Exploring the Origin of Supermassive Black Holes with Coherent Neutrino Scattering
Victor Munoz, Volodymyr Takhistov, Samuel J. Witte, George M. Fuller
IIPMU21-0005
Exploring the Origin of Supermassive Black Holes with Coherent Neutrino Scattering
V´ıctor Mu˜noz, ∗ Volodymyr Takhistov,
2, 3, † Samuel J. Witte,
1, 4, ‡ and George M. Fuller § Instituto de F´ısica Corpuscular (IFIC), CSIC-Universitat de Valencia,Apartado de Correos 22085, E-46071, Spain Department of Physics and Astronomy, University of California, Los AngelesLos Angeles, California, 90095-1547, USA Kavli Institute for the Physics and Mathematics of the Universe (WPI), UTIASThe University of Tokyo, Kashiwa, Chiba 277-8583, Japan Gravitation Astroparticle Physics Amsterdam (GRAPPA),Institute for Theoretical Physics Amsterdam and Delta Institute for Theoretical Physics,University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands Department of Physics, University of California, San Diego, La Jolla, CA 92093-0319, USA (Dated: February 2, 2021)Collapsing supermassive stars ( M (cid:38) × M (cid:12) ) at high redshifts can naturally provide seedsand explain the origin of the supermassive black holes observed in the centers of nearly all galaxies.During the collapse of supermassive stars, a burst of non-thermal neutrinos is generated with aluminosity that could greatly exceed that of a conventional core collapse supernova explosion. Inthis work, we investigate the extent to which the neutrinos produced in these explosions can beobserved via coherent elastic neutrino-nucleus scattering (CE ν NS). Large scale direct dark matterdetection experiments provide particularly favorable targets. We find that upcoming O (100) tonne-scale experiments will be sensitive to the collapse of individual supermassive stars at distances aslarge as O (10) Mpc. While the diffuse background from the cosmic history of these explosions isunlikely to be detectable, it could serve as an additional background hindering the search for darkmatter. CONTENTS
I. Introduction 1II. Neutrinos from Supermassive Star Collapse 2A. Neutrino burst 2B. Diffuse neutrino background 3III. Large Direct Detection Experiments 4A. Experimental configurations 4B. Scattering rates 5C. CE ν NS 5IV. Supermassive Star Neutrino Signal Detection 5V. Disentangling Dark Matter from the DiffuseNeutrino Background 5VI. Conclusions 7Acknowledgments 7References 8 ∗ victor.manuel.munoz@ific.uv.es † [email protected] ‡ [email protected] § [email protected] I. INTRODUCTION
In this paper we explore the utility of using coher-ent elastic neutrino-nucleus scattering in dark matter ex-periments for detecting the neutrinos produced in thecollapse of supermassive stars to black holes. Two is-sues are at the heart of why detecting these neutrinosis problematic: (1) Unlike in conventional massive starcore collapse, the neutrinos generated in the collapse ofa supermassive star are relatively lower energy, reflectingtheir thermal origin, and making them hard to detect;and (2) As yet there is no direct observational evidencefor the existence of supermassive stars. However, newexploration of this subject is called for, first because themystery of the existence of supermassive black holes athigh redshift continues to deepen, and second becausethere is a novel method for detecting low energy cosmicneutrinos.Supermassive black holes (SMBHs) with masses ∼ − M (cid:12) are thought to be ubiquitous in the centersof galaxies [1], and serve as the central engines poweringquasars and Active Galactic Nuclei (AGN) [2]. The exis-tence of 10 M (cid:12) SMBHs at redshifts as high as z ∼ O ( M (cid:12) ) black holes to these masseson the relevant timescales [3–6].Many proposals have been put forth to explain the ori-gin and formation mechanism of SMBHs (see e.g. Ref. [7]for review). Of the standard astrophysical pathways toSMBH formation [8], several go through an intermediatesupermassive star (SMS) with mass M (cid:38) × M (cid:12) . a r X i v : . [ a s t r o - ph . H E ] F e b Large black holes would be the likely result of the col-lapse of such SMSs. In turn, these black holes would actas seeds [9]. Through accretion or mergers, these couldgrow into SMBHs. There is no compelling argument forthe existence of such SMSs, and no direct observation ofthem. However, they could plausibly arise either from aprimordial gas cloud or as a consequence of the evolu-tion of a dense star cluster. All we can say for certain isthat such a configuration, should it