PRIMORDIAL BLACK HOLES AS DARK MATTER
Bernard Carr Queen Mary, University of London
SUSY2018, Barcelona, 26/7/18
AND SEEDS FOR COSMIC STRUCTURE PLAN OF TALK
• Introduction and early history
• Formation of PBHs
• PBHs and dark matter
• PBHs and gravitational waves
• PBHs and large-scale structure
•• ConstraintsPBHs and inflationon evaporating PBHs BLACK HOLE FORMATION
2 18 -2 3 RS = 2GM/c = 3(M/MO) km => rS = 10 (M/MO) g/cm 1-2 3-5 6-9 Stellar BH (M~10 MO), IMBH (M~10 MO), SMBH (M~10 MO)
Small “primordial” BHs can only form in early Universe
cf. cosmological density r ~ 1/(Gt2) ~ 106(t/s)-2g/cm3
10-5g at 10-43s (minimum) 3 15 -23 MPBH ~ c t/G = 10 g at 10 s (evaporating) => huge range -5 1MO at 10 s (maximum)
NoneCygnus of these X1 10M BHsO couldNGC1313 solve the 500M darkO matter problem8 horizon mass QSO 10 MO WHEN BLACK HOLES FORM
Stellar IMBH BH SMBH
PBH But still no definite evidence for PBHs
Accel’ BH on 09November2017 by guest Downloaded fromhttps://academic.oup.com/mnras/article-abstract/152/1/75/2604549
1971MNRAS.152...75H 1967SvA....10..602Z on 09November2017 by guest Downloaded fromhttps://academic.oup.com/mnras/article-abstract/168/2/399/2604878
1974MNRAS.168..399C Þ => no need to consider quantum observational evidence against effects them! PBHs are important even if they never formed! Thermodynamics
General Relativity Quantum Mechanics
PBHs are important even if they never formed! PBH EVAPORATION
Black holes radiate thermally with temperature
T = ~ 10-7 K
64 => evaporate completely in time tevap ~ 10 y
M ~ 1015g => final explosion phase today (1030 ergs)
15 -8 g-ray background at 100 MeV => WPBH(10 g) < 10
=> explosions undetectable in standard particle physics model
26 T > TCMB=3K for M < 10 g => “quantum” black holes
(Page & Hawking 1976) But PBHs are important even if they never formed! Only PBHs with M >> 1015g could provide dark matter First paper on PBHs as dark matter 1975A&A....38....5M Carr (1977) corrected some errors BLACK HOLES HIGHER DIMENSIONS
-5 22 Planck 10 g 10 MO Universal
9 10 MO QSO
10 6 exploding 10 g 10 MO MW
15 2 evaporating 10 g 10 MO IMBH
lunar 1021g 1 MO Stellar
terrestrial 1025g
QUANTUM/CLASSICAL FORMATION MECHANISMS
Primordial inhomogeneities Inflation
Pressure reduction Form more easily but need spherical symmetry
Cosmic strings PBH constraints => G µ < 10-6
Bubble collisions Need fine-tuning of bubble formation rate Domain walls PBHs can be very large http://www.damtp.cam.ac.uk/research/gr/public/cs_phase.html
String necklaces PBH FORMATION => LARGE INHOMOGENEITIES
To collapse against pressure, need (Carr 1975)
2 when d ~ 1 => dH > a (p=arc )
2 1/2 Gaussian fluctns with
Þ fraction of PBHs
b(M) ~ e(M) exp
e(M) constant => b(M) constant =>
p=0 => subhorizon holes but need spherical symmetry
=> b(M) ~ 0.06 e(M)6 (Khlopov & Polnarev 1982 )
e(M) decreases with M => exponential upper cut-off Separate universe for dH > 1 but recently reinterprted Limit on fraction of Universe collapsing b(M) fraction of density in PBHs of mass M at formation
General limit
-6 -18 => b ~ 10 WPBH ~ 10 WPBH
So both require and expect b(M) to be tiny => fine-tuning
15 Unevaporated M>10 g => WPBH < 0.25 (CDM) 15 -8 Evaporating now M~10 g => WPBH < 10 (GRB) Evaporated in past M<1015g
=> constraints from entropy, g-background, BBNS
-8 -1/2 fDM(M) ~ (b /10 ) (M/Mo) PBHS AS PROBE OF PRIMORDIAL FLUCUTUATIONS
Constraints on b(M) => Constraints on e(M)
b(M) ~ e(M) exp
LSS
Need blue spectrum or spectral feature to produce them. PBHs are unique probe of e on small scales.
Carr, Gilbert & Lidsey (1994) CONSTRAINTS FOR EVAPORATING PBHS
B. Carr, K. Kohri, Y. Sendouda & J. Yokoyama PRD 81(2010) 104019
Big bang nucleosynthesis
Gamma-ray background
Extragalactic cosmic rays
Neutrino relics
LSP relics
CMB distortions
ReionizationThis assumesand monochromatic 21cm mass function PBHs from near-critical collapse
=> broad mass spectrum => strong constraints above 1014g
(g = 0.35) (Yokoyama 1998)
-10 dC ~ 0.45 and applies to d - dC ~ 10 (Musco & Miller 2013) DM from 1016g PBHs without violating GRB constraints?
But this slope does not apply in all scenarios (Kuhnel et al. 2016) PBHS AND INFLATION
PBHs formed before reheat inflated away =>
-2 M > Mmin = MPl(Treheat / TPl) > 1 gm
16 CMB quadrupole => Treheat < 10 GeV
But inflation generates fluctuations
Can these generate PBHs?
[HUGE NUMBER OF PAPERS ON THIS] Primordial black holes as Dark Matter PROPRIMORDIAL BLACK HOLES AS DARK MATTER • BH exist PBH can do it! • NoPRO new physics is needed
• LIGO* Black motivation holes exist CON* No new physics needed • Fine* LIGO tuning results is needed CON
* Requires fine-tuning BBNS => Wbaryon= 0.05
Wvis= 0.01, Wdm= 0.25 Þ need baryonic and non-baryonic DM MACHOs WIMPs PBHs are non-baryonic with features of both WIMPs and MACHOs 1017-1020g PBHs excluded by femtolensing of GRBs 1026-1033g PBHs excluded by microlensing of LMC (2010) 3 Above 10 M0 excluded by dynamical effects => windows at 1016-1017g or 1020-1024g or 1033-1036g for dark matter
Asteroid Sublunar Intermediate Mass MACHO
For this reason, there was no motivation to suspect that there might be MACHOs which EROS led to higher-longevity microlensing events. The longevity, tˆ, of an event is
1 M 2 tˆ =0.2yrs PBH (27) M⊙ ! " which assumes a transit velocity 200km/s. Subsituting our extended PBH masses, one 3 4 5 finds approximately tˆ 6, 20, 60 years for MPBH 10 , 10 , 10 M⊙ respectively, and ∼ ∼ˆ searching for light curves withEarly these highermicrolensing values of t couldsearches be very suggested rewarding. MACHOs with 0.5 MO Our understanding is that the original=> PBH telescope formation used by the at MACHOQCD transitionCollaboration? [7] at the Mount Stromlo Observatory in Australia was accidentally destroyed by fire, and that some other appropriate telescopesPressure are presently reduction being used => to PBH search mass for extasolar function planets, peak at 0.5 M of which two thousand are already known. O It is seriously hoped that MACHOLater searches found will that resume at most and focus20% on of g reaterDM can longevity be in these objects microlensing events. Some encouragement can be derived from this, written this month by a member of the original MACHO Collaboration :
There is no known problem with searching for events of greaterlongevitythanthosedis- covered in 2000; only the longevity of the people!
That being written, convincing observations showing only a fraction of the light curves could suffice? If so, only a fraction of the e.g. six years, corresponding to PIMBHs with one thousand solar masses, could well be enough to confirm the theory.
Finally, going back to the 2010 Vera Rubin quote mentioned in the Introduction, it is
”If I could have my pick, I would like to learn that Newton’s laws must be modified in order to correctly describe gravitational interactions at large distances. That’s more appealing than a universe filled with a new kind of sub-nuclear particle.”
If our solution for the dark matter problem is correct, Rubin’s preference for no new elementary particle filling the Universe would be vindicated, because for dark matter microscopic particles become irrelevant. Regarding Newton’s law of gravity, it would not need modification beyond general relativity theory which is needed for the black holes. In this sense, Rubin did not need to pick either alternative to explain darkmatter.
