- Email: [email protected]
Primordial black holes and short gamma-ray bursts
Physics Reports 307 (1998) 173—180
Primordial black holes and short gamma-ray bursts David B. Cline* Department of Physics and Astronomy, Box 951547, University of California Los Angeles, Los Angeles, CA 90095-1547, USA
Abstract The possible existence of primordial black holes (PBHs) has long been a key observational question. At present, the only known way to detect low-mass ones (below 10 g) is through the Hawking radiation process. This radiation in turn depends on the nature of hadron interactions in the 100 MeV region and beyond. In the case of a first-order quantum-chromodynamics phase transition, we expect a sharp burst of gamma rays from the PBH. We have pointed out that there is a class of gamma-ray bursts that have this property and could provide evidence for PBHs in the galaxy. Future study of these events is crucial. Recently, we have shown that a diffuse gamma-ray glow should exist in the halo from these PBHs. There now seems to be evidence for this effect as well. 1998 Elsevier Science B.V. All rights reserved. PACS: 97.60.Lf
1. Introduction The search for evidence for primordial black holes (PBHs) has continued since the first discussion by Hawking [2]. In fact, this was about the time that gamma-ray bursts (GRBs) were first discovered, making a natural association with PBHs [3]. However, in the intervening years it has become clear that the time history of the typical GRB is not consistent with the expectations of PBH evaporation. While the theory of PBH evaporation has been refined, there are still no exact predictions of the GRB spectrum, time history, etc. [4]. However, reasonable phenomenological models have been made, and the results again indicate that most GRBs could not come from PBHs [5,6]. In addition, there are new constraints on the production of PBHs in the Early Universe that indicate that the density of PBHs in the Universe should be very small, but not necessarily zero [7].
* E-mail: [email protected]. Sections 1—4 have been adapted; see Ref. [1] for further details. 0370-1573/98/$ — see front matter 1998 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 0 - 1 5 7 3 ( 9 8 ) 0 0 0 4 6 - 5
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D.B. Cline / Physics Reports 307 (1998) 173—180
After the initial discovery of GRBs, it took many years to uncover the general properties. Around 1984, several GRBs were detected, indicating that there was a class of short bursts with time duration of &100 ms and a very short rise time [8]. A separate class of GRBs was declared [9]. This classification seems to have been forgotten and then rediscovered by some of us [10]. It is still possible that there is a sizable density of PBHs in our galaxy and that some of the GRBs could be due to PBH evaporation. Recently, we showed that the BATSE 1B data [11] have a few events that are consistent with some expectation of PBH evaporation (short bursts with time duration (200 ms and that are consistent with »/» & [10].
2. Primordial black-hole evaporation Ever since the theoretical discovery of the quantum-gravitational particle emissions from black holes by Hawking [2], there have been many experimental searches (see Ref. [4] for details) for high-energy gamma-ray radiation from PBHs. They would have been formed in the Early Universe [7,12] and would now be entering their final stages of extinction. The violent final-stage evaporation or explosion is the striking result of the expectation that the PBH temperature is inversely proportional to the PBH mass, e.g., ¹ +100 MeV (10 g/m ), since the black hole becomes . & . & hotter as it radiates more particles and can eventually attain extremely high temperatures. In 1974, Hawking showed in a seminal paper [2] that an uncharged, non-rotating black-hole emits particles with energy between E and E#dE at a rate per spin of helicity state of
8pGME \ C dN , " Q exp !(!1)Q hc dtdE 2ph
(1)