arise, will collapse viathe Feynman-Chandrasekhar general relativistic instabil-ity once it is primarily supported against gravitation bycomponents moving at or near the speed of light, photonsin the case of SMSs, and stars in the dense star clustercase. SMS collapse to a black hole will be accompaniedby a prodigious neutrino burst.The physics accompanying the collapse of SMSs hasbeen extensively studied in a variety of environmentalconditions, including accretion and rotation (e.g. [10–16]). These events are expected to produce an arrayof experimental signatures (e.g. [10, 17, 18]), includingthe generation of gravitational waves [19–21], gamma-raybursts [18, 22], and neutrinos [23–25].Detection of neutrinos from SMS explosions would pro-vide invaluable information regarding SMBH seed forma-tion. In contrast to standard core-collapse supernovae,SMS neutrinos would be produced with an energy spec-trum generated by the annihilation of thermal e ± pairs,and that is similar among the various emitted neutrinospecies. Note, however, that the ν e and ¯ ν e fluxes willbe larger than those of the mu and tau flavor species [23]because of the charged current annihilation channel avail-able for production of electron flavor neutrinos. The neu-trinos produced via thermal e ± -pair annihilation could bedetected either directly from the collapse of individualrelatively nearby objects, or via the diffuse backgroundproduced from the cumulative history of SMS collapses.In the latter case, the spectrum may suffer significantredshift, causing the entirety of the spectrum to becomeburied under the large neutrino fluxes generated by theSun, reactors, nuclear processes in the Earth, etc. Thepossibility of detecting neutrinos from SMS explosionsthrough inverse beta decay (IBD) ν e + p → n + e + has been previously considered [23, 24], both with con-ventional neutrino telescopes, such as Cerenkov-basedSuper-Kamiokande [26, 27], and with IceCube [28].Coherent elastic neutrino-nucleus scattering (CE ν NS)could provide a new way to search for the low en-ergy neutrinos of a SMS collapse-generated neutrinoburst. In contrast to IBD, CE ν NS is unconstrainedby the IBD kinematic threshold on neutrino energy.Moreover, CE ν NS will have sensitivity to all six( ν e , ν e , ν µ , ν µ , ν τ , ν τ ) neutrino flavors. CE ν NS has beenrecently directly observed [29], and has been consideredin a range of studies related to neutrino physics, includ-ing sterile neutrinos (e.g. [30, 31]), non-standard neutrinointeractions (e.g. [32, 33]), solar neutrinos (e.g. [31, 34–36]), geoneutrinos [37], neutrinos from dark matter (DM)annihilation and decays [38–40], as well as supernova [41– 45] and pre-supernova neutrinos [46].Large scale direct detection experiments, whose pri-mary target is dark matter (DM) observation, are them-selves effective neutrino telescopes and can explore com-plementary parameter space compared to that of con-ventional neutrino experiments. In particular, such ex-periments have very low keV-scale thresholds, poten-tially providing sensitivity to a complementary part ofthe neutrino spectrum. Furthermore, with heavy nucleias detector targets, these experiments are particularlywell suited for signal detection via CE ν NS, whose cross-section scales approximately as neutron number squared.In this study we explore the detection capabilities oflarge scale direct DM detection experiments via CE ν NSof neutrinos produced from SMS collapse. We examineboth the signal arising from the collapse of individualobjects, as well as the diffuse signal generated by thecumulative collapse rate throughout their history. Theformer of these could be detectable from collapsing starsin nearby galaxies. On the other hand, the latter servesas a novel experimental background for DM direct detec-tion experiments – introducing additional uncertaintiesand potentially hindering the detection of DM candidatesresiding below the neutrino floor.This work is organized as follows. In Sec. II B we de-scribe neutrino production from the collapse of supermas-sive stars. Sec. III presents an overview of large directdetection experiments and their sensitivity to coherentneutrino scattering. The sensitivity of these experimentsto an individual explosion of a supermassive star and thediffuse background is presented in Sec. IV. In Sec. V weelaborate on the extent to which uncertainties from thesupermassive star collapse history may impede the dis-covery of dark matter. We conclude in Sec. VI.
