Question

The supermassive black hole in the center of the Milky Way has a mass of roughly 3 million M⊙and the Milky Way is approximately10 billion years old. Estimate the average amount of matter accreted by the black hole per year since that time and use that information to propose modes by which the black hole has grown. That is, make some simple models which describe what the black hole might have eaten, and how much it has eaten as a function of time

Answer 1

Supermassive black holes have properties that distinguish them from lower-mass classifications. First, the average density of a SMBH (defined as the mass of the black hole divided by the volume within its Schwarzschild radius) can be less than the density of water in the case of some SMBHs.[7] This is because the Schwarzschild radius is directly proportional to its mass. Since the volume of a spherical object (such as the event horizon of a non-rotating black hole) is directly proportional to the cube of the radius, the density of a black hole is inversely proportional to the square of the mass, and thus higher mass black holes have lower average density.[8] In addition, the tidal forces in the vicinity of the event horizon are significantly weaker for supermassive black holes. The tidal force on a body at the event horizon is likewise inversely proportional to the square of the mass:[9] a person on the surface of the Earth and one at the event horizon of a 10 million M☉ black hole experience about the same tidal force between their head and feet. Unlike with stellar mass black holes, one would not experience significant tidal force until very deep into the black hole.[10]

Some astronomers have begun labeling black holes of at least 10 billion M☉ as ultramassive black holes.[11][12] Most of these (such as TON 618) are associated with exceptionally energetic quasars.

Doppler measurements[edit]

Simulation of a side view of black hole with transparent toroidal ring of ionised matter according to a proposed model[47] for Sgr A*. This image shows the result of bending of light from behind the black hole, and it also shows the asymmetry arising by the Doppler effect from the extremely high orbital speed of the matter in the ring.

Some of the best evidence for the presence of black holes is provided by the Doppler effect whereby light from nearby orbiting matter is red-shifted when receding and blue-shifted when advancing. For matter very close to a black hole the orbital speed must be comparable with the speed of light, so receding matter will appear very faint compared with advancing matter, which means that systems with intrinsically symmetric discs and rings will acquire a highly asymmetric visual appearance. This effect has been allowed for in modern computer generated images such as the example presented here, based on a plausible model[47] for the supermassive black hole in Sgr A* at the centre of our own galaxy. However the resolution provided by presently available telescope technology is still insufficient to confirm such predictions directly.

What already has been observed directly in many systems are the lower non-relativistic velocities of matter orbiting further out from what are presumed to be black holes. Direct Doppler measures of water masers surrounding the nuclei of nearby galaxies have revealed a very fast Keplerian motion, only possible with a high concentration of matter in the center. Currently, the only known objects that can pack enough matter in such a small space are black holes, or things that will evolve into black holes within astrophysically short timescales. For active galaxies farther away, the width of broad spectral lines can be used to probe the gas orbiting near the event horizon. The technique of reverberation mapping uses variability of these lines to measure the mass and perhaps the spin of the black hole that powers active galaxies.

In the Milky Way[edit]

Inferred orbits of 6 stars around supermassive black hole candidate Sagittarius A* at the Milky Way galactic center[48]

Astronomers are confident that the Milky Way galaxy has a supermassive black hole at its center, 26,000 light-years from the Solar System, in a region called Sagittarius A*[49] because:

• The star S2 follows an elliptical orbit with a period of 15.2 years and a pericenter (closest distance) of 17 light-hours (1.8×1013 m or 120 AU) from the center of the central object.[50]
• From the motion of star S2, the object's mass can be estimated as 4.1 million M☉,[51][52] or about 8.2×1036 kg.
• The radius of the central object must be less than 17 light-hours, because otherwise S2 would collide with it. Observations of the star S14[53] indicate that the radius is no more than 6.25 light-hours, about the diameter of Uranus' orbit.
• No known astronomical object other than a black hole can contain 4.1 million M☉ in this volume of space.

Infrared observations of bright flare activity near Sagittarius A* show orbital motion of plasma with a period of 45±15 min at a separation of six to ten times the gravitational radius of the candidate SMBH. This emission is consistent with a circularized orbit of a polarized "hot spot" on an accretion disk in a strong magnetic field. The radiating matter is orbiting at 30% of the speed of light just outside the innermost stable circular orbit.[54]

On January 5, 2015, NASA reported observing an X-ray flare 400 times brighter than usual, a record-breaker, from Sagittarius A*. The unusual event may have been caused by the breaking apart of an asteroid falling into the black hole or by the entanglement of magnetic field lines within gas flowing into Sagittarius A*, according to astronomers.[55]

Detection of an unusually bright X-ray flare from Sagittarius A*, a supermassive black hole in the center of the Milky Way galaxy.[55]

Outside the Milky Way[edit]

See also: List of most massive black holes

Artist's impression of a supermassive black hole tearing apart a star. Below: supermassive black hole devouring a star in galaxy RX J1242-11 – X-ray (left) and optical (right).[56]

