Innovations in the Analysis of Chandra-ACIS Observations
Patrick S. Broos, Leisa K. Townsley, Eric D. Feigelson, Konstantin V. Getman, Franz E. Bauer, Gordon P. Garmire
AAccepted by the ApJ, 2010 Mar 10 (
Innovations in the Analysis of
Chandra -ACIS Observations
Patrick S. Broos, Leisa K. Townsley, Eric D. Feigelson, Konstantin V. Getman, Franz E. Bauer, Gordon P.Garmire [email protected] ABSTRACT
As members of the instrument team for the Advanced CCD Imaging Spectrometer (ACIS) on NASA’s
Chandra X-ray Observatory and as
Chandra
General Observers, we have developed a wide variety of dataanalysis methods that we believe are useful to the
Chandra community, and have constructed a significantbody of publicly-available software (the
ACIS Extract package) addressing important ACIS data and scienceanalysis tasks. This paper seeks to describe these data analysis methods for two purposes: to document thedata analysis work performed in our own science projects, and to help other ACIS observers judge whetherthese methods may be useful in their own projects (regardless of what tools and procedures they choose toimplement those methods).The ACIS data analysis recommendations we offer here address much of the workflow in a typical ACISproject, including data preparation, point source detection via both wavelet decomposition and image recon-struction, masking point sources, identification of diffuse structures, event extraction for both point and diffusesources, merging extractions from multiple observations, nonparametric broad-band photometry, analysis oflow-count spectra, and automation of these tasks. Many of the innovations presented here arise from several,often interwoven, complications that are found in many
Chandra projects: large numbers of point sources (hun-dreds to several thousand), faint point sources, misaligned multiple observations of an astronomical field, pointsource crowding, and scientifically relevant diffuse emission.
Subject headings: methods: data analysis; methods: statistical; techniques: image processing; X-rays: general
1. INTRODUCTION
Since its launch in 1999, the
Chandra X-ray Observatory (Weisskopf et al. 2002) has revolutionized X-rayastronomy.
Chandra provides remarkable angular resolution—unlikely to be matched by another X-ray observatorywithin the next two decades—and its most commonly used instrument, the Advanced CCD Imaging Spectrometer(ACIS), produces observations with a very low background (Garmire et al. 2003). These two technical capabilitiesallow detection of point sources with as few as ∼ Chandra ’s excellent sensitivity to point sources and angular resolution also provide a unique capability for studyingdiffuse emission superposed onto those point sources, since they can be effectively identified and then masked.For many types of ACIS “imaging” studies, most observers follow a data analysis workflow that is similar tothat outlined in Figure 1. Relatively raw data derived from satellite telemetry, known as “Level 1 Data Products” (L1), are passed through a variety of repair and cleaning operations to produce “Level 2 Data Products” (L2) that Department of Astronomy & Astrophysics, 525 Davey Laboratory, Pennsylvania State University, University Park, PA 16802, USA Space Science Institute, 4750 Walnut Street, Suite 205, Boulder, Colorado 80301, USA Pontificia Universidad Cat´olica de Chile, Departamento de Astronom´ıa y Astrof´ısica, Casilla 306, Santiago 22, Chile See also the Chandra Proposers’ Observatory Guide ( http://asc.harvard.edu/proposer/POG/pog_pdf.html ). Our discussion here is limited to data taken in the most common ACIS configuration, called Timed Exposure Mode, at either theACIS-I or ACIS-S aimpoint. Dispersed data from the
Chandra gratings are not addressed here. http://cxc.harvard.edu/ciao/dictionary/levels.html a r X i v : . [ a s t r o - ph . H E ] M a r maskedimagerydiffuse source(DS) detectionDS catalogDS extractionimagerypoint source(PS) detectionPS catalogPS extraction maskedL2 event dataL2 event datarepair; mild cleaningL1 event dataprune/repositionsources astrophysicalanalysis(e.g. spectral modeling)tables for publicationaggressive cleaning masking observed properties;calibration products observed properties;calibration productsintrinsic properties Fig. 1.— The data analysis workflow described here for a single ACIS field containing multiple point sources (PS,left branch) and diffuse sources (DS, right branch).Many
Chandra studies exhibit one or more of five characteristics that significantly complicate this familiarworkflow.1. In many studies hundreds to thousands of point sources can be readily identified; executing the workflow isintractable without significant automation.2. Numerous sources with very few detected counts are identified in most
Chandra studies; common statisticalmethods based on large-N assumptions break down at several points in the workflow.3. Many studies require covering a large field of view with multiple
Chandra pointings (e.g., Figure 2). For manyreasons, such mosaicked pointings usually overlap significantly and/or are observed at a variety of roll angles.Thus, many sources are observed multiple times at very different locations on the ACIS detector. Analysis of suchsources can be very complex, because the
Chandra point spread function (PSF) exhibits large variations in sizeand shape across the focal plane. Analysis of diffuse emission is also complicated by multiple pointings, since asingle diffuse region may be only partially covered by a particular ACIS observation. See Figure 8 and Figure 10 in the HRMA User’s Guide ( http://cxc.harvard.edu/cal/Hrma/users_guide/ ). Right Ascension (J2000) D ec li n a t i on ( J2000 ) Fig. 2.— Exposure map for the Chandra Carina Complex Project (Townsley et al. 2010) study of the Carina Nebulacomprised of 22 ACIS-I pointings (38 observations), with point sources masked ( § § Chandra studies often exhibit all five of these issues, we have developed a set of data analysis methodsthat incorporate a variety of enhancements to standard techniques. Publicly available software implementing thesemethods—the
ACIS Extract package—has been cited in publications for at least 50
Chandra targets.This paper seeks to describe these methods at a moderate level of detail. Our primary purpose is to encourageother ACIS observers to consider whether the various departures from standard techniques described here maybe useful in their own projects (regardless of what tools and procedures those observers use to implement thosemethods). Our secondary purpose is to document the data analysis methods used in our own
Chandra studies. Inmany cases, the only documentation available for software and data analysis methods is on-line; thus this paper is 4 –liberally footnoted with relevant URLs. We acknowledge that URLs are more ephemeral than journal citations butwe believe that they are better than no documentation at all.The high-level structure of our data analysis workflow differs from standard practice in two ways. First, fortechnical reasons, the optimal data cleaning steps for point sources and diffuse sources differ for ACIS data ( § § § § Throughout the text, we makeliberal use of footnotes that direct the reader to on-line documentation, much of it provided by the Chandra X-rayCenter (CXC), that is useful for understanding ACIS data analysis and issues. The process of preparing L2 dataproducts is discussed in §
3. Point source detection is reviewed in §
4. Extraction of point sources and backgroundestimation are presented in §
5. Section 6 describes our approach to handling multiple observations of a source.Estimation of observed and intrinsic source properties is discussed in §
7. In § developedby the CXC, and by analysis tools such as XAssist (Ptak & Griffiths 2003) and yaxx (Aldcroft 2006) developed byother researchers.
2. The
ACIS Extract
Package
Although the focus of this paper is to discuss data analysis techniques, rather than implementation of thosetechniques, in fact most of the software and recipes that we use for ACIS data analysis are publicly available in apackage called
ACIS Extract ( AE ), which was first released to the community in 2002. This paper will refer to AE when discussing any data analysis method that is implemented in ACIS Extract . We do not attempt to describe hereeither the full capabilities of AE or how to use the software, but instead refer the reader to the extensive AE manualand recipes. AE can also be applied to X-ray data from the EPIC instrument on the XMM-Newton observatory,with reduced capabilities and documentation. AE significantly automates the extraction and analysis of both point-like and diffuse sources; our largest projectto-date (Townsley et al. 2010) involved 14,000 point sources and complex diffuse emission in a mosaic of 38 separateACIS observations, shown in Figure 2. AE relies heavily on tools in the Chandra Interactive Analysis of Observa-tions ( CIAO ) package (Fruscione et al. 2006). Other software packages employed by AE include the IDL AstronomyUser’s Library (Landsman 1993), MARX , SAOImage DS9 , , FTOOLS (Blackburn 1995), XSPEC (Arnaud http://cxc.harvard.edu/ciao/threads http://asc.harvard.edu/csc/ http://xassist.pha.jhu.edu/zope/xassist http://cxc.harvard.edu/contrib/yaxx/ http://cxc.harvard.edu/ciao/ http://idlastro.gsfc.nasa.gov/ http://space.mit.edu/ASC/MARX http://heasarc.nasa.gov/ftools/ftools_menu.html http://heasarc.gsfc.nasa.gov/lheasoft/xanadu/xspec/ LaTeX2e (Lamport 1994), and our own Tools for ACIS Review and Analysis ( TARA ). AE is written in the IDL language. Several dozen studies by several independent groups (including at least nine Large and Very Large projects)have employed AE . Examples include: extragalactic survey fields: Chandra
Deep Field North (Alexander et al. 2003);
Chandra
Deep Field South (Luoet al. 2008; Lehmer et al. 2005); the Serendipitous Extragalactic X-ray Source Identification program (Eckart etal. 2006); SSA22 (Lehmer et al. 2009) lensed quasars:
PG 1115+080 (Pooley et al. 2006), 1RXS J1131-1231 (Blackburne et al. 2006), survey of 10 (Pooleyet al. 2007) galaxy clusters:
Coma Cluster (Hornschemeier et al. 2006), Abell 85 and Abell 754 (Sivakoff et al. 2008a), various(Fassnacht et al. 2008) nearby galaxies and LINERs:
IC 10 (Bauer & Brandt 2004), sample of LINERs (Flohic et al. 2006), SN 2006gyin NGC 1260 (Smith et al. 2007), M 33 (Plucinsky et al. 2008), Centaurus A (Sivakoff et al. 2008b), SN 1996cr inCircinus (Bauer et al. 2008), NGC 6946 and NGC 4485/4490 (Fridriksson et al. 2008) globular clusters:
47 Tucanae (Heinke et al. 2005), Terzan 1 (Cackett et al. 2006), Terzan 5 (Heinke et al. 2006),NGC 288 (Kong et al. 2006), M30=NGC 7099 (Lugger et al. 2007), NGC 6366 and M 55 (Bassa et al. 2008), G1(Kong et al. 2009) the Galactic Center: point sources (Muno et al. 2003, 2006, 2009) young stellar clusters and star formation regions:
M 17 (Townsley et al. 2003; Broos et al. 2007), the OrionNebula (Getman et al. 2005), L 1448 (Tsujimoto et al. 2005), Cep B (Getman et al. 2006), Wd 1 (Muno et al.2006), 30 Dor (Townsley et al. 2006a,b), W 49A (Tsujimoto et al. 2006), NGC 6357 (Wang et al. 2007), RCW 49(Tsujimoto et al. 2007), IC 1396N (Getman et al. 2007), Coronet cluster (Forbrich & Preibisch 2007), Tr 16(Albacete-Colombo et al. 2008), W 3 (Feigelson & Townsley 2008), CG 12 (Getman et al. 2008), the RosetteNebula (Wang et al. 2008, 2009, 2010), NGC 6334 (Feigelson et al. 2009), Cygnus OB2 (Albacete Colombo et al.2007; Wright & Drake 2009), and the Carina Nebula (Townsley et al. 2010).Note that the present paper describes the capabilities of AE as of 2009 November, and that not all features werepresent in earlier studies.
