12/6, 2019
高エネ研究会@蔵王温泉

宇宙初期天体の形成：初代星＆初代BH

大向一行
東北大学 天体理論

First StarsBefore First Stars=Simple Universe？

• well-defined initial condition Cosmological Initial Condition
Streaming motion(velocity difference between baryon and DM) was overlooked(Tseliakhovich& Hirata 2010)• simple chemistry and thermal process
Simple primordial gas (H, He,& slight amount of D, Li)
no external radiation field other than CMB, no Cosmic Ray
This is still OK(But: new missing process is sometimes found and added e.g., Li chemistry
DM annihilation might have played a role in heating/ionization)• simple dynamics weak magnetic fieldmagnetic fields may have been amplified by small-scale turbulent dynamo,
and may have played some role in dynamics and heating by ambipolar diffusion

Except very early universe,
predictable theory is well established ？？

Radiative cooling in primordial gas
Barkana & Loeb 2001

Atomic cooling(H Ly a transition)
efficient only T>8000K

H2 rovibrational coolingis importantin lower temperature

H2 is needed formaking the gas cold

H2 formation in primordial gas
At low densities (<108cm-3)

H- channel : e catalyzed
H + e  H- + g
H- + H  H2 + e(Peebles & Dicke 1968; Hirasawa+1969)

rate higher by an order of mag.

H2+ channel : H+ catalyzed (Saslaw & Zipoy 1967)
can be important
H + H+  H2+ + g
in strong radiation fields.
H2+ + H  H2 + H+At higher densities (>108cm-3)

3-body reactions (Palla, Salpeter & Stahler 1983)
H + H + H  H2 + H
H + H + H2  H2 + H2 . Makes the gas fully molecular at ~1011cm-3

First Star Forming Sites
ΛCDM cosmologySimulate starting from the density fluctuations
up to the formation of first object

First Objects to form stars:
small halos withvirial temperature Tvir > 1000K（minihalos ~106Msun, z~20-30）
600h-1kpc

First Star-forming Site

the gas in which cools by
H2 line emission andbecome denser

Star formation
Yoshida, Abel, Hernquist & Sugiyama (2003)

Thermal evolution of primordial gas
106Msun

104Msun

102Msun

1Msun

H2 CIE

H2 formation& cooling

adiabatic
contraction
H2 line optically thickLTE

adiabatic contraction

10-2Msun

10-4MsunH- channelH23-body reactione

collisional
dissociation

Runaway Collapse of Dense Cores to Protostars

PopI（KO & Nishi 1998)
Self-similar Collapse（up to n~1020cm-3）

Density, temperature,
velocity higher than in Pop Icase
０－７ in Figure is time
sequence

protostar（＝hydrostatic core)state 6; n~1022cm-3, Mstar~10-3Msun（similar to Pop I case）
temperature and density in the envelope arehigher than in Pop I case.

Birth of the first protostar
protostar~1000Msun~1/100Msun

Yoshida, KO,Hernquist 2008

densecore• Dense core (~1000Msun)
forms at ~104cm-3• Hydrostatic protostar(initial mass ~10-2Msun)
forms at ~1021cm-3

Protostar grows by accretion
1000Msunprimordial gas (Z=0)
no dust, low opacity⇒ lower radiation pressure
higher temperature (a few 100K)⇒ higher accretion rate

~0.01Msun

Both effects work to weaken
the stellar feedback effect Massive star will be formed.
Accretion terminates Final stellar mass

How much?

Cases with different accretion rates
KO & Palla (2003)

dM*/dt=8.8, 4.4, 2.2, 1.1 x 10-3 Msun/yrprotostellar
radius3b. “inflation”

KH timetKH=GM*2/R*L*
accretion time
tacc=M*/(dM*/dt)

All protostars go through the adiabatic and the KH contraction phases.
Subsequent phase depends on the accr. rate.
With low accretion rate (<dM/dtcrit=4 10-3Msun/yr):the star reaches ZAMS and accretion continues

With higher accretion rate (>dM/dtcrit) :the star starts inflating when L (=L*+Lacc ) becomes close to LEdd.