II. NEUTRINOS FROM SUPERMASSIVE STARCOLLAPSEA. Neutrino burst
Supermassive stars with masses M (cid:38) × M (cid:12) areexpected to directly collapse into a black hole as a resultof the Feynman-Chandrasekhar instability, unless cen-trifugal forces from rapid rotation or magnetic fields aresufficiently strong [10]. During the collapse, only a frac-tion of the initial star, the homologous core (HC) com-prising M HC5 /M init5 ’ . M being stellar mass in units of 10 M (cid:12) , plunges throughthe event horizon, resulting in prompt black hole forma-tion. Most of the HC binding energy will be trappedwithin the BH, but a small fraction could be emitted inthe form of neutrinos and (an even smaller fraction) ingravitational waves.Neutrino emission from SMS collapse has been ana-lyzed in Ref. [23, 24], whose discussion we follow. Theentropy-per-baryon in SMS is large, corresponding tolow density and modestly high temperature, with elec- − E ν [MeV] − − F l u x [ s − c m − M e V − ] SMS BurstDSMSB8B17Fheppp15O13NReactorGeo UGeo ThGeo KAtmDSNB7Bpep
FIG. 1. Neutrino flux from a single SMS explosion (black) andthe diffuse background generated from the cosmological evo-lution of SMS collapse (DSMSB, blue). The band detailingthe burst signal assumes a SMS with mass 10 M (cid:12) collaps-ing at 100 kpc (solid), at 1 Mpc (dashed), at 1 Mpc withenhancement due to non-negligible rotation or magnetic field(dash-dotted) and a SMS with mass 3 × M (cid:12) explodingat a distance of 1 Mpc (dotted). The band detailing the dif-fuse background signal corresponds to the R flat (upper) and R Pop3 (lower) models. Shown for comparison are the solar( B, F, O, N, Be,hep,pp,pep), geo ( U, Th, K), re-actor, atmospheric neutrino and diffuse supernovae neutrinobackground (DSNB) fluxes – reactor and geoneutrino fluxeshave been computed assuming the experiment is located atSNOLAB [36]. tromagnetic equilibrium consequently implying a largeelectron-positron ( e ± ) pair density. Neutrino pairs areproduced by e + e − annihilation in the in-falling HC, withmost of the neutrino luminosity being generated as theradius of the star nears trapped surface formation, itsSchwarzschild radius. Unlike core collapse supernovae,the in-falling material is transparent to emitted neutri-nos. Consequently, the luminosity, spectrum, and timeprofile are well-defined quantities . In particular, thetotal neutrino luminosity is expected to be a sizablefraction of the HC gravitational binding energy E s ’ M HC5 erg. Reference [21] showed that the SMS HCmass range that gives an optimal fraction of the rest massradiated as neutrinos is 5 × M (cid:12) < M HC < × M (cid:12) .Other factors that determine the ultimate neutrino flu-ence from collapse of these objects include the time profileof the collapse, dictated by a number of features of the Numerical hydrodynamic simulations of Ref. [25] show emissionsuppressed by up to two orders compared to the analytic resultsof Ref. [23]. These differences stem from differing treatmentsof the in-fall and collapse timescales, pressure, and the adiabatof collapse, and are exacerbated by the T dependence of theneutrino emissivity. Significant uncertainties remain. We employthe results of Ref. [23] throughout this study as an example (forcomparison of models see Fig. 3 of Ref. [21]) The in-fall time can increase in the presence of rotation or strongmagnetic fields.
