Harrison+17 (KMOS, \(z=1\))

Spiral galaxies \(\leftrightarrow\) high \(J_\star\)

What's the arrow of causality?

Angular momentum: controls disk formation?

SMHM - Behroozi+19 | Romanowsky & Fall+13

Main driver of galaxy formation is mass

⇒ halo-mass main driver

Dark matter
\(80\%\) of mass

Gas
\(20\%\) of mass (initially)

Stars
\(<1\%\) of mass

Galaxy formation in a 🥜 shell

1. Dark matter halo formation from cosmic fluctuations
2. Gas condenses in DM halo
3. Stars form out of gas
4. Supernova + AGNs reinject energy

increasingly non-linear

increasingly non-linear

increasingly chaotic?

⇒

Galaxy formation in a 🥜 shell

1. Dark matter halo formation from cosmic fluctuations
2. Gas condenses in DM halo
3. Stars form out of gas
4. Supernova + AGNs reinject energy

Tidal torque theory: White 84
Stochastic spin: Vitviska+ 02, Beson+ 20
Spin prediction, Porciani+ 02

Theoretical predictions of angular momentum are, at best, inaccurate

First complication

Spin prediction / measured
(in simulation)

Note: spin is \(\lambda \propto J/M_\mathrm{vir}R_\mathrm{vir}V_\mathrm{vir}\)

Second complication

Let's be optimistic and assume we can predict DM spin

Jiang+ 19

Butterfly effect: Genel+ 19, see also Thiébaut+ 08

Third complication

Resimulating the same galaxy twice yields different results ⇒ galaxies are chaotic

Why can't we predict angular momentum?

1. No good model for dark matter angular momentum,
2. Stellar AM poorly correlates with DM AM,
3. Galaxies seem chaotic.

But are galaxies truly chaotic?

Credits: Dennis Bogdan

Example of the S-curve:

2D manifold embedded in 3D

Compute \(k\)-nearest neighbors
→ edges of a graph

Draw a point
→ find shortest path to all others

Take a radius
count number of points, \(p\) within \([r, r+\mathrm{d} r]\)

\(\Rightarrow p(r) \propto r^{D-1}\)

\(r\)

\(\#(<r)\)

Actually \(p(r)\propto \sin^{D-1}(r)\), Granata & Carnevalle 16

COSMOS dataset

300,000 observed galaxies

Horizon-AGN

700,000 simulated galaxies

We have a method to measure
the intrinsic dimensionality of any dataset.

• Magnitude measurements (not images!)
• 14 photometric wide-bands (u*, g, r, i, z, y, Y, J, H, Ks, B, V, IRAC CH1 & CH2)
  + 14 narrow-bands
• SNR > 2
• passive/active selection

Note: we are not working with images, but integrated magnitudes

COSMOS dataset

300,000 observed galaxies

Horizon-AGN

700,000 simulated galaxies

No more than \(\sim 4\) independent parameters? (with comparable magnitudes)

See Disney 08 for even more controversial results, although with smaller statistics

Horizon-AGN

700,000 simulated galaxies

No more than \(\sim 3\) independent parameters!

Galaxy formation is tightly constrained

With simulated noise

Without simulated noise

\(z=0\)

\( z = 100\)

\(z=0\)

\( z = 100\)

[White 84]

\(z=0\)

\( z = 100\)

[Genetic modifications: Roth+16, see also Rey&Pontzen 18, Stopyra+20]

Time

Angular
momentum

\(z\rightarrow \infty\)

\(z=0\)

✅ AM of fixed DM regions responds ~linearly (so is not chaotic!)

