始原ガス円盤分裂による多重星系形成と数値計算の不定性
島 和宏 (京都大学)

共同研究者: 細川 隆史 (京都大学)

初代星・初代銀河研究会2019@名古屋

mini halo

ownloaded from https://academic.oup.com/mnras/article-abstracponent. Within the central few au,
ur orders of magnitude higher than
PopIII andstars
sink particles,
does binary
not show aformationcles (e.g. Clark et al. 2011b). This is
Cosmologicalsimulationss typicallydo not resolve
the gas on
and instead the mass is accreted onmeter therefore does not diverge atl below unity, which is reflected byspiral arm patterns on sub-au scales
low mass starfrequency on these scales drops to survivors?

fragmentation& binary formation ?

GW source?

withradii,
the orbital
frequency#, whichappropriate
Kepleribmall
but decreases
to wellbelow isunity,
which isfor
reflected
scs.
TheQ
parameter
determines
whether
perturbationsinhedevelopmentof
pronounced
spiralarm
patterns
onsub-auscale
Fragmentation of primordial gas disk
thin,times.
isothermal
disc cangrow. For
thickscales
discs, drops
as is ttfinitely
very early
The orbital
frequency
on thesecollapse of primordial gas

gravitational instability
and fragmentation(Greif et al. 2012)binary?

only for ~10 yrs after the first protostar formation-> A sub-grid model (sink particle) is necessary

Resolution dependency with sink particles
higher resolution
0.5 pc0.013
pc haloes
0.12 pc
Fragmentation in atomic
cooling4643(Regan and Downes 2018)

5 sinks

22 sinks

81 sinks

physical ? or numerical ?

or an entire cluster of stars. In our study here, the numerical particle
efinement level.
the dark matter par=0.3183,"=0.0463,
σ=0.8347,
andh=0.6704.
We
further−1b,
08
introduced will be a proxy for star formation (fragmentation) sites
0.01 pc h cofurther the dark ma
assume a spectral
index
for
theprimordial
densityfluctuationsofrepresent
only regions in which we expect star formation to be
fectiveGridtemper-codeand+sink
particle
dark matter particle
n = 0.9616.
likely to occur. Star (sometimes also known as sink) particles
were
30 000 K. This
Whitworth(2002) a
initially2018)
introduced into grid codes by Krumholz, McKee& We
Klein
rum of(Regana popu-and Downes(2015).
split part(2004). The SmartStar implementation used hereasalso
follows012; Sugimura,
foundfrom lowe
2 NUMERICALF R Awith
M EsomeWORK
thismodelmodifications.
We employ the samemodel side
for leng
ive temperature
comoving
gashaveaccretionas publicly
Krumholz
et al. (2004)
formeshour star particles
usingparticl
mperatureIndeter13 daughter
this study, weused theavailable
adaptive1 accretion radius of four cells and accreting gas
withbaseda dark on
matter p
fixed
in the irradiatedto study the fragmentation properties of gas
refinement codea ENZO
is done at
the Bondi–Hoyle
prescription.
althoughKrumholz
et aal.redshi
ux abovewithin
whichhaloes irradiatedhaveby a background
LW field.However,Into ENZOwe
Convergence
t
only
twowe
criteria
to evaluate
the formation halo.
of sink
partiis observed
dueaddeda new star(2004)
particleuse
type,
whichhave dubbed
SmartStar.
massesWe now describe
boththatcomponents.
cles;
the gas is at the highest refinement level andparticle
that thecell wasof Jcrit depends
density exceeds the Jeans density (see equation 6 in Krumholz et al.
2010; Sugimura2004), we also employ additional sink particle formation criteria.
2 Changeset:fedb30ff3
Similar to the prescriptions described by Federrath et al.
(2010), weed from a given
3 https://grackle.readth
only form sink particles when the following criteria aremet:pectra canvary
1 http://enzo-project.org/
4 Changeset:482876c7
e that in an ex(i) The cell is at the highest refinement level.
black hole for(ii) The cell exceeds the Jeans Density.
curve
thehttps://academic.oup.com/mnras/article-abstract/475/4/4636/4810577
H2nloadedinfrom(iii) The flow around the cell is converging along each axis.
Kyoto University userrther
09
May confirmed
2018(iv) The cooling time of the cell is less than the freefall time.
gh our choice of(v) The cell is at the minimum of the gravitational potential.
d by these studrom population
We calculate the gravitational potential in a region of twice theAMR:

