Detecting Planet 9 via Hawking radiation
DDetecting Planet 9 via Hawking radiation
Alexandre Arbey a,b, , Jérémy Auffinger a, a Univ Lyon, Univ Claude Bernard Lyon 1, CNRS/IN2P3, IP2I Lyon, UMR 5822, F-69622,Villeurbanne, France b Institut Universitaire de France (IUF), 103 boulevard Saint-Michel, 75005 Paris, France
Abstract
Concordant evidence points towards the existence of a ninth planet in the Solar System atmore than 400 AU from the Sun. In particular, trans-Neptunian object orbits are perturbed bythe presence of a putative gravitational source. Since this planet has not yet been observationallyfound with conventional telescope research, it has been argued that it could be a dark compactobject, namely a black hole of probably primordial origin. Within this assumption, we discussthe possibility of detecting Planet 9 via a sub-relativistic spacecraft fly-by and the measure of itsHawking radiation in the radio band. We also present some perspectives related to the study ofsuch a Hawking radiation laboratory in the Solar System.
Perturbations of orbits of known objects in the Solar System have led astronomers to search for grav-itational sources from which they originate, under the form of unknown planets. After the discoveryof Neptune in 1846, no more planets were found beyond dwarf planets such as Pluto or Eris. Howeverconcordant evidences have recently appeared in direction of what has been a proofless obsession formany astronomers: the existence of Planet 9, which may become an object under even more intensescrutiny. The apparent clustering of trans-Neptunian objects (TNOs) orbits in the Kuiper belt sug-gests the presence of a massive body of a mass M ∼ − M ⊕ orbiting between 300 and 1000 AU[1, 2]. Even though the statistics of clustered TNOs is not sufficient enough to robustly exclude co-incidental observations, the probability of accidental correlations is (cid:46)
1% [3]. The parameters of thishypothetical Planet 9 are further constrained by ephemeride measurements such as those of Cassini[4, 5].In spite of telescope searches, no new object has been found in the sky to be Planet 9. Ref. [6]thus suggests that Planet 9 may be a compact dark object, invisible to telescopes – namely, a BlackHole (BH). A BH with such a light mass certainly points towards a non-stellar origin because of theChandrasekhar limit; this BH could be one of the putative primordial BHs (PBHs) that are underintense scrutiny since they could represent some or all of dark matter (DM) (for a recent review onPBH formation mechanisms and constraints, see e.g. [7] and references therein). PBH abundance isseverely constrained for about 50 orders of magnitude in mass, but there still exists an open parameterspace for them to represent all DM in the sub-lunar mass range, or part of it in various other masswindows. The fraction of dark matter under the form of PBHs is expected to be f ∼ . − .
01 inthe Planet 9 mass region. PBHs are believed to have formed after inflation from primordial densityinhomogeneities that collapsed when the overdensity was above some threshold. No confirmed PBHhas been observed yet, but OGLE has recently found PBH candidates in microlensing events [8] whosemasses would correspond to the mass of Planet 9. Thus, it is plausible to consider that if a populationof terrestrial mass PBHs exists, one of them could have been captured by the Sun gravity and couldbe orbiting beyond Neptune, providing an explanation for the "invisible" body responsible for thegravitational anomalies of TNOs. [email protected] [email protected] a r X i v : . [ g r- q c ] J un uccessively, two experiments have been proposed to detect Planet 9 if it were a BH (hereaftercalled P9). Both are based on ideas similar to the Breakthrough Starshot proposal , in which it isproposed to send a fleet of very small spacecrafts ( m ∼ g − kg) at sub-relativistic speeds ( v ∼ . c )in different directions of the sky to reach nearby stars in order to study their planetary systems andachieve the most distant explorations ever [9]. Their advantage is that such light and fast spacecraftswould reach the orbit of an eventual P9 in a few years. By sending many of those across the skytowards the hypothetical location of P9 orbit, one gets a chance that one of them experiences a fly-by of P9. The first proposal is to measure the time delay in the line of sight trajectory of a givenspacecraft (hereafter called SC0 for spacecraft 0, the discoverer), induced by the presence of a nearbymassive body [10]. This would necessitate an on-board precision clock to measure a ∼ − s timedelay over a one year trajectory. The second proposal is to measure the transverse inclination of thetrajectory of SC0 induced by the presence of P9 [11]. This alleviates the on-board clock problem butnecessitates a ∼ − rad angular displacement measurement, which could be doable with VLBI forexample. However, in Ref. [12] the authors examined the environment in which SC0 would travel toreach the orbit of P9 and concluded that the interstellar medium turbulence – drag and magneticfields – would make the precise gravitation-perturbed trajectory measurements cited above impossibleto achieve due to noise signals from unknown medium local properties.There also exists a completely different approach to P9 detection proposed in [13], based on the factthat icy objects of the Oort cloud would get disrupted by the P9 gravitational field and the accretionof such material could cause flares detectable by the LSST survey [14]. A few of such events couldoccur per year, making them detectable. In addition, it would prove the BH nature of P9, and solvethe trajectory difficulties of the sub-relativistic spacecrafts described in [12].Here we suggest a new proposal, based on the fact that P9, if it is indeed a BH, will emit Hawkingradiation [15]. When classical general relativity is mixed up with quantum mechanics effects, thefluctuations of the vacuum at the horizon of a BH give rise to a net emission of particles at spatialinfinity, causing the BH to slowly evaporate away. Thus even if P9 is not visible from the Earth (notbeing a reflective planet but a BH), it would still emit a small amount of radiation. This was alreadyconsidered in the original paper about the BH nature of P9 [6] but the authors concluded that theamount of Hawking radiation was too small to be detectable from Earth , which is true. What weconsider here is the detection of this very Hawking radiation by the flying-by SC0, in the vicinity ofP9, as described in the next section. This would be of particular importance since, even if rather welltheoretically motivated, Hawking radiation has not yet been observed, because the power receivedon Earth is much too small for conventional BHs, such as stellar ones like Cygnus X-1 [16–18] orsupermassive ones like Sagitarius A ∗ [19, 20]. Hawking radiation by smaller BHs results in constraintson their abundance but not in detection signals, see e.g. the recent work on BBN [7, 21], CMB [21–23],gamma rays [24–26], electrons-positrons annihilation or detection [27–30], neutrinos [30, 31], local PBHburst rate [32–34], dark matter production [35, 36] and even primordial gravitational waves [37, 38].Nevertheless the precise spectrum of Hawking radiation may contain information on the quantumstructure of BH horizons. Therefore directly observing the BH Hawking radiation would be of greatimportance, and a PBH in our Solar System would represent the best laboratory to study it. The setup of the experiment would be the following. SC0 passes by P9 at speed v and with impactparameter b . We define t = 0 to be the time of minimal approach. When SC0 approaches P9, theradiation flux will increase, reach maximum at t = 0 and then decrease. Since we consider sub-relativistic velocities, Doppler effect is negligible. The spatial displacements considered in [10–12]have however to be taken into account as an uncertainty on the precise trajectory of the ship. Weneglect them for the moment and consider an ideal straight line trajectory for SC0.P9 has a super-terrestrial mass M P9 ∼ − M ⊕ , thus its peak electromagnetic emission frequency https://breakthroughinitiatives.org/Initiative/3 −3 −2 −1 ν (GHz)10 −30 −29 −28 −27 −26 −25 −24 d P / d ν ( W · G H z − ) M = 5 M ⊕ , a ∗ = 0M = 5 M ⊕ , a ∗ = 0.99M = 10 M ⊕ , a ∗ = 0M = 10 M ⊕ , a ∗ = 0.99 Figure 1: Total power emission of photons by P9 as a function of frequency for different values of theP9 parameters M = { , } M ⊕ and a ∗ = { , . } .lies around the GHz radio band. We do not have any indication of P9 dimensionless spin a ∗ ; as a PBHit is expected to have a negligible spin but it has been shown that transient matter-domination eraat the end of inflation can produce high-spin PBHs that can conserve their spin until today despiteHawking evaporation [39]. We show in Fig. 1 the power emission as a function of frequency for differentP9 masses and spins such as d P ( M, a ∗ )d ν = E d N d t d ν , (1)where d N d t d ν is the number of photons