Limits on Primordial Black Hole evaporation with the H.E.S.S. array of Cherenkov telescopes
333 RD I NTERNATIONAL C OSMIC R AY C ONFERENCE , R
IO DE J ANEIRO T HE A STROPARTICLE P HYSICS C ONFERENCE
Limits on Primordial Black Hole evaporation with the H.E.S.S. array ofCherenkov telescopes
J-F.G
LICENSTEIN , A.B ARNACKA , M.V IVIER , T.H ERR , FOR THE
H.E.S.S. C
OLLABORATION . CEA Saclay, DSM/Irfu, F-91191 Gif-Sur-Yvette Cedex, France Nicolaus Copernicus Astronomical Center, ul. Bartycka 18, 00-716 Warsaw, Poland Max-Planck-Institut f¨ur Kernphysik, P.O. Box 103980, D 69029 Heidelberg, Germany [email protected]
Abstract:
Data collected by the H.E.S.S. array between 2004 and 2012 have been used to search for photonbursts from primordial black hole explosions. Bursts were searched for in a 30 second time-window. The durationof the search window has been optimized to increase the burst signal while keeping the statistical backgroundlow. No evidence for a burst signal was found. Preliminary upper limits on the local rate of PBH explosionsof 1 . × pc − yr − have been obtained, which improve previously published limits by almost an order ofmagnitude. Keywords:
Gamma rays - Primordial Black Holes
Primordial black holes (PBH) [1] are compact objects thatmay have been formed in the early Universe via a variety ofmechanisms. These include (see e.g. [2] for a review) thegravitational collapse of overdense regions with significantdensity fluctuations, pressure reduction or bubble collisionsduring cosmic phase transitions, and collapse of topologicaldefects such as cosmic strings or domain walls. The massfunction of PBHs depends on the formation mechanism.PBHs could have masses ranging from 10 − g for PBHscreated at the Planck time [5] upwards.Black holes were predicted by Hawking [3] to radiateoff particles with a black body spectrum of energies. Theemission can thus be described by an effective temperature T BH = M p π M BH , (1)where M p and M BH are the Planck mass and the PBH massrespectively. For black holes of stellar masses or higher,Hawking’s radiation is quite negligible but for small enoughPBHs, it becomes the predominant process that governsthe black hole evolution. Black holes lose their mass byHawking radiation at a rate inversely proportional to theirsquared mass: dM BH dt = − α ( M BH ) M BH2 , (2)where α ( M BH ) is a parameter counting the number of de-grees of freedom available to the radiated particles. Theparameter α is an increasing function of the black holetemperature and strongly depends on the particle physicsmodel at high energies [4]. Since the particle emission rateincreases with black hole temperature, PBH evaporation isa runaway process that eventually leads to a violent explo-sion and bursts of particles. PBHs can evaporate more orless rapidly depending on the number of available particlespecies that can be produced. In a Friedman universe and inthe standard model of particle physics, PBHs whose initialmass does not exceed 5 × g are expected to have fully evaporated within the 10 years of our Universe history.Consequently, PBHs a little more massive than this willstill be emitting particles at a rate large enough so that theywould be detectable.The cosmological constraints on PBHs have been reviewedby Carr et al [5]. The best method for constraining lowmass PBHs ( M BH ≤ × g) is thus through their γ -ray emission. Previous searches have attempted to detect adiffuse photon signal from a distribution of PBHs [6] or tosearch directly for the final stage emission of an individualhole [9, 7, 8, 10]. The EGRET observation of the diffuse γ -ray background allowed to set an upper limit on the lowmass PBH density Ω PBH of 0 . × − to 2 . × − [6].The search for direct PBH explosions through γ -ray burstsdid not find any evidence of their presence yet. The currentupper limits on the local PBH explosion rate lie in the 10 -10 pc − yr − range [5]. Note however that it has beenargued that a class of very short gammay ray bursts areactually the final stage of PBH evaporation[11].The present paper reports on the search for TeV γ -raybursts with a timescale of a few seconds, as expected fromthe final stage of PBHs evaporation, using the H.E.S.S. arrayof Imaging Atmospheric Cherenkov Telescopes (IACTs).The H.E.S.S. array is presented in Sec. 2. A modelling ofthe expected PBH γ -ray signal is carried out in Sec. 3. Thedata analysis procedure and the burst search strategy arepresented in Sec. 4 and 5. Finally, preliminary upper limitson the local PBH explosion rate are derived in Sec. 6. H.E.S.S. is an array of five imaging atmospheric Cherenkovtelescopes dedicated to observing very-high energy (VHE) γ -rays with energies above 50 GeV from astrophysicalsources. It is located in the Khomas Highland of Namib-ia. The first four telescopes have been installed in 2003(H.E.S.S-1 phase of the experiment, with an energy thresh-old of ∼