However, particle membership hence DM halo does not

Angular
momentum

Time

Dark matter spin is hard to predict

⇒ the usual culprit are mergers

Cadiou+24
Based on the critical event theory (Cadiou +20)
itself based on Hanami 2001

We can make some reasonable predictions
of orbital spin of mergers

Given: tides + density peaks

\(z\gg 100\)

1 peak = 1 halo

Critical event:
\(\nabla \delta = 0\quad\&\quad\lambda_1 \leq \lambda_2 \leq \lambda_3=0.\)

Critical point:
\(\nabla \delta = 0\)

Maximum: \(\lambda_1 \leq \lambda_2 \leq \lambda_3 \leq 0\)
    Saddle:     \(\lambda_1 \leq \lambda_2 \leq 0 \leq \lambda_3\)

A small detour at critical event theory

Critical event:
\(\nabla \delta = 0\quad\&\quad\lambda_i = 0.\)

a few pages of math…

Based on the critical event theory (Cadiou +20)

We can compute

\(\mathcal{P}\left( m \textbf{r}\times\textbf{v}\ \middle|\  \text{peak of mass $M$}\right)\)

Changes to tides at \(z=100\), effect at \(z<1\)

\(\lambda_\mathrm{DM}\)

Full hydro simulations
(RAMSES, New-Horizon model):

• Resolved disk height
  \(\Delta x_\mathrm{min} = 35\ \mathrm{pc}\)
• \(M_\mathrm{200c} = 10^{12}\ \mathrm{M}_\odot\)
  at \(z=2\)
• SF, AGN, SN feedback
• 3 galaxies, 5× scenario each

Lowest tides

Low tides

Higher tides

Highest tides

\( j_0 \times 0.66\)

\( j_0 \times 0.8\)

\( j_0 \times 1.2\)

\( j_0 \times 1.5\)

See Cadiou+21a

\( j_0 \times 0.66\)

\( j_0 \times 0.8\)

\( j_0 \times 1.2\)

\( j_0 \times 1.5\)

See Cadiou+21a

Stellar angular momentum responds ~linearly
to large-scale tides

See Cadiou+21a

Halo and disk evolve separately,

this allows stellar AM to be ~linear despite halo AM not being

See Cadiou+21a

Special case: no massive satellite

See Cadiou+21a

Two intermediate conclusions:
 

1. Stellar angular momentum is driven by cosmological tides
   ⇒ failure of theory, not fundamental limitation
    
2. Galaxies respond quasi-linearly to perturbations
   ⇒ morphology, bulge fraction, spin are not chaotic!

\(\rho_\mathrm{i}, v_\mathrm{i}\)

\(\Lambda\)CDM+baryon non-linear evolution

halo & galaxy properties

What if the galaxy had formed here instead?

What if the galaxy had formed here instead?

or here?

The “splicing” technique

1. Generate ICs
2. Integrate (\(N\)-body)
3. Select region of interest
4. Trace back to ICs
5. “Splice” the region
6. Integrate again

Splicing: equivalent of constraining density field at all points in region

\(\longleftarrow  50\,\mathrm{Mpc} \longrightarrow\)

Splicing in 1D

Splicing in 1D

Most likely field \(f\) with

• same value in spliced region (\(a\)),
• as close as possible outside (\(b\))

Mathematically, \({\color{green}f}\) is the unique solution that satisfies:

• \( {\color{green}f(x)}= {\color{blue}a(x)},\qquad\qquad\qquad\forall x \in\Gamma\)
• minimizes \[\mathcal{Q} = ({\color{red}b}-{\color{green}f})^\dagger\mathbf{C}^{-1}({\color{red}b}-{\color{green}f}),\quad \forall x \not\in \Gamma \]

The causal origin of DM halo concentration

The causal origin of DM halo concentration

The causal origin of DM halo concentration

\(\log\left|\dfrac{{\color{blue}\rho_\mathrm{i}} - \color{red}\rho_\mathrm{i}}{\sigma_\rho}\right|\)

\(\log\left|\dfrac{{\color{blue}v_\mathrm{i}} - \color{red}v_\mathrm{i}}{\sigma_v}\right|\)

Issue : splicing the density does not fix the velocity & tides

Issue : splicing the density does not fix the velocity & tides
 

Solution: splice the potential

\(\log\left|\dfrac{{\color{blue}\rho_\mathrm{i}} - \color{red}\rho_\mathrm{i}}{\sigma_\rho}\right|\)