3. DATA PREPARATION
The Chandra Data Archive provides cleaned and calibrated X-ray data products, known as “Level 2 Data”(L2). We rebuild L2 data products from the more primitive L1 products, also found in the archive, in order toapply additional processing steps. Much of our L1-to-L2 processing (Townsley et al. 2003, Appendix B) will not bedescribed in detail here because it follows the standard recommendations shown in the CXC’s Science Threads. For example, like many observers we take the precaution of verifying and improving (if possible) the astrometryof every observation, even though the absolute astrometry assigned to
Chandra observations using the star trackeraspect solution is often quite accurate ( ∼ . (cid:48)(cid:48) , 90% confidence radius ). Astrometric alignment is particularlyimportant when multiple observations overlap, so that the single celestial position adopted for a source will producewell-positioned extraction apertures in each of its constituent observations. Our procedure for this task is similar http://asc.harvard.edu/cda/ http://cxc.harvard.edu/ciao/threads http://cxc.harvard.edu/cal/ASPECT/celmon/ provided by the CXC. We typically align each ACIS observation to a publishedastrometric catalog, rather than to a reference ACIS observation, using preliminary ACIS sources in the inner8 (cid:48) × (cid:48) portion of the field identified by the wavdetect tool (Freeman et al. 2002). Our current catalog matchingprocedure derives only offset corrections (no roll correction), which are applied to the observation’s aspect file andevent data using the CIAO tools wcs update and reproject events . In favorable circumstances with many matchingsources,
Chandra fields can be aligned to the reference astrometric frame to better than 0 . (cid:48)(cid:48) precision.Other standard L1-to-L2 processing steps are applied. We remove events whose “grades” are in the standardset of “bad” grades; we remove events arriving during time intervals designated as “bad”; we remove events arrivingduring periods of very high instrumental background due to solar activity; we construct an exposure map foreach observation. In the early years of the Chandra mission we developed and implemented a technique to mitigatethe effects of charge transfer inefficiency (CTI) in both front- and back-illuminated ACIS CCDs (Townsley et al.2000, 2002, available in the Physics database of ADS). Since this method has been incorporated into the standarddata processing by the CXC and its calibration is maintained by them, we now use the CXC’s version of the CTIcorrector, part of the CIAO tool acis process events .A few aspects of our L1-to-L2 processing warrant discussion:
Improving event locations
Two procedures are used here. First, standard CXC pipeline processing adds a ± . (cid:48)(cid:48) random number to each event’s position, blurring the excellent PSF at the center of the field, as discussed inpresentations at the Chandra Calibration Workshop by Marshall, Pease (page 8), and Smith (page 3). Wedisable this randomization when the data are reprocessed by the
CIAO tool acis process events .Second, the positions of events with non-zero event grades (i.e., where some charge appears in neighboring pixels)can be somewhat improved by “sub-pixel resolution” algorithms described by Tsunemi et al. (2001); Mori et al.(2001) and Li et al. (2004). Either of these two procedures will tighten the PSF in the inner portion of the field;the degree to which the PSF is improved depends upon the fraction of multi-pixel events, which in turn dependson the spectrum of the source and whether the source is imaged on a front-illuminated or a back-illuminated CCD.
Bad Pixel List
For most studies we use and recommend a less-aggressive Bad Pixel List than the one produced by CIAO . The ACIS pixels in the default list that we choose to revive were originally deprecated because they haveelevated background at very low energies (usually < . . < . . >
4% of the columns in the ACIS-I array. A somewhat larger http://cxc.harvard.edu/ciao/threads/reproject_aspect/index.html Galactic X-ray sources are often found in the Naval Observatory Merged Astrometric Dataset (NOMAD) (Zacharias et al. 2004)or the near-infrared band 2MASS Point Source Catalog (Skrutskie et al. 2006), which are on the accurate Hipparcos reference frame. http://asc.harvard.edu/ciao/download/doc/detect_manual http://cxc.harvard.edu/ciao/dictionary/grade.html http://cxc.harvard.edu/ciao/threads/acisbackground/index.py.html http://cxc.harvard.edu/ciao/why/cti.html http://cxc.harvard.edu/ciao/why/acispixrand.html http://cxc.harvard.edu/ccr/proceedings/05_proc/presentations/marshall3 http://cxc.harvard.edu/ccr/proceedings/05_proc/presentations/pease http://cxc.harvard.edu/ccr/proceedings/05_proc/presentations/smith/pg03.html Both the Tsunemi ( ) and Li ( ) groups have released tools implementing their sub-pixel resolution algorithms. http://cxc.harvard.edu/ciao/dictionary/bpix.html A new observation-specific Bad Pixel Table is constructed by re-running the
CIAO tool acis run hotpix with its badpixfile parameterpointing to an edited list of permanent bad pixels in place of the default list. http://cxc.harvard.edu/cal/Acis/Cal_prods/badpix/index.html Bifurcated Workflow
One component of the ACIS instrumental background is a cosmic ray artifact known as“afterglow,” operationally defined as a group of events appearing at nearly the same location on the detectorin nearly consecutive CCD frames. Eliminating afterglow events is essential to any project that seeks to detectweak point sources, since a group of afterglow events can easily be mistaken as a weak point source. Prior to 2004the CXC used a tool named acis detect afterglow to identify afterglow events; this aggressive tool is quite effective(few false negatives), but suffers from many false positives—events from even moderately bright sources that aremistakenly identified as afterglows. In 2004 the CXC adopted an alternative tool named acis run hotpix ; thisgentle tool effectively controls false positives, but misses most afterglow series containing fewer than 10 events.In many ACIS observations, even these short afterglow series will be interpreted as statistically significant pointsource detections.Two additional standard techniques for reducing the ACIS instrumental background suffer the same problem offalse positives near bright sources. The first involves an event grading technique (implemented by the CIAO tool acis process events ) that is available for data taken in Very Faint Mode. The second involves removing a typeof artifact found on the ACIS-S4 CCD (implemented by the CIAO tool destreak ).The lowest instrumental background level can be obtained by applying these two cleaning procedures and theaggressive afterglow detection procedure. This aggressive cleaning scheme is preferred when searching for weakpoint sources and when studying diffuse emission, but is not appropriate when extracting bright sources becausethe number, spatial distribution, and spectral distribution of events mistakenly removed by these algorithms (falsepositives) near bright sources is not well known.Thus, we recommend the bifurcated data reduction workflow shown in Figure 1. An aggressively cleaned L2 eventlist is used to detect point sources and to extract diffuse sources, whereas point sources are extracted from anL2 event list that has been only mildly cleaned. This strategy is not ideal because point source extractions willoccasionally contain some detectable afterglow events contaminating the actual X-ray events that produced thedetection. We mitigate this problem by checking each extracted source for residual afterglow events and flaggingsources dominated by afterglows.Appendix A shows one method for applying both afterglow detection tools and for then performing either thegentle or aggressive cleaning criteria discussed above. Recipes and software implementing this L1-to-L2 processingare available upon request.
4. POINT SOURCE DETECTION4.1. An Iterative Source Detection Strategy
Typically, the process of source detection is a distinct precursor to source extraction and analysis. Source detec-tion algorithms must estimate some sort of significance for a putative source’s signal with respect to the backgroundexpected to contaminate that signal. In other words, source detection algorithms must perform some type of extrac-tion of a proposed source, estimate the local background, and compute some type of significance statistic from thosetwo quantities.Much of this paper describes the algorithms we have developed to perform those same three tasks—extraction( § § § Chandra
PSF, and are not designed for multiple misalignedobservations. http://cxc.harvard.edu/ciao/why/afterglow.html http://cxc.harvard.edu/ciao/threads/aciscleanvf/ http://cxc.harvard.edu/ciao/why/destreak.html § § § We construct the list of candidate sources using a combination of several methods. Many sources can be identifiedby a wavelet-based detection algorithm for Poisson images that has been widely used on
Chandra data— the
CIAO tool wavdetect (Freeman et al. 2002)—run with the liberal threshold of 1 × − rather than the commonly usedlevel of 1 × − in order to nominate as many actual sources as possible without nominating an excessive numberof candidates that will later be found to be insignificant. For a simple field with one pointing, twelve images aresearched—corresponding to three energy bands (0.5–2 keV, 2–7 keV, and 0.5–7 keV) and four image pixel sizes (0.25 (cid:48)(cid:48) ,0.5 (cid:48)(cid:48) , 1 (cid:48)(cid:48) , and 2 (cid:48)(cid:48) ) to sample appropriately the variable Chandra
PSF. All the wavdetect catalogs are merged—pairs ofcatalogs are matched using the algorithm described in §
8, and the most accurate position from each matching pairis retained. The resulting catalog is visually examined to remove any obvious duplicates remaining.Wavelet decomposition of images is often not effective in resolving closely spaced sources, as the method isdesigned to find structures on a range of spatial scales. For such situations, image reconstruction algorithms thatremove the blurring effects of the point spread function can significantly improve source identification. We searchfor faint and crowded sources by locating peaks in reconstructed images obtained with the Lucy-Richardson algo-rithm (Lucy 1974), implemented in the
IDL Astronomy User’s Library . Similar image reconstructions have beeninvaluable for achieving effective spatial resolution as good as ∼ . (cid:48)(cid:48) FWHM in observations of
Chandra targets, forexample a jet in the
Chandra first-light target (Chartas et al. 2000) and SN 1987A (Burrows et al. 2000). As thePSF varies strongly across the
Chandra field due to the telescope optics, the image reconstruction is performed onmany small overlapping tiles (Figure 3) using local PSFs. The candidate sources identified in these tiles are mergedwith those obtained with the wavdetect algorithm.Figure 4 shows an example of the effectiveness of image reconstruction in regions with crowded, faint sources. The wavdetect procedures located 50 sources in this sub-image of the center of the young stellar cluster Trumpler 14; anadditional 50 are found as peaks in the reconstructed images (Townsley 2006; Townsley et al. 2010). The reliabilityof most of these sources is confirmed; 89 of the 100 reconstruction sources coincide with stars detected in deep,high-resolution near-infrared exposures (Thomas Preibisch, private communication; Ascenso et al. 2007), some withseparations < (cid:48)(cid:48) . Of the 11 unconfirmed X-ray sources, 9 appear in close pairs where the other member of the pairis confirmed by an IR counterpart. Testing the validity of these X-ray sources will require very high-resolution,sensitive IR data, as it may be difficult to find faint, close companions in IR observations of such crowded regionssuffused by diffuse IR emission. Since the X-ray flux of a young star does not correlate closely with its IR brightness, http://asc.harvard.edu/ciao/download/doc/detect_manual http://idlastro.gsfc.nasa.gov/ . (cid:48) × . (cid:48) image reconstruction tiles covering an ACIS-I pointing. Tiles nominally overlap by1/4 along both axes. Individual tiles can be seen at the field edges; a single tile at the field center is highlighted.Each tile image is reconstructed using a local Chandra -ACIS PSF; peaks in the reconstruction produce point sourcecandidates.it is not unreasonable for us to find close X-ray pairs that are not seen in IR images, and vice versa.When a project’s scientific goals include the search for faint X-ray emission from a previously-defined catalog ofinteresting objects found in other wavebands, the candidate X-ray source catalog can be supplemented with sourcepositions that are not derived from the ACIS image. The AE procedures can then judge whether significant emissionis present from each single source, and the positions can be ‘stacked’ for high-sensitivity examination of the collectiveproperties of the user-provided catalog ( § DS9 visualization program) of the X-ray data. This visual review alsoallows removal of obviously spurious candidate sources that occasionally emerge (e.g., from detector artifacts suchas bright source readout-streaks) and duplicate sources.
