# Thread: First image of a black hole on April 10, 2019

1. Originally Posted by George
It was not about observing infalling objects. I was demonstrating the big difference in gravitational gradients between BH masses, thus a difference might be discernible for the velocity profile comparison. The question is whether or not, even with perhaps nano-arcsec resolution, what is observed for the BH diameter, along with a velocity profile, will improve distance determinations?
I think I can do some quantitative thought-exercise analysis here. Suppose we have systems A and B, each consisting of a black hole with stars orbiting in close where it is gravitationally dominant. Let B be 10 times as far away as A, but the observed mean orbital velocity is the same at a given angular separation from the central body. Since this is 10 times as much linear orbital radius for B, the centripetal acceleration is 1/10 as great. This is consistent with a central mass 10 times that of A. The event horizon diameters will be in this same proportion, so their angular diameters will be equal. So far, the two systems look alike.

If by velocity profile you mean the orbital velocity as a function of orbital radius, that will be inversely as the square root of the radius for both systems. They still look alike, so with just the data given so far we have no means of determining the distance.

Now let us consider the tidal stress on a star at a given angular separation from the center. That varies in proportion to the central mass and inversely as the cube of the linear separation. So yes, A would be rougher than B on a star at a given angular separation. The challenge would be to use the telescope of our dreams to observe stars close to the centers and look for signs of disruption. If we can do that, we can get more direct distance indicators from statistical analysis of the apparent magnitudes of the stars, as we have been doing for many decades.

If I am missing something in your line of thought, please let me know.

2. Originally Posted by Hornblower
If by velocity profile you mean the orbital velocity as a function of orbital radius, that will be inversely as the square root of the radius for both systems. They still look alike, so with just the data given so far we have no means of determining the distance.
Yep, darn it. Since the math isn't that hard, I crunched some numbers....

Comparing a 1 million sol mass BH to a 10 million sol mass BH gives an EH radius (or Shadow radius) of 10x for the more massive BH. At, say, 100 AU, the 1M BH will have velocities of about 30,000 kps and the 10M BH at 100 AU will have velocities of about 95,000 kps. But when we match for angular scaling, we get the same velocities. The 100M BH extended to 10x the distance (for our angular match) will have the 30,000 kps velocity at 1000 AU (10x the 100AU of the 1M mass BH).

Only if the mass of the BH is predetermined can the shadow size be useful, though it would be nice to have this as perhaps the only direct form of distance measurement in the tool box. My guess that the velocity profile could be useful seems highly unlikely after all.

3. Originally Posted by antoniseb
I had thought that they were going to do Sgr A* as their first target. M87's is 1/3 the angular diameter of our central black hole. I am guessing this means that Sgr A* is too inactive to produce an interesting telltale image.
Hurray for the EHT team for their huge effort to get this image!
It sounds like Sgr A* is next on the list nonetheless, using essentially the same techniques.

4. Order of Kilopi
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Originally Posted by Fiery Phoenix
It sounds like Sgr A* is next on the list nonetheless, using essentially the same techniques.
I think someone mentioned earlier but the big issue with SgrA* is mainly its variability. Over the long data collection times and repeat observations this effectively adds in noise, making the reconstruction poorer. Mainly because your assumption that you are looking at the same 'object' every time breaks down if it varies too much.

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