Early Milky-Way in the Megatron sims

Corentin Cadiou

CNRS @ IAP, Paris

Early Milky-Way galax(ies) in the Megatron simulations

Co-Is: Harley Katz, Martin Rey

Collaborators: Oscar Agertz, Jeremy Blaizot, Alex J. Cameron, Nicholas Choustikov, Julien Devriendt, Uliana Hauk, Gareth Jones, Taysun Kimm, Isaac Laseter, Aayush Saxena, Sergio Martin-Alvarez, Kosei Matsumoto, Camilla T. Nyhagen, Autumn Pearce, Francisco Rodriguez-Montero, Victor Rufo-Pastor, Joki Rosdahl, Adrianne Slyz, Richard Stiskalek, Anatole Storck, Wonjae Yee

High-\(z\) galaxy formation challenges

What is setting the structure in the CGM?

Can we reproduce the diversity of high-\(z\) spectra?

Observational prospects of Pop. III stars?

Bridge high-\(z\) JWST/ALMA to Gaia?

[…]

Harikane+24

Cullen+24

Cameron+24

Typical path from sims to observations

Lots of assumptions

(equilibrium, geometry, element abundances, …)

\(\rho, T, Z,v\)
sometimes \(n_\mathrm{H}, n_{\mathrm{H^+}}, n_\mathrm{He}, n_\mathrm{He^+},n_\mathrm{He^{2+}},n_\mathrm{e^{-}}\)

Physical space

Observable

Megatron suite of simulations

On-the fly radiative transfer,
81-ions non-equilibrium thermochemistry,
Chemical enrichment from SN and stellar winds,
Milky-Way progenitor,
4 “high-resolution” sims at \(10\,\mathrm{pc}\) comoving,
3+1 “low-\(z\)” sims at \(23\,\mathrm{pc}\) proper.

\(\Sigma\)HI

\(\Sigma\)HII

\(\Sigma\)MgII

\(\Sigma\)OII

Mocks in absorption:

Main object, \(z=4\), raw file outputs, no postprocessing

Mocks in emission:

Main object, \(z=9\), w/ nebular cont. Pyneb (Luridiana+15) & coll. Chianti (Del Zanna+21)

The Megatron suite of simulations

4 High-z ISM

The Megatron suite of simulations

4 High-z ISM

3+1 "low"-z CGM

State of the CGM of a MW progenitor at \(z \approx 3-4\)

CGM at \(z \approx 3-4\)

Is the CGM in equilibrium?

Relax to photo-ionisation equilibrium (PIE)

No local radiation field, no time-dependence, assume \(n_\mathrm{e}\) dominated by primordial species, self-shielding

\[\frac{\mathrm{d}n_i}{\mathrm{d}t} = 0 = \text{Recomb} + \text{Collisional} + \text{UVB}\]

CGM at \(z \approx 3-4\)

Is the CGM in equilibrium?

CGM at \(z \approx 3-4\)

Is the CGM in equilibrium?

CGM at \(z \approx 3-4\)

Is the CGM in equilibrium?

NEq.

PIE

Assuming PIE ⇒ biased towards colder/denser gas

\(T\)

\(n_\mathrm{H}\)

CGM at \(z \approx 3-4\)

Is the CGM in equilibrium?

\(\pm0.5\,\mathrm{dex}\)

CGM at \(z \approx 3-4\)

Is the CGM in equilibrium?

Non-equilibrium effects:

\(\Delta(T, n_\mathrm{H}) \sim 0.2-0.5\,\mathrm{dex}\)

⇒ \(\Delta L \sim 1\,\mathrm{dex}\)
for some lines

CGM at \(z \approx 3-4\)

CGM out of equilibrium: why?

40 kpc

Local radiation dominate locally over UVB
Anisotropic effects
Recombination lag
\(t_\mathrm{cool} \ll t_\mathrm{rec}\), worse with time

CGM at \(z \approx 3-4\)

CGM out of equilibrium: why?

