300. Event horizon of Sgr A*
ASTRO — By Dmitry Podolsky on March 11, 2009 at 4:05 pm
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Dear friends,
I am really sorry for leaving you without a physics post (the video clearly cannot be counted 
) – the reason was my faulty internet connection. The post that you will see below was almost ready but I wanted to make a short last check before it gets posted, and that’s when my faithful internet provider decided to cut me out. Anyway, all this just means that today you are going to have two nice posts instead of one.
By the way, I cannot help acknowledging the very fact that this post’s number is 300 (while 200th wasn’t that long time ago)… Why this observation did make me happier, another thing which made my day yesterday is the paper by Avery Broderick (CITAzen!), Abraham Loeb and Ramesh Narayan titled “The event horizon of Sagittarius A*“.
About two months ago we had a discussion of BH physics with Ervin Goldfain. At some point he argued that “as explained to me by Sabine Hossenfelder, astrophysical data alone cannot settle the issue of where the BH entropy is coming from.” What we are going to talk about in this post is the first robust conclusion based on astrophysical data alone that Sagittarius A*, a compact object in the center of our Galaxy, has all features intrinsic to black holes – for example, event horizon. As Brits say, if it walks like a duck and quacks like a duck, then it must be a duck.
So, as I said, Sagittarius (Sgr) A* is an extremely bright (in radio waves) compact object in the center of the Milky Way which is believed to a supermassive black hole. (By the way, the Milky Way center is hidden from us by the dust cloud, and in order to study it we have to use wavebands other than optical: IR, X-ray and radio). That is how it looks like:
or, on a bit larger scale,
Why do we (or at least many of us) believe that Sgr A* is a black hole? First of all, by studying motion of stars in the vicinity of the Sgr A*, we can determine its mass – and the latter turns out to be about 4 million solar masses. Second, very long base line interferometry (VLBI) instruments currently allow us to estimate the angular size of the very object with rather good precision. The latter is found to be around 27 microarcsecs, which corresponds the linear size of the object about 44 million kilometres (diameter – compare it to 150 million kilometres – distance between the Earth and the Sun).
If you squeeze 4 million Suns into the volume of 22 million kilometres cubed, the outcome of this operation is almost inevitably black hole – although there are other non-BH configurations with the same mass and characteristic linear scale possible, all of them are expected to collapse very rapidly. Indeed, the Schwarzchild radius for the configuration of this mass is
.
This scale is approx. 2 times smaller than the observed scale 22 million km followed from the observations, but we also need to properly take relativistic effects into account – if Sgr A* is indeed a black hole, spacetime around it is strongly curved leading to the gravitational lensing effect (so that its angular size observed from the distance of 26000 ly is quite a bit larger than the actual one). When lensing is accounted for, the only conclusion that can be made is that Sgr A* is indeed a supermassive black hole.
Now, if metastasis of crackpotism have already poisoned your brain, you may be left unhappy since GR was quietly implemented in our considerations (in the estimation of the gravitational lensing effect) What if the underlying theory of gravity is not GR, can we still make a conclusion that Sgr A* is a black hole? (as we remember, existence of BHs is a general phenomenon not intrinsic to just GR) The paper by Broderick et al. shows that the answer to this question is positive.
Their proof that Sgr A* possesses a horizon is based on the following three simple assumptions:
1. Emission from Sgr A* is powered by accretion. This is now generally accepted and indeed sounds quite reasonable even for arrogant non-astrophysicist like myself. Since the population of stars (and matter density in general) is extremely high in the region near the center of the Galaxy, there is no surprise that part of this matter will be captured by the gravitational well of a dense object with a mass of 4 million Suns. Typically, in systems like neutron stars, BH candidates and simply binaries (where one of the components is heavier than the other and pulls matter from it) infalling matter forms a disk around gravitationally attracting body called accretion disk. It can speed up to relativistic velocities and rapidly loose energy due to radiative friction.
The energy released in the process can be very high (like in AGNs, and that is what allows us to detect such systems albeit their angular size being extremely small.
2. Sgr A* lives for a sufficiently long time for the gravitationally attracted matter to achieve a steady state regime of infalling. This is again reasonable since the age of Sgr A* is estimated to be 10 Gyrs, while the correlation time in kinetics of infalling matter is of the order 
.
