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X-ray Stacking
Tom Aldcroft SAO/CXC

X-ray Stacking 2008-Apr-22 Astrostats


Motivation for stacking


Multiwavelength analysis is a major theme in modern astrophysics Many types of astrophysical sources emit (at some level) over a wide range spanning radio to gamma rays Detection efficiency of a source class (e.g. obscured active galactic nuclei) is often best in a particular band Observations in other bands may result in non-detections How can we get the most information from the non-detections? Individual SEDs ­ upper limits constrain physical models Survival analysis for a sample Stacking ­ mean properties of sample Chandra X-ray data (faint point sources) are photon-limited with low background => stacking in X-rays is very effective



X-ray Stacking 2008-Apr-22 Astrostats


Stacking basics: Make an image
Define source positions from input catalog EXAMPLES: 1376 (2308) optically-selected unobscured QSOs from SDSS ~1600 (2150) IR-selected sources from Spitzer (obscured AGN) Extract image cutouts in X-ray data at each source position Co-add images for sources that are not detected in X-ray


X-ray Stacking 2008-Apr-22 Astrostats


Source, background and exposure map


At the position of source i in input catalog define source region Si based on local PSF and background region Bi Exclude sources that are known from X-ray or input catalogs Exposure map ES,i is effective area (cm2) в exposure time (sec) at each pixel
X-ray photons for source i Exposure map



Source region

Background region

X-ray Stacking 2008-Apr-22 Astrostats


Stacking basics: Net counts and flux


Net counts C and mean flux f

X-ray photons for source i

Exposure map
Edge of detector

Source region

Background region

X-ray Stacking 2008-Apr-22 Astrostats


Issues


The sample of X-ray "non-detections" depends on detect method and draws a hard distinction between sources straddling the detection limit Are a few sources dominating the signal?

Rosati et al. ApJS 139 (2002)

X-ray Stacking 2008-Apr-22 Astrostats


Issues


Estimate distribution in N or f by random resampling of input sources Question ­ what is this really telling us?

http://saturn.phys.cmu.edu/cstack User: guest Password: guest

X-ray Stacking 2008-Apr-22 Astrostats


Advanced stacking: ChaMP + SDSS




Simple stacking tools calculate net counts or flux assuming homogenous data sets - exposure and responses are fairly uniform. The Chandra Multiwavelength Project (ChaMP) is a very large X-ray survey using archival data spanning 6 years: GOOD The ChaMP has with a wide range in exposure and responses: BAD The goal is to properly account for these complications to explore AGN and galaxy physics and evolution. The Sloan Digital Sky Survey (SDSS) is a massive optical survey of the sky which provides > 100,000 spectroscopically confirmed quasars with redshifts (and much much more). There is a 30 deg2 overlap between ChaMP and SDSS.

X-ray Stacking 2008-Apr-22 Astrostats


Advanced stacking: Luminosity for a heterogenous sample


Since we have redshift (distance) estimates for the input SDSS samples we want to infer luminosity rather than flux.
Dependencies Units

Mean of L values

Weight by exposure as per flux calculation Is this even "stacking" any more? X-ray Stacking 2008-Apr-22 Astrostats


Discussion!


Now the real question: Some mean luminosity will be generated but how do we calculate the confidence intervals?

~0 to 5 cts

~5 to 25 cts



Would it be useful to plot / analyze histograms of Li? This avoids the (somewhat) arbitrary distinction between detected and non-detected sources.
X-ray Stacking 2008-Apr-22 Astrostats