Towards Modeling Supernovae in Galaxy Formation Simulation
112Yuri Oku , Kentaro Nagamine , Ikkoh Shimizu
1Theoretical Astrophysics, Department of Earth & Space Science,Graduate School of Science, Osaka University
2National Astronomical Observatory of Japan
3.2. Result2: Eﬀect of supernova feedback and star formation eﬃciency

Understanding physical processes of galaxy evolution is one of the mostimportant goals in modern astronomy. From Subaru Hyper Supreme-Cam
survey data, Harikane et al. (2018) found a tight relation of SFR/Ṁh – Mhshowing no signiﬁcant evolution beyond 0.15 dex in the wide mass range
over redshift z ∼ 4-7. This weak evolution suggests that the SFR/Ṁh – Mhrelation is a fundamental relation in high-redshift (z ≥ 4) galaxy formation.
In this study, we investigate whether the SFR/Ṁh – Mh relation obtained
from observations can be reproduced using cosmological hydrodynamicalsimulation. SFR and Ṁh are related to the time evolution of galaxies, andsince materials accreted in galaxies are thought to contribute to starformation through various physical processes, it is important forunderstanding galaxy formation to verify the relation between thesequantities theoretically using cosmological simulation.

Table 2: List of simulations with diﬀerent parameters compared in this study.

Run name
L10N128
L10N128 sfeﬃciency0005
L10N128 K70T30

L10N128 sniieventnumber4nspawn1
10 1
10 2

2. Method

10 3

We use smoothed particle hydrodynamics code Gadget3-Osaka[Aoyama et al.(2017), Shimizu et al.(2019)]. We employ four diﬀerent
resolution and volume simulations as summarized in Table 1. We use theFOF algorithm and SUBFIND algorithm [Springel et al.(2001)] to identify
halos and galaxies in simulations (Figure 1).

410 101Box size
particle number(h−1Mpc (comoving))
2 × 5123
32 × 128
2 × 1283
2 × 2563

100201010102

10 2gravitational
softening length−1(h kpc (comoving))
6.5
5.2
2.6
1.3

10 3
4
10 10
1Ha18
fit using Mc09
L10N128
L10N128_sfefficiency0005
L10N128_K70T30
L10N128_sniieventnumber4nspawn1

101
100Mh(1010M )10210010 1SFR/Mh

L100N512
L20N128
L10N128
L10N256

101100Mh(1010M )10 1
SFR/MhName

Ha18
fit using Mc09
L10N128
L10N128_sfefficiency0005
L10N128_K70T30
L10N128_sniieventnumber4nspawn1

100

Table 1: The four diﬀerent resolution and volume simulations are employed in this study.

10 2
10 3
410 101SFR(M /yr)

10 3
10 4

10 2 10 1 100 101Mh(1010M )Ha18
fit using Mc09
L10N256
L10N128
L20N128
N512L100102 103

Figure 2: SFR/Ṁh – Mh relation

10 4

10 2100
M * (1010M )Sc15
L10N256
L10N128
L20N128
L100N512102

Figure 3: Star-Forming
Main Sequence104103102

McBride+2009
Be13L10N256L10N128
L20N128
N512L100
102 103101100

1Figure 2 shows SFR/Ṁh – Mh relation at redshift
10 10
2 10 1 100
101Mh(1010M )z = 6. SFR/Ṁh increases as spatial resolution
Figure 4: Halo mass
increases. To identify the reason SFR/Ṁh – Mhaccretion rate
relation depends on resolution, we compare otherstatistical properties with previous studies. Figure 31010shows star forming main sequence compared with
Schreiber et al. (2015; Sc15), and ﬁgure 4 shows halo 1010mass accretion rate compared with Behroozi et10al. (2013;Be13) and McBride et al. (2009;Mc09).
10These relations do not show resolution dependence
10 101010101010
M (10 M )and ﬁt with previous studies. Figure 5 shows galaxy
stellar mass function and this function show the same Figure 5: Galaxy stellar
mass function
trend with SFR/Ṁh – Mh relation.

dn/dlogM* (Mpc 3dex 1)

2346321*0101

We ﬁnd our simulation has dependence on resolution, and one major reason of thisdepencency is the modeling of supernovae. Now we are trying a new scheme ofmodeling supernovae. And also, now we are studying about blast wave of supernovae
and its eﬀect on ISM.
References
Aoyama, S., Hou, K., Shimizu, I. et al. 2017, MNRAS, 466, 105
Harikane, Y., Ouchi, M., Ono, Y., et al. 2018, PASJ, 70, S11
McBride, J., Fakhouri, O. & Ma, C. 2009, MNRAS, 398, 1858
Planck Collaboration XIII 2016, A&A, 594, A13
Schreiber, C., Pannella, M., Elbaz, D., et al. 2015, A&A, 575, A74

57

Our results are summarized below:
1 We investigate whether the SFR/Ṁh – Mh relation obtained from observations
can be reproduced using cosmological hydrodynamical simulation. However, oursimulation results show resolution dependence, and the result of high resolution
simulation show higher SFR compared with observation.
2 We run a series of simulations as summarized in Table 2 to investigate therelation between resolution, star formation eﬃciency and feedback. We ﬁnd starformation is suppressed by change of parameters, but our result still have higher
SFR compared with observation.

Behroozi, P., Wechsler, R. H., & Conroy, C. 2013, ApJ, 770, 57

L10N256L10N128
L20N128
L100N512
N216L10
N400L34
N600L120
Be19Duncon
GrazianSongStefanon

1102

5. Further work

105Mh(M /yr)

SFR/Mh10 2101100Mh(1010M )4. Summary

3.1. Result1: Dependence on resolution

10 1

Ha18fit using Mc09
L10N128
L10N128_sfefficiency0005
L10N128_K70T30
L10N128_sniieventnumber4nspawn1

We run a series of simulations assummarized in Table 2 to investigate therelation between resolution, star formationeﬃciency and feedback. The parametersof our ﬁducial run is as follows: starformation eﬃciency is 0.05, 30 per centkinetic feedback and 70 per cent thermal
feedback, number of feedback event
number nfb is 8 and number of starparticles spawn from a gas particle nspawn
is 2. Figure 6 shows the redshift evolutionof SFR/Ṁh – Mh relation. We ﬁnd thatstar formation is suppressed by increasing
the energy released by single supernova (L10N128 sniieventnumber4nspawn1)
and by increasing the ratio of kinetic
feedback (L10N128 K70T30). Thissuggests that the eﬀect of blowing gas bykinetic feedback suppress star formation
more eﬀectively than thermal feedback.
We also ﬁnd that our results show thedecreasing trend of SFR/Ṁh – Mh, which
is opposite to Behroozi et al. (2013).

Figure 6: SFR/Ṁh – Mh relation atz =6 (top), 5 (middle), 4 (bottom)

Figure 1: A halo identiﬁed by using FOF algorithm (left), the central galaxy identiﬁed byusing SUBFIND (center) and the diﬀerence of left and center panel (right). Gray points
represent dark matter particles, yellow points represent star particles. Blue points represent
SFR-weighted gas particles.

103102101
100
10 110 210 3410 10
6NotesFiducial run
Fiducial run but star formation eﬃciency 0.005
Fiducial run but 70 per cent kinetic
feedback and 30 per cent thermal feedback
Fiducial run but nfb = 4, nspawn = 1

100

SFR/Mh

1. Introduction

Shimizu, I., Todoroki, K., Yajima, H., & Nagamine, K. 2019, MNRAS, 484, 2632
2103

Springel, V., White, S. D. M., Tormen, G., & Kauﬀmann, G. 2001, MNRAS, 328,726