Can we measure black hole kicks using gravitational waves?

Article: Black hole kicks as new gravitational wave observables
Authors: Davide Gerosa, Christopher J. Moore
Reference: arXiv:1606.04226Phys. Rev. Lett. 117, 011101 (2016)

On September 14 2015, something really huge happened in physics: the first direct detection of gravitational waves happened. But measuring a single gravitational wave was never the goal—.though freaking cool in and of itself of course!  So what is the purpose of gravitational wave astronomy?

The idea is that gravitational waves can be used as another tool to learn more about our Universe and its components. Until the discovery of gravitational waves, observations in astrophysics and astronomy were limited to observations with telescopes and thus to electromagnetic radiation. Now a new era has started: the era of gravitational wave astronomy. And when the space-based eLISA observatory comes online, it will begin an era of gravitational wave cosmology. So what is it that we can learn from our universe from gravitational waves?

First of all, the first detection aka GW150914 was already super interesting:

  1. It was the first observation of a binary black hole system (with unexpected masses!).
  2. It put some strong constraints on the allowed deviations from Einstein’s theory of general relativity.

What is next? We hope to detect a neutron star orbiting a black hole or another neutron star.  This will allow us to learn more about the equation of state of neutron stars and thus their composition. But the authors in this paper suggest another exciting prospect: observing so-called black hole kicks using gravitational wave astronomy.

So, what is a black hole kick? When two black holes rotate around each other, they emit gravitational waves. In this process, they lose energy and therefore they get closer and closer together before finally merging to form a single black hole. However, generically the radiation is not the same in all directions and thus there is also a net emission of linear momentum. By conservation of momentum, when the black holes merge, the final remnant experiences a recoil in the opposite direction. Previous numerical studies have shown that non-spinning black holes ‘only’ have kicks of ∼ 170 km per second, but you can also have “superkicks” as high as ∼5000 km per second! These speeds can exceed the escape velocity of even the most massive galaxies and may thus eject black holes from their hosts. These dramatic events have some electromagnetic signatures, but also leave an imprint in the gravitational waveform that we detect.

Fig. 1: This graph shows two black holes rotating around each other (without any black hole kick) and finally merging during the final part of the inspiral phase followed by the very short merger and ringdown phase. The wave below is the gravitational waveform. [Figure from 1602.03837]
The idea is rather simple: as the system experiences a kick, its gravitational wave is Doppler shifted. This Doppler shift effects the frequency f in the way you would expect:

Doppler shift from black hole kick.

with v the kick velocity and n the unit vector in the direction from the observer to the black hole system (and c the speed of light). The black hole dynamics is entirely captured by the dimensionless number G f M/c3 with M the mass of the binary (and G Newton’s constant). So you can also model this shift in frequency by using the unkicked frequency fno kick and observing the Doppler shift into the mass. This is very convenient because this means that you can use all the current knowledge and results for the gravitational waveforms and just change the mass. Now the tricky part is that the velocity changes over time and this needs to be modelled more carefully.

A crude model would be to say that during the inspiral of the black holes (which is the long phase during which the two black holes rotate around each other – see figure 1), the emitted linear momentum is too small and the mass is unaffected by emission of linear momentum. During the final stages the black holes merge and the final remnant emits a gravitational wave with decreasing amplitude, which is called the ringdown phase. During this latter phase the velocity kick is important and one can relate the mass during inspiral Mi with the mass during the ringdown phase Mr simply by

Mass during ringdown related to mass during inspiral.

The results of doing this for a black hole kick moving away (or towards) us are shown in fig. 2: the wave gets redshifted (or blueshifted).

Fig. 2: If a black hole binary radiates isotropically, it does not experience any kick and the gravitational wave has the black waveform. However, if it experiences a kick along the line of sight, the waveform can get redshifted (when the system moves away from us) as shown on the left of blueshifted (when system moves toward us) as shown on the right. The top and lower panel correspond to the two independent polarizations of the gravitational wave.[Figure taken from this paper]
Fig. 2: If a black hole binary radiates isotropically, it does not experience any kick and the gravitational wave has the black waveform. However, if it experiences a kick along the line of sight, the waveform can get redshifted (when the system moves away from us) as shown on the left of blueshifted (when system moves toward us) as shown on the right. The top and lower panel correspond to the two independent polarizations of the gravitational wave. [Figure from 1606.04226]
This model is refined in various ways and the results show that it is unlikely that kicks will be measured by LIGO, as LIGO is optimized for detecting black hole with relatively low masses and black hole systems with low masses have velocity kicks that are too low to be detected. However, the prospects for eLISA are better for two reasons: (1) eLISA is designed to measure supermassive black hole binaries with masses in the range of 105 to 1010 solar masses, which can have much larger kicks (and thus are more easily detectable) and (2) the signal-to-noise ratio for eLISA is much higher giving better data. This study estimates about 6 detectable kicks per year. Thus, black hole (super)kicks might be detected in the next decade using gravitational wave astronomy. The future is bright 🙂

