Black Holes: Some Recent Observations

[lpetrich]

Not directly, of course, but from their gravity.

The Gaia satellite recently detected evidence of three black holes, though very indirectly. It is an astrometric satellite, one designed to make precision measurements of the angles between stars. It does so repeatedly, and from repeated observations of each star, one can find

• Parallax from the Earth's orbit
• Angular velocity (proper motion)
• Being pulled on by another celestial body

Gaia has observed a large number of binary stars - Gaia Data Release 3 - Astrometric binary star processing | Astronomy & Astrophysics (A&A) - and also an exoplanet - HIP 66074 | NASA Exoplanet Archive - though Gaia's data may contain evidence of many more - [2403.08226] Astrometric detection of exoplanets

Among Gaia's discoveries are these binary stars with black holes in them (distance, BH mass, major axis, period, eccentricity, companion mass, companion radius, companion luminocity, companion surface temperature):

•  Gaia BH1 - 1,560 ly, 478 pc - 9.62 Ms - 1.40 AU - 185.59 d, 0.508 y - 0.451 - 0.93 Ms - 0.99 Rs - 1.06 Ls - 5,850 K (Sunlike)
•  Gaia BH2 - 1,276.7 ly, 4.96 pc - 8.94 Ms - 4.96 AU - 1276.7 d, 3.495 y - 0.5176 - 1.07 Ms - 7.77 Rs - 24.6 Ls - 4,604 K (red giant)
•  Gaia BH3 - 1,930 ly, 591 pc - 32.70 Ms - 16.17 AU - 4253.1 d, 11.644 y - 0.7291 - 0.76 Ms - 4.936 Rs - 16.3 Ls - 5,212 K (red giant)

Neither of the first two black holes have any observable X-ray emissions: [2311.05685] No X-Rays or Radio from the Nearest Black Holes and Implications for Future Searches Other observed ones do have such emissions: Observed Black Hole Masses | stellarcollapse.org Like  Cygnus X-1 a 21-solar-mass black hole which orbits a blue giant star called HDE 226868. These emissions come from material from the companion star falling onto the BH.

 

[lpetrich]

The Event Horizon Telescope is not any one radio telescope, but several radio telescopes whose signals are combined to create the effect of a single Earth-sized telescope. That makes it possible for the EHT to resolve the event horizons of the black holes that it has observed so far, the two with the largest angular size of event horizon: the central black holes of our Galaxy (Sgr A*) and of M87 (M87*).

These most recent observations were done by looking for radio-wave polarization, and this polarization is a probe of the magnetic fields at the emitting electrons. These fields make the electrons orbit their field lines, making those electrons' emissions polarized.

March 24, 2021:
Astronomers Image Magnetic Fields at the Edge of M87’s Black Hole | Event Horizon Telescope
Harvard, Smithsonian Astronomers Help Capture First Image of Black Hole’s Magnetic Fields | Center for Astrophysics | Harvard & Smithsonian
and
March 27, 2024:
Astronomers Unveil Strong Magnetic Fields Spiraling at the Edge of Milky Way’s Central Black Hole | Event Horizon Telescope
Astronomers Unveil Strong Magnetic Fields Spiraling at the Edge of Milky Way’s Central Black Hole | Center for Astrophysics | Harvard & Smithsonian

A remarkable result is that the accretion disks of Sgr A* and M87* are very similar in structure, despite M87* being 1,500 times more massive than Sgr A*.

 

[steve_bank]

This may be the book I read on amateur radio astronomy. From the American Radio Relay League,.

https://www.amazon.com/Amateur-Radio-Astronomy-John-Fielding/dp/1905086164

People build their own antenna arrays.

 

[lpetrich]

General-relativity effects have been observed in the orbit of one of the closest stars to  Sagittarius A* (Sgr A*) --  S2 (star) -- a blue giant

This star's orbit:
Period = 16.0518 years (astronomers use Julian years of 365.25)
Major axis = 995.68 AU (observed angular) 0.12540"
Mean orbital velocity = 1847.55 km/s = 0.0061628 c
Eccentricity = 0.88466
Distance range = 114.84 to 1876.52 AU
Velocity range = 457.06 km/s to 7468.3 km/s = 0.0015246 to 0.024912 c (1/40 c)


Black-hole masses: Gaia BH3: 32.70 Msun, Sgr A*: 4.297*10⁶ Msun, M87*: 6.5*10⁹ Msun
Black-hole (Schwarzschild) radii: Earth: 8.87 mm, Sun: 2.953 km, Gaia BH3: 98.6 km, Sgr A*: 0.0848 AU, M87*: 130 AU


From observations of S2's radial velocity and angular separation:
A Geometric Determination of the Distance to the Galactic Center - IOPscience - 2003 October 24

Distance: 7,940 parsecs = 25,900 light years.