References
[1] P.H. Frampton, Searching for Dark Matter Constituents with Many Solar Masses. arXiv:1510.00400[hep-ph]
9 NORDITA-2016-XX
PRIMORDIAL BLACK HOLES AS DARK MATTER
1, 2, 3, Bernard Carr, ⇤ Florian K¨uhnel, † and Marit Sandstad ‡ 1Department of Physics and Astronomy, Queen Mary University of London, MilePRD End 94, Road, 083504, London arXiv:1607.06077 E1 4NS, United Kingdom 2 The Oskar Klein Centre for CosmoparticleM/M Physics, Department of Physics, Stockholm University, AlbaNova,⊙ 11 SE–106 91 Stockholm, Sweden 10-17 10-7 103 1013 3 Nordita,EGB KTHF Royal InstituteK of TechnologyWB and Stockholm University, RoslagstullsbackenNS 23, ML SE–10691E Stockholm, Sweden 0.100 LSS (Dated: Saturday 4th June, 2016, 1:11pm)FIRAS The possibility of primordial black holes constituting dark matter is studied in detail, focussing 8 2 on the intermediate-mass range from 10 M to 10 M . All relevant up-to-date constraints are 0.001 WMAP reviewed and any e↵ect necessary for a precision calculation of the primordial black-hole abun- D f C B A DF dance, such as non-Gaussianity, non-sphericity, critical collapse, merging, etc., is discussed in depth. A general novel procedure for confronting observational constraints with an extended primordial black-hole mass spectrum10-5 is introduced. This scheme together with the various formation e↵ects provides a guideline, for arbitrary constraints, for how to systematically approach the problem of primordial black holes as dark matter, both from a model-independent observational point of view and starting from a fundamental formation model for primordial black holes. It is also pointed 10-7 out which e↵ects in the1016 formation process1026 should be1036 studied further1046 in order to provide a realistic mapping from inflationary power spectra toM the/g mass function of primordial black holes in order to use the observational constraints on the latter11 to put constraints on inflation and early-universe physics.Three This scheme windows: is applied (A) intermedate to two specificmass; inflationary (B) sublunar models.mass; It is demonstrated (C) asteroid under mass. which conditions these models can yield primordial black holes constituting 100% of the dark matter. Interestingly, the respective distributionsAlso (D) Planck peak mass in the relics? mass region where the recent LIGO black- hole mergers were found. We also show which model-independent conclusions can be drawn from observable constraints in this mass range. Scenario A => black holes detected by LIGO might be primordial But some of these limits are now thought to be wrong
I. INTRODUCTION
Primordial black holes (PBHs) have been a source of intense interest for nearly 50 years [1], despite the fact that there is still no evidence for their existence. One reason for this is that only PBHs can be small enough for quantum radiation to be important [2]. After 42 years there is still no direct evidence for this e↵ect and people are still grappling with conceptual puzzles associated with the process [3]. Nevertheless, this discovery is generally recognised as one of the key developments in physics of the last century because it beautifully unified general relativity, quantum mechanics and thermodynamics. The fact that Hawking was only led to this discovery as a result of contemplating the properties of PBHs illustrates that it can be useful to study something even if it may not exist! PBHs smaller than 1015g would have evaporated by now with many interesting cosmological consequences [4, 5]. Studies of such consequences have placed useful constraints on models of the early universe [6–13] and, more positively, evaporating PBHs have also been invoked to explain certain features (such as the extragalactic and Galactic gamma- ray backgrounds [14–17], a primary antimatter component in cosmic rays [18, 19], the annihilation line radiation from the Galactic centre [20] and some short-period gamma-ray bursts [21]). However, there are usually other possible explanations for these features, so there is no definitive evidence for evaporating PBHs. Attention has therefore shifted to the PBHs larger than 1015g, which are una↵ected by Hawking radiation. Such PBHs might have various astrophysical consequences (seeds for supermassive black holes in galactic nuclei [22–25], the generation of large-scale structure through Poisson-fluctuations [26, 27], heating the Galactic disc Marit:Refmissing, reionization of the pregalactic medium [28–30]). But perhaps the most exciting possibility – and the main focus of this paper – is that they could provide the dark matter which comprises 25% of the critical density [31, 32]. Since
⇤Electronic address: [email protected]
†Electronic address: fl[email protected]
‡Electronic address: [email protected] WHICH MASS WINDOW IS MOST PLAUSIBLE?
20 PBH dark matter @10 Mo PBH dark matter @10 g from hybrid inflation from double inflation Clesse & Garcia-Bellido Inomata et al arXiv:1701.02544 arXiv:1501.07565 4
recombination and then have grown mostly by merging 1 to form black holes with stellar masses today. femto!lensing EROS 0.1 WMAP3 MACHO III. HYBRID-WATERFALL INFLATION
DM 0.01 "
! FIRAS PBH It has been shown recently that the original non-
PBH 0.001 NS capture supersymmetric hybrid model [31, 32] and its most well- " known supersymmetric realizations, the F-term and D- 10!4 term models [69, 70], own a regime of mild waterfall [36– EGB 40]. Initially the field trajectories are slowly rolling along a nearly flat valley of the multi-field potential. When tra- 10!5 10!18 10!13 10!8 0.001 100 107 jectories cross a critical field value, denoted φc,thepo- M !M tential becomes tachyonic in the orthogonal direction to PBH ! the valley. In the mild-waterfall case, inflation continues for more than 50 e-folds of expansion after crossing the FIG. 1. Limits on the abundance of PBH today, from ex- tragalactic photon background (orange), femto-lensing (red), critical instability point and before tachyonic preheat- micro-lensing by MACHO (green) and EROS (blue) and ing [33] is triggered. This scenario has the advantage CMB distortions by FIRAS (cyan) and WMAP3 (purple). that topological defects formed at the instability point The constraints fromc starf. heavy formation and versus capture by neu- lightare stretcheddark outsidematter our observable particle patch of the Uni- Glob.Cl. tron stars in globular clusters are displayed for ρDM = verse by the subsequent inflation. 2×103 GeVcm−3 (brown). The black dashed line corresponds According to Refs. [37–39], the mild waterfall can be to a particular realization of our scenario of PBH formation. decomposed in two phases (called phase-1 and phase-2). Figure adapted from [56]. During the first one, inflation is driven only by the infla- ton, whereas the terms involving the auxiliary field can be neglected. At some point, these terms become dominant and trajectories enter in a second phase. When the wa- of the star in presence of the PBH gravitational field. terfall lasts for much more than 50 e-folds, the observable PBH of masses larger than 1018 kg are potentially ob- scales exit the Hubble radius in the second phase, when servable [62]. Even if highly unlikely (1 event in 107 trajectories are effectively single field and curvature per- 12 ∼ years for ρPBH = ρDM with MPBH 10 kg), the turbations are generated by adiabatic modes only. For > ∼12 transit of PBH of masses MPBH 10 kg through or the three hybrid models mentioned above (original, F- nearby the Earth could be detected∼ because of the seis- term and D-term), the observable predictions are conse- mic waves they induce [63]. X-rays photons emitted by quently modified and a red scalar spectral index is pre- non-evaporating PBH should ionize and heat the nearby dicted (instead of a blue one for the original model fol- intergalactic medium at high redshifts. This produces lowed by a nearly instantaneous waterfall). If one denotes specific signatures in the 21cm angular power spectrum by N∗ the number of e-folds between horizon exit of the −1 from reionization, which could be detected with the SKA pivot scale k∗ =0.05Mpc and the end of inflation, the 2 radio-telescope [64]. For PBH of masses from 10 M⊙ scalar spectral index is given by ns =1 4/N∗, too low 8 > −9 − to 10 M⊙, densities down to ΩPBH 10 could be for being within the 95% C.L. limits of Planck. Only seen. A PBH transiting nearby a pulsar∼ gives an impulse a low, non-detectable, level of local non-gaussianitiy is acceleration which results in residuals on normally or- produced, characterized by fNL 1/N∗ [37]. derly pulsar timing data [65, 66]. Those timing residuals When inflation continues during≃− the waterfall for a could be detected with future giant radio-telescope like number of e-folds close but larger than 50 e-folds, the the SKA. The signal induced by PBH in the mass range pivot scale becomes super-Hubble during the phase-1. 19 < < 25 10 kg MPBH 10 kg and contributing to more Trajectories are not effectively single-field, and entropic than one∼ percent to∼ dark matter should be detected [66]. perturbations source the curvature perturbations [37]. Binaries of PBH forming a fraction of DM should emit This leads to a strong enhancement in the scalar power gravitational waves; this results in a background of grav- spectrum amplitude, whose thus cannot be in agreement itational waves that could be observed by LIGO, DE- with observations. CIGO and LISA [67, 68]. In this paper, we focus on an intermediate case, be- Finally, the recent discovery by CHANDRA of tens of tween fast and mild waterfall. We consider the regime black hole candidates in the central region of the An- where inflation continues for a number of e-folds be- dromeda (M31) galaxy [42–46] provides a hint in favor tween about 20 and 40 after crossing the instability point. of models of PBH with stellar masses. As detailed later There is a major difference with the previous case: ob- in the paper, such massive PBH can be produced in our servable scales leave the Hubble radius when field tra- model. The CMB distortions and micro-lensing limits jectories are still evolving along the valley, when the could be evaded if PBH were less massive at the epoch of usual single-field slow-roll formalism can be used to de- CONSTRAINTS ON PRIMORDIAL BLACK HOLES
1, 2, 3, 4, 2, 5, Bernard Carr, ⇤ Kazunori Kohri, † Yuuiti Sendouda, ‡ and Jun’ichi Yokoyama § 1 School of Physics and Astronomy,Progress Queen Theoretical Mary University Physics of London,(2018) Mile End Road, London E1 4NS, UK 2 Research Center for the Early Universe (RESCEU), Graduate School of Science, The UniversityCURRENT of Tokyo, STATUS Tokyo AND 113-0033, FUTURE Japan PROSPECTS 3 DepartmentM/M⊙ of Physics, Tohoku University, Sendai 980-8578, Japan 10-20 10-15 10-10 10-5 1 105 1010 1015 10 4 GraduateGRBP School of Science and Technology, Hirosaki University, Hirosaki, Aomori 036-8561, Japan (BATSE) Quasar 1 5 InstituteSN MACHO forWB the Physics and Mathematics of the Universe (IPMU), Kepler 0.1 GRBF Icarus X/Radio RS (Fermi) NS The UniversityEri II GC of Tokyo, Kashiwa, Chiba 277-8568, Japan SF EROS Seg 1 aLIGO 0.01 LSS DH nd -3 HSC-M31 (Dated: Friday 2 March, 2018, 1:34pm) 10 XRB Planck
(sph) 10-4 We update the constraints onDF the fraction of the Universe going into primordial black holes (PBHs) BBN (disk) -5 9 50 15
Fraction 10 over the mass range 10 –10 g. Those smaller than 10 g would have evaporated by now due EGRB ⇠ 10-6 to Hawking radiation, so their abundance at formation is constrained by the e↵ects of evaporated -7 10 particlesGGRB on big bang nucleosynthesis, the cosmic microwave background (CMB), the galactic and p / n -8 extragalactic -ray backgroundsGWs and the pssible generation of stable Planck mass relics. PBHs 10 reheating 15 -9 larger than 10 g are subject to a variety of constraints associated with gravitational lensing, 10 Snowmass Cosmic Frontier ⇠ -distortion CMB Non-linear Acoustic μ dynamical e↵ects, influence on large-scale structure,Working accretion Group (2013) and gravitational waves. We discuss 10-10 1010 the1015 constraints1020 1025 on10 both30 10 the35 initial1040 collapse1045 1050 fraction and the current fraction of the cold dark matter in PBHs at eachM mass[g] scale. We also consider indirect constraints associated with the amplitude on the primordial density fluctuations, such as19 May second-order 14 tensor perturbations and µ-distortions Feng 10 arising from the e↵ect of acoustic reheating on the CMB. These constraints apply if and only if Each constraintPBHs are created comes from high-with peakscaveats of nearly and Gaussian may fluctuations.improve or There go is away. no single mass scale on which PBHs can provide all the dark matter but an extended mass function may do so. We therefore extend our analysis to cover this case. Still no definite evidence, although some affects claimed to be PBH signature.
