How to measure the diameter of a star?

Question

I am thinking about something I read somewhere (if only I could find it again) in a textbook. It is about the size of a star and its ER peaks. It has to do with the waves coming off the edge (maybe) and arriving later than those from "head on" and therefore you can know something about its diameter.

It has been puzzling me but I can't quite remember it. Just yesterday I was reading about a black hole that pulses at a minimum of 10 minutes and so it is at least 10 light-minutes across. (I probably am not getting it just right, but help me out!) Is this the same principle?

Anyone know what I'm talking about? I would love to have this explained and/or would like to know what it is called, so I can look it up.

Answer 1

In the first case, in regards to star measurement, I believe you're thinking of how the diameter of very large stars are measured using interferometry. Because light waves from the edges of these stars arrive at us in parallel, and they are waves, we can determine the diameter of the star by measuring the interference pattern between these light waves. (That's probably what you were thinking of — the "peaks" and "troughs" in the interference pattern.)

Stars like Betelgeux, Antares and Aldebaran have been measured in this way and the size agrees with the Stefan–Boltzmann law which can be used to calculate the radius of a spherical body if the luminosity and temperature are known.

I found this 1921 Popular Science article which describes it in detail.

The black hole pulsing thing is a completely different concept. I'm not sure what the logic of that is, perhaps it was talking of the doppler shifts of light rotating around the black hole or its interaction with a binary companion star?

Answer 2

I don't know what "ER peaks" means, but I think I get the idea. (Did you mean "EM", i.e., electromagnetic?)

Suppose you see a spiral galaxy that's 100,000 light-years across, and you're seeing it nearly edge-on. Suppose the entire galaxy's brightness increases and decreases significantly with a 1-year cycle.

It's not possible (or rather, it's vanishingly unlikely) that this is the result of all the stars pulsating in unison. The near edge of the galaxy is 50,000 light-years closer to us than the center, which is 50,000 light-years closer than the far edge. That means that the light that we're seeing now from the far edge must have originated 100,000 years sooner than the light we're seeing now from the near edge. Since nothing can travel faster than light, there is no natural phenomenon that could keep all the stars over that 100,000 light-year expanse synchronized with each other. And even if there were, they would appear to be synchronized only as seen from one particular direction.

If a 100,000 light-year galaxy appears to pulse with a 1-year cycle, then the pulses are coming from a much smaller body, probably at the galaxy's core. And that body is probably substantially smaller than 1 light-year, because the waves within it that cause it to pulsate are probably moving substantially slower than the speed of light.

If you see a light source pulsating with a 1-year cycle, then it must be less than 1 light-year across. If it's any bigger, then (a) whatever waves cause it to pulsate will take more than a year to cross it, so it can't stay synchronized with itself, and (b) even if it could, the pulses would be "blurred out" because we simultaneously see parts of the light source at different distances.

In your example, you got it backwards. If a black hole visibly pulses on a 10-minute cycle, then the body that's emitting the light must be smaller than 10 light-minutes.

Answer 3

To calculate the linear diameter of a star, we need only to know its effective temperature, the bolometric correction, and its absolute magnitude. And if, instead of the absolute magnitude, we know the apparent diameter can then calculate the angle.

The formula used to determine the size of a star appeared in Article Stellar Masses of Daniel M. astrnomo Popper (Annual Review of Astronomy & Astrophysics, edition 1980, pages 115-164). Although this Article does not address the issue of diameter SPECIFIC $star-ms$ well, the calculation of the mass in type eclipsing binary systems, the data offered by Popper and ecuations are $ m $ $ s $ it appropriate to get a good aproximacin the diameter of a star. The formula is:

$$Mv= log R = -0.2 - + 0.2 2Fv C1$$ where log represents the logarithm function in base 10, R is the radius of the star expressed in solar units (or equally, the diameter, since it is not an absolute figure, but comparative) $Mv$ is the absolute magnitude of the star (in V filter), $Fv$ is a function of luminosity per unit area, and solar $C1$ is a constant whose value is approximately 42.3615 (Popper uses the value of $42 255$). i hope to be usefull.