Title: Dancing with invisible partners: Three-body exchanges with primordial black holes
Authors: Badal Bhalla, Benjamin V. Lehmann, Kuver Sinha, Tao Xu
First Author’s Institution: Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, Norman, OK 73019, USA
Status: Available on ArXiv
Primordial black holes (PBHs), the hypothetical class of black holes that may have formed in the extreme densities of the early universe, have gained significant momentum as an explanation for dark matter (DM) in recent decades—and it’s not hard to see why. PBHs fit many of the necessary criteria for a successful DM candidate: they are dark (as implied by their name), they gravitate, and (depending on their individual masses) there could be a surprisingly huge number of them in our universe without us ever encountering one directly. Of course, this last quality is a double-edged sword: in order to test the hypothesis that these black holes can explain at least some of the DM in our universe, we would like to eventually find one. In today’s paper, the authors take a look at how often we might find PBHs in binary systems with non-PBH objects like stars, planets, or even a wayward asteroid, and try to shed some light on how we might seek out these “invisible partners”.
The Three Body Problem: Solving A Complicated Love Triangle
In order for a PBH to end up in a binary, it would typically have to participate in an exchange process with an existing binary system. This is because unlike stellar black holes which form within existing astrophysical environments like stellar binaries, PBHs form all at once in the early universe and should be dispersed throughout space (tracing out the DM density). In an exchange scenario, a freely-floating PBH encounters a binary system and interacts with the bound masses gravitationally. If conditions are right, the incoming PBH may give away some of its kinetic energy to one of the bound objects, ejecting it from the system outright. The PBH, now with less kinetic energy of its own, can then find itself bound to the remaining object.
Of course, an exchange is only one possible outcome of a three-body interaction like this one. One possibility is that a passing PBH could transfer some kinetic energy to one of the bound objects, simply widening the binary orbit (this is known as “softening”). Sometimes, this process can trap the PBH as well, forming a triple system (“capture”). In the extreme case, the binary softening can go so far as to completely separate the binary, leaving three completely unbound objects (“disruption”). Alternatively, the bound objects could transfer some of their own kinetic energy to the PBH as it passes through, shrinking the binary orbit (“hardening”).
The dynamics of these astrophysical love-triangles can be infamously complicated to predict, as is made evident by the fact that the term “three-body problem” has seeped into some corners of popular culture as a way to reference hard-to-solve problems. Nonetheless, it is possible with simplifying assumptions, numerical simulations, and statistical considerations, to come up with some general rules which define when certain outcomes are more or less likely. For example, in order to prevent a complete disruption of a binary, the incoming PBH has to approach with sufficiently low velocities. The outcome of a PBH encounter also greatly depends on the relative masses of the three objects, as well as the orbital separation of the initial binary. By combining considerations like these with estimates of average DM particle velocities throughout DM haloes, the authors of today’s paper were able to generate predictions for the rate of PBH exchanges given different binary parameters, PBH masses, and PBH abundances. Understanding the rates of PBH exchanges across all these environments will then hopefully allow us to identify ideal systems in which to search for PBHs.
When the (Black Hole) Planets Align
Exchange processes like these can occur in a wide variety of environments—basically any astrophysical binary from asteroid-asteroid pairs to star-planet systems can have one of their component members swapped for a PBH if the conditions are right. The resulting binaries will all look largely similar to any other non-PBH binary, with at least one major difference: one of the objects in the pair will be invisible (with one caveat we will get to). Whether it is even possible to identify such pairings depends greatly on the sort of observations we can get of the non-PBH object in the pair, so the authors of today’s paper analyze a few general categories.
First, the authors imagine some PBHs exchanging with existing compact object binaries—systems containing some combination of black holes, neutron stars, and/or white dwarf stars. In this case, it may be hard to distinguish between systems containing a PBH and those containing astrophysical (stellar-origin) black holes. Given the “dark” nature of many of these systems, they are more commonly “heard” than “seen”: gravitational wave (GW) detectors can pick up the periodic warping of spacetime that occurs in the final moments before these systems merge. But unless the PBH in the pairing is lighter than any astrophysical black holes, there would be essentially no way to tell one from the other—and unfortunately, three-body exchanges are the most common when the exchanger’s mass is close to the initial binary masses, making detection of ultralight-PBH exchange systems in GW detectors exceedingly unlikely. Even in the most optimistic possible scenario, the authors calculate a rate of 1 detectable exchange per every 100 years (see Figure 2 for a depiction of exchange rates for all the systems discussed here across a range of PBH masses and abundances).