In typical source detection schemes, the existence of a candidate source is evaluated using the signal-to-noise ratio(SNR), which is a photometry value divided by its uncertainty. When photometry values have Gaussian distributions,then a SNR threshold directly corresponds to a level of significance in a statistical test of the null hypothesis thatthere is no source signal present, only background.However, most ACIS sources are quite weak with very few counts extracted from the source aperture, andin crowded fields sometimes very few counts available to estimate the background. Gaussian approximations tophotometric confidence intervals in such cases can be quite poor. We prefer to test directly the null hypothesis thata candidate source does not exist using the method described by Weisskopf et al. (2007, Appendix A2) based on thePoisson distribution. Computation of this significance statistic, P B , is described in Appendix B.The observer must set, either a priori or after careful examination of the image and possible multi-wavelengthcounterparts, a threshold value of P B that strikes a reasonable balance between the competing goals of low falsedetection rates and high sensitivity. Analytical methods to estimate false detection rates and sensitivity have beendeveloped (e.g., by Nandra et al. 2005; Georgakakis et al. 2008), however extending these methods to studies that 10 – - : : : Fig. 4.— The central 100 ACIS X-ray sources (diamonds) identified in the crowded core of the young star clusterTrumpler 14 (Townsley 2006; Townsley et al. 2010) by combining wavdetect sources (50 green ellipses) and peaks ina reconstructed image ( § (cid:48)(cid:48) per pixel; the coordinateaxes are J2000 Right Ascension and Declination. X-ray source extraction apertures constructed by AE ( § (cid:48)(cid:48) . An additional 3 sources(magenta) are confirmed by new VLT/HAWK-I observations (Thomas Preibisch, private communication). The 11sources currently not identified in other wavebands are shown in blue.involve crowded source apertures ( § §
5. POINT SOURCE EXTRACTION
The process of “extracting” a putative point source consists of several tasks: defining an appropriate aperturearound the source position, defining an appropriate background region that is expected to be a good estimator for thebackground contaminating the source aperture, collecting the observed events within the aperture and backgroundregions, and constructing a model for the response of the observatory that correctly calibrates the extraction so thatintrinsic source properties can be derived.When the source is assumed to be point-like, all of these tasks are best performed by algorithms that considerthe shape of the local
Chandra -ACIS point spread function (PSF). Thus, AE begins the extraction process byconstructing a model of the local PSF (Appendix C). Many
Chandra observers obtain extraction apertures for their point sources either from the
CIAO tool wavde-tect (Freeman et al. 2002) (the most popular source detection tool in the Chandra community), or by drawing theapertures by eye. Because wavdetect does not have explicit knowledge of the
Chandra
PSF, and because it seeks todetect both point-like and extended sources, it sometimes produces aperture shapes that are radically different fromthe PSF (e.g., ellipses with extreme eccentricity). An additional concern with apertures from wavdetect or visual in-spection is the risk of introducing an upward bias into photometry because both tend to “follow the light”—includingonly regions of the image where, by chance, the source produced an excess of events over the background. In ouropinion, a region derived from the local PSF is the most objective and appropriate extraction aperture for pointsources.When a source is “extended” (resolved by
Chandra ) the spatial distribution of its observed events do not followthe local PSF, and application of the point source extraction techniques in this section ( §
5) will underestimate theflux of the source. Such sources are more properly designated as “diffuse” and should be extracted by proceduresthat do not make the point-like assumption (see § wavdetect does),or apply a priori information about the structure of the source to define a suitable aperture. Observers often struggleto decide if a source is extended. The Chandra
Source Catalog provides a sophisticated analysis of source extent ,and the CXC has recently introduced a science thread for measuring source extent. AE does not currently addressthis task.Several observers employ elliptical approximations to the PSF as extraction apertures, e.g., Nandra et al. (2005)and the Chandra
Source Catalog use ellipses that enclose 70% and 90% of the PSF power respectively. AE extraction apertures are built from contours of the local PSF at 1.5 keV, as shown in Figures 5 and 6. By default, AE apertures enclose ∼
90% of the PSF power, which we have found is a reasonable trade-off between maximizing thesource’s signal and minimizing the background’s signal in typical fields. AE does not currently attempt to optimizethe aperture size based on the source and background levels (e.g., use a large aperture for bright sources and a smallone for sources just above the background).For many Chandra observations, some of these default apertures will overlap significantly due to source crowding. AE iteratively reduces the aperture sizes of crowded sources until the apertures no longer overlap (Figure 6). Thebrighter member of a pair of crowded sources maintains its default aperture until the aperture for the weaker memberhas been driven down to a minimum allowed size (enclosing ∼
40% of the PSF power). Of course, some light from http://asc.harvard.edu/ciao/download/doc/detect_manual See for example the analysis threads “Using psextract to Extract ACIS Spectra and Response Files for Pointlike Sources” ( http://asc.harvard.edu/ciao/threads/psextract/ ) and “Step-by-Step Guide to Creating ACIS Spectra for Pointlike Sources” ( http://asc.harvard.edu/ciao/threads/pieces/ ). http://cxc.harvard.edu/csc/columns/srcextent.html http://cxc.harvard.edu/ciao/threads/srcextent/ The
Chandra
Source Catalog performs two extractions for each source ( http://asc.harvard.edu/csc/columns/fluxes.html )—oneusing a wavdetect ellipse and one using a PSF ellipse.
12 – θ = 3.7’ θ = 4.1’θ = 9.1’ merged
Fig. 5.— Example of extraction apertures (contours of the local PSF) enclosing 90% of the PSF power constructedby AE ( § (cid:48) (upper-left), 4.1 (cid:48) (upper-right), and 9.1 (cid:48) (lower-left).The shape and overall size of the Chandra
PSF varies significantly across the field of view. Combining all of theavailable extractions of a source (lower-right) will in some cases produce lower-quality estimates of source propertiesthan could be obtained by ignoring some observations (e.g., the far off-axis data in the lower-left panel). Techniquesfor deciding which observations to ignore are discussed in § AE provides a sophisticated background algorithm that models and subtractsthis component ( § AE ( § § Fig. 6.— Example of crowded extraction apertures (contours of the asymmetric local PSF at ∼ (cid:48) off-axis) that havebeen reduced in size (enclosing 56% and 44% of the PSF power) until they do not overlap. These two X-ray sourcepositions (plusses) are confirmed by a high-resolution infrared observation.A PSF model and an extraction region must be constructed independently for each observation of a source. Apair of sources may be well-separated with nominally-sized apertures in an on-axis observation, but may suffer severecrowding with reduced apertures in an off-axis observation. Even a source observed twice at similar off-axis angles 13 –may have apertures with very different shapes, since the azimuthal shape of the Chandra
PSF varies across the focalplane. Once apertures are determined for each observation of a source, a mostly routine extraction process is followedfor each observation using standard
CIAO tools— dmextract selects the events within the aperture and constructsa Type I HEASARC/OGIP-compatible “source” spectrum; mkarf queries the Chandra
Calibration Database andconstructs an ancillary reference file (ARF); mkacisrmf queries the
Chandra
Calibration Database and constructs aresponse matrix file (RMF). When an aperture dithers across multiple CCDs, standard extraction methods willover-estimate the source flux (by as much as 50%) because the response at the source position of only one CCD iscomputed (using a single call to mkarf ). AE avoids this mis-calibration of the extraction by computing and summingthe response at the source position of all the CCDs (using multiple calls to mkarf ). Perhaps the most important calibration facilitated by the PSF model is accounting for the point source lightfalling outside the aperture and not extracted—a standard part of optical and infrared data analysis commonlyreferred to as “aperture correction.” Such correction is necessary because the Chandra Calibration Database effectivearea data assume an infinitely large detector and extraction aperture. Since the size of the
Chandra
PSF varies significantly with photon energy, the aperture correction is a functionof energy. AE builds images of the local PSF at five monochromatic energies (Appendix C), and calculates for eachPSF image the fraction of the power that falls within the aperture. Those five “PSF fractions” are interpolated toestimate a PSF fraction at every energy. The product of this PSF fraction curve and the nominal ARF producedby CIAO represents the true observatory effective area that is supplying photons within the aperture; this correctedARF is carried forward in the analysis. The energy and off-axis dependence of this aperture correction is illustratedin Figure 7.Omitting an aperture correction has two scientific effects. Firstly, flux estimates are biased downward (by ∼ shape of the source spectrum is somewhat distorted, especially for off-axis sources, because the PSF fraction varies withenergy (Figure 7, lower panel). Assessment of the detection significance and the spectral properties of a weak source depend critically onestimation of unbiased background spectra for each extraction (each observation) of the source. Often, backgroundestimates must be performed “locally” for each source to account for spatial variations due to diffuse emission, orwings of nearby point sources. AE supports three methods of constructing local background spectra.1. When all sources are well separated, a traditional approach using annular background regions is adequate. AE implements this approach by first masking (removing) virtually all the point source light from the data set using See Figure 10 in the HRMA User’s Guide ( http://cxc.harvard.edu/cal/Hrma/users_guide/ ). http://heasarc.gsfc.nasa.gov/docs/xanadu/xspec/fits/fitsfiles.html See for example the analysis threads “Using psextract to Extract ACIS Spectra and Response Files for Pointlike Sources” ( http://asc.harvard.edu/ciao/threads/psextract/ ) and “Step-by-Step Guide to Creating ACIS Spectra for Pointlike Sources” ( http://asc.harvard.edu/ciao/threads/pieces/ ). For example, the ahelp page for mkarf says “The ARF is computed assuming that the spectral extraction region is large enough toinclude the entire PSF (e.g., PSF fraction=1.0).” See Figures 5 and 6 in the HRMA User’s Guide ( http://cxc.harvard.edu/cal/Hrma/users_guide/ ).
14 – E ff ec ti v e A r ea [ c m ] PSF F r ac ti on Fig. 7.— Effective area as a function of X-ray energy (upper panel) for typical on-axis (black) and off-axis (gray)sources extracted by AE using default extraction apertures (90% PSF fraction at 1.5 keV, § mkarf ) and a PSF fraction curve (lowerpanel) obtained by interpolating measurements at five energies (dots).circular mask regions with a nominal radius that is 1.1 times a radius that encloses 99% of the PSF. Circularbackground regions are then defined independently for each source to encompass a number of background eventsspecified by the observer.2. AE also provides an alternative masking algorithm that first models the surface brightness expected from thepoint sources (using the PSF models and rough estimates of source fluxes), and then iteratively seeks to mask(remove) all portions of the field where the ratio of that point source glow to the local background level exceeds athreshold. This algorithm allows the large wings of bright sources to be removed with large masks, while avoidingexcessive loss of background area around weak sources, as shown in Figure 2. Circular background regions arethen defined independently for each source to encompass a number of background events specified by the observer.3. When sources are crowded, the concept of creating background spectra from a data set cleaned of all point sourcelight is not appropriate. By definition, a significant component of the background for a crowded source arises fromthe wings of its neighbors; those wings must be modeled.The ultimate analysis strategy would conceptually separate a source’s background into a point source wing com-ponent and a traditional smooth component not associated with detected point sources. The latter would beestimated via the masking techniques described above, and the former would be modeled via a complex multi-source spatio-spectral modeling process. Lacking the resources to implement that strategy, we have implemented aless complex strategy that seeks to estimate both components within each source’s aperture by carefully sampling the observed event data. AE first constructs a spatial model for every source (using the PSF models and rough estimates of source fluxes),and then iteratively constructs a background region for each source that seeks to sample fairly the light that eachneighbor’s wing is depositing into the source aperture. In the simple case where the source has one neighbor thatis contributing background to the source aperture, the algorithm will tend to build a background region that is anannulus around the neighbor, as shown in Figure 8. As the background region grows during the iteration, it will seekto avoid the wings of more distant sources that are not contributing light to the source aperture; thus for uncrowdedsources this algorithm produces similar background regions as algorithm AE tries to balance the competinggoals of acquiring the desired number of background events, fairly representing each background component (wingsfrom each neighboring point source, diffuse emission, and instrumental background), and sampling the backgroundlocally (acquiring background events in a compact region around the target source).For either masking-based approach, the observer can manually specify masks to remove portions of the fieldthat are not suitable background estimators, such as CCD readout streaks associated with bright sources. For the 15 –Fig. 8.— A background region constructed by AE (pixels marked in yellow) for a crowded source (red polygon). Theregion seeks to sample neighboring sources (purple circles) in proportion to their expected contamination of the redsource’s extraction aperture.spatial modeling-based approach, the observer can supply a spatial model for background structures that are notpoint sources, such as CCD readout streaks; such structures will be avoided or included in individual backgroundregions to the extent that the source aperture is contaminated by them.Regardless of how the background region is defined, we believe that the scaling traditionally applied to the back-ground spectrum—the ratio of the geometric areas of the source aperture and background region—is not appropriatefor ACIS data because the ACIS exposure map contains significant small-scale features caused by the dithering ofCCD edges and bad columns. For example, a source lying in a so-called chip gap may have an effective exposuretime that is less than half of nominal, while the majority of its background region may have nominal exposure. AE accounts for these exposure map features by adopting a background scaling equal to the ratio of the integrals of theexposure map over the source aperture and background region.
6. MERGING EXTRACTIONS FROM MULTIPLE OBSERVATIONS
Multiple observations of the same or overlapping fields have occurred throughout the
Chandra mission; evolvingconstraints on mission operations now commonly require projects to be split into short segments. When the aimpoints and roll angles are nearly identical, it is appropriate to join the segments and treat them as a single observation(e.g., Getman et al. 2005). But when the observations are misaligned, extraction must be performed separately oneach observation. In principle, X-ray properties for a source could be estimated directly from the multiple extractions of thesource (multiple source spectra, background spectra, ARFs, and RMFs). For example, photometric quantities couldbe estimated by maximizing a likelihood function involving terms for all of the observations (source and backgroundextractions). Similarly, a spectral model for the source could be derived by simultaneously fitting all of the extractions.However, this approach is impractical for the majority of faint
Chandra sources, where a few counts are spread overa number of separate observations. The
CIAO thread Merging Data from Multiple Imaging Observations ( http://cxc.harvard.edu/ciao/threads/combine/ ) states:“The merged event list should not be used for spectral analysis, since it does not contain sufficient information to generate correct responsefiles. The recommended technique for the spectral analysis case is to generate separate PHA, RMF, and ARF files for each observation...”.
