The Black Hole in the Center of our Galaxy

[lpetrich]

There is a very massive and compact object in the center of our Galaxy,  Sagittarius A* (A-star), or Sgr A* for short. Strictly speaking, that is a radio source near our Galaxy's central object, as it may be called.

That central object's presence is inferred from the approximately Keplerian orbits of several stars near it. These stars have been observed in infrared light, since visible light cannot get through all the interstellar dust and gases in the way. Two of them have been observed around their entire orbits:  S2 (star) or S0-2 in 15.6 years,  S0-102) in 11.5 years. Both stars orbit in highly eccentric orbits, with eccentricities 0.876 and 0.62.

For S2, radial-velocity observations have been made, and these observations have been used to do "dynamical parallax", finding the parallax across S2's orbit instead of the Earth's. This gives a distance of around 8 kiloparsecs or 26,000 light years, in close agreement with other methods. This also indicates a mass of the central object of around 4 million solar masses.

S2's average distance is around 970 AU's or 5.6 light days. But it approaches as close as 120 AU's or 17 light hours. When it is that close, it travels at 7400 km/s relative to the central object, or 2.5% of c.

Update on S2, the star plunging past the Milky Way's black hole | Space | EarthSky, Astronomers Discover S0-2 Star is Single and Ready for Big Einstein Test W. M. Keck Observatory, Investigating the Binarity of S0-2: Implications for Its Origins and Robustness as a Probe of the Laws of Gravity around a Supermassive Black Hole - IOPscience

At least with no companion more than a tenth its mass. Astronomers hope to observe S2's gravitational redshift as it goes through pericenter this year. If they do so, then they may be able to see other "post-Newtonian" effects, like its GR pericenter precession. Such tests may be contaminated by the gravitational influences of nearby stars, like white dwarfs and neutron stars and the current upper limit on those is about 1% of the mass of the central object.

 

[lpetrich]

Another approach is to observe stars somewhat farther from the central object, out to 1 parsec (3.26 light years or 206,000 AU's): [0902.3892] The nuclear star cluster of the Milky Way: proper motions and mass. This gives a mass close to other estimates for the central object.

So we have to think of something that has 4 million times the Sun's mass while being smaller than 120 AU's, a little more than the current distance of TNO Eris from the Sun. It is hard for that object to be anything other than a black hole, because if it was a cluster of neutron stars, those objects would run into each other and coalesce into a few black holes -- or one. White dwarfs would do this even quicker.


One can look closer, but very indirectly, with quasi-periodic oscillations of the luminosity of what is presumably the black hole's accretion disk. These have been observed in several X-ray binary stars: [1603.07885] Quasi periodic oscillations in black hole binaries, [1701.01760] Constraining black hole spins with low-frequency quasi-periodic oscillations in soft states, "Stable" Quasi-periodic Oscillations and Black Hole Properties from Diskoseismology - IOPscience, [1603.07366] Models of quasi-periodic oscillations related to mass and spin of the GRO J1655-40 black hole They have also been observed in some active galactic nuclei: [1510.01111] Quasi periodic oscillations in active galactic nuclei, [1601.07639] Detection of a possible X-ray Quasi-periodic Oscillation in the Active Galactic Nucleus 1H~0707-495, [1009.3615] Modeling the time-resolved quasi-periodic oscillations in AGNs

If you have guessed where this discussion may be leading to, you are correct. I recently found Calculating the Spin of Black Hole Sagittarius A*, and that article linked to [1306.2033] Spin and mass of the nearest supermassive black hole, the one in our Galaxy, observed in X-rays and the near infrared. Author Vyacheslav I. Dokuchaev found a mass of 4 million solar masses, close to other estimates, and a relative rotation rate of about 0.65. The latter quantity is dimensionless, and is (angular momentum) / (mass)^2 for c = G = 1.


Can the gravitational effects of this rotation be observed on nearby stars like S2? [0906.2226] On post-Newtonian orbits and the Galactic-center stars addresses that question, and finds rather disappointing results. While post-Newtonian effects from the mass are about O(v/c)^2, about 6*10^(-4) for S2, those from rotation are O(v/c)^3, about 10^(-5) for S2. This is close to what nearby stars do.

 

[lpetrich]

Let's consider observing this black hole. I have found discussions of plans for an "Event Horizon Telescope", coordinating several telescopes to do VLBI in millimeter wavelengths.

• Sgr A*: 4 million solar masses, black-hole angular radius = 10 microarcseconds
• galaxy M87: 6.6 billion solar masses, black-hole angular radius = 7.5 microarcseconds

The EHT would do about 20 - 30 microarcseconds.

So we are almost there. Space-based VLBI can have much longer baselines, and thus much better resolution.


But let's say that we went to our Galaxy's central object.

First, the distance to Alpha Centauri, about 1.3 parsecs of 4.2 light years. The central object's BH radius would be 60 milliarcseconds. One would need a big telescope to see it.

Let's now go to star S2. It spends most of its time at about 1000 - 2500 AU from the central object, but its closest is 120 AU. So over much of S2's orbit, the BH radius would be 7 - 17 seconds of arc, easily resolvable with a small telescope. At its closest, it is 2 minutes of arc, close to our eyes' resolution and very easily visible with binoculars or a small telescope.

At the Earth's distance from the Sun, the BH radius would be about 5d, about the width of one's hand at arm's length. One would orbit it every 4 hours, so one could easily watch the BH pass in front of the stars.

The closest one could orbit is about 0.12 times the Earth's distance from the Sun, with a period of around 11 minutes. The black-hole radius itself is 0.08 times that distance, and if one gets closer to that, one will not be able to escape. Instead, one will spend the next few minutes falling in without noticing very much that is different until the last second. That is when one will be squeezed and stretched to oblivion.


As to what the stars will look like around a black hole, the BH won't simply look like some black disk. The stars will look pushed outward near it, and stars' light going near it may travel around the BH a few times before escaping. This will make a glowing ring around the BH.

 

[Loren Pechtel]

Sagittarius A* really sucks.

 

[lpetrich]

Getting into a low orbit around a black hole will be *very* difficult. That is because one will be orbiting at some sizable fraction of c, and it's very hard to get that much delta-V (velocity change). One would have to do what the Galileo, Cassini, and Juno spacecraft have done with Jupiter and Saturn: go into a very eccentric orbit.

Even so, there is a minimum closest distance where one can escape again. It is
rmin = (2*rmax*rbh)/(rmax - rbh)

where rmax is the maximum distance in the orbit and rbh is the black-hole radius. For rmax = rmin, we get the closest stable circular orbit, at 3*rbh. For rmax at infinity, one gets rmin = 2*rbh. One can get closer if one was traveling faster at long distances, but the limit there is if one is traveling at c. One's closest distance will be (3/2)*rbh, and one's impact parameter will be (3*sqrt(3)/2)*rbh. That is the distance where one aims at when at long distances.


One's orbital velocity will be sqrt( (rbh/2) / (r - rbh) ) * c for a circular orbit at distance r. This is c/2, c/sqrt(2), and c for r = 3*rbh, 2*rbh, (3/2)*rbh.