Unambiguous dynamical evidence for supermassive black holes exists only in a handful of galaxies;[57] these include the Milky Way, the Local Group galaxies M31 and M32, and a few galaxies beyond the Local Group, e.g. NGC 4395. In these galaxies, the mean square (or rms) velocities of the stars or gas rises proportionally to 1/r near the center, indicating a central point mass. In all other galaxies observed to date, the rms velocities are flat, or even falling, toward the center, making it impossible to state with certainty that a supermassive black hole is present.[57] Nevertheless, it is commonly accepted that the center of nearly every galaxy contains a supermassive black hole.[58] The reason for this assumption is the M-sigma relation, a tight (low scatter) relation between the mass of the hole in the 10 or so galaxies with secure detections, and the velocity dispersion of the stars in the bulges of those galaxies.[59] This correlation, although based on just a handful of galaxies, suggests to many astronomers a strong connection between the formation of the black hole and the galaxy itself.[58]

Hubble Space Telescope photograph of the 4,400 light-year long relativistic jet of Messier 87, which is matter being ejected by the 6.4×109 M☉ supermassive black hole at the center of the galaxy

The nearby Andromeda Galaxy, 2.5 million light-years away, contains a (1.1–2.3)×108 (110–230 million) M☉ central black hole, significantly larger than the Milky Way's.[60] The largest supermassive black hole in the Milky Way's vicinity appears to be that of M87, at a mass of (6.4±0.5)×109 (c. 6.4 billion) M☉ at a distance of 53.5 million light-years.[61][62] The supergiant elliptical galaxy NGC 4889, at a distance of 336 million light-years away in the Coma Berenices constellation, contains a black hole measured to be 2.1×1010 (21 billion) M☉.[63]

Masses of black holes in quasars can be estimated via indirect methods that are subject to substantial uncertainty. The quasar TON 618 is an example of an object with an extremely large black hole, estimated at 6.6×1010 (66 billion) M☉.[64] Its redshift is 2.219. Other examples of quasars with large estimated black hole masses are the hyperluminous quasar APM 08279+5255, with an estimated mass of 2.3×1010 (23 billion) M☉, and the quasar S5 0014+81, with a mass of 4.0×1010 (40 billion) M☉, or 10,000 times the mass of the black hole at the Milky Way Galactic Center.

Some galaxies, such as the galaxy 4C +37.11, appear to have two supermassive black holes at their centers, forming a binary system. If they collided, the event would create strong gravitational waves.[65] Binary supermassive black holes are believed to be a common consequence of galactic mergers.[66] The binary pair in OJ 287, 3.5 billion light-years away, contains the most massive black hole in a pair, with a mass estimated at 18 billion M☉.[67] In 2011, a super-massive black hole was discovered in the dwarf galaxy Henize 2-10, which has no bulge. The precise implications for this discovery on black hole formation are unknown, but may indicate that black holes formed before bulges.[68]

On March 28, 2011, a supermassive black hole was seen tearing a mid-size star apart.[69] That is the only likely explanation of the observations that day of sudden X-ray radiation and the follow-up broad-band observations.[70][71] The source was previously an inactive galactic nucleus, and from study of the outburst the galactic nucleus is estimated to be a SMBH with mass of the order of a million solar masses. This rare event is assumed to be a relativistic outflow (material being emitted in a jet at a significant fraction of the speed of light) from a star tidally disrupted by the SMBH. A significant fraction of a solar mass of material is expected to have accreted onto the SMBH. Subsequent long-term observation will allow this assumption to be confirmed if the emission from the jet decays at the expected rate for mass accretion onto a SMBH.

A gas cloud with several times the mass of the Earth is accelerating towards a supermassive black hole at the centre of the Milky Way.

In 2012, astronomers reported an unusually large mass of approximately 17 billion M☉ for the black hole in the compact, lenticular galaxy NGC 1277, which lies 220 million light-years away in the constellation Perseus. The putative black hole has approximately 59 percent of the mass of the bulge of this lenticular galaxy (14 percent of the total stellar mass of the galaxy).[72] Another study reached a very different conclusion: this black hole is not particularly overmassive, estimated at between 2 and 5 billion M☉ with 5 billion M☉ being the most likely value.[73] On February 28, 2013 astronomers reported on the use of the NuSTAR satellite to accurately measure the spin of a supermassive black hole for the first time, in NGC 1365, reporting that the event horizon was spinning at almost the speed of light.[74][75]

Hubble view of a supermassive black hole "burping".[76]

In September 2014, data from different X-ray telescopes has shown that the extremely small, dense, ultracompact dwarf galaxy M60-UCD1 hosts a 20 million solar mass black hole at its center, accounting for more than 10% of the total mass of the galaxy. The discovery is quite surprising, since the black hole is five times more massive than the Milky Way's black hole despite the galaxy being less than five-thousandths the mass of the Milky Way.

Some galaxies, however, lack any supermassive black holes in their centers. Although most galaxies with no supermassive black holes are very small, dwarf galaxies, one discovery remains mysterious: The supergiant elliptical cD galaxy A2261-BCG has not been found to contain an active supermassive black hole, despite the galaxy being one of the largest galaxies known; ten times the size and one thousand times the mass of the Milky Way. Since a supermassive black hole will only be visible while it is accreting, a supermassive black hole can be nearly invisible, except in its effects on stellar orbits.

In December 2017, astronomers reported the detection of the most distant quasar currently known, ULAS J1342+0928, containing the most distant supermassive black hole, at a reported redshift of z = 7.54, surpassing the redshift of 7 for the previously known most distant quasar ULAS J1120+0641.[77][78][79]