where M is the PBH mass, s is the particle spin, and C is the absorption probability. It can be Q considered that this particle emission comes from the spontaneous creation of particle—antiparticle pair escapes to infinity, while the other returns to the black hole. Thus, the PBH emits massless particles, photons, and light neutrinos, as if it were a hot black-body radiator with temperature ¹ 10 g/M MeV, where M is the black-hole mass. A black hole with one solar mass, M 2;10 g, has an approximate temperature of 10\ K, while a black hole with mass of 6;10 g has a temperature of &20 MeV. The temperature of a black hole increases as it loses mass during its lifetime. The loss of mass from a black hole occurs at a rate, in the context of the standard model of particle physics, of a(M) dM "! , M dt
(2)
where a(M), the running constant, counts the particle degree of freedom in the PBH evaporation. The value of a(M) is model dependent. In the standard model (SM), with a family of three quarks and three leptons, it is given [2,6,13] as a(M)"(0.045 S #0.162 S );10\, where H> H S and S are the spin and color degrees of freedom for the fermions and gauge particles, H> H respectively. For the SM, a(M)"4.1;10\. A reasonable model of the running coupling constant is illustrated in Fig. 1, where the regions of uncertainty are indicated. These are the regions where there could be a rapid increase in the
D.B. Cline / Physics Reports 307 (1998) 173—180
175
Fig. 1. Running coupling or density of states factor a, showing regions of uncertainty due to the QGP transitions (I) or the increase in the number of new elementary particles (II). It is possible that intense short GRBs could occur at either of these temperatures (the decrease of mass of the black hole is given by dm /dt"!a/m ). A rapid mass decrease or . & . & burst can occur when m 410 g or if a changes rapidly near the QGP transition. . &
effective number of degrees of freedom due to the quark—gluon phase (QGP) transition. The phase transition would lead to a rapid burst in the PBH evaporation or, at high energy, there could be many new particle types that would also lead to an increase in the rate of evaporation. Also shown in Fig. 1 are the regions in PBH temperature where short duration GRBs may occur when the PBH mass is either 10 or 10 g. Black holes at the evaporation stage at the present epoch can be calculated as having M* [3a(M*)q ] 7;10 g for a(M*) 1.4;10\. The bound on the number of black holes at their critical mass, constrained by the observed diffuse gamma-ray background, has been put in the 10—100 MeV energy region [4]:
N"
dn d(ln M)
410 pc\ .
(3)
++*
Thus, the number of black holes with critical mass M* in their final state of evaporation is 3a(M*) dn "! "N"2.2;10\ N pc\ yr\ . M* dt
(4)
176
D.B. Cline / Physics Reports 307 (1998) 173—180
3. Concept of a primordial black-hole fireball Based on previous calculations and numerous direct observational searches for high-energy radiation from an evaporating PBH, we might conclude that it is not likely to be able to single out such a monumental event. However, we pointed out [6] a possible connection between very short GRBs observed by the BATSE team [11] and PBH evaporation emitting very short energetic gamma rays. If we want to accept this possibility, we may have to modify the method of calculating the particle emission spectra from an evaporating PBH, in particular, at or near the quark—gluon plasma (see Refs. [14], for a review, and [15]) phase transition temperature at which the ¹ arrives eventually. We briefly discussed [15] that inclusion of the QGP effect around the . & evaporating PBH at the critical temperature may drastically change the resulting gamma-ray spectrum. The QGP interactions around the evaporating PBH form an expanding hadronic (mostly pions) matter fireball. Shortly, after the decay of pions, the initial hadronic fireball converts to a fireball with mixtures of photons, leptons, and baryons. Using the simplest picture, i.e., only ns produced in the QGP transition, we can obtain the properties of the fireball. We find out that given that ¸ &¸ &5;10 ergs and . & /%. ¹ &¹ 5160 MeV, a simple radiation-dominated model would give q &10 cm, which . & /%. Q implies that q is of order 100 ms. However, this is very uncertain and could even be the order of seconds in some cases. Thus one can expect GRBs from a fireball to have both a very short rise time (41 ls) and duration (&50—200 ms) also in this model.