HC. Roughly, this collapse time scale will be t s ’ M HC5 s.The neutrino energy spectra and fluxes are determinedmostly by the evolution of the density and temperaturedistributions near the Schwarzschild radius (i.e. a rapidrise as the mass in-falls, followed by a rapid fall as mate-rial is absorbed by the black hole).Considering the peak emission occurring near theSchwarzschild radius, the resulting neutrino luminosityfrom pair-production during SMS star collapse can beestimated as [23] L ν ’ × ( M HC5 ) − . erg cm − s − . (1)The associated neutrino spectrum can be well-fit by f ν ( E ) ’ . p M HC5 ! − F (2) E e ( E √ M HC5 / . − + 1 , (2)where F k ( η ν ) = Z ∞ x k dxe x − η ν + 1 (3)and the average neutrino energy is h E ν i ’ M HC5 ) − / MeV.The presence of a strong magnetic field or rapid ro-tation will delay the SMS collapse. Neutrinos producednear the Schwarzschild radius will then have a higherchance of escaping before the core moves through theevent horizon. This results in the possibility of an in-crease in the emitted neutrino fluence by up to an orderof magnitude, and an increase in neutrino energies bya factor of two compared to the case of a non-rotatingand non-magnetized collapse scenario [23]. The partitionof energy among the neutrino species remains the same,however.Despite the enormous neutrino luminosities from SMScollapse, the detection of this signal on large cosmologicalscales is unlikely [23]. However, detection prospects arefavorable if the redshift of SMS collapse event is z (cid:46) . ∼ B. Diffuse neutrino background
An isotropic background of redshifted neutrinos will begenerated by the cosmological history of SMS collapse.Given the complete ignorance of the formation and col-lapse rate of such large stars, we adopt a phenomenologi-cal perspective in which we motivate a variety of differentredshift-dependent collapse rates, and investigate the de-tection prospects for each.The flux of diffuse neutrinos from SMSs can be com-puted from the neutrino emission spectrum and the col-lapse rate R SMS ( z ) via dφdE ν ( E ν ) = Z dz R SMS ( z ) H ( z ) f ν ( E ν (1 + z )) , (4)where we adopt cosmological parameters consistent withthe latest Planck-2018 measurements [47].In what follows, we adopt five different parameteri-zations of the collapse rate in order to obtain a roughestimation of uncertainty in the flux and spectral shape.The models assume1. The collapse rate of SMSs traces the quasar forma-tion rate. If we assume the typical quasar lifetime(which is much shorter than the Hubble time) isredshift-independent, then we can assume that theformation rate directly follows the quasar numberdensity. We take this rate to be consistent with theresults of Ref. [48, 49], and call this model R Q .2. In order to asses the impact of additional redshift-dependent factors not directly included in thequasar formation rate, we consider two models inwhich R Q is re-scaled by a factor of (1 + z ) α . Inorder to understand extreme variations in this fac-tor, we adopt α = ±
3, and denote each model by R ± .3. As will be shown, R Q decreases dramatically atredshifts z ∼
2. Should SMSs be the origin ofSMBHs, the collapse rate must extend to muchlarger redshifts. To account for this, we adopt amodel which is consistent with the quasar forma-tion rate at z ≤ .
5, and is flat at 1 . ≤ z (cid:46)
20, theupper cut-off taken to be roughly consistent withthe onset of star formation. We call this model R flat .4. Finally, we adopt a model in which SMSs are as-sumed to form predominately in metal-free envi-ronments at high redshifts. It has been suggestedthat low-metallicity environments could allow forthe rapid cooling and formation of such objects,implying a preferential formation rate peaking near z ∼
15. We model this using a Gaussian distribu-tion centered at z = 15 with a width ∆ z = 1. Wecall this model R P op , as it would suggest thesestars are among those first produced in the Uni-verse (i.e. Pop-III stars, or perhaps stars producedby tidal disruption in dense star clusters).The aforementioned models are assumed to characterizeonly the redshift dependence of the collapse rate. In orderto determine normalization of the rate, we assume thatless than 10% of the baryons have resided in SMSs. Thatis, we define the baryon density in SMSs to be ρ SMS = Z dt M R SMS ( z )(1 + z ) . (5)If these black holes do indeed serve as the seeds for super-massive black holes at the center of galaxies, it would bereasonable to estimate that approximately one SMS ex-ists per galaxy, or equivalently ρ SMS ∼ ( M/ M (cid:12) ) ρ b .We use this to normalize the SMS collapse rate, andshow the resultant histories, and the subsequent neutrinofluxes as observed here at Earth, in Fig. 2. Target Mass Threshold Reference(tons) (keV)Ar 300 0.6 ARGO [50, 51]Xe 50 0.7 DARWIN [52, 53]Pb 2.4 1.0 RES-NOVA [54]TABLE I. Considered detector configurations.