16 – AE adopts an alternate strategy—multiple extractions of a source are merged into “composite” data products(PSF model, source spectrum, background spectrum, ARF, and RMF), which are carried forward for analysis. Sourcespectra and exposure times are summed. Weighted averages of the PSFs, ARFs, and RMFs are computed using IDL and the FTOOLS addarf and addrmf . In order to support “grouping” of low-count spectra at later stages of theanalysis, the composite background spectrum is represented in the same way as the source spectrum, as an integer“counts” vector (the sum of the extracted background spectra) with an associated scaling value (to account for thedifferent sizes of the source and background regions), rather than as a real-valued “rate” vector with uncertaintieson each rate value. Extraction data products from each observation are retained so that the observer can analyzethem separately (or simultaneously) if desired.An important constraint on the design of the individual extractions arises from the decision to sum the integer-valued background spectra, namely that all the individual background regions must be designed to have similarscaling values. This constraint arises because each individual background spectrum must be fairly represented inthe composite background in order for Poisson ( √ N ) uncertainty estimates to apply to the composite background.This can be understood by considering an extreme example. Imagine a background channel in which observation /
25) + (1 × / × ) = 2 .
0. However, the Poisson uncertaintyestimated (by a fitting package) for that background rate would be far too small, since it is based on the notionthat 10,025 counts were observed. In fact, the 25-count extraction totally dominates the uncertainty on the scaledcomposite background, which actually has an approximate uncertainty of (cid:113) ( √ ) + ( √ , , ) (cid:39) . AE includescode and workflow recommendations to ensure that all extractions of a source result in similar scaling of theirbackground spectra. When multiple observations of a field are available, astronomers commonly choose to disregard observationsthat are judged to be unhelpful to whatever astrophysical measurement is desired. For example, in ground-basedoptical studies, exposures with unusually bad seeing or unusually high background might be ignored. In all ACISstudies, observers are encouraged to discard data obtained during periods of very high instrumental background (due to solar activity). In ACIS studies involving multiple misaligned pointings, observers often choose to ignoredata taken far off-axis (where the
Chandra
PSF is significantly degraded ) if on-axis coverage is available (e.g.,Plucinsky et al. 2008). ACIS observers also commonly choose to search for sources both within each observationseparately and within observer-defined combinations of observations (e.g., Muno et al. 2009). AE tries to formalize this common practice of ignoring unhelpful observations by implementing three data-selection strategies that are applied independently to each source.1. When the observer is interested in the validity of proposed sources using AE ’s P B statistic ( § AE option that selects whatever subset of the available extractions that optimizes (minimizes) P B foreach source. Under this option, an extraction will be included only when the particular signal and background itcontributes lowers P B . This option is appropriate when the observer wishes to adopt the scientific policy that asource is deemed to exist if it is significant in any observation, or in any combination of observations. For highlyvariable astrophysical sources, such as young stars, this is a reasonable strategy even when multiple observations When a fitting package groups several spectral channels together, if the spectrum is expressed as integer counts then the Poissonuncertainty on the group can be estimated accurately from the total number of counts in the group (e.g., via √ N ). In contrast, groupinga spectrum expressed as a rate vector with uncertainties requires Gaussian propagation of those uncertainties; many channels in typicalACIS spectra have zero or one count, with virtually meaningless uncertainties. http://cxc.harvard.edu/ciao/threads/acisbackground/index.py.html For convenience, this is commonly performed in the early stages of data analysis, guided by the damage that the enhanced backgroundwill do to the sources most susceptible to background (e.g., diffuse sources). A somewhat better strategy would be to choose high-background periods to discard on a source-by-source basis, since very bright point sources would benefit more from extra integration timethan from a reduction to their already insignificant background. AE has not yet adopted this optimum strategy because implementationis difficult. See Figure 8 in the HRMA User’s Guide ( http://cxc.harvard.edu/cal/Hrma/users_guide/ ).
17 –have similar PSFs. The price paid for increased sensitivity to variable sources is an increased false detection ratefrom the additional number of random “trials” that can produce spurious detections.2. When the observer is interested in the position of sources, then we recommend an AE option that selects whateversubset of the available extractions optimizes (minimizes) the expected position uncertainty ( § is outweighed by the advantage of averaging over more counts. Since we register each of our observation to anabsolute astrometric reference frame, all observations of a source are well-aligned and it is appropriate to estimatethe position using only the best data we have.3. When the observer is interested in time-averaged photometric properties (e.g., fluxes, spectra) then selecting theextractions to merge becomes more problematic. Anytime extractions are discarded in order to optimize a pho-tometric quantity (e.g., SNR) a bias can be introduced into all photometric properties because the discardedextraction may have, by chance, lower observed flux than the long-term average. Thus, the observer must bal-ance two undesirable outcomes: sources whose photometric accuracy is degraded by including very poor-qualityextractions, and sources whose photometry suffers the suspicion of bias because some extractions were discardedafter examining their data. AE offers an option that strikes this balance by discarding extractions only whenretaining them would drive the SNR of the merged data set significantly below the optimal SNR. The observerspecifies the minimum acceptable ratio between the SNR achieved by the merge and the optimal SNR achievableby discarding more extractions. This strategy tolerates limited deterioration to the SNR in order to avoid photo-metric bias arising from data selection. Bright sources will tend to incorporate all observations since backgroundis unimportant, whereas weak sources will tend to reject observations that have backgrounds much higher thantheir peers (e.g., those with much larger apertures).
7. SOURCE PROPERTIES
After merging the appropriate set of extractions (observations) for each source, AE calculates various photo-metric quantities, estimates various source properties, fits astrophysical models to source spectra using XSPEC , andconstructs light curves. These analysis capabilities are described in the AE manual, but a few warrant discussionhere. While initial source positions are provided by a source detection process, these may not be optimal. AE providesthree procedures for improving source positions. One position estimate is constructed by calculating the centroidof the extracted events. A second estimate is determined from the peak of the spatial correlation between the Chandra -ACIS PSF (Appendix C) and the events in a neighborhood around the source. A third position estimateis obtained from the location of the peak in a maximum-likelihood (Lucy 1974) image reconstruction of the sourceneighborhood. In a multi-observation reduction, the correlation and reconstruction operations are performed usinga composite (multi-observation) event image and a composite PSF image because a given source may be undetectedin an individual observation.In our experience, all three methods give very similar positions for most on-axis sources; the centroid positionis simplest to calculate and is often used. The PSF correlation position is best for sources far off-axis ( θ (cid:38) (cid:48) );centroid positions are biased estimates of the true locations due to the asymmetry of the off-axis PSFs. For veryclosely-spaced sources with overlapping PSFs (Figure 6), the best positions are provided by the maximum-likelihoodreconstructed images. Since the centroid position is calculated using the extracted events, it should be re-calculatedafter a source is repositioned to verify convergence.Positional errors are estimated separately along the right ascension and declination axes according to σ RA = σ model,RA / √ N (1) σ Dec = σ model,Dec / √ N (2) σ r = (cid:113) σ RA + σ Dec (3) 18 –where σ model,RA and σ model,Dec are the standard deviations along the right ascension and declination axes of a modelof the counts falling within the extraction region. That model consists of the PSF projected onto each axis plusa flat background component appropriately scaled, both truncated by the source’s extraction region; the spatialdistribution of the observed data is not considered. N is the total number of extracted counts. The quantity σ r ,commonly known as the distance root-mean-square error, is generally reported as the “1 σ ” error, or 68% confidenceinterval, for the source position. Standard ACIS spectral files divide the energy range covered by the instrument into many hundreds of pulse-invariant (PI) energy channels, many of which have very few counts for typical sources. Energy channels are thereforefrequently grouped. AE offers only one of the several grouping criteria found in standard grouping tools—groups areconstructed to have similar signal-to-noise ratios—but improves on standard implementations in several importantways:1. Standard algorithms provide no convenient way for the observer to define precisely the energy range over whichspectral models will be fit. AE allows the observer to specify the boundaries of the first and last groups. Forexample, if the energy range 0.5–8.0 keV is specified, then the first group will span all the channels below 0.5 keVand the last group will span all the channels above 8.0 keV; these terminal groups can be subsequently “ignored”within a fitting package.2. The criterion AE uses to define a group is a target SNR for the net counts in the group. Standard grouping toolsdo not consider the background spectrum, and thus produce background-subtracted grouped spectra with SNRvalues lower than the target.3. Standard algorithms are asymmetric, filling groups from low to high energies. For sources with fewer than severalhundred counts, groups often begin with a string of empty channels and end on a channel that happens to have anobserved event. This permits anomalies in the grouped spectra, such as narrow-width groups with overestimatedflux adjacent to wide groups with underestimated flux. These distortions can bias the spectral fitting and inflatethe best-fit χ value. AE ’s grouping algorithm attempts to mitigate this problem by selecting group boundariesmid-way in the run of empty channels (if any) that lie between events belonging to adjacent groups. X-ray spectra observed with ACIS energy resolution typically show some combination of continuum components,line emission, and absorption features from interstellar matter. Accurate characterization requires fitting with non-linear astrophysical models ( § AE provides estimates of the 25% quartile, median (50% quartile), and 75% quartile of the observed eventenergies over a variety of bands. These statistics are background-corrected, meaning that they seek to characterize The
Chandra
Source Catalog takes a different approach to positional errors, ( http://asc.harvard.edu/csc/columns/positions.html ) adopting error ellipses ( http://asc.harvard.edu/csc/why/err_ellipse_msc.html ) directly from the wavdetect program for singleobservations, and combining ellipses for multiple observations.
