Expert: James Gort - 5/8/2007

Question
Hi James,

Thanks very much for the hint for the last problem... I'm struggling on another that I hope you can give me a hand with.

The question is:
This problem requires you to look at the predicted observables for an accretion disk around a
black hole binary, A0620-00. Use the equation from your notes which relates temperature to radius
T(r), to plot 2 log-log graphs:
(1) disk temperature as a function of radius r
(2) peak temperature of the black body spectrum as a function of r.

Using the formula:
T=(GMM'/8pi(sbc)R^3)^(1/4) * (R/r)^(3/4)
for the first log-log graph I plotted T from the above equation vs r/Rs (Rs = swarzchild radius of the black hole) and obtained an almost straight but slowly decreasing line... How do I know if this is the expected outcome or not? I'm a little confused by the theory and consequently uncertain of what to expect...

For part 2 I'm confused about how to obtain the peak temperature of the black body spectrum... Wien's law would give me a temperature for a given wavelength, but I have nothing to determine the wavelength from...

Any tips would be appreciated!

Answer
Hi Loz,

1)  Without plugging in actual numbers, I would guess that your graph has the right form.  For problems such as these, make sure it makes sense in the extremes - i.e., when r=R and when r>>R.

2)  Don't always look for an equation to "plug in".  Think about what's being asked.  To get the maximum T, simply differentiate T with respect to r, and set that equal to zero!

If I can get across only one thing, it's to think about what's being asked, and not trying to just pick the right equation.

Hope that helps.

Prof. James Gort