III. LARGE DIRECT DETECTIONEXPERIMENTSA. Experimental configurations
In this study, we consider detector configurations con-sistent with the proposed specifications of the upcomingdirect DM detection experiments DARWIN [52, 53], us-ing xenon (Xe) as a target material, and ARGO [50, 51]using argon (Ar) as a target material. These experimentsare able to achieve considerable fiducial volume while alsotaking advantage of a keV-level energy threshold. In ad-dition, we also consider a configuration based on lead(Pb), following the recently proposed RES-NOVA [54]experiment for detection of core-collapse SN neutrinosvia CE ν NS. An overview of these configurations is listedin Table I.We assume the experiments are located at SNOLAB(Sudbury, Canada), which is likely to host a number ofnext-generation direct detection experiments. We stress,however, that this assumption does not strongly affectour conclusions. The depth of this lab (6010 m.w.e.)ensures that backgrounds due to cosmogenic muons arehighly suppressed.Throughout this work, we will optimistically considerthat experiments have perfect detection efficiency and en-ergy resolution, and we adopt detection thresholds con-sistent with the targeted low-energy searches of each ex-periment. Furthermore, when considering neutrino co-herent interactions with the nuclei, the expected back-ground is assumed to arise exclusively from other neu-trino sources . This assumption allows us to treat allanalyses on an equal footing, and provide general resultsindependent of specific configurations that could changein the future. We note that low-background xenon and argon detectors havebeen in development for many years and the scalability of thesesetups has been established. The feasibility of Pb-based detectoron a competitive scale is still to be demonstrated. This assumption is in principle not fully realistic as, e.g., theionization signal “S2-only” analyses of argon and xenon [55] haveunavoidable electronic backgrounds (but allow for lower signalthresholds). However, since the SMS burst signal occurs over aperiod of ∼ O (1s), time correlations should easily allow one todifferentiate this signal from background.
Redshift − − − − − C o ll a p s e R a t e [ y r − M p c − ] R Q R flat R Pop R + R − − E [MeV] − − − F l u x [ s − c m − M e V − ] R Q R flat R Pop R + R − FIG. 2. Historical SMS collapse rate [Left] and the resulting diffuse neutrino flux at Earth [Right] for each of the modelsconsidered in Sec. II B.
B. Scattering rates
Given a neutrino flux φ ν ( E ν ) the resulting differentialevent rate per unit time and detector mass as a functionof the recoil energy E R , per unit time and mass m I of atarget nuclide I in a detector is given by dR Iν dE R = C I m I Z E min ν φ ν ( E ν ) dσ I ( E ν , E R ) dE R dE ν , (6)where dσ I ( E ν , E R ) /dE R is the coherent neutrino-nucleusscattering differential cross-section and C I is the fractionof nuclide I in the material. In case several nuclides arepresent, individual contributions are summed.For a target mass m I at rest, the minimum neutrinoenergy required to produce a recoil of energy E R is E min ν = r mE R . (7)The maximum recoil energy due to a collision with aneutrino of energy E ν is E max R = 2 E ν m + 2 E ν . (8) C. CE ν NS The Standard Model coherent-scattering neutrino-nucleus cross-section is given by [56] dσ I ( E ν , E R ) dE R = G f m I π Q w (cid:18) − m I E R E ν (cid:19) F I ( E R ) , (9)where m I is the target nuclide mass, G f is Fermi couplingconstant, F I ( E R ) is the form factor, which we take to bethe Helm form factor [57], Q w = [(1 − θ W ) Z I − N I ] isthe weak nuclear charge, N I is the number of neutrons, Z I is the number of protons, and θ W is the Weinbergangle. Since sin θ W = 0 .
223 [58], the coherent neutrino-nucleus scattering cross-section follows an approximate N I scaling. IV. SUPERMASSIVE STAR NEUTRINOSIGNAL DETECTION
In Fig. 1 we depict the expected neutrino flux for SMScollapse at a distance of 0.1-1 Mpc and with varying HCmass and inclusion of rotation/magnetic fields. In Fig. 3we illustrate the expected number of events from the col-lapse of a SMS as a function of explosion distance. Inthis case, we illustrate the enhancement effect (shadedband) that may arise should the SMS star rotate or havestrong magnetic fields. Fig. 3 shows the event rate nor-malized by the fiducial volume as a function of the de-tection threshold, highlighting that lead and xenon willbenefit particularly from lowering the detection thresh-old. Note that the adopted thresholds are shown withthe colored vertical lines.In Fig. 4 we illustrate the event rate produced in axenon-based experiment by the diffuse SMS neutrinobackground. Various background neutrino sources areshown for comparison. We expect no more than oneevent will be detected using the experimental configu-rations listed in Table I, implying that it will be a diffi-cult task to disentangle the diffuse background from theother neutrino sources. Nevertheless, DSMSB will con-tribute to the irreducible background in the searches fordark matter. For neutrino sources with a well-definedspectrum and flux, this irreducible background may bepartially circumvented via background subtraction tech-niques; this is not the case, however, for the diffuse neu-trino flux from SMSs. We now turn our attention towardaddressing the potential difficultly that could arise fromsuch a background in the search for dark matter.