Detection of the gravitational redshift in the orbit of the star S2 near the Galactic centre massive black hole | Astronomy & Astrophysics (A&A) - 26 July 2018
Relativistic redshift of the star S0-2 orbiting the Galactic Center supermassive black hole | Science - 25 Jul 2019

Both teams found agreement with general relativity to within 20%, or at least special relativity with the equivalence principle (gravity ~ inertia).


Detection of the Schwarzschild precession in the orbit of the star S2 near the Galactic centre massive black hole | Astronomy & Astrophysics (A&A) - 16 April 2020

They also find agreement to within 20%. But unlike redshift, precession is cumulative, so with more observations, one can get stronger results.

This precession was first observed in the planet Mercury's orbit, which precesses about 43"/cy more than what one finds from the gravitational pulls of the other planets on that planet. It is also observed in binary pulsars.

 

[lpetrich]

First gravitational-wave detection of a mass-gap object merging with a neutron star - Northwestern Now - "The ‘mass gap’ might be ‘less empty than previously thought,’ researcher says"

The LIGO-Virgo-KAGRA collaboration detected the signal from GW230529 in May 2023, shortly after the start of its fourth observing run. By analyzing the signal, astrophysicists determined it came from the merger of two compact objects: One with a mass between 1.2 to 2.0 times the mass of our sun and the other with a mass between 2.5 to 4.5 times the mass of our sun. The researchers say the less massive object likely is a neutron star and the more massive object is potentially a black hole. But scientists are confident the more massive object is within the mass gap.

[2210.00425] On the Neutron Star/Black Hole Mass Gap and Black Hole Searches - the mass gap is between the most massive known neutron stars at around 2 Msun and the least massive known black holes at around 5 Msun (rather approximate numbers).

 Tolman–Oppenheimer–Volkoff limit also mentions that mass gap. Computing that limit from stellar-structure theory is very difficult, because nucleons, protons and neutrons, interact very strongly with each other, unlike for a similar limit for white dwarfs, the  Chandrasekhar limit where electrons and nuclei are close to non-interacting.

There is now a sizable  List of gravitational wave observations They are mostly very distant objects, in the billions of light-years away, and most parent objects observed so far are black holes, with the rest being neutron stars and mass-gap objects.

 

[lpetrich]

For inspiral, most of the observations are of the last half-second, and after the merger, the resulting black hole "rings" for a short time more.

With more than one observation of some event, one can find the direction of the event's source. With two, it is in a ring in the sky, with three, it is two points, and with four or more, one has more than enough data, and one can see if one has a good fit.

 Gravitational-wave astronomy and  Gravitational-wave observatory -- these are two long tubes with mirrors at their ends. A laser beam is split in two and sent down each tube, then combined when it returns. This combination will make interference, and this interference is watched for evidence of one tube getting stretched or squeezed relative to the other.

The G-wave observatories that have detect G-waves are

•  LIGO at Hanford WA and Livingston LA in the US
•  Virgo interferometer at Pisa, Italy

As with position, more observations of an event can give us a better idea of the polarizations of G-waves. In GR, there are two possible polarizations, much like the polarizations of EM waves. In the EM case, looking along the direction of motion:

Linear: a combination of

• horizontal: left, then right
• vertical: up, then down

Circular: combination of these modes in sequence

• up, left, down, right
• up, right, down, left

These are all transverse, with no longitudinal component, a component along the direction of motion.

In GR, G-waves make stretching, squeezing, and shearing:

• horizontal stretch vertical squeeze, then horizontal squeeze vertical stretch
• diagonal 1 stretch diagonal 2 squeeze, then diagonal 1 squeeze diagonal 2 stretch

Circular polarization is combinations of these modes in sequence analogous to EM circular polarization.

This set of modes is called transverse traceless (TT). Alternatives to GR often have more possible modes, like horizontal and vertical together stretch then together squeeze, transverse-longitudinal diagonal stretch then squeeze, and all-longitudinal stretch then squeeze.

With more than two observations of G-waves, one can look for departures from TT, though for a full test, one will need at least six observations.

 

[lpetrich]

I'll now consider the prospects of observing black hole Sgr A* from star S2.  Main sequence - for definiteness, I will make it a B0V (main-sequence) start, with mass 18 Msun, radius 7.4 Rsun, luminosity 20,000 Lsun, and temperature 30,000 K.

One would have to be in orbit around S2, but what would be a good distance? From  Wien's displacement law the peak emission of S2 is at 100 nm, compared to the Sun at 500 nm. That's well within the ultraviolet range, at the short end of UV-C, and its visible light is mostly bluish.

