Rapid Microlensing Classification: A Lonely SOBH Story

Title: On Finding Black Holes in Photometric Microlensing Surveys

Authors: Zofia Kaczmarek, Peter McGill, Scott E. Perkins, William A. Dawson, Macy Huston, Ming-Feng Ho, Natasha S. Abrams, and Jessica R. Lu

First Author’s Institution: Space Science Institute, Lawrence Livermore National Laboratory, 7000 East Ave., Livermore, CA 94550, USA

Status: Available on ArXiv [open access]

Searching for stellar-mass black holes is no simple task—how do you look for an object floating in the vastness of space, hundreds or thousands of light years away, that is at best the size of Houston, Texas and emits no light? As our surveys of the night sky become more and more regular and increase in resolution, there is hope that we will be able to observe more and more chance alignments of these objects with stars, generating an observable effect known as microlensing. This mechanism provides us with a way to pick a proverbial black hole needle from the galactic stellar haystack, but the data we get from these surveys is still difficult to efficiently process. Today’s paper introduces a new method for rapidly assessing the chances that a given microlensing event is indeed caused by a wandering black hole, allowing astronomers to make more effective decisions about which events to follow-up on with targeted observation campaigns.

A Microlensing SOBH-Story

While astrophysical black holes were once squarely in the realm of speculative science fiction, it is now commonplace to find these extreme objects through a variety of techniques. One such technique involves observing a star that is moving around in a binary system, making its motion regular and predictable. Astronomers can use this regular motion to deduce the mass of its partner—and if there’s no visible signal associated with it, this companion object may turn out to be a black hole. 

Another more recent technique which has proven successful in finding these exotic objects involves listening for the gravitational waves produced when a black hole merges with another compact object like a black hole, neutron star, or white dwarf. From these observations, astronomers can learn about the overall population of black holes in our universe, and by proxy can learn about the last stages of stellar evolution. But relying on these measurements alone would generate a biased picture of stellar evolution, because they only pick out black holes which formed in (or evolved into) binary systems. This leaves us without much information about the non-negligible fraction of stars (and therefore black holes) which prefer the “single life”.

This is where the topic of today’s paper comes in: microlensing is a phenomenon wherein any object with mass, through the (not-quite) magic of Einstein’s Theory of General Relativity, is able to deflect rays of light like a lens, occasionally magnifying that light in a particular direction. This is useful for astronomers, because if a black hole passes in front of a star and the alignment is just right, we might observe a temporary brightening of that background star. This is occasionally paired with other optical distortions like the formation of multiple images of the star. Figure 1 depicts this process in more detail. Microlensing is a great way of looking for stellar-origin black holes (SOBHs), but it comes with inherent limitations due to the chance nature of these alignments and the subtlety of the effect. In fact, to date (October 2024) there has only been one candidate microlensing event which was confirmed to be a black hole after follow-up observations were made with the Hubble Space Telescope (HST). This is despite the fact that collaborations like The Optical Gravitational Lensing Experiment (OGLE) have cataloged over 10,000 microlensing events to date. 

One Quick Classification Trick

For the most part, microlensing events are found by looking for subtle changes in the light coming from a star—this observation is a photometric measurement of the microlensing event. Photometric data for a microlensing event is generally able to provide at least some constraints on two important microlensing parameters: the Einstein timescale (related to how long the foreground object lenses the background as it passes by) and the microlensing parallax which results from the Earth’s acceleration towards or away from a particular lensing event. Unfortunately, from these variables alone it can be hard to confidently determine the nature of the lensing object, motivating attempts to make higher-resolution follow-up observations of these events. Telescopes with strong spatial resolution can sometimes pick up on the way the lensing object subtly distorts the apparent position of the background star. These so-called astrometric observations can help pin down important information such as the size and/or mass of the lensing object, letting astronomers confirm the presence of a SOBH, or another object of interest. 

One problem that arises in this process, however, is the fact that astrometric follow-up is difficult to conduct and can take up valuable time on busy telescopes like HST. For this reason, it is important to try and do as much as possible with the limited photometric data products and ensure that only the most-likely-to-succeed follow-up campaigns are performed. The authors of today’s paper worked on this particular problem by developing a fast and flexible classification program which assesses the likelihood of a given microlensing event fitting into a given source category using only the photometric estimates of , , and an underlying galactic stellar population model. By simulating the distribution of stars, white dwarfs, neutron stars, and SOBHs in the galaxy, the authors were able to simulate the expected distributions of lensing parameters and produced they produced. Understanding these underlying distributions allowed the authors to perform Bayesian estimations of the probability that a given photometrically-observed microlensing event was caused by a particular type of lens. In Figure 2, the distributions of events from different sources given by a representative galactic population model are shown in and space. Promisingly, SOBH lensing events tend to be well separated from stellar, white dwarf, and neutron star events in these simulations.

After introducing their classification pipeline, the authors applied it to an existing microlensing dataset from the OGLE collaboration. This dataset contained nearly 10,000 events, from which the classification pipeline returned 23 high-probability SOBH candidates that were agreed upon across all three models of star-to-black-hole evolution (“initial-final mass relations”, IFMRs) the authors used. Applying further selection rules to find candidate events that could potentially be observed by the Gaia telescope, the list was whittled down to just 4 events. Unfortunately, all 4 of these remaining candidates were found to be unlikely to produce significant astrometric deviations, meaning we will likely have to wait for larger microlensing surveys coming up in the near future for a solid chance of finding a new SOBH candidate with this method.

OB110462: A Chance Encounter?

Using a stellar-population-model-informed classification method like the one presented in this paper may also allow us to directly examine weaknesses in these models. For example, if in the future we find many microlensing events that are later confirmed to be SOBHs but exist outside of the expected SOBH region of – parameter space, it could point us towards a flaw in the underlying population models. As of the publication of this paper, however, we only have one confirmed SOBH microlensing event to compare to (denoted OB110462). Working with a sample size of 1 is pretty uninformative (to say the least) but the authors do note that this event is already somewhat of an outlier given their population model. In Figure 3, you can see the recovered and probability contour for OB110462 only barely overlaps with the region corresponding to SOBHs, and the contours fit more snugly in the region corresponding to white dwarfs. This tension is interesting, because even if it doesn’t point to a problem with the stellar population models, it could indicate that the successful confirmation of this event as a SOBH was an unlikely success, and so choosing to dedicate time on the Hubble Space Telescope to do follow-up measurements was, in retrospect, a high-risk move that paid off.

Regardless of how things turned out with OB110462, this sort of analysis points to a more general benefit this classification scheme provides: it allows for a very rapid estimation of which microlensing events we should focus our attention on with follow-up observations. The authors propose that this makes their method ideally suited as an initial filter through which microlensing events can pass before more complicated analyses are performed. As surveys like LSST begin to take unfathomably huge amounts of time-domain data, the number of detected microlensing events is going to sharply increase, making it more important than ever that we think carefully about which events are worth following up on.

Astrobite edited by Lindsey Gordon

Featured image credit: Images from IconDuck, NASA/ESA/Kailash Sahu (STScI)/Joseph DePasquale (STScI), and Kaczmarek et al. (2024). Modified by the author.