100 GeV) and have been operational since 2004.Each telescope of H.E.S.S-1 comprise a tesselated opticalreflector of 107m [12] and a camera with 960 photomul- a r X i v : . [ a s t r o - ph . H E ] J u l .E.S.S. limits on PBH evaporation33 RD I NTERNATIONAL C OSMIC R AY C ONFERENCE , R
IO DE J ANEIRO tiplier tubes. The camera field of view is 5 ◦ in diameter.The stereoscopic technique [13] allows for an accurate re-construction of the direction and the energy of the prima-ry gamma-ray. H.E.S.S-1 has an angular resolution of lessthan 0 . ◦ , a source location accuracy of ∼ (cid:48)(cid:48) for strongsources and an effective detection area of ∼ m . Thesensitivity for point-like sources reaches 2 × − cm s − above 1 TeV for a 5 σ detection in 25 hours of a source ata 20 ◦ zenith angle [14]. A fifth telescope with a reflectivearea of 596 m and a camera of 2048 photo multipliers hasstarted its operations in 2012. This paper uses only datacollected with the four telescopes of H.E.S.S-1. The theoretical number of γ -rays emitted from a PBHlocated at a distance r and in the direction ( α , δ ) in the sky,during the last ∆ t seconds of its life is given by: N γ ( r , α , δ , ∆ t ) = π r (cid:90) ∆ t dt (cid:90) ∞ dE γ d NdE γ dt ( E γ , t ) A ( E γ , α , δ ) , (3)where d N/dE γ dt is the instantaneous γ -ray spectrum emit-ted by the PBH at a time t before complete evapora-tion. This spectrum is folded with the H.E.S.S. acceptanceA(E γ , α , δ ) to take into account the instrument’s efficien-cy in collecting γ -rays of energy E γ at equatorial coordi-nates ( α , δ ) in the sky. The response of the H.E.S.S. in-strument to γ rays depends on the zenith angle and off-set angle of observation. The acceptance A ( E γ , α , δ ) is anaverage over many runs with different zenith and offsetangle s . It can be approximately factored into an energydependent term and a spatially dependent term by writ-ing A ( E γ , α , δ ) = A ( ) ( E γ ) A ( ) ( α , δ ) . The factor A ( ) ( α , δ ) corresponds basically to the normalised sky acceptance mapto γ -rays, which is maximum at the center of the cameraand drops toward the edges. It is directly estimated fromthe data. The A ( ) term is the effective area and is obtainedfrom Monte Carlo simulations with different zenith anglesand offsets.The instantaneous γ -ray spectrum d N/dE γ dt emitted bythe PBH depends on specific particle physics models [4]. Itis assumed in this paper that the standard model of particlephysics remains valid at high ( >
200 GeV) temperatures.The presence of an atmosphere around the PBH is animportant theoretical question which is still debated [15].The PBH atmosphere would drastically alter the evaporationsignal [16, 17] by suppressing the high energy component.In this paper, we assume that any existing PBH atmospherehas a negligible effect on the evaporation signal.The integrated spectrum above the energy E D is given byby Halzen et al [4] and shown on Fig 1 for several values ofthe time remaining before total evaporation ∆ t.The signature of a PBH explosion consists in the detec-tion of several photons within a time-window of a few sec-onds. The number of photons in the burst is the size of theburst.The probability of detecting a burst of size b whenobserving a PBH which emits N γ (r, δ , α , ∆ t) γ -rays followsa Poisson statistics: P ( b , N γ ) = e − N γ N b γ b ! (4) Energy (GeV) ) - s - G e V N / d E d t ( d -1 t = 1 sec D t = 5 sec D t = 30 sec D t = 120 sec D Fig. 1 : Integrated PBH spectrum at several values of theremaining time before explosion ∆ t.Integrating this probability over space, and summing overeach run give the number of expected bursts of size b to bedetected in the data: n signal ( b , ∆ t ) = ˙ ρ PBH V eff ( b , ∆ t ) (5)where ˙ ρ PBH is the local PBH explosion rate and the effectivespace-time volume of PBH detection is defined by V eff ( b , ∆ t ) = ∑ i T i (cid:90) d Ω i (cid:90) ∞ drr P i ( b , N γ ) , (6)where the indice i goes over each run of the H.E.S.S. dataset,T i and d Ω i being the corresponding run live time and obser-vation solid angle respectively.The average number of photon detected by H.E.S.S. as afunction of distance is shown in Fig. 2. Distance (pc) -2 -1
10 1 10 i n H ESS g N -3 -2 -1 t = 1 sec D t = 5 sec D t = 30 sec D t = 120 sec D Fig. 2 : Average number of photons from a PBH explosiondetectable by H.E.S.S. as a function of the distance tothe burst, for several values of the remaining time beforeexplosion ∆ t.The total number of bursts n tot is the sum of the signalfrom PBH explosions n sig , given by equation (5) and acontribution from statistical background bursts n back . Alikelihood analysis is performed on the observed n obs ( b ) bursts of size b ≥ ρ PBH . .E.S.S. limits on PBH evaporation33 RD I NTERNATIONAL C OSMIC R AY C ONFERENCE , R