emitted by Hawking radiation per units of time and frequency.We clearly see that the low-mass high-spin setup is favoured by detection because it implies moreenergetic and abundant emission.Let us consider that the solar sail of the Breakthrough Starshot-like spacecrafts considered here isused as a radio antenna in the GHz band, with a surface area of S ∼ m [9]. The power received bythe ship, if the sail is considered perpendicular to its trajectory, is then of the form P ( t ) = η S ( t )4 πr ( t ) Z + ∞ E d N d t d E d E (2)where the energy integral covers the radio GHz band, r ( t ) is the distance between SC0 and P9 and S ( t )is the area of the sail projected in the direction of P9. Here d N d t d E is the number of photons emittedper units of time and energy. The emission rates of particles by evaporating BHs are computed usingthe public code BlackHawk [40]. The efficiency coefficient η corresponding to the absorption of the sailis considered in Eq. (2) for completeness, but since we do not make any assumption on the material ortechnology, we do not have an estimation of it; in any case it has to be maximized. Finally we assumethe sail to be perpendicular to the direction of motion for simplicity, but we note that there probablyexists more optimized geometries to maximize the power received during a fly-by while keeping asufficient acceleration via laser propulsion. 3 .2 Ideal straight line trajectory We geometrically compute S ( t ) and r ( t ) by defining α as the angle between SC0 velocity ~v and position ~r relative to the origin at P9, and consider that the (one dimensional) sides of an area A have lengthsof the order √ A . We obtain cos( α ) = p S ( t ) √S ⇐⇒ S ( t ) = cos( α ) S , (3)and tan( α ) = b − √S| r ∗ ( t ) | . (4)Thus the projected area is S ( t ) = cos " arctan b − √S| r ∗ ( t ) | ! S , (5)where r ∗ ( t ) = vt is the distance to minimal approach in the straight trajectory approximation and r ( t ) = p r ∗ ( t ) + b . We see that even if the distance is minimal at ( t = 0 , r ∗ ( t ) = 0 , r ( t ) = b ),the projection of the flux on the sail is zero at this point. Thus we expect a peak feature in thetime-dependent radio signal with a discontinuity at t = 0. If the kinetic energy carried by SC0 becomes comparable to the gravitational potential energy of P9,we can expect a gravitational perturbation of the trajectory, i.e. for E kin ∼ E pot ⇐⇒ mv ∼ GM mr ⇐⇒ r ∼ GMv . (6)Considering the speed and mass at stake here, it occurs when b (cid:46)
100 km. The trajectory will bedeviated as given in [11, 12] because of the time build-up of small shifts, but this will occur attimescales much larger than this fly-by detection time. However if the impact parameter becomesvery small the full trajectory needs to be taken into account to predict the form of the signal. Thiscan be done by taking again the geometrical definitions given in the previous section and redefiningan effective instantaneous (at time t ) impact parameter ˜ b ( t ) and effective instantaneous distance tothe minimal approach point ˜ r ∗ ( t ), which could be seen as the geometric quantities obtained in caseSC0 were to continue in a straight line from time t . Thus the ˜ α ( t ) angle is the angle between theinstantaneous velocity and position vectors cos( ˜ α ) = ~v · ~rvr , (7)and the perturbed quantities to be considered in the area projection formula in Eq. (5) are˜ b = r sin( ˜ α ) , ˜ r ∗ = r cos( ˜ α ) . (8) The expressions (2) and (5) (with ideal or perturbed geometrical quantities) allow us to compute thelight curve received by SC0 as it passes by P9. A test result is shown in Fig. 2. The main aspect ofthis test signal is that it is symmetrical, making the detection easier with respect to the background.Doppler effect would make it asymmetrical but due to the sub-relativistic speed it has negligible effectsin our analysis. One can extract the parameters from the signal by using the following approximation,which is valid far from the minimal approach position vt (cid:29) b P ( t ) = S ( t )4 πr ( t ) Z + ∞ E d N d t d E ≡ S ( t )4 πr ( t ) P ≈ P S π vt ) − (cid:18) bvt (cid:19) ! , (9)4
10 −5 0 5 10t (s)10 −32 −31 −30 −29 −28 P ( t )( W ) datamodel Figure 2: Example of a light curve for a speed v = 0 . c , impact parameter b = 10 m, sail area S = 1 m , and P9 parameters M = 5 M ⊕ and a ∗ = 0 (solid line). The approximation of Eq. (9) leadsto the dashed line. Table 1: Parameters of the P9 and SC0 setups used in Fig. 3.setup M a ∗ b S setup 1 5 M ⊕ .
