1. Seed BH formation via direct collapse
EWASS 2015
22 June
Tenerife, Spain
Seed BH formation via direct collapse
Kazu Omukai （Tohoku）
Major contributers
Kazu Sugimura (Tohoku)
Kohei Inayoshi （Columbia）Takashi Hosokawa （Tokyo）
I appreciate the organizers so much for giving the opportunetity to visit here and give a talk on ..

2. Why we want massive seeds?
Mortlock
Several z >6.5 SMBHs found (Mortlock+ 2011, Venemans +2013)
e.g., ULAS J
MBH=2x109Msun at z= (0.77Gyr)
Either very massive seed or
very rapid growth is required!
BUT
Growth by accretion/merging was probably inefficient due to radiative feedback/recoil by GW kick.
 So we want massive seeds.
Why we consider SMS formation?
This is motivated by discovery of SMBHs at very high redshift.
The current record holder is ULAS J1120, with estimated mass of 2x10^9Msun
at redshift 7, where the age of the universe is less than 0.8 Gyr.
This very existence of SMBH at such early universe requires either very massive seed BH from the beginning or very rapid growth after its birth.
BHs grow in mass by accretion or merging.
But both processes were probably inefficient due to radiative feedback or recoil by GW kick.
Super-critical accretion is a possibility, but specific mechanism to drive it is still uncertain.
That is the reason we want massive seeds.

3. How massive were the first stars?
Mass of First Stars is set by
the UV feedback
(McKee & Tan 08, Hosokawa+11/12,
Stacy+12, Hirano +14, Susa )
Accretion stops at 40Msun
Not enough for high-z SMBH seed
20M8
30M8
40M8
One natural candidate of the seed BH is the remnant of first stars.
According to studies in last several years,
the first stars are now considered to be ordinarily
massive but not supermassive.
The mass of first stars is set by the radiative feedback,
And according to Takashi Hosokawa’s original results,
The mass was 40Msun, not enough for high-z SMBH seeds.
HII region
contour: density, color: temperature
Hosokawa, KO, Yoshida, Yorke 2011, 2012

4. getting more massive these days…
Hirano et al. (+KO)
2014, 2015
studied
> halos
2014
2015
Flat distribution in a wide mass range: a few Msun
Even 1000Msun first stars can be formed
But these days, the claimed mass of first stars are getting more massive according to Hirano’s more statistical studies.
He studied a number of halos and found the mass spectrum, which is flat distribution in a wide mass range form a few 10 to 100Msun. And Even 1000Msun first stars can be formed. According to his updated results, they are even more shifted toward higher mass.

5. 1000Msun first stars can end up with SMBHs at z=7
as long as the Eddington-limited accretion is sustained all the time.
Still rather stringent
Even more massive (>105Msun)seeds are more preferred … What is the plausible mechanism for supermassive star formation?
If the first stars are as massive as 1000Msun, they can end up with SMBH at z=7,
As long as i.e. 100 per cent duty cycle at the Eddington limit.
Ｔｈｉs OK, but still rather stringent condition.
So we still want even more massive seeds mass to relax the condition of their growth.
But what is the plausible mechanism for SMS formation? Is it really possible?

6. Standard picture for (low-mass) star formation
Established in ’80s
Clump formation
collapse
& accretion
Stellar feedback
A new star is born!
To think about the SMS formation mechanism, let’s review how the stars are formed in local universe.
This scenario was originally invented to explain low mass star formation,
But perhaps also applicable for SMS formation.
The evolution from clump formation until the completion of a new-born star is summarized here schematically.
(perhaps) valid also
for supermassive star formation