cf. constraints on particle dark matter Contents
I. Introduction cf. constraints given in Jonathan Feng’s talk 4 A. Overview 4 B. PBH formation 4 1. Collapse from inhomogeneities 5 2. Soft equation of state 5 3. Collapse of cosmic loops 5 4. Bubble collisions 5 5. Collapse of domain walls 5 C. Mass and density fraction of PBHs 6 D. Evaporation of PBHs 7 1. Mass loss and evaporation timescale 8 2. Primary and secondary emission 9
II. Constraints on evaporating PBHs 11 A. Big bang nucleosynthesis 11 1. Early studies 11
§[email protected] CKS 2016
EXTENDED MASS FUNCTION?
Most constraints assume monochromatic PBH mass function
Can we evade standard limits with extended mass spectrum?
But this is two-edged sword!
PBHs may be dark matter even if fraction is low at each scale
PBHs giving dark matter at one scale may violate limits at others Do Do we PBHS AND LIGO need Pop III or primordial primordial or III Pop BHs ? (Smootslide)
Mass 20 40 60
Courtesy: Salvatore Vitale (MIT) The Astrophysical Journal, 487:L139–L142, 1997 October 1 q 1997. The American Astronomical Society. All rights reserved. Printed in U.S.A. The Astrophysical Journal, 487:L139–L142, 1997 October 1 q 1997. The American Astronomical Society. All rights reserved. Printed in U.S.A.
GRAVITATIONAL WAVES FROM COALESCING BLACK HOLE MACHO BINARIES Takashi Nakamura Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606, Japan Misao Sasaki and Takahiro Tanaka Department of Earth and Space Science, Osaka University, Toyonaka 560, Japan GRAVITATIONALand WAVES FROM COALESCING BLACK HOLE MACHO BINARIES Kip S. Thorne Theoretical Astrophysics, California Institute of Technology, Pasadena, CA 91125 Takashi Nakamura Received 1997 April 11; accepted 1997 July 23; published 1997 September 2 Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606, Japan ABSTRACT Misao Sasaki and Takahiro Tanaka If MACHOs are black holes of mass 0.5 M,, they must have been formed in the early universe when the temperature was 1 GeV. We estimate thatª in this case in our Galaxy’s haloDepartment out to 50 kpc of there Earth exist and5 # Space Science, Osaka University, Toyonaka 560, Japan 10 8 black hole binariesª the coalescence times of which are comparable to the age ofª the universe, so thatª the coalescence rate will be 5 # 1022 events yr21 per galaxy. This suggests that we can expect a few events per and year within 15 Mpc. Theª gravitational waves from such coalescing black hole MACHOs can be detected by the first generation of interferometers in the LIGOZVIRGOZTAMAZGEO network. Therefore, the existence of black Kip S. Thorne hole MACHOs can be tested within the next 5 yr by gravitational waves.Theoretical Astrophysics, California Institute of Technology, Pasadena, CA 91125 Subject headings: black hole physics — dark matter — gravitation — gravitationalReceived lensing — 1997 Galaxy: April halo 11; accepted 1997 July 23; published 1997 September 2
1. INTRODUCTION least 4 # 1011) of black holes in the halo, and it is natural to expectª that some of them are binaries. In § 2 we estimate theABSTRACT The analysis of the first 2.1 yr of photometry of 8.5 million fractionf(a, e)da de of all BHMACHOs that are in binaries stars in the Large Magellanic Cloud (LMC) byIf the MACHOs MACHO with are semimajor black axis holesa in range ofda and mass eccentricity0.5e in deM.We, they must have been formed in the early universe when the collaboration (Alcock et al. 1996) suggests that 0.6210.3 of the , 20.2 then use this distribution to estimate two observableª event rates. halo consists of MACHOs of mass 0.510.3 M in the standard 20.2 temperature, Prescience wasFirst of (at 1 theJapanese GeV. end of § We 2), the! estimate rate of microlensing that events in this we case in our Galaxy’s halo out to 50 kpc there exist 5 # spherical flat rotation halo model. The preliminary8 analysis of shouldª expect toward the LMC that is due to binaries with ª ª 4 yr of data suggests the existence of at least10 fourblack additional hole binaries the14 coalescence times of which are comparable to the age of the universe, so that the separation *2 # 10 cm; our result is in accord with the ob- microlensing events with t 90 days in the direction of the 22 21 dur coalescence rateservation will of onebe such5 event# 10 thus farevents (Bennett et yr al. 1996).per galaxy. This suggests that we can expect a few events per LMC (Pratt 1997). The estimatedª masses of these MACHOs Second (§ 3), the rate of coalescence of BHMACHO binaries are just the mass of red dwarfs. However, the contribution of ª year within 15out Mpc. to 15 Mpc The distance. gravitational The gravitational waves waves from from such such coalescing black hole MACHOs can be detected by the the halo red dwarfs to MACHO events should be small since coalescences should be detectable by the first interferometers the observed density of halo red dwarfs is toofirst low (Bahcall generation et of interferometers in the LIGOZVIRGOZTAMAZGEO network. Therefore, the existence of black in the LIGOZVIRGOZTAMAZGEO network (Barish 1997; Bril- al. 1994: Graff & Freese 1996a, 1996b). As for white dwarf let 1996; Tsubono 1996; Hough 1996), and our estimated event MACHOs, the mass fraction of white dwarfshole in the halo MACHOs should can be tested within the next 5 yr by gravitational waves. rate is a few events per year. In § 4 we discuss some impli- be less than 10% since, assuming the Salpeter initial mass cations of our estimates. function (IMF), the bright progenitors of moreSubject white dwarfs headings: black hole physics — dark matter — gravitation — gravitational lensing — Galaxy: halo than this would be in conflict with the number counts of distant galaxies (Charlot & Silk 1995). If the IMF has a sharp peak around 2 M,, then the fraction could be 50% or so (Adams 2. FORMATION OF SOLAR MASS BLACK HOLE MACHO BINARIES & Laughlin 1996), sufficient to explain the MACHO obser- 11 vations. The existence of such a population of halo white 1. SinceINTRODUCTION it is impossible to make a black hole of mass 0.5 least 4 # 10 ) of black holes in the halo, and it is natural to ª ª dwarfs may or may not be consistent with the observed lu- M, as a product of stellar evolution, we must consider the expect that some of them are binaries. In § 2 we estimate the minosity function (Gould 1997;The Lidman analysis 1997; Freese of 1997). the firstformation 2.1 of solaryr of mass photometry black holes in the very of early 8.5 universe million In any case, future observations of high-velocity white dwarfs (Yokoyama 1997; Jedamzik 1997). Our viewpoint here, how- fractionf(a, e)da de of all BHMACHOs that are in binaries in our solar neighborhood (Lidmanstars 1997) in the will prove Large whether Magellanicever, is not to Cloud study detailed (LMC) formation by mechanisms the MACHO but to white dwarf MACHOs can exist or not. estimate the binary distribution that results. 10.3 with semimajor axis a in range da and eccentricity e in de.We If the number of high-velocitycollaboration white dwarfs turns (Alcock out to be etThe al. density 1996) parameter suggests of BHMACHOs, thatQ 0.62, must20.2 be com- of the 1 BHM then use this distribution to estimate two observable event rates. large enough to explain the MACHOs, then stellar formation parable to Q (or Q ) to explain0.3 the number of observed halo consists of MACHOs of massb CDM 0.520.2 M, in the standard theory should explain why the IMF is sharply peaked at 2 MACHO events. For simplicity, we assume that BHMACHOs First (at the end of § 2), the rate of microlensing events we ª M,. If it is not, there arisesspherical a real possibility flat that rotation MACHOs halodominate model. the matter The energy preliminary density, i.e., Q 5 QBHM analysis, although of are absolutely new objects such as black holes of mass 0.5 it is possible to consider other dark matter components in ad- should expect toward the LMC that is due to binaries with M which could only be formed4 yr in the of early data universe, suggests or bosonª thedition existence to BHMACHOs. of To determineat least the four mean separation additional of 14 , separation *2 # 10 cm; our result is in accord with the ob- stars with the mass of the boson 10210 eV. Of course, it is the BHMACHOs, it is convenient to consider it at the time of microlensing events with tdur 90 days in the direction of the still possible that an overdense clumpª of MACHOs exists to- matter-radiation equality, t 5 t . At this time, the energy den- ª eq servation of one such event thus far (Bennett et al. 1996). ward the LMC (Nakamura, Kan-ya,LMC & Nishi(Pratt 1996), 1997). MACHOs Thesities estimated of radiation and masses BHMACHOs of are these approximately MACHOs equal 215 2 4 23 Second (§ 3), the rate of coalescence of BHMACHO binaries are brown dwarfs in the rotating halo (Spiro 1997), or and are given byreq 5 1.4 # 10 (Qh ) g cm , where h is are just the mass of red dwarfs. However, the contribution21 21 of MACHOs are stars in the thick disk (Turner 1997). the Hubble parameter in units of 100 km s Mpc . Corre- out to 15 Mpc distance. The gravitational waves from such In this Letter we considerthe the case halo of black red hole dwarfs MACHOs tospondingly, MACHO the mean events separation should of BHMACHOs be small with mass since (BHMACHOs). In this case, there must be a huge number (at MBH at this time is given by coalescences should be detectable by the first interferometers the observed density of halo red dwarfs is too low (Bahcall et L139 in the LIGOZVIRGOZTAMAZGEO network (Barish 1997; Bril- al. 1994: Graff & Freese 1996a, 1996b). As for white dwarf let 1996; Tsubono 1996; Hough 1996), and our estimated event MACHOs, the mass fraction of white dwarfs in the halo should rate is a few events per year. In § 4 we discuss some impli- be less than 10% since, assuming the Salpeter initial mass cations of our estimates. function (IMF), the bright progenitors of more white dwarfs than this would be in conflict with the number counts of distant galaxies (Charlot & Silk 1995). If the IMF has a sharp peak
around 2 M,, then the fraction could be 50% or so (Adams 2. FORMATION OF SOLAR MASS BLACK HOLE MACHO BINARIES & Laughlin 1996), sufficient to explain the MACHO obser- vations. The existence of such a population of halo white Since it is impossible to make a black hole of mass 0.5 ª dwarfs may or may not be consistent with the observed lu- M, as a product of stellar evolution, we must consider the minosity function (Gould 1997; Lidman 1997; Freese 1997). formation of solar mass black holes in the very early universe In any case, future observations of high-velocity white dwarfs (Yokoyama 1997; Jedamzik 1997). Our viewpoint here, how- in our solar neighborhood (Lidman 1997) will prove whether ever, is not to study detailed formation mechanisms but to white dwarf MACHOs can exist or not. estimate the binary distribution that results.
If the number of high-velocity white dwarfs turns out to be The density parameter of BHMACHOs, QBHM, must be com- large enough to explain the MACHOs, then stellar formation parable to Qb (or QCDM) to explain the number of observed theory should explain why the IMF is sharply peaked at 2 MACHO events. For simplicity, we assume that BHMACHOs ª M,. If it is not, there arises a real possibility that MACHOs dominate the matter energy density, i.e., Q 5 QBHM, although are absolutely new objects such as black holes of mass 0.5 it is possible to consider other dark matter components in ad- ª M, which could only be formed in the early universe, or boson dition to BHMACHOs. To determine the mean separation of stars with the mass of the boson 10210 eV. Of course, it is the BHMACHOs, it is convenient to consider it at the time of ª still possible that an overdense clump of MACHOs exists to- matter-radiation equality, t 5 teq. At this time, the energy den- ward the LMC (Nakamura, Kan-ya, & Nishi 1996), MACHOs sities of radiation and BHMACHOs are approximately equal 215 2 4 23 are brown dwarfs in the rotating halo (Spiro 1997), or and are given byreq 5 1.4 # 10 (Qh ) g cm , where h is MACHOs are stars in the thick disk (Turner 1997). the Hubble parameter in units of 100 km s21 Mpc21. Corre- In this Letter we consider the case of black hole MACHOs spondingly, the mean separation of BHMACHOs with mass
(BHMACHOs). In this case, there must be a huge number (at MBH at this time is given by L139 MNRAS 442, 2963–2992 (2014) doi:10.1093/mnras/stu1022
Possible indirect confirmation of the existence of Pop III massive stars by gravitational waveMNRAS 442, 2963–2992 (2014) doi:10.1093/mnras/stu1022
Tomoya Kinugawa,‹PossibleKohei Inayoshi, indirect confirmation Kenta Hotokezaka, of the existence Daisuke of Nakauchi Pop III massive stars by and Takashi Nakamuragravitational wave Department of Physics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan Tomoya Kinugawa,‹ Kohei Inayoshi, Kenta Hotokezaka, Daisuke Nakauchi Accepted 2014 May 21. Received 2014and May Takashi 16; in original Nakamura form 2014 February 20 Department of Physics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan MNRAS 442, 2963–2992 (2014) doi:10.1093/mnras/stu1022 Accepted 2014 May 21. Received 2014 May 16; in original form 2014 February 20 ABSTRACT We perform population synthesis simulations for Population III (Pop III) coalescing com- pact binary which merges within the age of the Universe. We found that the typical mass of ABSTRACT Pop III binary black holesWe (BH–BHs) perform population is 30 synthesis M so simulations that the inspiral for Population chirp signal III (Pop of III) gravita- coalescing com- ∼ ⊙ tional waves can be detectedpact binary up to whichz merges0.28 by within KAGRA, the age Adv. of the LIGO, Universe. Adv. We found Virgo that and the GEO typical mass of = network. Our simulationsPossiblePop suggest III binary that black the holes detection indirect (BH–BHs) rate is of30 the M coalescingso that confirmation the Popinspiral III chirp BH–BHs signal of gravita- of the existence of Pop III massive stars by ∼ 1 tional waves2 can.5 be detected1 up to3z 0.28 by⊙ KAGRA, Adv. LIGO, Adv. Virgo and GEO is 140(68) events yr (SFRp/(10 M yr Mpc )) Errsys for the flat (Salpeter) initial − − − − =· mass function, respectively,network. where Our simulations SFR⊙ and suggest Err thatare the the detection peak value rate of of the the coalescing Pop III Pop star III BH–BHs gravitationalp 1 sys 2.5 wave1 3 is 140(68) events yr− (SFRp/(10− M yr− Mpc− )) Errsys for the flat (Salpeter) initial formation rate and the possible systematic errors due to the⊙ assumptions· in Pop III population mass function, respectively, where SFRp and Errsys are the peak value of the Pop III star synthesis, respectively. Errsys 1correspondstoconventionalparametersforPopIstars. formation= rate and the possible systematic errors due to the assumptions in Pop III population From the observation ofsynthesis, the chirp respectively. signal of the Err coalescingsys 1correspondstoconventionalparametersforPopIstars. Pop III BH–BHs, we can determine = both the mass and the redshiftFrom the of observation the binary of the for chirp the signal cosmological of the coalescing parameters‹ Pop III determined BH–BHs, we canby determine the Planck satellite.Tomoya Ourboth simulations the mass and suggest the Kinugawa, redshift that of the the cumulative binary for the redshift cosmologicalKohei distribution parameters of thedetermined Inayoshi, by Kenta Hotokezaka, Daisuke Nakauchi the Planck satellite. Our simulations suggest that the cumulative redshift distribution of the coalescing Pop III BH–BHs depends almost only on the cosmological parameters. We might coalescing Pop III BH–BHs depends almost only on the cosmological parameters. We might be able to confirmand the existencebe able Takashi to of confirm Pop III the massive existence stars of Nakamura Pop of III mass massive30 stars M of massby the30 detections M by the of detections of ∼ ⊙ ∼ ⊙ gravitational wavesDepartment if thegravitational merger rate waves of of Physics,the if the Pop merger III massive rate Graduate of the BH–BHs Pop III massive School dominates BH–BHs of that Science, dominates of Pop that I Kyoto of Pop I University, Kyoto 606-8502, Japan BH–BHs. BH–BHs.
