The prospect of measuring the mass of the most massive known objects in the universe would send most people into a cold sweat, but for astronomers using the monster Atacama Large Millimeter/submillimeter Array (ALMA) in Chile, it's all in a day's work. However, ‘weighing' a supermassive black hole from millions of light-years away is far from being a simple task.
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Supermassive black holes are known to lurk inside the cores of most galaxies. They can have galaxy-wide impacts on star formation and are intimately tied to the billions of years of evolution of their host galaxies. To understand how supermassive black holes grow and impact the health of their interstellar environment is therefore one of the most important studies in modern astrophysics.
So, first things first, like any health check, we need to find a way of measuring the mass of these black hole behemoths.
There are several ways to gauge the mass of a supermassive black hole, but it depends on how far away the block hole is and what kind of galaxy it inhabits.
For the supermassive black hole in the core of our galaxy, the Milky Way, astronomers have been able to zoom into Sagittarius A* - a region bright in radio wave emissions - and track the motions of individual stars around an invisible point using incredibly precise infrared telescopes. This invisible point, of course, is the location of a supermassive black hole that is now known to have a mass 4 million times the mass of our sun.
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Gauging the mass of the closest supermassive black hole to Earth is one thing - it is, after all, ‘only' 25,000 light-years from the nearest observatory - what about measuring black holes in the cores of other galaxies?
Because they are so distant, measuring the velocity of stars in the cores of other galaxies is not possible. So, to measure the masses of these objects, astronomers will be on the lookout for radio-bright objects called ‘megamasers' speeding around the central black hole and use them as a beacon of sorts. Unfortunately, megamasers are very rare.
Alternatively, astronomers will try the next best thing and measure the motion of ionized gases inside the galactic core; the velocity of these gas clouds can reveal the mass of the black hole. But this method is best suited for elliptical galaxies; it cannot be used to gauge the mass of supermassive black holes in the cores of spiral galaxies.
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But now, it seems astronomers have found a way to measure the mass of supermassive black holes in the cores of sprial (and barred) galaxies using the observing power of ALMA.

Turning their attention to the barred-spiral galaxy NGC 1097, around 45 million light-years away in the constellation of Fornax, researchers led by Kyoko Onishi at SOKENDAI (the Graduate University for Advanced Studies) in Japan precisely measured the distribution of hydrogen cyanide (HCN) and formylium (HCO+) molecules in the galaxy's central region. Then, using computer models to simulate different distributions of these molecules around supermassive black holes of different masses, they were able to find a black hole mass that fitted with the observations.
It turns out that NGC 1097′s black hole is the definition of supermassive. This black hole has a mass of around 140 million times the mass of our sun, approximately 35 times more massive than our galaxy's humble, not-so-supermassive black hole Sagittarius A*.
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"Recent observation results indicate the relationship between supermassive black hole mass and host galaxy properties varies depending on the type of galaxies, which makes it more important to derive accurate supermassive black hole masses in various types of galaxies," said Onishi in an ALMA press release.
"This is the first use of ALMA to make such measurement for a spiral or barred spiral galaxy," added co-investigator Kartik Sheth, at the National Radio Astronomy Observatory in Charlottesville, Va. "When you look at the exquisitely detailed observations from ALMA, it's startling how well they fit in with these well tested models. It's exciting to think that we can now apply this same technique to other similar galaxies and better understand how these unbelievably massive object affect their host galaxies."
So, that's how you measure the mass of a supermassive black hole in the core of a spiral galaxy. All in a day's work...
Source: ALMA

Composite image of the barred spiral galaxy NGC 1097. The ALMA data is in red (HCO+) and green/orange (HCN) superimposed on an optical image taken by the Hubble Space Telescope.

Artist's impression of a spinning supermassive black hole with a surrounding accretion disk and relativistic jets.

How to measure the spin of a black hole: This chart illustrates the basic model for determining the spin rates of black holes. The three artist's concepts represent the different types of spin: retrograde rotation, where the disk of matter falling onto the hole, called an accretion disk, moves in the opposite direction of the black hole; no spin; and prograde rotation, where the disk spins in the same direction as the black hole.

Two models of black hole spin: Scientists measure the spin rates of supermassive black holes by spreading the X-ray light into different colors. The light comes from accretion disks that swirl around black holes, as shown in both of the artist's concepts. They use X-ray space telescopes to study these colors, and, in particular, look for a "fingerprint" of iron -- the peak shown in both graphs, or spectra -- to see how sharp it is. Prior to observations with NASA's Spectroscopic Telescope Array, or NuSTAR, and the European Space Agency's XMM- Newton telescope, there were two competing models to explain why this peak might not appear to be sharp. The "rotation" model shown at top held that the iron feature was being spread out by distorting effects caused by the immense gravity of the black hole. If this model were correct, then the amount of distortion seen in the iron feature should reveal the spin rate of the black hole. The alternate model held that obscuring clouds lying near the black hole were making the iron line appear artificially distorted. If this model were correct, the data could not be used to measure black hole spin.

This chart depicts the electromagnetic spectrum, highlighting the X-ray portion. NASA's Nuclear Spectroscopic Telescope Array (NuSTAR) and the European Space Agency's XMM-Newton telescope complement each other by seeing different colors of X-ray light. XMM-Newton sees X-rays with energies between 0.1 and 10 kiloelectron volts (keV), the "red" part of the spectrum, while NuSTAR sees the highest-energy, or "bluest," X- ray light, with energies between 3 and 70 keV.

This image taken by the ultraviolet-light monitoring camera on the European Space Agency's (ESA's) XMM-Newton telescope shows the beautiful spiral arms of the galaxy NGC1365. Copious high-energy X-ray emission is emitted by the host galaxy, and by many background sources. The large regions observed by previous satellites contain so much of this background emission that the radiation from the central black hole is mixed and diluted into it. NuSTAR, NASA's newest X-ray observatory, is able to isolate the emission from the black hole, allowing a far more precise analysis of its properties.

What XMM-Newton saw: The solid lines show two theoretical models that explain the low-energy X-ray emission seen from the galaxy NGC 1365 by the European Space Agency's XMM-Newton. The red line explains the emission using a model where clouds of dust and gas partially block the X-ray light, and the green line represents a model in which the emission is reflected off the inner edge of the accretion disk, very close to the black hole. The blue circles show the measurements from XMM-Newton, which are explained equally well by both models.

Two X-ray observatories are better than one: NASA's Nuclear Spectroscopic Telescope Array, or NuSTAR, has helped to show, for the first time, that the spin rates of black holes can be measured conclusively. It did this, together with the European Space Agency's XMM-Newton, by ruling out the possibility that obscuring clouds were partially blocking X-ray right coming from black holes. The solid lines show two theoretical models that explain low-energy X-ray emission seen previously from the spiral galaxy NGC 1365 by XMM-Newton. The red line explains the emission using a model where clouds of dust and gas partially block the X-ray light, and the green line represents a model in which the emission is reflected off the inner edge of the accretion disk, very close to the black hole. The blue circles show the latest measurements from XMM-Newton, and the yellow circles show the data from NuSTAR. While both models fit the XMM-Newton data equally well, only the disk reflection model fits the NuSTAR data.