7. SMS formation by atomic cooling
If FUV radiation is more intense than the critical value Jcrit, the cloud cools solely by atomic cooling.
No rapid cooling phase  monolithic collapse
high temperature (at ~8000K) during the collapse
high accretion rate in protostellar phase
dM*/dt ~cs3/G ~ 0.06Msun/yr (T/104K)3/2
H atomic cooling
J>Jcrit
H2 molecular cooling
J<Jcrit
Omukai 01
Based on this SF picture,
the proposed mechanism for SMS formation is by collapse of cloud induced by the atomic cooling.
This is the temperature plot both for the ordinary Pop III star formation and
the direct collapse.
In ordinary Pop III star formation, H2 cooling becomes important at some point and the temperature evolution follows this track.
On the otherhand, in the direct collapse case, H2 cooling is not available, for example by
photodissociation.
In this case, the collapse proceeds only via atomic cooling along this track, which is almost isothermal at 8000K.
Then a protostar will be formed eventually, and grows by rapid accretion.
Finally, once the protostar becomes massive enough, about 10^5Msun, it collapses by GR instability forming a BH.
But I’ll examine here whether this scenario really works or not.
Specifically, I consider the following 3 points:
First, how much radiation is needed? Is not it unreallistically high?
Second, does the protostellar collapse results in a single massive eobject without fragmentation?
Finally, does the accretion continue until the star becomes massive enough to trigger GR collapse?
Super-massive stars (>105Msun) will form

8. Long way to supermassive stars
photodissociation
1.How much radiation needed?
isothermal collapse at 〜8000K
by atomic cooling
2.Monolithic collapse or fragmentation?
protostar growth by rapid accretion ~1M8/yr
But there is still a long way to go.
Basic scenario to form SMS by direct collapse is summarized here.
In the rest of my talk, I will consider the following three problems.
3.Accretion continues or halted?
Collapse by GR instability
→105M8 BH

9. 1. How much radiation needed?
Sugimura, KO, Inoue 2014
Jcrit : intensity at LW wavelenths (12.4eV) needed for atomic cooling.
Radiation (color) temperature
hard
soft
Pop III
Pop II
+ H- photodetachment
H2 photodissociation
H2 photodissociation
As for the first point,
This is the so-called critical intensity, that is, threshold intensity for direct collapse by suppressing H2 formation and cooling. This depends on the radiation temperature i.e., hardness of spectrum.
In literatures, Tuv=10^5 K is regarded as a typical value for Pop III galaxies,
And Tuv=10^4K is for Pop II galaxies.
The dependence on radiation temperature comes from the fact that for low Tuv
not only H2 photodissociation but also H- photodetachment, which is the intermediary
of H2 formation reaction becomes important.
These values, in particular, Pop II value of 30 has been often used in estimating the number of direct collapse BHs until last year.
Jcrit increases with radiation temperature (i.e., hardness)

10. Jcrit for Starburst Galaxies
time after starburst
Salpeter IMF 1-100Msun
z=20
z=10
age of the universe
But with realistic spectra of starburst galaxies, we found the Jcrit value
is rather high even for Pop II galaxies
unless its age is more than 100Myr, which is comparable or even longer than the age of the universe at supposed seed BH formation epoch.
Jcrit is very high (~1000) even for PopII galaxies (unless >several 100Myr)

11. Possible role of H2+ channel
Dominant without radiation field
H- channel : e catalyzed (Peebles & Dicke 1968; Hirasawa+1969)
H + e  H- + g H- + H  H2 + e
Can be dominant under strong radiation field
(cf. binding energy H- 0.75eV, H eV)
H2+ channel : H+ catalyzed (Saslaw & Zipoy 1967)
H + H+  H2+ + g H2+ + H  H2 + H+
Here I would like to point out possible role of H2+ channel in H2 formation.
There are two channels for H2 formation in the gas phase, that is so-called H- channel and H2+ channel.
Without radiation field, H- channel is dominant since its rate is about an order of magnitude larger than the rate of the H2+ channel.
But H- is more fragile than H2+ (2.65eV), so under strong radiation field, H2+ channel
When H2+ channel is dominant
-> need to solve H2+ level population.
Sugimura, Coppola, KO

12. Jcrit and non-LTE H2+ population
Sugimura, Coppola, KO
Black body spectrum
So we derived Jcrit by considering the non-LTE H2+ population.
This is the result for the BB type spectra.
Above the Trad=7000K, H- channel is dominant.and non-LTE population does not affect the results.
On the other hand, below 7000K, H2+ channel becomes impotant due to H- photodissociation and non-LTE population need to be considered.
However, realistic young galaxy’s spectra, although are not in BB shape,
are harder than this value. So it was found that we don’t need to H2+ channel in finding Jcrit.
H2+ channel and its non-LTE level population are important for Trad < 7000K.
For realistic young galaxy spectrum (Trad~20000K), we don’t need to consider its effect.

