Large Eddy Simula/ons of Isolated Disc Galaxies Harald Braun
CRC 963
With thanks to
Wolfram Schmidt, Jens C. Niemeyer; Institute for Astrophysics Göttingen
Ann S. Almgren; Lawrence Berkeley National Laboratory
•  resources are limited...
•  ...so are temporal and spatial resolution in numerical simulations
Large Eddy Simulations (LES) of galaxy formation
•  construct effective model for ISM at scales 10 – 100 pc:
couple LES with non-adiab. physics
•  use SGS-(subgrid-scale) turbulence energy to estimate ISM properties
below resolution scales
Isolated Disk Galaxies Testing environment:
LES of idealized isolated
disk galaxies
Future application:
LES of galaxy formation
(zoom-in simulations
from cosmological initial
conditions)
NGC 4414 (HST), an actual IDG
Subresolu/on Processes a single volume
element....
contains:
•  stars
•  gas
•  dust
•  radiation
•  cosmic rays
•  magnetic fields
...
and is an open
dynamical system
turbulence, heating/
cooling, chemistry,
fragmentation, SF,
stellar feedback,
...
30 Dor (HST)
Turbulence Subgrid Model injection
cascade
physical
dissipation
‚numerical
dissipation‘
resolution
scale
€
resolved motions
unresolved
motions
heat
Decomposition into resolved and unresolved kinetic energy budgets
(Schmidt & Federrath, 2011)
Mul/-­‐phase ISM Star forma/on and Turbulence model (MIST) •  split mass contents of a subvolume into cold and warm phases ρc and ρw with separate thermal energy budgets •  assume the phases in equilibrium of effec/ve pressure (thermal + turbulent) mass-exchange scheme
•  set of 6(7) coupled ODEs (dynamical or equilibrium solutions)
(HB & Schmidt, 2012, HB et al., submitted)
•  SN energy deposited into:
•  warm gas
•  hot gas ~10%
•  SGS-energy ~10%
Star forma/on & stellar feedback •  Stars are allowed to form of molecular cold gas fH2
(Krumholz et al. 2009-alike)
•  Rate depends on how much of the density PDF of
the cold gas exceeds a critical density
(Padoan & Nordlund, 2011), and εcore
SFR ff f H ρ c
ρ˙ st ff
, where ρ˙ s = ε core
ε ff =
t c, ff
ρ
2
•  critical density computed from local αvir and Mc
€
•  Stars act on €
gas via Lyc-radiation and SNe
according to their evolutionary stages
Turbulent energy budget besides advection...
Sources of mean turbulent energy at length scale (grid scale) :
ρK˙ = (ε SN uSN − K ) ρ˙ s, fb + (1 − f th )ε tt Λ eff ρ w + ΠSGS
ℓ
K3 2
− Cε ρ
ℓ
€
Internal Driving:
€
Πint
•  Production by thermal instability
where ∝ ρ w Λ eff
Λ eff = Λ rad − ΓPAH − ΓLyc − ε
€
•  Production by supernova
feedback ∝ uSN ρ˙ s, fb
€
€
External Driving: Π
SGS
Turbulence energy
flux (via turbulent cascade)
from length scales L >> ℓ
due to grav. instabilities and
shear€of galactic disk...
€
Dissipation:
ε
Nyx (Almgren et al. 2013) •
•
•
•
cosmology code developed at LBNL (Berkeley) C++ / fortran, MPI + OpenMP parallelized block-­‐structured AMR unsplit PPM hydro scheme + parJcles + PM gravity addi/onal physics: •  turbulent SGS model (Schmidt&Federrath(2011), Schmidt et al.(2014)) •  star parJcles with feedback + mulJ-­‐phase ISM model (MIST) ini/al condi/ons: •  0.5 Mpc box (256 + 6 refined levels -­‐> ℓ ≈
30
pc
) •  adiabaJcally stable setup (Wang et al., 2010) •  isothermal, purely gaseous disk: T = 4 ×
10
4 K , M disk = 1010 M sun
•  staJc NFW DM-­‐halo €
€
€
A Movie... contours blue:
age ~ 0
green:
age < 3 Myr
red: 4 < age < 40 Myr
contours blue: shielded gas
red: cold gas
Evolu/on of the global star forma/on rate τ
€
•  most of cold gas does not produce stars (ambient pressure too low)
•  self regulation limits star formation to few Msun/yr
•  short term variations caused by single SF-ing regions τ life,SF ≈ 10…30Myr
SF-­‐rela/ons shielded cold gas
total gas
30 pc
scale
2
1.5
slope?
1
ρ˙ s = ε core
SFR ff f H 2 ρ c
t c, ff
ρ = ρc + ρw
~const.
no correlation, unless shielded fraction > 0.1
SF-­‐rela/ons -­‐ con/nued ff-efficiency vs. spec. turb. energy
ff-efficiency vs. rate
average free-fall efficiency: total gas < 1% (dense fraction ~10%)
typical SGS-turb. velocity dispersion: ~10 km/s
€
Drivers of SGS-­‐turbulence production by
resolved motions
total production
Πtot
∝ K
ρK
due to balance of
production and
dissipation
driving of resolved
motions
SF
internal sources:
dominant at large K
(SN-feedback)
Effect of underlying SF-­‐model work in progress...
6
P N m ult i-ff
global SFR @Msunê yrD
5
P HN
HC m ult i-ff
4
KM m ult i-ff
KM
PN mff
3
gas density slices (1.2 Gyr)
2
1
0
1.
1.1
1.2
time @GyrD
1.3
1.4
coefficients as in Federrath & Klessen, 2013
self regulation (feedback) leads to similar
global SFR (although disk structure varies)
PHN
Summary •  AddiJonal degree of freedom: kineJc/turbulent SGS-­‐energy -­‐ important for (self-­‐) regulaJon of star formaJon -­‐ important for support of cold gas against gravity -­‐ need for cooling suppression greatly reduced •  State of cold gas depends on environment •  Just being cold is not enough to form stars •  SimulaJons reproduce: ε ff < 0.01
Σ˙ SF ∝ Σ mol
€
€
σSF ≈ 10km /s
ε ff ,dense ≈ 0.1
τ life,SF ≈ 10…30Myr
€
Outlook: €
•  explicit molecular Hydrogen chemistry, addiJonal feedback mechanisms €
•  treatment of extremely metal-­‐poor gas •  IDG -­‐> halos from cosmological iniJal condiJons •  Lyman alpha transport on simulaJon output (work in progress)