Corentin Cadiou
@KITP | 7 Feb 2023

The origin of angular momentum:
from cosmic web to galaxy formation

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?

Angular momentum: bridging galaxies to cosmology?

Tillson+15

[AM: Dekel & Birboim 06; Stewart+11; Kim+11; Pichon+11; Codis+12; Danovich+12,15; Stewart+13; Codis+15; Prieto+15; Tillson+15; Stewart+17, Cadiou+21,…]

Dekel&Birnboim 06

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

Lower-zs:
intrinsic alignment problem

Tempel+13

Angular momentum: bridging galaxies to cosmology?

Tillson+15

Dekel&Birnboim 06

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

Lower-zs:
intrinsic alignment problem

Tempel+13

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: 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?
    Can we do better than statistical correlations?
  2. Do \(j_\mathrm{gal}\) retain memory of their environment?
    Can we spin a simulated galaxy up?
  3. Where is the CW/galaxy boundary?
    Need detailed sims of the CGM

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

Predicting angular momentum

\(z=0\)

\( z = 100\)

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:

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

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

Time

“Poorer” predictions

“Good” predictions

Predicting angular momentum

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

Improve theory?
Good model of Lagrangian patch boundaries (cf. M. Musso future talk)

or

Find more robust definition of AM?

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

Baryon angular momentum

Full hydro simulations
(10Mh @ DiRAC):

  • Resolve disk height
    \(\Delta x = 35\ \mathrm{kpc}\)
  • \(z \geq 2\), \(M_\mathrm{200c} = 10^{12}\ \mathrm{M}_\odot\)
  • SF + AGN & SN feedback
  • Tracer particles
    CC+19
  • 3 galaxies, 5× scenario each

\( j_0 \times 0.66\)

\( j_0 \times 0.8\)

\( j_0 \times 1.2\)

\( j_0 \times 1.5\)

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

Baryon angular momentum

Full hydro simulations
(10Mh @ DiRAC):

  • Resolve disk height
    \(\Delta x = 35\ \mathrm{kpc}\)
  • \(z \geq 2\), \(M_\mathrm{200c} = 10^{12}\ \mathrm{M}_\odot\)
  • SF + AGN & SN feedback
  • Tracer particles
    CC+19
  • 3 galaxies, 5× scenario each

\( j_0 \times 0.66\)

\( j_0 \times 0.8\)

\( j_0 \times 1.2\)

\( j_0 \times 1.5\)

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

… by delaying/hastening time of last major merger

INPUT  \(z=\infty\)

OUTPUT
\(z=2\)

\( j_0 \times 0.66\)

\( j_0 \times 0.8\)

\( j_0 \times 1.2\)

\( j_0 \times 1.5\)

\( j_0 \times 0.66\)

\( j_0 \times 0.8\)

\( j_0 \times 1.2\)

\( j_0 \times 1.5\)

✅ Stellar AM driven by (past) tides with the cosmic web (which can be predicted)

✅ Useful to make sense out of e.g. JWST data

✅ Changes in baryon spAM \(\propto\) changes in Halo spAM

\({\color{#808080}{\lambda_\mathrm{DM}}} \underset{f_j}{\Longrightarrow} \lambda_\mathrm{\color{#0000ff}{bar}\color{#daa520}{yon}} \underset{\text{SF+fb}}{\Longrightarrow} \color{#daa520}\lambda_\star\)

❗Per-galaxy fluctuation of \(\lambda_\star/\lambda_\mathrm{DM} \)

\(\Rightarrow\) cannot be captured with HOD modelling (cf. Boryana Hadzhiyska talk this morning)

Gas + stars spAM

Stars spAM

Halo spAM

Halo spAM

Where is the
CW — galaxy boundary?

Spoiler: probably within the CGM

CC+Pichon+Dubois, 21, arXiv: 2110.05384

 

By no means complete review!

[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

(looking for a PhD in the US!)

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

[Kocjan, CC+ in prep]

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]

Ongoing work by Z. Kocjan

(looking for a PhD in the US!)

\(z\approx 4-5\)

\(z\approx 2-3\)

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

Conclusion & outlook

Conclusion & outlook

  1. \(j_\mathrm{DM}\) responds linearly to perturbations
    Good accuracy (few ~10%) achievable for individual halos in principle iff correct growth rate+boundary
     
  2. \(j_\mathrm{gal}\) retain memory of the cosmic web
    Galaxies may be less stochastic than expected
    Intrinsic alignment to be expected
    Galactic spin & DM spins are (partially) independent at level of individual galaxies
     
  3. Boundary CW \(\rightarrow\) galaxy formation: CGM
    Buffer zone: transition from gravity-dominated to baryon-dominated regime

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

Effect(s) 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?

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 (\(N\)-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

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?