13. How many seeds? Jcrit~1000 from our result
Dijkstra et al. (2014)
Agarwal et al. (2012)
We now understand Jcrit is as large as ~1000.
So how many direct collapse halos in the universe?
Is their number enough for the SMBH seeds?
Currently there appears to be discrepancies in estimate
of halo number under a certain radiation intensity.
To be conservative, if we take this smaller value, it means that
Direct collapse occurs only in very rare enviromnets.
It can still account for the high-z SMBH.
But cannot be the origin of all the SMBHs in the galaxy centers.
Large discrepancies in estimate for JLW distribution
Direct collapse occurs only in very rare environments but may still account for high-z SMBH.

14. Alternative channel: high-density shock in primordial gas
Inayoshi & KO 2012
Isothermal collapse
shocks at >103-4/cc, with> several 103K
H2 collisionally dissociated
Fragments at 8000K with >~105Msun
Isothermal collapse thereafter
There is an alternative channel without relying on the strong FUV field,
to initiate atomic cooling collapse.
To initiate atomic cooling collapse,
we just need to put a cloud in this high density and high temperature region,
After that H2 is collisionally dissociated and the cloud collapse solely by
the atomic cooling.
FUV is one way to keep clouds warm and put them inside this region.
Another possibility to put the cloud inside this region is by a shock.
In the process of galaxy formation, colliding flows ubiquitously develop shocks.
If the postshock density is less than 10^3 cm-3, the shocked gas cools first by Lya emission,
then by H2, and finally HD line emission, and contracts isobarically until the cooling time becomes longer than the free-fall time.
At this point, the shocked layer fragments into clumps,
and clumps collapse and form stars inside.
But if the postshock density is higher than 10^3, the gas cools first by the Ly alpha and
Temperature reaches ~8000K. But, as the density is high enough for H2 to be in LTE,
the collisional dissociation from the excited states is effective.
So the H2 is collisionally dissociated and the temperature does not fall further.
Fragmentation occurs at this point with mass scale > ~10^5Msun.
The isothermal collapse follows after that, leading to SMS formation.
The hatched region shows the postshock (n,T) domain, leading to the isothermal collapse and the
SMS formation.
For details, see next talk by Kohei

15. 2. Protostellar Collapse:
Monolithic Collapse or fragmentation?
e.g., Bromm & Loeb 2003, Latif +, Regan +
Inayoshi, Omukai & Tasker (2014 )
Even if the enough UV radiation is available, whether the protostellar collapse results in a
single star is not still uncertain.
So far, several groups reported the formation of a single object.
At the end of the protostellar collapse, a small protostar is formed, which is supposed to grow supermassive.
But this can be biased because we all want to form SMSs.
I think we need to study more about the initial condition dependence.
Closely related issue is also discussed in van Borm’s poster.
No major eposode of fragmentation
small protostar (~0.1Msun) is formed

16. Really, no fragmentation?
linear growth
elongation=(b-a)/a
atomic cooling cloud a b
H2 cooling cloud
Isothermal collapse
According to linear theory, atomic-cooling clouds become elongated significantly.
Clouds with elongation > ~3 (in the linear theory) are known to fragment (from numerical experiment by Tsuribe & KO 2006)
Whether fragmentation occurs or not probably depends on initial condition (density concentration, turbulence , magnetic field
etc.)?
Although many groups concludes no or inefficient fragmentation for the atomic cooling clouds, this cannot be readily understood.
According to the linear theory, during the runaway collapse phase, the elongation grows by a factor of 1000, while for ordinary first star formation case, elongation decreases.
From some numerical experiment, it’s observed that clouds fragments if its elongation
Exceeds > 3 in the linear theory.
In fact, during the isothermal collapse, the cloud becomes very elongated as this figure shows and eventually fragments.
So whether fragmentation occurs or not depends on the initial setting e.g.,
Density cencentratin, turbulence etc. , and we cannot just assume no fragmentation during the atomic cooling phase.
Mizuno + in prep.