Key words: gravitationalKey waves words: – binaries:gravitational general. waves – binaries: general. Prediction before LIGO discovery 1INTRODUCTION Accepted 2014 May 21. Received 2014 May 16; in original form 2014 February 20 1INTRODUCTION Gravitational-wave astronomy with KAGRA,1 Adv. LIGO,2 Adv. Virgo3 and GEO4 will reveal the formation and evolution of binaries through Gravitational-wave astronomy withthe observedKAGRA, merger1 Adv. rates LIGO, of compact2 Adv. binaries, Virgo3 suchand asGEO binary4 will neutron reveal stars the (NS–NSs), formation neutron and evolution star–black hole of binaries binaries (NS–BHs)through and binary the observed merger rates of compactblack holesbinaries, (BH–BHs). such as For binary this gravitational-wave neutron stars (NS–NSs), astronomy, neutron estimates star–black of the merger hole rate binaries of compact (NS–BHs) binaries play and key binary roles to develop observational strategy and to translate the observed merger rates into the binary formation and evolution processes. black holes (BH–BHs). For this gravitational-waveThere are two methods astronomy, to estimate estimates the merger of rate the of merger compact rate binaries. of compact One is to use binaries observational play key facts roles such toas the develop observed NS–NSs observational strategy and to translatewhose coalescencethe observed time merger due to the rates emission into the of gravitational binary formation waves is and less evolution than the age processes. of the Universe. Taking into account the observation There are two methods to estimatetime, the the sensitivity merger of rate the radioof compact telescope, binaries. the luminosity One is function to use observational of pulsars and the facts beaming such as factor the so observedABSTRACT on, the probability NS–NSs distribution whose coalescence time due to thefunction emission of the of merger gravitational rate can be waves found. Foris less example, than Kalogerathe age of et al. the (2004b Universe.) found Taking that the into event account rate of the the coalescing observation NS–NSs is in the 5 1 1 4 1 1 5 range from 10− events yr− galaxy− to 4 10− events yr− galaxy− at the 99 per cent confidence level (see their fig. 2). time, the sensitivity of the radio telescope, the luminosity function× of pulsars and the beaming factor so on, the probabilityWe distribution perform population synthesis simulations for Population III (Pop III) coalescing com- The merger rate of NS–NSs can be restricted by the rate of the observed Type Ib and Ic supernovae (SNe), supposing that the formation function of the merger rate can be found. For example, Kalogera et al. (2004b) found that the event rate of the coalescing NS–NSs is in the of NS–NSs really starts from the massive binary zero-age main sequence (ZAMS) stars. This is because the formation of the second neutron 5 1 1 4 1 1 5 pact binary which merges within the age of the Universe. We found that the typical mass of range from 10− events yr− galaxy− to 4 10− events yr− galaxy− at the 99 per cent confidence level (see their fig. 2). star should occur× in association with Type Ib and Ic SNe in which the H-rich envelope and the He layer are lost, respectively, otherwise the The merger rate of NS–NSs can be restricted by the rate of the observed Type Ib and Ic supernovae (SNe), supposing thatPop the formation III binary black holes (BH–BHs) is 30 M so that the inspiral chirp signal of gravita- of NS–NSs really starts from the massive binary zero-age main sequence (ZAMS) stars. This is because the formation of the second neutron ∼ ⊙ star should occur in association with⋆ E-mail: [email protected] Ib and Ic SNe in which the H-rich envelope and the He layer are lost, respectively,tional otherwise waves the can be detected up to z 0.28 by KAGRA, Adv. LIGO, Adv. Virgo and GEO 1 http://gwcenter.icrr.u-tokyo.ac.jp/en/ 2 http://www.ligo.caltech.edu/ = 3 http://www.ego-gw.it/index.aspx/ network. Our simulations suggest that the detection rate of the coalescing Pop III BH–BHs 4 ⋆ http://www.geo600.org/ E-mail: [email protected] Note here that there are errors in Kalogera et al. (2004a)sothattheratesinKalogeraetal.(2004b) are the correct ones. 1 2.5 1 3 1 http://gwcenter.icrr.u-tokyo.ac.jp/en/ is 140(68) events yr− (SFRp/(10− M yr− Mpc− )) Errsys for the flat (Salpeter) initial 2 C 2014 The Authors · http://www.ligo.caltech.edu/ ⃝ ⊙ 3 http://www.ego-gw.it/index.aspx/Downloaded fromPublished https://academic.oup.com/mnras/article-abstract/442/4/2963/1338478 by Oxford University Press on behalf of the Royal Astronomical Society mass function, respectively, where SFRp and Errsys are the peak value of the Pop III star by guest 4 http://www.geo600.org/on 04 March 2018 5 Note here that there are errors in Kalogera et al. (2004a)sothattheratesinKalogeraetal.(2004b) are the correct ones. formation rate and the possible systematic errors due to the assumptions in Pop III population
C ⃝ 2014 The Authors synthesis, respectively. Errsys 1correspondstoconventionalparametersforPopIstars. Downloaded fromPublished https://academic.oup.com/mnras/article-abstract/442/4/2963/1338478 by Oxford University Press on behalf of the Royal Astronomical Society = by guest on 04 March 2018 From the observation of the chirp signal of the coalescing Pop III BH–BHs, we can determine both the mass and the redshift of the binary for the cosmological parameters determined by the Planck satellite. Our simulations suggest that the cumulative redshift distribution of the coalescing Pop III BH–BHs depends almost only on the cosmological parameters. We might be able to confirm the existence of Pop III massive stars of mass 30 M by the detections of ∼ gravitational waves if the merger rate of the Pop III massive BH–BHs dominates⊙ that of Pop I BH–BHs.
Key words: gravitational waves – binaries: general.
1INTRODUCTION Gravitational-wave astronomy with KAGRA,1 Adv. LIGO,2 Adv. Virgo3 and GEO4 will reveal the formation and evolution of binaries through the observed merger rates of compact binaries, such as binary neutron stars (NS–NSs), neutron star–black hole binaries (NS–BHs) and binary black holes (BH–BHs). For this gravitational-wave astronomy, estimates of the merger rate of compact binaries play key roles to develop observational strategy and to translate the observed merger rates into the binary formation and evolution processes. There are two methods to estimate the merger rate of compact binaries. One is to use observational facts such as the observed NS–NSs whose coalescence time due to the emission of gravitational waves is less than the age of the Universe. Taking into account the observation time, the sensitivity of the radio telescope, the luminosity function of pulsars and the beaming factor so on, the probability distribution function of the merger rate can be found. For example, Kalogera et al. (2004b) found that the event rate of the coalescing NS–NSs is in the 5 1 1 4 1 1 5 range from 10− events yr− galaxy− to 4 10− events yr− galaxy− at the 99 per cent confidence level (see their fig. 2). × The merger rate of NS–NSs can be restricted by the rate of the observed Type Ib and Ic supernovae (SNe), supposing that the formation of NS–NSs really starts from the massive binary zero-age main sequence (ZAMS) stars. This is because the formation of the second neutron star should occur in association with Type Ib and Ic SNe in which the H-rich envelope and the He layer are lost, respectively, otherwise the
⋆ E-mail: [email protected] 1 http://gwcenter.icrr.u-tokyo.ac.jp/en/ 2 http://www.ligo.caltech.edu/ 3 http://www.ego-gw.it/index.aspx/ 4 http://www.geo600.org/ 5 Note here that there are errors in Kalogera et al. (2004a)sothattheratesinKalogeraetal.(2004b) are the correct ones.
C ⃝ 2014 The Authors Downloaded fromPublished https://academic.oup.com/mnras/article-abstract/442/4/2963/1338478 by Oxford University Press on behalf of the Royal Astronomical Society by guest on 04 March 2018 Did LIGO detect dark matter?
