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The following section has in general been extracted from Snowden et al. (1994) but has been updated and annotated for use with the described software. The following procedures require some consideration by the observer and for best results must occasionally be run iteratively. The cookbook covers only those programs in § 3 for the PSPC.
NOTE: The detector area excluded because of the reduced PB vetoing efficiency near the walls of the detector (see Plucinsky et al. 1993) must be excluded consistently throughout the analysis.
1) Preliminary review of the observation data set: Examine the hard copy distributed with the observation data set. The background spectrum will yield an indication of the AP contamination level by an excess in the lowest useful channel (Channel 8 or Channel 11 for the high and low gain states, respectively) over the next higher channel. The background count rate versus time plot (light curve) provides an overall view of background contamination and an estimate of the difficulty of the data reduction. Periods of strong scattered solar X-ray (SB) contamination will appear as sharply falling (rising) count rate enhancements at the start (end) of observation intervals. Short-term enhancements (STEs) appear as erratic and asymmetrical peaks anywhere in the observation intervals, while Long- term enhancements (LTEs) are seen as a gradual drift in the minimum count rate. The information on point sources identified in the field should be searched for strong or variable objects. If the contributions from individual sources are small compared to the total background count rate or the sources are constant, they can be ignored when modelling the temporal variation of the SB and LTE background components. If not, they can possibly affect the results. At this time, however, the software is not capable of excluding regions from the following procedures.
2) Initial time selection - program VALID_TIMES: Apply a time selection to the accepted data to eliminate all periods where the Master Veto count rate averaged over s is greater than (conservatively) 170 counts s . Observations later in the mission appear less affected by the particle background excesses noted at higher master veto rates and a higher threshold may produce acceptable results, and with experience I've found no problems using a threshold of 220 counts s . (See Snowden et al. 1992 and Plucinsky et al. 1993; averaging over this relatively long interval helps smooth across glitches in the MV count rate produced by non-uniform time sampling which is not accounted for correctly in SASS.)
The software automatically eliminates all events occurring within 0.35 ms of a previous event to reduce the afterpulse contamination. The livetime of the observation is appropriately reduced to compensate for this time selection (although the effect is in general small). A telemetered event causes a deadtime of 0.25 ms. Increasing the deadtime to 0.35 ms by this selection reduces the livetime per second by 0.1 ms multiplied by the count rate of telemetered events (available, along with the MV count rate, in the event rate file distributed with the observation data set). Times of obvious short-term enhancements should also be eliminated at this point to make it easier to fit other background components. The output of the program VALID_TIMES, valid_times_all.dat can be edited as needed.
3) Create light curves - program RATE: Determine the event count rates in the seven pulse-height bands.
If examination of the observation data set hard copy shows evidence for strongly flaring sources, masking the the source may be necessary.
4) SB modelling - program AO: Determine the nominal count rates from the scattered solar X-ray background. Since the light curves are being modelled on an individual band basis, an exact model for the intrinsic solar spectrum is not necessary. Reasonable input for the solar spectrum consists of a component with log T=6.2 with a scale factor of 0.8 and a component with log T=5.7 with a scale factor of 0.2.
5) Determine the SB and LTE scale factors from the light curves - program RATE_FIT: Fit the light curves with the following model function:
is the total event count rate for band i as a function of time, t (where for fitting purposes, t is in units of seconds where t=0 is at observation start) from program RATE. is the model PB count rate as a function of time from program RATE. is the model SB count rate as a function of time assuming a constant solar flux from program RATE; and are fitted parameters that allow for a linear variation in the solar flux during the observation. The R4-R7 band values will vary together because of their joint origin as O K at 0.53 keV. After fitting the values of and for the R4 band, those same values should be fixed for the R5-R7 bands. In practice, there are essentially no SB counts in the R7 band and so and can be set to zero. The parameters , , and are fitted to a fourth-order time variation of the LTE component. Note that negative values for the sum are non-physical.
The fitted parameter contains both the true cosmic X-ray rate and the constant component of the LTE fourth-order polynomial variation. In general, the entire fourth-order polynomial will not be needed to fit the LTE. The program should be run iteratively to find the best reasonable fit (with the smallest number of non-zero parameters). The best reasonable fit may not, however, be a formally acceptable fit. Bright sources or strong extended emission near the edge of the field of view or near the window support structure can produce temporal structure with the wobble period. The polynomial will not in general fit these variation (when the exposure is long compared to the wobble period of 400 s) so the data can have considerable scatter around the fitted curve. The accuracy of the determination of the LTE contamination can be significantly reduced with a possible over estimation of the contamination. The determination of the SB background will not in general be so strongly affected. We stress again that this method of background modelling can only account for the time varying component of the long-term enhancement. The fitted count-rate minimum over the observation interval is not necessarily the level of the true cosmic X-rays.