4. Study of BATSE 3B data The BATSE catalogs are cumulative; therefore, the 3B Catalog also includes the data from the 1B Catalog. The fit was made to a combination of a Gaussian and a fourth-order polynomial. The Gaussian fit the peak and the polynomial fit the background events. The duration was calculated as equal to 3 times the full width (3p) for the Gaussian fit. The cuts on the data were based on the burst duration, the completeness of the data, and the quality of the data. These cuts were: 1. short duration bursts where ¹ (250 ms; 2. insisting that complete sets of data were available for both the hardness ratio and spatial distribution analysis, which includes TTE data for the duration calculation, the fluence data for the hardness ratio, and the counts in the peak C /C for the »/» tests;
3. a cut on the quality of the data was made, requiring single-spike data and a peak count rate at least twice the background level. This removed weak bursts and bursts with multiple peaks. 4. a cut was made on data with a duration of (100 ms. The hardness ratio of the bursts selected, after making the listed cuts, from the BATSE 3B data [16] is shown in Table 1; the table also lists the calculated duration and the ¹ duration. Fig. 2 shows a tendency for an increasing hardness ratio with the shorter GRBs. Within the given statistics, we believe these GRBs are candidates for PBH evaporation in our galaxy. We cannot
D.B. Cline / Physics Reports 307 (1998) 173—180
177
Table 1 Hardness ratio versus duration (BATSE 3B) Trigger no.
Duration (s)
¹ (s)
Hardness ratio
1453 0512 0207 2615 3173 2463 0432 0480 3037 2132 0799
0.006$0.0002 0.014$0.0006 0.030$0.0019 0.034$0.0032 0.041$0.0020 0.049$0.0045 0.050$0.0018 0.062$0.0020 0.066$0.0072 0.090$0.0081 0.097$0.0101
0.192 0.183 0.085 0.028 0.208 0.064 0.034 0.128 0.048 0.090 0.173
6.68$0.33 6.07$1.34 6.88$1.93 5.43$1.16 5.35$0.27 1.60$1.55 7.46$1.17 7.14$0.96 4.81$0.98 3.64$0.66 2.47$0.39
Fig. 2. Hardness ratio for some GRBs reported in the BATSE 3B Catalog. A simple fitting to Eq. (12) of these data indicates an anti-correlation of hardness versus burst duration. The dashed line represents the average hardness for the bursts of time duration greater than 2 s. The hardness for events longer than 2 s is about of the value for the events below 2 s. Note that these short time bursts have a much harder spectrum, a trend that would be expected if some of the short bursts came from PBH evaporation. Events have been selected with a single spike time history as would be expected for PBH evaporation.
exclude the possibility that all of the short (&1 s) GRBs are due to PBH evaporation, since a change in the average distance to the PBH—GRB changes the rate like the distance cubed. 5. Diffuse gamma-ray flux — a galactic halo? Over the past two decades, the reality of a diffuse component of the gamma-ray flux has been established [17,18]. While there is no firm explanation of the source of these gamma rays, one
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D.B. Cline / Physics Reports 307 (1998) 173—180
possible candidate is due to the evaporation of PBHs in the Universe [2,13]. In fact, the diffuse gamma-ray spectrum and flux have been used to put the only real limit on the density of PBHs in the Universe, leading to a limit of X (10\ [5,19]. The recent work of Dixon et al. [20] has . & claimed the existence of an important component of gamma rays in the galactic halo. This method of analysis is very different from previous analyses and gives some confidence that the results are consistent with those of Osborne et al. [18]. This suggests that there is a halo component of diffuse gamma rays. The flux level of this component is very similar to the extragalactic diffuse flux. The existence of a local diffuse flux from PBH evaporation will depend on the level of clustering of the PBHs in galaxies and galactic halos. This same clustering magnitude will determine whether signals from individual PBH evaporation can be detected in real time [1], as discussed in the previous sections. A powerful argument would result from the detection of the galactic component of the diffuse gamma rays from PBH evaporation. There are two possibilities: 1. There could be a glow or distinct component of the diffuse radiation from the halo due to PBH evaporation. This may have been detected by EGRET [20]. In this analysis, a statistically significant large-scale halo surrounding the Milky Way is identified. The analysis uses GeV photons but shows that the effect is likely larger for 100 MeV photons, which are used in the work presented here. The basic concept is to identify a component of the gamma-ray flux that has the scale of the halo using a method of Hoar wavelets. Further information can be found in Ref. [20]. 