\(\log\left|\dfrac{{\color{blue}v_\mathrm{i}} - \color{red}v_\mathrm{i}}{\sigma_v}\right|\)

Remember \(\nabla^2\phi = 4\pi G\rho\) so

\[\rho_n\propto\frac{\phi_{n+1}-2\phi_n+\phi_{n-1}}{\Delta x^2}\]

\[v_n\propto\frac{\phi_{n+1}-\phi_{n-1}}{2\Delta x}\]

Same halo (same initial tides + density)

forming closer and closer to filament

Repeat for 5 halos, 9 positions

Deviation from the mean

For different quantities

\(\sigma\)

\(\langle q\rangle\)

In practice, we change the potential so we're testing sensitivity to non-linear gravitational coupling to large-scale structures

Simple isothermal CGM             vs.           Complex multiphase CGM

• Well-mixed (isothermal)
• "Bathtub" modelling

• Not well-mixed (turbulence)
• How much gas reaches the galaxy?

Megatron simulations:
first simulation to combine at high-\(z\)
+ non-equilibrium chemistry
+ radiative transport
+ \(\sim 50-100\,\mathrm{pc}\) resolution
 

Reveals

• Complex, multiphase structure,
• Smallest structures at resolution limit,
• Non-equilibrium ionized structures
  • impact on thermochemical structure,
  • impact on observations.

O I

O II

O III

Megatron simulations:
first simulation to combine at high-\(z\)
+ non-equilibrium chemistry
+ radiative transport
+ \(\sim 50-100\,\mathrm{pc}\) resolution
 

Reveals

• Complex, multiphase structure,
• Smallest structures at resolution limit,
• Non-equilibrium ionized structures
  • impact on thermochemical structure,
  • impact on observations.

Megatron simulations:
first simulation to combine at high-\(z\)
+ non-equilibrium chemistry
+ radiative transport
+ \(\sim 50-100\,\mathrm{pc}\) resolution
 

Reveals

• Complex, multiphase structure,
• Smallest structures at resolution limit,
• Non-equilibrium ionized structures
  • impact on thermochemical structure,
  • impact on observations.

OIII column density
in simulation

assuming ionization equilibrium

Most powerful clusters are switching to GPUs
(following the AI hype...)

Manage grid, simple computation

Computation-heavy
(hydro, gravity, …)

CPU

GPU

[…]

wasted
time

wasted
time

Typical approach: offloading*

Dyablo's approach:

* Arepo, Gadget3, RAMSES, ...

Amdahl's law: latency kills gains of parallelisation

Manage grid, simple computation

Computation-heavy
(hydro, gravity, …)

CPU

GPU
(or CPUs)

[…]

Typical approach: offloading

Dyablo's approach: “true” GPU computing, CPU as a puppeteer

Dyablo: Implemented physics

• Adaptive mesh-refinement,
• Hydrodynamics / MHD / radiative transfer
• Gravity
• Particles,
• Gas cooling
• Star formation and feedback,
• Cosmology,
• Diffusion terms: thermal conduction, viscosity,
• Cosmic rays, thermochemistry...

Agora initial conditions, Kim+16

Dyablo: how does it scale?

weak scaling: solar convection

Image credits: Maxime Delorme

Ad Astra CPU (2 x AMD Epyc Genoa 96 cores)

Conclusions

1. Tides set merger orbital parameters & angular momentum accretion
   Mergers are not stochastic/not rerolling the dice
    
2. Trickling down to galactic scale, which drives scaling relations
   Galaxies are less stochastic than expected
   Galaxy & DM spin are partially independent at the level of individual galaxies
    
3. Non-linear effects on halo shape and alignment are comparable to population-level
   Crucial to investigate further for the success of Euclid or LSST
    
4. Knowledge/modelling frontier: Circum Galactic Medium transport
   Non-equilibrium, multiphase state in obs. (low-\(z\)) and sims (high-\(z\))
   Cosmic web → CGM → ISM: how does AM evolve in this picture?

