The edge of darkness, and other halo surprises

The edge of darkness, and other halo surprises Benedikt Diemer ITC Fellow, Harvard-Smithsonian Center for Astrophysics (in collaboration with Andrey Kravtsov and Surhud More) APEC Seminar IPMU 4/7/26

Strength of density fluctuations Dark matter power spectrum 4 2 P (k) [(Mpc/h) 3 ] 2 4 6 8 2 4 3 2 2 3 4 k [Mpc h] Large < Scale > Small CAMB, Lewis et al. 2

Dark matter power spectrum P (k) [(Mpc/h) 3 ] 4 2 2 4 6 5 Mpc/h δ = ρ/ρ m - 8 2 P (k) [(Mpc/h) 3 ] 4 4 3 2 2 3 4 3 2 k [Mpc h] k [Mpc h] P (k) [(Mpc/h) 3 ] 4 2 2 4 6 8 2 4 3 2 2 3 4 k [Mpc h]

N-body simulations P (k) [(Mpc/h) 3 ] 4 2 2 4 6 8 2 4 3 2 2 3 4 k [Mpc h] Crocce et al. 26

89 Mpc Visualization code: Phil Mansfield

Mpc

N-body simulations 2 Mpc/h 3 Density at z = 2 2 2 y (h Mpc) 5 2 2 4 6 y (h Mpc) 8 2 6 6 5 4 4 3 2 3 2 3 8 2 5 2 5 5 3 log ( / m ) 25 log ( / m ) 3 z (h Mpc) 2 2 log ( / m ) z (h Mpc) 4 3 62.5 Mpc/h 4 25 Mpc/h 5 z (h Mpc) 6 log ( / m ) 2 25 Mpc/h z (h Mpc) 8 3 z (h Mpc) log ( / m ) Mpc/h 5 Mpc/h log ( / m ) 2 2 3 y (h Mpc) 4 5 5 5 y (h Mpc) 2 25 2 4 6 8 y (h Mpc) 2 2 3 4 y (h Mpc) 5 6 Diemer & Kravtsov 24, 25 Springel 25 Crocce et al. 26 Behroozi et al. 23ab

2 3 4 2 Mpc/h 4 3 2 25 Mpc/h z (h Mpc) log ( / m ) z (h Mpc) 2 4 6 y (h Mpc) 6 2 5 62.5 Mpc/h 3 2 4 2 3 log ( / m ) 2 6 8 y (h Mpc) 5 y (h Mpc) 4 2 5 2 3 y (h Mpc) 4 2 8 3 2 25 8 5 8 4 4 6 y (h Mpc) 6 8 2 6 25 Mpc/h 4 5 2 3 2 y (h Mpc) z (h Mpc) 2 2 5 2 5 Mpc/h log ( / m ) z (h Mpc) 6 5 log ( / m ) 8 2 Mpc/h z (h Mpc) 3 log ( / m ) 2 3 4 y (h Mpc) 5 6 Springel 25 Crocce et al. 26 Behroozi et al. 23ab

Initial peaks δ Top hat Real peak Gaussian r Bardeen et al. 986 Dalal et al. 28

Mass accretion history M(z) δ r Slow accretion regime Fast accretion regime Formation time time Wechsler et al. 22 van den Bosch 22 Zhao et al. 23/29 Dalal et al. 28

Density profile δ log ρ r Shallow inner profile M(z) time Steep outer profile log r Dalal et al. 28 Ludlow et al. 23

Density profile log ρ Scale radius: d log(ρ) / d log(r) = -2 Outer radius (enclosing some mean overdensity) Mass: M Δ = 4π/3 Δ ρ ref R Δ 3 rs R2c Rvir R2m log r

Navarro-Frenk-White profile log ρ ρ r - ρ r -2 ρ r -3 Concentration: c Δ = R Δ / r s rs R2c Rvir R2m log r Navarro et al. 995/996/997

Navarro-Frenk-White profile log ρ high concentration low concentration rs rs R2m log r Navarro et al. 995/996/997

Questions. Can we find a universal concentration-mass relation? 2. Are the outer profiles universal? 3. Is there a well-defined edge to a halo?

