Re: Formula for converting a spectrum model to counts

From: John Houck <houck_at_email.domain.hidden> Date: Mon, 10 Jan 2011 12:21:19 -0500 · This archive was generated by hypermail 2.2.0 : Mon Jan 17 2011 - 08:52:23 EST

On Mon, Jan 10, 2011 at 08:59 -0800, Rob Gibson wrote:
> Hi, John.  Thanks for the response.  Sorry I'm following up on this slowly.
> 
> So it sounds like the one part I need to work out is the
> bin-integration of the model M(E).  For a powerlaw model, I was
> using M(E_mid)*dE, but are you saying that it should technically be
> integral{ m(E)dE } over the bin, which would be similar to what I
> used but slightly different?
> 

Yes - ideally it should be the integral over the bin width
(assuming an additive model component).

If computing the integral is impractical, one can use a simpler
approximation for the integral, but such an approximation may
be valid only for a given range of small bin-widths.  Models
computed for coarser grids will then have discretization errors
at some level.

Thanks,
-John
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