Zurich, September 18 th 2007 Adrianne SlyzUniversity of Oxford Lessons on ISM modelling from...

Zurich, September 18th 2007

Adrianne Slyz University of Oxford

Lessons on ISM modellingfrom kiloparsec scale simulations


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


Link between density structure & star formation ?


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)


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


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


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>


∞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


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)


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)


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


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


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


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


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)


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)


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


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


4.5 Myr

22 Myr

41 Myr

Slyz, Devriendt, Bryan, Silk (2005)

Non-instantaneous feedback

pressuretempdensity


4.5 Myr

22 Myr

41 Myr


Instantaneous feedback

pressuretempdensity


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 . . . ?


Time evolution of density PDF green: inst fbk, black: non-inst fbk


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


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


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


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)


Effect on starformation rate


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


Time evolution of density PDF non-instantaneous feedback run



SFR

~85 MyrTime →


Time evolution of thermal phase diagrams

Initialconditions


Thermally unstable regime


Lines ofconstantpressure

(kB-1 cm-3 K)


1D cut

Densi

ty,

p

ress

ure

x-v

elo

city

2D pressure map

Accretion shock!

X (kpc)


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


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


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 » …


Sly

z &

Devri

endt

(in p

rep)

2


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 18 th 2007 Adrianne SlyzUniversity of Oxford Lessons on ISM modelling from...

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