Angular momentum and galaxy formation
replacing galaxies in their cosmological environment
Corentin Cadiou
KITP Cosmic Web program 2023
The effects of environment on halo properties
\(v/\sigma\) at fixed \(M_\star\)
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
\(v/\sigma\) at fixed \(M_\star\)
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
Anisotropic 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
[also Dekel & Birboim 06, Danovich+15, Cadiou+21c]
Dekel&Birnboim 06
Highz:
most of mass + AM flow along filaments
Lowerzs:
intrinsic alignment problem
Tempel+13
Angular momentum: bridging galaxies to cosmology?
Tillson+15
[also Dekel & Birboim 06, Danovich+15, Cadiou+21c]
Dekel&Birnboim 06
Highz:
most of mass + AM flow along filaments
Lowerzs:
intrinsic alignment problem
Tempel+13
How do we detect 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
Adapted from Park+22
RodriguezGomez+22
Predictions for \(j_\mathrm{DM}\) remain qualitative
\(j_\mathrm{DM}j_\mathrm{\star}\)
strong detection of weak correlation
 Is \(j_\mathrm{DM}\) chaotic or our theory poor?
Can we do better than statistical correlations?  Do \(j_\mathrm{gal}\) retain memory of their environment?
Can we spin a simulated galaxy up?  What effect does anisotropic environment play in DM/gal formation?
Can we simulate a galaxy in ≠environments?
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:
\[ \mathbf{L} \propto \epsilon_{ijk} T_{jl}I_{lk},\quad\text{with T the tidal tensor and I the inertia tensor}\]
Predicting angular momentum
\(z=0\)
\( z = 100\)
[Genetic modifications: Roth+16, see also Rey&Pontzen 18, Stopyra+20]
Predicting angular momentum
Time
Predicting angular momentum
Time
Time
Poor predictions
Good predictions
✅ AM of fixed DM regions can be predicted (so is not chaotic!)
Improve theory? Need good model of Lagrangian patch boundaries
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
\( j_0 \times 0.66\)
\( j_0 \times 0.8\)
\( j_0 \times 1.2\)
\( j_0 \times 1.5\)
INPUT \(z=200\)
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)
More complex for DM / baryons
✅ Changes in baryon spAM \(\sim\) Changes in Halo spAM
Insight: matter in the outskirts (mostly gas & DM)
dominate spAM magnitude (& direction?)
Gas + stars spAM
Stars spAM
Halo spAM
Halo spAM
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
 Generate ICs
 Integrate (\(N\)nody)
 Select region of interest
 Trace back to ICs
 “Splice”
 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
Conclusion & outlook
Conclusion & outlook

Is \(j_\mathrm{DM}\) chaotic or our theory poor?
Poor theory! Good accuracy (few ~10%) achievable for individual halos in principle.

Do \(j_\mathrm{gal}\) retain memory of their environment?
Individual galaxies retain memory of env, can be controlled in simulations!
Galaxies may be less stochastic than expected

What effect does anisotropic environment play in DM formation?
Changing env causes
⇒ ~15% change in mass
⇒ 50% of population scatter for concentration
Very promising for intrinsic alignment studies!
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 LucieSmith+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 \(\mathcal{Q} = (bf)^\dagger\mathbf{C}^{1}(bf) \) 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 semianalytical models
⇒ galaxyhalo 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 selfregulation
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 preaccretion 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 preaccretion 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 preaccretion AM?
Alignment with environment?
Angular momentum and galaxy formation  KITP 2023
By Corentin Cadiou
Angular momentum and galaxy formation  KITP 2023
 25