3. Surface emission from compact object has the blackbody spectrum (in this respect, note that no thermal component is observed in the spectrum of Sgr A*). What surface emission we are talking about? Suppose that Sgr A* is not a black hole (that is, it does not have an event horizon). Instead, say, it is a very large star. In this case, all the gravitational binding energy of the infalling matter should be eventually emitted back into space. Partially, this energy is emitted in the process of accretion due to the radiative friction as we discussed above but some amount of matter certainly reaches the surface of the star and feeds thermonuclear reaction. In this case, the remaining energy should be emitted by the star itself. That is the part of the flux from Sgr A* we are looking for in the data – surface emission.
At the technical level, the authors want to estimate so called radiative efficiency for Sgr A*. What is it? Suppose a massive matter particle falls on Sgr A*, and its gravitational binding energy is reemitted back into space. Let us denote the overall outgoing flux at infinity as 
. Not all the energy is emitted in the form of radiation, but only a certain (small) fraction
.
The flux 
is exactly what we observe by our instruments, and the coefficient 
is called the radiative efficiency. Another part of the gravitational binding energy can be released in the form of outgoing kinetic flows similar, say, to jets perpendicular to the plane of the accretion disk on the picture above; for that part of the energy we can write 
).
We want to estimate 
becuase we know the values of radiative efficiency for many systems such as active galactic nuclei (where 
is of the order 10%), etc. Clearly, it is very hard to get any information about the overall flux from observations, but what ultimately allows us to estimate radiative efficiency for Sgr A* are the accurate recent measurements of the flux from Sgr A* together with its apparent radius/angular size (vua VLBI).
Indeed, we can write for the surface flux (it is blackbody, see the cond. 3 above)
,
so the temperature of bb radiation from Sgr A* (as seen at infinity) will be given by
The surface flux is
,
where 
is the blackbody spectrum. Therefore, we can estimate the maximum possible temperature at the surface of Sgr A* as
and derive a limit upon 
directly as
.
The latter condition can be rewritten in terms of radiative efficiency as
Turning to the results of observations (see the Fig. below), we find that in order for an emitting surface of Sgr A* to exist, it should be expected that 
> 99.6%, that is,
if matter falls onto Sgr A*, somehow 99.6% of the liberated gravitational binding energy must be radiated, powering either the observed luminosity or kinetic outflows. Otherwise the emission of the reminder upon settling onto the surface would have been detected.
Radiative efficiency like 99.6% is way larger than 10% observed for active galactic nuclei, so ultimately we either have to come out with absolutely new revolutionary mechanism of accretion/gravitational binding energy release or say that emitting surface is simply absent, that is, Sgr A* is a black hole.
Let me note that Sgr A* is a pretty much single black hole candidate in this sense, since the angular sizes of other candidates are very far from being determined at this moment, and knowing angular size of the object is crucially important for the Broderick-Loeb-Narayan argument.
Instead of making a conclusion (I am sure this story is very far from the end!), let me briefly mention another argument why the theory being black holes and Sgr A* in particular is most probably GR.
The flux outgoing from Sgr A* exhibits flares in mm, sub-mm, IR and X-ray wavebands (see for example this article in the Oct 2001 issue of Scientific American). These flares are supposed to take place when large chunks of infalling matter reach the black hole and the gravitational binding energy gets released. As it turns out, rise times for flares and variability timescales are compatible to the periods of innermost stable orbits around black holes described by General Relativity. This, however, is another story…
10 Comments
To see how limited progress there has been (or how visionary I have always been), see this 1998 report of mine for an astrophysics class at Rutgers
http://lumajs.googlepages.com/sgr-narayan.pdf
Unedited since 1998. Does your blog post of 2009 go really beyond it? What’s the ten-year difference?
Dear Lubos,
you are extremely visionary. Narayan is even more visionary, since he keeps pushing the subject for decades. Thanks for the link, it is a nice reading.
The ten year difference is experimental, they were able to measure angular size of Sgr A* with relatively large precision only last year, and that is what allows Broderick-Loeb-Narayan to make their strong statement.
Cheers,
Dmitry.
Dear Dmitry,
thanks for the interesting summary. The improving observational skills should be expected – they’re a part of the “brute force” approach. A brute force allows one more direct, straightforward analysis, reducing the role of theorists.
In this sense, I find the models 11 years ago more sophisticated than the present ones. He had to construct things like the two-temperature plasma models. Has it been silently abandoned? It was a dirty phenomenological astrophysics that I never enjoyed too much.