IO DE J ANEIRO
The data set used for the burst search includes a largefraction of targeted and survey observations made with theH.E.S.S-1 array from March 2004 through May 2012. Ob-servations are organized in runs of approximately 28 min du-ration. Poisson fluctuations of photon candidates (“ gamma -like events”) arrival times could accidentally mimic PBHbursts. Since the major fraction of the H.E.S.S. observationsis taken towards astrophysical sources, the contribution ofthese sources to background bursts has to be considered.A few thousands photon candidates, mostly misidentifiedhadrons, are reconstructed in a typical observation run ofan empty field. The actual number depends on the data tak-ing condition and the reconstruction method. The candidatephoton background in a point source search is thus a fewphotons per minutes, at the level of the count rate of theCrab nebula. Thus, strong sources such as the active galax-ies PKS 2155-304, MRK 421 and the Crab pulsar windnebula have to be excluded. However, most VHE gamma-ray sources are too weak to accidentally mimic PBH bursts.The evaluation of the effective sensitivity volume of obser-vations (equation 6) implies the calculation of spatial ac-ceptance maps. To obtain maps with sufficient statisticalaccuracy, targets with only a small observation time wereexcluded from the data set. Only observations where at leastthree of the four telescopes participated in data taking wereused to improve the angular resolution. Finally, each runhas to pass certain quality criteria which ensure that thedata used for analysis was taken under good environmentaland instrumental conditions. After these cuts cuts, the dataset includes 6424 runs, covering ∼
45% of all H.E.S.S-1observations between 2004 and 2012, and corresponds toroughly 2600 hours of observation time.
The vast majority of imaged air showers in the data is notcaused by VHE γ -rays but by an unwanted backgroundof hadronic cosmic rays. To suppress this background andreconstruct the direction and energy of the γ -ray candidates,an implementation of the ’model’ technique[14], Model++has been used. In the ’model’ technique, the air showers aredescribed by a semi-analytical model. Expected propertiesof the camera images are then compared to the observationaldata based on a maximum likelihood method. The modeltechnique is known to provide an improved sensitivity,particularly at lower energies, and a better hadron rejectioncompared to the more traditionnal Hillas reconstruction.The angular resolution, defined as the 68% containmentradius, is 0.06 ◦ . Additional cuts such as a minimum chargeof 60 photo-electrons were applied. Gamma-like eventswith a distance to the center of the camera larger than 2 ◦ are excluded. The analysis chain and the algorithms havebeen cross-checked with an independent analysis chain.Finally, arrival times and geometrically reconstructed arrivaldirections in the RA-Dec (J2000) coordinate system of all γ -like events (a few thousands per run) were stored in eventlists. γ -ray bursts The event lists have been searched for bursts of differentdurations τ =
1, 5, 10 , , ,
60 and 120 seconds. As these time scales are much shorter than the duration of a singlerun, all runs can be analyzed individually. Each of the N ev entries i stored in the run’s event list marks the start time t i of a possible burst that could include additional γ -likeevents reconstructed within the time interval [ t i , t i + τ ] . SincePBHs are point sources, these additional γ candidates weresearched in a circle of radius θ = . ◦ in the RA-DEC plane.This radius corresponds to a 90% containment probabilityfor point sources. As the sensitivity within the H.E.S.S. FoVfor VHE gamma-ray events drops off rapidly for angulardistances greater than approximately 2 ◦ from the telescopespointing direction, the burst search is restricted to the inner2 ◦ of the FoV. To account for the finite size of PSF weinclude all events within a maximum distance of 2 . ◦ to thetelescopes’s pointing direction. For all events lying withinthe time interval [ t i , t i + τ ] , the burst search algorithm findsthe maximal subset that fits in a circle with radius θ in theRA-Dec plane. This maximal subset is said to be a burstof a size b . Each photon candidate is thus associated witha burst size b . To prevent multiple counting of bursts, thenumber N ( b ) of detected bursts of size b is defined as