Last Updated: 2016-Sep-27

Chandra | Cal | HRC

Chandra Empirical PSF

Vinay Kashyap & Diab Jerius

Summary

We have constructed empirical Chandra PSFs using on-axis HRC-I observations of AR Lac, using events filtered to remove most of the effects that cause the observed PSF to broaden.

Introduction

There are some known discrepancies between the raytrace model and the observed PSFs for Chandra. For example, observed HRC profiles are sharper than suggested by the model, despite the model not taking into account sources of systematic uncertainties like tailgating and degap; and in contrast, observed ACIS profiles are broader than suggested by the model, which is attributable to an incomplete model of the ACIS pixellation and to the difficulties of obtaining a "clean" unpiled point source.

We have therefore undertaken to put together an empirical model of the on-axis PSF using HRC-I observations of AR Lac. AR Lac is an unresolved spectroscopic eclipsing RS Cvn type binary (K0IV+G5IV, m_V=6.11, d=43 pc), which emits optically thin radiative emission primarily in the 1-10 MK temperature range. It has been observed regularly over the Chandra mission as part of a calibration program to monitor the HRC gain. It has been known to flare often, though the base emission is steady (Drake et al. 2014)

We expect the images provided below to be useful for carrying out comparisons with observed datasets, as well as for further calibration efforts to improve the SAOtrace raytrace model. Care must be used before these images are used to compare to ACIS sources, since the effects of the HRC detector PSF has not been removed from them. That is, these images must be first deconvolved using the HRC detector PSF, and then blurred with a model of the ACIS detector PSF before comparing with on-axis ACIS sources. Efforts to construct a direct ACIS counterpart of the empirical PSF using a variety of on-axis sources are ongoing.

HRC Data and Processing

The full list of ObsIDs and exposure times for the data used here is given in Table 1. Each dataset was first downloaded from the archive, and the Level 1 events list was reprocessed using hrc_process_events, which applies the latest degap corrections to the data. The data were then derolled around the aimpoint such that all datasets are oriented the same way in the detector plane. A tailgating test (Juda 2012) was performed for all events, for a variety of time and radial distance offsets. (Tailgating is an HRC detector effect where if a photon is followed too soon and too close by another one, the following photon's location determination is not as precise, which causes a point source dominated by such events to be broader than it would be otherwise.) For the purposes of constructing the empirical PSFs, we adopt default values for the tailgating parameters of 50 ms and 20 HRC pix -- that is, if an event follows within 50 ms of another event and within 20 HRC pixels of the preceding event, it is ticketed as a tailgater. Efforts to determine the optimum values for the tailgating parameters are ongoing.

Each dataset is then filtered to remove events flagged as bad with status bits set accordingly. At this stage the data are in a form equivalent to the Level 2 event lists (the differences are that detector coordinates like AMP_SF, CRSU, and CRSV are preserved, and no standard GTI time filtering is done). Next, events with PI outside of the range [30,300] are excluded in order to minimize the effect of the background. We now compute the centroids in sky coordinates and recenter the data so that proper motion and small misalignments are removed. The effect of such recentering on the profiles is discussed in Appendix A below. Next, we carry out filterings on the amplifier scale factor (AMP_SF) along two separate but parallel pathways, A and B. Along pathway A, we filter out events with AMP_SF=3, which are known to have larger residual degap errors. The remaining events are pooled into individual taps ((U,V)=(29,29),(29,30),(29,31),(30,29),(30,30),(30,31)). If there are >500 counts in a tap in a given observation, then those events are recentroided separately in each case, and then recombined. The reason for doing this is that there are known uncorrected systematic shifts in the degapping corrections between taps. Along the other pathway, B, no AMP_SF filtering is applied, and no recentering by taps is performed. We then filter out all events that have been flagged as tailgating that still remain, from both pathways, and construct empirical PSFs from the remaining events. This gives us two versions of the empirical PSF: an "ideal" version, from pathway A, that represents the sharpest core PSF that can be observed with the instrument, and a "practical" version, from pathway B, that represents the best core PSF that can be derived from Level 2 products.

Empirical PSFs

Here we present the images binned at 1/8 HRC pixels (0.01647 arcsec) for the combined AR Lac HRC-I dataset that result from both pathways A and B, in Table 2. In addition, we compute the (circular) radii (in units of HRC pixels) that enclose 39%, 50%, 85%, and 90% of the enclosed counts fractions for combined data, both before and after filtering for tailgating, in Table 3.

