Pulling it all together - the Point Spread Function

At this point I have a radial profile for the source, in physical units - ie, units that can be compared to theoretical predictions.  However, there are three components to the surface brightness at any point: (1) the point spread function (PSF) of the mirror, (2) the diffuse background, and (3) the actual scattered X-rays that I care about.  I need to come up with some way to estimate the value of (1) and (2).  As it turns out, the diffuse background (term #2) is basically flat, so I can fit that pretty easily by just adding in a constant term.  However, the PSF (term #1) is energy-sensitive and position-dependent.

There are a number of ways to get Chandra's PSF.  The calibration database contains images of point sources that show the PSF, but these only have information near the source, out to ~10'' or so.  There is also the Chandra Ray Trace code (ChaRT) that can model the Chandra PSF for any set of energies.  The problem there is that ChaRT (also called SAOsac) is tuned up using the same calibration database images, and so it tends to give the wrong answers when looking more than 10'' away from the source.  The problem here is that I need the PSF from about 2'' to about 100'' or even 1000'' away from the source, and the models just won't do that.  I've included Figure 4 from Smith, Edgar & Shafer (2002) to demonstrate the problem.  This figure compares observations of Her X-1, a nearly-perfect point source compared to the best-possible ChaRT/SAOsac model.  Although near the source all is well, even by 30'' - 40'' away there are problems.

The solution is to use long observations of bright point sources, which inherently measure the PSF.  In this case, the quasar 3C273 observed with the HRC-I (ObsID 461) is about as good as it gets.  I used this source in Smith (2008) when measuring the halo of GX13+1, and it worked reasonably well.  The biggest problem is that the PSF is energy dependent, and the spectrum of 3C273 is not the same as GX13+1 or GX5-1 for that matter.

However, the energy-dependence isn't that great, and there isn't a better choice, so one works with what one can. Of course, trusting statements like that is the road to disaster. So I've attached two figures that prove it.  The first is the PSF measured from Her X-1 (and modelled with SAOsac) fit to a power-law for a range of energies.  The units in the y-axis are 'arcmin^-2', which are really the surface brightness in units of photons/cm^2/s/arcmin^2 divided by the source flux, in units of photons/cm^2/s. This gives the rather strange, but handy, units of arcmin^-2.  This figure shows that the PSF really is pretty well fit with a power law - and that the ChaRT/SAOsac fits are awful far off-axis.  The second figure simply plots the actual fit parameters for the power-law fits. This plot shows that the power-law slope is roughly constant around alpha=1.9, while the amplitude of the PSF increases almost linearly with energy.  The 'bobble' around 2 keV is almost certainly due to the Silicon K edge at that energy, since both the mirrors and the detectors include lots of silicon.  The upshot of all this is that I feel confident that the biggest problem with using 3C273 as a surrogate for the PSF of GX5-1 (and GX9+1 for that matter) will be a slight offset up or down in the total PSF power.  For example, if 3C273 has more emission at high energies than GX5-1, then the predicted PSF from 3C273 will be slightly larger than the 'real' GX5-1 PSF, since the power-law fits show that the PSF gets more intense at higher energies.

This opens up the question: If the power-law fits work so well, why not just use them?  Well, I do, for ACIS halo measurements.  But these energy-dependent fits can only be made using an energy-sensitive detector like the ACIS.  However, ACIS suffers from pileup when observing bright sources, making measurements of the near-source PSF impossible.  Measurements in the 10''-30'' range can only be done well with the HRC, which has no energy resolution.  Fits to the PSF of 3C273 show that this simple power-law fit don't work so well, as this figure shows.  This fit uses a Gaussian model for the core of the PSF, and then two power-laws, one with a slope of 4 (primarily for the 1-10'' region) and a second with a slope of 2.4 for the 10-100''.  There is also a constant term to handle the background.  And, even with all of these terms, the fit isn't all that good at 10''.  So, I think it's best to use real observations rather than fits at this point.