V. DISENTANGLING DARK MATTER FROMTHE DIFFUSE NEUTRINO BACKGROUND
Individual collapses of super-massive stars are unlikelyto obstruct the search for dark matter, as they will typi-cally generate multiple nuclear recoils within a time win- Distance (pc) N u m b e r o f e v e n t s M il ky W a y C e n t e r M il ky W a y Ed g e A n d r o m e d a M = 10 M (cid:12) PbXeAr − E thr [keV] − E v e n t s p e r t o nn d = 1 [Mpc] PbXeAr
FIG. 3. [Left] Number of events detected from the burst of a SMS with mass M = 10 M (cid:12) for each experimental configurationas a function of distance. The shaded regions indicate the potential enhancement in the signal that may arise if the SMS hasa non-negligible rotation or magnetic field. Shown for comparison are distance markers denoting the location of the galacticcenter, the edge of the Milky Way, and Andromeda. [Right] Number of events per tonne of detector mass for each targetelement as a function of threshold energy E th , computed assuming M = 10 M (cid:12) and d = 1 [Mpc]. The adopted experimentalthresholds are shown with vertical lines. Recoil Energy [keV] E v e n t R a t e [ t o n y r k e V ] DSMSBhepReactorGeo UGeo Th
FIG. 4. Detection of diffuse supermassive star neutrino back-ground (DSMSB), assuming a xenon target and experimentlocated at SNOLAB. DSMSB signal is shown for R Q model(solid) and the R flat model (dashed), with shaded region ex-tending down to the signal detection obtained for the R Pop3 model. Contributions for solar (hep), geo ( U, Th) andreactor neutrinos are displayed (see Ref. [36] for details). dow of t (cid:46) O (few) seconds. The diffuse background onthe other hand has no strong time correlation, and inanalogy to the effect of the diffuse supernova background(DSNB), this will necessarily contribute to the irreduciblebackground in the direct detection searches for DM.The extent to which CE ν NS inhibits DM searches hasbeen discussed extensively in the literature within thecontext of an irreducible neutrino background constitut-ing a “neutrino floor” (e.g. [36, 59–61]). This question isoften posed in the following manner: What exposure isrequired in order for an experiment to identify a partic-ular DM candidate (with a well-defined mass and scat-tering cross section) at the statistical confidence level of Xσ (where X is often taken to be 3)? For a particularmodel of DM, and for a fixed experimental exposure, thisdefines a “discovery floor”. The extent to which this dis-covery floor scales with exposure is critically dependentupon the level of degeneracy between the recoil spectrumof DM interactions and neutrinos.The limitations on the DM discovery potential couldprove to be rather concerning when considering the dif-fuse neutrino background from SMS. This is because theassociated SMS diffuse neutrino energy spectrum is de-termined by the assumed SMS collapse rate. In turn,this is a completely unknown function of redshift. As dis-cussed previously, it is reasonable to conjecture that theSMS redshift-dependent collapse rate could be stronglyrelated to the quasar and AGN formation rate. How-ever, this need not be the case and possible deviationsfrom such scaling can lead to significant differences inthe shape of the resulting scattering rate within the ex-periments. Furthermore, the normalization of the SMScollapse rate contains only an upper limit, which we canestimate by ensuring no more than ∼
10% of the baryonshave resided in SMS.In order to illustrate the importance of the diffuse SMSbackground, we plot in Fig. 4 a comparison of the nuclearrecoil event rate produced by the diffuse SMS backgroundand that from solar, geo, and reactor neutrinos. We showboth the R Q model (blue, solid) and the R flat model(blue, dashed), and we shade down to the event rate pro-duced by the R P op model (not shown). While the ratenever exceeds those coming from known neutrino sources,it does become sizeable at low energies. In Fig. 5, we fitthe event rate arising from the R Q model assuming darkmatter interacts with nuclei through a spin-independentcontact interaction (SI), a electric dipole (ED), a mag-netic dipole (MD), or a pseudo-scalar contact interaction(PS) (see Ref. [37] for the details of each interaction). Recoil Energy [keV] E v e n t R a t e [ t o n y r k e V ] DSMSB comparison