Local radiation dominate locally over UVB
Anisotropic effects
Recombination lag
\(t_\mathrm{cool} \ll t_\mathrm{rec}\), worse at low \(z\)

Pop. III star formation

A. Storck

Pop. III star formation

At least 2dex gap to observe Pop. III haloes

On their observability at high-\(z\)

Not observable (unless really lucky with a lens)

Not close to UV-bright galaxies (6/10,000 form within \(R_\mathrm{vir}\))

A. Storck

A detour to ultra-faint dwarves

\(z=8\) sim

\(z=0\) data

Excellent agreement between \(z=8\) sim and \(z=0\) local dwarf galaxies

A detour to ultra-faint dwarves

22% Fe-poor UFDs

(not observed!)

1 high-mass PISN

1 Pop. II CCSN

1 low-mass PISN

Pop. III star formation

On their observability at low-\(z\)

High-\(z\) kinematics

ALMA-like observations (at 0.1")

\(L=\textcolor{green}{\epsilon(n_\mathrm{X},T)} \textcolor{red}{n_\mathrm{X}n_\mathrm{e}}\bigotimes\mathrm{PSF}\)

Tabulated

From simulation

PRELIMINARY RESULTS

High-\(z\) cold disks?

\(M_\star \approx 10^{10}\,M_\odot, \quad z=4,\quad r>R_\mathrm{vir}/4\)

Overall trend:

lower-ionization lines damped with neq

\(\mathrm{CII\, 158µm}\)

\(\mathrm{OIII\, 88µm}\)

Take-home messages

Megatron simulation suite
200,000+ spectra in 4 “ISM” runs (\(z\gtrapprox 8\)) ⇒ Katz, CC+ Wednesday
3+1 “CGM” runs (\(z\gtrapprox 3.5\)) ⇒ CC+ Wednesday
Link to low-\(z\) UFDs ⇒ Rey, ..., CC+ Wednesday
Properties of Pop. III stars ⇒ Storck, ..., CC+ Thursday
Sensitivity of line diagnostics to subgrids ⇒ Choustikov, ..., CC+ Thursday
Origin of steep \(\beta\) slopes ⇒ Katz, CC+ Thursday
CGM (incl. inner CGM!) is out-of-equilibrium
Assuming PIE leads to 0.5 dex (median), and factors of
2-3× on individual line of sight
High-\(z\) kinematics
Very easy to make ALMA-like maps (or JWST IFU)
from \(z=3-15\) and \(M_\star\lessapprox 10^{10}\,M_\odot\)

Model [i]

Based on RAMSES-RT (Rosdahl+13)
Out-of-equilibrium chemistry (Katz 23)
Primordial species: \(\text{H~{\small I}-{\small II}}\), \(\text{He~{\small I}-{\small III}}\), \(e^{-}\)
Metal ions: \(\text{C~{\small I}-{\small VI}}\), \(\text{N~{\small I}-{\small VII}}\), \(\text{O~{\small I}-{\small VIII}}\), \(\text{Ne~{\small I}-{\small X}}\), \(\text{Mg~{\small I}-{\small X}}\), \(\text{Si~{\small I}-{\small XI}}\), \(\text{S~{\small I}-{\small XI}}\) & \(\text{Fe~{\small I}-{\small XI}} \)
Molecules: \(\text{H}_2\) & \(\text{CO}\)
Dust model (Rémy-Ruyer+14)
Assuming dust-to-gas ratio
Heating & Cooling
photoheating, photoelectric heating, excitation/dissociation heating, primordial, dust recombination, dust-gas collisions, metal lines
- \(\text{C~{\small I}}\), \(\text{C~{\small II}}\), \(\text{N~{\small II}}\), \(\text{O~{\small I}}\), \(\text{O~{\small III}}\), \(\text{Ne~{\small II}}\), \(\text{Si~{\small I}}\), \(\text{Si~{\small II}}\), \(\text{S~{\small I}}\), \(\text{Fe~{\small I}}\), \(\text{Fe~{\small II}}\)

\(\text{O\small{II}}\)

\(\text{O\small{I}}\)

\(\text{N\small{I}}\)

\(\text{Mg\small{II}}\)

\(\text{Ne\small{II}}\)

\(\text{CO}\)

\(\rho\)

\(v_r\)

\(\text{O\small{III}}\)

Model [ii]

