Corentin Cadiou
IAP symposium

13/12/23

The causal origin of galactic angular momentum:
replacing galaxies in their cosmological context

With Z. Kocjan, A. Storck, E. Pichon-Pharabod, Agertz, Dubois, Peiris, Pontzen, Pichon, Pogosyan, …

Cadiou, Pontzen & Peiris 21 · Cadiou, Pontzen +21 · Kocjan, Cadiou, Agertz, Pontzen 23 · Cadiou, Pichon-Pharabod+23

Angular momentum: bridging galaxy formation to cosmology

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

Angular momentum: bridging galaxy formation to cosmology

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

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

MEGATRON
Rey, Katz & Cadiou in prep

  • Large volumes (TNG, HAGN, …)
    • statistical results only
    • relatively poor resolution
  • Small volumes & zoom-ins
    • few formation scenarios
  • Genetically modified simulations

tides ×0.5 ⇒ merger @ \(z=0.7\)

tides ×1.1 ⇒ merger @ \(z=0.55\)

tides ×1.2 ⇒ merger @ \(z=0.5\)

tides ×2 ⇒ merger @ \(z=0.2\)

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

Unraveling the origin of baryonic angular momentum

Full hydro simulations
(10Mh @ DiRAC):

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

\( j_0 \times 0.66\)

\( j_0 \times 0.8\)

\( j_0 \times 1.2\)

\( j_0 \times 1.5\)

Corentin Cadiou

INPUT: Changes to tides  \(z=\infty\)

OUTPUT: Ang. mom
\(z=2\)

\( j_0 \times 0.66\)

\( j_0 \times 0.8\)

\( j_0 \times 1.2\)

\( j_0 \times 1.5\)

\( j_0 \times 0.66\)

\( j_0 \times 0.8\)

\( j_0 \times 1.2\)

\( j_0 \times 1.5\)

See Cadiou, Pontzen & Peiris+21

Corentin Cadiou

\( j_0 \times 0.66\)

\( j_0 \times 0.8\)

\( j_0 \times 1.2\)

\( j_0 \times 1.5\)

\( j_0 \times 0.66\)

\( j_0 \times 0.8\)

\( j_0 \times 1.2\)

\( j_0 \times 1.5\)

See Cadiou, Pontzen & Peiris+21

INPUT: Changes to tides  \(z=\infty\)

OUTPUT: Ang. mom
\(z=2\)

Corentin Cadiou

Stellar disk angular momentum responds ~linearly to large-scale tides

See Cadiou, Pontzen & Peiris+21

INPUT: Changes to tides  \(z=\infty\)

OUTPUT: Ang. mom
\(z=2\)

Corentin Cadiou

Gas + stars spAM

Stars spAM

Halo spAM

Halo spAM

See Cadiou, Pontzen & Peiris+21

Corentin Cadiou

Halo and disk evolve separately,

but \(\lambda_\mathrm{baryon} \propto \lambda_\mathrm{DM}\)

Gas + stars spAM

Stars spAM

Halo spAM

Halo spAM

See Cadiou, Pontzen & Peiris+21

Corentin Cadiou

See Cadiou, Pontzen & Peiris+21

Special case: no massive satellite

Low tides

High tides

\(\mathcal{B}\searrow\)

\(R_\mathrm{eff} \nearrow \)

\(v/\sigma\nearrow\)

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

This suggests a way to predict ab initio merger orbital parameters (e.g. spin)

See Cadiou, Pichon-Pharabod+23

Corentin Cadiou

So far, I've shown effect of linear perturbations on galaxy formation.

How to probe non-linear couplings?

Corentin Cadiou

Corentin Cadiou

What if the galaxy had formed here instead?

Corentin Cadiou

What if the galaxy had formed here instead?

or here?

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

Conclusions

Corentin Cadiou

  1. Tides drive stellar angular momentum, which drives scaling relations
    AM causes bulge to reduce, radius and \(v/\sigma\) to increase
    Explains \(j_\star-M_\star-\mathcal{B}\) relation (and Tully-Fisher?)
     