SIPS-PSMDED
FIG. 5. Comparison of event rates for recoil spectra inducedin a Xenon target from a DSMSB with the recoil spectraarising in various DM interaction models (see text). The bestfit values for the DM parameters are given in table II.Model Mass (GeV) σ (cm )SI 4.34 1.02 × − ED 4.15 4.41 × − MD 3.79 2.18 × − PS 3.79 1.42 × − TABLE II. Best-fit mass and cross section for dark mat-ter scattering with nuclei via a spin-independent (SI), electricdipole (ED), magnetic dipole (MD), or pseudoscalar (PS) in-teraction. Fits are to the R Q model of SMS collapse rate. The best-fit masses and cross sections are presented inTable II. We see here that the diffuse SMS backgroundcould dramatically hamper the search for dark mattercandidates with masses m (cid:46) N evts (cid:29) O (10 ) events (neglect-ing astrophysical uncertainties) [65]. With backgrounds,this number is likely orders of magnitude higher. Conse-quently, such a technique will not prove easy. A betterunderstanding of halo uncertainties [66–68] or the use ofnovel analysis methods [69, 70] may improve the situa-tion. Alternatively, directional detection could allow oneto efficiently remove isotropic backgrounds, leaving onlythe dark matter scattering rate [71–73]. VI. CONCLUSIONS
Supermassive stars with mass M (cid:38) × M (cid:12) areexpected to directly collapse to black holes via theFeynman-Chandrasekhar instability. While no such starshave yet been directly observed, supermassive black holesat redshifts as high as z ∼ z ∼
15. Should theseobjects exist, their collapse can yield a broad array of ob-servable signatures, including gamma-rays, gravitationalwaves, and neutrinos. In this paper we have analyzedthe extent to which neutrinos emitted from the collapseof such objects could be detected via coherent neutrinoscattering, focusing on massive direct dark matter exper-iments.We have demonstrated that large scale undergroundexperiments built for the purpose of detecting dark mat-ter might be capable of identifying the collapse of indi-vidual supermassive stars in nearby galaxies, such as inAndromeda. A diffuse and isotropic neutrino backgroundwill also be produced from the cumulative historical col-lapse of such objects. We have analyzed a variety of po-tential redshift-dependent collapse rates that may arise,e.g., if the SMS collapse rate follows the AGN formationrate, or if SMSs are preferentially formed in metal-freeenvironments, as would occur at higher redshifts (e.g.near z ∼ z ∼
7. The only way to truly reveal the existence of theseobjects is to observe them. The neutrino flux producedfrom the collapse of SMSs offers a particularly intriguingchannel in which to test their existence, as the neutrinoenergy spectra are non-thermal and easily distinguishablefrom other sources. Current direct dark matter experi-ments are already designed in a manner that is ideal forthe search of such neutrino flux, with near-future exper-iments capable of probing the collapse of such objects onextra-galactic scales.
ACKNOWLEDGMENTS
