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See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/317399546
Gravitational wave bursts from Primordial Black
//Article · June 2017/Juan Garcia-Bellido \Universidad Aut;noma de Madrid
\
We propose that Gravitational Wave (GW) bursts with millisecond durations can be explained by the GW emission from the hyperbolic encounters of Primordial Black Holes in dense clusters. These bursts are single events, with the bulk of the released energy happening during the closest approach, and emitted in frequencies within the AdvLIGO sensitivity range. We provide expressions for the shape of the GW emission in terms of the peak frequency and amplitude, and estimate the rates of these events for a variety of mass and velocity configurations. We study the regions of parameter space that will allow detection by both AdvLIGO and, in the future, LISA. We find for realistic configurations, with total mass M ; 60 M, relative velocities v ; 0.01 c, and impact parameters b ; 10;3AU, for AdvLIGO an expected event rate is O(10) events/yr/Gpc3 with millisecond durations. For LISA, the typical duration is in the range of minutes to hours and the event-rate is O(103 ) events/yr/Gpc3 for both 103 M IMBH and 106 M SMBH encounters. We also study the distribution functions of eccentricities, peak frequencies and characteristic timescales, that can be expected for a population of scattering PBH with a log-normal distribution in masses, different relative velocities and a flat prior on the impact parameter.
Advanced LIGO has opened a new era of Gravitational Wave Astronomy, with the detection of at least three very massive Black Hole (BH) merger events [1–3], and probably a fourth one [4], in a few months of running. The signal corresponds to the inspiralling of two BH of several tens of solar masses in almost circular orbits, and the emission of GW leading to the final merger, in perfect agreement with the predictions of General Relativity (GR). These massive BH binaries were completely unexpected, suggesting a new population of BH. This led to the speculation that AdvLIGO could have detected Primordial Black Holes (PBH) contributing to a significant fraction of Cold Dark Matter (CDM) [5–7], thus providing a natural explanation for its nature without resorting to exotic particles or modifications of gravity. Furthermore, these PBH could also provide the seeds for the Supermassive Black Holes (SMBH) found in the centers of the galaxies, as well as explaining the missing satellite and too-big-to-fail problems of CDM, thus solving several key problems in cosmology and galaxy formation in a unique and unified framework [8]. In the scenario of clustered PBH [9], it is expected that a large fraction of BH encounters will not end up producing bounded systems, which would then inspiral, but rather produce a single scattering event, via a hyperbolic encounter. This could happen, e.g. if the relative velocity or relative distance of the two PBH is high enough
that capture is not possible. The emission of GW in parabolic and hyperbolic encounters of compact bodies
has been studied in the past in Refs. [10], and [11, 12], respectively.
These events generate bursts of gravitational waves, which can be sufficiently bright to be detected at distances up to several Gpc. For clustered PBH, the waveform and characteristic parameters of the GW emission in hyperbolic encounters are different to those of the
inspiralling binaries, and both provide complementary information that can be used to determine the evolved mass distribution of PBH, as a function of redshift, as well as their spatial distribution.
Hyperbolic encounters are single scattering events where the majority of the energy is released near the point of closest approach, and have a characteristic peak frequency which is a function of only three variables, the impact parameter b, the eccentricity e and the total
mass of the system M. Furthermore, the duration of such events is of the order of a few milliseconds to several hours, depending on those parameters. The case of inspiralling and merging PBH has been studied extensively, see e.g. Refs. [6, 13], and estimated to produce
a few tens of events/year/Gpc3 in the range of MPBH ; O(10 ; 100) M. In this letter we will show that, within the parameter space of the clustered PBH scenario [6], we expect a similar rate of GW burst events in the millisecond range.
For a detector like AdvLIGO, such events will look like bursts with a characteristic frequency at peak strain amplitude. In fact, AdvLIGO has already reported several events of this type, which were attributed to accidental noise coincidences [14]. However, events from hyperbolic encounters of PBH produce exactly the “tear drop glitch” shapes described in Ref. [15]. It is thus worth exploring
the possibility that those events are actually PBH hyperbolic encounters. Their time-frequency profiles, discussed in this letter, could help the analysis of the AdvLIGO glitches. Moreover, if indeed these glitches arise from hyperbolic encounters of BH, they could be used to
obtain valuable information about the PBH mass, velocity and spatial distribution.
We thus consider a hyperbolic encounter between a BH of mass m with asymptotic velocity v0 against another BH of mass m0 = q m ; m. The total mass of the system is then given by M = (1 + q) m and the reduced mass is µ = q M/(1 + q) 2
.