Measuring a Tiny, Yet Mighty, Black Hole

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One topic that people always ask astronomers about is black holes. These seemingly mysterious and bizarre objects are known to gobble up everything around them, even light, and physics as we know it cannot accurately describe what goes on inside.

From the outside, however, we consider black holes to be pretty simple objects, described completely by their mass, or size, spin and charge. This is often called the "no-hair" theorem of black holes.

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For the most part, something that massive is almost certainly neutral, so astronomers really only care about how big a black hole is and how fast it is spinning.

As you might imagine, actually measuring these quantities can be a bit tricky, as by definition the black hole doesn't give off any light of its own. But researchers are pretty darn clever, and three recent papers detail the precise experiments to measure these quantities with telescopes that range across the electromagnetic spectrum for the Cygnus X-1 system. This binary system is composed of a black hole and a massive blue giant star.

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One of the most difficult quantities to measure in astronomy is the distance to an object. Though we can pinpoint objects in the sky with high accuracy, we can't say much for the actual physics of the object until we know how far away it is.

One of the most basic tools of distance measurement is "trigonometric parallax." This method uses observations of some astronomical object from when the Earth is at different places in its orbit, and a bit of geometry, to figure out the distance to an object.

The geometry behind astronomical parallax. "D" is the distance to the object in question, and "p" is the amount that the object appears to move in the image relative to fixed background objects. 1 AU, or astronomical unit, is the average distance between the Earth and the sun.

A century ago, optical telescopes like our own 26-inch refractor at the University of Virginia took on the task of mapping the distances to all the nearest stars using trigonometric parallax. The blue star of Cygnus X-1, however, is too distant for parallax to be measured accurately with current optical telescopes. To get extremely good precision of measurement on the sky, astronomers turned to a radio telescope the size of the Earth, the Very Long Baseline Array.

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I love talking about what the VLBA can do, since it seems rather unappreciated for the excellent science that has come from it in the last 20 years. It comprises 10 identical radio telescopes spread across North America, the signals of which are combined in a way that allows astronomers to map the sky with extremely high precision. Like, milliarcsecond precision. That's like if you held your hand out at arm's length with an atomic nucleus between your thumb and forefinger. If you could see THAT, your vision would be as good as the VLBA's.

So, with such excellent radio vision, astronomers, led by Mark Reid of the Harvard-Smithsonian Center for Astrophysics, tracked the position of Cygnus X-1, specifically the radio emissions from the accretion disk surrounding the black hole, over the course of a year.

They measured the orbital motion, the proper motion of the system through the galaxy, and the perceived motion due to parallax, finding it to be a distance of just over 6,060 light-years away, with an error of less than 10 percent. With the distance in hand, they could now move on to studying the intrinsic properties of the black hole system.

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A group led by Jerome Orosz of San Diego State University used data from optical and ultraviolet telescopes to determine the orbital velocity of the blue star around its black hole companion. From this, and knowing the distance, the astronomers found the star to be 19 times the mass of the sun and the black hole to be 15 times the mass of the sun.

It may surprise you to think that the star dominates the mass of the binary system, but not by very much. The gravitational pull of the black hole, however, is strong because of the object's very high density as a result of its small radius.

Lijun Gou, also of the Center for Astrophysics, and his collaborators put the final pieces of the puzzle in place with data from several X-ray telescopes.

The accretion disk around the black hole gives off X-ray light with what is called a "soft" spectrum. That is, it is dominated by lower-energy X-rays. When in a state in which this emission dominates, as opposed to during a flare of some kind, the disk can be modeled fairly simply and the inner radius of that disk measured.

Schematic of the black hole and its accretion disk, from Gou et al. The ISCO is the innermost stable circular orbit and goes up to the edge of the gray ellipse that represents the edge of a Kerr black hole. "kT" refers to the energy of the X-ray photons emitted from either the disk or surrounding stellar material.

Where the disk ends is where the black hole begins. Having measured both the mass and the radius, the scientists determined the black hole to be rapidly spinning and thus complete the physical description of Cygnus X-1, 47 years after its discovery with an X-ray detector onboard a rocket, and 39 years after it was determined to be a candidate for this mysterious thing called a "black hole."

The scientific papers don't make a big deal out of the value of the radius, or physical size, of the black hole. Though it is typical for a black hole, it is still a bit mind-blowing that almost 15 times the mass of the sun can be compacted into something 44 kilometers, or 27 miles, across. That's just the size of an asteroid! All that mass compacted into such a small place is what makes black holes so weird and different from our everyday experience and explains why their gravity is literally legendary.

This research was published in Astrophysical Journal, and links to the preprints can be found in the text.

Images: Top – Artist's conception of Cygnus X-1 system. (Credit: Chandra/NASA); Middle – Diagram of trigonometric parallax as used in astronomy. (Credit: Me); Bottom – Schematic of the black hole. (Credit: Gou et al., R. Reis).