Primordial Black Holes (PBHs), which may have been created in the early Universe, are predicted to be detectable by their Hawking radiation. The Fermi Gamma-ray Space Telescope observatory offers increased sensitivity to the gamma-ray bursts produced by PBHs with an initial mass of $\sim 5\times 10^{14}$ g expiring today. PBHs are candidate progenitors of unidentified Gamma-Ray Bursts (GRBs) that lack X-ray afterglow. We propose spectral lag, which is the temporal delay between the high and low energy pulses, as an efficient method to identify PBH evaporation events with the Fermi Large Area Telescope (LAT).
Deep Dive into Sensitivity of the FERMI Detectors to Gamma-Ray Bursts from Evaporating Primordial Black Holes (PBHs).
Primordial Black Holes (PBHs), which may have been created in the early Universe, are predicted to be detectable by their Hawking radiation. The Fermi Gamma-ray Space Telescope observatory offers increased sensitivity to the gamma-ray bursts produced by PBHs with an initial mass of $\sim 5\times 10^{14}$ g expiring today. PBHs are candidate progenitors of unidentified Gamma-Ray Bursts (GRBs) that lack X-ray afterglow. We propose spectral lag, which is the temporal delay between the high and low energy pulses, as an efficient method to identify PBH evaporation events with the Fermi Large Area Telescope (LAT).
The formation of Primordial Black Holes (PBHs) has been postulated in many theories of the early Universe (for a recent review see Ref. 1). Black holes of mass M bh continually emit Hawking radiation 2 with a temperature of T bh = 1.06 GeV/ M bh /10 13 g in the form of all available fundamental particle species. The emitted particles decay quickly on astrophysical timescales into γ, ν e,µ,τ , νe,µ,τ , p, p, e + and e -. PBHs with an initial mass 3 of M * ∼ 5 × 10 14 g should be expiring today with a burst of high energy particles including gamma-rays. The current upper limit on the number expiring today per volume per unit time is 4 R 10 -7 η local pc -3 yr -1
(1)
where η local is the density enhancement of PBHs in the local region. Typically η local is ∼ 10 6 (for clustering in the Galactic halo) or larger. Such PBH bursts may be detectable by the Fermi Gamma-ray Space Telescope observatory’s Large Area Telescope (LAT). Conversely, non-detection by the LAT may lead to tighter bounds on the PBH distribution.
In the standard model 3 , the total number of photons emitted per second by a T bh ∼ 0.3 -100 GeV black hole scales as 5 Ṅbh γ ≃ 1.4 × 10 29 T bh TeV
The number of photons per second per unit area reaching the Earth from a PBH bursting at a distance d from the Earth is
Let us assume an ideal detector of effective area A eff which can detect every photon that falls on it. (If the detector is non-ideal then the efficiency can be incorprated into the value of A eff .) If the detector requires X photons over time t to distinguish an incoming event as a burst, then to detect a burst we require F bh A eff t ≥ X. That is the PBH must be closer than
What T bh maximizes the chance of detection? The remaining lifetime 6 of a PBH of temperature T bh is τ evap ≃ 7.4 × 10 3 / (T bh /TeV) 3 f s where f (T bh ) weights the number of emitted species. (The remaining lifetime of a 300 GeV, 1 TeV, or 5 TeV black hole is 1 hour, 1 minute, or 1 second, respectively.) Taking t = τ evap , a PBH will be detected by the ideal detector if it is closer than
Thus the detectability is maximized for the lowest T bh black hole visible above the background and/or by using the longest detector exposure time. For a detector of angular resolution Ω to resolve the PBH above the gamma-ray background F γ , we also require that F bh A eff ≥ F γ ΩA eff . The PBH will be resolved above the observed (EGRET) extragalactic background 7
at energy E by the ideal detector if the PBH is closer than
and E is less than the average energy 5 of the PBH photons E γ ≈ 10 (T bh /TeV) 0.5
GeV. The isotropic diffuse gamma-ray background, which is an upper limit on the extragalactic background, recently measured 8 by the LAT at mid-Galactic latitudes is consistent with the earlier EGRET measurements Eq. ( 6), although the extragalactic component may 9 be weaker by up to a factor of 2.
For a given detector, the scanned volume of space is then V bh = (ω A /sr) d 3 S /3 where ω A is the detector acceptance angle (field of view) and d S = min(d D , d R ). Extensive air shower arrays characteristically have A eff 10 4 m 2 , large ω A and small Ω but very high threshold energy (typically 10 TeV) and hence are background-limited, while atmospheric Cerenkov detectors 10 characteristically have A eff 200 m 2 and small Ω but high threshold energy (typically 100 GeV although the Whipple SGARFACE system 11 has a threshold of 100 MeV) and very small ω A ( 10 -2 sr). In contrast, the Fermi LAT has 12 a smaller A eff ∼ 0.8 m 2 but large ω A ∼ 2.4 sr, finer source position angular resolution (0.3 -2 ′ ), low energy thresholds (down to 20 MeV), good time resolution and is essentially background-free with respect to burst sensitivity. Additionally, most of the photons emitted by expiring T bh 1 TeV PBHs are in the LAT energy range (20 MeV -300 GeV).
The Fermi LAT offers greater sensitivity to local PBH bursts than ground-based detectors. We have proposed 13 spectral lag measurements (the temporal delay between high and low energy pulses) of the incoming light curve in two different energy bands as a method to identify PBH bursts. A PBH burst arriving at the detector will exhibit positive to negative evolution with increasing energy because the black hole temperature and E γ increase over time as the black hole loses mass. Because spectral lag measurements require counts in only two energy bands, and not the full spectrum, spectral lag can be measured even for weak events that last for very short time scales. Work is in progress to calculate quantitative values for the PBH spectral lags for the characteristics of the Fermi LAT.
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