19 –the observable spectrum of the astrophysical source as if background were not present. AE implements an intuitiveand straightforward background correction for standard quartiles, based on the observed cumulative distribution ofthe net spectrum, as shown in Figure 9. This method appears to be equivalent to that described by Hong et al.(2004, Appendix C), which was developed independently. AE does not yet estimate individual confidence intervalsfor these background-corrected quartiles. C u m u l a t i v e D i s t r i bu t i on Fig. 9.— Example calculation of the background-corrected median energy statistic. The 20 large upward jumps inthe cumulative distribution of net counts (rising curve) represent the 20 counts observed in the source aperture; the100 small downward jumps (not individually visible) represent the 100 counts observed in the background region,scaled down to match the source aperture size. The lowest energy (left vertical line) and highest energy (right verticalline) at which the 50th percentile (dotted line) is reached are averaged to produce an estimate of the median energyof the parent source. Here, the median energy is ∼ . Chandra studies of young stars have chosen to use the median energy statistic, rather than multiplequartiles, for deriving intrinsic properties of absorbed thermal plasmas ( § The common procedure for obtaining broad band source fluxes and luminosities (given astronomical distances)is to fit the spectrum derived above with astrophysical models convolved with the ARFs and RMFs representing theobservatory response. This path (which we follow in § AE begins by performing standard aperture photometry, computing “net counts” quantities for various energybands, S ( E ), by subtracting a scaled background from the counts observed near the source. S ( E ) = C s ( E ) − ( A s /A b ) C b ( E ) (4) C s ( E ) is the number of counts observed in the source aperture in energy band E . C b ( E ) is the number of countsobserved in the background region in energy band E . The source and background “areas”, A s and A b , are derivedby integrating exposure maps rather than computing geometric areas ( § § C s and C b are estimated using the common analytical approximationsto confidence intervals of the Poissonian distribution constructed by Gehrels (1986, equations 7 and 12). Theseconfidence intervals are propagated through equation 4, using the method described by Lyons (1991, equation 1.31),to estimate an asymmetric confidence interval for S ( E ). This technique is not ideal, and we anticipate adopting theBayesian technique for estimating confidence intervals used by the Chandra
Source Catalog, which is implemented http://cxc.harvard.edu/csc/why/ap_vals_errs.html
20 –in the
CIAO tool aprates .These standard “net counts” quantities are used to construct two estimates of incident photon flux onto the
Chandra telescope, designated here F (cid:63) and F , in units of photon cm − s − (not the usual erg cm − s − ). For thefirst estimate, the net count rate is divided by the observatory response in each of many narrow channels, and thesenearly-monochromatic photon flux densities are summed over a chosen energy band: F (cid:63)phot ( E ) = S ( E )EXPOSURE × ARF( E ) (5) F (cid:63)phot ( E min < E < E max ) = E max (cid:88) E min F (cid:63)phot ( E ) (6)where S ( E ) is the net observed counts (equation 4), ARF( E ) is the observatory effective area ( § E min and E max are the energy range provided by the user. Commonly used energybands are E min = 0 . E max = 2 keV for the Chandra “soft band” and E min = 2 keV and E max = 8 keVfor the Chandra “hard band.”For the second photon flux estimate, the net count rate in a user-supplied band is divided by the observatoryresponse averaged over the band:ARF( E min < E < E max ) = E max (cid:88) E min ARF( E ) (7) F phot ( E min < E < E max ) = (cid:80) E max E min S ( E )EXPOSURE × ARF( E min < E < E max ) (8)The F (cid:63) estimator can suffer from large Poisson errors because events (either source or background) at energieswhere the ARF is very small have a large effect on the estimator, and is thus not recommended for weak sources.For example, an event at 8 keV where the ARF value is tiny makes a much larger contribution to F (cid:63) than an eventat 2 keV where the ARF value is large. The F estimator suffers from a systematic bias with respect to the trueincident photon flux because the effective area averaged over the energy band (equation 7) is the correct calibrationof the net counts photometry only for the non-physical case of a flat incident spectrum.When a priori information provides constraints on the shape of a source’s intrinsic spectrum, these photon fluxestimates F (cid:63) and F can be combined with the background-corrected median energy ( § E median , and with theastronomical distance d to estimate apparent source luminosities L x in a chosen broad energy band: L x ≈ πd [ F (cid:63) or F ] E median . (9)Getman et al. (2010) has studied in detail the accuracy and precision of this estimate for both bright and faintsources, particularly when absorption from line-of-sight interstellar matter is present. E median is an accurate, thoughnonlinear, predictor of interstellar column density N H when the intrinsic family of spectral models (e.g., power law,thermal plasma) for the source is known (Feigelson et al. 2005; Getman et al. 2010, Figure 4). E median thus entersthe calculation twice, once to scale the photon flux to the observed luminosity in equation (9), and again to scalethe observed luminosity to the intrinsic luminosity (corrected for absorption; Getman et al. 2010, Figure 5).Simulations (Getman et al. 2010) indicate that these nonparametric estimates of observed luminosities andabsorption column densities are quite accurate, with only moderate biases and statistical errors. Systematic errorsare larger for estimates of the absorption-corrected luminosities, and can be extremely large for heavily absorbedsources when the chosen spectral band includes the soft X-ray regime. In our work on faint sources, we choose to usethe more statistically stable F photon flux estimator and prefer absorption-corrected luminosities in the hard band(2–8 keV) (which is less vulnerable to errors in absorption correction) over luminosities in the total band (0.5–8 keV). A similar method is used in the
Chandra
Source Catalog where it is called “aperture source energy flux” ( http://asc.harvard.edu/csc/columns/fluxes.html ).
21 – AE relies on the widely-used XSPEC package (Arnaud 1996) for spectral fitting. XSPEC provides a widerange of intrinsic spectral models (such as non-thermal power laws and thermal plasmas), absorption by interveningmaterial, and convolution with the
Chandra /ACIS instrumental response. Models derived from χ minimizationbecome inaccurate for sources with few counts, and the problem is exacerbated when a significant fraction of theextracted events are background that is subtracted. Spectral fitting of faint sources is thus usually pursued using theC-statistic applied to unbinned data, an application of the Likelihood Ratio Test under the assumption that the datafollow the Poisson distribution (Cash 1979). Background subtraction is not possible for likelihood-based statisticalprocedures; instead, a background model must be included in the spectral model that is fit to the data (source plusbackground) extracted from the source aperture, and that background model should be simultaneously fit to thedata extracted from the background region. This fitting procedure is depicted in Figure 10 as a data flow diagram. spectrum from source region spectrum from background region ACIS response flat response (e.g. cplinear ) + C-statisticC-statistic + minimize C-statistic predictedinstrumentalspectramodelincidentspectra extracted instrumental spectrumextracted instrumental spectrum background model(e.g. tbabs*vapec )source model Fig. 10.— Data flow diagram of parametric fitting procedure using the C-statistic with the cplinear backgroundspectral model ( § XSPEC implements such a background model, which was derived by Wachter et al. (1979), for use with theC-statistic. This model consists of a free parameter representing the background flux in each of the hundreds ofspectral channels used in an ACIS spectrum. Such a model raises two theoretical concerns. First, in most caseswhere the C-statistic would be used, there are many more free model parameters than background events. Second,such a model is completely unconstrained—extremely narrow and quite non-physical features (one channel wide) inthe incident background spectrum are presumed to be possible. Indeed, observers have found that this algorithmsometimes provides very poor “best fits” to the observed spectrum, with incorrect normalizations and non-physicalspectral parameters. We found that substituting a more constrained model for the ACIS background stabilized the algorithm andlessened the problem of non-physical fits. For sources with relatively few ( ∼ cplinear model; an example is shownin Figure 11. Figure 12 gives an example where the background model of Wachter et al. (1979) gives a poor fit and The
Sherpa package ( http://cxc.harvard.edu/sherpa/ ) provides similar fitting capabilities, but the authors had more experiencewith
XSPEC at the time AE development began. See Appendix B of the
XSPEC manual ( http://heasarc.gsfc.nasa.gov/docs/xanadu/xspec/manual/manual.html ). See http://xspector.blogspot.com/2007/01/cstat-with-background-files-and-low.html and http://xspector.blogspot.com/2005/07/cstat.html . See the discussion of the cplinear model in the AE manual. A comparison of source models using the Wachter et al. (1979) and cplinear background models for 900 ACIS sources is available in Appendix B of that document.
22 –the cplinear model gives a good fit. P ho t on s c m − s − k e V − Energy (keV)
Fig. 11.— Example of a cplinear background spectral model ( § cplinear model is inadequate to model high quality background spectra which exhibitcomplex structure. More physically-based background models would be useful to the ACIS community; our goalhere is to emphasize that severely under-constrained background models should be avoided, rather than to claimthat cplinear is optimal. The ultimate solution to modeling low-count X-ray spectra may lie in Bayesian approaches,such as the innovative technique of van Dyk et al. (2001). Those authors also suggest that background models withappropriate functional forms are useful, however the background model presented in that published work employeda free parameter for each channel in the spectrum (van Dyk et al. 2001, eq. 22), similar to the Wachter model.Another algorithmic innovation to spectral fitting provided by AE is the improved method for grouping spectra(either for fitting with the χ statistic or for plotting ungrouped spectra fit with the C-statistic) described earlier( § AE also offers the observer several procedural conveniences. XSPEC scripts that drive fits to threecommon astrophysical models (absorbed one- and two-temperature thermal plasmas, absorbed power law), usingeither χ or the C-statistic with the cplinear background model, are provided. AE automates the execution of thesefitting scripts; fitting multiple models to thousands of sources is feasible. When multiple models have been fit to asource, the observer can visualize those models and select the most appropriate one using the graphical interface inthe AE tool Spectra Viewer ; an example screen shot is shown in Figure 13. Numerical output of the fitting process(in the form of a FITS table) includes best-fit spectral parameters with their confidence intervals and model fluxesintegrated over various spectral bands.
For visualization of source variability, light curves for all observations of the source are depicted on a single plot,which is shown in calibrated units (photon ks − cm − ) rather than observed units (count ks − ) to avoid spuriousapparent variability arising from differences in observatory response or PSF fraction between observations. Two lightcurves are constructed. One is a histogram with variable-width time bins, constructed by the same algorithm usedto group spectra ( § AE also produces a “photon arrival diagram”—a scatter plot of event arrival time andenergy. Figure 14 shows an example multi-observation light curve and a photon arrival diagram for a flaring source.For quantification of variability, the null hypothesis of a uniform source flux is tested using a one-sampleKolmogorov-Smirnov statistic. For multi-observation cases, variability is tested both within and between ob- The
Chandra
Source Catalog also provides variability tests ( http://asc.harvard.edu/csc/columns/variability.html ) based on
23 – n o r m a li z e d i n t e g r a t e d c o u n t s r e s i d u a l s N H =9.02, kT=0.167, SRC_CNTS=61 thermalmodelnet observed spectrum N H =3.06, kT=14.6, SRC_CNTS=61 background spectrum and model scaled background modelthermalmodelextracted spectrum; thermal+background model n o r m a li z e d i n t e g r a t e d c o u n t s r e s i d u a l s Fig. 12.— Example of spectral models for a faint stellar member of the M 17 star forming region derived with theC-statistic in
XSPEC using the Wachter et al. (1979) (top panel) and cplinear (bottom panel) background models(see Figure 10). Residuals are shown at the bottom of each panel. The top panel shows the observed cumulative net spectrum (black stair-step curve) and the best-fit thermal plasma model (blue continuous curve) for the star;the Wachter background model is not shown. Note that the fit is incorrect above 1 keV. The bottom panel showscumulative spectra from the source aperture and background region separately.
XSPEC is configured so that thespectrum extracted from the background region (red stair-step curve) is compared to a cplinear model (red continuouscurve), and the spectrum extracted from the source aperture (black stair-step curve) is compared to the sum (blackcontinuous curve) of a scaled copy of the cplinear model (purple curve) and a thermal plasma model of the star (bluecurve). Best-fit parameters for the two models are then derived simultaneously.servations (accounting for variations in effective area among the observations).The current timing analysis has some deficiencies. No tests for autocorrelation, periodicity, or other temporalbehaviors are made. The KS statistic is insensitive to variations near the beginning or end of the observation.Variability in the background is not considered in the uniform flux model, and background is not accounted forin the light curves or median energy time series. Although the ACIS background is often quite stable within anobservation, multiple observations of a source can easily suffer very different background count rates within thesource apertures because the aperture sizes can be quite different. Thus, for example, a spurious indication ofvariability can be produced for a weak source observed at two very different off-axis angles. We plan to eliminatethis problem by adding to the uniform light curve model independent background levels for each observation. the variance, Kuiper statistic, and Bayesian method ( http://asc.harvard.edu/csc/why/gregory_loredo.html ) of Gregory & Loredo(1996).
24 –Fig. 13.— Screen shot of three spectral fits to an AE source presented in the Spectra Viewer tool. An IDL “widget”(top) provides navigation controls to select a source from the catalog, displays tabular information about all thespectral fits available for the selected source, and allows the observer to choose the preferred fit. Standard
XSPEC plots from each spectral fit are shown in separate ghostview windows. A FITS header containing various propertiesof the selected source is shown (lower left window).
It is often desirable to “stack” a sample of similar sources to construct a summed spectrum with higher SNR thanavailable from individual objects. This can be performed either for sources detected in the ACIS data or at locationsof objects known only from independent observations. Stacking many similar objects can thus give extremely longeffective exposures and sensitivities, however stacking results can be dominated by the few brightest objects in thegroup. This technique has been widely used in
Chandra deep extragalactic field studies (e.g., Hornschemeier et al.2001; Brandt et al. 2001; Lehmer et al. 2007).In AE , stacking is achieved by relabeling extraction subdirectories of interesting sources to resemble extractionsof distinct observations of a single source. Then the extractions are merged ( §
6) and source properties are estimatednormally ( § P h o t o n s / k s / c m Time (ks)1 2 3 4 5 6 M e d i a n E n e r g y ( k e V ) Time (hrs) E n e r g y ( k e V ) C u m u l a t i v e D i s t r i b u t i o n , d a t a & u n i f o r m m o d e l Fig. 14.— Concatenated light curves for a source observed six times (six numbered epochs in upper panel) andphoton arrival diagrams for two of those observations (lower panels). The light curves show variations in photon flux(black histogram bins and blue adaptively smoothed curves) and median energy (red histogram bins); the spectrumis seen to harden when the source flares. The photon arrival diagrams depict the arrival time and energy of eachevent (black dots) in a single observation, the cumulative distribution of event arrival times (red curve), and thecumulative distribution expected from a constant source (magenta curve).