2. There could be an anisotropy of the diffuse gamma rays if there is a sufficient density of PBHs in the halo, which may also have been detected [18,21]. Point no. 2 has been discussed by Wright [21] in order to put a limit on PBH evaporation. In fact, his analysis of the uncorrected EGRET map indicates the possible existence of such an anisotropy due to PBH evaporation, which we believe provides additional evidence for the existence of PBHs clustered in the Milky Way. The analysis [18] of the diffuse extragalactic background identified a larger anisotropy in 1994. We note that the direction of this effect is the same as the dipole anisotropy in the cosmic microwave background radiation according to the work of Osborne et al. [18]. We now turn to a simple model that explains the current observations by assuming the existence of PBHs at the level of the relaxed Page—Hawking bound discussed previously and the galactic clustering enhancement factors of 5;10 or greater. In Fig. 3, we show the logic of the possible detection of individual PBHs by very short GRBs and the connection with the diffuse gamma-ray background [1]. We now make a very simple estimate of the photon flux. The emissivity from the local flux from PBHs compared with the flux from the Universe can be estimated by using the ratio from Eqs. (12) and (13) of Ref. [21]: 3H R I %" ) G , (5) 4c I 3 where H is the Hubble constant, R the galactocentric radius, G the clustering factor, I is the % diffuse or halo “glow” flux, and I is the diffuse flux from the Universe. We take G from the 3 observations of GRBs consistent with PBH evaporation [1] to be 5;10 for a normal
D.B. Cline / Physics Reports 307 (1998) 173—180
179
Fig. 3. Schematic of the connection between GRB events and the diffuse c background, I , where N3 is density of PBHs A in the Universe, X3 is ratio of density of the Universe, ¹/%. is QGP transition temperature, S is GRB luminosity from PBH, N% is number of PBHs in the Galaxy, G is galaxy clumping factor, S is fluence sensitivity of GRB detectors, r is distance to the source, NQ % is rate of PBH decay in the Galaxy, q is age of the Universe, R is number of GRBs detected 3 per year from PBHs, m is GRB detector efficiency (including the fraction of energy detected).
Page—Hawking bound of 2;10 pc\ from Fig. 3 (we use the relaxed bound here), which is a clustering factor consistent with the GRB observations and the model of PBH evaporation [1]. We then find I "0.12 photons m\ s\ sr\ , % which is consistent with the value from Osborne et al. [18] and Dixon et al. [22] of I(E)"9.6;10\E\ m\ s\ sr\ GeV\ .
(6)
(7)
We predict that most of the isotropic background is due to the halo radiation from PBHs and that the anisotropy continues to be observed.
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D.B. Cline / Physics Reports 307 (1998) 173—180
There are several possibilities for the production of PBHs in the Early Universe [13,23,24]. While some of these schemes are for solar mass PBHs, it is very possible that similar mechanisms could produce the lower mass PBHs described here. At the very small level of X &10\, there . & could be several ways to produce them. The real test is whether they can be detected in our Galaxy by direct observation of the gamma-ray halo or the anisotropy, as suggested by Wright [21] or by the individual evaporation of a PBH, as suggested in the work of Cline et al. [1]. We therefore have data that suggest the existence of PBHs in the local galaxy.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24]
