ever removed to form a star
B
Zurich, September 18th 2007
Identify Jeans unstableboxes Mbox/MJ > 1
where MJ = <J3
= avg density in box
J = (/G<)1/2 tot
tot = (<cs>2 + 1/3<2)1/2
(Chandrasekhar 1951)
SFR = Mbox/tff where = 0.3 or 1
= 1
= 0.3
~ 1 order of magnitude
predictions
SFRs derived from input SN rates
Compare estimated SFR to input SN rates
Joung & MacLow 2006
(2 input supernovae rates:assuming 130 and 200 Msol
required per SN)
Zurich, September 18th 2007
Gotoh & Kraichnan (1993) found power law PDFs for 1D sims of Burgers flows ⇒infinitely compressible flows
no fbk, with s-g
Mrms=11.8 Mrms=5.1
Mrms=5.2 Mrms=5.8
Is that because they ignore self-gravity in their model?
(Slyz et al. 2005)
Zurich, September 18th 2007
v < 0 ->contracting
t cool < t dyn -> cooling rapidly
> thresh -> dense
T < T thresh -> cold
m* = ε ρgasVcell ∆t/tdyn
Heyer
et
al. 1
998
if the gas satifies:
(FCRAO CO survey)
Cen & Ostriker 1992
First make stars . . .A
Zurich, September 18th 2007
Then do stellar feedback . . .
Calculate a time dependent SFR:
Stellar winds: f ∆mSF
returned to gas
Supernovae: ∆mSF c2
injected as thermal energy
mSF (t) = m*(t-t*)/т2 exp [-(t-t*)/τ]
where τ = max(tdyn, 10 Myr)
Cen & Ostriker 1992
1.2
8 k
pc
100 pc @ 10 Myrif v=10 km/s
f, determined by IMF
Zurich, September 18th 2007
4.5 Myr
22 Myr
41 Myr
Slyz, Devriendt, Bryan, Silk (2005)
Non-instantaneous feedback
pressuretempdensity
Zurich, September 18th 2007
4.5 Myr
22 Myr
41 Myr
Slyz, Devriendt, Bryan, Silk (2005)
Instantaneous feedback
pressuretempdensity
Zurich, September 18th 2007
When put supernova thermal energy ESN = 1051 ergsin 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 parcelsas pure kinetic energy (Navarro & White 1993) 3)introduce a thermalization efficiency whereby assignsome 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)
Is this the same old story . . . ?
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
compressible
solenoidal
ratio
∇ ⋅ vsol = 0
∇ ✘ vcom= 0
no s-gno fbk
s-gno fbk
no s-g fbk
s-gfbk
Zurich, September 18th 2007
Time evolution of energy spectra
compressible
solenoidal
ratio
∇ ⋅ vsol = 0
∇ ✘ vcom= 0
no s-gno fbk
s-gno fbk
no s-g fbk
s-gfbk
Instantaneous feedback
Zurich, September 18th 2007
Comparison of inputs into Silk prescription
with non-instantaneous fbk, with gravity
with non-instantaneous fbk, no gravity
Diff
ere
nt
ph
ysi
cs
no fbk, no gravity
no fbk, with gravity
0.
8
0.
6
0.
4
0.
2
0.
0
SFR
(Msu
n/y
r)Poro
sity
log
10<
ρ>
(Msu
n/p
c3)
<σ>
MW
(km
/s)
0 100 200 300time (Myr)
54321
-1.5
-2.0
-2.5
-3.0
40
30
20
10
0
with instantaneous fbk, with gravity
Q = SFR G-1/2 ρgas-3/2 (σgas / σf )
-2.72
density
density temp pressure
temp pressure
Slyz, Devriendt, Bryan, Silk (2005)
4.5 Myr
22 Myr
41 Myr
0 100time (Myr)
0.2
0.4
0.6
0.8
200 300
non-instantaneous feedback
instantaneous feedback
SFR
(Msu
n /yr)
Zurich, September 18th 2007
Effect on starformation rate
Zurich, September 18th 2007
Time evolution of density PDF green: inst fbk, black: non-inst fbk
Zurich, September 18th 2007
Vazquez-Semadeni, Gazol, Scalo 2000
log
log
(n
um
ber
of
cells
)How to erase a thermal instability…
1 kpc2 box
> thresh
v < 0heat for6 X 106 yrsto mimic« photo-ionization »
P(k) ∝ k-4
vsSmall scale forcing
Large scale forcing
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
SFR
~85 MyrTime →
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
Initialconditions
Zurich, September 18th 2007
Time evolution of thermal phase diagrams
Initialconditions
Zurich, September 18th 2007
Thermally unstable regime
Zurich, September 18th 2007
Lines ofconstantpressure
(kB-1 cm-3 K)
Zurich, September 18th 2007
1D cut
Densi
ty,
p
ress
ure
x-v
elo
city
2D pressure map
Accretion shock!
X (kpc)
Zurich, September 18th 2007
Different philosophies for adding supernovae explosions in ISM models
m* = ρgasVcell ∆t/tdyn
+Stellar Initial Mass Function
Calculate energy and massreturned to interstellar mediumvia supernovae and stellar winds
Model star formation Model observed supernovaerates & mimic their distribution(e.g. isolated, clustered)
e.g. SN frequency Milky WayGalaxy:1/330 yr-1 for Type I and1/44 yr-1 for Type II (Tammann et al. 1994)
Scale heights: Type I :325 pc (Heiles 1987) Type II :90 pc
Power law distribution of superbubbles: dNB ~ n*
-2dn*
(Kennicutt et al. 1989, McKee & Williams 1997)
A B
Zurich, September 18th 2007
How can we begin to capture the complicated gas physics in a cosmological simulation?
HO
RIZ
ON
Mare
nostru
m S
imula
tion
~ 1 billionDM particles~1 billion cellroot grid(3 -6 AMR levels)
50h
-1 M
pc
~ 1.5 kpc physical resolution
Zurich, September 18th 2007
e.g. For a given star formation rate do a high ressimulation of a stratified disk to measure theefficiency of the energy transfer of a superwind,then use result as a subgrid model in a cosmologicalsimulation.
Enourmous parameter space!How many boxes do you have to simulate to captureconditions of ISM in different environments, at differentredshifts, with different IMFs etc.
How to make progress?
Run many local models at high resolutionand use them to construct subgrid-models
1
9 h
-1 M
pc
spatial resolution~ 1 pc (physical) on finest level
3 h-1 Mpc
128 root grid,3 nested grids11-15 AMR refinement levels
AMR « resimulations » …
Zurich, September 18th 2007
Sly
z &
Devri
endt
(in p
rep)
2
Zurich, September 18th 2007
No single density thresholdth for gravitational collapse?
small subbox~ 4 pc
large subbox~ 32 pc
th dependson scale on whichcollapse occurs
Joung & Maclow 2006
Zurich, September 18th 2007