Corentin Cadiou
cadiou@iap.fr

Bureau 118c

Tracing Cosmic Evolution:

From the CMB to the Web, the CGM, and Galactic Disks

kpc

100 kpc

Mpc

Gravitational
collapse

Baryonic physics, star form, AGNs

Feedback processes

Perturbations

Simulations

Perturbation
theory

Galaxy formation in a 🥜 shell

Dark matter (DM) halo formation
Gas condenses in DM halo
Stars form out of gas
Supernova + AGNs reinject energy

T [K]

Cooling rate $\Lambda$

$\dfrac{\mathrm{d}T}{\mathrm{d}t} = \Lambda(T) \rho^2$

$\dfrac{\mathrm{d}M_\star}{\mathrm{d}t}\propto \rho^{3/2}$

increasingly non-linear

Accretion shocks, adiabatic heating, KH instabilities etc.

Vallés-Pérez+24

Galaxy formation in a 🥜 shell

Dark matter (DM)
Gas condenses in DM potential
Stars form out of gas
Supernova + AGNs reinject energy

increasingly non-linear

increasingly chaotic?

⇒

Intrinsic alignment measurement: Ganeshaiah Veena+ 19 · Alignment: M. Sachs

Neighbouring galaxies' shapes are aligned
(on the plane of the sky)

Intrinsic alignment

Baryon dominated?
No cosmo information?

Weak lensing

L.o.s. measurement of
dark matter density

⇒

Galaxy formation: the biased point of view of the spin

Stochastic spin: Vitviska+ 02, Beson+ 20
Spin prediction, Porciani+ 02

Spin: \[\lambda = \dfrac{j}{\sqrt{2}R_\mathrm{vir}V_{vir}}\]

Spin jumps at mergers
Distribution well reproduced by drawing mergers' parameters randomly
Theoretical predictions are, at best, inaccurate

First complication

$\pm 100\%$!

“Mergers bring chaos”

Second complication

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

DM spin is not even a good predictor for the galaxy's!

Jiang+ 19

$\lambda_\mathrm{DM}$

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

Third complication

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

But are galaxies truly chaotic?

How complex are galaxies?

Results from Cadiou+ 24a

1 How complex are galaxies?

Results from Cadiou+ 24a

1

Example of the S-curve:

2D manifold embedded in 3D

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

$\#(<r)$

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

Galaxies populate a 3D attractor?

$M$

$z$

$j$?

With simulated noise

Without simulated noise

Is DM angular momentum chaotic?

Results from Cadiou+21, 22

2 Is DM angular momentum chaotic?

Results from Cadiou+21, 22

2

DM angular momentum

$z=0$

$ z = 100$

$z=0$

$ z = 100$

[White 84]

DM angular momentum

$z=0$

$ z = 100$

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

DM angular momentum

Time

Angular
momentum

DM angular momentum

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

However, particle membership hence DM halo does not

Angular
momentum

Time

DM angular momentum

Dark matter spin is hard to predict

the usual culprit are mergers

Are mergers really
stochastic?

Results from Cadiou +24b

3

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

$z\gg 100$

$z = 0$

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: $\lambda_1 \leq \lambda_2 \leq 0 \leq \lambda_3$

1 peak = 1 halo

1 peak disappearing = 1 merger

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: $\lambda_1 \leq \lambda_2 \leq 0 \leq \lambda_3$

Counting haloes & galaxies

Counting filaments

Counting mergers

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 $z<1$

How chaotic is baryonic
angular momentum?

Results from Cadiou +21a

4 How chaotic is baryonic
angular momentum?

Results from Cadiou +21a

4

$\lambda_\mathrm{DM}$

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

$ j_0 \times 0.66$

$ j_0 \times 0.8$

$ j_0 \times 1.2$

$ j_0 \times 1.5$

$ j_0 \times 0.66$

$ j_0 \times 0.8$

$ j_0 \times 1.2$

$ j_0 \times 1.5$

See Cadiou+21a

INPUT: Changes to tides $z=\infty$

OUTPUT: Ang. mom
$z=2$

Halo and disk evolve separately,

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

Gas + stars spAM

Stars spAM

Halo spAM

See Cadiou+21a

Special case: no massive satellite

Low tides

High tides

$\mathcal{B}\searrow$

$R_\mathrm{eff} \nearrow $

$v/\sigma\nearrow$

See Cadiou+21a

Impact of the cosmological-scale tides on halo properties

Results from Storck, Cadiou+25

5

Impact of the cosmological-scale tides on halo properties

Results from Storck, Cadiou+25

5

$\rho_\mathrm{i}, v_\mathrm{i}$

$\Lambda$CDM+baryon non-linear evolution

halo & galaxy properties

What if the galaxy had formed here instead?

or here?

The “splicing” technique

Generate ICs
Integrate ($N$-body)
Select region of interest
Trace back to ICs
“Splice” the region
Integrate again

$t$

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

$\longleftarrow 50\,\mathrm{Mpc} \longrightarrow$

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

Same halo (same initial tides + density)

forming closer and closer to filament

Repeat for 5 halos, 9 positions

$\sigma$

$\langle q\rangle$

Deviation from the mean

For different quantities

spin alignment

shape alignment

$\sigma$

$\langle q\rangle$

Conclusions

On global scales galaxies aren't that complex: success of simulations
Actual complexity is on the order of 3 (mass, redshift, $j$? SFR?)
Tides set merger orbital parameters & angular momentum accretion
Mergers are not stochastic/not rerolling the dice
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
Non-linear effects on halo shape and alignment are comparable to population-level
Crucial to investigate further for the success of Euclid or LSST