D.B. Cline, D.A. Sanders, W.P. Hong, Astrophys. J. 486 (1997) 169. S.W. Hawking, Nature 248 (1974) 30. R.W. Klebesadel, I.B. Strong, R.A. Olsen, Astrophys. J. 182 (1973) L85. F. Halzen, E. Zas, J.H. MacGibbon et al., Nature 353 (1991) 807. J.H. MacGibbon, B.J. Carr, Astrophys. J. 371 (1991) 447. D.B. Cline, W.P. Hong, Astrophys. J. 401 (1992) L57. B.J. Carr, J.E. Lidsey, Phys. Rev. D 41 (1993) 543. C. Barat, R.I. Hayles, K. Hurley et al., Astrophys. J. 285 (1984) 791. J.P. Norris, T.L. Cline, U.D. Desai et al., Nature 308 (1984) 434. D.B. Cline, Astropart. Phys. 5 (1996) 175. G.J. Fishman, C.A. Meegan, R.B. Wilson et al., Astrophys. J. Suppl. 92 (1994) 229. B.J. Carr, J.H. Gilbert, J.E. Lidsey, Phys. Rev. D 50 (1994) 4853. S.W. Hawking, Commun. Math. Phys. 43 (1975) 199. J. Rafelski, B. Muller, Phys. Rev. Lett. 48 (1982) 1066. D.B. Cline, Nucl. Phys. A 610 (1996) 500. C.A. Meegan, G.N. Pendleton, M.S. Briggs et al., Astrophys. J. Suppl. 106 (1996) 65. G.E. Fichtel, G.A. Simpson, D.J. Thompson, Astrophys. J. 222 (1978) 833. J.L. Osborne, A.W. Wolfendale, L. Zhang, J. Phys. G 20 (1994) 1089. D.N. Page, S.W. Hawking, Astrophys. J. 206 (1976) 1. D. Dixon, D.H. Hartman, E.D. Koloczyk et al., Evidence for a GeV halo surrounding the milky way, U. California Riverside, preprint, 1998; also D. Dixon, private communication, 1998. E.L. Wright, Astrophys. J. 459 (1996) 487. J.H. MacGibbon, B.R. Webber, Phys. Rev. D 41 (1990) 3052. M. Crawford, D.N. Schramm, Nature 298 (1982) 538. A. Dolgov, J. Silk, Phys. Rev. D 47 (1993) 4244.
Primordial black holes and short gamma-ray bursts David B. Cline* Department of Physics and Astronomy, Box 951547, University of California Los Angeles, Los Angeles, CA 90095-1547, USA
Abstract The possible existence of primordial black holes (PBHs) has long been a key observational question. At present, the only known way to detect low-mass ones (below 10 g) is through the Hawking radiation process. This radiation in turn depends on the nature of hadron interactions in the 100 MeV region and beyond. In the case of a first-order quantum-chromodynamics phase transition, we expect a sharp burst of gamma rays from the PBH. We have pointed out that there is a class of gamma-ray bursts that have this property and could provide evidence for PBHs in the galaxy. Future study of these events is crucial. Recently, we have shown that a diffuse gamma-ray glow should exist in the halo from these PBHs. There now seems to be evidence for this effect as well. 1998 Elsevier Science B.V. All rights reserved. PACS: 97.60.Lf
1. Introduction The search for evidence for primordial black holes (PBHs) has continued since the first discussion by Hawking [2]. In fact, this was about the time that gamma-ray bursts (GRBs) were first discovered, making a natural association with PBHs [3]. However, in the intervening years it has become clear that the time history of the typical GRB is not consistent with the expectations of PBH evaporation. While the theory of PBH evaporation has been refined, there are still no exact predictions of the GRB spectrum, time history, etc. [4]. However, reasonable phenomenological models have been made, and the results again indicate that most GRBs could not come from PBHs [5,6]. In addition, there are new constraints on the production of PBHs in the Early Universe that indicate that the density of PBHs in the Universe should be very small, but not necessarily zero [7].
* E-mail: [email protected]. Sections 1—4 have been adapted; see Ref. [1] for further details. 0370-1573/98/$ — see front matter 1998 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 0 - 1 5 7 3 ( 9 8 ) 0 0 0 4 6 - 5
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D.B. Cline / Physics Reports 307 (1998) 173—180
After the initial discovery of GRBs, it took many years to uncover the general properties. Around 1984, several GRBs were detected, indicating that there was a class of short bursts with time duration of &100 ms and a very short rise time [8]. A separate class of GRBs was declared [9]. This classification seems to have been forgotten and then rediscovered by some of us [10]. It is still possible that there is a sizable density of PBHs in our galaxy and that some of the GRBs could be due to PBH evaporation. Recently, we showed that the BATSE 1B data [11] have a few events that are consistent with some expectation of PBH evaporation (short bursts with time duration (200 ms and that are consistent with »/» & [10].
