Constraining the evaporation rate of primordial black holes using archival data from VERITAS
CConstraining the evaporation rate of primordialblack holes using archival data from VERITAS
Sajan Kumar , for the VERITAS collaboration ∗† Department of Physics, McGill University, Montreal, CanadaE-mail: [email protected]
Primordial black holes (PBHs) are thought to have been formed as a result of density fluctuationsin the very early Universe. It is suggested that PBHs of mass ∼ × g or less have evaporatedthrough the release of Hawking radiation by the present day. However, PBHs of initial mass10 g should still be evaporating at the present epoch. Over the past few years, very high-energy(VHE; E >
100 GeV) gamma-ray emission from PBHs in the form of a burst has been searchedfor using ground-based gamma-ray instruments. However, no observational evidence has beenreported on the detection of VHE emission from PBHs yet. Previously, an upper limit on therate density of PBHs was calculated using 750 hours of archival data taken between 2009 and2012 by the VERITAS gamma-ray observatory. We will augment this study with additional datataken between 2012 and 2017. In addition to more data, the lower energy threshold on the newerdata will help to produce an improved upper limit on the rate at which PBHs are evaporating inour local neighborhood. This work is still in progress, therefore we will only report an expectedchange to the upper limit on the rate density of PBH evaporation. ∗ Speaker. † for the VERITAS collaboration. c (cid:13) Copyright owned by the author(s) under the terms of the Creative CommonsAttribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). https://pos.sissa.it/ a r X i v : . [ a s t r o - ph . H E ] S e p onstraining evaporation rate of PBHs with VERITAS Sajan Kumar , for the VERITAS collaboration
1. Introduction
The observational evidence for the existence of primordial black holes (PBHs) is still lacking.But even their non-detection can lead to important constraints on the physics of the early Universe,high energy particle physics and quantum gravity [1]. PBHs are theoretical objects that are pre-dicted to be formed due to fluctuations in the density of early Universe [2, 3]. These cosmologicaldensity fluctuations could have caused the over dense regions to collapse gravitationally, thus lead-ing to the formation of PBHs. The initial mass of a PBH depends upon its creation at the time, t ,after the Big Bang, according to the equation 1.1 in [4]. M BH ∼ (cid:18) t − sec (cid:19) g (1.1)Thus PBHs can span a large range of masses, from 10 − g formed at the Planck time (10 − second)to 10 M (cid:12) formed at 1 second after the Big Bang.The presence of such PBHs in the Universe could be confirmed by detecting Hawking radiation(HR) from black holes [5]. As the black hole evaporates, its temperature is given by kT BH = . (cid:18) g M BH (cid:19) GeV (1.2)where k is the Boltzmann constant. From the Equation 1.2, it is clear that the temperature ofa black hole is inversely proportional to its mass. As the black hole evaporates, its mass decreases,and therefore the temperature increases. This increase in temperature leads to an increase in emittedparticle flux. Therefore, it emits a burst of particles in the last few seconds of its life time. Thisburst includes gamma-ray photons in the MeV to TeV energy range. The life time of a PBH can beapproximated as [4] τ BH ∼ . × − (cid:18) M BH (cid:19) sec (1.3)PBHs which were formed in the early universe with an initial mass ∼ g would have alifetime close to the age of the Universe. Therefore, they should be in the final stages of theirevaporation at the present time and might be seen using ground based Cherenkov gamma-ray tele-scopes. In order to verify this, the Very Energetic Radiation Imaging Telescope Array System(VERITAS) has searched for the burst signal from evaporating PBHs with a remaining lifetimewindow of 1 second. From the study, a 99% confidence-level upper limit, on the rate-density ofPBHs evaporation, has been placed at a value of 1 . × pc − yr − [6]. The Milagro experimentalso tried to detect a burst signal from evaporating PBHs and calculate an upper limit for 1 secondtime window at a value of 3 . × pc − yr − [7]. A similar study was performed by the HighEnergy Stereoscopic System (H.E.S.S) using a time window of 30 seconds to put an upper limit onthe PBHs evaporation rate at 1 . × pc − yr − [8]. More recently, VERITAS obtained their bestlimits for the rate-density of 2 . × pc − yr − using a time window of 30 seconds [9].1 onstraining evaporation rate of PBHs with VERITAS Sajan Kumar , for the VERITAS collaboration
2. The VERITAS observatory
The VERITAS observatory is a system of four ground-based atmospheric Cherenkov tele-scopes situated in southern Arizona (31 .
