Metallicity dependence of the H/H2 and C+/C/CO
distributions in a resolved self-regulating ISM
arXiv:2103.03889
Chia-Yu Hu (MPE)
with Amiel Sternberg and Ewine van Dishoeck
13.05.2021
ISM 2021, Beirut (virtual)
Chemistry properties change with metallicity
low metallicity => low dust-to-gas ratio => less shielding by dust
=> FUV radiation penetrates deeper into clouds
C+/C & C/CO boundaries contract significantly.
H/H2 boundary contracts too, but not as much (self-shielding).
“CO-dark” H2 gas
high
metallicity
low
metallicity
Take-home message
The CO-dark H2 mass fraction is over-estimated (especially at
low metallicities) in the steady-state model, because the
time-dependent (dynamical) effect strongly suppresses the
formation of H2 but not CO.
Challenge for modeling CO in ISM simulations
1) Need high resolution (sub-pc!) to resolve the dense gas (n > 103 cm-3) where CO lives.
2) CO chemistry network is complicated and expensive to solve.
Previous simulations often adopt a simplified CO network (NL97) which tends to over-produce CO.
- e.g. SILCC (resolution dx=4 pc), SILCC-Zoom (dx=0.06 pc), Cloud Factory (dx ~ 0.1 pc)
More accurate CO networks can only be applied in post-processing, but need to assume the
chemistry is in steady state (equilibrium).
- e.g. TIGRESS (dx=1 pc)
Can we improve?
Stratified disk simulation (similar to SILCC & TIGRESS)
solar-neighborhood conditions: Sgas = 10 M☉pc-2, Sstar = 40 M☉pc-2
box size = [1kpc, 1kpc, 10kpc]
solar metallicity
(Z’ = 1)
1 kpc
Run four simulations with metallicity Z’ = Z/Z☉ = 3, 1, 0.3 and 0.1
Each simulation is run for 500 Myr.
simulation
Simulation details:
- GIZMO (resolution mgas= 1 M☉ , h ~ 0.2pc)
- time-dependent H2 chemistry network
- HealPix-based column densities for shielding:
Npix = 12 different sightlines up to 100 pc
- Star formation with individual stars
- Feedback: supernovae & photoionization
simulation
Simulation details:
- GIZMO (resolution mgas= 1 M☉ , h ~ 0.2pc)
- time-dependent H2 chemistry network
- HealPix-based column densities for shielding:
Npix = 12 different sightlines up to 100 pc
- Star formation with individual stars
- Feedback: supernovae & photoionization
Post-processing chemistry (publicly available!):
- 31 species, 286 reactions
- Same HealPix-based shielding as in simulations
- Use time-dependent H2 abundances from simulations
as input and evolve for 1 Gyr.
post-processing
* time-dependent (non-equilibrium) model:
use time-dependent H2 abundance as input.
* steady state (equilibrium) model:
evolve all species (including H2) up to steady state.
tform,H2 ≫ tdyn , especially at low Z
~ 1 Gyr /(nZ’)
~ 3Myr at n=100 cm-3
H2 has no time to reach steady state.
- shallow transition profiles up to the
photodissociation front.
H2 abundance
Transitions of H/H2 & C+/C/CO
volume density
effective column density
* time-dependent (non-equilibrium) model:
use time-dependent H2 abundance as input.
* steady state (equilibrium) model:
evolve all species (including H2) up to steady state.
tform,H2 ≫ tdyn , especially at low Z
~ 1 Gyr /(nZ’)
~ 3Myr at n=100 cm-3
H2 has no time to reach steady state.
- shallow transition profiles up to the
photodissociation front.
H2 abundance
Transitions of H/H2 & C+/C/CO
volume density
effective column density
tdyn ~ 3 Myr (n/100 cm-3)-0.3 independent of Z
xH2 = 1 – exp(-tdyn / tform)
Transitions of H/H2 & C+/C/CO
* time-dependent (non-equilibrium) model:
use time-dependent H2 abundance as input.