  2. \(j_\mathrm{gal}\) retain memory of the cosmic web
    Galaxies are less stochastic than expected
    Galactic spin & DM spins are partially independent at the level of individual galaxies
     
  3. Non-linear effects are important to understand the origin of spin fully (so disk!)
    At MW mass, the closer to a filament, the more \(\perp\) the halo spin
    Galaxy simulations are in the pipes

Conclusions

Corentin Cadiou

What's the effect of anisotropic env DM/gal formation?

 Study same object, different environment.

 

CC+21, arXiv: 2107.03407

 

Cosmic web drives AM acquisition... what scales? what's affected?

The “splicing” technique

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

\(t\)

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

The causal origin of DM halo concentration

\(M^{(1)}_{200\mathrm{c}}, c^{(1)}_\mathrm{NFW}, \dots\)

\(M^{(2)}_{200\mathrm{c}}, c^{(2)}_\mathrm{NFW}, \dots\)

\(M^{(\dots)}_{200\mathrm{c}}, c^{(\dots)}_\mathrm{NFW}, \dots\)

\(M^{(10)}_{200\mathrm{c}}, c^{(10)}_\mathrm{NFW}, \dots\)

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)

\(M^{(1)}_{200\mathrm{c}}, c^{(1)}_\mathrm{NFW}, \dots\)

\(M^{(2)}_{200\mathrm{c}}, c^{(2)}_\mathrm{NFW}, \dots\)

\(M^{(\dots)}_{200\mathrm{c}}, c^{(\dots)}_\mathrm{NFW}, \dots\)

\(M^{(10)}_{200\mathrm{c}}, c^{(10)}_\mathrm{NFW}, \dots\)

The causal origin of DM halo concentration

Same halo in 10× different environments

Repeat experiment for 7 halos (70 realisations in total)

\(M^{(1)}_{200\mathrm{c}}, c^{(1)}_\mathrm{NFW}, \dots\)

\(M^{(2)}_{200\mathrm{c}}, c^{(2)}_\mathrm{NFW}, \dots\)

\(M^{(\dots)}_{200\mathrm{c}}, c^{(\dots)}_\mathrm{NFW}, \dots\)

\(M^{(10)}_{200\mathrm{c}}, c^{(10)}_\mathrm{NFW}, \dots\)

The causal origin of DM halo concentration

50% of population

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

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

What's the arrow of causality?

Rodriguez-Gomez+22 (TNG)

Angular momentum: controls disk formation?

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 \(p(\mathbf{J}|M_\star, M_\mathrm{DM}, d_\mathrm{fil}, \dots)\)

Angular momentum: bridging galaxy to cosmology

Lower-zs:
intrinsic alignment problem

Angular momentum: where are we?

Porciani+02

Rodriguez-Gomez+22

Predictions for \(j_\mathrm{DM}\) remain qualitative

\(j_\mathrm{DM}-j_\mathrm{\star}\)
weak correlation
(statistically strong)

  1. Is \(j_\mathrm{DM}\) chaotic or our theory poor?
  2. Do \(j_\mathrm{gal}\) retain memory of their environment?

  3. How is AM transported to the disk?

1. Is \(j_\mathrm{DM}\) chaotic or our theory poor?

First controlled experiment of testing tidal torque theory for individual halos

 

CC+21a, arXiv: 2012.02201

2. Do \(j_\mathrm{gal}\) retain memory
of the environment?

3. How is AM transported
to the disk?

Predicting angular momentum

\(z=0\)

\( z = 100\)

Predicting angular momentum

\(z=0\)

\( z = 100\)

[White 84]

Predicting angular momentum

\(z=0\)

\( z = 100\)

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

Predicting angular momentum

Time

Sampling \(p(\mathbf{J}|M_\mathrm{DM}, d_\mathrm{fil}, \dots)\)

Predicting angular momentum

Time

Predicting angular momentum

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

Improve theory?