ADAPTIVE-MESH REFINEMENT• create and destroy gridpatches dynamically (blockstructured)• grids at multiple resolutions• multiple refinement criteria:• density (gas or dark matter)• gradients, shocks• cooling time
• Jeans length• refine regions around particles• easy to create new criteria

Enzo v2.6 is now available!

https://enzo-project.org/

Initial conditions(density, x-y plane)

collapse

1 pc(an ideal rotating sphere)
cloud mass = 1.8 x 104 [Ms]mean density = 1.7 x 10-20 [g/cc]
rotation speed = 2.6 x 10-14 [rad/s]

Resolution dependency testwith sink particles

v.s.

with smart stars

run1: refinement level = 12
r_sink = 1.5e-04 pc = 31 AU
run2: refinement level = 14
r_sink = 7.6e-05 pc = 8 AU
run3: refinement level = 16
r_sink = 3.8e-05 pc = 1 AU

The number of particles v.s. time

The number of particles v.s. timeWhat is the difference?
sink particle

smart star

Sink particle creation(Federrath et al. 2010)+ on the highest level of refinement+ over density+ converging flow
+ not within the radius of an existing sink+ gravitational potential minimum
center 
sink radius<latexit sha1_base64="GKYudEs27NZth1tMIV7YQVkGYDA=">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</latexit>

racc ⇠<latexit sha1_base64="O47/tWgsUnOtgybHSWFGLJ1wim4=">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</latexit>

J(i, j, k)(additional checks)+ Jeans-unstable|Egrav | > 2 Eth+ is boundEgrav + Eth + Ekin < 0Gas accretion into sinks(Federrath et al. 2010)

criteria for gas accretionri < racc(within the radius)⇢gas > ⇢crit(overdense)

vrad < 0(incoming)

ekin + egrav < 0(bound)<latexit sha1_base64="2okWBsktvnp9pA8piidOOXvGdDk=">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</latexit><latexit sha1_base64="0hXJJqPjr13GZrfw7FQXN0JOU40=">AAACfXichVHLSsNAFD2N7/qquhHcBEvFhYSJClUXIrpx6asqqJQkju1gmoRkWtBSP8AfcOFKUUREf8KNP+DCTxCXCm4EvU0iIqLeYWbuPXPPnTNzTc8WgWTsIaE0NDY1t7S2Jds7Oru6Uz29q4Fb9i2es1zb9ddNI+C2cHhOCmnzdc/nRsm0+Zq5O1c/X6twPxCusyL3PL5VMgqO2BGWIQnKp/o3/aKbrxaMoKZOq1Fg+ULW8qk00yZDUyMnOx47k7qqayy0NGJbcFMX2MQ2XFgoowQOB5J8GwYCGhvQweARtoUqYT55IjznqCFJ3DJlccowCN2ltUDRRow6FNdrBiHboltsmj4xVWTYPbtkz+yOXbFH9vZrrWpYo65lj3Yz4nIv333Yv/z6L6tEu0Txi/WnZokdTIRaBWn3QqT+CiviV/aPnpenljLVIXbKnkj/CXtgt/QCp/JinS/ypWMkwwZEv6z+dD4bsDqq6WOavjienpmNW9GKAQximP47ixnMYwE5uvcAZ7jGTeJdySgjihalKomY04dvpmQ/ADkolI0=</latexit><latexit sha1_base64="N1t14EA7yiy111lbSkYXolhvvAM=">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</latexit>

sink radius<latexit sha1_base64="lfkvd1wFFUW7chN9s6GMivuZ6Vs=">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</latexit><latexit sha1_base64="GKYudEs27NZth1tMIV7YQVkGYDA=">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</latexit>

racc ⇠<latexit sha1_base64="O47/tWgsUnOtgybHSWFGLJ1wim4=">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</latexit>

JSummary

We performed simulations of primordial gas disk fragmentation
varying the resolution with two different sub-grid model.
sink particle

v.s.

smart star

Both of them are based on the same model (Federrath et al. 2010).
However, the results are different.
(the number of formed particles, the mass evolution)