How Do You Calculate Astronomical Magnitudes and Photon Count Rates?

[big man]

Hey I've been practicing these example questions that our lecturer gave us as part of the preparation for the upcoming exam. I'd appreciate any help. I find it really difficult to do his work because his lecture notes barely explain anything. It would have been nice to have a textbook for the unit but we don't...
Anyway sorry if this is too simple and is in the wrong section.

1. The Keck I telescope was used to detect an object with V~30. Estimate the photon count rate for this detection.

Thoughts: I don't really know how to do this question exactly. I think you'd need the area of the telecope to find the collecting area. The equations of magnitude show that you need the ratio of the flux from the object to a reference flux. So I guess if I knew a reference flux then I could easily find the flux of the object, but I don't so I'm not too sure.

Edit: Actually I was thinking that maybe I could use the apparent magnitude of the sun along with the apparent magnitude of the object. You know the amount of energy per square metre from the sun and you know the area of the telescope so you can find the energy/sec incident on the telescope. Then to find the number of counts per second you'd just divide that value by the energy of a photon...although the visible light has a range of wavelengths so do I just choose a wavelength??

2. A millimagnitude is 1/1000 of a magnitude. Using Excel, plot how many millimagnitudes correspond to an n percent increase in brightness, where n=1,2...20. Ignore the sign. Give a rule-of-thumb concerning the percentage brightness and millimagnitudes.

Thoughts: For this question I used the formula $$m=2.5*log(L/L_0)$$. Since it said it wanted thenumber of millimagnitudes per percentage increase in brightness, I determined m for each percentage increase. That is for 1% $$L/L_0=1.01$$. Then to find the number of millimagnitudes I just multiplied the calculated m value for the percentage increase by 1000. I get a logarithmic function so it kind of looked semi-ok...I'm really not sure if what I've done is right though.

3. A B star is known to be located behind the Coal Sack (a 20pc thick dark cloud of dust and gas near the southern cross) 1.5 kpc from the sun. Its V was measured to be 10.0 and Mv is known to be -4.0. What is the absorption due to the coal sack alone?? (b) What is the absorption in magnitudes/pc? What is the colour excess??

Thoughts:With this question I was wondering if you could just use the distances of 1.5kpc and 1.5kpc - 20pc to find the absorption using the equation: $$m-M=5*log(d/10pc) + A$$
Where A is your extinction. Then obviously you subtract the value from 1.5kpc - 20pc from the 1.5kpc value. However, I don't think that's right because you aren't really taking into account a greater amount of absorption from the cloud...or don't you bother? For part (b) I can find the colour excess given that you have the absorption based on the relationship $$A_v/C_e_x_t=3$$, but yeah I don't really understand the absorption thing. I mean I'm sure you'd have to take into account the absorption by a more dense gathering of dust (Coal Sack) and add that to the general absorption through the distance of 1.5kpc

Thanks again

 

[lightgrav]

1) How can you know the Area of some particular mirror,
but don't know the base of the measurement system?!
Calibrate to the Sun ... good idea ...use yellow photons.
2) was there a question here?
3) the 20pc thickness is novelty information, normally
not used in calculating extinction along an optical path.
(you *would* use it to find density, of course)

I don't recall Av/C = 3 ... is this an approximation?

 

[big man]

the second one I was just asking if you thought it seemed right.

For the A/C thing, yes it is an approximation. It's meant to be around that and in his notes it says it is a constant...I think it is more accurately about 3.2.


Cheers for the feedback