Low Mass Black Holes from Dark Core Collapse
TTIFR/TH/20-32, CERN-TH-2020-145
Low Mass Black Holes from Dark Core Collapse
Basudeb Dasgupta ID , ∗ Ranjan Laha ID , † and Anupam Ray ID ‡ Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India Theoretical Physics Department, CERN, 1211 Geneva, Switzerland (Dated: September 4, 2020)Unusual masses of the black holes being discovered by gravitational wave experiments pose fun-damental questions about the origin of these black holes. Black holes with masses smaller thanthe Chandrasekhar limit ≈ . M (cid:12) are essentially impossible to produce through stellar evolution.We propose a new channel for production of sub-Chandrasekhar mass black holes: stellar objectscan catastrophically accrete non-annihilating dark matter in dense regions of the Universe, owingto interactions of dark matter and ordinary matter, and the dark core subsequently collapses. Thewide range of allowed dark matter masses allows a smaller effective Chandrasekhar limit, and thussmaller mass black holes. We point out several avenues to test our proposal. Introduction –
A non-baryonic form of matter, knownas dark matter (DM), forms a dominant component ofour Universe [1]. Experimental searches have been tryingto search for DM particles but no conclusive evidencehas shown up yet. Primordial black holes (PBHs) arean alternate well-motivated DM candidate [2–5] that canconstitute all of the DM density [6–11]. PBHs as a DMcandidate have received renewed attention [12–15]. Nu-merous constraints exist on their density [9, 16–38] andmany other tests have been proposed [6, 39–43]. However,there are no established formation mechanisms whichnaturally produce the correct abundance of PBHs. Theinitial abundance of PBHs is exponentially sensitive tothe spectrum of density perturbations and the thresh-old for collapse; fine-tuning of parameters is required toachieve a non-negligible abundance.With the remarkable advances in gravitational wave(GW) and multi-messenger astronomy, the detection ofa sub-Chandrasekhar mass ( (cid:46) M (cid:12) ) BH may be justaround the corner signaling new physics. Usual stellarevolution cannot lead to sub-Chandrasekhar mass BHs,and the most discussed alternatives are PBHs. The re-cent detections of GW190425 [50] and GW190814 [51],which are either the heaviest neutron stars (NSs) or thelightest BHs ever seen, have ignited interest in O (1) M (cid:12) BHs [52–56]. These developments motivate our study onsub-Chandrasekhar and O (1) M (cid:12) BHs.The key question is, given the GW observation of amerger involving sub-solar-mass object(s), how can wepinpoint their identity? As pointed out in Refs. [57, 58],DM accretion in stars can in fact transmute them tosuch BHs. However, these models, employing dark quan-tum electrodynamics sector DM or a fermionic asym-metric DM with non-negligible self-interaction strength,are not generic. Transmutation of stellar objects to BHsdue to core collapse has been extensively studied in or-der to set stringent constraint on DM-nucleon scatteringcross section from the existence of old NSs [47–49, 59–66], from connection with type-Ia supernovae [7, 67–70]as well as connections to several other astrophysical phe-nomenon [71–75]. In this
Letter , we propose a simple and generic mech-anism to trigger dark core collapse and convert a sub-Chandrasekhar or O (1) M (cid:12) stellar object to a compara-ble mass BH and propose several tests for the proposal.We show that non-annihilating DM with usual interac-tions with nuclei is sufficient for such transmutations.Continuous accumulation of non-annihilating DM parti-cles in the core, followed by their gravitational collapse ata modified Chandrasekhar limit set by DM particle prop-erties, can produce sub-Chandrasekhar or O (1) M (cid:12) BHsand is a viable alternative to PBHs. We try to answera few basic questions: what particle physics parameterspace can these explore, how do we test the origin ofthese BHs, and especially, how to distinguish them fromPBHs?