The properties of individual sources obtained by AE can be collated into a summary FITS table with > fv or chips FITS viewers,
IDL two- and three-dimensional plotting, and R multivariate statistical analysis. AE R is a large, public-domain ( ) statistical analysis software package.
26 –also prepares standard quantities for publication as
LaTeX tables, illustrated by Tables 1 and 2. This feature isparticularly valuable for fields with hundreds or thousands of sources.
8. Matching Point Source Catalogs
The task of “matching” point source catalogs—identifying entries in two or more catalogs that are believedto represent the same physical source—is fundamental to astronomical research, and is growing increasingly morecommon as publicly available and high quality catalogs covering many wavebands proliferate. As yet, no standardalgorithm for this task has been adopted by the community, and thus no single software tool for matching is inwidespread use.We currently use a matching tool written by one of the authors, the
IDL program match xy in TARA (Broos et al.2007). The basic criterion used to evaluate whether a proposed pair of sources from two catalogs could be detectionsof the same physical object is very simple. Given a significance threshold chosen by the observer, Gaussian positionaluncertainties specified individually for the two sources are used in a classical test of the null hypothesis that they areobservations of the same object. This matching criterion does not represent an innovation; the astronomy literaturecontains several more sophisticated catalog matching algorithms, such as ones that provide individual probabilitiesthat each asserted match is merely a chance coincidence (Downes et al. 1986; Sutherland & Saunders 1992; Rutledgeet al. 2000; Bauer et al. 2000), ones that consider non-positional source properties (such as fluxes) (Brand et al.2006; Budav´ari & Szalay 2008), and ones that operate on more than two catalogs simultaneously (e.g., the
XMatch algorithm in the SkyQuery service designed for the Virtual Observatory).However, we do recommend four features of our matching tool for use in any catalog matching procedure appliedto
Chandra sources. First, individual estimates of positional uncertainty for each source, rather than a canonicalvalue for the whole catalog, are employed because they often span a wide range due to
Chandra ’s variable PSF;the uncertainties estimated by AE ( § < . (cid:48)(cid:48) (not including systematic errors) to > (cid:48)(cid:48) . Second, our algorithm enforces a one-to-one relationship among the pairs of sources declared to be “successful”matches, i.e., no source participates in multiple successful matches. The algorithm reports a “failed” match whena pair of sources pass the matching criterion, but one of them is already participating in another (more reliable)match. Third, we have found that visual depictions of the matching results, such as the DS9 region files producedby match xy , are invaluable aids to reviewing the general performance of the algorithm and to understanding specificsources. We have used these region files in a prototype
Source Viewer tool that facilitates visual examination of thevicinity of each source in two or more images (e.g., X-ray and near-infrared), and records the observer’s subjectivecomments on individual sources. Fourth, all matching procedures should measure and correct astrometric offsetsbetween catalogs at the outset; any large astrometric uncertainty should be included in the individual estimates ofpositional uncertainty.
9. ANALYSIS OF DIFFUSE X-RAY STRUCTURES
Extended emission from hot diffuse plasma is commonly present in X-ray studies. This occurs in galaxy groupsand clusters, elliptical and spiral galaxies, Galactic star formation and starburst regions, supernova remnants, plan-etary nebulae, and wind-blown bubbles. Since point sources are often superposed onto the diffuse emission, thefirst step in our diffuse analysis workflow (Figure 1) is to identify and mask (remove) as many point sources aspossible, using the procedures described in § http://openskyquery.net/Sky/SkySite/help/algo.aspx
27 –
As described in § AE provides two methods for constructing mask regions that remove pointsource photons that would contaminate an analysis of diffuse emission. The remaining event distribution, consistingof instrumental background and possible astrophysical diffuse emission, is often best studied in smoothed images.Although the CIAO task csmooth (Ebeling et al. 2006) is effective and popular for smoothing unmasked data thatcontain both point sources and diffuse emission, it is poorly suited to working with images that contain unobservedregions, either masked point sources or regions beyond the edges of the detector, because the tool does not allow afield mask to be supplied. The
CIAO thread for diffuse emission with embedded point sources replaces pixel valuesin source regions of an image with values interpolated from surrounding background regions using random Poissonnumbers or local polynomial regression.We prefer to apply an adaptive kernel smoothing tool in TARA that handles excised pixels and field edges,which is similar to the asmooth tool in the
XMM-SAS package and the new dmimgadapt tool in CIAO − ) by dividing the number of counts under the kernel by the integrated exposure map under the kernel.Maps of photon flux, flux error, and kernel size are produced. The observer can choose to retain or smooth over theholes in the data introduced when point sources are masked. The method is described in detail, with sample images,in Townsley et al. (2003, Appendix C). As the AE package does not attempt to delineate the morphology of diffuse structures, the observer must defineeach diffuse source of interest in the form of a DS9 region file that is accepted by
CIAO . We have found the WVTBinning algorithm (Diehl & Statler 2006), which is a generalization of the Voronoi binning algorithm describedby Cappellari & Copin (2003), to be a very effective method for tessellating a field with compact regions of similarSNR. Figure 16 shows an example if its use.The procedure for extracting each diffuse source with AE is analogous to the point source procedure. For eachobservation, events within the source region are extracted, calibration products are constructed, and backgroundspectra are extracted. All the extractions are merged, photometric quantities are estimated, and spectra are fit viaautomated scripts. However, more complex procedures are required to calibrate diffuse extractions and to accountfor background, as described in the next two sections. The ARF data product constructed for point sources by the tool mkarf can be thought of more abstractly asan observatory response function, ARF( E, p ), computed at a position on the sky, p , for a monochromatic energy E ,with units of cm count photon − . For
Chandra data, this function represents both variations in the observatoryresponse across the focal plane and the exposure time variations across the sky caused by dithering over bad detector http://asc.harvard.edu/ciao/threads/diffuse_emission/ http://xmm.vilspa.esa.es/external/xmm_sw_cal/sas_frame.shtml http://cxc.harvard.edu/ciao/ahelp/dmimgadapt.html We can provide the reader with a small tool that converts the output of the WVT Binning package into a set of
DS9 region files. http://cxc.harvard.edu/ciao/dictionary/arf.html An ARF is a product of a mirror effective area with units of cm and a detector quantum efficiency with units of count photon − .
28 –pixels and detector edges. Essentially, ARF( E, p ) describes the “depth” of the observation, since effective area andobserving time are degenerate terms in a flux calculation. For example, ARF( E, p ) trends downward with off-axisangle, due to vignetting of the mirrors. ARF( E, p ) is reduced at any sky position that dithered across bad pixels ordithered off of ACIS. Conceptually, ARF( E, p ) is zero in regions on the sky that have been masked to remove pointsources ( § E, p ) function for any particular observation will vary within a diffuse extraction region, and in amulti-observation study may be zero over much of that region. Figure 15 shows an example diffuse region that isfully contained in one ACIS-I observation (left panel) but barely intersects another ACIS-I observation (right panel).Just as a diffuse extraction can be viewed as an integration of the observed counts over the extraction region, theproper calibration of that extraction can be viewed as an integration of ARF( E, p ) over the region.ARF R ( E ) = (cid:90) R ARF( E, p ) d p (10)Fig. 15.— A diffuse extraction region (black polygon) that is fully observed by one ACIS-I observation (maskedexposure map, left panel) and partially observed by another observation (masked exposure map, right panel).Note that this integration over a region on the sky gives ARF R ( E ) units that include a geometric area term,such as cm count photon − arcsec . As ARF R ( E ) is carried forward into photometry calculations and spectralfitting, all “flux” quantities derived should be interpreted as surface flux quantities, with arcsec − appended to theunits. Flux integrated over the diffuse region is then estimated by multiplying the surface flux by the region’s total geometric area on the sky; the area lost to point source masks, bad pixels, and detector edges is already accountedfor in ARF R ( E ).Recasting the diffuse ARF of each extraction to include the notion of “area on the sky” is particularly convenientwhen multiple extractions are to be combined (i.e., merged by AE , just as is done with point sources). Just as eachextraction of a point source may have a different PSF fraction ( § R ( E ) cannot be directly calculated with existing tools. The CIAO point source tool mkarf implementsmost of the behavior of the integrand ARF( E, p ) described above, but has no mechanism to set ARF R ( E, p ) to zeroat positions where the event data have been masked. The CIAO tool mkwarf (“make weighted ARF”) implementsan effective area averaging calculation that is related to Equation 10, however for each observation mkwarf averagesover only the detector area that intersects the diffuse region, not over the entire diffuse region, which may includeareas with zero response due to masking or detector boundaries. The difference between the diffuse ARF we havedescribed here, ARF R ( E ), and the data product returned by mkwarf can be summarized with the aid of Figure 15.For both extractions shown there, the mkwarf data products will have similar normalizations, because responses areaveraged over the detector areas intersecting the extraction region. In contrast, ARF R ( E ) will be much larger forthe left-hand extraction than for the right-hand extraction, because responses are averaged over the entire region. The
Chandra convention is that the exposure time (FITS keyword “EXPOSURE”) recorded for a point source is always the nominalexposure time for the observation. If necessary, a source’s ARF is reduced to account for the amount of time the source was not observeddue to dither motion.
29 –Although the full ARF R ( E ) function is not available as a standard data product, the value of ARF R ( E ) at asingle energy E is easily calculated by integrating over the extraction region a standard CIAO exposure map builtfor a monochromatic energy E and masked in the same way as the event data. In the context of an AE extraction,the exposure map is “un-normalized” with units of s cm count photon − , built by supplying the “normalize=no”option to the CIAO tool mkexpmap . This exposure map is related to the integrand ARF( E, p ) asemap E ( p ) = EXPOSURE × ARF( E , p ) , (11)where EXPOSURE is the “exposure time” of the observation. Thus, the diffuse ARF we seek is easily calculated atone energy as ARF R ( E ) = (cid:82) R emap E ( p ) d p EXPOSURE (12)With the normalization of ARF R ( E ) established at energy E , AE then relies on the mkwarf result to establishthe shape of ARF R ( E ) as a function of energy. AE ’s complete calculation of ARF R ( E ) is thusARF R ( E ) = ARF mkwarf ( E )ARF mkwarf ( E ) × (cid:82) R emap E ( p ) d p EXPOSURE (13)where ARF mkwarf is constructed by mkwarf .To summarize this section, we calibrate each diffuse extraction by constructing ARF R ( E ), which has unitsof cm count photon − arcsec and accounts for the area on the sky lost to point source masks, bad pixels, anddetector edges. “Flux” quantities subsequently derived should be interpreted as surface flux quantities, with arcsec − appended to the units. Flux integrated over the diffuse region is estimated by multiplying the surface flux by theregion’s total geometric area on the sky. Diffuse sources are often heavily contaminated by background—both instrumental background and emissionfrom foreground and background astrophysical sources that are not of interest. Several strategies to account forbackground in diffuse sources are described in the AE manual. We choose to subtract from each diffuse extraction astandard instrumental background spectrum obtained by scaling the so-called “ACIS stowed event data” providedin the Chandra
Calibration Database (Hickox & Markevitch 2006). After merging the multiple observations of adiffuse region (with the same methods that are used for point sources in §
6, with no optimization options enabled),standard “source” and “background” spectra with calibration data products are available. Astrophysical backgroundcontaminating a diffuse region can be handled in either of two ways. First, if a nearby “sky” region thought to bemostly free from the emission under study is available, then its observations and “stowed backgrounds” are extracted,and two net spectra from the diffuse region and the sky region are simultaneously fit using a shared model for theastrophysical background in both regions plus a source model for the emission of interest in the diffuse region.Alternatively, if no suitable “sky” region is available, then the astrophysical background must be directly modeled(Snowden et al. 2008). If appropriate fitting scripts are constructed, AE can automate this spectral fitting in thesame way that point source spectral fitting is automated. When more than a few diffuse regions are defined, many observers have found that spectral fitting results canbe best understood by creating maps that show various results, e.g., model parameters and fluxes. Standard gray-scale or false-color maps effectively depict to the human eye spatial variations in a parameter. We are currentlyexperimenting with a complementary map-coloring technique that seeks to depict both a parameter’s value and itsuncertainty, using hue to encode the parameter value and brightness to encode its uncertainty, as shown in Figure 16. http://cxc.harvard.edu/ciao/threads/acisbackground/index.py.html
30 – medianmedian- 50% median+ 50% σ > 70%σ = 0%
Right Ascension (J2000) D ec li n a t i on ( J2000 ) N H [10 cm -2 ] o f t e ss e l a t e s Fig. 16.— AE analysis of the Chandra Carina Complex Project (Townsley et al. 2010) study of the Carina Nebula(see Figure 2), a region with strong diffuse emission with complex morphology. Diffuse regions (yellow) are definedby tesselating an image of diffuse emission using the WVT Binning algorithm (Diehl & Statler 2006). In this examplemap the color inside each region represents the absorption parameter ( N H ) from the spectral model derived fromthe corresponding extracted spectrum. As shown in the legend, the hue (red ... blue) of the color encodes the N H value (relative to the median): red hues represent values 50% below the median; green hues represent the medianvalue, 0.29; blue hues represent values 50% above the median. The brightness of the color encodes the uncertainty of that value. For example, a highly certain low N H value would be bright red; a highly uncertain low value wouldbe maroon. Regions where the parameter was frozen in the fit are marked with white diagonal lines. The inset plotshows the distribution of mapped N H values ( in units of 10 cm − ) with the values corresponding to the red, green,and blue hues marked by vertical lines.