2. Primordial black-hole evaporation Ever since the theoretical discovery of the quantum-gravitational particle emissions from black holes by Hawking [2], there have been many experimental searches (see Ref. [4] for details) for high-energy gamma-ray radiation from PBHs. They would have been formed in the Early Universe [7,12] and would now be entering their final stages of extinction. The violent final-stage evaporation or explosion is the striking result of the expectation that the PBH temperature is inversely proportional to the PBH mass, e.g., ¹ +100 MeV (10 g/m ), since the black hole becomes . & . & hotter as it radiates more particles and can eventually attain extremely high temperatures. In 1974, Hawking showed in a seminal paper [2] that an uncharged, non-rotating black-hole emits particles with energy between E and E#dE at a rate per spin of helicity state of
8pGME \ C dN , " Q exp !(!1)Q hc dtdE 2ph
(1)
where M is the PBH mass, s is the particle spin, and C is the absorption probability. It can be Q considered that this particle emission comes from the spontaneous creation of particle—antiparticle pair escapes to infinity, while the other returns to the black hole. Thus, the PBH emits massless particles, photons, and light neutrinos, as if it were a hot black-body radiator with temperature ¹ 10 g/M MeV, where M is the black-hole mass. A black hole with one solar mass, M 2;10 g, has an approximate temperature of 10\ K, while a black hole with mass of 6;10 g has a temperature of &20 MeV. The temperature of a black hole increases as it loses mass during its lifetime. The loss of mass from a black hole occurs at a rate, in the context of the standard model of particle physics, of a(M) dM "! , M dt
(2)
where a(M), the running constant, counts the particle degree of freedom in the PBH evaporation. The value of a(M) is model dependent. In the standard model (SM), with a family of three quarks and three leptons, it is given [2,6,13] as a(M)"(0.045 S #0.162 S );10\, where H> H S and S are the spin and color degrees of freedom for the fermions and gauge particles, H> H respectively. For the SM, a(M)"4.1;10\. A reasonable model of the running coupling constant is illustrated in Fig. 1, where the regions of uncertainty are indicated. These are the regions where there could be a rapid increase in the
D.B. Cline / Physics Reports 307 (1998) 173—180
175
Fig. 1. Running coupling or density of states factor a, showing regions of uncertainty due to the QGP transitions (I) or the increase in the number of new elementary particles (II). It is possible that intense short GRBs could occur at either of these temperatures (the decrease of mass of the black hole is given by dm /dt"!a/m ). A rapid mass decrease or . & . & burst can occur when m 410 g or if a changes rapidly near the QGP transition. . &
effective number of degrees of freedom due to the quark—gluon phase (QGP) transition. The phase transition would lead to a rapid burst in the PBH evaporation or, at high energy, there could be many new particle types that would also lead to an increase in the rate of evaporation. Also shown in Fig. 1 are the regions in PBH temperature where short duration GRBs may occur when the PBH mass is either 10 or 10 g. Black holes at the evaporation stage at the present epoch can be calculated as having M* [3a(M*)q ] 7;10 g for a(M*) 1.4;10\. The bound on the number of black holes at their critical mass, constrained by the observed diffuse gamma-ray background, has been put in the 10—100 MeV energy region [4]:
N"
dn d(ln M)
410 pc\ .
(3)
++*
Thus, the number of black holes with critical mass M* in their final state of evaporation is 3a(M*) dn "! "N"2.2;10\ N pc\ yr\ . M* dt
(4)
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D.B. Cline / Physics Reports 307 (1998) 173—180
3. Concept of a primordial black-hole fireball Based on previous calculations and numerous direct observational searches for high-energy radiation from an evaporating PBH, we might conclude that it is not likely to be able to single out such a monumental event. However, we pointed out [6] a possible connection between very short GRBs observed by the BATSE team [11] and PBH evaporation emitting very short energetic gamma rays. If we want to accept this possibility, we may have to modify the method of calculating the particle emission spectra from an evaporating PBH, in particular, at or near the quark—gluon plasma (see Refs. [14], for a review, and [15]) phase transition temperature at which the ¹ arrives eventually. We briefly discussed [15] that inclusion of the QGP effect around the . & evaporating PBH at the critical temperature may drastically change the resulting gamma-ray spectrum. The QGP interactions around the evaporating PBH form an expanding hadronic (mostly pions) matter fireball. Shortly, after the decay of pions, the initial hadronic fireball converts to a fireball with mixtures of photons, leptons, and baryons. Using the simplest picture, i.e., only ns produced in the QGP transition, we can obtain the properties of the fireball. We find out that given that ¸ &¸ &5;10 ergs and . & /%. ¹ &¹ 5160 MeV, a simple radiation-dominated model would give q &10 cm, which . & /%. Q implies that q is of order 100 ms. However, this is very uncertain and could even be the order of seconds in some cases. Thus one can expect GRBs from a fireball to have both a very short rise time (41 ls) and duration (&50—200 ms) also in this model.