Concentration-mass models Navarro et al. 996 Navarro et al. 997 Avila-Reese et al. 999 Jing 2 Bullock et al. 2 Eke et al. 2 Wechsler et al. 22 Zhao et al. 23 Colin et al. 24 Dolag et al. 24 Neto et al. 27 Duffy et al. 28 Maccio et al. 28 Gao et al. 28 Zhao et al. 29 Klypin et al. 2 Munoz-Cuartas et al. 2 Prada et al. 22 Giocoli et al. 22 Bhattacharya et al. 23 Ludlow et al. 24 Dutton & Maccio 24 Klypin et al. 25

Power-law fits Munoz-Cuartas et al. 2 log (c) log (M) Avila-Reese et al. 999 Jing 2 Neto et al. 27 Duffy et al. 28 Maccio et al. 28 Gao et al. 28 Klypin et al. 2 Munoz-Cuartas et al. 2 Dutton & Maccio 24

History-based models Wechsler et al. 22 cvir = Rvir / rs Formation scale Navarro et al. 997 Bullock et al. 2 Eke et al. 2 Wechsler et al. 22 Zhao et al. 29 Giocoli et al. 22 Ludlow et al. 24

Concentration-mass relation Concentration c2c 5 4 z =. z =.5 z =. z =.5 z =2. z =4. z =6. 3 2 3 4 5 M 2c (h M ) Halo mass Diemer & Kravtsov 25

Is there an upturn? All Relaxed Ludlow et al. 22 Prada et al. 22 Ludlow et al. 22 Meneghetti & Rasia 23

Concentration-mass relation Concentration c2c 5 4 z =. z =.5 z =. z =.5 z =2. z =4. z =6. 3 2 3 4 5 M 2c (h M ) Halo mass Diemer & Kravtsov 25 Dutton & Maccio 25

Peak height ν δ / σ Bardeen et al. 986

Peak height ν δ / σ Bardeen et al. 986

Concentration-peak height relation Concentration c2c 5 4 z =. z =.5 z =. z =.5 z =2. z =4. z =6. c2c 5 4 z =. z =.5 z =. z =.5 z =2. z =4. z =6. 3 3 2 3 4 5.5 2 3 4 5 M 2c (h M ) 2c Halo mass Peak height Prada et al. 22 Ludlow et al. 23 Diemer & Kravtsov 25

Power spectrum slope Halo mass (h M ) 5 5 P (k) [(Mpc/h) 3 ] 4 2 2 4 6 8 Eisenstein & Hu 998, no BAO c2c 5 z =. z =.5 z =. z =.5 z =2. z =4. z =6. 4 n = d ln P/d ln k.5 2. 2.5 3.5 2 3 4 5 2c 3. 2 3 4 k [h/mpc] Eisenstein & Hu 998 Diemer & Kravtsov 25

Effects of power spectrum slope Substructure Peak shape Isolated halo Accreted subhalos Smooth accretion Bardeen et al. 986 Moore et al. 998 Dalal et al. 2

3 n = -2.5 n = -2 2 log ( / m) 3 8 2 z (h Mpc) 6 n = -.5 n = - 4 log ( / m) 2 2 4 6 8 y (h Mpc)

Simulation Model z =. z =.5 z =. z =.5 z =2. z =4. z =6. c2c 5 c = c(m, z, Ω x, ) 4 3 c 2c = c 2c (ν, n) c/cfit... 2 3 4 5 M 2c (h M ) Diemer & Kravtsov 25

Comparison to CLASH observations 7 6 This work, z=.4 CLASH, This work, weak z= and strong, Merten + 4 CLASH, weak, and Umetsu strong, + 4 Merten + 4 CLASH, weak, Umetsu + 4 c2c 5 4 3 2 cobs/cmodel.4.2..2.4 5 4 5 M 2c (h M ) Umetsu et al. 24 Merten et al. 24 Meneghetti et al. 24

Micro-halos at high redshift z 3 M M earth -M 6 Simulation, z= 26 (Diemand + 25) Simulation, z= 3 (Anderhalden + 23) Simulation, z= 32 (Ishiyama 24) 4 c2c 2 2 3 Diemand et al. 25 Anderhalden & Diemand 23 Ishiyama 24

Micro-halos at high redshift z 3 M M earth -M 6 orders of mag. below calibrated masses! c2c 6 4 Simulation, This work, z= 3 26 (Diemand + 25) Simulation, This work, n= z= 33.5 (Anderhalden + 23) Simulation, z= 32 26 (Ishiyama (Diemand + 24) 25) Simulation, z= 3 (Anderhalden + 23) Simulation, z= 32 (Ishiyama 24) 2 2 3 Diemand et al. 25 Anderhalden & Diemand 23 Ishiyama 24

Mass accretion history Ω x, σ 8, P(k) c

We found a universal c-m relation, and thus a universal inner profile. But what about the outer profile?

