Compact binaries through a lens

Summary of work published in Physical Review D and also available on the arXiv.

What are gravitational waves?

Gravitational wave detectors track the oscillations of the spacetime itself, which propagate towards Earth at the speed of light. Unlike light, these ripples of space-time are not absorbed by the many intervening objects between us and the catastrophic event we observed, which may have happened a billion or so years ago. However, their detection is quite challenging because the spacetime is very stiff and can thus only be shaken to a detectable level by very massive events such as the collision of dead stars, which are very dense. Gravitational wave detectors on Earth have seen the merging of black holes or neutron stars or black-hole - neutron star pairs. The observations provide a first map of the stellar graveyard.

Although when black holes collide, the energy they spend that shakes the vacuum of the spacetime is a lot more that they had used to shine as stars they only shake the spacetime a very tiny little bit. By the time these vibrations reach Earth, and we can measure them, they change the arm length of LIGO or Virgo, which are 4 km (or 3 km for Virgo) by less than an electron, which is less than a hair width. So the change is very, very tiny and buried in deep noise. Detecting it is quite challenging, but the LIGO-Virgo-Kagra observatories have a large team of people who do these searches, and make sure the signals are real. In order to find them through the noise, it's crucial to know what we are looking for.

We are looking at the colliding compact objects in the stellar graveyard through a lens, which acts as a magnifying glass. The lens is formed from the material that lies between us and the binary we are observing. The more massive and the closer to the line of sight, the more it affects the signal. In this manuscript, we assumed the lens is a point mass, i.e., can be assumed to be a compact object.

How do lensed waveforms look?

• amplified (e.g., the signal is stronger than the unlensed version), the higher the frequency the more the amplification. The frequency is always highest at merger. Some signals display only amplification.
• a beating pattern may appear with destructive (holes) and constructive interference (brighter spots) of two nearby images produced by the same event. The frequency of the bright spots and holes can be predicted analytically for the point mass lens model.
• separate images/waveforms from the same event appear minutes to months apart if the lens is a galaxy (strong lensing), and less if the lens is smaller (microlensing).

The lensing amplification causes the source's distance from the detector to be underestimated. Not only does it appear to be closer, but it also appears more massive because the redshift is underestimated. A binary at z=3 will appear four times more massive when detected on Earth than it is at the source. So, it's important to know where the source is to be able to accurately predict its mass.

What is the mismatch with unlensed waveforms?

For waveforms that look very similar one might not be able to tell whether they are lensed or not. We compute the match (the number on the white contours is the match) and the signal to noise increase (coloured bar) due to lensing as a function of the mass of the lens that sits between Earth and the merging binary and the source position, y. The smaller the y, the closer to the lens is to the line of sight between the source and Earth. We find that under 20% of all detected events are lensed, and out of those under 5% of events would be detectably lensed with a mismatch greater than 10%. However, our model only includes point masses lenses, and our computation are an upper limit for when all dark matter is formed from these lenses. More realistic studies will include composite lenses between Earth and the binary.

How far could lensed events be?

It depends on the mass of the binary. We see that an event detected at a typical total binary mass that is 60 times more massive than the sun, could be at a redshift z=2. This means the source frame mass would be 3 times less, and thus closer to Xray observations. Similary, if we see an 120 solar mass event, it could be at a redshit z=3, which would make it the detected value 4 times larger that the actual black hole masses.

A redshift of 3, means the signal from the event would have traveled some 11 billion years to reach us, while a z=2 impilies a travel time of 10 billion years. At a z=0.1, the event happened a billion years ago. However, even if the events are lensed, since mismatch to the unlensed template is relatively low, we are likely never know it. The plots of the right shows the distribution of (a) all lensed objects (b) lensed objects with a mismatch of 5% from their unlensed counterparts and (c) lensed objects with a mismatch of 10%. All are are above a threshold SNR of 10 for the estimated O4 noise curve (average expected noise for the current LVK run).

What have we seen to date?

Up to now, we have seen of the order of 100 black hole merger events, two neutron star mergers, and some black-hole neutron star collisions. Ground based detectors are again operational in the US with Virgo soon expected to be joining. However, most black hole binaries detected are unlike any seen in the Milky Way before. There are about more massive than those found in X-ray studies with an average total mass of about 60 solar Masses, while those found in our galaxy are closer in mass to our sun (the pink are the black holes and the yellow the neutron stars).

Are the black holes seen by gravitational waves observatories really different? or do we percieve them as different? Could they be lensed?

It could be that our galaxy is different from the typical galaxies out there. Or it could be that there is something between us and the source that make the black holes appear more massive. We are looking at them through a magnifying glass formed from intervening matter. If that matter is massive enough, it makes them seem more massive than they are. The more distant the event, the more likely it is to be lensed. A lensing pattern has not been observed by the LVK to date. Our results predict that under 5% of events are detectably lensed, which is consistent with observations to date.

Ok, so you've explained gravitational waves, but what are Xray observations?
Xrays are light of high energy and very short wavelength that can pass through materials that are opaque to visible light. Since different materials absorb light at different lates, they can be used in medicine to show broken bones or in astrophysics to see dying stars (supernova), dead stars with disks (black holes), and merging galaxies.

Our team
Our team is 50% female (me and Helena), while Oleg and Andy represent the other side (males, still 50%). This post is a summary of work published in Physical Review D. The paper is also available on the arXiv. Please read the paper for more details.