6) Second time selection: The fitted light curves can be compared to the data to identify additional periods affected by STEs, which can then be excluded by editing the valid_times_all.dat file. The remaining data can then be refit. It is not necessary to rerun AO after this refined time selection since AO only evaluates the scattered solar X-ray background at the *ORBIT.FITS or *_ANC.FITS orbit extension time steps; the calculated values will remain unchanged within the accepted time intervals and the time points will remain the same. It is also not necessary to rerun the program RATE, although the start and stop times for the intervals will probably shift somewhat. The times to be excluded, if any, can be identified by comparing the plot_n.qdp output files from RATE_FIT with the RATE1.DAT and RATE2.DAT output files from RATE, which have the S/C clock time for the individual data points along with the count rates in the different bands.
If the fits are reasonable (the definition of reasonableness here is up to the observer and their analysis goals), a significant reduction in the observation noncosmic background can often be made by eliminating the time periods of highest SB contamination. By eliminating time periods with the SB contribution of the observation of MBM 12 (Snowden, McCammon, and Verter 1993) was counts s , which amounted to of the exposure, 80% of the SB contamination was eliminated. This increased the signal to background ratio in the keV band from to . By including the high SB count-rate data in the first time selection, a more accurate fit to the SB contamination can usually be achieved. The final selection of the accepted times for the analysis must be placed in a file valid_times.dat with the same format as the original valid_times_all.dat
7) Determination of LTE contamination - program LTE: The fitted polynomial coefficients from the program RATE_FIT must be evaluated to determine the number of LTE events in the observation. Beware of round-off errors when evaluating higher-order polynomials.
8) Cast the event images - program CAST_DATA: Cast the observed events in seven pulse-height bands.
9) Cast the exposure - program CAST_EXP: Using the livetimes and appropriate detector maps, cast the efficiency weighted exposure for the chosen bands in sky coordinates for the accepted time intervals.
10) Determination of SB contamination - program TILT: The fitted linear scale factor from the program RATE_FIT must be combined with the modelled nominal SB count rates to determine the number of SB counts, gradient across the field, and rotation angle of that gradient.
11) Determination of AP contamination (if necessary: see Plucinsky et al. 1993) - program FIT_AP: The program CAST_DATA creates a spectrum from the event file of afterpulse events (pulses occurring within 0.35 ms of a preceding event) and a spectrum of the remaining ``good'' events. The good events in the 1/4 keV band (channels 8,11-30) can be fit with a four component model: SB, PB, thermal spectrum of K, and a scaling of the selected afterpulse spectrum. The number of SB and PB counts are taken from the output of programs TILT and CAST_PART (CAST_PART should be run to the point where it prints out the diagnostic information containing the total number of PB events, and then terminated). Enter values of the temperature for the thermal component until the best fit is achieved. The best fit in this case is likely to not be a statistically significant fit, but does produce a reasonable estimate for the number of afterpulse events still in the accepted events. Negative values for the AP events are non-physical. The afterpulse contamination only affects the R1 and R1L bands.
12) Determination of PB contamination - CAST_PART: Using the PB detector maps, livetimes, and the calibration of Plucinsky et al. (1993), cast the particle background for the internally-produced component, two externally produced components, and AP component into sky coordinates.
13) Cast the LTE and SB backgrounds - program CAST_SSX: Cast the LTE and SB contamination by appropriately scaling the cast exposure maps.
14) Create a point-source mask - program DETECT: use the cast count maps and exposure maps to do source detection on the field.
15) Create the surface brightness images - program FINAL_IMAGE: Combine all of the event, model background count, and exposure images into intensity images for the chosen bands (i.e., subtract all of the background maps from the event map on a pixel-by-pixel basis, and then divide by the exposure map). Point sources can be deleted at this point by including a point-source mask. To include all data, enter the exposure map for the mask.
16) Produce a smoothed image - program ADAPT: Using the count, modeled background count, and exposure maps, produce an adaptive-filter smoothed image of the data. For display purposes only.
The author wishes to thank those people who were very helpful in bringing
this set of code and cookbook to general release.
Cui Wei at Wisconsin,
Michael Dahlem at Johns Hopkins,
Dave Davis at GSFC,
Pat Knezek at Michigan,
K. D. Kuntz at Maryland,
Michael Ledlow at New Mexico State,
Jeff Mendenhall at Penn State
deserve special mention.