4. Study of BATSE 3B data The BATSE catalogs are cumulative; therefore, the 3B Catalog also includes the data from the 1B Catalog. The fit was made to a combination of a Gaussian and a fourth-order polynomial. The Gaussian fit the peak and the polynomial fit the background events. The duration was calculated as equal to 3 times the full width (3p) for the Gaussian fit. The cuts on the data were based on the burst duration, the completeness of the data, and the quality of the data. These cuts were: 1. short duration bursts where ¹ (250 ms; 2. insisting that complete sets of data were available for both the hardness ratio and spatial distribution analysis, which includes TTE data for the duration calculation, the fluence data for the hardness ratio, and the counts in the peak C /C for the »/» tests;
3. a cut on the quality of the data was made, requiring single-spike data and a peak count rate at least twice the background level. This removed weak bursts and bursts with multiple peaks. 4. a cut was made on data with a duration of (100 ms. The hardness ratio of the bursts selected, after making the listed cuts, from the BATSE 3B data [16] is shown in Table 1; the table also lists the calculated duration and the ¹ duration. Fig. 2 shows a tendency for an increasing hardness ratio with the shorter GRBs. Within the given statistics, we believe these GRBs are candidates for PBH evaporation in our galaxy. We cannot
D.B. Cline / Physics Reports 307 (1998) 173—180
177
Table 1 Hardness ratio versus duration (BATSE 3B) Trigger no.
Duration (s)
¹ (s)
Hardness ratio
1453 0512 0207 2615 3173 2463 0432 0480 3037 2132 0799
0.006$0.0002 0.014$0.0006 0.030$0.0019 0.034$0.0032 0.041$0.0020 0.049$0.0045 0.050$0.0018 0.062$0.0020 0.066$0.0072 0.090$0.0081 0.097$0.0101
0.192 0.183 0.085 0.028 0.208 0.064 0.034 0.128 0.048 0.090 0.173
6.68$0.33 6.07$1.34 6.88$1.93 5.43$1.16 5.35$0.27 1.60$1.55 7.46$1.17 7.14$0.96 4.81$0.98 3.64$0.66 2.47$0.39
Fig. 2. Hardness ratio for some GRBs reported in the BATSE 3B Catalog. A simple fitting to Eq. (12) of these data indicates an anti-correlation of hardness versus burst duration. The dashed line represents the average hardness for the bursts of time duration greater than 2 s. The hardness for events longer than 2 s is about of the value for the events below 2 s. Note that these short time bursts have a much harder spectrum, a trend that would be expected if some of the short bursts came from PBH evaporation. Events have been selected with a single spike time history as would be expected for PBH evaporation.
