The black hole at the center of the galaxy M87 came into view this year. EVENT HORIZON TELESCOPE COLLABORATION

Black Hole – How Do Scientist Calculate the Mass of a Black Hole?

Black Hole

A black hole is a region of spacetime where gravity is so strong that nothing—no particles or even electromagnetic radiation such as light—can escape from it. The theory of general relativity predicts that a sufficiently compact mass can deform spacetime to form a black hole. The boundary of the region from which no escape is possible is called the event horizon. Although the event horizon has an enormous effect on the fate and circumstances of an object crossing it, it has no locally detectable features. In many ways, a black hole acts like an ideal black body, as it reflects no light. Moreover, quantum field theory in curved spacetime predicts that event horizons emit Hawking radiation, with the same spectrum as a black body of a temperature inversely proportional to its mass. This temperature is on the order of billionths of a kelvin for black holes of stellar mass, making it essentially impossible to observe.

Black holes are the one the most intriguing and awe-inspiring forces of nature. They are also one of the most mysterious because of the way the rules of conventional physics break down in their presence. Despite decades of research and observations, there is still much we don’t know about them. In fact, until recently, astronomers had never seen an image of a black hole and were unable to gauge their mass.

However, a team of physicist from the Moscow Institute of Physics and Technology (MIPT) recently announced that they had devised a way to indirectly measure the mass of a black hole while also confirming its existence. In a recent study, they showed how they tested this method on the recently-imaged supermassive black hole at the centre of the Messier 87 active galaxy.

This wide-field image of the galaxy M87 was taken by NASA’s Spitzer Space Telescope.
This wide-field image of the galaxy M87 was taken by NASA’s Spitzer Space Telescope. The top inset shows a close-up of two shockwaves, created by a jet emanating from the galaxy’s supermassive black hole. The Event Horizon Telescope recently took a close-up image of the silhouette of that black hole, show in the second inset. | Image Credit: NASA/JPL-Caltech/Event Horizon Telescope Collaboration

The study appeared in the August issue of the Monthly Notices of the Royal Astronomical Society. In addition to researchers from the MIPT, the team included members from the Netherlands-based Joint Institute for VLBI ERIC (JIVE), the Academia Sinica’s Institute of Astronomy & Astrophysics in Taiwan, and the NOAJ’s Mizusawa VLBI Observatory in Japan.

If astronomers want to learn about how supermassive black holes form, they have to start small—really small, astronomically speaking.

In fact, a team including University of Michigan astronomer Elena Gallo has discovered that a black hole at the centre of a nearby dwarf galaxy, called NGC 4395, is about 40 times smaller than previously thought. Their findings are published in the journal Nature Astronomy.

Currently, astronomers believe that supermassive black holes sit at the centre of every galaxy as massive as or larger than the Milky Way. But they’re curious about black holes in smaller galaxies such as NGC 4395 as well. Knowing the mass of the black hole at the centre of NGC 4395—and being able to measure it accurately—can help astronomers apply these techniques to other black holes.

“The question remains open for small or dwarf galaxies: Do these galaxies have black holes, and if they do, do they scale the same way as supermassive black holes?” Gallo said. “Answering these questions might help us understand the very mechanism through which these monster black holes were assembled when the universe was in its infancy.”

For some galaxies, the amount of radiation produced by the core region is so bright that it actually overpowers the light coming from all the stars in its disk combined. These are known as Active Galactic Nuclei (AGN) galaxies since they have active cores and other galaxies are comparatively “quiet”. Another telltale identifier that a galaxy is active it is the long beams of superheated matter that extend.

