Corentin Cadiou
Online @ Hyderabad 10/07/24
Based on work by A. Storck, Z. Kocjan, E. Pichon-Pharabod
Cadiou, Pontzen & Peiris 21 · Cadiou, Pontzen +21 · Kocjan, Cadiou, Agertz, Pontzen 24 · Cadiou, Pichon-Pharabod+24
My interests:
and high-performance computing & visualisation
Intrinsic alignment measurement: Ganeshaiah Veena+ 19 · Alignment: M. Sachs
Neighbouring galaxies' shapes are aligned
(on the plane of the sky)
Baryon dominated?
No cosmo information?
L.o.s. measurement of
dark matter density
+
⇒
Stochastic spin: Vitviska+ 02, Beson+ 20
Spin prediction, Porciani+ 02
Spin: \[\lambda = \dfrac{j}{\sqrt{2}R_\mathrm{vir}V_{vir}}\]
\(1\,\mathrm{dex}\)!
“Mergers bring chaos”
Let's be optimistic and assume we can predict DM spin
DM spin is not even a good predictor for the galaxy's!
TR: Jiang+ 19, BL: Rodriguez-Gomez+ 22
\(\lambda_\mathrm{DM}\)
Butterfly effect: Genel+ 19, see also Thiébaut+ 08
Resimulating the same galaxy twice yields different results ⇒ galaxies are chaotic
But are galaxies truly chaotic?
Results from Cadiou+ 24a
Results from Cadiou+ 24a
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
\(\#(<r)\)
300,000 observed galaxies
700,000 simulated galaxies
Note: we are not working with images, but integrated magnitudes
300,000 observed galaxies
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
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
Results from Cadiou+21, 22
Results from Cadiou+21, 22
\(z=0\)
\( z = 100\)
\(z=0\)
\( z = 100\)
[White 84]
\(z=0\)
\( z = 100\)
[Genetic modifications: Roth+16, see also Rey&Pontzen 18, Stopyra+20]
Time
Angular
momentum
✅ AM of fixed DM regions responds ~linearly (so is not chaotic!)
However, particle membership hence DM halo does not
Angular
momentum
Time
Halo AM is hard to predict
the usual culprit are mergers
Results from Cadiou +24b
Based on the critical event theory (Cadiou +20)
We can make some reasonable predictions
of orbital spin of mergers
Given: tides + density peaks
Changes to tides at \(z=100\), effect at \(z<1\)
tides ×0.5 ⇒ merger @ \(z=0.7\)
tides ×1.1 ⇒ merger @ \(z=0.55\)
tides ×1.2 ⇒ merger @ \(z=0.5\)
tides ×2 ⇒ merger @ \(z=0.2\)
Results from Cadiou +21a
Results from Cadiou +21a
Full hydro simulations
(RAMSES, New-Horizon model):
\( j_0 \times 0.66\)
\( j_0 \times 0.8\)
\( j_0 \times 1.2\)
\( j_0 \times 1.5\)
\( j_0 \times 0.66\)
\( j_0 \times 0.8\)
\( j_0 \times 1.2\)
\( j_0 \times 1.5\)
\( j_0 \times 0.66\)
\( j_0 \times 0.8\)
See Cadiou+21a
INPUT: Changes to tides \(z=\infty\)
OUTPUT: Ang. mom
\(z=2\)
\( j_0 \times 0.66\)
\( j_0 \times 0.8\)
\( j_0 \times 1.2\)
\( j_0 \times 1.5\)
\( j_0 \times 0.8\)
See Cadiou+21a
INPUT: Changes to tides \(z=\infty\)
OUTPUT: Ang. mom
\(z=2\)
Stellar angular momentum responds ~linearly
to large-scale tides
Gas + stars spAM
Stars spAM
Halo spAM
Halo spAM
See Cadiou+21a
Halo and disk evolve separately,
this allows stellar AM to be ~linear despite halo AM not being
Gas + stars spAM
Stars spAM
Halo spAM
Halo spAM
See Cadiou+21a
Low tides
High tides
\(\mathcal{B}\searrow\)
\(R_\mathrm{eff} \nearrow \)
\(v/\sigma\nearrow\)
See Cadiou+21a
Results from Cadiou +21b
What if the galaxy had formed here instead?