Simeon Bird,⇤ Ilias Cholis, Julian B. Mu˜noz, Yacine Ali-Ha¨ımoud, Marc Kamionkowski, Ely D. Kovetz, Alvise Raccanelli, and Adam G. Riess1 1 Department of PhysicsarXiv:1603.00464 and Astronomy, Johns Hopkins University, 3400 N. Charles St., Baltimore, MD 21218, USA week ending PHYSICAL REVIEW LETTERS -15 AUGUST-1 2016 PRL 117, Dark061101 matter (2016) in 20-100 MO binaries may provide observed rate of 2-53 Gpc yr We consider the possibility that the black-hole (BH) binary detected by LIGO may be a signature of dark matter. Interestingly enough, there remains a window for masses 20 M Mbh 100 M . . Primordialwhere primordial Black black Hole holes Scenario(PBHs) may for constitute the Gravitational-Wave the dark matter. If two Event BHs in a GW150914 galactic halo pass su ciently close, they radiate enough energy in gravitational waves to become gravitationally bound. The bound BHs1 will rapidly spiral2 inward due to emission3,1 of gravitational radiation4 and ultimatelyMisao merge. Sasaki, UncertaintiesTeruaki in Suyama, the rate forTakahiro such events Tanaka, ariseand from Shuichiro our imprecise Yokoyama knowledge of the 1Center for Gravitational Physics, Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan 2 phase-space structure of galactic halos on the smallest scales. Still, reasonable estimates span a range Research Center for the Early Universe (RESCEU),3 1 Graduate School of Science, The University of Tokyo, Tokyo 113-0033, Japan that overlaps the 23 53 Gpc yr arXiv:1603.08338rate estimated from GW150914, thus raising the possibility that LIGO has detectedDepartment PBH of dark Physics, matter. Kyoto PBH University, mergers Kyoto are 606-8502, likely to Japan be distributed spatially 4Department of Physics, Rikkyo University, Tokyo 171-8501, Japan more like darkOnly matter need than small luminous f and mattercomparable and have to no limits optical from nor neutrinoCMB distortion counterparts. They may be distinguished from(Received mergers 3of April BHs 2016; from morepublished traditional 2 August astrophysical 2016) sources through the observedWe point mass out spectrum, that the gravitational-wave their high ellipticities, event GW150914 or their stochastic observed gravitational by the LIGO wavedetectors background. can be LIGONextexplained generation gravitational by the experiments coalescence wave of will primordial detection, be invaluable black holesprimordial in performing (PBHs). It is black these found tests. that holes the expectedand the PBH near-IR merger rate would exceed the rate estimated by the LIGO Scientific Collaboration and the Virgo Collaboration if cosmic infrared background anisotropies P EOP LE PBHs were the dominant component of dark matter, while it can be made compatible if PBHs constitute a 1 The naturefraction of the of dark dark matter. matter Intriguingly, (DM) is the one abundance of the of PBHsmerge required via emission to explain the of suggestedGWs in lesslower than bound a Hubble time. A. Kashlinsky1, most longstandingon the and event puzzling rate, > 2 events questions Gpc−3 inyr− physics.1, roughly coincidesBelow withwe first the existingestimate upper roughly limitthe set by rate the of such mergers Cosmological measurements have now determined with and then present the results of more detailed calcula- nondetection of the cosmic microwave backgroundarXiv:1605.04023 spectral distortion. This implies that the proposed PBH exquisite precisionscenario the may abundance be tested of in DM the not-too-distant [1, 2], and from future. tions. We discuss uncertainties in the calculation and both observations and numerical simulations weABSTRACT know some possible ways to distinguish PBHs from BH bina- PBHs generate early structure => infrared backgroundThe cosmic infrared background (CIB)—possibly featuring primordial black holes. (Credit: NASA/JPL-Caltech/ quite a bit aboutDOI: its10.1103/PhysRevLett.117.061101 distribution in Galactic halos. Still, ries from more traditionalA Kashlinsky (Goddard)). astrophysical sources. black holes was at frst controversial, with neither funded and what will gain you a PhD and a job. the nature of the DM remains a mystery. Given the ef- Consider two PBHsEinstein nor Eddington approaching believing in them, and it eachBut the most otherexciting issues to on my mind a are those hy- was 50 years before the evidence became incon- which go beyond the mainstream, because that’s LIGO’s discovery of a gravitational wave from two mergingtrovertible. black Now people holes argue about(BHs) whether where the of new paradigms are likely to emerge. ficacy with which weakly-interacting massive particles— perbolic orbit withthe some black holes areimpact rotating and how they parameter are Theories-3 of the multiverse, and quantum relative-2 gravity, Tidal forcesarXiv:1605.04932 of inflationary perturbations suppress merger accreting.rate => f ~ 2 x10extra dimensions– 2 etc.x are 10 inevitably regarded Introduction.similar—The masses gravitational-wave rekindled suggestions event GW150914 that primordialhaving a sufficiently BHs (PBHs) small make separation up the can darkwith form skepticism ainitially binary—and such ideas in might for many years the favored particle-theory explanation— velocity vpbh. As the PBHs near eachalso be regarded other, as lying on they the border of pro- phys- What you’re talking about is an amazing observed by the LIGO detectors [1] revealed the existence the early Universe and coalesce withinics and the metaphysics age by some of people the—but they matter (DM). If so, PBHs would add a Poissonian isocurvaturejourney ofdensity physics. If you could fluctuationsay something may turn out to be more important in the long have eluded detection, it may be warranted to consider duce a time-varyingto a young quadrupole physicist, what would you momentsay to and thus GW run. Young people probably shouldn’t work in of black holes (BHs) with a mass of around 30M in the Universe. We applythem the at the formation beginning of their journey scenario now? these areas in if you Ref. want to get[8] a job. Onto the other other possibilitiescomponent for DM. to Primordial the inflation-produced black holes⊙ (PBHs) adiabaticemission. density The fluct PBHuations.If it was pair a young Forperson, becomes I would LIGO’s say that gravitationallyyou hand, BH young people are inevitably boundinterested in form of binaries. Although there are several possible the present case wherehave to the toe the party PBHs line if you want are to pursue about a these areas30 andM are mostand likely to theproduce the are one such possibility [3–6]. if the GW emissioncareer, exceeds because mainstream the physics initial is what gets new kinetic paradigms. energy. The explanationsparameters, for the origin this of extra those component BHs as well would as the dominatefraction the of small- PBHsscale in dark power matter responsible is a free for parameter.⊙ We > cross section for this process is [19, 20], Here we considercollapse whether of early the DM two halos30 atM z ∼black10, where holes first luminous sources formed. We quantify formation of the binaries (see Ref.⇠ [2] and references present a detailed computation of the event rate in the next detectedtherein), by the LIGO answer [7] couldis yet to plausibly be elucidated. be PBHs. Assuming There all is 2/7 18/7 the resultant increase in high-z abundancessection. of collapsed The resultant halos85 that event⇡ are rate suitable2 turnsvpbh out for to exceed the a window for PBHs to be DM if the BH mass is in the = ⇡ R −3 −1 the BH binariesproducing relevant the to first the LIGO generation observation of stars have and the luminousevent rate sources mentioned.Thesignificantlyincreased above3 (2–53sGpcc yr ) if PBHs are rangesame 20 physicalM . M parameters,. 100 M such[8, as 9]. masses Lower and masses spins, are as the dominant component✓ ◆ of dark⇣ matter.⌘ Intriguingly, abundance of the early halos would naturally explain the observed source-subtracted14 2 18/7 2 excludedthose of by GW150914, microlensing the merger surveys event [10–12]. rate was Higher estimated masses as however, it falls=1.37 in the10 LIGOM30 rangevpbh if200 PBHspc , are a (1) ⇥ would2–53 disruptGpc−near-IR3 yr wide−1 [3] binaries cosmic. infrared[9, 13, 14]. background It has been (CIB) ar- fluctuations,subdominant whi componentch cannot of be dark accounted matter with for the fraction where Mpbh is the PBH mass, and M30 the PBH mass guedIn that this PBHs Letter,by known in we this discuss massgalaxy range the populations. possibility are excluded that For the by LIGO’s CMB event BHthat parameters nearly saturates this increase the upper is limit such set that by2 the the nondetection in units of 30 M , Rs =2GMpbh/c is its Schwarzschild constraintsGW150914 [15,observed was 16]. caused However, CIB by fluctuation a merger these constraints of levels a primordial at 2 require to BH 5 µmcanbeproducedifonlyatinyfractionof the cosmic microwave background (CMB) spectral radius, vpbh is theSeptember relative 2016 velocity3 of two PBHs,Physics Education and modeling(PBH) binary. of several PBHs complex are BHs that physical have existed processes, since the includ- very distortion due to gas accretion onto PBHs [9]. 