thenumber of events N ev ( b ) that have been assigned the burstsize b divided by b [9]: N ( b ) = N ev ( b ) b (7)Using this convention, the following intuitive normalizationrelation holds: N ev = ∑ b N ev ( b ) = ∑ b bN ( b ) (8)Note that the maximal subset defining b is not necessarilyunique, as there may be more than one valid maximal subset.Also, by optimizing for the largest possible burst size, thealgorithm may underestimate the number of smaller sizebursts. However, because the number of bursts N ( b ) foundat burst size b is always much greater than N ( b + ) thiseffect can safely be neglected. The major background to physical bursts is caused by cos-mic ray primaries that accidentally happen to arrive fromneighboring directions within a narrow time window. Es-timating the contribution of this statistical background isessential for extracting a possible VHE gamma-ray burstsignal. In our analysis, the estimation of background relieson the “scrambling” method. In the scrambling method,new simulated datasets are created by keeping the arrivaldirection of each γ candidate and scrambling their arrivaltimes. This method automatically accounts for all instru-mental characteristics and effects determining the spatialdistribution of events in the FoV. To reduce statistical errorsof the background estimate, ten simulated datasets wereproduced for each H.E.S.S. observation run.The simulated background burst size spectrum, calculatedfor the whole H.E.S.S. dataset, is shown on Fig. 3 for sever-al values of the search time window τ . Previous PBH explosion searches with Cherenkov tele-scopes [9, 10] have used a τ = .E.S.S. limits on PBH evaporation33 RD I NTERNATIONAL C OSMIC R AY C ONFERENCE , R
IO DE J ANEIRO burst size
30 s time window1 s time window5 s time window
Fig. 3 : Simulated background burst size spectrum for burstssearches in the H.E.S.S. dataset within different τ searchtime windows.the statistical background, which both increase with τ , al-beit at different rates. The optimal time-window obviouslydepends strongly on the rejection of hadrons by the photonanalysis program. Since Model++ has a very good rejec-tion of hadrons, it turns out that it is possible to extend thetime-window τ . The optimal time-window was selected bycomputing a sensitivity limit with 250 hours on the fieldof view of radiogalaxy Centarus A. The sensitivity limit isobtained by optimizing the likelihood L under the assump-tion that n obs ( b ) = n back ( b ) . The variation of the sensitivitylimit as a function of the duration of the search window τ has a broad minimum around τ = τ wasused for the limits on the PBH evaporation rate derived insection 6. Bursts were searched for in the dataset defined in Sec 4. Theobserved burst size spectrum is shown by a solid line on Fig.4 for the nominal value of the search window τ =
30 s. Theestimated statistical background is displayed with a dashline. Fitting the observed size spectrum by the expectedstatistical background gives χ / d.o.f = . /
7. This showsthat the observed spectrum is in excellent agreement withthe statistical background.The H.E.S.S. dataset shows thus no indication for anexcess of bursts over the statistical background.The agreement between the observed burst distributionand the estimated statistical background can be translatedinto an upper limit on the PBH explosion rate ˙ ρ PBH . The95% CL upper limit on ˙ ρ PBH is obtained by demanding that2 ln L < . . The preliminary upper limit on the explosion rate is˙ ρ PBH < . × pc − yr − at the 95% CL for τ =
30 s.The sensitivity limit, defined in section 5.3 is 1 . × pc − yr − . By comparison, the preliminary upper limitobtained with the τ = ρ PBH < . × pc − yr − (95% CL).The 95% upper limit on the local rate of PBH explosionobtained with the τ = s search time-window improvesthe best published result obtained with Cherenkov telescopearrays [10] by almost an order of magnitude. Improvementof a factor of 10 is still needed before the hypothesisthat the very short gamma ray bursts originate from PBHexplosions [11] can be tested. Our limit depends strongly burst size
30 s time window, datastatistical background
Fig. 4 : Preliminary observed burst size distributions (solidline) and estimated statistical background (dashed line). Thesearch time window has the nominal value τ = s .on the hypothesis that the PBH atmospheric effects arenegligible. In the second phase of H.E.S.S, H.E.S.S-2, itwill become possible to constrain models of PBH withatmospheres such as that of Dahigh and Kapusta [17] thanksto the lowering of the energy threshold below 50 GeV. Acknowledgment:
Please see standard acknowledgement inH.E.S.S. papers, not reproduced here due to lack of space.