17. 3. Accretion evolution to supermassive stars
End product of the collapse phase：　
protostar of 0.1 Msun surrounded by gas envelope of Msun,
accreting with 1Msun/yr
Accretion rate
So far we have seen how the collapse proceeds and how a small protostar is formed at the center.
Let me summarize the end product of the protostellar collapse phase:…..
Important point is the high accretion rate in this case.
Whether this small protostar grows supermassive is still an unsolved problem.
Does the star becomes super-massive? or
Does the stellar feedback terminate its growth?

18. Super-giant protostar.
Hosokawa, Yorke, KO (2012)
Super-giant protostar
With rapid mass accretion (> 0.01 Msun/yr), protostar does not reach the main sequence, with its radius inflating enormously to ~10AU.
Stellar radius ( R8 )
Main Sequence Star
With such rapid accretion, the protostellar evolution becomes completely different from the ordinary first stars.
This figure shows the evolution of protostellar radius during the accretion phase. Different lines correspond to different accretion rates.
This is the case of the ordinary first stars, where accretion rate is about 1e-3Msun/yr.
After the KH contraction, the star reaches the MS and emit copious amount of UV photons, which heat the envelope gas and stop the accretion eventually.
But with rapid accretion, the protostar does not reach the MS.
Instead its radius inflates enormously to ~10AU.
We named it supergiant protostar.
stellar mass ( M8 )

19. Super-giant protostar on HR diagram
Hosokawa et al. (+KO) (2013)
low effective temperature at several 103K (looks like a red-giant star ) negligible UV luminosity
and feedback accretion continues unhindered and the star becomes supermassive
Main-sequence
This is the HR diagram of the supergiant protostars.
Due to its extended size, the effective temperature remains at 5000K, and the star looks like a red-giant star.
So its UV luminosity and the feedback are negligible.
The accretion continues unhindered and the star becomes supermassive.
But the problem is that: is such a high accretion rate maintained throughout the evolution?
If the accretion rate drops temporarily by for example the effect of angular momentum, the star reaches the MS star and UV feedback would stop the accretion, prohibiting the star reaching the supermassive.
Note: Accretion can be episodic.
For its effect on the stellar feedback, see Yuya Sakurai’s poster.

20. General relativistic stability
Hosokawa +(KO)
2013
3x104Msun
105Msun
Radius (Rsun)
Finally, let’s see the GR stability or PN stability of SGPSs.
If the radius is below this regions, the star becomes unstable.
The radial structure of 10^5Msun SGPS is like this. So, this is still GR stable and
If there are plenty of mass reservoir for accretion it can grow further.
But it is already close to and approaching the instability domain.
So, whether or not the accretion continues, the SGPSs would soon
becomes GR unstable and would collapses to BHs.
Mass (Msun)
105Msun supergiant protostar is still GR stable.
But already close and approaching to instability.  It will probably collapse soon after >105Msun is reached.

21. SUMMARY
SMSs are formed in clouds collapsing isothermally at 8000K via the atomic cooling.
Jcrit for realistic young galaxy spectra is rather high ~1000, which indicates that SMSs are formed only in very rare circumstances.
No or inefficient fragmentation is observed during the collaopse in numerical simulations, but the condition needs further study.
SMS grows by accretion up to ~105Msun , then collapses to BH by GR instability.
Gracias !

22. Gas must be primordial?
KO, Schneider, Haiman 2008
dust
cooling
For the almost isothermal collapse to realize, gas must be close to primordial.
This figure shows the temperature evolution with different amount of metals.
Here dust-gas-metal ratio is assumed to be the same as in local universe.
We can see that with only dust metallicity of -5, the dust causes rapid cooling and the isothermal evolution is terminated.
The condition on dust amount seems very severe, but dust yield in the early SNe
is very uncertain. Although once formed, only <10% can survive after SN reverse shock.
So the dust-gas-metal ratio can be significantly lower than the local value.
This means with small amount of dust grains, the cloud fragments by the rapid cooling.
However, separation of those fragments is not big, less than AU, and they are surrounded by a dense envelope which accretes rapidly onto the system of fragments.
So they may eventually coalesce to a single object and there is still a possibility for it
to grow supermassive.
For [M/H]dust > ~-5, dust causes rapid cooling and fragmentation
But,
fragments are very close each other (<AU) and might coalesce and grow very massive via subsequent accretion.