4 Small halos ( <M<3 ) / m 3 2 = d log /d log r 2 3..5 5 r/r vir 4 NFW fit Einasto fit..5 5 r/r vir Large halos (M> 5 ) / m 4 3 2 = d log /d log r 2 3..5 5 4 NFW fit Einasto fit..5 5 Diemer & Kravtsov 24 r/r vir r/r vir

3 3 < M < 4 (r/r2m) 2 / m 2 < < < < 2 2 < < 3 > 3..5 5 = d log /d log r 2 3 4..5 5 r/r 2m r/r 2m Γ = Δ log(m vir ) / Δ log(a) Diemer & Kravtsov 24

New fitting function M>.5 5 3.4 3 <M<.4 4.4 <M<2.6 (r/r2m) 2 / m 2 = d log /d log r 2 3 4..5 5 r/r 2m..5 5 r/r 2m % accuracy (selected by mass or accretion rate) Valid between. and 9 R vir

The outer profiles are not universal, they exhibit a steepening that depends on the mass accretion rate Is there an edge to a halo?

R 2c Halo finder: Rockstar (Behroozi et al. 23)

R vir Halo finder: Rockstar (Behroozi et al. 23)

Spherical collapse model Turnaround radius, r ta Outermost infalling shell Fillmore & Goldreich 984 Bertschinger 985 Diemand & Kuhlen 28 Vogelsberger et al. 2 Lithwick & Dalal 2 Adhikari et al. 24

Spherical collapse model 5 4 3 Secondary infall ( = 3.) ρ r -9/4 / m 2 2 r/r ta Fillmore & Goldreich 984 Bertschinger 985 Diemand & Kuhlen 28 Vogelsberger et al. 2 Lithwick & Dalal 2 Adhikari et al. 24

Spherical collapse model Adhikari et al. 24 cf. Diemand & Kuhlen 28

The Splashback Radius 5 4 Secondary infall ( = 3.) Diemer & Kravtsov 24 / m 3 2 Edge in self-similar model 2 r/r ta Fillmore & Goldreich 984 Bertschinger 985 Diemand & Kuhlen 28 Vogelsberger et al. 2 Lithwick & Dalal 2 Adhikari et al. 24

The Splashback Radius R vir R 2m R splashback R splashback = f(γ, z) R 2m.8 f.6 2 =.8 2 =2.7 4 3 2 y (h Mpc) z (h Mpc) log ( / m) 2 2 2 2 x (h Mpc) 2 2 x (h Mpc) Low accretion rate High accretion rate Diemer & Kravtsov 24 More, Diemer & Kravtsov 25

R sp /M sp as a function of MAR.6.4 z =. z =.5 z =. z =2. z =4..4 Rsp/R2m.2 Msp/M2m.2...8 2 3 4 5.8 2 3 4 5 More, Diemer & Kravtsov 25 cf. Vogelsberger et al. 2 cf. Adhikari et al. 24

Do the Milky Way and Andromeda halos overlap? R sp 425 kpc R vir = 244 kpc R sp 54 kpc R vir = 33 kpc Milky Way, M vir = 8 M Andromeda, M vir =.7 2 M distance = 78 kpc More, Diemer & Kravtsov 25 Diaz et al. 24

Mass accretion rate dm 2c /dt dm sp /dt dm 4r s /dt M vir () = 9 M /h M vir () = 2 M /h M vir () = 5 M /h dm/dt/mvir, [Gyr ] 2 2 3 z More, Diemer & Kravtsov 25

R sp in cluster member profiles Patej & Loeb 25 cf. Tully 25

R sp in cluster member profiles More et al. 25 Miyatake et al. 25

R sp in cluster member profiles More et al. 25 Miyatake et al. 25

R sp in cluster member profiles More et al. 25

Can we measure R sp in individual simulated halos?

R sp in individual halos 3 R 2m 2 [ m] r [Mpc/h] Mansfield et al. 26 (in prep.)

SHELLFISH Mansfield et al. 26 (in prep.)

Finding R sp in trajectories 9 9 9 2 8 7 R 2m Particle 8 7 R 2m Particle 8 7 R 2m Particle R 2m Particle 6 6 6 8 r (h kpc) 5 4 r (h kpc) 5 4 r (h kpc) 5 4 r (h kpc) 6 3 3 3 4 2 2 2 2 2 4 6 8 2 4 2 4 6 8 2 4 2 4 6 8 2 4 2 4 6 8 2 4 6 6 3 4 4 4 2 3 vr (h kpc/gyr) 2 2 vr (h kpc/gyr) 2 2 vr (h kpc/gyr) 2 vr (h kpc/gyr) 2 2 4 4 3 3 6 2 4 6 8 2 4 6 2 4 6 8 2 4 4 2 4 6 8 2 4 4 2 4 6 8 2 4 t (Gyr) t (Gyr) t (Gyr) t (Gyr)