And a final note: If you have found this software useful in the preparation of data for publication, kindly reference this document and acknowledge the support of the USRSDC. Thank you.
APPENDIX A - SAMPLE FITS HEADER
The following is a sample header produced by the software discussed here. It is for the count-rate image for the R4 band. The units are counts s arcmin , the pixel size is , the pointing direction is , and the projection is tangential. It is a two-dimensional array with pixels and is REAL*4.
SIMPLE = T / file does conform to FITS standard BITPIX = -32 / number of bits per data pixel NAXIS = 2 / number of data axes NAXIS1 = 512 / length of data axis 1 NAXIS2 = 512 / length of data axis 2 COMMENT FITS (Flexible Image Transport System) format defined in Astronomy and COMMENT Astrophysics Supplement Series v44/p363, v44/p371, v73/p359, v73/p365. COMMENT Contact the NASA Science Office of Standards and Technology for the COMMENT FITS Definition document #100 and other FITS information. COMMENT Count rate map for band R4 RADECSYS= 'FK5 ' / Equatorial system reference EQUINOX = 2000 / Equinox BZERO = 0.0000 / BSCALE = 0.00000100 / BUNIT = 'c/s/am2 ' / Units of data CRPIX1 = 256.5000 / Reference pixel CRVAL1 = 172.9600 / Right Ascension CDELT1 = -0.00415203 / Pixel size CUNIT1 = 'deg ' / Units of coordinate CTYPE1 = 'RA---TAN' / Projection CRPIX2 = 256.5000 / Reference pixel CRVAL2 = 63.8400 / Declination CDELT2 = 0.00415203 / Pixel size CUNIT2 = 'deg ' / Units of coordinate CTYPE2 = 'DEC--TAN' / Projection COMMENT This file was produced using the ESAS software written by COMMENT S. L. Snowden, and written using the FITSIO package of COMMENT W. D. Pence. END
APPENDIX B - TABLE OF ROSAT BANDS
This table is extracted from Snowden et al. (1994) and contains the band definitions for the ROSAT bands used in this cookbook.
10% of peak response. Bands with the same upper (or lower)
channel boundaries can have different upper (or lower) energy limits
of the different width of the bands and the definition of the energy limits
as a fixed fraction of the peak response.
SASS channel 1 also includes PI channel 7.
R1 band for low-gain observations.
APPENDIX C - SAMPLE FITS HEADER FOR MERGED IMAGES
The following is a sample header produced by the image-merging software discussed here. It is for the count image for the R4 band. The units are counts, the pixel size is , the pointing direction is (l,b)=(318.5,-3.5), and the projection is zenith equal area. It is a two-dimensional array with pixels and is REAL*4.
SIMPLE = T / file does conform to FITS standard BITPIX = -32 / number of bits per data pixel NAXIS = 2 / number of data axes NAXIS1 = 512 / length of data axis 1 NAXIS2 = 512 / length of data axis 2 COMMENT FITS (Flexible Image Transport System) format defined in Astronomy and COMMENT Astrophysics Supplement Series v44/p363, v44/p371, v73/p359, v73/p365. COMMENT Contact the NASA Science Office of Standards and Technology for the COMMENT FITS Definition document #100 and other FITS information. COMMENT Merged count map CONTENT = 'IMAGE ' / TELESCOP= 'ROSAT ' / mission name INSTRUME= 'PSPC ' / instrument name OBS_MODE= 'POINTING' / obs mode: POINTING,SLEW, OR SCAN RADECSYS= 'FK5 ' / Equatorial system reference EQUINOX = 2000 / Equinox BZERO = 0.0000 / BSCALE = 1.00000000 / BUNIT = 'counts ' / Units of data CRPIX1 = 256.5000 / Reference pixel CTYPE1 = 'GLON-ZEA' / Projection CRVAL2 = -3.5000 / Galactic longitude CDELT1 = -0.03333334 / Pixel size CUNIT1 = 'deg ' / Units of coordinate CRPIX2 = 256.5000 / Reference pixel CTYPE2 = 'GLAT-ZEA' / Projection CRVAL2 = -3.5000 / Galactic latitude CDELT2 = 0.03333334 / Pixel size CUNIT2 = 'deg ' / Units of coordinate COMMENT This file was produced using the ESAS software written by COMMENT S. L. Snowden, and written using the FITSIO package of COMMENT W. D. Pence. END