What if the galaxy had formed here instead?
or here?
\(t\)
Splicing: equivalent of constraining density field at all points in region
\(\longleftarrow 50\,\mathrm{Mpc} \longrightarrow\)
Most likely field \(f\) with
Mathematically, \({\color{green}f}\) is the unique solution that satisfies:
\(M^{(1)}_{200\mathrm{c}}, c^{(1)}_\mathrm{NFW}, \dots\)
\(M^{(2)}_{200\mathrm{c}}, c^{(2)}_\mathrm{NFW}, \dots\)
\(M^{(\dots)}_{200\mathrm{c}}, c^{(\dots)}_\mathrm{NFW}, \dots\)
\(M^{(10)}_{200\mathrm{c}}, c^{(10)}_\mathrm{NFW}, \dots\)
Same halo in 10× different environments
Repeat experiment for 7 halos (70 realisations in total)
Same halo in 10× different environments
Repeat experiment for 7 halos (70 realisations in total)
\(M^{(1)}_{200\mathrm{c}}, c^{(1)}_\mathrm{NFW}, \dots\)
\(M^{(2)}_{200\mathrm{c}}, c^{(2)}_\mathrm{NFW}, \dots\)
\(M^{(\dots)}_{200\mathrm{c}}, c^{(\dots)}_\mathrm{NFW}, \dots\)
\(M^{(10)}_{200\mathrm{c}}, c^{(10)}_\mathrm{NFW}, \dots\)
Same halo in 10× different environments
Repeat experiment for 7 halos (70 realisations in total)
\(M^{(1)}_{200\mathrm{c}}, c^{(1)}_\mathrm{NFW}, \dots\)
\(M^{(2)}_{200\mathrm{c}}, c^{(2)}_\mathrm{NFW}, \dots\)
\(M^{(\dots)}_{200\mathrm{c}}, c^{(\dots)}_\mathrm{NFW}, \dots\)
\(M^{(10)}_{200\mathrm{c}}, c^{(10)}_\mathrm{NFW}, \dots\)
50% of population
Results from Storck, Cadiou in prep.
Results from Storck, Cadiou in prep.
\(\rho_\mathrm{i}, v_\mathrm{i}\)
\(\Lambda\)CDM+baryon non-linear evolution
halo & galaxy properties
\(\log\left|\dfrac{{\color{blue}\rho_\mathrm{i}} - \color{red}\rho_\mathrm{i}}{\sigma_\rho}\right|\)
\(\log\left|\dfrac{{\color{blue}v_\mathrm{i}} - \color{red}v_\mathrm{i}}{\sigma_v}\right|\)
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
Variation compared to mean value
For different quantities
spin alignment
shape alignment
The title might have been clickbait… but
Angular momentum:
Corentin Cadiou
Porciani+02
Vitviska+02, Benson+20
Fall+80
Corentin Cadiou
Vitviska+02, Benson+20
Porciani+02
Fall+80
Angular momentum:
Corentin Cadiou
Fall+80
Vitviska+02, Benson+20
Porciani+02
Angular momentum:
Angular momentum:
Corentin Cadiou
Fall+80
Vitviska+02, Benson+20
Porciani+02
See Cadiou+21a
based on genetic modifications: Roth+16, Rey&Pontzen 18, Stopyra+20
“Find the most likely \(\Lambda\)CDM realisation
that increases the torques by factor \(f\)”
This is actually done by minimizing \((\delta_\mathrm{new}-\delta_\mathrm{old})^\dagger \textbf{C}^{-1}(\delta_\mathrm{new}-\delta_\mathrm{old})\)
with the constrains \(\tau^{(i)}_\mathrm{new} = f \tau^{(i)}_\mathrm{old}, \quad i=x,y,z\)
MEGATRON simulation
With Rey & Katz
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
Most of re-alignment happens in the inner CGM \(0.1\leq \displaystyle\frac{r}{R_\mathrm{vir}}\leq 0.3\)
The longer gas remains in inner CGM, the more it realigns (with disk)
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 \(2R_\mathrm{vir}\rightarrow R_\mathrm{vir}/3\)
Time \(R_\mathrm{vir}/3 \rightarrow ⭐\)
2 Spin \(\leftrightarrow\) morphology
Romanowsky&Fall 12
Harrison+17
Hasan+23 (TNG)
3 Cosmic web \(\leftrightarrow\) SFR
Kraljic+CC+19 (HAGN)
1 Cosmic web \(\leftrightarrow\) spin
1 Cosmic web \(\leftrightarrow\) spin
Ganeshaiah Veena+21
Corentin Cadiou
2 Spin \(\leftrightarrow\) morphology
Romanowsky&Fall 12
Harrison+17
Hasan+23 (TNG)
3 Cosmic web \(\leftrightarrow\) SFR
Kraljic+CC+19 (HAGN)
1 Cosmic web \(\leftrightarrow\) spin
1 Cosmic web \(\leftrightarrow\) spin
Ganeshaiah Veena+21
Corentin Cadiou
\(z=0\)
\( z = 100\)
[Genetic modifications: Roth+16, see also Rey&Pontzen 18, Stopyra+20]
Tide \(\nearrow\) delay merger
Tide \(\searrow\) hasten merger
Corentin Cadiou
Corentin Cadiou
Cadiou+21b
So far, I've shown effect of linear perturbations on galaxy formation.