Turbulence-based star formation (Padoan & Nordlund 11, Agertz+21)
\(\dot{\rho_\star} = \varepsilon_\star\rho/t_\mathrm{ff}\)
- if \(Z<10^{-6}Z_\odot\) ⇒ Pop. III
- if \(Z\geq10^{-6}Z_\odot\) ⇒ Pop. I & II, Kroupa
\(M_\star = 500\,\mathrm{M}_\odot\)
\(M_{\star,\rm III} \sim 100\,\mathrm{M}_\odot\)
Feedback (Agertz+21; Rey+23)
core-collapse SN, type Ia, winds + HN (Nomoto+06).
Yields (Limongi & Chieffi 18)
AGB winds (Ritter+18)

Model [iii]

MW analogue @ \(z=0\)
Genetically engineered to form earlier
ICs generated with genetIC
2 main runs
- constant physical \(\Delta x_\mathrm{min} \approx 20-40\,\mathrm{pc}\)
  3 runs with ≠ ICs
- constant comoving \(\Delta x_\mathrm{min}(z=2) = 20\,\mathrm{pc}\)
  \(\Delta x_\mathrm{min}(z=5)=10\,\mathrm{pc}\)
  \(\Delta x_\mathrm{min}(z=14)=4\,\mathrm{pc}\)
  3 runs: efficient feedback, variable IMF, hypernova

Early forming MW mass galaxy
\(1.6\times 10^{4}\mathrm{M}_\odot\) DM, \(500\, \mathrm{M}_\odot\) Pop. II stars, individual Pop III stars, \(1\, \mathrm{pc}\) resolution at first star formation
IMF sampled chemical enrichment from individual stars for all relevant elements
SN (CC, Ia, HN, PISN), Winds → follows Vintergatan (validated for MW galaxies at z = 0)
81 species chemistry coupled to 8 bin RT
PRISM ISM model
Enhanced resolution in the CGM
Calibration sims with IMF variations and physical model variations

Introducing MEGATRON

Processes that control ion and molecular properties:

Collisional, photo, cosmic-ray ionization
Radiative, dielectronic, dust recombination
Charge exchange

RAMSES-RTZ + PRISM: Non-equilibrium chemistry coupled to on-the-fly radiative transfer

Processes that control gas temperature:

Cosmic-ray, photo, photo-electric, H2, dust heating
Primordial, \(\mathrm{H}_2\), CO, metal, dust* recombination, dust-gas collisional cooling
Adiabatic (expansion), shocks (e.g. SN, turbulence), gravitational, etc.

Katz, CC 2024

\(\Sigma\)OI

\(\Sigma\)OII

\(\Sigma\)OIII

Create “twin” simulation relaxed to photo-ionization equilibrium (PIE):

Haardt-Madau UV bg,
Local Habing field (\(6-13.6\,\mathrm{eV}\)),
Dust-to-gas ratio (Rémy-Ruyer+14),
Iterate until

\(\dfrac{\mathrm{d} n_{X_i}}{\mathrm{d} t} = 0\quad\) at fixed \(T\).

Code: Katz & CC, in prep.

Electron abundances

\(M_\star \approx 10^{10}\,M_\odot, \quad z=4\)

Effect on \(\mathrm{He\,III}\)

Data within \(r>R_\mathrm{vir}/4\)

\(M_\star \approx 10^{10}\,M_\odot, \quad z=4\)

Effect on \(\mathrm{He\,II}\)

\(M_\star \approx 10^{10}\,M_\odot, \quad z=4\)

Overall trend:

high-ionization lines boosted with neq

\(M_\star \approx 10^{10}\,M_\odot, \quad z=4,\quad r>R_\mathrm{vir}/4\)

Overall trend:

intermediate-ionization lines unchanged

Tillson+15

Dekel&Birnboim 06

High-\(z\):
most of mass + AM flow along filaments

⇒ Natural interface between cosmo scales & galaxy formation
Circum Galactic Medium (\(r>R_\mathrm{vir}/3\))

HeII @ (PIE)

\(M=1.2\,10^9\,\mathrm{M_\odot}\)

HeII @ (neq)

\(M=8.8\,10^8\,\mathrm{M_\odot}\)

+\(30\%\)

[CIII]\(\lambda\lambda 1907\rm Å\) @ (PIE)

[CIII]\(\lambda\lambda 1907\rm Å\) @ (neq)

[CIII]\(\lambda\lambda 1907\rm Å\) @ (PIE)

[CIII]\(\lambda\lambda 1907\rm Å\) @ (neq)

[OIII]\(\lambda\lambda 1664\rm Å\) @ (PIE)