* steady state (equilibrium) model:
evolve all species (including H2) up to steady state.
H2
tform,H2 ≫ tdyn , especially at low Z
~ 1 Gyr /(nZ’)
~ 3Myr at n=100 cm-3
H2 has no time to reach steady state.
- shallow transition profiles up to the
photodissociation front.
CO
tdyn ~ 3 Myr (n/100 cm-3)-0.3 independent of Z
xH2 = 1 – exp(-tdyn / tform)
CO forms rapidly and is in steady sate.
- sharp profile controlled by photodissociation.
- nearly unaffected by the under-abundant H2
C
volume density
effective column density
Effective 1D cloud model:
power-law density profile n(x) = B xb
correlation between N & n: N = A na
=> b = 1/(a-1) , B = (Aa / (1-a))(1/(1-a))
1D PDR calculation with the effective cloud
profile is in excellent agreement with the timeaveraged simulation results!
>10x
At low Z, steady-state model significantly over-estimates H2
in the diffuse medium (while C+/C/CO is almost unchanged).
At low Z, steady-state model significantly over-estimates H2
in the diffuse medium (while C+/C/CO is almost unchanged).
=> CO-dark H2 fraction is overestimated!
Summary
arXiv:2103.03889
• We propose a fast & accurate hybrid method to model the ISM chemistry in hydro simulations
- time-dependent H/H2 + post-processed C+/C/CO (code is publicly available)
• H2 is far from steady state (under-abundant) as tform >> tdyn
- gradual transition up to the photodissociation front.
• CO forms at much higher densities where H/H2 transition is complete.
- sharp transition controlled by photodissociation
- almost unaffected by the over-estimated H2
• Effective 1D PDR models successfully reproduce time-averaged chemical properties in simulations
• The time-dependent effect significantly suppresses formation of H2 but not CO especially at low Z.
- the CO-dark H2 mass fraction is much lower than what the steady-state model predicts.
Back up slides
Correlation between volume density (n) & effective column density (Neff)
effective column density
(effective) column density
dominated by the sightline
with the shallowest column
100 pc
volume density
Neff is a monotonically increasing function of n
CO formation timescale
much shorter than tdyn => steady state
C recombination timescale
much shorter than tdyn
=> steady state
Volume density (n) vs. temperature (T)
Thermal-equilibrium curves are insensitive to Z’.
- Fine-structure metal cooling rate ∝ Z’
cancels out!
- Photoelectric heating rate also ∝ Z’
arXiv:2103.03889
Correlation between volume density (n) & column density (N)
geometric average
(over 12 sightlines)
insensitive to Z’!
100 pc
arXiv:2103.03889
Correlation between volume density (n) & column density (N)
geometric average
(over 12 sightlines)
insensitive to Z’!
arXiv:2103.03889
The correlation is due to
gravitational instability.
(cloud size ~ Jeans length LJ)
Correlation between volume density (n) & effective column density (Neff)
effective column density
dominated by the sightline
with the shallowest column
100 pc
arXiv:2103.03889
Mass Budget
>10x
Steady-state model significantly over-estimates
the amount of H2 at low Z, but only mildly so for CO.
Correlation between volume density (n) and column density (N)
Average N
Jeans length
effective N
SFR time evolution
C+ recombination time
CO formation time
Convergence
Shielding length
Recombination on grains
Density PDF for H2 & CO
Density & temperature PDFs for total gas
with grain recombination
without grain recombination
Star formation correlates with molecular hydrogen (H2)
Star formation rate
Bigiel et al. 2008
no correlation
HI
linear correlation
H2 (traced by CO)
H2 Chemistry
H2 formation: mainly on the surfaces of dust grains
H
H
H2
dust
H2 destruction: photodissociation by FUV starlight
shielded by dust and H2 itself
CO Chemistry
CO formation relies on the presence of H2
CO destruction: photodissociation by FUV starlight
shielded by dust, H2 and CO itself