The AspectBlur Parameter in MARX
The AspectBlur parameter was introduced in MARX 5.0, replacing the DitherBlur parameter used by prior MARX versions, which included additional effects now handled directly in the code. The MARX developers set the default value of the parameter to 0.07″—the measured uncertainty of the aspect solution. However, the simulated encircled counts fraction profile is observed to be narrower than the profile obtained from observed data. We therefore recommend increasing the value of AspectBlur to broaden the PSF to better match observations. The origin of this discrepancy is being investigated by the MARX team.
Experience has shown that the ray tracing simulations generated by MARX will have a roughly correct total intensity but tend to have PSF wings that are broader than observations and a PSF core narrower than observed (ApJS 194 37, Appendix A). SAOTrace/ChaRT-generated simulations, projected using MARX, will in general better reflect the observed PSFs but will still display some deviations. These discrepancies can be reduced by blurring the PSF when projecting it to the detector-plane.
In MARX 5.0, the AspectBlur parameter was introduced to account for the known uncertainty in the determination of the aspect solution. This replaces the DitherBlur parameter found in prior MARX versions, which encompassed the effects from pixel quantization, and pixel randomization, now addressed directly in the code. The value of DitherBlur was empirically adjusted to give the correct PSF for MARX 4 versions. Sub-pixel effects were not included prior to MARX 5.0.
Subsequent comparisons of the encircled counts fraction (ECF) profile of the projected MARX 5.0 ray trace simulations using the default AspectBlur value of 0.07″ shows that the PSF core is too narrow for ACIS and wider for HRC-I, suggesting an issue with the instrument or dither models within MARX and the externally obtained aspect solution blurring value.
ECF Profiles with Default AspectBlur
In previous versions of MARX, varying the DitherBlur parameter allowed users to adjust the width of the PSF. A similar behavior can be generated in MARX 5 by varying the AspectBlur parameter. However, we do not currently have a physical interpretation of the discrepancy between the simulated and observed profiles.
On-axis, point source observations of AR Lac (ObsID 13182, HRC-I), τ CMa (ObsID 4469, ACIS-I), and RS Oph (ObsID 7457, ACIS-S) were simulated with the Chandra Ray Tracer (ChaRT), a web-based interface to SAOTrace, using their respective aspect solution files and projected to the detector-specific plane while varying the AspectBlur parameter value in increments of 0.01″. Offsets from the nominal science instrument module (SIM) position were applied, and the SIM drift was accounted for using the aspect solutions. One hundred realizations for each blur factor were sampled, using RandomSeed=-1, and events files for each realization were created with marx2fits, using --pixadj=EDSER for the ACIS observations and --pixadj=EXACT for the HRC. In addition to ChaRT-generated rays, a further one hundred realizations for each AspectBlur value were created using MARX as both the ray-tracer and projector.
The ACIS point source was selected to be as close to the optical-axis as possible, while having a low count rate to minimize pileup affects, since source pileup causes the shape of the core to be highly distorted. It is also necessary to have a large number of counts in order to unambiguously distinguish the source from the underlying background, which necessitates long duration observations for the low count rate source.
The spectral energy distribution of source photons used for the ray trace simulations were obtained from the unconvolved source spectra extracted from the observations. While the spectra used in these example source simulations were background subtracted—since the sources were on-axis, the background contribution to the PSF should be insignficant—in general, the background should be accounted for in order to appropriately compare simulated PSFs with the observed PSF. Underestimating the background in the simulation will cause the ECF profile of the observed PSF to be wider than that of the simulated PSF, since the observed source will include background photons. In the specific cases presented here, the differences between the PSFs generated from the background subtracted and non-background subtracted spectra were negligible. For the τ CMa observation, a circular extraction region of radius 8.2 ACIS pixels has 8385 counts; given the region size and typical background rate for the observation, ≈15 background counts are expected. Using the same extraction region the RS Oph observation has 6300 counts and ≈110 estimated background counts. The AR Lac observation with an extraction region of radius 25 HRC pixels has 118079 counts with an estimated background of ≈30 counts.
There are several strategies to account for the background, such as using the non-background subtracted source spectrum or including a random subset of events from "blank sky" background files with the simulated events. If the source is very faint, then simulating the background may be necessary.
ECF profiles for each realization were produced using centroided positions with the ecf_calc script, binned to a pixel size of 0.2 times the physical detector pixels. The ECF and radii for a given blur-value were averaged and then overplotted with the ECF profile from the observed source.
Encircled Counts Fractions
The ECF profiles for the projected ChaRT- and MARX-generated PSFs show that the MARX default AspectBlur to be too narrow, with the exception of the ChaRT-generated HRC-I PSF, which matches the observation well. The MARX-generated rays with the default blur factor produce a narrow PSF, while a somewhat larger blur factor of ≈0.10″ matches the HRC-I observation.
AR Lac ChaRT2-simulated ECF Profiles
τ CMa ChaRT2-simulated ECF Profiles
RS Oph ChaRT2-simulated ECF Profiles
AR Lac MARX-simulated ECF Profiles
τ CMa MARX-simulated ECF Profiles
RS Oph MARX-simulated ECF Profiles
Since the PSF is dependent on the source's energy distribution,
the AspectBlur values determined for each detector
The AspectBlur values suggested in this document are just suggested starting points to explore this particular parameter-space.
The ECF profile shapes of the ChaRT-generated simulations on ACIS-I within 0.5″ are irregular and we believe to be unreliable, but at larger radii the profiles begin to match the observed ECF, most closely when a blur factor of ≈0.2″ is chosen. The MARX-generated rays for ACIS-I require a larger blur factor than used for the ChaRT-generated rays, closer to 0.3″. In the case of τ CMa, an AspectBlur of 0.27″-0.28″ compares well with the observation at a radius greater than 1.5 ACIS pixels. Note that the ECF radii for the PSFs cut off at ≈4 ACIS pixels while the observed ECF continues on past 5 ACIS pixels, suggesting that the wings of the simulated PSFs are also narrower than observed.
The ECF profile shapes of the ChaRT-generated simulations on ACIS-S for RS Oph within a radius of 2 ACIS pixels match the observed ECF with a blur factor of ≈0.25″, but requires a larger blur factor of ≈0.34″ for larger radii. The MARX-generated simulations on ACIS-S is more complex. For a sub-pixel radii, an AspectBlur of ≈0.25″ reflects the observed ECF profile, but increases slightly to ≈0.28″ for a radius of 1-2 ACIS pixels. At larger radii, blur factors >0.3″ all approximately converge, with PSF wings narrower than observed.
It should be emphasized that these AspectBlur values are starting off points. These values are merely suggestions since they are determined from only a small set of observations, and does not necessarily mean these blurring parameters are good for all observation dates.