Methods & Results –
Non-annihilating DM scatterswith stellar nuclei, gets captured via single [76, 77] ormultiple scattering [78–80], and accumulates inside a stel-lar object linearly with time. An estimate of the totalnumber of captured DM particles inside a stellar objectcan be found in [81, 82] and [49], in the contact inter-action approximation and for interactions mediated byany arbitrary mass mediators, respectively. Once thecaptured DM particles satisfies the collapse criterion,i.e., N χ | t age ≥ max (cid:2) N Cha χ , N self χ (cid:3) , transmutation occurs,where N χ | t age is the total number of accumulated DMparticles within a celestial object throughout its age t age . N Cha χ and N self χ denote the Chandrasekhar limit (whichdepends on the DM particle spin) and the number ofDM particles required for initiating the self-gravitatingcollapse. For bosonic (fermionic) DM, zero point en-ergy is provided by the Heisenberg uncertainty principle(Pauli exclusion principle). The Chandrasekhar limit, N Cha χ , for bosonic DM, ∼ . × (100 GeV /m χ ) canbe met more easily than for its fermionic counterpart, ∼ . × (100 GeV /m χ ) , explaining an easier trans-mutation for bosonic DM [47, 68]. The required numberof DM particles for self-gravitation, N self χ , does not de-pend on the spin statistics of the DM particles, and isset by the condition that DM density has to exceed thebaryonic density within the stellar core. a r X i v : . [ a s t r o - ph . H E ] S e p E ff i c i e n t H a w k i ng r a d i a t i on Excluded fromexistence ofPSR J0437 - - IIXENON1TBosonic DM m ϕ → ∞ ρ χ = G e V c m - ρ χ = G e V c m - Transmuted BHformation
10 10 - - - - - - - - - - - - m χ [ GeV ] σ χ n [ c m ] E ff i c i e n t H a w k i ng r a d i a t i on ρ χ = G e V c m - ρ χ = G e V c m - Fermionic DM m ϕ → ∞ Excluded fromexistence ofPSR J0437 - - - - - - - - - - - m χ [ GeV ] σ χ n [ c m ] E ff i c i e n t H a w k i ng r a d i a t i on Excluded fromexistence ofPSR J0437 - - IIBosonic DM m ϕ =
10 MeVTransmuted BHformation ρ χ = G e V c m - ρ χ = G e V c m -
10 10 - - - - - - - - - m χ [ GeV ] σ χ n [ c m ] E ff i c i e n t H a w k i ng r a d i a t i on Fermionic DM m ϕ =
10 MeV ρ χ = G e V c m - ρ χ = G e V c m - Transmuted BHformation - - - - - - m χ [ GeV ] σ χ n [ c m ] FIG. 1. DM mass and scattering cross section required for a dark core collapse and subsequent transmutation of an 1.3 M (cid:12) NS to a comparable mass BH are shown in the red shaded regions. The interaction between DM and stellar nuclei is assumedto be mediated by an infinitely heavy and a 10 MeV scalar in the top and bottom panels, respectively. The left (right)panel corresponds to non-annihilating bosonic (fermionic) DM. Two representative values of ambient DM densities, ρ χ = 1and 10 GeV cm − , are considered. Exclusion limits from underground direct detection experiments PandaX-II [44] and
XENON1T [45] as well as from existence of a ∼ Once the captured DM particles satisfy the collapsecriterion, dark core collapse can ensue and a tiny BH isformed within the stellar object. This BH accumulatesmatter from the host star and transmutes the star into acomparable mass BH. For typical NS parameters, if thistiny BH is lighter than ∼ − M (cid:12) , it evaporates fasterthan its mass accretion rate and cannot transmute theNS to a BH [9, 62]. For non-annihilating bosonic andfermionic DM, transmutation of a typical NS ceases dueto efficient Hawking evaporation for masses (cid:38) O (10 )GeV and (cid:38) O (10 ) GeV respectively. Transit of a tiny PBH through a compact object andsubsequent conversion of the host to a BH can producesub-Chandrasekhar and O (1) M (cid:12) BHs [71, 83]. The esti-mated capture rate of a tiny PBH by a NS was revisitedin [7, 84], which showed that the actual capture rate isquite small, ∼ − yr − for a NS residing in a Milky-Way-like galaxy with ambient DM density, ρ χ = 1 GeVcm − . The capture rate scales linearly with the ambientDM density and has a strong dependence on the velocitydispersion, (¯ v − ). An O (1) Gyr old NS in a DM denseregion ( ρ χ = 10 GeV cm − ) inside a globular cluster(¯ v ∼ − ) can in principle implode due to a PBH transit.However, such over-dense DM cores in a globular clusterare quite speculative and not yet well established. It hasin fact been shown that globular clusters do not haveany DM over-densities [85–88]. Hence, the explanationof a sub-Chandrasekhar or O (1) M (cid:12) BH due to a PBHtransit hinges on the contentious assumption of a highDM density in globular clusters, and remains uncertainuntil the provenance of globular clusters is settled.Fig. 1 shows the parameter space where a sub-Chandrasekhar mass NS (1 . M (cid:12) ) can transmute to acomparable mass BH for both bosonic and fermionic DM.DM-nucleon interactions mediated by an infinitely heavymediator (light mediator of mass 10 MeV) is assumedin the top (bottom) panel. Exclusion limits from un-derground direct detection experiments PandaX-II [44]and XENON1T [45] (similar limits also exist from the
