Evolution of the angular momentumof the dark matter subhaloes

Daiki Osafune1, Keiichi Wada2, Tomoaki Ishiyama3, Takashi Okamoto1
1.Hokkaido University, 2.Kagoshima University, 3.Chiba University

Introduction To investigate the evolution of subhaloes, substructures of dark matter haloes, is important for understanding the evolutionof dark matter halo and galaxies. However, the mechanism of acquisition of angular momentum of subhaloes is not clear. The major axis of thedark matter subhalo tends to be in the radial direction of the host halo, and it was caused by the tidal ﬁeld of the host halo (Knebe et al. 2020).
Therefore, we infer that the subhaloes gain angular momentum from the torque exerted by the tidal force of the host halo, and we investigated
the inﬂuence of the host halo on the angular momentum of the subhaloes using high-resolution cosmological N-body simulation data.

Data : Shin-Uchuu simulation

We analyzed the high-resolution cosmological N-body simulation data,
Shin-Uchuu simulation (Ishiyama et al. 2021).

NameN

Shin-Uchuu

64003

Lϵmp

−1(h Mpc)−1(h kpc)−1(h M⊙)140.00.4

8.97 × 105

Analysis : The angle between vectors of angular momentum
We calculated the angle between the internal angular momentum (spin)of the subhalo (Jsub ), host halo (Jhost ) and the orbital angular momentumof the subhalo (Jorb ) and investigated its dependence on the distancefrom the center of the host halo (r /Rhost ).

We calculated Jorb and r /Rhost based on the position, radius, and velocity
in the data.

N : the total numbers of particle L : box length
ϵ: softening length m p: particle mass

Haloes and subhaloes are identiﬁed by ROCKSTAR halo ﬁnder (Behrooziet al. 2013a) and merger tree are constructed by the consistent tree
code (Behroozi et al. 2013b). We restricted our sample to subhalos with⃗
J host⃗J orbJ⃗

subcos θ (X1, X 2) ≡X1 ⋅ X 2
X1X2

⃗
V sub

X1,2 = Jhost , Jhost or Jorb

⃗
X sub

N > 10 3 particles and analyzed about 1.4 × 106 samples at z = 0.

Result 1: Dependence of cos θ (Jsub, Jhost) on the position at z = 0Fig.1：Sub-halo distribution divided by r /Rhost and cos θ (Jsub, Jhost) bins.
・The 1D (2D) Histgram shows the number of subhaloes belonging to bins r /Rhost or (and)cos θ (Jsub, Jhost), divided into 32 bins.
・Redline and error bars represent median and 25th and 75th percentile
・At the outskirt of the host halo (0.6 ≲ r /Rhost), Jsub is oriented randomly.
・At near the center of the host halo (r /Rhost ≲ 0.4), cos θ (Jsub, Jhost) tends to increase toward
the center, i.e. Jsub tends to orient in the same direction as Jhost.

Result 2: Dependance of cos θ (Jsub, Jhost)on Msub /Mhost

Fig.2: Same as Fig.1 but sample with 10−3 ≤ Msub /Mhost < 10−2( left panel)and 10−1 ≤ Msub /Mhost < 1(right panel)
・When Msub /Mhost is large (right), many subhaloes exist near the centerof host halo, and the tendency is stronger than Result1.
・On the other hand, when Msub /Mhost is small (left), fewer subhalos areexist near the center than on the outskirt of the host halo, and thedirection of the angular momentum of subhaloes tends to be random
to the center of the host halo from the outskirt of the host halo.

Result 3: Subhalo orbit and spin of subhalo and host halo

Fig.3: Same as Fig.1 but the Y-axis of left and right panel representcos θ (Jsub, Jorb) and cos θ (Jorb, Jhost) respectively.

・The spin and orbital momentum of subhaloes tends to align near thecenter of the host halo.
・It is consistent with the scenario where angular momentum is gainedby tidal torque from the host halo.
・The direction of the orbital angular momentum of many subhaloes isaligned with the spin direction of the host halo.

Summary and Discussion
・The subhalo acquires Jsub in the same direction as Jorb due to the tidal force exerted by the host halo.
・Jorb tends to align with the direction of Jhost.

・As a result, Jsub and Jhost tend to be oriented in the same direction near the center of the host halo.
・The dependence on the Msub /Mhost is due to the diﬀerence in timescales falling in the center.

Reference・Knebe, A., et al. 2020, MNRAS, 495, 3002
・Ishiyama T., et al., 2021, MNRAS, 506, 4210
・Behroozi P.S., et al. 2013a, ApJ, 762, L109
・Behroozi P.S., et al. 2013a, ApJ, 763, L18