1 of baryons in the collapsed DM halos forms luminousvpbh 200 sources.is this velocityGas accretion in units onto of 200 these km sec . ingearly the accretion epoch in cosmic of gas history onto a before moving any BH, other the astrophysical conversion Recently,We begin it with was claimed a rough in but Ref. simple[10] (see and also illustrative Ref. [11]) es- object had beenPBHs formed in collapsed[4]. The most halos, popular where mechanism first stars to shouldthat the also event form, GW150914 would as straightforwardly well as the event rate estimated of the accreted mass to a luminosity, the self-consistent timate of the rate per unit volume of such mergers. Sup- produce PBHsaccount is the for direct the observed gravitational high collapse coherence of between a by LIGO the CIB can and be explained unresolved by the cosmic merger X-ray of PBHs even if feedback of the BH radiation on the accretion process, pose that all DM in the Universe resided in Milky-Way primordial density inhomogeneity [5,6]. If the primordial PBHs are the dominant component of dark matter. Our arXiv:1603.00464v2 [astro-ph.CO] 30 May 2016 and the depositionbackground of the in radiated soft X-rays. energy We as discussheat in themodifications possiblyrequiredintheprocesses12 like halos of mass M = M12 10 M and uniform mass photon-baryonUniverse wereof firstplasma. highly star inhomogeneous formationA significant if LIGO-type [ (andO 1 diin termscult BHs ofto indeedstudy make differs up from the Ref. bulkorallofDM.The[10] in the following3 two points: the comoving curvature perturbation] onð Þ superhorizon (1)density the formation⇢ =0.002 process⇢0.002 M of PBHpc binarieswith ⇢0 and.002 (2)1. the As- quantify) uncertaintyarguments should are valid therefore only be if associated the PBHs with make upsuming all, or a at uniform-density least most, of DM, halo but of volume at the V = ⇠M/⇢,the thisscales, upper as limit realized [17], in and some it inflation seems worthwhile models (see to Ref. exam-[7] fraction of PBHs in dark matter. First, in Ref. [10] PBH same time the mechanism appears inevitable ifrate DM of is mergers made of per PB haloHs. would be ineand whether references PBHs therein), in this an mass inhomogeneous range could region have other upon binaries are assumed to be formed due to energy loss by horizon reentry would undergo gravitational collapse gravitationalN radiation(1/2)V (⇢ when/M two)2 PBHs v accidentally pass by observational consequences. ' pbh and form a BH. The mass of the BH is approximately each other with a sufficiently12 small impact11 parameter./7 1 This In this Letter, we show that if DM consists of 30 M 3.10 10 M12 ⇢0.002 vpbh 200 yr . (2) equal to the horizon mass at the time of formation,⇠ mechanism' is different⇥ from what we consider in this Letter BHs, then the rate for mergers11 of such2 PBHs falls1. within Introduction MBH ∼ 30 M 4 × 10 = 1 zf , where zf is the (see the next section). Second, in Ref. [10] the fraction of the merger rate⊙ inferred½ð fromÞ ð GW150914.þ Þ In any galactic PBHs in dark matter to explain the estimated gravitational- arXiv:1605.04023v1 [astro-ph.CO] 13 May 2016 formation redshift. Thus, it is possible that PBHs with a halo,mass there of around isLIGO’s a chance30 recentM twoare BHsdiscovery formed will undergodeep of the in gravitational the a hard radiation- scat- wavewave1 In (GW) our event analysis, from ratean by PBH inspiralling the binaries LIGO-Virgo are binary formed Collaboration black inside hole halos is at ofz =0. ter,dominated lose(BH) energy systemera. to a softof⊙ essentially gravitational equal wave mass (GW) BHs burst ( 30Morder⊙)atRef. unity, [18]z considered while0.1(Abbott in our instead case et al.we binaries require2016b) which it has to form be led as at tosmall early as times ∼ and merge∼ over a Hubble time. and becomeThesuggestion event gravitationally rate that of the all or PBH bound. at leastbinary This a mergers significant BH binary has part been will of thethe dark upper m limitatter obtained (DM) is in made Ref. [9] up. Namely, of primordial our claim is that PBHs as a small fraction of dark matter can explain the alreadyBHs given (PBH) in Ref.(Bird[8] etfor al. 2016; the case Clesse where & PBHsGarc´ıa-Bellido are 2016). In particular, Bird et al. (2016) argue massive compact halo objects with their mass around event rate suggested by the detection of GW150914. 0.5Mthatand this constitute PBH mass the dominantrange is not component ruled out of by dark astronomicalThroughout observations this Letter, and we the set observedthe speed ofrate light at to be −3 −1 matter.⊙(a In few) Ref. [8] Gpcit wasyr found(Abbott that two et neighboring al. 2016a) PBHs can beunity, accountedc 1. for if DM PBHs are distributed in ∼ ¼ dense, low velocity-dispersion concentrations which escaped merging. There is abundant motivation 0031-9007=16=117(6)=061101(5) 061101-1 © 2016 American Physical Society 1 Code 665, Observational Cosmology Lab, NASA Goddard Space Flight Center, Greenbelt, MD 20771 and SSAI, Lanham, MD 20770; email: Alexander.Kashlinsky@nasa.gov Primordial black holes with an accurate QCD equation of state The QCD phase transition 1, 1, 2, 1, 3, Christian T. Byrnes, ⇤ Mark Hindmarsh, † Sam Young, ‡ and Michael R. S. Hawkins § • As the Universe1 Departmentcools below 1 ofGeV, Physics strong andinteractions Astronomy, confine University quarks of Sussex, Brighton BN1 9QH, UK into hadrons and the equation of2Department state (w) dips. of Physics and Helsinki Institute of Physics, Borsanyi et al (2016)The have resultant recently madePL 64,thearXiv:1801.06138 first FI-00014 mass definitive University predictions function of Helsinki, Finlandof PBHs of this period (to 1% accuracy) 3 2 Institute for Astronomy, University of Edinburgh, c 1/2 2 2 Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK The Hubble volume (horizon) mass (MH) during the peak decrease is f(M) M e • (Dated: January 19, 2018) about one solar mass. PBHs form with a comparable mass /
0.35Making use of definitive new lattice computations of the Standard Model thermodynamics during 0.100 10-4 the quantum chromodynamic (QCD)2 phase transition, we calculate the enhancement 2 =0.003 in the mass 0.30 =0.004 10-5 distribution0.010 of primordial black holes (PBHs) due to the softening of the equation of state. We find that0.25 the enhancement peaks at approximately 0.7M , with the formation rate increasing by at least 10 -6
0.20 f two orders0.001 of magnitude due to the softening of thef equation of state at this time, with a range of approximately0.15 0.3M !6 QCD PHASE RANSIITON arXiv:1801.06138v1 [astro-ph.CO] 18 Jan 2018 ⇤ [email protected] † [email protected] ‡ [email protected] § [email protected] Primordial black holes in the axion-like curvature model and the LIGO events K Ando, K Inomata, M Kawasaki, K Mukaida, T Yanagida THIS MEETING Seven hints for PBH-DM Hint 1: spins ofHint LIGO from spinblack of LIGO holes black holes? III PARAMETER INFERENCE e↵ =[m1S1 cos(✓LS1 )+m2S2 cos(✓LS2 )]/(m1 + m2) GW170814 FIG. 3. A Mollweide projection of the posterior probability density for the location of the source in equatorial coordinates (right ascension is measured in hours and declination is mea- sured in degrees). The location broadly follows an annulus +0.4 corresponding to a time delay of 3.0 0.5 ms between the ⇠ Hanford and Livingston observatories. We estimate that the FIG. 5. Posterior probability densities for the e↵ective in- area of the 90% credible region is 1200 deg2. ⇠ spiral spin e↵ for GW170104,GW150914,LVT151012and AdaptedGW151226 from Adv.LIGO/VIRGO [13], together with June the 2017 prior release probability (supl. distri-material) bution for GW170104. The distribution for GW170104 uses both precessing waveform models, but, for ease of compari- son, the others use only the e↵ective-precession model. The prior distributions vary between events, as a consequence of di↵erent mass ranges, but the di↵erence is negligible on the scale plotted. FIG. 4. Posterior probability density for the source luminos- ity distance DL and the binary inclination ✓JN.Theone- dimensional distributions include the posteriors for the two waveform models, and their average (black). The dashed lines mark the 90% credible interval for the average posterior. The two-dimensional plot shows the 50% and 90% credible regions plotted over the posterior density function. FIG. 6. Posterior probability density for the final black hole values because of the greater preference for spins with mass Mf and spin magnitude af .Theone-dimensionaldis- components antialigned with the orbital angular momen- tributions include the posteriors for the two waveform mod- tum. els, and their average (black). The dashed lines mark the The final calibration uncertainty is su ciently small 90% credible interval for the average posterior. The two- to not significantly a↵ect results. To check the impact dimensional plot shows the 50% and 90% credible regions of calibration uncertainty, we repeated the analysis using plotted over the posterior density function. the e↵ective-precession waveform without marginalising 4 PBHS AS GENERATORS OF COSMIC STRUCTURES B.J. Carr & J. Silk arXiv:1801.00672 What is maximum mass of PBH? 6 10 Could 10 -10 MO black holes in galactic nuclei be primordial? 5 -6 1/2 BBNS => t < 1 s => M < 10 MO …..but b < 10 (t/s) Supermassive PBHs could also generate cosmic structures on larger scale through ‘seed’ or ‘Poisson’ effect 4 12 Upper limit on µ distortion of CMB excludes 10 < M/MO < 10 for Gaussian fluctuations but some models evades these limits. 