Seeing through Dark Matter with gravitational waves

We covered the topic of dark matter before in this post (Dark Matter under the microscope). Dark matter remains one of the bigegst mysteries of Science. One of the candidates for dark matter are Primordial Black Holes or PBH. PBH are black holes that formed during the first instants of the universe. Like dark matter, PBH do not emit light and interact with the rest of the universe basically only through gravity. The LIGO experiment has been detecting a surprisingly high number of massive black holes. The origin of these black holes is uncertain but one of the possibilities is that they could be PBH. We also discussed LIGO detections in this earlier post (Did LIGO really see massive black holes?) . In order to explain the current observations by LIGO, only a fraction of the dark matter needs to be in the form of PBH. In particular, a fraction as small as 1% of the total dark matter would be sufficient to explain the unusually elevated rate of black hole mergers with masses above 20 solar masses.

In a new work we discuss a novel method to explore the possibility that PBH constitute part of the dark matter. Our latest paper (see link at the end of this post) studies for the first time the interference produced when gravitational waves cross a portion of the sky populated with a realistic distribution of stellar bodies (stars, neutron stars or black holes) or microlenses. Earlier work have considered only the simple, but unrealistic, case of isolated microlenses and at most assuming that they are located near a larger lens (galaxy or cluster) but always on the side with positive parity (a tecnicallity that describes one of the two possible configurations for a lensed image). Our work goes further than these simple exmaples by studying the combined effect produced by a realustic population of microlenses and also considers the unexplored regime of macroimages with negative parity (they constitute roughly half  the images produced in the string lensing regime). The figure accompanying this post shows an example of a single microlens embeded in a macrolens and on the side of the lens plane with negative parity. The numbers in orange represent relative time delays (in milliseconds) between the different microimages (the numbers in white indicate the magnification of each microimage and the grey scale shows the magnification in the lens plane with the critical curves shown as two white circular regions. The inset in the bottom-right shows the corresponding magnification in the source plane with the position of two sources, one white and one yellow). At LIGO frequencies (approx 100-500 Hz), a time delay between 1/500 seconds or 1/100 seconds (that is or 2 or 10 milliseconds  respectively)  can produce constructive or destructive interference in the incoming gravitational wave at the detector. For the example in the figure, the microlens has a mass of 100 solar masses. These type of masses where known before to be capable of producing such interference but what our work show is that the mass can still be significantly smaller (a few solar masses) provided several microlenses can work together to produce time delays of order several milliseconds. This cooperative behaviour takes place naturally when one is observing gravitational waves that are being lensed by large factors (of order 100 or more) since in this case, two microlenses which are relatively distant from each other in the lens plane, can overlap their regions of high magnification (known as caustics) in the source plane, if the magnification from the macromodel (galaxy or cluster) is sufficiently large (in a fashion similar to how a magnifying glass works that can bring photons that are separated by some relatively large distance to come together at the focal point of the magnifying glass). Our study shows that interference of a gravitational wave with itself due to microlenses is not only possible, but unavoidable if the magnification from the macromodel is sufficiently large.

This result opens the door to constrain the abundance of PBH. If PBH are as abundant as 1% of the total dark matter, the interference signal observed in detected gravitational waves here on Earth would be significantly different. Next in the list is to study by how much we can constrain this abundance as a function of the mass function of the PBH. Stay tunned …

Preprint to the science article