Tracing cosmic evolution

The (not so) new frontier:
physics in the circumgalactic medium

Tracing cosmic evolution: what's next?

Conclusions

Come talk to me if you're interested in…

• galaxy formation,
• the cosmic web,
   
• numerical simulations (on GPUs, load-balancing, on-the-fly, …),
• data visualization (interactive, volume rendering, …).

🖥️ 118c — cadiou@iap.fr — https://cphyc.github.io —@cphyc.bsky.social

Angular momentum:

1. Qualitatively understood
2. Abrupt changes with mergers
3. Crucial for galaxy formation + weak lensing

Corentin Cadiou

Corentin Cadiou

Angular momentum:

1. Qualitatively understood
2. Abrupt changes with mergers
3. Crucial for galaxy formation + weak lensing

Corentin Cadiou

Angular momentum:

1. Qualitatively understood
2. Abrupt changes with mergers
3. Crucial for galaxy formation + weak lensing

• What's the origin of angular momentum?
• Are mergers truly stochastic?
• How does it translate to galaxy properties?

Large-scale torques control mergers deterministically
which controls secondary galaxy properties

… what happens to the gas?

Corentin Cadiou

Large-scale torques control mergers deterministically
which controls secondary galaxy properties

… what happens to the gas?

Corentin Cadiou

Corentin Cadiou

Tracers: Cadiou+19
Cadiou+21b, see also Danovich+15, Prieto+17

Tracking Lagrangian trajectories, comparing \(\vec{j}\) to

\(\parallel\) to direction @ \(R_\mathrm{vir}\)

\(\perp\) to direction @ \(R_\mathrm{vir}\)

⚠️ Only looking at gas that will form stars eventually

Kocjan, Cadiou+24

Corentin Cadiou

Time \(2R_\mathrm{vir}\rightarrow R_\mathrm{vir}/3\)

Angular momentum: bridging galaxy formation to cosmology

Corentin Cadiou

Corentin Cadiou

• Why is the effect of the cosmic web at % level?
• What's the arrow of causality?
      CW ⇒ spin ⇒ morphology?
• How stochastic is galaxy formation?

Splicing technique Cadiou, Pontzen & Peiris 21

Extended by A. Storck

Corentin Cadiou

Splicing technique Cadiou, Pontzen & Peiris 21

Extended by A. Storck

Corentin Cadiou

See Anatole Storck's poster for more information!

Far

Close

Halo (mis-)aligns itself to filament

Corentin Cadiou

Dynamics of angular momentum

Realignment between…

…\(3R_\mathrm{vir}\) and \(R_\mathrm{vir}\)

…\(R_\mathrm{vir}\) and \(R_\mathrm{vir}/3\)

…\(R_\mathrm{vir}\) and \(R_\mathrm{vir}/10\)

[CC+21]

[Kocjan, CC+ in prep]

What happens in the CGM?

✅ Cold accretion is slow to form stars

Quick depletion right after merger

[Kocjan, CC+ in prep]

The effects of environment on halo properties

• \( M_\mathrm{DM}(\text{node}) \) > \(M_\mathrm{DM}(\text{fil}) \) >\(M_\mathrm{DM}(\text{void})\), higher clustering
• spins align with cosmic web ⇒ issue for weak lensing
• \(v/\sigma(\mathrm{fil})>v/\sigma(\mathrm{void})\) ⇒ bias in galaxy formation
• ….

The effects of environment on halo properties

Isotropic effects

Kaiser bias, cluster vs. groups, ...

From theory: \(M\propto \int\mathrm{d}^3R\rho\)

Mass regulated

An-isotropic effects

Intrinsic alignment, formation of disks?

From theory: \(J \propto \int\mathrm{d}^3R \nabla \phi\)

Angular momentum regulated?