Table 2: Empirical PSFs

pathway	File	Comment	Image
A	empPSF_A.img	Filtered on status bits, AMP_SF=3, PI outside of [30,300], and tailgated events, and recentered by taps	Smoothed image at 1/8 HRC pix binning
B	empPSF_B.img	Filtered on status bits, PI outside of [30,300], and tailgated events	Smoothed image at 1/8 HRC pix binning

Appendix A: Systematic Errors due to Recentering

There is a well known systematic bias that occurs when multiple profiles are coadded after centroiding. Because centroiding removes a degree of freedom that is present in the data, the coadded profiles become sharper (see Figures A.1a and A.1b).

Figure A.1a: Demonstrating that profiles sharpen if segments are centroided and coadded. 200 2D Gaussians with 50 counts each are coadded directly, as well as after centroiding and recentering, and the 50% enclosed points radius was calculated for each case. The figure shows a histogram of 1000 simulations of the ratio of these 50% EE radii, showing that centroiding and recentering tends to sharpens the profile by ~1%.

Figure A.1b: Trend of sharpening of profile with counts in segment. This figure is a generalization of Figure A.1a, and shows how much sharpening occurs as the number of counts in each subsegment is increased. The ratio of the true-to-recentered 50% enclosed fraction of the events is shown for counts in subsegments ranging from 10 to 500. The correction is >50% at low counts, and becomes negligible at ~500 counts.

This bias turns out to be ignorable for the HRC-I empirical PSF construction, where we require at least 500 counts to be present in any subsegment before they are centroided and coadded. This is confirmed by simulations (Figure A.2) where we construct equivalent datasets using a Gaussian PSF and by bootstrapping the empirical PSF, and find that the correction to the profile is ≪1% over the core of the PSF.

Figure A.2: Demonstrating that recentering bias is ignorable for HRC-I AR Lac compilation. The figure shows the ratio of "true" profiles to the centroied-by-segment and recentered profiles as contour plots and the corresponding distribution of the ratios of 50% EE radii as histograms based on 100 simulations. Each row represent different levels of filtering -- top is status bit filtered, second is AMP_SF=3 and PI outside of [30,300] removed, third is with tailgated events removed, and last is for those with (U,V)-tap recentering. The left two columns represent simulations carried out assuming a Gaussian profile, which is known to be significantly broader than the true PSF profile, for 2D (left) and 1D (right). The right two columns represent bootstrapped simulations using the recentered events, again for 2D (left) and 1D (right). The contour levels for the 2D images are shown at the top of the plot in corresponding colors. The sample mean and standard deviation of the ratios of the true and recentered 50% EE radii are also shown for the histogram plots. In all cases, the number of segments and the number of events in the simulation or the bootstrap sampling match the observed cases exactly.

Appendix B: HRC Detector PSF

The HRC readout blurs the event locations. Initially a simple 2D Gaussian (of sigma=0.0077 mm -- see the parameters HRC-I-BlurSigma and HRC-S-BlurSigma in marx.par -- which translates to a fwhm of 13.28 in 1/4-size HRC pixels) was used. However, the analysis of some isolated transient hotspots observed in HRC-I reveal a more complex shape; these were modeled as a combination of a 2D Gaussian and a 2D Beta Profile, whose best-fit parameters are reported in Table B.1.

References

AMP_SF

Juda, M., 2001, CXC Memo, Amplifier Scale Correction Scheme
- cxc.harvard.edu/contrib/juda/memos/amp_scale/scale_correction.html

Juda, M., 2001, CXC Memo, Comparison of AMP_SF Correction Methods
- cxc.harvard.edu/contrib/juda/memos/amp_scale/compare.html

Juda, M., 2002, CXC Memo, An Improved AMP_SF Correction Scheme
- cxc.harvard.edu/contrib/juda/memos/amp_scale/improved_scale_correction.html

AR Lac

Drake, J.J., Ratzlaff, P., Kashyap, V., Huenemoerder, D.P., Wargelin, B.J., & Pease, D.O., 2014, ApJ 783, 2
- 2014ApJ...783....2D

HRC background reduction

Kashyap, V., & Posson-Brown, J., 2010, HRC-I Background PI Spectra
- cxc.harvard.edu/cal/Hrc/pibgspec.html

CIAO Thread: The HRC-I Background Spectra Files
- cxc.harvard.edu/ciao/threads/hrci_bg_spectra

Status bits

cxc.harvard.edu/cal/Hrc/filter_20060216.html

Tailgate

Juda, M., 2012, CXC Memo
- cxc.cfa.harvard.edu/contrib/juda/memos/hrc_pileup/index.html

changelog

• 2016-sep-23: internally circulated draft
• 2016-sep-25: added appendix B: HRC detector PSF
• 2016-sep-26: public version
• 2016-sep-27: included PI filtering, and added ratio of EE 50 radii and trend plot to Appendix A
• 2017-feb-09: some typo fixes (thx kjg)