LUX collaboration [89]) as well as from the existenceof an old nearby pulsar PSR J0437-4715 [47–49] are alsoshown along with the required parameter space for darkcore collapse for two given ambient DM densities. In thecontact interaction approximation, asymmetric bosonicDM of mass O (100) GeV in a DM dense environmentwith a non-zero interaction strength with nuclei is suffi-cient to explain a sub-Chandrasekhar mass BH. On theother hand, O (1) PeV asymmetric fermionic DM can alsoexplain the same. For DM-nucleon interaction mediatedvia lighter mediators, transmutation of compact objectsis more economical as exclusion limits weaken and im-plosions can be achieved with wider range of parameters.Similar analysis can also be performed for transmutationof a white dwarf (WD) due to dark core collapse. How-ever, because of the lower baryonic density compared to aNS, the implosion criterion is harder to achieve for a WD.The required parameter space for transmutation turnsout to be narrower with respect to that obtained from aNS: in order to implode a solar mass WD with ambientDM density 10 GeV cm − , the scattering cross sectionhas to be (cid:38) − cm for a 10 PeV asymmetric bosonicDM, whereas, the corresponding cross-section for a NSwith the same ambient DM density is ∼ − cm .The ambient DM density around a sub-Chandrasekharor O (1) M (cid:12) BH plays a pivotal role to determine its ori-gin. It is a simple yet powerful probe to determine theorigin of the BH, more specifically, to distinguish a trans-muted BH from a PBH. Since the DM rich environmentfavors implosion of stellar objects, detection of a sub-Chandrasekhar or O (1) M (cid:12) BH in a low DM dense re-gion will prefer a primordial origin. Coexistence of a sub-Chandrasekhar or O (1) M (cid:12) BH and an NS of similar agecan be a smoking gun signature of its primordial origin,as the required parameter space for such transmutationwill be disfavored by the existence of the companion NS.Fig. 2 shows the spatial distribution of the NSs within aMilky Way like galaxy. Three components, of the NS dis-tributions, disk, bulge and the nuclear star cluster com- r [ kpc ] N S nu m b e r d e n s i t y [ k p c - ] ρ NFW [ GeV cm - ] FIG. 2. Spatial distribution of Galactic NSs is shown withdistance from the Galactic Center. NSs in the Galactic disk,bulge, and nuclear star cluster are considered. The modelparameters are taken from [90–92]. DM density assuming anNFW profile is also labelled in the upper x-axis [93]. ponent are added together [90]. Since the DM dense innerregions potentially contain a large number of NSs, detec-tion of an ∼ O (1) Gyr old NS by the next generationradio telescopes like FAST [94] and SKA [95] will signifi-cantly strengthen the exclusion limits. As a consequence,the allowed parameter space for dark core collapse andsubsequent transmutation of a stellar object will shrinkand support the PBH scenario for a sub-Chandrasekharor O (1) M (cid:12) BH.Fig. 3 shows the cosmic evolution of the binary mergerrate as well as mass distributions of the compact ob-jects that can be used to determine the stellar or pri-mordial origin of BHs. Left panel of Fig. 3 shows thecosmic evolution of the PBH-PBH merger rate and rateof mergers involving one or more BHs which form outof a transmuted NS. The merger rate of a binary NSspeak at O (1) redshift as the star formation rate is max-imum at that redshift, and the merger rate of binaryNSs [97, 98, 101, 102] traces the cosmic star formationrate [97, 103]. On the other hand, the merger rate of PBHbinaries keeps rising with higher redshift simply becauseof the fact that PBH binaries can form more easily in theearly universe [15, 96, 104, 105]. This distinct redshiftdependence of the merger rates, especially at higher red-shifts, can be measured with the upcoming GW detectorslike Cosmic Explorer [106] and space based GW detectorPre-DECIGO [107] which will distinguish the transmuta-tion via implosion scenario from PBHs.Mass distributions of the compact objects provide yetanother powerful way to distinguish transmuted BHsfrom PBHs. Since, the transmuted BHs track the massdistribution of their progenitors, it can be compared PBH - PBH mergerTBH - TBH mergerTBH - NS merger Redshift M e r g e rr a t e [ G p c - y r - ] Mass [ M ⊙ ] N u m b e r o f ob se r ve d N S Mass [ M ⊙ ] N u m b e r o f ob se r ve d W D FIG. 3. Cosmic evolution of the binary merger rate and mass distributions of the compact objects provide a simple yet noveltechnique to determine the stellar or primordial origin of BHs. Left panel shows redshift dependence of the merger rate for abinary PBH merger and a binary NS merger. 