To get where its flux of light equals the average of the Sun on the Earth, one will need to be 140 AU away. The star will be about 1.6 arcminutes across, barely resolvable without a telescope. Its light will be dangerous; one can easily get a bad case of sunburn (starburn?) from it.

One will orbit with a period of 400 years, and since that is much longer than S2's period around Sgr A*, one's orbit will not be stable.

Even so, Sgr A*'s angular diameter will not be very great. Using its Schwarzschild diameter, it has minimum 0.3', mean 0.6', maximum 5' (arcminutes). Multiplying by 3*sqrt(3)/2 to get the minimum observable angular distance of anything beyond it, I find minimum 0.8', mean 1.5', maximum 13' (arcminutes).

The BH's gravitational-lens effect will be much larger, and a star directly behind the BH will look like a ring around it, an  Einstein ring Its radius is the  Einstein radius and it has minimum 0.54d, mean 0.75d, and maximum 2.20d (degrees of arc) -- about 4 times the angular size of the Sun and the Moon. So one will see its lensing.

 

[lpetrich]

I will now turn to what the Solar System would be like with Gaia BH3 in its orbit around its companion. For definiteness, I will make its mass 16 Msun, its distance 16 AU, and its eccentricity 0.451. It will have period 11.1 years.

It would make the orbit unstable of anything between Mars and the Oort cloud. The inner Solar System would remain but the outer Solar System would not exist. In its main-sequence days, it would have been a blue giant, and it would have lasted only a few million years. But that would have been enough to keep the inner Solar System from forming in anything like its actual form, with temperatures there of some 1,000 - 2,000 K.

Leaving that aside, what would the BH look like?

Its Schwarzschild radius would be 47 km, and its minimum-passing-light diameter 3*sqrt(3) this or 246 km. Its size would be minimum 15, mean 21, maximum 39 milliarcseconds.

But its gravitational-lens effect would be much larger, with Einstein radius minimum 0.57', mean 0.68', maximum 0.92' (arcminutes), at the limit of human visual acuity. But that effect should be easily visible in a small telescope.

 

[lpetrich]

I will now consider gravitational lensing.

First, the Schwarzschild or black-hole radius for mass M, gravitational constant G, and speed of light c:

\( \displaystyle{ R_{bh} = \frac{2GM}{c^2} } \)

For initial angle a_src, final angle a_obs, and impact parameter b

\( \displaystyle{ a_{obs} = a_{src} + \frac{2R_{bh}}{b} } \)

The impact parameter is \( \displaystyle{ b = D a_{obs} } \)

where D is the reduced distance: D(src-mass) * D(mass-obs) / D(src-obs) very close to D(mass-obj) if D(src-mass) >> D(mass-obj). That gives us

\( \displaystyle{ a_{obs} = a_{src} + \frac{2R_{bh}}{D a_{obs}} = a_{src} + \frac{(a_{ring})^2}{a_{obs}} } \)

where the Einstein-ring radius is

\( \displaystyle{ a_{ring} = \sqrt{ \frac{ 2R_{bh} }{ D } } } \)

Note that a_ring >> R_bh / D unless D is not much greater than R_bh. So one will see a ring around the black-holey effects except if the source is close to the BH, like an accretion disk.

If an object is behind the mass, with a_src = 0, then a_obs = a_ring and one sees a ring around the mass.

 

[lpetrich]

There are two solutions, one for the light coming nearly directly and one for the light making a detour around the mass:

\( \displaystyle{ a_{obs} = \frac12 \left( a_{src} + \sqrt{(a_{src})^2 + (2 a_{ring})^2} \right) } \)
and
\( \displaystyle{ a_{obs} = \frac12 \left( a_{src} - \sqrt{(a_{src})^2 + (2 a_{ring})^2} \right) = \frac{ 2(a_{ring})^2 }{ a_{src} + \sqrt{(a_{src})^2 + (2 a_{ring})^2} } } \)

with long-distance limits

\( \displaystyle{ a_{obs} \to a_{src} + \frac{(a_{ring})^2}{a_{src}} ,\ a_{obs} \to \frac{(a_{ring})^2}{a_{src}} } \)

The relative luminosity of each image is

\( \displaystyle{ L = \frac{ (a_{obs})^2 }{ a_{src} \sqrt{(a_{src})^2 + (2 a_{ring})^2} } } \)

with asymptotic values

\( L \to 1 \) and \( \displaystyle{ L \to \left( \frac{a_{ring}}{a_{src}} \right)^4 } \)

Which adds to the difficulty of seeing black-holey effects in light deflection. Images close to the black-hole radius will be very faint.