Last Updated: 2016-Sep-27

Chandra | Cal | HRC

Chandra Empirical PSF

Vinay Kashyap & Diab Jerius


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.


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, mV=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.

Table 1: List of HRC-I AR Lac datasets used
ObsID Observation Date Exposure [s] Offaxis [arcmin] azimuth [deg]
1284 1999-08-31T21:15:28 789.6 0.355 20.25
62507 1999-10-04T23:08:34 1588.1 0.347 25.35
62506 1999-10-04T23:37:49 1173.1 0.257 14.37
62505 1999-10-04T23:58:27 1042.8 0.323 35.78
1385 1999-10-05T00:21:05 18619.8 0.283 25.39
1484 1999-12-09T09:41:42 1204.9 0.336 20.21
996 2000-12-12T16:31:38 789.4 0.255 27.65
2608 2002-01-27T00:44:33 1189.7 0.233 19.04
4294 2003-02-22T11:07:21 1176.8 0.234 28.17
5060 2004-09-13T20:19:58 1136.3 0.227 16.74
6133 2004-11-25T21:04:40 1075.9 0.268 29.76
5979 2005-09-27T08:06:24 2698.5 0.237 22.01
6519 2006-09-20T19:20:57 3143.1 0.241 23.60
8298 2007-09-17T13:08:38 3142.8 0.240 19.30
9640 2008-09-07T09:35:46 3150.3 0.245 18.25
11889 2010-09-25T05:43:56 3150.0 0.243 20.84
13182 2010-12-16T18:45:33 17964.4 0.259 20.05
13265 2011-09-18T20:48:16 2157.5 0.128 50.72
14299 2012-09-27T02:28:47 3130.8 0.242 19.19
15409 2013-09-16T15:20:29 3145.6 0.236 17.71
16376 2014-09-16T02:03:03 3125.2 0.240 19.78
17372 2015-03-08T17:11:00 5142.3 0.284 22.83
17351 2015-09-26T14:11:24 5132.7 0.261 15.18

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

Table 3: EE radii [HRC pix]
Stage Events EE=0.39 EE=0.50 EE=0.85 EE=0.90
Status bits 398438 2.526 3.087 6.320 7.640
Pathway B 283967 2.482 3.032 6.321 7.791
Status bits
242379 2.422 2.977 6.248 7.567
Pathway A 167414 2.348 2.889 6.177 7.598
Improvement over Lev2 7.0% 6.4% 2.3% 0.5%

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.

Table B.1: HRC Detector PSF model
Parameter Value
gauss2d.fwhm [1/4 HRC pix] 12.93
gauss2d.ampl 16.1
beta2d.r0 [1/4 HRC pix] 12.3
beta2d.ampl 2.3
beta2d.alpha 2.2
beta2d.xpos [1/4 HRC pix] +5.24 -6.29
beta2d.ypos [1/4 HRC pix] +0.3 -0.36


Juda, M., 2001, CXC Memo, Amplifier Scale Correction Scheme
Juda, M., 2001, CXC Memo, Comparison of AMP_SF Correction Methods
Juda, M., 2002, CXC Memo, An Improved AMP_SF Correction Scheme
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
CIAO Thread: The HRC-I Background Spectra Files
Status bits
Juda, M., 2012, CXC Memo


HRC Data and Processing
Table 1: List of AR Lac datasets
Empirical PSF
Table 2: PSF images
Table 3: EE radii
Appendix A: Recentering Bias
Figure A.1a: Recentering bias
Figure A.1b: Strength of recentering bias
Figure A.2: Bias ignorable for HRC-I
Appendix B: HRC Detector PSF
Table B.1: HRC-I Detector PSF
Vinay Kashyap (CfA/CXC)