# The Hole-y Grail: Looking into (near) the singularity

Black holes are at the intersection of the exotic and everyday.  An intrinsically General Relativistic phenomenon, they are also at the center of most galaxies, including our own.  The supermassive black holes (translation: huge, around ten billion Sun’s worth of mass!) at galaxies’ centers appear somehow to set some properties of the normal things (stars) in the galaxy. This is hinted at by the “M-sigma” relation, which relates the random velocities of the stars near a galaxy’s center to the mass of the black hole.  However, how the “M-sigma” relation comes about, and, more generally, how black holes may influence the shape and formation of galaxies, is not really understood.  For that reason, detailed observations of black holes’ properties, especially structures at the scales nearest the singularity, are vital.  The paper I discuss today uses radio observations with a network of telescopes spanning oceans to resolve near the event horizon of the black hole in M87, a giant elliptical galaxy (shaped like a football) discovered by French astronomer Charles Messier in 1781 (hence the M).

To understand the observations in the paper, let me lay out some black hole basics.  Black holes were actually first thought about in 1783, by another Frenchman, who pointed out that one could imagine a mass so dense that even light could not escape its gravity.  This idea was developed later by the famous mathematician Laplace, but dropped out of sight because no one could understand how gravity would affect light, since light was massless.  It was only with the advent of Special Relativity in 1905, which with the famous $E=mc^2$ related energy to mass, that one could imagine how gravity might affect light.  Still, even without this, one can calculate the size of a black hole of a given mass, by asking: when would the velocity needed to escape gravity’s pull be equal to the speed of light?  The answer one gets, remarkably, is right, and gives the size of a black hole of mass $M$ as $R_S=2GM/c^2$, with $G$ Newton’s gravitational constant.  $R_S$ is called the Schwarzschild radius, and, since light cannot escape from inside it, we are never going to see the inside of a black hole!  Well, modulo quantum tunneling.

However, what we can now see, as the observations of this paper show, is what goes on near the Schwarzschild radius, also called the “event horizon”.  This is particularly important because many so-called active galactic nuclei (basically, regions at galaxies’ centers that emit a lot more light than we expect) launch jets near the speed of light.  Why care about jets at all?  Jets can redistribute mass and energy on galactic scales, so it is hoped they will shed light on how black holes determine the formation and properties of the galaxies around them.

Artist's rendering of a black hole; the white things are jets, the grayish ring is the accretion disk of material being sucked into a spiral around the black hole! From http://www.universetoday.com/84006/astronomy-without-a-telescope-black-hole-entropy/

The jets are thought to be powered by the energy that has to be lost as matter falls into the black hole.  Here’s a simple explanation that we’ll later add to. Near a black hole, since they are so massive, for even a small movement of an object inwards, the gravitational force changes hugely.  This means objects at different distances from the center are orbiting (really, spiraling inwards around the black hole) at vastly different speeds.  Much like rubbing your hands together quickly does, as they pass by each other they generate heat, which powers the jets!

However, the real story is a bit more complex.  In particular, the type of jets the authors study may be powered by magnetic fields.  There are two important mechanisms implicated. First, there is the Blandford-Znajek process, where the magnetic field lines actually cross the event horizon.  This requires a spinning black hole, as well as electrical currents in the disk outside the black hole—these latter are what produce the magnetic field (recall from basic E&M that moving charge creates a magnetic field!)  As the magnetic field lines thread around and into the spinning black hole, they can induce an electrical potential difference (just like the familiar phenomenon of induction, when a changing magnetic field induces an electric current to produce more magnetic field and thereby dampen the change).  The electrical potential difference causes the vacuum itself to produce electron-positron pairs ( that is not really intuitively explainable!), and these in turn allow the outflow of energy and angular momentum. Second, there is the Blandford-Payne mechanism, in which a magnetic field causes an outflow from a disk, perhaps initially driven by pressure from the gas near the disk, to become a very narrow jet.  The key aspect of this latter mechanism is that it “collimates” (narrows) the jet.  Taken together, the Blandford-Znajek process and the Blandford-Payne mechanism produce internal structure in the jet: there is a narrow, quickly moving jet (“spine”) surrounded by a slower-moving, mass-carrying “sheaf”.

In the paper, Doeleman and collaborators use Very-Long Baseline Interferometry (VLBI) to determine the size of M87 core, the jet width as a function of distance from the core, and the black hole’s spin and direction of spin (the black hole can rotate either with the disk surrounding it or in the opposite direction).  A word about  VLBI, and then some pictures!  VLBI essentially uses interference effects over very long distances to make observations of e.g. radio sources (“radio” here means with wavelengths around one millimeter, which is much shorter than the typical wavelengths you pick up on your car radio!)  Doeleman and colleagues used 4 telescopes in 3 different places over three nights in April 2009 to make the measurement: the James Clerk Maxwell Telescope (JCMT) on Mauna Kea in Hawaii, the Submillimeter Telescope (SMT) in Arizona, and two dishes from the Combined Array for Research in Millimeter-wave Astronomy (CARMA) in California.

Now for some pictures, with discussion!

Here, Doeleman and collaborators have fit a circular Gaussian (think bell curve!) to the core of M87; that is the solid line.  Basically this is saying that the energy emitted from the core goes like a bell curve as one gets farther away from the center of the core.  The red points are from the measurement along the distance from CARMA to SMT, the magenta and teal are two baselines between the two CARMA dishes and JCMT, and finally the SMT-JCMT measurements are in blue.  The dotted line fits a  Gaussian plus a thin ring outside it also emitting; this second part comes from the black hole’s being illuminated by light from a second jet behind it.  The vertical axis here is in units of Janskys, a favorite of radio astronomers that is laughably small: it is an emission of $10^{-26}$ watts per square meter at a given frequency.  This Gaussian fit gives that the size of the core of M87 is about $5.1$ Schwarzschild radii.

This plot shows the width of the jet as a function of distance from the core of M87, where lives the black hole.  The purple and black solid lines are models based on different opening angles at the base of the jet, indicated on the plot.  The solid light blue bar is the size Doeleman et al. measure, which is the size of the jet near its base.  It is good that this intersects the models as they approach the base of the jet (near the core)!

The light blue bar is the innermost stable circular orbit (ISCO), which is usually a multiple of the Schwarzschild radius, that Doeleman et al. measure.  This is the closest-in orbit that is stable to a perturbation; go closer than this, and you have to be careful not to fall into the black hole!  The value of the ISCO’s radius depends on how fast the black hole is spinning, and whether it spins with the disk outside it (prograde) or opposite to it (retrograde). The diagonal lines are model predictions for prograde (solid) and retrograde (dashed).   Doeleman et al.’s constraint clearly shows the spin must be prograde, because that is the only set of models it intersects.