Gravitational Waves

The recent publication by LIGO of two events (GW190412 and GW190814) with high mass ratios, and with one of the masses close to the mass gap (that is, a mass between 3 and 5 solar masses which are difficult to explain with standard models) has created an intense debate on the nature of these objects. If confirmed, the implications of these observations are important since they can give us information about the equation of state of neutron stars (where one can study exotic forms of matter, such as axions or hyperons), or reveal a new type of black hole, including a leading dark matter candidate, primordial black holes.

However, a simpler alternative could be that these events are strongly lensed. Gravitational lensing can amplify the signal of observed gravitational waves, allowing their observation from much farther distances (and hence much larger volumes). In earlier work, we showed that if the rate of mergers (that produce gravitational waves) at redshift z>1 is sufficently high, observation of these distant events by LIGO is not only possible, but unavoidable. On fact, for rates larger than a few times 10^4 mergers per year and Gpc^3, lensed events will dominate over not-lensed events, in a similar fashion as lensed gravitational lensed IR galaxies dominated over not-lensed IR galaxies in the bright end of Herschel observations.

The left plot shows the prediction from our lensing model (colored circles) compared with the observations (squares and diamonds with error bars). All events concentrate around two locus regions. BBH and NSBH. Note how observations match perfectly the prediction.

Lensed gravitational waves get stretched due to cosmic expansion as they travel from their originating source to the detector. The farther the source is, the lager the stretch. The stretch is proportional to (1+z), where z is the redshift if the source. Higher z translates into gravitational waves that, when observed, appear as having a longer wavelength. If the gravitational wave is being magnified by strong lensing, and this magnification goes unnoticed (there is no way a priori to know if a gravitational wave is being magnified), the longer wavelength will be missinterpreted as being due to a larger mass of the two compact objects that ar causing the gravitational wave. For instance, if a neutron star with a mass of 1.3 solar masses is merging with a black hole of 12 solar masses (these are the typical masses found in our Galaxy for these objects) at redhift z=1, the observed gravitational wave will appear identical as the one from a much closer merger (z =0) with a neutron star of 2.6 solar masses and a blackhole with 24 solar masses. This example is not arbitrary since it was chosen to match the observed masses of the latest published gravitational wave event , GW190814, interpreted as being a local event (z=0), but which based on our interpretation could be also a lensed event at z=1 or z>1.

The lensing model interpretauon makes a series of interesting predictions, but among these, it is interesting to pay attention to the predicted mass ratio for binary black holes and neutron star black hole mergers. As shown in the figure illustrating this blog, lensing predicts these type of events will appear in the M1-M2 plane in two well defined regions. Interestingly, all observed data points so far agree remarkably well with this prediction. The two possible mass gap events are marked with a big yellow circle and follow well the predicted locus for lensed NSBH events. If confirmed, our lensing model would offer a simple solution to the mass gap problem, and would imply a much higher rate of events at z>1 that previously thought.

You can see our full work below. A Fun Fact about this paper is that it was put “On Hold” by arxiv moderators after being submitted to arxiv on June 19 (Friday). After requesting an explanation from arxiv, none was given. At the time of our original submission, we where unaware of the upcoming publication, by the LIGO team, of the GW190814 “Mass Gap” event. The following week, in June 24 we saw in arxiv the LIGO paper with the values of M1 and M2 for GW190814. The same day, the “Hold” on our paper was lifted and we where able to just add the new data point to our figure (see point marked GW190814 in the figure above), before it appeared on arxiv the following day (June 25). I do understand (and support) the need for moderation in arxiv, but this process is far from transparent. The lack of communication and explanation of why papers are being put on hold, inhebitably leads to one suspect foul play, which is something that should be avoided at all cost, specially in portals such as arxiv, that makes research freely available.

Link to paper https://arxiv.org/pdf/2006.13219.pdf

Click to access 2006.13219.pdf

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

Is LIGO really seeing Mass Gap events?

Seeing through Dark Matter with gravitational waves