23. Requirements for SMS formation by direct collapse
Runaway 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
Here we consider the SMS formation by monolithic direct collapse.
We do not consider the other possibilities, for example, the stellar merger scenario.
There are two requirements for the SMS formation by the direct collapse.
First, the fragmentation into lower mass objects must be suppressed.
Since the rapid cooling induces fragmentation, without such rapid cooling, we expect the fragmentation does not occur.
H2 is the efficient coolant in the primordial gas.
To suppress its cooling, FUV photodissociation is the mechanism we first think of.
Another necessary condition is that the formation process must be completed before the star dies, i.e., formation timescale must be shorter than the stellar lifetime.
This requires the accretion rate to be higher than this value.
Without H2, the temperature remains ~10^4K, which is set by the atomic cooling.
This high temperature environment assures the high accretion rate needed.

24. SMS formation by the isothermal collapse
Latif
Bromm & Loeb 2003
What kind of object will be formed as a result of isothermal collapse by atomic cooling?
Bromm and Leob studied the isothermally collapse of the clouds by numerical simulation.
They studied 10^8Msun halo virializing at z~10, corresponding to 2sigma overdensity,
With strong FUV J~4000.
These figures show the end products in non-rotating and rotating cases.
In the non-rotating case, the fragmentation does not occur and the cloud collapses monolithically
to a single massive object.
On the other hand, in the rotating case, a binary system is formed, but the cloud does not fragment
into numerous pieces. So also in this case, one or two supermassive stars are expected to form.
This calculation demonstrated that the SMS is in fact formed by the atomic-cooling isothermal collapse.
Recent numerical simulations also confirm
~108Msun halo virializing at z~10
w/o H2 cooling, fragmentation is inefficient direct collapse to 106Msun supermassive star

25. Why Jcrit exists? For > ncr,LTE~104cm-3,
KO 2001
For > ncr,LTE~104cm-3,
collisional dissociation rate increases ( less H2 available)
H2 cooling efficiency decreases ( more H2 needed)
If FUV prevents H2 cooling until ~104cm-3,
sufficient H2 for coolng never forms thereafter.
collisional dissociation
limited
UV shielding  H2 fraction jumps up!

26. Possible sites of high-density shocks
Cold-accretion-flow shock in the central ~10pc region of the first galaxy (Wise, Turk & Abel 2008)
Galaxy merger driven inflow (Mayer et al. 2010)  probably metal-rich
We learned that if the postshock density is >10^3, the isothermal collapse naturally occurs even without strong radiation field.
Now we look for possible sites of such high-density shocks.
One promissing site is the cold-accretion-flow shock in the center of the first galaxy.
This is the simulation by Wise et al., showing the structure in and around a first galaxy.
From recent numerical simulations, we know that young galaxies assemble materials in a way
the cold gas flows via the filamentary structure.
Those flows collide each other and develop shocks in the galaxy.
Some flows reach close to the center and shock can occur at high enough density for the SMS formation.
Another possibility is a shock by galaxy merger driven inflow.
But in this case, the galaxies are expected to be already metal-rich.
For the isothemal collapse, the cloud must be close to the pristine gas, as I will talk shortly,
So, I think the SMS formation does not occur in such a condition.
My bit is on the cold accretion flow shock

27. Interior Structure 10-3 M8 / yr
Most part of the stellar interior contracts, and central temperature increases
H-burning begins at 700M8, but the star is still bloating (different from the ZAMS )

28. Physics of MR relation
The stellar luminosity L* is now close to the Eddington luminosity:
Constant Teff at 5000 K ← strong T-dependence of H- opacity
(the Hayashi limit)
If Teff takes the constant value, we get