Further Reading

Cosmic Microwave Background: The Role of Particles in Astrophysics

Over the past decade, a new trend has been emerging in physics, one that is motivated by several key questions: what do we know about the origin of our universe? What do we know about its composition? And how will the universe evolve from here? To delve into these questions naturally requires a thorough examination of the universe via the astrophysics lens. But studying the universe on a large scale alone does not provide a complete picture. In fact, it is just as important to see the universe on the smallest possible scales, necessitating the trendy and (fairly) new hybrid field of particle astrophysics. In this post, we will look specifically at the cosmic microwave background (CMB), classically known as a pillar of astrophysics, within the context of particle physics, providing a better understanding of the broader questions that encompass both fields.

Essentially, the CMB is just what we see when we look into the sky and we aren’t looking at anything else. Okay, fine. But if we’re not looking at something in particular, why do we see anything at all? The answer requires us to jump back a few billion years to the very early universe.

Particle interactions shown up to point of recombination, after which photon paths are unchanged.
Figure 1: Particle interactions shown up to point of recombination, after which photon paths are unchanged.

Immediately after the Big Bang, it was impossible for particles to form atoms without immediately being broken apart by constant bombardment from stray photons. About 380,000 thousand years after the Big Bang, the Universe expanded and cooled to a temperature of about 3,000 K, allowing the first formation of stable hydrogen atoms. Since hydrogen is electrically neutral, the leftover photons could no longer interact, meaning that at that point their paths would remain unaltered indefinitely. These are the photons that we observe as CMB; Figure 1 shows this idea diagrammatically below. From our present observation point, we measure the CMB to have a temperature of about 2.76 K.

Since this radiation has been unimpeded since that specific point (known as the point of ‘recombination’), we can think of the CMB as a snapshot of the very early universe. It is interesting, then, to examine the regularity of the spectrum; the CMB is naturally not perfectly uniform, and the slight temperature variations can provide a lot of information about how the universe formed. In the early primordial soup universe, slight random density fluctuations exerted a greater gravitational pull on their surroundings, since they had slightly more mass. This process continues, and very large dense patches occur in an otherwise uniform space, heating up the photons in that area accordingly. The Planck satellite, launched in 2009, provides some beautiful images of the temperature anisotropies of the universe, as seen in Figure 2. Some of these variations can be quite severe, as in the recently released results about a supervoid aligned with an especially cold spot in the CMB (see Further Reading, item 4).


Planck satellite heat map images of the CMB.
Figure 2: Planck satellite heat map images of the CMB.


Composition of the universe by percent.
Figure 3: Composition of the universe by percent.

So what does this all have to do with particles? We’ve talked about a lot of astrophysics so far, so let’s tie it all together. The big correlation here is dark matter. The CMB has given us strong evidence that our universe has a flat geometry, and from general relativity, this provides restrictions on the mass, energy, and density of the universe. In this way, we know that atomic matter can constitute only 5% of the universe, and analysis of the peaks in the CMB gives an estimate of 26% for the total dark matter presence. The rest of the universe is believed to be dark energy (see Figure 3).

Both dark matter and dark energy are huge questions in particle physics that could be the subject of a whole other post. But the CMB plays a big role in making our questions a bit more precise. The CMB is one of several pieces of strong evidence that require the existence of dark matter and dark energy to justify what we observe in the universe. Some potential dark matter candidates include weakly interacting massive particles (WIMPs), sterile neutrinos, or the lightest supersymmetric particle, all of which bring us back to particle physics for experimentation. Dark energy is not as well understood, and there are still a wide variety of disparate theories to explain its true identity. But it is clear that the future of particle physics will likely be closely tied to astrophysics, so as a particle physicist it’s wise to keep an eye out for new developments in both fields!


Further Reading: 

  1. The Cosmic Cocktail: Three Parts Dark Matter”, Katherine Freese
  2. “Physics of the cosmic microwave background anistropy”, from the arXiv:astro-ph
  3. Summary of dark matter vs. dark energy and other resources from NASA
  4. Summary of the supervoid aligned with a cold spot in the CMB, Royal Astronomical Society monthly notices