68 N, 110 .
95 W), at an elevation of 1268 m above sealevel. Each telescope has a 12 m diameter optical reflector, providing a total reflecting area of ∼
110 m . At the focus of each telescope, a pixelated camera consists of 499 photomultiplier tubes(PMTs) is placed giving a field of view of 3 . ∼ . >
30 TeV [10].
3. Data selection and analysis
This work uses good weather VERITAS archival data from the summer 2009 until the endof 2017. In order to achieve minimal energy threshold for the detection, only data taken withpointing above 50 degree elevation was selected. Furthermore, the selected data after applying theabove criterion is divided into two epochs, each depending on the telescope camera configuration.Dataset I consists of data taken after the summer of 2009 and before the summer of 2012. The totaluseful data between these dates amount to about 750 hours. Dataset II consists of observationstaken after the summer of 2012 when the telescope cameras were upgraded with high efficiencyphotomultiplier tubes resulting in an energy threshold below 100 GeV. The total useful data afterthe summer of 2012 until the end of 2017 is approximately 1300 hours. In the total, this study usesabout 2100 hours of data to evaluate the limits on the rate-density of PBH evaporation.Before applying the PBH search methodology, it is important to remove the background eventsfrom the sample of all the events that triggered the telescope readout. This is achieved using theboosted decision tree (BDT) method discussed in [11]. For the PBH burst search, the previousmethodology discussed in [9] is used. However, since the Dataset II is taken with a different tele-scope configuration, it is necessary to re-evaluate the angular resolution of instrument for DatasetII before applying the the burst search methodology. For the Dataset I, we will be using the samevalues as already estimated in the previous work [9].
The basic requirement for the definition of a burst is that all the events from a burst shouldcome within a certain time window defined a priori . In addition, it is also required that the arrivaldirections, of all events belonging to a particular burst, should fall within the region defined tomatch the angular resolution of VERITAS. The calculation for the angular resolution (also calledpoint spread function(PSF)) of the VERITAS instrument is performed by plotting events in the θ space, where θ is a measure of angular distance between the reconstructed event direction andthe location of gamma-ray source, and then fitting the θ distribution with a modified hyperbolicsecant distribution following [9]: S ( θ , σ ) = . N πσ sech ( √ θ / σ ) (3.1)2 onstraining evaporation rate of PBHs with VERITAS Sajan Kumar , for the VERITAS collaboration where σ is the width of the distribution, estimated from fitting procedure, representing 55 . θ distribution of events from the Crab Nebulae, fitted with the functiondefined in Equation 3.1 plus a constant function (used to model the background level). Sincethe PSF of the instrument vary with elevation and energy, separate fits were performed in threeelevation bins; 50-70 ◦ , 70-80 ◦ , 80-90 ◦ and four energy bins; 0.08-0.32 TeV, 0.32-0.5 TeV, 0.5-1TeV, 1-50 TeV. Table 1 shows the values of the σ parameter, estimated in different energy andelevation bins using Crab data.Figure 1: θ -distribution of all the events from 3 hours of Crab observations at mean zenith angle of17 degrees. The red dotted line represents the constant level of background events and black dotted linerepresent the signal plus, background profile of the distribution. In order to separate a real burst of gamma-rays, coming from a point source in the sky, from aset of background coincidental events that appear to mimic a burst, a likelihood method is employedas explained in [9]. The likelihood function for the set of events whose arrival directions arecontained within the angular resolution of the camera ( ∼ . L = ∏ i . N πσ i sech ( (cid:113) ( θ i − µ ) / σ i ) (3.2)where σ i and θ i are the width parameter and direction of event i respectively. The width canbe derived from the Table 1 for a given event falling in a particular energy and elevation bin. µ onstraining evaporation rate of PBHs with VERITAS Sajan Kumar , for the VERITAS collaboration Table 1: Estimation of dependence of width parameter ( σ ) on energy and elevation angle, usingCrab data Elevation Elevation Elevation(50-70 deg) (70-80 deg) (80-90 deg)Energy 0.067 ± ± ± ± ± ± ± ± ± ± ± ± Left ) shows the centriod found usingEquation 3.2 from a set of randomized events that represents background (in red), and centroidof group of events generated randomly according to the Equation 3.1 that represents a simulatedsignal (in blue).Figure 2 (
Right ) shows a likelihood distribution for groups of 5 events coming from back-ground bursts (red curve) and simulated signal bursts (blue curve). In order to maximize the amountof signal bursts and minimize the contamination from background bursts, a cut on the likelihoodvalue is determined which retains 90% of the signal bursts. The same procedure is repeated fora burst size of 2, 3, 4, up to 10 events, after which the likelihood of finding bursts with so manyevents becomes low, and the cuts tend to stay fairly constant between burst sizes.Figure 2:
Left : Event centroid for a random group of events (red) and a group of events whosepositions were randomly generated from Equation 3.1, to simulate a real burst (blue). The circlerepresents the field of view of VERITAS.
