Expert: Philip A. Stahl - 4/9/2011

Question
sir
I went through following link

http://quarknet.fnal.gov/quarknet-summer-research/QNET2010/Astronomy/Plotting.ht...

i was facing some problems..please help me out with them
While calculating equivalent widths of stellar spectra why have we divided by 2.35 for calculating SIGMA.
Also what is the physical significance of this formula for calculating area under the peak..
please help me out with these confusions.

Thank you

Answer
Hello,

The answer to your first question isn't very clear, and certainly not from the link! (where it clearly states after the sigma, "more to come".) This may mean the factor hasn't been fully physically vetted, or may perhaps be a fudge factor. In any case, it's difficult to say what exactly it is without further elaboration from the authors. That is, exactly HOW they arrive at 2.35.

The physical significance of the formula is basically the same for any equivalent width computation, which is to say, providing a quantitative measure of the *strength* of a spectral line. Thus, what we do is calculate a proxy area equal to the area of the spectral line: e.g. is has the width in angstroms (A) of a box with the same area as the spectral line. In pure physics-theoetical terms, one is really taking the integral:

EqW = INT(a to b) (F_c - F-L) dL/ F_c

which is taken from one side of the line to the other, where a to b define these limits.

F_L is the radiant flux which is normally expressed as a fraction of F_c, the value associated with the flux from the continuous spectrum *outside* the line. Then the quantity:

(F_c - F-L)/ F_c

denotes the *depth* of the line.

Your referenced formula (from our link) is slightly different from this in that it evidently uses the depth:

(F_c - F_L)/ (F_c - F_Lo) = 1/2

which is defined as the full width at half- maximum and usually denoted as (delta L)_1/2

In light of the above theoretical basis, it might well be that the factor 2.35 emerges as a result of computation for the quantity, F_Lo, which refers to the flux at the exact *center* of the line.

As I said, we'd need to know more from the authors (who promised "more to come") to determine exactly how they arrive at this. From the information given, this is the best we can do for now.