Finding R sp in trajectories 3 35 3 3 25 R 2m Particle 3 R 2m Particle 25 R 2m Particle 25 R 2m Particle r (h kpc) 2 5 r (h kpc) 25 2 5 r (h kpc) 2 5 r (h kpc) 2 5 5 5 5.6.65.7.75.8 5.6.65.7.75.8.6.65.7.75.8.6.65.7.75.8 5 2 3 5 2 vr (h kpc/gyr) 5 5 vr (h kpc/gyr) vr (h kpc/gyr) vr (h kpc/gyr) 5 5 5 2 2 5 2.6.65.7.75.8 3.6.65.7.75.8 3.6.65.7.75.8 2.6.65.7.75.8 t (Gyr) t (Gyr) t (Gyr) t (Gyr)

Finding R sp in trajectories R 2m 5th percentile 2. 2.8.6.4 r (h kpc) 8 6.2..8 log (N + ) 4.6 2.4.2 2 4 6 8 2 4 t (Gyr).

Finding R sp in trajectories 2 R 2m 5th percentile, smr. 5th percentile, smr. 5th percentile, smr. 2..8.5.6.4. r (h kpc) 8 6.2..8 log (N + ).5 log (msub/mhost) 2. 4.6 2.4 2.5.2 2 4 6 8 2 4 t (Gyr). 3.

Finding R sp in trajectories 2 R 2m 5th percentile 75th percentile 9th percentile 2..8.5.6.4. r (h kpc) 8 6.2..8 log (N + ).5 log (msub/mhost) 2. 4.6 2.4 2.5.2 2 4 6 8 2 4 t (Gyr). 3.

Finding M sp in trajectories 4 3 M 2m 5th percentile, smr. 5th percentile, smr. 5th percentile, smr. 2..8.5.6.4. M (h M ) 3 3 2 3.2..8 log (N + ).5 log (msub/mhost) 2..6 3.4 2.5.2. 2 4 6 8 2 4 t (Gyr). 3.

Finding M sp in trajectories 4 3 M 2m 5th percentile 75th percentile 9th percentile 2..8.5.6.4. M (h M ) 3 3 2 3.2..8 log (N + ).5 log (msub/mhost) 2..6 3.4 2.5.2. 2 4 6 8 2 4 t (Gyr). 3.

Results: R sp -Γ relation 2.5 SPLASH (75th pcntl.) MDK5 2. Rsp/R2m.5..5 2.5 z =. z =.5 z =. z =2. z =4. Msp/M2m 2..5..5 5 5 5 5 5 5 5 5 5 5 2m 2m 2m 2m 2m

Results: Δ sp 5 z =., SPARTA z =2., SPARTA 4 3 75 sp 2 2 2 4 6 8 2m

Spherical collapse model Shi 26

Results: Δ sp 5 4 z =., SPARTA Shi 26 z =2., SPARTA 3 75 sp 2 2 2 4 6 8 2m Shi 26

Results: Δ sp 5 4 z =., SPARTA Adhikari et al. 24 z =2., SPARTA 3 75 sp 2 2 2 4 6 8 2m Adhikari et al. 24

Future directions Measure R sp in individual halos Quantify the mass function and accretion rates of M sp Create halo catalogs and merger trees based on R sp Find more observational signatures of R sp

The Colossus Code Cosmology from colossus.cosmology import cosmology cosmo = cosmology.setcosmology('wmap9') xi = cosmo.correlationfunction(.) Concentration from colossus.halo import concentration as hc c = hc.concentration(e2, 'vir',., model = diemer5') Density profiles from colossus.halo import profile_nfw as nfw from colossus.halo import profile_dk4 as dk4 p = nfw.nfwprofile(m = E4, mdef = 'vir', c = 4., z =.) Sigma = p.surfacedensity(5.) p2 = dk4.dk4profile(m = E4, mdef = 'vir', c = 4., z =.) splashback_radius = p2.rsp() http://www.benediktdiemer.com/code/

Conclusions Concentrations are universal when expressed as a function of peak properties The outer profiles are not universal, they depend on the mass accretion rate and are not well described by the NFW form The splashback radius provides a physical halo boundary Diemer & Kravtsov 24 ApJ 789, arxiv 4.26 Diemer & Kravtsov 25 ApJ 799, 8 arxiv 47.473 More, Diemer & Kravtsov 25 arxiv 54.559