・Lacc ∝M*/R*

Feedback-limited mass of first stars
In non-spherical accretion:
mass of first stars is set by
the UV feedback
photoevaporation of disk

(McKee & Tan 08, Hosokawa+11/12,
Stacy+12, Hirano +14, Susa + 2014)

Accretion stops at ~40Msun
20M830M840M8

HII region
contour: density, color: temperature

Hosokawa, KO, Yoshida, Yorke 2011, 2012

Statistical Study: toward IMF
3D cosmological simulation+2D radiation hydro simulation
for star formation

Hirano et al. (+KO)
2014, 2015
studied>100-1000 halos

mass distribution of first stars
Hirano+ (KO)2014, 2015
studied>100-1000 halos

flat distribution in a widemass range:a few 10-100 Msun
even 1000Msun first stars
can be formed

First Binaries ?

Some first stars were also binaries
fragmentation during the collapse(“turbulent fragmentation”)

Turk et al. 2009

Stacy et al. 2010

From 2009 onward,
it becomes known
thatbinaries/multiples
are formed in thefirst star formation.

fragmentationof circumstellar disk
after protostar formation(“disk fragmentation”)
Clark et al. 2011

Greif et al. 2011

Earlier work on first binary formation
Rotation/Gravitational Energy

Machida, KO+ 2008

barotropic EOS from one-zone modelidealistic initial condition:
BE sphere (103cm-3)
density x 1.01 (α 0=0.83)
Rotation β 0Perturbation (bar Aφ + m=3)

All the cores with some rotation(b0> 10-6 - 10-5 fragment.
More prone to fragmentation
than present-day
Bar-mode perturbation

Radiative feedback in 3D
Hosokawa + (KO) 2016

fragmentation and migration…
Hosokawa + (KO) 2016

The central star grows very massive
before the UV feedback shut off the accretion.

But, radiation comes only from the central source.
 massive binary formation remains unexplored.

Multi-source simulation in AMRSugimura +(KO). in prep.
AMR + (M)HD + self-gravity+ sink particle method(Matsumoto 07 etc.)+ adaptive ray-tracing (ART) method for multiple soruces(e.g., Abel & Wandelt 02; Rosen et al. 2017)of EUV (H ionizing) & FUV (H2 dissociating) rad.
+ chemistry network & cooling/heating processes
w/ the primordial composition (zero metallicity)+ Cosmological initial cond. (Hirano et al. 15)
Halos C & D of Hosokawa+ (2016)

3D movieyr

8000auhalo C, rsink=64au

sink particle evolutionminihalo C, r =64au
sink(a)Evolutionary phases(a) initial frag.

(b)

(c)

sp0
sp2
sp3 sp4sp5(d)

sp6(b) acc. binary(c) late-time frag.

(d) photo-evap. ofmini-multiple system

0-2
2-3

0-6

0-4

50Msun + 50Msun

M M M

0-5 M 5-7

0-1

(t: time after 1st sink formation)

22

sink particle evolutionhalo D, rsink=64au
Evolutionary phases

(a)

(b)

(c)

(a) initial frag.
sp1(d)

(e)

sp0
sp2

(b) merger induced bya-few-body effect(c) accreting binary(d) internal photoevaporation(e) external photoevaporation

60Msun + 30Msun

0-2

0-1

M

Massive binaries are common among first stars
23

Toward MHD calculation:accurate ionization degree modelling neededMagnetic fields will change the picture ?
In Galactic ISM, B-fileds are almost in energy equi-partition:
EB ～Ekin～EgravRoles:•Support against the collapse•Jet/Outflow launching•Angular momentum transport
by magnetic braking, magneto-rotational instability•Suppressing fragmentation of diskdetermines frequency of binary formation(e.g., Machida & Doi ‘13)

Even in low-metallicity ISM, significant B-fields may be present
seed field (～10-19G) amplified by e.g., small-scale dynamo

Magnetic field dissipation
Ionization degree in star forming clouds is low  magnetic dissipation can occure.g., Wardle 2007
balance of Lorentz and drag forces for charged particles j
Hall parameterwith Ohmic, Hall, andPedersen conductivities

Ohmic, Hall and ambipolar diffusivities

Ionization degree controls magnetic dissipation

new chemical network
107+107=214 reactions among 23 species.