10. VISUALIZATION
Visualization of data products throughout the analysis workflow shown in Figure 1 can reveal various problemsthat commonly arise, including artifacts in the data, mistakes in execution of the workflow such as skipping a stepor failing to recognize a failure, bugs in software tools or unexpected changes in the algorithms implemented bytools, astrometric offsets in observations, or uncommon features in the data such as CCD readout streaks, severely 31 –piled-up sources, and sources lying on the edge of or just outside the field of view. We display the events removedfrom the observation at each cleaning step of the L1-to-L2 processing ( §
3) to look for unexpected patterns. We plotcandidate point sources arising from the detection process ( § AE , each observation’s source apertures are examined in DS9 to verify that they are not overlapping ( § AE masks the data to remove point sources ( § § AE source position estimates ( § DS9 , overlaid with color-coded
DS9 regions depicting sources of interest. AE provides a complementary tool (the“SHOW” option) that examines a single source in detail, as shown in Figure 5. The neighborhood around the sourcein each observation is shown in a separate DS9 frame, overlaid with the extraction aperture; another frame showsthe merged neighborhood. If a reconstructed image of the merged neighborhood is available, then it is shown in anadditional frame. Basic information about each extraction is presented in tabular form.After the catalog is extracted and source properties are collated, we plot the distributions of key source properties,looking for outliers that signify mistakes (or discoveries). Light curves are examined for sources exhibiting strongvariability ( § §
11. SUMMARY
Many
Chandra -ACIS imaging studies face significant data analysis challenges arising from large numbers of weakand sometimes crowded point sources embedded in scientifically relevant diffuse emission, observed with multiplemisaligned pointings. We have discussed here a variety of innovations to standard ACIS analysis methods thataddress these challenges; the most important of these are summarized below.1. Currently, a single set of data cleaning procedures is not adequate if the observer plans to study both very weak( ≤
10 counts) point sources (or diffuse emission) and bright point sources, because several cleaning algorithmsremove legitimate X-ray events from bright sources. Thus, we find that distinct data cleaning procedures arerequired for different types of analyses ( § § § § § § § § § mkwarf ( § ACIS Extract (AE) softwarepackage, which has been freely available to the community since its development began in 2002. AE is written inthe IDL language, and makes extensive use of tools in
CIAO and in several other public packages.Although much of the analysis we perform on our ACIS observations has been automated, we believe thatthe obserer should retain many vital roles in the process. The human eye is often able to spot omissions andspurious entries in the set of candidate sources derived from detection procedures ( § § § § §
10) data cleaning steps,extraction apertures, catalog pruning and source repositioning proposed by algorithms, spectral fitting results, andmulti-wavelength associations asserted by our matching algorithm.The authors greatly appreciate discussions with Keith Arnaud regarding background modeling when the C-statistic is used in
XSPEC , and several good suggestions for expanding AE ´s capabilities from Mike Muno. Wewould have enjoyed considerably less success in our studies of diffuse sources had Steven Diehl and Thomas Statlerchosen to not release their WVT Binning software to the community; we thank them for this valuable service. Weappreciate the time and useful suggestions contributed by our anonymous referee. We would have been lost withoutthe invaluable tools of NASA’s Astrophysics Data System, and without CIAO , XSPEC , and
DS9 .This work is supported by the ACIS Instrument Team contract SV4-74018 (PI: G. Garmire), issued by theChandra X-ray Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of NASAunder contract NAS8-03060. Additional support comes from Chandra General Observer grants GO8-9131X, GO8-9006X, GO6-7006X, GO5-6143X, GO4-5006X, several previous Chandra General Observer grants, the NASA grantNNX06AE56G, and the NASA/ADP grant NNX09AC74G.CXO (ACIS)
A. RUNNING TWO AFTERGLOW ALGORITHMS
We concur with the CXC’s recommendation to use both afterglow tools ( acis detect afterglow and acis run hotpix )for identifying afterglow events ( §
3) when seeking to detect weak sources. Since both algorithms use bit 16 in theevent STATUS word to represent afterglows, the operational details of applying both algorithms can be confusing.We show below one method for doing this. First, the afterglow flag returned by the gentle algorithm in the tool acis run hotpix is moved from bit 16 to the unused bit 31 ( dmtcalc call below). Second, the aggressive algorithm inthe tool acis detect afterglow is applied, storing its results in bits 16–19. (Note that in the dmtcalc syntax below bitsare numbered 0 to 31, counting from right to left.) dmtcalc infile=acis.evt1 outfile=temp.evt \expression="status=status,status=X0F,if(status==X15T)then(status=X0T)"acis_detect_afterglow infile=temp.evt outfile=acis.evt1 \pha_rules=NONE fltgrade_rules=NONE Gentle cleaning that does not damage bright point sources ( §
3) can be performed on the resulting STATUSword by ignoring the bits assigned by the destreak tool (bit 15), the acis detect afterglow tool (bits 16–19), and theVery Faint Mode grading algorithm (bit 23): dmcopy "acis.evt1[status=00000000x000xxxxx000000000000000]" gently_cleaned.evt Development of AE is on-going; observers can be notified of new releases by joining the AE mailing list ( http://lists.psu.edu/cgi-bin/wa?A0=L-ASTRO-ACIS-EXTRACT ). http://cxc.harvard.edu/ciao/threads/acishotpixels/index.html http://space.mit.edu/CXC/docs/docs.html
33 –Aggressive cleaning that is suitable for source detection and for analysis of diffuse emission ( §
3) can be performedby requiring all STATUS bits to be zero: dmcopy "acis.evt1[status=0]" aggressively_cleaned.evt
B. Source Significance AE provides two measures that quantify the validity of a source. First, a traditional “signal-to-noise ratio” isdefined to be the ratio of the net source counts observed to the estimated uncertainty on that quantity.Second, the null hypothesis that a source does not exist in the source aperture is tested by the method describedby Weisskopf et al. (2007, Appendix A2), which is derived under the more physical assumption that X-ray extractionsfollow Poisson distributions. Assuming the null hypothesis—all the events in the source aperture are background—they show that the joint probability of finding at least the observed number of events in the source aperture andfinding the observed number of events in the background region can be found by integrating a binomial distribution.This calculation can be performed with the following call to the binomial function in IDL : P B = Binomial ( C s ; C s + C b ,
11 + A b /A s ) , (B1)where C s and C b are the number of counts observed in the source aperture and background region in a specifiedenergy band. The source aperture and background region “areas,” A s and A b , are discussed in § C b ) and the uncertainty of the events observed within the source aperture (i.e., the Poisson nature of C s ). Thus, the significance of a given source extraction will tend to decrease ( P B will rise) if its background regionis reduced in size because fewer background counts ( C b ) will be detected (regardless of whether the backgroundsurface brightness inferred from C b increases or decreases). This behavior can be intuitively rephrased as “weaksources benefit more than strong sources from accurate estimates of the background.” AE sizes background regionsso that Poisson uncertainty on the background contributes no more than 3% of the total uncertainty on the sourcephotometry. When C b is large and the background is thereby accurately estimated, P B approaches the familiarintegral of the Poisson distribution over the interval [ C s , ∞ ] (Weisskopf et al. 2007, Appendix A2), P B (cid:39) − C s − (cid:88) i =0 P oisson ( i ; ( A s /A b ) C b ) . (B2)We recommend using the quantity P B as the principal measure of the validity of a source’s existence, in thecontext of the iterative source detection strategy described in § P B can be read as “the probability that all countsin the source aperture are background” or “the probability that no source exists at the extracted location in thepresence of the observed local background.” C. MODELING THE POINT SPREAD FUNCTION
The
Chandra
PSF varies both with position on the detector and with energy. Several models of the
Chandra
High Resolution Mirror Assembly (HRMA) are available, including
ChaRT , SAOTrace,
MARX , and the mkpsf tool in
CIAO . ChaRT has an interactive interface and is thus not suited for automated processing; SAOTrace is available ononly a limited set of computer platforms. The mkpsf output has technical limitations such as coarse spatial samplingacross the detector, and omission of PSF blurring effects not related to the HRMA. We therefore use the
MARX ray-trace simulator, running simulations for each observation of each source at five monochromatic energies: 0.277,1.4967, 4.51, 6.4, and 8.6 keV. MARX dithers the simulated source using the observation’s aspect file, allowingaccurate modeling of distortions caused by the PSF dithering over the boundaries of the ACIS CCDs. These are the five PSF energies used by the
Chandra
PSF Library ( http://cxc.harvard.edu/ciao/dictionary/psflib.html ).
34 –On-axis, the PSF of a real source observed by ACIS differs strongly from the HRMA PSF due to three blurringeffects. First, significant quantization effects arise because ACIS pixels do not fully sample the HRMA PSF. Second,the reported positions of ACIS events are reconstructed from an imperfect aspect solution that measures the dithermotion. Third, the default
CIAO pipeline adds a ± . (cid:48)(cid:48) random number to each event’s position. The standardmodel for these blurring effects is a Gaussian blurring function built into
MARX . Calibration of this blurring model(the standard deviation of the Gaussian) is available only for all three blurring effects combined; this is not suitablefor our needs because we choose to remove the event position randomization during our event pre-processing ( § MARX simulations with its post-HRMA blurring model disabled, and then blur thesimulated event positions ourselves in two steps. First, ACIS quantization is modeled by convolving the HRMA PSFimage with a “box kernel” sized to match the ACIS pixel. We feel a Gaussian kernel, which has infinite extent, isan inappropriate model for pixel quantization (and for the event position randomization, when present). Second,aspect reconstruction errors are modeled by convolving the PSF image with a two-dimensional Gaussian kernelwith σ x = σ y = 0 . (cid:48)(cid:48) . REFERENCES
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ChaRT and SAOTrace generate “rays” from the HRMA, and recommend using
MARX to model all three blurring effects. http://asc.harvard.edu/cal/ASPECT/img_recon/report.html
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This preprint was prepared with the AAS L A TEX macros v5.2.