  1. Go to non-linear order (non-linear TTT)
  2. Accurate prediction of Lagrangian patch boundaries (see Musso&Sheth 23)

1. Is \(j_\mathrm{DM}\) chaotic or our theory poor?

2. Do \(j_\mathrm{gal}\) retain memory
of the environment?

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

3. How is AM transported
to the disk?

1. Is \(j_\mathrm{DM}\) chaotic or our theory poor?

2. Do \(j_\mathrm{gal}\) retain memory
of the environment?

3. How is AM transported
to the disk?

CC+Pichon+Dubois, 21, arXiv: 2110.05384

Kocjan, CC in prep.

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

✅ 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]

What happens in the CGM?

Ongoing work by Z. Kocjan

✅ Cold accretion is slow to form stars

Quick depletion right after merger

[Kocjan, CC+ in prep]

The effects of environment on halo properties

Kraljic+18 [see also Laigle15, Song+21,…]

  • \( M_\mathrm{DM}(\text{node}) \) > \(M_\mathrm{DM}(\text{fil}) \) >\(M_\mathrm{DM}(\text{void})\), 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?

Predicting angular momentum

\(z=0\)

\( z = 100\)

\[\mathbf{L}_\mathrm{lin.} \propto \int\mathrm{d}^3q(\mathbf{q}-\bar{\mathbf{q}})\times \nabla\phi\]

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:

\[ \mathbf{L} \propto \epsilon_{ijk} T_{jl}I_{lk},\quad\text{with \textbf{T} the tidal tensor and \textbf{I} the inertia tensor}\]

[See also Danovich+15, Prieto+17]

✅ Most of re-alignment happens in the CGM  \(0.1\leq \displaystyle\frac{r}{R_\mathrm{vir}}\leq 0.3\)

The longer gas remains in CGM, the more it realigns with disk

[See also Danovich+15, Prieto+17]

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

Ex Uno Plures: direct measure of the impact of the cosmic web on individual objects to shed light on their population statistics

Corentin Cadiou
The Co-evolution of the CW and Galaxies across Cosmic Time

The causal origin of DM halo concentration

$$\rho_\mathrm{DM}(r) = \frac{\rho_0}{\frac{r}{R_\mathrm{vir}/c} \left(1 + \frac{r}{R_\mathrm{vir}/c}\right)^2}$$

Wechsler+02

Origin of scatter at fixed \(M_\mathrm{vir}\)?

Predicting angular momentum

  • Angular momentum of individual regions can be predicted accurately.
  • AM of halos ⇒ requires boundaries of patch

\[\mathbf{L}_\mathrm{lin.} \propto \int\mathrm{d}^3q(\mathbf{q}-\bar{\mathbf{q}})\times \nabla\phi\]

[On patch boundaries: see Lucie-Smith+18]

Splicing in 1D

Splicing in 1D

Most likely* field \(f\) with

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

Mathematically \(f\) is solution of:

\( f= a\) in \(\Gamma\)

minimizes \(\mathcal{Q} = (b-f)^\dagger\mathbf{C}^{-1}(b-f) \) outside \(\Gamma\)

Can we control baryonic
angular momentum?

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.

Temporary conclusions

  • 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

Galaxy formation in cosmology: the role of the environment

Environmental effects:

  • source of “pollution” in weak lensing surveys
    ⇒ intrinsic alignment
     
  • extra parameters in semi-analytical models
    ⇒ galaxy-halo correlation

+

\( R_{1/2} \)

\( l_0 \times 1.2\)

\( l_0 \times 1.5\)

\( l_0 \times 0.66\)

\( l_0 \times 0.8\)

\( l_0 \times 0.66\)

\( l_0 \times 0.8\)

\( l_0 \times 1.2\)

\( l_0 \times 1.5\)

\( l_0 \times 1.2\)

\( l_0 \times 1.5\)

\( l_0 \times 0.66\)

\( l_0 \times 0.8\)

\( l_0 \times 1.2\)

\( l_0 \times 1.5\)

\( l_0 \times 0.66\)

\( l_0 \times 0.8\)

  • 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?

How to explain environmental effects?

[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

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?

The origin of high \(z\) angular momentum

[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?

The origin of high \(z\) angular momentum

[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?