Constraining the Rate of Primordial Black Hole Explosions and Extra-Dimension Scale Using a Low-Frequency Radio Antenna Array

Abstract

An exploding primordial black hole (PBH) may produce a single pulse of electromagnetic radiation detectable at the low-frequency end of the radio spectrum. Furthermore, a radio transient from an exploding PBH could be a signature of an extra spatial dimension. We describe here an approach for searching for PBH explosions using a low-frequency radio antenna array, and as a practical example, the results of such a search using the Eight-meter-wavelength Transient Array (ETA). No compelling astrophysical signal was detected in ≈4 hr of data, implying an observational upper limit on the rate of exploding PBHs is 2.3 × 10-7 pc-3 yr-1 for an exploding PBH with a fireball Lorentz factor of 104.3 for the standard scenario of Page and Hawking. This rate limit is the strongest constraint yet set for PBH explosions with this fireball Lorentz factor. Observations (∼300 hr) using the Arecibo Observatory were used to set a stronger constraint on the rate of PBH explosions for a fireball Lorentz factor of 104.6, but the limit set by those observations for the fireball Lorentz factor considered here are less stringent by more than an order of magnitude. The limits considered here are applicable to exploding PBHs in the halo of the Galaxy. These observations also imply an upper limit of 2.3 × 10-4 pc-3 yr-1 on the rate of PBH explosions in the context of certain extra dimension models, as described by Kavic et al. This rate limit is for a fireball Lorentz factor of 104.3, which corresponds to an extra dimension compactification scale of 5.0 × 10-18 m.