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Constraining the abundance of primordial black holes with gravitational lensing of gravitational waves at LIGO frequencies

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 Publication date 2019
  fields Physics
and research's language is English
 Authors Jose M. Diego




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Gravitational waves from binary black holes that are gravitationally lensed can be distorted by small microlenses along the line of sight. Microlenses with masses of a few tens of solar masses, and that are close to a critical curve in the lens plane, can introduce a time delay of a few millisecond. Such time delay would result in distinctive interference patterns in the gravitational wave that can be measured with current experiments such as LIGO/Virgo. We consider the particular case of primordial black holes with masses between 5 and 50 solar masses acting as microlenses. We study the effect of a population of primordial black holes constituting a fraction of the dark matter, and contained in a macrolens (galaxy or cluster), over gravitational waves that are being lensed by the combined effect of the macrolens plus microlenses. We find that at the typical magnifications expected for observed GW events, the fraction of dark matter in the form of compact microlenses, such as primordial black holes, can be constrained to percent level. Similarly, if a small percentage of the dark matter is in the form of microlenses with a few tens of solar masses, at sufficiently large magnification factors, all gravitational waves will show interference effects. These effects could have an impact on the inferred parameters. The effect is more important for macroimages with negative parity, which usually arrive after the macroimages with positive parity.



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Primordial black holes (PBHs) have been proposed to explain at least a portion of dark matter. Observations have put strong constraints on PBHs in terms of the fraction of dark matter which they can represent, $f_{rm PBH}$, across a wide mass range -- apart from the stellar-mass range of $20M_odotlesssim M_{rm PBH}lesssim 100M_odot$. In this paper, we explore the possibility that such PBHs could serve as point-mass lenses capable of altering the gravitational-wave (GW) signals observed from binary black hole (BBH) mergers along their line-of-sight. We find that careful GW data analysis could verify the existence of such PBHs based on the $fitting~factor$ and odds ratio analyses. When such a lensed GW signal is detected, we expect to be able to measure the redshifted mass of the lens with a relative error $Delta M_{rm PBH}/M_{rm PBH}lesssim0.3$. If no such lensed GW events were detected despite the operation of sensitive GW detectors accumulating large numbers of BBH mergers, it would translate into a stringent constraint of $f_{rm PBH}lesssim 10^{-2}-10^{-5}$ for PBHs with a mass larger than $sim10M_odot$ by the Einstein Telescope after one year of running, and $f_{rm PBH}lesssim 0.2$ for PBHs with mass greater than $sim 50M_odot$ for advanced LIGO after ten years of running.
We investigate the formation and growth of massive black hole (BH) seeds in dusty star-forming galaxies, relying and extending the framework proposed by Boco et al. 2020. Specifically, the latter envisages the migration of stellar compact remnants (neutron stars and stellar-mass black holes) via gaseous dynamical friction towards the galaxy nuclear region, and their subsequent merging to grow a massive central BH seed. In this paper we add two relevant ingredients: (i) we include primordial BHs, that could constitute a fraction $f_{rm pBH}$ of the dark matter, as an additional component participating in the seed growth; (ii) we predict the stochastic gravitational wave background originated during the seed growth, both from stellar compact remnant and from primordial BH mergers. We find that the latter events contribute most to the initial growth of the central seed during a timescale of $10^6-10^7,rm yr$, before stellar compact remnant mergers and gas accretion take over. In addition, if the fraction of primordial BHs $f_{rm pBH}$ is large enough, gravitational waves emitted by their mergers in the nuclear galactic regions could be detected by future interferometers like Einsten Telescope, DECIGO and LISA. As for the associated stochastic gravitational wave background, we predict that it extends over the wide frequency band $10^{-6}lesssim f [{rm Hz}]lesssim 10$, which is very different from the typical range originated by mergers of isolated binary compact objects. On the one hand, the detection of such a background could be a smoking gun to test the proposed seed growth mechanism; on the other hand, it constitutes a relevant contaminant from astrophysical sources to be characterized and subtracted, in the challenging search for a primordial background of cosmological origin.
Primordial black holes (PBHs) from the early Universe have been connected with the nature of dark matter and can significantly affect cosmological history. We show that coincidence dark radiation and density fluctuation gravitational wave signatures associated with evaporation of $lesssim 10^9$ g PBHs can be used to explore and discriminate different formation scenarios of spinning and non-spinning PBHs spanning orders of magnitude in mass-range, which is challenging to do otherwise.
Primordial black hole (PBH) mergers have been proposed as an explanation for the gravitational wave events detected by the LIGO collaboration. Such PBHs may be formed in the early Universe as a result of the collapse of extremely rare high-sigma peaks of primordial fluctuations on small scales, as long as the amplitude of primordial perturbations on small scales is enhanced significantly relative to the amplitude of perturbations observed on large scales. One consequence of these small-scale perturbations is generation of stochastic gravitational waves that arise at second order in scalar perturbations, mostly before the formation of the PBHs. These induced gravitational waves have been shown, assuming gaussian initial conditions, to be comparable to the current limits from the European Pulsar Timing Array, severely restricting this scenario. We show, however, that models with enhanced fluctuation amplitudes typically involve non-gaussian initial conditions. With such initial conditions, the current limits from pulsar timing can be evaded. The amplitude of the induced gravitational-wave background can be larger or smaller than the stochastic gravitational-wave background from supermassive black hole binaries.
Microlenses with typical stellar masses (a few ${rm M}_{odot}$) have traditionally been disregarded as potential sources of gravitational lensing effects at LIGO/Virgo frequencies, since the time delays are often much smaller than the inverse of the frequencies probed by LIGO/Virgo, resulting in negligible interference effects at LIGO/Virgo frequencies. While this is true for isolated microlenses in this mass regime, we show how, under certain circumstances and for realistic scenarios, a population of microlenses (for instance stars and remnants from a galaxy halo or from the intracluster medium) embedded in a macromodel potential (galaxy or cluster) can conspire together to produce time delays of order one millisecond which would produce significant interference distortions in the observed strains. At sufficiently large magnification factors (of several hundred), microlensing effects should be common in gravitationally lensed gravitational waves. We explore the regime where the predicted signal falls in the frequency range probed by LIGO/Virgo. We find that stellar mass microlenses, permeating the lens plane, and near critical curves, can introduce interference distortions in strongly lensed gravitational waves. For those lensed events with negative parity, (or saddle points, never studied before in the context of gravitational waves), and that take place near caustics of macromodels, they are more likely to produce measurable interference effects at LIGO/Virgo frequencies. This is the first study that explores the effect of a realistic population of microlenses, plus a macromodel, on strongly lensed gravitational waves.
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