1 M (cid:12) − M (cid:12) PBH binary with dark matter fraction of 1% is taken to estimatethe PBH merger rate [15, 96]. For binary transmuted BH (TBH) merger rate estimation, cosmic star formation rate is takenas log-normal [97] and all the other input parameters are adapted from [97, 98]. The middle panel corresponds to the massdistribution of all observed NSs [99] and the right panel corresponds to the mass distributions of all observed white dwarfs [100].Mass distributions of the progenitors can be compared against some well motivated PBH mass distributions to examine theorigin of sub-Chandrasekhar BHs. against well motivated PBH mass distributions to statis-tically determine the stellar or primordial origin of BHs.The last two panels of Fig. 3 correspond to the mass dis-tribution of all observed NSs and white dwarfs.In fact, apart from mass distribution and redshift de-pendence of the merger rate, several other probes suchas eccentricity measurement of binaries [108], the correla-tion between GW sources and galaxies [109, 110], whichare typically used to distinguish PBH binaries from stan-dard astrophysical binaries, can also be used to differen-tiate sub-Chandrasekhar mass or O (1) transmuted BHsfrom BHs of primordial origin. Extensive surveys for dis-appearing isolated NSs, though very challenging, may bea smoking gun of transmuted BHs.With imminent ground and space based GW detec-tors, about one binary NS merger event is expected perweek [111]. Considering the huge number of expectedevents, the greatly improved sky localization of the GWevents with a multi-detector network [111], as well as theGW lensing [112], the implosion scenario can easily betested in the near future. There also exist several waysto distinguish a transmuted BH binary from a binaryNS. The peak signal frequency of a binary NS merger ismuch lower than that of a binary BH merger due to theless compact nature of NSs compared to the similar massBHs [58]. Besides, the dimensionless tidal deformabilityparameter, which is zero for a BH and ∼
100 for a NS, canalso be used to probe this implosion scenario [113]. Moreimportantly, possible detection of an associated electro-magnetic counterpart from radio wavelengths to gammarays can also distinguish binary BHs from binary NSs orBH-NS merger.
Summary & Outlook –
Sub-Chandrasekhar mass BHscannot be explained by stellar evolution and will herald new physics. PBHs are the most discussed explanationof these objects. The notable alternative proposals, con-version of a compact object due to a PBH transit [83] andtransmutation of compact objects due to dark core col-lapse [57, 58] are either not effective or appeal to baroqueDM models. We study a simple mechanism for trans-mutation of compact objects that can naturally producethese sub-Chandrasekhar mass BHs without fine tuning.Non-annihilating DM with non-zero interaction strengthwith stellar nuclei, which is a vanilla DM model, alreadypredicts such transmutation. For sub-Chandrasekharmass progenitor, the imploded BH is a viable alterna-tive to PBHs, whereas, for a heavier mass progenitor, itcan possibly explains the lighter companions of recentanomalous GW events. Cosmic evolution of the mergerrate and the mass distributions of the progenitors aresimple yet powerful probes of our proposal. Observa-tion of an associated electromagnetic counterpart alongwith a GW event, as well as a precise measurement of thetidal deformability parameter, can differentiate merger ofsuch transmuted BHs from a binary NS merger or a BH-NS merger. Importantly, possible detection of any sub-Chandrasekhar mass BH in a DM deficient environmentor accompanied by an old NS can falsify our proposal.Improved sky localization with multi-detector networksas well as sub-arc second precision of a GW event fromGW lensing can also shed light on this topic in near fu-ture.
Note added –
Ref. [114], which is on a similar topic,appeared on arXiv while this paper was being written.Our work differs in several respects and we do not con-sider PBH capture on stars due to the recent calcula-tions [7, 84]. Both papers use different inputs but weagree on the general message: implosion scenarios can bea viable alternative of PBHs, as well as can explain recentGW events and can easily be tested via several techniquesin, and can be extensively tested in near future.
Acknowledgements –
We thank Lankeswar Dey foruseful discussions. B.D. is supported by the Dept. ofAtomic Energy (Govt. of India) research project 12-R & D-TFR5.02-0200, the Dept. of Science and Technol-ogy (Govt. of India) through a Ramanujan Fellowship,and the Max-Planck-Gesellschaft through a Max PlanckPartner Group. R.L. thanks CERN Theory group forsupport. ∗ [email protected] † [email protected] ‡ [email protected][1] Planck collaboration, N. Aghanim et al.,
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