Ongoing work by Z. Kocjan

[Kocjan, CC+ in prep]

Filamentary accretion ~ Cold flow = \(T \leq 10^5\mathrm{K}\) for \(0.3R_\mathrm{vir} < r < 2R_\mathrm{vir}\)

Filamentary accretion ~ Cold flow = \(T \leq 10^5\mathrm{K}\) for \(0.3R_\mathrm{vir} < r < 2R_\mathrm{vir}\)

Not necessarily fast-track to star formation ⇒ lose connection to CW?

[Kocjan, CC+ in prep]

\(M_\mathrm{DM}(z=2)\approx 10^{11}-10^{12} \mathrm{M_\odot}\)

Ongoing work by Z. Kocjan

Verify that

\[\xi_\mathrm{lin}(r) \sim \left\langle {\color{green}\underbrace{\delta(x=d)}_\mathrm{in}} {\color{purple} \underbrace{\delta(x=d+r)}_\mathrm{out}}\right\rangle \]

is the same in spliced / ref simulation.

Verify that

\[\xi_\mathrm{lin}(r) \sim \left\langle {\color{green}\underbrace{\delta(x=d)}_\mathrm{in}} {\color{purple} \underbrace{\delta(x=d+r)}_\mathrm{out}}\right\rangle \]

is the same in spliced / ref simulation.

Verify that

\[\xi_\mathrm{lin}(r) \sim \left\langle {\color{green}\underbrace{\delta(x=d)}_\mathrm{in}} {\color{purple} \underbrace{\delta(x=d+r)}_\mathrm{out}}\right\rangle \]

is the same in spliced / ref simulation.

\( R_{1/2} \)

\( l_0 \times 1.2\)

\( l_0 \times 1.5\)

\( l_0 \times 0.66\)

\( l_0 \times 0.8\)

\( l_0 \times 0.66\)

\( l_0 \times 0.8\)

\( l_0 \times 1.2\)

\( l_0 \times 1.5\)

\( l_0 \times 1.2\)

\( l_0 \times 1.5\)

\( l_0 \times 0.66\)

\( l_0 \times 0.8\)

\( l_0 \times 1.2\)

\( l_0 \times 1.5\)

\( l_0 \times 0.66\)

\( l_0 \times 0.8\)

• AM of baryons originates from initial conditions…
• can be controlled…
• and regulate galaxy morphology
• Negligible AGN/SN global self-regulation

Galaxy formation

[L. Cortese; SDSS.]

[Dubois+16]

AGN         no AGN

Origin of morphological diversity at fixed mass?

[L. Cortese; SDSS.]

[Dubois+16]

AGN         no AGN

Origin of morphological diversity at fixed mass?

[Kraljic+ in prep]

Galaxy formation

[Danovich+15]

The origin of high \(z\) angular momentum

[Danovich+15]

I. Torque with cosmic web

The origin of high \(z\) angular momentum

[Danovich+15]

I. Torque with cosmic web

II. Transport at constant AM

The origin of high \(z\) angular momentum

[Danovich+15]

I. Torque with cosmic web

II. Transport at constant AM

III. Torque down in inner halo

The origin of high \(z\) angular momentum

[Danovich+15]

I. Torque with cosmic web

II. Transport at constant AM

III. Torque down in inner halo

IV. Mixing in inner disk & bulge

The origin of high \(z\) angular momentum

The origin of high \(z\) angular momentum

[Danovich+15]

IV. Mixing in inner disk & bulge

III. Torque down in inner halo

II. Transport at constant AM

I. Torque with cosmic web

Predict pre-accretion AM?

Alignment with environment?

The origin of high \(z\) angular momentum

[Danovich+15]

IV. Mixing in inner disk & bulge

III. Torque down in inner halo

II. Transport at constant AM

I. Torque with cosmic web

Predict pre-accretion AM?

Alignment with environment?

The origin of high \(z\) angular momentum

[Danovich+15]

IV. Mixing in inner disk & bulge

III. Torque down in inner halo

II. Transport at constant AM

I. Torque with cosmic web

Predict pre-accretion AM?

Alignment with environment?