•all the reactions are reversed.
Rate coefficients for reverse reactions
calculated from the detailed balance.

accurate treatment of ionization degree
in primordial gas
Nakauchi, KO, Susa 2019

204 reactions (all reversed)
among 23 species:

major positive ions:

Li ionization by thermal photons
enhances ionization degreeat >1014cm-3

First Black HolesSupermassive BHs©EHTubiquitously reside at
the center of galaxies
BH mass correlateswith the bulge mass
© Cordes, Brown (STScI)

Like trainstations
Likecathedrals
in Japanesecities
inItalian towns

But its origin unknown

Highest-z SMBHs
SMBHs are already in existence in <Gyrs universe.
ULAS J1342
Banados+2017
MBH=0.8x109Msun z=7.54 (0.69Gyr)

ULAS J1120
Mortlock+2011
MBH=2x109Msun, z= 7.085 (0.77Gyr)

They are not alone:・Dozens of quasars have been found at z>6.5（Venemans +2014, Matsuoka+2017, 2018）

・Ultra-massive BH of 1.2x1010Msun at z=6.3 (Wu+2013)

SMBH growth time problem
via Eddington-limited
accretion:

MBH=Mini exp(t/tSal)
with Salpeter timetSal = esTc/4pGmH=0.05Gyr (e/0.1)© S.M.Chon© S.M. Chon (2018)

stellar-mass BH fails to reach supermassive by z~7.
More massive seeds or more rapid growth required.

seed BH formation scenarios
1) first star remnants2) direct collapse

3) stellar merger

Volonteri 2012

1) first star remnant BHs
1) first star remnants2) direct collapse

3) stellar merger

Volonteri 2012

getting more massive in recent years …
Hirano+ (KO)2014, 2015
studied>100-1000 halos

2014
2015

flat distribution in a widemass range:a few 10-100 Msun
even 1000Msun first stars
can be formed

Super-critical growth feasible?
Sugimura+ (KO) 2017, 2018

• accretion flow in the shadow can beprotected from radiative feedback.
But• angular momentum reduces theaccretion rate unlessaccretion rate
/ Bondi rate

centrifugal radius < ~5% Bondi radius

centrifugal radius/ Bond iradius

Rapid accretion growth is not so easy2) direct collapse BHs
1) first star remnants2) direct collapse

3) stellar merger

Volonteri 2012

Requirements for SMS formation
by direct collapse
Collapse phase:• Monolithic collapse without fragmentation– Rapid cooling  fragmentation
Without such cooling  no fragmentation.

Accretion phase:• Formation timescale shorter than lifetime (~2Myrs)– High accretion rate
>M*/t*~105Msun/2x106yr ~0.05Msun/yr• Protostellar Feedback suppressedCloud collapse in intense FUV field

H atomic cooling• No rapid cooling phase monolithic collapse

J>JcritJ<JcritH2 molecularcooling

If FUV radiation is more intensethan the critical value Jcrit,
the cloud cools solely by atomiccooling.

Omukai 01•high temperature (at ~8000K)
during the collapse
high accretion rate inprotostellar phasedM*/dt ~cs3/G~ 0.06Msun/yr (T/104K)3/2

Supermassive stars (>105Msun) will form

Monolithic Collapse of Atomically Cooling Cloud
Inayoshi, Omukai & Tasker (2014)

e.g., Bromm & Loeb 2003, Latif +, Regan +No major eposode of fragmentation
small protostar (~0.1Msun) is formed

Accretion evolution to supermassive stars
End product of the collapse phase：
protostar of 0.1 Msun
surrounded by gas envelope of 105-6 Msun,
accreting with 1Msun/yr
Accretion rate

Does the star becomes super-massive
without feedback stopping its growth?

“Stellar Inflation” by rapid accretion
Hosokawa, Yorke, KO (2012)

Stellar radius ( R8 )With rapid massaccretion(> 0.01 Msun/yr),
protostar does notreach the main
sequence.
stellar mass ( M8 )Instead, its radiusinflates enormously
to ~10AU.