4 -1 Otherwise need accretion factor of (M/10 Mo) Hoyle & Narlikar 1966, Meszaros 1975, Carr & Silk 1983, Carr & Rees 1984 II. PBHS AS DARK MATTER AND LIGO SOURCES [EXPAND] There are general arguments that PBHs rather than WIMPs provide the dark matter [17–19]. PBHs can provide DM with fine-tuning of the collapse fraction [3], A. Monochromatic PBH mass function9 1/2 (m) 10 (m/M ) . (2.1) ⇠ TheIf PBH the PBHs mass is have of order a single the horizon mass m mass, the at initial formation density but fluctuation there are only on few a scale massM windowsis allowed observationally [5, 6]. The most interesting is the IMBH range (10 100M ), which m/M (seed) would have implications for LIGO [20], although the LIGO observations would only require i 8 (4.1) ⇡ 1/2 a small fraction of the dark matter<> to(fm/M be in PBHs) (Poisson) [21], the infrared, background [22] and lensing of fast radio bursts [23]. The> other windows are the lunar-mass range (1020 1024g) where f is the fraction of the dark: matter in the PBHs. If PBHs provide the dark matter, 16 17 fand1andthePoissone atomic (sized) range↵ect (10 dominates10 g) for but all theseM but would we also be consider unimportant scenarios for large-scale with f 1. ⇠ ⌧ Thestructure, Poisson the e↵ seedect thenand Poisson dominates e↵ects for beingM>m/f negligible.and the [GRAVITY seed e↵ect WAVES.] for M 15 1 4 only a small fraction is bound by the seeds at the present epoch for f z 10 .On ⌧ eq ⇠ the other hand, for f>zB/zeq the bound fraction at zB would exceed 1, so competition between the seeds will reduce the mass of each bound region to at most M m/f. But ⇠ this is precisely the value of M above which the Poisson e↵ect dominates. If f is is treated as a free parameter, unconstrained by observations, the dependence of M on the redshift zB is as indicated in Fig. 2(b). However, it is interesting to obtain the constraints on the function M(zB)impliedbythelimitsonf(m)discussedinSec.II.Ifthe PBHs provide the dark matter (f 1), the Poisson e↵ect always dominates and Eq. (4.3) and ⇠ the condition m<102M imply M<109M . More generally, the wide-binary constraint (2.2) and the second expession in Eq. (4.3) imply 7 2 2 10 mzB (m 10 M ) . 8 9 2 2 3 M< 10 z M (10 M 4 4 1 2 3 10 (m/10 M ) (10 M 2 _ 10 Mo 15 where Meq 10 M is the horizon:> mass at teq. These fluctuations and the e↵ect on the | | | | > M | ⇠| | | < zB m m/f M M CDM eq binding4000 mass4000 aref shownzCDM 1 by the lines labelled “CDM” in Fig. 2. In the mass range M 17 Can constrain PBH scenarios by requiring that various cosmic structures do not form too early Extended PBH mass function => DM and cosmic structures => gravity wave background over huge frequency range the Schwarschild radius, so the Bondi formula gives (Bondi 1952) dm/dt R2c ⇢ (Gm2)/(c3t2) . (6.6) ⇠ a s ⇠ Integrating this equation gives 1/m 1/m (G/c3)(1/t 1/t )(6.7) i ⇠ i and hence m m /[1 m /M (t )+Gm /(c3t)] . (6.8) ⇠ i i H i i Therefore there is very little accretion for m M (t ) (i.e. for PBHs initially much smaller i ⌧ H i than the horizon). Although Eq. (6.8) suggests m M (t)form M (t ), implying that ⇠ H i ⇠ H i aPBHwiththehorizonmassatformationshouldcontinuetogrowlikethehorizon,this neglects the cosmic expansion. A more careful analysis shows that self-similar growth is impossible, so that accretion is always negligible in the radiation era (Carr & Hawking 1974). A. Predicted mass function of galaxies A. Predicted massDuring function the matter-dominated of galaxies era after teq, Ra is increased (since cs falls below c)andso the accretion rate is also increased. Providing the matter temperature T follows the usual An interesting consequence ofAn the interesting seed theory consequence is that of there the seedshould theory be a is simple that there relation should be a simple relation background evolution (i.e. before reheating), the Bondi formula gives between the mass spectrum of the holes and that of the resulting galaxies. If M m , between the mass spectrum of the holes and that of the resulting galaxies. If M m , g / g / where the above analysis2 suggests2 2 =1,weexpectthenumberofgalaxieswithmassinthe3 2 2 3/2 2 where the above analysis suggests dm/dt=1,weexpectthenumberofgalaxieswithmassintheRacs⇢ (G m )/(Gcst ) Gm (kTeq/mp) teq . (6.9) range (M,M +⇠dM)tobe⇠dNg(M)where ⇠ range (M,M + dM)tobedNg(M)where Integrating this gives (1 ↵)/ SUPERMASSIVE PBHS AS SEEDSdNg/dM FORM GALAXIES . (4.1) (1 ↵)/ / dN /dM M . (4.1) g 3/2 2 1/m/ 1/m ⌘t with ⌘ G(m /kT ) t . (6.10) The Schechter luminosity i function⇠ [39] is ⌘ p eq eq The Schechter luminosity function [39] is 3 1.07 HenceSeed effect => MB ~ 10 m (zB/10) (L) L exp( L/L ) , (4.2) / ⇤ Þ naturally explain1.07 MBH/Mbulge relation (L) L exp( L/Lm) , mi/(1 mi⌘t) , (4.2) (6.11) where the/ exponent increases ⇤ to 1⇡.8 at high redshift [REF]. On the other hand, the Press- where the exponentwhich increases divergesSchechter to 1.8 at at mass a high time function redshift [40] [REF]. is On the other hand, the Press- Schechter mass function [40] is 2 3 Also predict mass function⌧ =1 of/( galaxiesdN⌘mg/dM) ( M(cf.M /mPressexp()(c-Schechter)M/M/c) t) , , (4.3)(6.12) i ⇠ / eq i eq ⇤eq 2 12 withdNg/dM an3 exponentialM exp(16 upperM/M cut-o↵) ,at M 10 M and the(4.3) integrated4 density ⇢g(M)is Hence where Meq c teq/G/ 10 M is the⇤ horizon⇤ ⇠ mass at teq 10 yandceq c. Thus the logarithmically⇠ ⇠ divergent at the low mass end. Therefore,⇠ if =1,weneed⇠↵ 2. If the mass diverges at a time which12 precedes the present epoch (t 1010y) for ⇡ with an exponential upperBondi cut-o accretion↵ at M => 10mM mand/(1 the integratedm ⌘t) , density ⇢og(⇠M)is (4.11) PBHs are generated⇤ ⇠ by⇡ scale-invariant i fluctuations,i it is interesting that one would expect logarithmically divergent at the low mass end. Therefore, if =1,weneed10↵ 2. If the => dthisiverges if they by form now in afor ‘dust’mi (i.e.>M matter-dominated)eq(teq/to) 10 era.M⇡. (6.13) which diverges at a time ⇠ PBHs are generated by scale-invariantFor a monochromatic fluctuations, massit is interesting function, Eq. that (3.1) one and would the linear expect growth law t2/3 for / this if they form in a ‘dust’ (i.e. matter-dominated) era. t>teq imply that a mass M binds at a30 time 3 ⌧ =1/(⌘mi) (Meq/mi)(ceq/c) teq , 2/3 (4.12) For a monochromatic mass function, Eq. (3.1) and the3 linear/2 growth law 3/2 t for 3/2 ⇠ M M m 1015M 10 / tB(M) teq O 10 12 8 y , (4.4) t>teq imply that a mass3 M binds at15 a time ⇠ m ⇠ 10 M4 10 M where Meq c teq/G 10 M is horizon✓ mass◆ at teq ✓ 10 yand◆ ✓ ceq ◆c. Thus accretion 9 12 9 ⇠ so⇠ one3/ requires2 a PBH mass m3/2 10 M to bind⇠3/2 a galaxy mass of M⇠ 10 M by tB 10 y. M M ⇠ 10m ⇠ ⇠ is only importantt (M) t by the present1010 epoch (to 10 y) for [55]y , (4.4) B ⇠ eq Form an extended⇠ mass1012 function,M ⇠ one10 has8M ✓ ◆ ✓ ◆ ✓ ◆ 3/2 3(↵ 2)/2(↵ 1) 9 M 12 M 9 so one requires a PBH mass m 10 M to bind a galaxy mass of M 9 10 M by tB 10 y. ⇠ mi >MtB(Meq) (tteqeq/to) 10⇠ M . ⇠ , (4.13)(4.5) ⇠ mseed(M) / mdm For an extended mass function, one has ⇠ ✓ ◆ where we have used Eq. (3.6). 3/2 9 3(↵ 2)/2(↵ 1) This suggests that PBHs largerM than 10MM will not be found at the centres of galaxies t (M) t One can make very specific predictions about, the structure(4.5) of the galaxy which would B ⇠ eq m (M) / m because they wuld haveresult swallowed fromseed the seed the theory.✓ entiredm If we◆ galaxy. assume that each shell of gas virializes after it has stopped where weNote have used that Eq. accretion (3.6).expanding rate reaches (i.e. settles the down Eddington with a radius limit of about when half its radius at maximum expansion), 9/4 One can make very specificthen predictions one would about expect the the structure resultant galaxy of the to galaxy have awhich density would profile ⇢(r) r . This / result from the seed theory. If we assume thatdm/dt each shell⌘ ofm gas2 virializesm/t after, it has stopped (4.14) ⇠ ⇠ ED9 expanding (i.e. settles down with a radius of about half its radius at maximum expansion), 7 9/4 then onewhere wouldtED expect4 the10 resultanty is the galaxy Salpeter to have timescale a density [REF]. profile ⇢ Hence(r) r we would. This only have super- ⇡ ⇥ / Eddington accretion for 9 1 12 m>(⌘tED) Meq(teq/tED) 10 M . (4.15) ⇠ ⇠ But this never applies for the SMBHs of interest. Note that the density and temperaure at the accretion radius will only correspond to the mean cosmological condiitons initially. A more complicated analysis is required once the growing bound cloud around each PBH becomes larger than the accretion radius. V. EFFECTS ON OTHER COSMIC STRUCTURES A. Lyman-↵ forest To make Lyman-↵ clouds, here taken to be the precursors of galaxies somewhat smaller 10 than galaxies themselves [OK?], we require M 10 M and zB 10, which implies m ⇠ ⇠ ⇠ 104M for the Poisson e↵ect. Indeed, in this context Afshordi et al. [14] used observations of the Lyman-↵ forest to obtain an upper limit of about 104M on the mass of PBHs which provide the dark matter. This conclusion was based on numerical simulations, in which the 12 PRIMORDIAL BLACK HOLEs = PBHs LIGO Dark matter in Planck relics or sublunar or IMBHs PBHs of M~0.5M0 form at quark-hadron era Jedamizk & Nemeyer, -3 6y MACHO results èM>0.5MO Microlensing of QSOs èM>10 MO Hawkins Alcock et al POPULARITY Dynamical/accretion -3 limits exclude PBHs of M~10 M0form at quark-hadron era Microlensing constraints Crawford & Schramm Hamadache et al PBHs form from inhomogeneities Hawking, Carr | | | | | | | | 1971 1982 1993 1997 1999 2005 2010 2015 CONCLUSIONS PBHs have been invoked for three roles Dark matter LIGO events Cosmic structure These are distinct roles but with an extended mass function PBHs could possibly fulfill all three. This talk is dedicated to the memory of Stephen Hawking, He was a pioneer of primordial black holes. If they play any of the roles discussed in this talk, this may have been his most prescient and important work