99 10 m 100 m setup 2 5 M ⊕ m 10 m setup 3 10 M ⊕ as can be seen in Fig. 2. This approximation is valid in the straight line trajectory approximation,which is a good approximation as we will see below. In Fig. 3 we show the light curves for differentsetups as summarized in Table 1. According to Eq. (9) one has to draw the detection signal with arescaled time t = × m b ! s , (10)in order to display all signals of Fig. 3 in the same plot. This is only in the favourable setup 1 thatone gets an order of magnitude for the radio signal that is comparable with the currently most precise(Earth-based) detection tools. For example, the project Breakthrough Listen aims at detecting GHzsignals from nearby stars to search for artificial signals as hints of advanced civilizations. Ref. [41]claims a minimal flux detection of 7 . × − W · m − using the Green Bank Telescope – a 100 metersdiameter collecting antenna [42]. We do not expect the signal extraction from ambient noise to be anymore difficult in P9 neighbourhood than on Earth. In Fig. 3 we show also the results with the exacttrajectory calculations taking into account the gravitational well of P9. We see that for the consideredsetups the effect is very small.P9 mass M affects the energy of emission and thus its power. The resulting signal is proportionalto the inverse of the mass squared (temperature squared). The degeneracy in mass is small for P9,hence we expect a O (10) factor at best when going from higher masses to lower masses as permittedby current constraints. P9 spin a ∗ affects the emission rate and the power received, and we know thatthe signal can be enhanced by a factor of O (100) for photons when the spin is near extremal [24, 43]. https://breakthroughinitiatives.org/initiative/1
10 −5 0 5 10t/t −50 −47 −44 −41 −38 −35 −32 −29 −26 −23 −20 −17 P ( t )( W ) setup 1setup 2setup 3 Figure 3: Radio signals received by SC0 for different setups with parameters given in Table 1. Weshow both the ideal straight trajectories (plain lines) and the fully perturbed trajectories (dashedlines).The signal reception is proportional to the sail area S , so multiplying the area by O (10) gives anamplification factor of O (100). The impact parameter b fixes the minimum distance r ( t ) that can beachieved, so the peak result is inversely proportional to b . The impact parameter on the other handis a highly random parameter, which depends on the density of spacecrafts launched in the directionof the orbit of P9. Finally, we point out that our proposal of Hawking radiation detection during a fly-by can be viewedas a complementary mean of detection of P9, would it be a BH. Indeed, optimizations of proposalspresented in [10, 11], while taking into account the trajectory shifts estimated in [12], or proposal [13],may lead to a drastic reduction in the possible sky localization of P9 along its already constrainedorbit. Therefore, with a more precise determination of its localization and if P9 still appears as a BH,it will be of utmost importance to send a mission orbiting P9, or at least to try to achieve the closestpossible fly-by for a radio mission as described in this work. Hawking radiation would be the onlydirect measurement of the presence of P9, gravitational perturbations being only indirect evidence.The in situ measure of radio emission will give access to the form and properties of the BH horizon,thus giving exciting prospects for BH and fundamental physics. In case of satellization of a spacecraftaround P9, Fig. 4 shows the radio flux F as a function of the orbit radius r , defined as F = 14 πr Z + ∞ E d N d t d E d E . (11)Another direct probe of the presence of such a heavy BH via Hawking radiation is the emission ofgravitational waves (GWs). In a semi-classical view of gravity, GWs are dual to massless spin 2 particlesnamed gravitons. If the graviton is indeed a fundamental particle, it can be expected to be emittedby Hawking radiation. It has already been conjectured that graviton emission by PBH evaporationin the primordial universe could constitute a stochastic background carrying information on the firstseconds after the Big Bang [37, 38, 44–46]. The detection of this high-frequency background remainsa technical challenge. The amount of GWs emitted by present day BHs is again usually considered6 r (m)10 −37 −36 −35 −34 −33 −32 −31 −30 −29 −28 −27 −26 −25 F ( W · m − ) M = 5 M ⊕ , a ∗ = 0M = 5 M ⊕ , a ∗ = 0.99M = 10 M ⊕ , a ∗ = 0M = 10 M ⊕ , a ∗ = 0.99 Figure 4: Radio flux as a function of orbit radius for different P9 masses M = { , } M ⊕ and spins a ∗ = { , . } .too low to be detectable from Earth . If one were to put spacecrafts in orbit around P9, search forsuch gravitational waves would be of utmost importance to probe the existence and properties of thegravitons, constituting a portal to quantum gravity. In Fig. 5 we show the density of GHz GWs thatsuch a satellite would receive as a function of its orbit radiusΩ GW = 1 cρ c (cid:18) H
100 km · s − · Mpc − (cid:19) πr Z + ∞ E d N d t d E d E , (12)where c is the speed of light, ρ c ≈ . × − g · cm − is the critical density and H ≡ h × (100 km · s − · Mpc − ) with h ≈ .