Super-giant protostar on HR diagram
Hosokawa+(KO) (2013)

low effective temperature
at several 103K
(looks like a red-giantstar )negligible UV luminosityand feedback
accretion continues
unhindered and the star
becomes supermassive

General relativistic collapse
stellar evolution caluculation with rapid accretion

Umeda, Hosokawa,KO & Yoshida 2016

H burning(CN cycle)↑：H exhaustion

SMS collapses to BH at 105-106Msun
depending on its accretion ratefuel exhaustion

general relativistic instability

The onset of GR instability at 1.4x105Msun was predicted from n=3 polytrope model→BUT the collapse starts at somewhat later (more massive) in reality
It was believed that the collapse begins before the nuclear burning.
→BUT the hydrogen is exhausted in the ＜1Msun/yr cases.

45

entropy distribution：envelope not in n=3 polytrope

GR instability
criterion for
β=const. star46

Stringent condition for FUV channelJcrit : intensity at LW wavelenths (12.4eV)
needed for atomic cooling.

Sugimura, KO, Inoue 2014

Pop III
H2 photodissociation

Pop IIsofthard
Radiation (color) temperatureJcrit increases with radiation temperature(i.e., hardness)

H- photodetachment and H2 formation
H2 formation via H- channel
H + e  H- + g
H2 formation: H- + H  H2 + e: H- + g  H + e

Photodetachment

With the same J21,
softer (lower TUV)radiation is more
effective in suppressing H2formationJcrit for Starburst Galaxies
Using realistic spectra of starbursts…
starburst

Jcrit?

potential siteof direct collapse

Required Jcrit is very high (~1000)
even for PopII galaxies (unless >several 100Myr)

Only in rare environments ?
Jcrit~1000 from our result
Ahn et al. (2009)

At high redshift
UV radiation are weaker-> No/few direct collapse

At lower redshift
halos are metal enriched-> No /few direct collapse•Direct collapse occurs only in very rare environments(~1Gpc-3) .
•Direct collapse may still account for high-z SMBH.

Alternative channels?
shock heating in dense primordial gas
Inayoshi & KO 2012

direct collapse•

shocksat >103-4/cc,with> several 103K
– H2 collisionallydissociated– Fragments at8000K with>~105Msun– Isothermalcollapse
thereafterAlternative channels?
streaming motions of baryons
Hirano, Hosokawa, Yoshida & Kuiper (2017)•In halos with large streaming motions,high accretion rate (~0.1Msun/yr) is realized.
•Formed star grows to ~105Msun.
•Expected number ~1 Gpc-3
naturally account for highest-z SMBH
(how about other SMBHs in less early universe?)

3) stellar merger in dense clusters
1) first star remnants2) direct collapse

3) stellar merger

Volonteri 2012

What if there are some metals ?
KO, Schneider, Haiman 2008

log

dustcoolinglog•For [M/H] > ~-5,dust cooling causes rapid temperture dropFragmentation of metal-enriched clouds
radial distributions（Halo 1, 2; Z=0~10-4Zsun）

Latif, KO, Habouzit, Schleicher, Volonteri 2015

density distribution around the center-6-5-4• Filament-like structure is formed and fragments due
to sudden temperature drop in the case of Z~10-4Zsun• dense star cluster formation?

Seed BH formation in dense clusters
in cosmological simulations
Katz, Sijacki & Haehnelt 2015

pair halos where one ismetal-polluted by windfrom another .

dense cluster at its center N-body calculation

stellar mergers occur
at the center of cluster•stellar mergers occur in dense enough clusters•merger product is at most ~1000Msun, not more massive that first stars•may loose some fraction of mass by stellar winds before collapse to BH

What if there are some metals ?
Chon & KO in prep.
KO, Schneider, Haiman 2008log

dustcoolinglog•For [M/H] > ~-5,
dust cooling causes rapid temperture dropandfragmentation‘SuperCompetitive Accretion’Runaway growth of the central starby Super Competitive Accretion Chon & KO in prep.

•Cloud fragments into numerous objects•Some grow supermassive by merger/accretion

SummaryFirst star formationProtostellar radiative feedback sets the final stellar
mass at a few 10-100Msun
Massive binaries are maybe common
correct ionization model developed

Supermassive star as a seed BH

Photodissociation (or collisional dissociation indense, shocks) suppresses H2 cooling, leading toSMS formation via isothermal collapse at 8000K.
SMS grows by accretion up to ~105Msun ,then collapses to BH by GR instability.
Runaway formation of SMS by super competitive
accretion in metal-enriched cluster seems viable.

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