29. Accreting (ordinary) metal-free protostar
Protostellar Radius
Acc.rate=8.8, 4.4, 2.2, 1.1 x 10-3 Msun/yr
3b. expansion
1. adiabatic phase
tKH >tacc
2. KH contr.
tKH=tacc
3a. ZAMS
(KO & Palla 2003)
Due to rapid accretion, stars become massive before the onset of H burning (at Msun).
The star reaches ordinary ZAMS and accretion continues if accretion rate <dM/dtcrit=4 10-3Msun/yr
Otherwise (>dM/dtcrit) , the star starts inflate when L becomes close to LEdd. (no stationary solution ? )

30. H- photodetachment and H2 formation
H2 formation via H- channel
H + e  H- + g
H2 formation: H- + H  H2 + e
Photodetachment: H- + g  H + e
With the same J21,
softer (lower TUV)radiation is more effective in suppressing H2 formation

31. Obstacles in Forming Massive Stars
Standard accretion rate
Wolfire & Cassinelli 1987
1. Formation time problem
Time needed to form a massive star
exceeds the stellar life time.
2. Radiation barrier problem　
　Radiation pressure (on dust) by the star
becomes too high for the matter
　to be accreted.
Next we see　the massive star formation.
Massive stars cannot be formed in the same scenario but just more prolonged accretion.
There are following obstacles.
Rapid and non-spherical accretion is needed for massive star formation in local universe.

32. How long does it take to grow such massive?
BH growth by Eddington-limited accretion
MBH=Mseed exp(t/tSal) with　tSal = esTc/4pGmH=0.05Gyr e0.1
To make MBH=2x109Msun BH from a seed of Mseed=100Msun (or 1000Msun)
It takes
tgrow = tSal ln(MSMBH/Mseed)= 0.84Gyr (0.73Gyr)
Longer than (or very close to) the age of the universe at z=7 (0.77Gyr)!
Next, let’s see whether those first star remnant which are typically 100Msun, can grow by accretion.
It is known that in not-very-high redshift universe, SMBHs seem to grow by accretion.
This is because nearby BH mass density roughly coincides with the estimate assuming quasars are accreting at Eddington rate. This is so called Soltan’s argument.
If this is also the case for high-z seed BHs, the BH grows following this exponential relation.
Suppose now that 100Msun seed grows to 2x109Msun SMBH. The growth time is 0.84Gyr.
This exceeds the age of universe at redshift 7. Even if the seed is 1000Msun,
the growth time is 0.73Gyr although it is within the age of the univese, they are almost the same.
So very efficient accretion must continue.
Either more massive seed
or very efficient accretion/merging
is required!

33. Efficient Accretion/Merging Unlikely…
Milosavlievic+2009
Inefficient accretion
Eddington limit
Alvarez+2009, Milosavlievic+2009
Radiative feedback (heating & radiation force) keeps the accretion rate low
Averaged accretion rate
30% of Eddington-limited rate
0.2% of Bondi accretion rate
Inefficient merging
Koppitz+2007, Campanelli+2007, etc.
However, there are early bottle neckes in BH growth.
the accretion cannot be efficient especially in the early phase.
First, the Bondi accretion rate, which is proportional to M^2, is not high if M is small.
Even worse, radiative feedback from the accreting BH keeps the accretion rate low.
This figure shows result of numerical simulation, which shows how a seed BH put in
high density region grows. The is the accretion rate. This is variable almost periodially,
But the averaged accretion rate is 30% of Eddington rate and only 0.2 % of Bondi rate.
So the efficient accretion is not possible.
So how about the merging?
It turned out that the merging is also quite inefficient unfortunately.
At typical merging event, the merger is kicked with velocity of ~100km/s due to back reaction of
GW emission, while in the high-z, the escape velocity of halos are small.
So, they are ejected from the halos and cannot grow to SMBHs.
In summary, BHs are hard to grow in their infancy.
At BH merging, the merger is kicked with velocity
~100km/s due to back reaction of GW emission.
If > escape velocity (~10km/s, small in high-z), ejected from the halo.
BHs are hard to grow in their infancy