exclude the possibility that all of the short (&1 s) GRBs are due to PBH evaporation, since a change in the average distance to the PBH—GRB changes the rate like the distance cubed. 5. Diffuse gamma-ray flux — a galactic halo? Over the past two decades, the reality of a diffuse component of the gamma-ray flux has been established [17,18]. While there is no firm explanation of the source of these gamma rays, one
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possible candidate is due to the evaporation of PBHs in the Universe [2,13]. In fact, the diffuse gamma-ray spectrum and flux have been used to put the only real limit on the density of PBHs in the Universe, leading to a limit of X (10\ [5,19]. The recent work of Dixon et al. [20] has . & claimed the existence of an important component of gamma rays in the galactic halo. This method of analysis is very different from previous analyses and gives some confidence that the results are consistent with those of Osborne et al. [18]. This suggests that there is a halo component of diffuse gamma rays. The flux level of this component is very similar to the extragalactic diffuse flux. The existence of a local diffuse flux from PBH evaporation will depend on the level of clustering of the PBHs in galaxies and galactic halos. This same clustering magnitude will determine whether signals from individual PBH evaporation can be detected in real time [1], as discussed in the previous sections. A powerful argument would result from the detection of the galactic component of the diffuse gamma rays from PBH evaporation. There are two possibilities: 1. There could be a glow or distinct component of the diffuse radiation from the halo due to PBH evaporation. This may have been detected by EGRET [20]. In this analysis, a statistically significant large-scale halo surrounding the Milky Way is identified. The analysis uses GeV photons but shows that the effect is likely larger for 100 MeV photons, which are used in the work presented here. The basic concept is to identify a component of the gamma-ray flux that has the scale of the halo using a method of Hoar wavelets. Further information can be found in Ref. [20]. 2. There could be an anisotropy of the diffuse gamma rays if there is a sufficient density of PBHs in the halo, which may also have been detected [18,21]. Point no. 2 has been discussed by Wright [21] in order to put a limit on PBH evaporation. In fact, his analysis of the uncorrected EGRET map indicates the possible existence of such an anisotropy due to PBH evaporation, which we believe provides additional evidence for the existence of PBHs clustered in the Milky Way. The analysis [18] of the diffuse extragalactic background identified a larger anisotropy in 1994. We note that the direction of this effect is the same as the dipole anisotropy in the cosmic microwave background radiation according to the work of Osborne et al. [18]. We now turn to a simple model that explains the current observations by assuming the existence of PBHs at the level of the relaxed Page—Hawking bound discussed previously and the galactic clustering enhancement factors of 5;10 or greater. In Fig. 3, we show the logic of the possible detection of individual PBHs by very short GRBs and the connection with the diffuse gamma-ray background [1]. We now make a very simple estimate of the photon flux. The emissivity from the local flux from PBHs compared with the flux from the Universe can be estimated by using the ratio from Eqs. (12) and (13) of Ref. [21]: 3H R I %" ) G , (5) 4c I 3 where H is the Hubble constant, R the galactocentric radius, G the clustering factor, I is the % diffuse or halo “glow” flux, and I is the diffuse flux from the Universe. We take G from the 3 observations of GRBs consistent with PBH evaporation [1] to be 5;10 for a normal
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Fig. 3. Schematic of the connection between GRB events and the diffuse c background, I , where N3 is density of PBHs A in the Universe, X3 is ratio of density of the Universe, ¹/%. is QGP transition temperature, S is GRB luminosity from PBH, N% is number of PBHs in the Galaxy, G is galaxy clumping factor, S is fluence sensitivity of GRB detectors, r is distance to the source, NQ % is rate of PBH decay in the Galaxy, q is age of the Universe, R is number of GRBs detected 3 per year from PBHs, m is GRB detector efficiency (including the fraction of energy detected).
Page—Hawking bound of 2;10 pc\ from Fig. 3 (we use the relaxed bound here), which is a clustering factor consistent with the GRB observations and the model of PBH evaporation [1]. We then find I "0.12 photons m\ s\ sr\ , % which is consistent with the value from Osborne et al. [18] and Dixon et al. [22] of I(E)"9.6;10\E\ m\ s\ sr\ GeV\ .
(6)
(7)
We predict that most of the isotropic background is due to the halo radiation from PBHs and that the anisotropy continues to be observed.
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There are several possibilities for the production of PBHs in the Early Universe [13,23,24]. While some of these schemes are for solar mass PBHs, it is very possible that similar mechanisms could produce the lower mass PBHs described here. At the very small level of X &10\, there . & could be several ways to produce them. The real test is whether they can be detected in our Galaxy by direct observation of the gamma-ray halo or the anisotropy, as suggested by Wright [21] or by the individual evaporation of a PBH, as suggested in the work of Cline et al. [1]. We therefore have data that suggest the existence of PBHs in the local galaxy.
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