How to probe non-linear couplings?
Corentin Cadiou
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
Harrison+17 (KMOS, \(z=1\))
Spiral galaxies \(\leftrightarrow\) high \(J_\star\)
What's the arrow of causality?
Rodriguez-Gomez+22 (TNG)
Tillson+15
Dekel&Birnboim 06
High-z:
most of mass + AM flow along filaments
How do we study these effects?
Large volumes
sample \(p(M_\star, M_\mathrm{DM},\mathbf{J}, d_\mathrm{fil}, \dots)\)
This talk
sample \(p(\mathbf{J}|M_\star, M_\mathrm{DM}, d_\mathrm{fil}, \dots)\)
Lower-zs:
intrinsic alignment problem
Porciani+02
Rodriguez-Gomez+22
Predictions for \(j_\mathrm{DM}\) remain qualitative
\(j_\mathrm{DM}-j_\mathrm{\star}\)
weak correlation
(statistically strong)
How is AM transported to the disk?
First controlled experiment of testing tidal torque theory for individual halos
CC+21a, arXiv: 2012.02201
First controlled experiment of angular momentum accretion on individual galaxies
CC+22, arXiv: 2206.11913
Main idea: stars are deeper in potential well so less sensitive to what happens at large scales
⇒ stellar Lagrangian patch should be more stable to perturbations
CC+Pichon+Dubois, 21, arXiv: 2110.05384
Kocjan, CC in prep.
Realignment between…
…\(3R_\mathrm{vir}\) and \(R_\mathrm{vir}\)
…\(R_\mathrm{vir}\) and \(R_\mathrm{vir}/3\)
…\(R_\mathrm{vir}\) and \(R_\mathrm{vir}/10\)
✅ Most of realignment happens in “CGM” (\(\leq R_\mathrm{vir}/3\))
Mostly due to grav. torques (consistent with e.g. Danovich+15)
[CC+21]
\(t_{1/3}\)
\(t_{\star}\)
\(T_\mathrm{max}\) between \(2 R_\mathrm{vir}\) and \(R_\mathrm{vir}/3\)?
\(\leq 3\times10^4\,\mathrm{K}\)
Cold accretion
\(\geq 5\times10^5\,\mathrm{K}\)
Hot accretion
[Kocjan, CC+ in prep]
✅ Cold accretion is slow to form stars
Quick depletion right after merger
[Kocjan, CC+ in prep]
Kraljic+18 [see also Laigle15, Song+21,…]
Kaiser bias, cluster vs. groups, ...
From theory: \(M\propto \int\mathrm{d}^3R\rho\)
Mass regulated
Intrinsic alignment, formation of disks?
From theory: \(J \propto \int\mathrm{d}^3R \nabla \phi\)
Angular momentum regulated?