Thinking much smaller-scale, the authors also consider scenarios in which a PBH could exchange with an asteroid in a pre-existing asteroid binary. This category is interesting to consider given that we don’t yet have tight restrictions on the amount of asteroid-mass PBHs there could be in the universe, but the prospects for detecting such a system are fairly bleak. This is due to both the extremely low rate of predicted exchanges (~10-20 per every billion years) and the observational difficulties associated with carefully characterizing the orbital motion of distant and dim asteroids. The authors note that our best hope for spotting such a pairing in our own solar system would be simply looking for Hawking radiation coming directly off of the PBH. Hawking radiation is a quantum mechanical effect by which black holes can counterintuitively radiate photons and other particles—and because the intensity of this radiation is inversely proportional to a black hole’s mass, asteroid-mass and sub-asteroid-mass PBHs may actually shine brightly. Future missions like AMEGO-X may be sensitive to these sort of signals in our own solar system, which may at the very least help us put constraints on the abundance of these backyard binary black holes (try saying that three times fast!).
In the case that is perhaps most appealing to science fiction writers, the authors also consider PBH exchanges with planets orbiting around stars. These exchanges would result in what is essentially a primordial black hole planet—a scenario in which a PBH kicks out an existing planet and becomes a new member of that extrasolar system. Because observations of exoplanetary systems are becoming increasingly commonplace and the number of detected systems is expected to grow rapidly over the coming decades, we might expect this to be an ideal space in which to keep our eyes peeled for signs of a PBH. The observational signature would be fairly straightforward: the PBH would tug on its host star like any other planet, affecting its motion and creating astrometric or Doppler effects. However, unlike with many other massive exoplanets, these effects would not be accompanied by a periodic dimming of the star’s light as the PBH planet passed in front of it (a “transit”), owing to its extremely small size (a Jupiter-mass black hole would be about as big as a typical U.S. studio apartment). As the authors point out, however, we would need to observe many of these systems to be confident that we are seeing PBH planets, because transits are already somewhat rare to observe. Unfortunately, even under the most optimistic exchange rate scenarios, the authors find that we could hope to stumble upon approximately 1 PBH planet in all of the near-future exoplanet surveys. Bummer.
Finally, the authors turn to a slightly more optimistic scenario: PBH exchanges with stellar binaries. Because these systems are much more readily observable than exoplanets, we have a greater chance of finding an outlier system which could be explained by a PBH exchange. The main caveat here echoes the compact object binary case; identifying whether a black hole in a binary with some star is of primordial origin, rather than formed through astrophysical processes, is very tricky. After all, many stellar binaries eventually become a star and black hole pair just by virtue of one of the two stars completing its normal lifecycle and undergoing an ultimate gravitational collapse. One potential upside is that this process has been fairly extensively studied, and it is thought that this evolution should leave certain telltale imprints on the resulting system. For example, as the pre-collapse star in the pair puffs up and releases its outer layers, it is expected that this material will get deposited onto the remaining star, leaving unique chemical signatures in the companion’s spectrum. By identifying systems with anomalous stellar properties, orbital separations, and so-on, there may be room for a PBH to swoop in as the preferred explanation, just like it swoops in during an exchange.
Finding Invisible Partners
Owing to the generality of three-body exchange physics and the wide range of possible PBH masses, today’s paper makes clear that there are indeed a wide variety of systems in which we might expect to find “invisible partners” from the early universe. However, each system faces its own unique set of observational challenges, making it unlikely that we will spot PBHs engaged in these delicate dances anytime soon, if they exist at all. If there’s anything to keep your eye out for in the near future when it comes to this topic, it may be the final category we discussed: stellar binaries. As it turns out, Gaia has already detected at least three potentially problematic star-plus-black-hole couplings. Denoted BH1, BH2, and BH3, these systems exhibit combinations of orbital separations and chemical compositions that are somewhat difficult to explain with standard astrophysical formation channels. The authors of today’s paper, through some quick order-of-magnitude calculations, find that formation of these systems via PBH exchanges should occur with roughly similar frequency to the rates of formation given by some other non-standard formation scenarios like an exchange with an unbound stellar-origin black hole. Coincidence? Quite possibly, but at least for now we can still hold onto some hope of one day finding such an elusive primordial pairing.
Astrobite edited by Sonja Panjkov
Featured image credit: Adapted from Fig 1 in today’s paper by the author. Black hole and asteroid images from NASA and JPL.
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