Right : Distribution of simulated signal bursts comparedwith random groups, of 5 events each, to determine cut on likelihood value to use in the analysis.The black-dotted vertical line represents the cut value for likelihood that includes 90% of the signal.4 onstraining evaporation rate of PBHs with VERITAS
Sajan Kumar , for the VERITAS collaboration
4. Burst search method
For each run, consisting of ∼
30 minutes of observations, a list of gamma-like events (eventsthat passes gamma-hadron separation cuts) is created. For each gamma-like event arriving attime t i , a list is then compiled with any subsequent events arriving within a time window of1 , , , , , , , and 45 seconds.In order to estimate the expected background rate due to chance coincidence, the method in[12] is used. This methodology consists of taking all the gamma-like events in a data run, andscrambling their time of arrival while keeping their arrival direction unchanged. Any bursts foundin this scrambled data can be treated as background. This scrambling procedure is then repeated tentimes. By taking an average of these ten iterations, the average background rate can be estimated.For example, for a time-window of 20 seconds, Figure 3 shows a burst distribution found using thisburst search methodology described in detail in [9]. The top plot compares the data points with thebackground estimation, while the lower plot shows the residuals.Figure 3: Burst distribution for a burst duration of 20 seconds. Top: The blue squares are from the data,and the red triangles are the background estimation. Bottom: Residual plot showing the difference betweendata and background.
5. Model Predictions and expectations
The number of expected photons, detected by the VERITAS depends upon the emission modelof evaporation of PBH and the effective area of the instrument. Following the methodology of[7], we consider a time-integrated spectrum from an evaporation of a PBH for a given value of τ (remaining life time of PBH) as: dN γ dE γ ≈ × × (cid:40)(cid:0) GeVT τ (cid:1) / (cid:0) GeVE γ (cid:1) / GeV − for E γ < kT τ (cid:0) GeVE γ (cid:1) GeV − for E γ ≥ kT τ (5.1)5 onstraining evaporation rate of PBHs with VERITAS Sajan Kumar , for the VERITAS collaboration where T τ defined as kT τ = . ( τ / s ) − / TeV, is the temperature of the black hole at thebeginning of the final burst time interval. By convolving this model spectrum with the detectorresponse, expected number of gamma-ray events, N γ , can be estimated as: N γ ( r , α , δ , τ ) = π r (cid:90) ∞ E thresh dN γ dE γ ( E γ , τ ) A ( E γ , θ z , θ w , µ , α , δ ) dE γ (5.2)where E thresh is the threshold energy of VERITAS array, and A ( E γ , θ z , θ w , µ , α , δ ) is the detec-tor response function (effective area and camera radial acceptance) of VERITAS, as a function ofthe gamma-ray energy E γ , the observation zenith angle θ z , the offset of source from the center ofthe camera θ w , the optical efficiency µ , and the event reconstruction position in camera coordinates ( α , δ ) .The probability of seeing a burst of a certain number of photons b from a PBH emitting N γ VHE photons is expressed through Poisson statistics: P ( b , N γ ) = e − N γ N b γ / b !. This then is tranlatedinto effective detectable volume as: V e f f ( b , τ ) = (cid:90) ∆Ω (cid:90) ∞ drr P ( b , N γ ) (5.3)The expected number of bursts of size b seen by VERITAS over a total time period of obser-vations T obs can be written as: n exp ( b , τ ) = ˙ ρ PBH × T obs × V e f f ( b , τ ) (5.4)where ˙ ρ PBH is the rate-density of PBH evaporation. From Equation 5.4, an upper limit on therate density can be calculated by estimating the limit on the number of expected events.The previous reported limit, calculated using 747 hours of data belongs to Dataset I is givenby 2 . × pc − yr − . The new limit, which is still a work in progress, is expected to be a factorof two more constraining from the previous limit, at a value of about 10 pc − yr − . Acknowledgements
This research is supported by grants from the U.S. Department of Energy Office of Science, theU.S. National Science Foundation and the Smithsonian Institution, and by NSERC in Canada. Thisresearch used resources provided by the Open Science Grid, which is supported by the NationalScience Foundation and the U.S. Department of Energyâ ˘A ´Zs Office of Science, and resources ofthe National Energy Research Scientific Computing Center (NERSC), a U.S. Department of EnergyOffice of Science User Facility operated under Contract No. DE-AC02-05CH11231. We acknowl-edge the excellent work of the technical support staff at the Fred Lawrence Whipple Observatoryand at the collaborating institutions in the construction and operation of the instrument.
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