The work of S.J.W. was supported by a Juan de laCierva Formacion fellowship, and is part of a project thathas received funding from the European Research Coun-cil (ERC) under the European Union’s Horizon 2020research and innovation programme (Grant agreementNo. 864035 – UnDark). The work of V.M. was sup-ported by CONICYT PFCHA/DOCTORADO BECASCHILE/2018 - 72180000. The work of V.T. was sup-ported by the U.S. Department of Energy (DOE) GrantNo. DE-SC0009937. V.T. was also supported by theWorld Premier International Research Center Initiative (WPI), MEXT, Japan. G.M.F. and V.T. would like tothank Kavli IPMU, U. of Tokyo for hospitality where thiswork was initiated. G.M.F. acknowledges NSF GrantNo. PHY-1914242 at UCSD and the NSF N3AS PhysicsFrontier Center, NSF Grant No. PHY-2020275, and theHeising-Simons Foundation (2017-228). [1] R. van der Marel, P. de Zeeuw, H. Rix, and G. Quinlan,Nature , 610 (1997), arXiv:astro-ph/9702106.[2] M. J. Rees, Annual Review of Astron-omy and Astrophysics , 471 (1984),https://doi.org/10.1146/annurev.aa.22.090184.002351.[3] D. J. Mortlock, S. J. Warren, B. P. Venemans, M. Patel,P. C. Hewett, R. G. McMahon, C. Simpson, T. Theuns,E. A. Gonz´ales-Solares, A. Adamson, and et al., Nature , 616–619 (2011).[4] B. Venemans, J. Findlay, W. Sutherland, G. De Rosa,R. McMahon, R. Simcoe, E. Gonzalez-Solares, K. Kui-jken, and J. Lewis, Astrophys. J. , 24 (2013),arXiv:1311.3666 [astro-ph.CO].[5] X.-B. Wu, F. Wang, X. Fan, W. Yi, W. Zuo, F. Bian,L. Jiang, I. D. McGreer, R. Wang, J. Yang, and et al.,Nature , 512–515 (2015).[6] E. Banados et al., Nature , 473 (2018),arXiv:1712.01860 [astro-ph.GA].[7] M. Volonteri, The Astronomy and Astrophysics Review , 279–315 (2010).[8] M. C. Begelman and M. J. Rees, Mon. Not. Roy. Astron.Soc. , 847 (1978).[9] T. E. Woods et al., Publ. Astron. Soc. Austral. , e027(2019), arXiv:1810.12310 [astro-ph.GA].[10] G. M. Fuller, S. E. Woosley, and T. A. Weaver, Astro-phys. J. , 675 (1986).[11] T. W. Baumgarte and S. L. Shapiro, Astrophys. J. ,941 (1999), arXiv:astro-ph/9909237.[12] M. Saijo, T. W. Baumgarte, S. L. Shapiro, andM. Shibata, Astrophys. J. , 349 (2002), arXiv:astro-ph/0202112.[13] H. Umeda, T. Hosokawa, K. Omukai, and N. Yoshida,Astrophys. J. Lett. , L34 (2016), arXiv:1609.04457[astro-ph.SR].[14] L. Haemmerl´e, T. E. Woods, R. S. Klessen, A. Heger,and D. J. Whalen, Monthly Notices of the Royal Astro-nomical Society , 2757–2773 (2017).[15] L. Haemmerl´e, T. E. Woods, R. S. Klessen, A. Heger,and D. J. Whalen, The Astrophysical Journal , L3(2018).[16] C. Nagele, H. Umeda, K. Takahashi, T. Yoshida, andK. Sumiyoshi, Mon. Not. Roy. Astron. Soc. , 1224(2020), arXiv:2006.08834 [astro-ph.HE].[17] S. L. Shapiro and S. A. Teukolsky, Astrophys. J. Lett. , L177 (1979).[18] L. Sun, V. Paschalidis, M. Ruiz, and S. L. Shapiro,Phys. Rev. D , 043006 (2017), arXiv:1704.04502 [astro-ph.HE].[19] M. Shibata, Y. Sekiguchi, H. Uchida, and H. Umeda,Phys. Rev. D , 021501 (2016), arXiv:1606.07147 [astro-ph.HE].[20] H. Uchida, M. Shibata, T. Yoshida, Y. Sekiguchi, andH. Umeda, Phys. Rev. D , 083016 (2017), [Erratum: Phys.Rev.D 98, 129901 (2018)], arXiv:1704.00433 [astro-ph.HE].[21] J.-T. Li, G. M. Fuller, and C. T. Kishimoto, Phys. Rev.D , 023002 (2018), arXiv:1708.05292 [astro-ph.HE].[22] G. M. Fuller and X.-D. Shi, Astrophys. J. Lett. , L5(1998), arXiv:astro-ph/9711020.[23] X.-D. Shi and G. M. Fuller, Astrophys. J. , 307(1998), arXiv:astro-ph/9801106.[24] X.-D. Shi, G. M. Fuller, and F. Halzen, Phys. Rev. Lett. , 5722 (1998), arXiv:astro-ph/9805242.[25] F. Linke, J. A. Font, H.-T. Janka, E. Muller, andP. Papadopoulos, Astron. Astrophys. , 568 (2001),arXiv:astro-ph/0103144.[26] S. Fukuda et al., Nuclear Instruments and Methods inPhysics Research Section A: Accelerators, Spectrometers,Detectors and Associated Equipment , 418 (2003).[27] K. Abe et al., Nucl. Instrum. Meth. A , 253 (2014),arXiv:1307.0162 [physics.ins-det].[28] J. Ahrens et al. (IceCube), Nucl. Phys. B Proc. Suppl. , 388 (2003), arXiv:astro-ph/0209556.[29] D. Akimov et al. (COHERENT), Science , 1123(2017), arXiv:1708.01294 [nucl-ex].[30] M. Pospelov, Phys. Rev. D84 , 085008 (2011),arXiv:1103.3261 [hep-ph].[31] J. Billard, L. E. Strigari, and E. Figueroa-Feliciano,Phys. Rev.
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