# Surface brightness profiles: sech^2 fit in mag/arcsec^2 units?

1. Jun 26, 2008

### mdemone

Hi everybody, I have a very quick question about surface brightness profiles for an edge-on galactic disk.

I have surface brightness values (V-band, not that it matters) in units of mag/arcsec^2 as usual, as a function of z, which is the distance from the galactic disk's plane. I'd like to fit a typical sech^2 profile, usually quoted as:

I(z) = I(0)*(sech(z/z0))^2

where I(0) is the peak luminosity density and z0 is some scale height. Now this would be fine for me, except I'm working in magnitude units, i.e. the peak is something like 21 mag/arcsec^2 and it drops off quickly (for a thin disk) to ~30 mag/arcsec^2. Thus when I plot the above profile on a y-axis inverted for magnitude units, I get an upside-down profile that disappears off in the positive y-direction.

So my question, as dumb as it may be, is how do I convert the above density profile into magnitude units, i.e. I need mu(z) = mu(0) * some sech^2 function.

I know I've seen this form floating around somewhere before, but I can't find it and my first few attempts have been miserable. I really would appreciate just a quick answer for this simple problem.

Thanks in advance! Please mention a source if at all possible, either textbook or article or whatever, just for my own future benefit.

2. Jun 27, 2008

### mdemone

I solved it -- of course the easiest thing to do turned out to be converting the mag/arcsec^2 values into real luminosity density = L_sun/pc^2, then fitting the result and translating the fitted curve back into mag/arcsec^2 units.

Sort of awkward, but it seems to have worked without losing any information. I still could swear I've seen a magnitude version of the vertical disk sech^2 profile somewhere; ah well...