67 the reduced Hubble constant [47]. Since it would constitute a constantsignal, extraction from the noise may be easy. We see from Fig. 5 that a high P9 spin can increasethe amplitude of GWs by 4 orders of magnitude [43, 46].
In this exploratory work we have proposed a new way to probe the presence of a hypothetical Planet9 in the outer Solar System if it were actually a black hole, by using a Breakthrough Starshot-likefleet of nano-spacecrafts. Considering the difficulties of measuring tiny longitudinal or transversedisplacements that P9 would induce on a spacecraft during a pass-by, mostly related to the factthat trajectory perturbations arising from the interstellar medium would be of the same order, wepropose to measure in situ the Hawking radiation emitted by P9 in the form of GHz radio photons.This method has two main advantages, first it is not affected by the trajectory noise because itonly relies on classical on-board electromagnetic detection, second it would be a unique occasion tomeasure and thus prove the existence of Hawking radiation, a long-standing prediction of black holethermodynamics. The principal difficulty is to measure a very faint signal in the radio GHz band,with an amplitude inversely proportional to the square of the impact parameter b , therefore requiringeither great luck or a multitude of spacecrafts in order to reach a fly-by of P9 at ∼
100 km distance, orthe use of an extremely precise radio detection technology. Nevertheless, if P9 were indirectly localizedusing for example spacecraft trajectory measurements or LSST flares, an orbital mission would be ofgreat importance to study the properties of black holes and Hawking radiation.7 r (m)10 −35 −34 −33 −32 −31 −30 −29 −28 −27 −26 −25 −24 −23 −22 −21 Ω G W h M = 5 M ⊕ , a ∗ = 0M = 5 M ⊕ , a ∗ = 0.99M = 10 M ⊕ , a ∗ = 0M = 10 M ⊕ , a ∗ = 0.99 Figure 5: GWs density as a function of orbit radius for different P9 masses M = { , } M ⊕ and spins a ∗ = { , . } . References [1] K. Batygin and M. E. Brown,
Evidence for a Distant Giant Planet in the Solar System , Astron.J. (Feb., 2016) 22 [ ].[2] K. Batygin, F. C. Adams, M. E. Brown and J. C. Becker,
The planet nine hypothesis ,Phys. Rep. (May, 2019) 1–53 [ ].[3] M. S. Clement and N. A. Kaib,
Orbital precession in the distant solar system; furtherconstraining the Planet Nine hypothesis with numerical simulations , arXiv e-prints (May, 2020)[ ].[4] A. Fienga, J. Laskar, H. Manche and M. Gastineau, Constraints on the location of a possible 9thplanet derived from the Cassini data , Astron. Astrophys. (Mar., 2016) L8 [ ].[5] M. J. Holman and M. J. Payne,
Observational Constraints on Planet Nine: Cassini RangeObservations , Astron. J. (Oct., 2016) 94 [ ].[6] J. Scholtz and J. Unwin,
What if Planet 9 is a Primordial Black Hole? , arXiv e-prints (Sept.,2019) [ ].[7] B. Carr, K. Kohri, Y. Sendouda and J. Yokoyama, Constraints on Primordial Black Holes , arXiv e-prints (Feb., 2020) [ ].[8] P. Mróz, A. Udalski, J. Skowron, R. Poleski, S. Kozłowski, M. K. Szymański, I. Soszyński,Ł. Wyrzykowski, P. Pietrukowicz, K. Ulaczyk, D. Skowron and M. Pawlak, No large populationof unbound or wide-orbit Jupiter-mass planets , Nature (Aug., 2017) 183–186 [ ].[9] S. G. Turyshev, P. Klupar, A. Loeb, Z. Manchester, K. Parkin, E. Witten and S. P. Worden,