M87's powerful jet streams from the galaxy's black hole
M87's powerful jet streams from the galaxy's black hole like a cosmic searchlight, extending out some 5,000 light-years. The jet is believed to originate from tangled magnetic fields in the accretion disk of M87's supermassive black hole. NASA/The Hubble Heritage Team (STScI/AURA)

These “relativistic jets“, which can extend for millions of light-years outwards, are so-named because the material in them is accelerated to a fraction of the speed of light. While these jets are not fully understood just yet, the current consensus is that they are produced by a certain “motor effect” caused by a rapidly-spinning SMBH

A good example of an active galaxy with a relativistic jet is Messier 87 (aka. Virgo A), a supergiant galaxy located in the direction of the Virgo Constellation. This galaxy is the closest active galaxy to Earth, and therefore one of the best-studied. Originally discovered in 1781 by Charles Messier (who mistook it for a nebula), it has been studied on a regular basis ever since. By 1918, its optical jet became the first of its kind to be observed.

Thanks to its proximity, astronomers have been able to study Messier 87’s jet meticulously – mapping its structure and plasma velocities and measuring temperatures and particle densities near the jet’s stream. The jet’s boundaries have been studied in fine detail that researchers discovered that it was homogenous along its length and changed shape the farther it extended (going from parabolic to conical).

All of these observations have allowed astronomers to test hypotheses regarding the structure of active galaxies and the relationship between changes in the jet’s shape and the influence of the black hole in the galactic nucleus. In this case, the international research team took advantage of this relationship and to determine the mass of M87s SMBH.

The team also relied on theoretical models that predict a jet’s break, which allowed them to create a model where an SMBH’s mass would accurately reproduce the observed shape of M87’s jet. By measuring the jet’s width and the distance between the core and the break of its shape, they also found that the M87’s jet boundary is made up of two segments with two distinctive curves.

In the end, the combination of theoretical models, observations and computer calculations allowed the team to obtain an indirect measurement of the black hole’s mass and spin rate. This study not only provides a new model for black hole estimation and a new means of measurement for jets but also confirms the hypotheses underlying the structure of jets.

Essentially, the team’s results describe the jet as a flow of magnetized fluid, where the shape is determined by the electromagnetic field in it. This, in turn, is dependent things like the speed and charge of the jet particles, the electric current within the jet, and the rate at which the SMBH accretes matter from its surrounding disk.

The interplay between all these factors is what gives rise to the observed break in a jet’s shape, which can then be used to extrapolate the SMBHs mass and how fast it is spinning. Elena Nokhrina, the deputy head of the MIPT laboratory involved in the study and the lead author on the team’s paper, describes the method that they developed in the following way:

“The new independent method for estimation of black hole mass and spin is the key result of our work. Even though its accuracy is comparable to that of the existing methods, it has an advantage in that it brings us closer to the end goal. Namely, refining the parameters of the core ‘motor’ to deeper understand its nature.”


The supermassive black hole, a.k.a. Sagittarius A*
The supermassive black hole, a.k.a. Sagittarius A*, weighs in at slightly more than 4 million times the mass of the Sun. X-rays are produced by hot gas flowing toward the black hole. | Credit: NASA/CXC/MPE/G.Ponti et al; Illustration: NASA/CXC/M.Weiss

Thanks to the availability of sophisticated instruments for studying SMBHs (like the Event Horizon Telescope) and next-generation space telescopes that will be operational soon, it won’t take long for this new model to be thoroughly tested. A good candidate would be Sagittarius A*, the SMBH at the centre of our galaxy that is estimated to be between 3.5 million 4.7 million Solar masses.

In addition to placing more accurate constraints on this mass, future observations could also determine just how active (or inactive) the nucleus of our galaxy is. These and other black hole mysteries await!

Black Hole Mass Calculation

Black holes have only three measurable properties — mass, spin and charge — so calculating the mass is a huge part of understanding an individual black hole. In nearby galaxies, astronomers can observe how groups of stars and gas move around the galactic centre and use those movements to deduce the mass of the central black hole. But distant galaxies lie so far away that telescopes can’t resolve the stars and clouds of material around the black hole, according to the statement.

A technique known as reverberation mapping has made it possible for astronomers to measure the masses of these outlying black holes. First, researchers compare the brightness of the radiating gas in the outer region of the galaxy with the brightness of the gas found in the inner region of the galaxy. (This inner region, very close to the black hole, is known as the continuum region).