[OIII]\(\lambda\lambda 1664\rm Å\) @ (neq)

[OIII]\(\lambda\lambda 1664\rm Å\) @ (PIE)

[OIII]\(\lambda\lambda 1664\rm Å\) @ (neq)

Cooling length refinment

Refining where

\( \Delta x > 2 \sqrt{\dfrac{P_\mathrm{th}}{\rho}}\times {t_\mathrm{cool}},\)

(Rey+23)

up to \(80\,\mathrm{pc}\)
turned on at key moments

Cooling length refinment

\(+120\,\mathrm{Myr}\)

Quasi-Lagrangian + Jeans

Quasi-Lagrangian + Jeans + CGM ref

Cooling and chemical timescales go as \(n^2\)

Observables in the CGM?

Absorption

Emission

Zou+24

Pen+25 (\(z\approx2.8\))

⇒ Natural interface between cosmo scales & galaxy formation
Circum Galactic Medium (\(r>R_\mathrm{vir}/3\))

Modelling challenge:

space filling (\(\sim 30\times\) more \(V\) in CGM than ISM);
low-density (\(\lessapprox 10^{-2}\,\mathrm{m_p/cm^{-3}}\));
multiphase (see rev. by Fumagali 24);

Gible project, Ramesh+24

(My) route to high-\(z\) kinematics

Effect of cosmo. env. (Musso+19, Kraljic+20,21, Cadiou+21, Storck+24)
Cosmology-galaxy connection (Cadiou+21)
Cosmological accretion (Cadiou+19, Kocjan+24)
But what are we actually observing? This talk

Low grav. tides

Large grav. tides

cosmological environment \(\sim 50-100\,\mathrm{Mpc}\)
resolve Strömgren spheres \(\sim 10\,\mathrm{pc}\)
radiative-transfer
proper multi-phase ISM \(T \lesssim 10^4\,\mathrm{K}\)
Track ion abundances out-of-equilibrium

Wishlist for proper modelling of emission lines + kinematics

Background: Vintage Gordon (follow-up of Vintergatan) simulation
(PI: Cadiou)

\(t_\mathrm{chem} \propto 1/n^2\)

\(t_\mathrm{dyn} \propto 1/\sqrt{n}\)

\(t_\mathrm{burst} \sim 10-100\,\mathrm{Myr}\)

Halo-mass—stellar-mass relation

VG: Vintergatan (Agertz+21)
⇒ Well-regulated by \(z=0\)

High-resolution early \(<1\mathrm{pc}\)

Constant resolution \(\sim 20\,\mathrm{pc}\)

Most massive galaxy, edge-on

Most massive galaxy, face-on

Difference \([\mathrm{C{\small{II}}}]\)-weighted vs. \(n_\mathrm{H}\)-weighted

Early results

Stacked profiles

36 galaxies @ \(z=10\)

\(8.3\leq\log(M_\star/\mathrm{M}_\odot)\leq 10.0\)

⚠️ PRELIMINARY ⚠️

Only gas within \(\pm0.5\,\mathrm{kpc}\) height

All gas

Does non-equilibrium cooling matter?

Switching to equilibrium cooling

same stellar mass, but
ISM has much less cold gas

Katz 22

Results from Eddie

Tracer particles

High-cadence sampling

Puns

Martin Rey

Pop II modeling

Cooling length refinment

ICs generation

Harley Katz

RAMSES-RTZ

Pop III modeling

Calibrations

Stellar mass vs. Halo mass

CP not too bad compared to Vintergatan (Rey+23)
CC underregulates

Constant comoving

Constant physical

Varying IMF to the rescue?

Same model, but high-\(z\) dwarf \(M_\mathrm{dm}=10^{9}\,\mathrm{M}_\odot\) at \(z=6\)

Cooling length refinment

Refining where

\( \Delta x > 2 \sqrt{\dfrac{P_\mathrm{th}}{\rho}}\times \dfrac{1}{\Lambda_\mathrm{net}},\)

(Rey+23)

up to \(80\,\mathrm{pc}\)
turned on at key moments

\(z=5.8\)

\(z=5.8(+2\,\mathrm{Myr})\)

\(20\,\mathrm{kpc}\)

Cooling length refinment

How much does it cost?

\(\times 3\)

\(\times 70\)!

Conclusions

It works and stay tuned for results?