\(z=0\)
\( z = 100\)
\[\mathbf{L}_\mathrm{lin.} \propto \int\mathrm{d}^3q(\mathbf{q}-\bar{\mathbf{q}})\times \nabla\phi\]
Position w.r.t. center
Velocity
[White 84]
Note: vanishes at 1st order in a sphere
\[ \int_\Gamma \mathrm{d}^3{q}(\mathbf{q}-\mathbf{\bar{q}}) \times\nabla\phi = \int_{\partial\Gamma}\phi(q)(\mathbf{q}-\mathbf{\bar{q}})\times\mathrm{d}\mathbf{S}\]
Note: the following is a (poor) approximation:
\[ \mathbf{L} \propto \epsilon_{ijk} T_{jl}I_{lk},\quad\text{with \textbf{T} the tidal tensor and \textbf{I} the inertia tensor}\]
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
Corentin Cadiou
The Co-evolution of the CW and Galaxies across Cosmic Time
$$\rho_\mathrm{DM}(r) = \frac{\rho_0}{\frac{r}{R_\mathrm{vir}/c} \left(1 + \frac{r}{R_\mathrm{vir}/c}\right)^2}$$
Wechsler+02
Origin of scatter at fixed \(M_\mathrm{vir}\)?
\[\mathbf{L}_\mathrm{lin.} \propto \int\mathrm{d}^3q(\mathbf{q}-\bar{\mathbf{q}})\times \nabla\phi\]
[On patch boundaries: see Lucie-Smith+18]
Wechsler & Tinker 18
\({\color{red}M_\star} / M_\mathrm{h} \ll \Omega_b / \Omega_m \)
⇒ baryons & DM stem from different regions
Baryons more strongly bound
⇒ less prone to being ejected
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.
angular momentum is predictable
boundary of halos in the ICs is a hard problem
⇒ limits practicality of predictions (for now)
baryons appear to be simpler!
⇒ good news for weak lensing predictions
⇒ key to understand morphology
Environmental effects:
+
\( R_{1/2} \)
\( l_0 \times 1.2\)
\( l_0 \times 1.5\)
\( l_0 \times 0.66\)
\( l_0 \times 0.8\)
\( l_0 \times 0.66\)
\( l_0 \times 0.8\)
\( l_0 \times 1.2\)
\( l_0 \times 1.5\)
\( l_0 \times 1.2\)
\( l_0 \times 1.5\)
\( l_0 \times 0.66\)
\( l_0 \times 0.8\)
\( l_0 \times 1.2\)
\( l_0 \times 1.5\)
\( l_0 \times 0.66\)
\( l_0 \times 0.8\)
[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?
How to explain environmental effects?
[Kraljic+ in prep]
[Danovich+15]
[Danovich+15]
I. Torque with cosmic web
[Danovich+15]
I. Torque with cosmic web
II. Transport at constant AM
[Danovich+15]
I. Torque with cosmic web
II. Transport at constant AM
III. Torque down in inner halo
[Danovich+15]
I. Torque with cosmic web
II. Transport at constant AM
III. Torque down in inner halo
IV. Mixing in inner disk & bulge
[Danovich+15]
IV. Mixing in inner disk & bulge
Fraction that ends up in disk vs. IGM?
Influence of galactic physics?
III. Torque down in inner halo
Origin of torque down (pressure or gravity)?
Loss of link with cosmic AM?
II. Transport at constant AM
Same evolution in cold/hot accretion modes?
I. Torque with cosmic web
Predict pre-accretion AM?
Alignment with environment?
[Danovich+15]
IV. Mixing in inner disk & bulge
Fraction that ends up in disk vs. IGM?
Influence of galactic physics?
III. Torque down in inner halo
Origin of torque down (pressure or gravity)?
Loss of link with cosmic AM?
See Cadiou+21c
II. Transport at constant AM
Same evolution in cold/hot accretion modes?
I. Torque with cosmic web
Predict pre-accretion AM?
Alignment with environment?
[Danovich+15]
IV. Mixing in inner disk & bulge
Fraction that ends up in disk vs. IGM?
Influence of galactic physics?
III. Torque down in inner halo
Origin of torque down (pressure or gravity)?
Loss of link with cosmic AM?
II. Transport at constant AM
Same evolution in cold/hot accretion modes?
I. Torque with cosmic web
Predict pre-accretion AM?
Alignment with environment?