The gas in the continuum region affects the fast-moving gas farther out. However, light takes time to travel outward, or reverberate, causing a delay between the changes seen in the inner region and their effect on the outer region. Measuring the delay reveals how far away the outer disk of gas is from the black hole. Coupled with its rotation rate around the galaxy, this allows astronomers to measure the SMBH’s mass, Grier told in an email.

But the process is painfully slow. To observe the reverberation effect, an individual galaxy must be studied over and over again for several months, while distant quasars can take several years of repeated observations, researchers said in the statement. Over the past 20 years, astronomers have managed to use the reverberation technique for only about 60 SMBHs in nearby galaxies and a handful of distant quasars.

As a part of the SDSS Reverberation Mapping Project, Grier and her colleagues have begun mapping SMBHs faster than previously possible. The key to this faster mapping comes from the project’s dedicated wide-view telescope, located at the Apache Point Observatory in Sunspot, New Mexico, which can collect data on multiple quasars at the same time, according to Grier. It is currently observing a patch of the sky that contains about 850 quasars.

Black Hole – How Do Scientist Calculate the Mass of a Black Hole?
NASA's Chandra X-ray Observatory: PSR B1509-58 (upper left), RCW 38 (upper right), Hercules A (middle left), Kes 73 (middle right), Mrk 573 (lower left),NGC 4736 (lower right) | Credit: NASA/CXC/SAO

The researchers observed the quasars with the Canada-France-Hawaii-Telescope in Hawaii and the Steward Observatory Bok Telescope in Arizona to calibrate their measurements of the incredibly faint objects. In total, the researchers have now measured reverberation time delays for 44 quasars, and they used those measurements to calculate black hole masses ranging from 5 million to 1.7 billion times the mass of Earth’s sun, according to the statement.

“This is a big step forward for quasar science,” Aaron Barth, a professor of astronomy at the University of California, Irvine, who was not involved in the team’s research, said in the statement. “They have shown for the first time that these difficult measurements can be done in mass-production mode.”

The new measurements increase the total number of galactic SMBH mass measurements by about two-thirds. Because many of those galaxies are very far away, the new measurements reveal SMBH masses from further back in time, to when the universe was only half its current age.

By continuing to observe the 850 quasars with the SDSS telescope over multiple years, the team will accumulate years of data that will allow them to measure the masses of even fainter quasars, whose long time delays cannot be measured with a single year of data.

“Getting observations of quasars over multiple years is crucial to obtain good measurements,” said Yue Shen, an assistant professor at the University of Illinois and principal investigator of the SDSS Reverberation Mapping Project. “As we continue our project to monitor more and more quasars for years to come, we will be able to better understand how supermassive black holes grow and evolve.”

M87 Black Hole vs Solar System
Size comparison: M87 Black Hole vs our Solar System. The little circle is the orbit of Pluto. Voyager 1 spacecraft, which launched on September 5, 1977, and entered the interstellar space on August 25, 2012 is also annotated in the image. Image source: National Science Foundation

After the current fourth phase of the SDSS ends in 2020, the fifth phase, SDSS-V, will begin. SDSS-V features a new program called the Black Hole Mapper, in which researchers plan to measure the SMBH masses in more than 1,000 quasars, observing fainter and older quasars than any reverberation mapping project has ever managed.

“The Black Hole Mapper will let us move into the age of supermassive black hole reverberation mapping on a truly industrial scale,” Niel Brandt, a professor of astronomy and astrophysics at Penn State and a longtime member of the SDSS, said in the statement. “We will learn more about these mysterious objects than ever before.”

In the case of the Milky Way’s supermassive black hole, however, researchers observed the motion of stars around the object over the course of years. This allowed them to use Kepler’s laws to measure its mass: 4.3 million solar masses.


This is not meant to be a formal definition of how do scientist calculate the mass of a Black Hole, like most terms we define on but is rather an informal word summary that hopefully touches upon the key aspects of the meaning and usage of Black Hole term that will help our readers to expand their word mastery.

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