But I think it’s not too controversial to say that spectrum observations of two-temperature plasmas are more sophisticated than measurements of one angular size of the object.
Whether the methods are more advanced or more primitive than they were decade(s) ago, my main point was different, namely that it had to be 99% obvious to everyone who actually knew physics that it had to be a black hole – for some time.
One can really derive that such massive regions simply should collapse into black holes, so it shouldn’t be too surprising. It’s only surprising if one cherishes her own prejudice that black holes perhaps shouldn’t exist. Then almost no amount of evidence can be enough.
Of course, the very same comments apply to many other things that are presented as open. For example, neutrino masses. There are similar course reports of mine about neutrino oscillations and masses. There were surely no doubts about it in 1998. But still, after 2000, it’s presented as a hot question.
These are not coincidences and I didn’t have to be a visionary. It was always very clear, given the existing scientific knowledge that is – or is supposed to be – taught to students that certain things are established by evidence while others are not (I never wrote a paper about an observed effect that would later turn out to be false).
Of course, these things are happening for discoveries to be established in the future, too, like the Higgs. There’s no question that there is some Higgs – the only question is how many, how heavy, how composite (if at all), etc. I think that justifiable experiments must try to get more than just the binary information about the Higgs existence.
And then string theory. Well, yes, it’s a 21st century science that randomly dropped to the 20th century. That used to be a wise saying except that we are already in the 21st century and things should start to become common. I am afraid that with the mass manipulation by mediocre minds in groupthinking media etc., string theory will turn out to be a 25th century science that accidentally dropped among relative Smolin-like chimps of the 20th and 21st century.
Best wishes
Lubos
Dear Dmitry,
Thanks for this informative posting. What is unclear to me is whether the Broderick-Loeb-Narayan argument brings any new and compelling resolution to the issue of BH entropy and the information loss paradox. My feeling is that it might be premature to reach this conclusion, but I may very well be wrong. Recall that the information loss paradox was the main topic of our debate.
Regards,
Ervin
Dear Ervin,
I’ll just repeat what I said once – to determine whether BH has associated geometrical entropy, you only need to prove the presence of event horizon. After that existence of Hawking radiation is a mere fact – quanta are produced in strong gravitational field in the same way they produced in strong electric field (we already discussed it before and I thought that you agree). If Hawking radiation is present, then BH can evaporate, so it will eventually evaporate completely etc. etc.
For Sgr A* the temperature of Hawking radiation would be about
K, so it’s virtually undetectable as you understand, but the argument of undetectability reminds me an old conversation with a guy, who wanted to prove that electrons don’t exist since he is not able to touch them.
Cheers,
Dmitry.
Dear Dmitry,
Are you stating that the information loss paradox is now fully solved by the mere evidence for Hawking radiation ? I may be missing something here, but the paradox, as explained by Hawking himself in 2005 (University of Barcelona, July 5th)refers to the issue of whether or not the information is lost in the process of BH evaporation. In his own words, if quantum gravity is unitary, information is preserved in BH formation and evaporation. If, on the other hand, information is lost, the evolution is non-unitary and pure quantum states decay into mixed states.
So, is information lost or preserved in BH physics?
Regards,
Ervin
Dear Ervin,
as far as I remember, you made the statement that studying BH physics and QCD are very different, because we have a huge body of experimental data confirming QCD and no experimental data confirming existence of black holes, am I right?
I think I never claimed that information paradox is resolved, what I am (and was) saying is that information paradox is as legitimate piece of physics as QCD, which you were arguing with
Cheers,
Dmitry.
Dear Dmitry,
In my view, BH physics and infrared QCD are related in the sense that they both represent strongly coupled field theories (SCFT). As you well know, SCFT is a topic far from being settled since it describes a non-perturbative regime that is far richer in dynamical content than conventional QFT. It is also my view that SCFT cannot be properly dealt with in the traditional framework of equilibrium field theory, Botzmann-Gibbs statistics and Path Integrals. That is why I am always cautious about claims regarding solutions to these complex problems that are built upon conventional QFT.
The advantage that QCD has lies in the availability of experimental data and lattice simulations that match observations. But maybe this is about to change in BH physics with new astrophysical evidence for objects such as Sgr A*.
Regards,
Ervin
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