Pulling on Pulsars: Searching for Black Holes in Globular Clusters with Pulsars

Title: Intermediate mass black holes in globular clusters: effects on jerks and jounces of millisecond pulsars

Authors: Federico Abbate, Mario Spera, Monica Colpi

First Author’s Institution: Universit`a degli Studi Milano – Bicocca, Milano, Italy

Status: Published in Monthly Notices of the Royal Astronomical Society, open access on arXiv

Figure 1: Hubble image of the globular cluster 47 Tucanae (NGC 104). Credits: NASA, ESA, Hubble Heritage Team (STScI / AURA)

Globular clusters, dense groups of hundreds of thousands of stars bound together by their own gravity, are home to some of the most exotic objects in the universe. Among these are pulsars, highly magnetized neutron stars that beam radio emission out as they rotate. Some pulsars complete a full rotation in just a few milliseconds, and are aptly called millisecond pulsars. Globular clusters are also known to host black holes, some of the most elusive astronomical bodies known.

Just four years ago, observations with the Laser Interferometer Gravitational-Wave Observatory (LIGO) detected black holes with masses of 7 to 80 times the mass of the sun (stellar mass black holes) for the first time. This past year, the Event Horizon Telescope imaged a supermassive black hole, which have masses of a million to a billion times that of our sun, at the center of the galaxy M87.  Yet, there remains a population of black holes that has thus far eluded us: intermediate mass black holes (IMBHs), which have masses between a hundred to a hundred thousand times the mass of the sun.  IMBH’s could be the “missing link” between stellar mass black holes and supermassive black holes and help us learn how supermassive black holes form. But despite searches spanning several years, we have yet to detect them.

The best place to search for IMBHs has long been thought to be in the centers of globular clusters. This paper uses the millisecond pulsars in globular clusters to search for IMBHs.

Timing Millisecond Pulsars in Globular Clusters

As discussed previously in this astrobite, millisecond pulsars are incredibly stable clocks, some with rotation rates, or periods, known to nanosecond precision (or better!). By timing these pulsars over a few years, we can measure not only how fast they are spinning, but also other astrophysical properties, such as how much they slow down as they lose rotational energy. With enough observations, and if the pulsar is in a binary system, we can directly measure the acceleration of a millisecond pulsar due to the gravitational potential of a globular cluster from timing. If there is an IMBH in the center of a globular cluster and a millisecond pulsar passes close by it, the acceleration of the millisecond pulsar will change due to their gravitational interaction.

The authors of this paper use this change in the acceleration of many millisecond pulsars near the center of the globular cluster as a method to detect any IMBH that may be hiding there. The quantities of interest here are the first time derivative of the millisecond pulsar’s acceleration, or the “jerk”, and the second time derivative of the acceleration: the “jounce”.  By modeling the gravitational potential of the globular cluster, it is possible to predict what the effect of a central IMBH would have on the jerk and jounce of a millisecond pulsar orbiting it.

Searching for Intermediate Mass Black Holes

To test their methods for searching for IMBHs, the authors simulate many different globular clusters with different size IMBHs, ranging from a hundred to ten thousand times the mass of the sun (as well as globular clusters without an IMBH). These simulations allow them to predict what the contribution to the jerk and jounce of a millisecond pulsar orbiting up to a parsec (3.3 light years) away from the center of the cluster will be. Most globular clusters are 20-100 parsecs (66-330 light years) in diameter, so this region represents less than one thousandth of the total volume of the cluster.

The authors can then predict how many millisecond pulsars they will need to time in the globular cluster to confidently claim an IMBH detection.  They use the “Bayes factor” statistic to measure how much more likely the simpler model (just a normal globular cluster with no IMBH) is than a more complex model (here, a globular cluster with an IMBH).  So the smaller the Bayes factor, the more likely it is that there’s an IMBH in the globular cluster. To claim a statistically significant detection of an IMBH, the authors want a log Bayes factor of -2 or smaller, meaning that the model with an IMBH is at least 100 times more likely.

Simulations are good for testing methods, but what the authors are really interested in is searching for an IMBH in a real globular cluster, in this case 47 Tucanae (or Tuc). Previous searches of 47 Tuc for IMBHs have not involved using the jerk and jounce of millisecond pulsars. However, the authors do not have their own data on the millisecond pulsars in 47 Tuc, so they simulate it instead. What they do have are the known astrophysical parameters, including their positions and accelerations, of the 15 binary and 10 isolated millisecond pulsars known in 47 Tuc. Unfortunately, these millisecond pulsars had not been observed for long enough to have a measured jounce, so the authors were searching with just the acceleration and jerk.

After simulating 47 Tuc eighty times, the results are…inconclusive (see Figure 2). The authors cannot say for sure that there is an IMBH in the center of 47 Tuc. What they can say is that if there is one, it must be less than 7000 solar masses. Anything heavier than that would have caused jerks to show up in their simulations.

Figure 2: The log Bayes factor (or likelihood) of detecting IMBHs of various masses in 47 Tuc using different samples of millisecond pulsars within the cluster. The gray line uses just the accelerations of the millisecond pulsars in binary systems, the blue dashed line uses the same as the gray and adds the jerks of all millisecond pulsars, and the dot-dashed red line also adds statistically modeled accelerations of millisecond pulsars not in binary systems where the acceleration cannot be directly measured. The upper black dashed line is there to guide your eye. The lower black dashed line is where the authors can make a statistically significant detection of an IMBH. The authors set their upper limit to be when one of the three models reaches a log Bayes factor of -2 (the lower black dashed line), which occurs for the dot-dashed red line at an IMBH mass of 7000 solar masses. Figure 7 from the paper.

The Intermediate Mass Future

Even though the authors didn’t find an IMBH the methods they used are promising for future searches. The measurements of the millisecond pulsars acceleration, jerk, and jounce will get better, and the authors estimate that with 5 more years of data they will be able to detect IMBHs of masses down to 5000 solar masses. This is still pretty heavy, but using new radio telescopes like MeerKAT, they could get down to 1000 solar masses, which would be the most sensitive limit ever! The bottom line is, while we haven’t found an IMBH with millisecond pulsars yet, the future looks bright.


About Brent Shapiro-Albert

I'm a fourth year graduate student at West Virginia University studying various aspects of pulsars. I'm a member of the NANOGrav collaboration which uses pulsar timing arrays to detect gravitational waves. In particular I study how the interstellar medium affects the pulsar emission. Other than research I enjoy reading, hiking, and video games.

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