Exploration of the outer solar system with fast and small sailcraft , arXiv e-prints (May, 2020)[ ]. 810] E. Witten, Searching for a Black Hole in the Outer Solar System , arXiv e-prints (Apr., 2020)[ ].[11] S. Lawrence and Z. Rogoszinski, The Brute-Force Search for Planet Nine , arXiv e-prints (Apr.,2020) [ ].[12] T. Hoang and A. Loeb, Can Planet Nine Be Detected Gravitationally by a Sub-RelativisticSpacecraft? , arXiv e-prints (May, 2020) [ ].[13] A. Siraj and A. Loeb, Searching for Black Holes in the Outer Solar System with LSST , arXive-prints (May, 2020) [ ].[14] LSST Collaboration, LSST: From Science Drivers to Reference Design and Anticipated DataProducts , Astrophys. J. (Mar., 2019) 111 [ ].[15] S. W. Hawking,
Particle creation by black holes , Communications in Mathematical Physics (Aug., 1975) 199–220.[16] M. J. Reid, J. E. McClintock, R. Narayan, L. Gou, R. A. Remillard and J. A. Orosz, TheTrigonometric Parallax of Cygnus X-1 , Astrophys. J. (Dec., 2011) 83 [ ].[17] J. A. Orosz, J. E. McClintock, J. P. Aufdenberg, R. A. Remillard, M. J. Reid, R. Narayan andL. Gou,
The Mass of the Black Hole in Cygnus X-1 , Astrophys. J. (Dec., 2011) 84[ ].[18] L. Gou, J. E. McClintock, M. J. Reid, J. A. Orosz, J. F. Steiner, R. Narayan, J. Xiang, R. A.Remillard, K. A. Arnaud and S. W. Davis,
The Extreme Spin of the Black Hole in Cygnus X-1 ,Astrophys. J. (Dec., 2011) 85 [ ].[19] Gravity Collaboration,
A geometric distance measurement to the Galactic center black hole with0.3% uncertainty , Astron. Astrophys. (May, 2019) L10 [ ].[20] J. Dexter et. al. , A parameter survey of Sgr A* radiative models from GRMHD simulations withself-consistent electron heating , Mon. Not. R. Astron. Soc. (Apr., 2020) [ ].[21] S. K. Acharya and R. Khatri,
CMB and BBN constraints on evaporating primordial black holesrevisited , arXiv e-prints (Feb., 2020) [ ].[22] H. Poulter, Y. Ali-Haïmoud, J. Hamann, M. White and A. G. Williams, CMB constraints onultra-light primordial black holes with extended mass distributions , arXiv e-prints (July, 2019)[ ].[23] S. K. Acharya and R. Khatri, CMB spectral distortions constraints on primordial black holes,cosmic strings and long lived unstable particles revisited , J. Cosmol. Astropart. Phys. (Feb., 2020) 010 [ ].[24] A. Arbey, J. Auffinger and J. Silk,
Constraining primordial black hole masses with the isotropicgamma ray background , Phys. Rev. D (Jan., 2020) 023010 [ ].[25] G. Ballesteros, J. Coronado-Blázquez and D. Gaggero,
X-ray and gamma-ray limits on theprimordial black hole abundance from Hawking radiation , arXiv e-prints (June, 2019)[ ].[26] R. Laha, J. B. Muñoz and T. R. Slatyer, INTEGRAL constraints on primordial black holes andparticle dark matter , arXiv e-prints (Apr., 2020) [ ].[27] M. Boudaud and M. Cirelli, Voyager 1 e ± Further Constrain Primordial Black Holes as DarkMatter , Phys. Rev. Lett. (Feb., 2019) 041104 [ ].[28] W. DeRocco and P. W. Graham,
Constraining Primordial Black Hole Abundance with theGalactic 511 keV Line , Phys. Rev. Lett. (Dec., 2019) 251102 [ ].929] R. Laha,