38 – T a b l e . S a m p l e A E O u t pu t T a b l e : B a s i c S o u r ce P r o p e r t i e s S o u r ce P o s i t i o n E x tr a c t i o n C h a r a c t e r i s t i c s S e q . N o . C X O U J α ( J . ) δ ( J . ) E rr o r θ C t , n e t σ t , n e t B t C h , n e t P S FF r a c . S i g n i f .l og P B A n o m . V a r . E ff . E x p . E m e d i a n ( ◦ )( ◦ )( (cid:48)(cid:48) )( (cid:48) )( c o un t s )( c o un t s )( c o un t s )( c o un t s )( k s )( k e V ) ( )( )( )( )( )( )( )( )( )( )( )( )( )( )( )( )( ) . − . . - . . . . . . . . . < - .... b . . . − . . - . . . . . . . . . < - .... a63 . . . − . . - . . . . . . . . . < - .... b . . . − . . - . . . . . . . . . < - .... a58 . . . − . . - . . . . . . . . . < - .... a61 . . N o t e . — C o l. ( ) : X - r a y c a t a l og s e q u e n ce nu m b e r , s o rt e db y R A . C o l. ( ) : I AU d e s i g n a t i o n . C o l s . ( ) a nd ( ) : R i g h t a s ce n s i o n a ndd ec li n a t i o n ( i nd ec i m a l d e g r ee s ) f o r e p o c h J . . C o l. ( ) : E s t i m a t e d s t a nd a r dd e v i a t i o n o f t h e r a nd o m c o m p o n e n t o f t h e p o s i t i o n e rr o r , (cid:113) σ x + σ y . T h e s i n g l e - a x i s p o s i t i o n e rr o r s , σ x a nd σ y , a r ee s t i m a t e d f r o m t h e s i n g l e - a x i ss t a nd a r dd e v i a t i o n s o f t h e P S F i n s i d e t h e e x tr a c t i o n r e g i o n a nd t h e nu m b e r o f c o un t s e x tr a c t e d . C o l. ( ) : O ff - a x i s a n g l e . C o l s . ( ) a nd ( ) : N e t c o un t s e x tr a c t e d i n t h e t o t a l e n e r g y b a nd ( . k e V ) ; a v e r ag e o f t h e upp e r a nd l o w e r σ e rr o r s o n c o l. ( ) . C o l. ( ) : B a c k g r o und c o un t s e x p ec t e d i n t h e s o u r cee x tr a c t i o n r e g i o n (t o t a l b a nd ) . C o l. ( ) : N e t c o un t s e x tr a c t e d i n t h e h a r d e n e r g y b a nd ( k e V ) . C o l. ( ) : F r a c t i o n o f t h e P S F ( a t . k e V ) e n c l o s e d w i t h i n t h ee x tr a c t i o n r e g i o n . A r e du ce d P S F f r a c t i o n ( s i g n i f i c a n t l y b e l o w % ) m a y i nd i c a t e t h a tt h e s o u r ce i s i n a c r o w d e d r e g i o n . C o l. ( ) : P h o t o m e tr i c s i g n i f i c a n cec o m pu t e d a s n e t c o un t s d i v i d e db y t h e upp e r e rr o r o nn e t c o un t s . C o l. ( ) : L oga r i t h m i c p r o b a b ili t y t h a t e x tr a c t e d c o un t s (t o t a l b a nd ) a r e s o l e l y f r o m b a c k g r o und . S o m e s o u r ce s h a v e P B v a l u e s a b o v e t h e % t h r e s h o l d t h a t d e f i n e s t h ec a t a l og b ec a u s e l o c a l b a c k g r o und e s t i m a t e s c a n r i s e du r i n g t h e f i n a l e x tr a c t i o n i t e r a t i o n a f t e r s o u r ce s a r e r e m o v e d f r o m t h ec a t a l og . C o l. ( ) : S o u r ce a n o m a li e s : ( g ) f r a c t i o n a l t i m e t h a t s o u r ce w a s o n a d e t ec t o r( F R A C E X P O f r o m m k a r f ) i s < . . C o l. ( ) : V a r i a b ili t y c h a r a c t e r i z a t i o nb a s e d o n K - S s t a t i s t i c (t o t a l b a nd ) : ( a ) n o e v i d e n ce f o r v a r i a b ili t y ( . < P K S ) ; ( b ) p o ss i b l yv a r i a b l e ( . < P K S < . ) ; ( c ) d e f i n i t e l yv a r i a b l e ( P K S < . ) . N o v a l u e i s r e p o rt e d f o r s o u r ce s w i t h f e w e rt h a n f o u r c o un t s o r f o r s o u r ce s i n c h i p ga p s o r o n f i e l d e d g e s . C o l. ( ) : E ff ec t i v ee x p o s u r e t i m e : a pp r o x i m a t e t i m e t h e s o u r ce w o u l dh a v e t o b e o b s e r v e d a tt h e a i m p o i n t o f t h e A C I S - I d e t ec t o r i n C y c l e ??? t oo b t a i n t h e r e p o rt e dnu m b e r o f n e t c o un t s ( s ee http://asc.harvard.edu/cgi-bin/build_ viewer.cgi?ea ) . C o l. ( ) : B a c k g r o und - c o rr ec t e d m e d i a nph o t o n e n e r g y (t o t a l b a nd ) .
39 – T a b l e . S a m p l e A E O u t pu t T a b l e : Sp ec t r a l F i t s S o u r ce a Sp ec tr a l F i t b X - r a y L u m i n o s i t i e s c N o t e s d C X O U J C t , n e t S i g n i f .l og N H k T l og E M l og L s l og L h l og L h , c l og L t l og L t , c ( c m − )( k e V )( c m − )( e r g s − ) ( )( )( )( )( )( )( )( )( )( )( )( )( ) . − . . . . . . . . . . . T . − . . . . + . ··· . + . − . . + . − . . . . . . ··· . − . . . . + . − . . + . − . . + . − . . . . . . ··· . − . . . . + . − . . + . − . . + . − . . . . . . T . − . . . . + . − . . + . − . . + . − . . . . . . ··· a F o r c o n v e n i e n ce , c o l s . ( ) – ( )r e p r o du ce t h e s o u r ce i d e n t i fi c a t i o n , n e t c o un t s , a ndph o t o m e tr i c s i g n i fi c a n ce d a t a f r o m T a b l e . b A ll fi t s u s e d t h e s o u r ce m o d e l “ t b a b s * v a p ec ” i n X S PE C . C o l s . ( ) a nd ( ) p r e s e n tt h e b e s t - fi t v a l u e s f o rt h ee x t i n c t i o n c o l u m nd e n s i t y a ndp l a s m a t e m p e r a t u r e p a r a m e t e r s . C o l. ( ) p r e s e n t s t h ee m i ss i o n m e a s u r e d e r i v e d f r o m t h e m o d e l s p ec tr u m , a ss u m i n ga d i s t a n ce o f . k p c . Q u a n t i t i e s m a r k e d w i t h a n a s t e r i s k ( * ) w e r e f r o ze n i n t h e fi t . U n ce rt a i n t i e s r e p r e s e n t % c o n fi d e n ce i n t e r v a l s . M o r e s i g n i fi c a n t d i g i t s a r e u s e d f o r un ce rt a i n t i e s < . i n o r d e rt o a v o i d l a r g e r o und i n g e rr o r s ; f o r c o n s i s t e n c y , t h e s a m e nu m b e r o f s i g n i fi c a n t d i g i t s i s u s e d f o r b o t h l o w e r a ndupp e r un ce rt a i n t i e s . U n ce rt a i n t i e s a r e m i ss i n g w h e n X S PE Cw a s un a b l e t o c o m pu t e t h e m o r w h e n t h e i r v a l u e s w e r e s o l a r g e t h a tt h e p a r a m e t e r i s e ff ec t i v e l y un c o n s tr a i n e d . F i t s l a c k i n g un ce rt a i n t i e s , fi t s w i t h l a r g e un ce rt a i n t i e s , a nd fi t s w i t h f r o ze np a r a m e t e r ss h o u l db e v i e w e d m e r e l y a ss p li n e s t o t h e d a t a t oo b t a i n r o u g h e s t i m a t e s o f l u m i n o s i t i e s ; t h e li s t e dp a r a m e t e r v a l u e s a r e n o tr o bu s t . c X - r a y l u m i n o s i t i e s d e r i v e d f r o m t h e m o d e l s p ec tr u m a r e p r e s e n t e d i n c o l s . ( ) – ( ) : ( s ) s o f t b a nd ( . k e V ) ; ( h ) h a r db a nd ( k e V ) ; (t)t o t a l b a nd ( . k e V ) . A b s o r p t i o n - c o rr ec t e d l u m i n o s i t i e s a r e s ub s c r i p t e d w i t h a c . C o l s . ( ) a nd ( ) a r e o m i tt e d w h e n l og N H > . c m − s i n ce t h e s o f t b a nd e m i ss i o n i s e ss e n t i a ll y un m e a s u r a b l e . d “2 T ” m e a n s a t w o - t e m p e r a t u r e m o d e l w a s u s e d ; t h e s ec o nd t e m p e r a t u r e i ss h o w n i np a r e n t h e ss
39 – T a b l e . S a m p l e A E O u t pu t T a b l e : Sp ec t r a l F i t s S o u r ce a Sp ec tr a l F i t b X - r a y L u m i n o s i t i e s c N o t e s d C X O U J C t , n e t S i g n i f .l og N H k T l og E M l og L s l og L h l og L h , c l og L t l og L t , c ( c m − )( k e V )( c m − )( e r g s − ) ( )( )( )( )( )( )( )( )( )( )( )( )( ) . − . . . . . . . . . . . T . − . . . . + . ··· . + . − . . + . − . . . . . . ··· . − . . . . + . − . . + . − . . + . − . . . . . . ··· . − . . . . + . − . . + . − . . + . − . . . . . . T . − . . . . + . − . . + . − . . + . − . . . . . . ··· a F o r c o n v e n i e n ce , c o l s . ( ) – ( )r e p r o du ce t h e s o u r ce i d e n t i fi c a t i o n , n e t c o un t s , a ndph o t o m e tr i c s i g n i fi c a n ce d a t a f r o m T a b l e . b A ll fi t s u s e d t h e s o u r ce m o d e l “ t b a b s * v a p ec ” i n X S PE C . C o l s . ( ) a nd ( ) p r e s e n tt h e b e s t - fi t v a l u e s f o rt h ee x t i n c t i o n c o l u m nd e n s i t y a ndp l a s m a t e m p e r a t u r e p a r a m e t e r s . C o l. ( ) p r e s e n t s t h ee m i ss i o n m e a s u r e d e r i v e d f r o m t h e m o d e l s p ec tr u m , a ss u m i n ga d i s t a n ce o f . k p c . Q u a n t i t i e s m a r k e d w i t h a n a s t e r i s k ( * ) w e r e f r o ze n i n t h e fi t . U n ce rt a i n t i e s r e p r e s e n t % c o n fi d e n ce i n t e r v a l s . M o r e s i g n i fi c a n t d i g i t s a r e u s e d f o r un ce rt a i n t i e s < . i n o r d e rt o a v o i d l a r g e r o und i n g e rr o r s ; f o r c o n s i s t e n c y , t h e s a m e nu m b e r o f s i g n i fi c a n t d i g i t s i s u s e d f o r b o t h l o w e r a ndupp e r un ce rt a i n t i e s . U n ce rt a i n t i e s a r e m i ss i n g w h e n X S PE Cw a s un a b l e t o c o m pu t e t h e m o r w h e n t h e i r v a l u e s w e r e s o l a r g e t h a tt h e p a r a m e t e r i s e ff ec t i v e l y un c o n s tr a i n e d . F i t s l a c k i n g un ce rt a i n t i e s , fi t s w i t h l a r g e un ce rt a i n t i e s , a nd fi t s w i t h f r o ze np a r a m e t e r ss h o u l db e v i e w e d m e r e l y a ss p li n e s t o t h e d a t a t oo b t a i n r o u g h e s t i m a t e s o f l u m i n o s i t i e s ; t h e li s t e dp a r a m e t e r v a l u e s a r e n o tr o bu s t . c X - r a y l u m i n o s i t i e s d e r i v e d f r o m t h e m o d e l s p ec tr u m a r e p r e s e n t e d i n c o l s . ( ) – ( ) : ( s ) s o f t b a nd ( . k e V ) ; ( h ) h a r db a nd ( k e V ) ; (t)t o t a l b a nd ( . k e V ) . A b s o r p t i o n - c o rr ec t e d l u m i n o s i t i e s a r e s ub s c r i p t e d w i t h a c . C o l s . ( ) a nd ( ) a r e o m i tt e d w h e n l og N H > . c m − s i n ce t h e s o f t b a nd e m i ss i o n i s e ss e n t i a ll y un m e a s u r a b l e . d “2 T ” m e a n s a t w o - t e m p e r a t u r e m o d e l w a s u s e d ; t h e s ec o nd t e m p e r a t u r e i ss h o w n i np a r e n t h e ss e ss