Primordial Black Holes as a Dark Matter Candidate Are Severely Constrained by theGalactic Center 511 keV γ -Ray Line , Phys. Rev. Lett. (Dec., 2019) 251101 [ ].[30] B. Dasgupta, R. Laha and A. Ray, Neutrino and positron constraints on spinning primordialblack hole dark matter , arXiv e-prints (Dec., 2019) [ ].[31] P. Dave and I. Taboada, Neutrinos from Primordial Black Hole Bursts , in , vol. 36 of
International Cosmic Ray Conference , p. 863,July, 2019. .[32] S. Kumar,
Constraining the evaporation rate of Primordial black holes using archival data fromVERITAS , in , vol. 36 of
InternationalCosmic Ray Conference , p. 719, July, 2019. .[33] T. Tavernier, J. F. Glicenstein and F. Brun,
Search for Primordial Black Hole evaporations withH.E.S.S. , in , vol. 36 of
InternationalCosmic Ray Conference , p. 804, July, 2019. .[34] HAWC Collaboration,
Constraining the local burst rate density of primordial black holes withHAWC , J. Cosmol. Astropart. Phys. (Apr., 2020) 026 [ ].[35] I. Masina,
Dark matter and dark radiation from evaporating primordial black holes , arXive-prints (Apr., 2020) [ ].[36] I. Baldes, Q. Decant, D. C. Hooper and L. Lopez-Honorez, Non-Cold Dark Matter fromPrimordial Black Hole Evaporation , arXiv e-prints (Apr., 2020) [ ].[37] K. Inomata, M. Kawasaki, K. Mukaida, T. Terada and T. T. Yanagida, Gravitational WaveProduction right after Primordial Black Hole Evaporation , arXiv e-prints (Mar., 2020)[ ].[38] D. Hooper, G. Krnjaic, J. March-Russell, S. D. McDermott and R. Petrossian-Byrne, HotGravitons and Gravitational Waves From Kerr Black Holes in the Early Universe , arXive-prints (Apr., 2020) [ ].[39] A. Arbey, J. Auffinger and J. Silk, Evolution of primordial black hole spin due to Hawkingradiation , Mon. Not. R. Astron. Soc. (Mar., 2020) 1257–1262 [ ].[40] A. Arbey and J. Auffinger,
BlackHawk: a public code for calculating the Hawking evaporationspectra of any black hole distribution , Eur. Phys. J. C (Aug., 2019) 693 [ ].[41] S. Z. Sheikh, A. Siemion, J. E. Enriquez, D. C. Price, H. Isaacson, M. Lebofsky, V. Gajjar andP. Kalas, The Breakthrough Listen Search for Intelligent Life: A 3.95-8.00 GHz Search forRadio Technosignatures in the Restricted Earth Transit Zone , arXiv e-prints (Feb., 2020)[ ].[42] D. H. E. MacMahon et. al. , The breakthrough listen search for intelligent life: A wideband datarecorder system for the Robert C. Byrd Green Bank Telescope , Publications of the AstronomicalSociety of the Pacific (Feb., 2018) 044502.[43] D. N. Page,
Particle emission rates from a black hole. II. Massless particles from a rotatinghole , Phys. Rev. D (Dec., 1976) 3260–3273.[44] R. Anantua, R. Easther and J. Giblin, John T., Grand Unification Scale Primordial BlackHoles: Consequences and Constraints , Phys. Rev. Lett. (Sept., 2009) 111303 [ ].[45] A. D. Dolgov and D. Ejlli,
Relic gravitational waves from light primordial black holes ,Phys. Rev. D (July, 2011) 024028 [ ].1046] R. Dong, W. H. Kinney and D. Stojkovic, Gravitational wave production by Hawking radiationfrom rotating primordial black holes , J. Cosmol. Astropart. Phys. (Oct., 2016) 034[ ].[47] Planck Collaboration,
Planck 2018 results. VI. Cosmological parameters , arXiv e-prints (July,2018) [1807.06209