Crab Calibrations on the XRT+GIS Energy Response Functions
Y. Fukazawa^1, M. Ishida^2, and
1: University of Tokyo,
The GIS and the XRT teams have improved the XRT+GIS energy response function several times, based on the pre-launch and in-orbit calibrations (Ishida et al. 1994; Tashiro et al. 1995; Serlemitsos et al. 1995; Tsusaka et al. 1995; Kunieda et al. 1996; Ohashi et al. 1996; Makishima et al. 1996). Here we report results of the Crab Calibrations on the XRT+GIS energy response function. The topics include; arf filter, dependences of fitting parameters on integration radius and observed position, and temporal changes.
1 Crab Observation Log
Table 1 gives the log of Crab observations, whose data can be utilized in calibrations of the XRT+GIS energy response matrices. The Crab positions, summarized in figure 1, scatter over the GIS field of view, thus enabling the study of position dependence of the fitting parameters. We use the long-exposure data obtained in 1994 at the 1 CCD nominal position to define the standard spectra, because their statistics are comparable to those of the brightest Galactic sources.
Table 1: The Crab observation log.
No. of pointings Typ. exposure per pointing Remarks
________________________________________________________________________________________________ Apr. 1993 12 1 ksec Sep. 1993 6 6 ksec Sep. 1994 1 50 ksec 1 CCD nominal position Sep. 1995 2 25 ksec including 1 CCD position Sep. 1996 4 10 ksec including 1 CCD position ________________________________________________________________________________________________
2 The Latest Version Responses and the Arf Filter
The energy response function consists of RMF (Redistribution Matrix File) and ARF (Ancillary Response File). The former is related only to the GIS, while the latter is determined by an effective area of the XRT and a detection efficiency of the GIS. The latest version of the GIS RMF are gis2v4_0.rmf and gis3v4_0.rmf for GIS2 and GIS3, respectively. They have been available since March 1995. The latest version of the XRT+GIS ARF can be generated with the software "ascaarf'" or "jbldarf'", together with the XRT response functions given as xrt_psf_v2_0.fits and xrt_ea_v2_0.fits which have been available since July, 1996.
________________________________________________________________________________ Sensor photon index flux+ 2/v ________________________________________________________________________________ GIS2 2.10 +/- 0.10 3.00 +/- 0.05 2.0 2.10 GIS3 2.11 +/- 0.10 3.20 +/- 0.05 2.0 2.45 GIS2 + arf filter 2.09 +/- 0.10 2.90 +/- 0.05 2.16 1.13 GIS3 + arf filter 2.09 +/- 0.10 2.90 +/- 0.05 2.16 1.43 ________________________________________________________________________________ *: In unit of cm. : In 2--10 keV, in unit of erg cm .
Figure 2 shows the 1994 Crab spectra fitted with a power-law model modified by photoelectric absorption, using the latest RMF and ARF. The integration radius is 6'. The best-fit parameters are summarized in Table 2. The fluxes are determined after a dead-time correction (Makishima et al. 1996) by using only high-bit-rate data. Thus, results from GIS2 and GIS3 are fully consistent with each other. The photon index and column density are consistent with the previously observed values (Toor and Seward 1974), =2.08--2.11 and =(2.7--3.3) x cm , although our flux is by 10--15% less than the previous ones.
Residuals from the best-fit model have been significantly reduced, compared with the case of the previous response matrices (Tashiro et al. 1995). However there still remain some residuals, both in GIS2 and GIS3, at a level of 1--2% and 2--3% at 2 keV and 6 keV, respectively. The high energy tail is seen in the GIS3 fit, up to 5% at 9 keV. Although these residuals can usually be ignored in analyzing extra-Galactic sources, some caution may still be needed when analyzing bright Galactic sources.
In order to suppress such residual structures temporarily, and make the Crab flux agree with the previous ones, we introduce a concept called "arf filter''. This filter represents a ratio between the Crab data and the best-fit model incorporating the previously reported Crab flux of 2.16 x erg in 2--10 keV (Toor and Seward 1974). In practice, the arf filter consists of a constant value plus several broad gaussians, as shown in figure 3. When we re-fit the Crab spectra employing this arf filter, the residuals reduce to 2% or less, as show in figure 4. As shown in Table 2, the fitting results agree with what should be. The arf filter slightly changes the best-fit parameters, by =--0.01 and =--0.1 cm for GIS2, and by =--0.02 and =--0.3 cm for GIS3.
As described above, the latest RMF and ARF, together with the arf filters, provide the best combination in spectral fitting of the GIS data. Since this arf filter is independent of the source position, we can create an ARF modified with the arf filter. Thus modified ARF is available in "ascaarf'', whose version is later than 2.6, since 1996 July. In the latest "ascaarf'', applying the arffileter is the default, but users can make ARFs without the filter by specifying the hidden parameter 'arffil=no'. On the other hand, the software "arffilter'' multiplies ARF generated with "jbldarf'' by this arf filter. Note that this arf filter is effective for the latest RMF and ARF. In the following, we use ARF modified with this arf filter. More detailed information is available on
The absolute fluxes between GIS and SIS are adjusted by introducing the arffilter for SIS, too. Normalization of the SIS arffilter is made so that the SIS fluxes of 3C273 and other sources agree with those observed by GIS. On the 'wavy' part (energy dependence) of the arffilter, average shape of the GIS2 and GIS3 arffilter is used for SIS0 and SIS1. This is because insufficient statistics of SIS spectra do not allow to determine the responses within a few percents.
3 Stabilities of the Spectral Parameters
3.1 Dependence on the integration radius
Since the XRT+GIS point spread functions depend on the photon energy, the spectra integrated over different radii, , are apparently different. The ARF should take into account this difference and return the same fitting parameters, regardless of the employed integration radius. Utilizing the Crab data obtained in 1994, we examined how the fitting results depend on .
We found that the fitting parameters agree well when is larger than 3'. When <3', decreases, while and flux become larger. Therefore, the integration radius is recommended to be 3--6'.
3.2 Dependence on the observed position
Using all the available Crab data obtained at different pointings, we investigate the dependence of the spectral parameters on the observed position. We fit these data in the same way as before, employing an integration radius of 6'. The fittings are successful in all the cases, with the fit residuals less than 5%. The derived best-fit parameters are plotted in figure 5, against the radius R from the optical axis. The fluxes are evaluated after a dead-time correction by using only high-bit-rate data.
As seen in figure 5, neither nor depend very much on R, although the scatter increases towards larger R. The best-fit values are distributed in the range of = and = . Slight systematic differences are seen; values of from GIS2 are larger than those from GIS3 by ~0.005, and the values of from GIS2 are smaller than those of GIS3 by 0.1 x cm . However, these differences are smaller than the scatter.
On the other hand, we see that the flux significantly increases as R gets larger, and moreover, they scatter widely at large R. The position-dependent difference in the flux is 20% at maximum. We do not find any azimuthal dependences. The cause of this radial dependence is yet to be investigated.
3.3 Temporal changes
We observed the Crab Nebula at the 1 CCD nominal position in 1994, 1995, and 1996. Thus we can investigate temporal changes in the responses. When we fit the spectra from the 1995 and 1996 observations with the best-fit model of the 1994 data, we find a discrepancy between data and model up to 4%, both in GIS2 and GIS3. However, the source positions are slightly different among these 3 data sets, by ~1', which could be responsible for the observed discrepancy. As a result, we constrain the temporal change in the XRT+GIS responses at the 1 CCD nominal positions to 4% or less.
Further work of improving the XRT+GIS response matrices is in progress, so that we do not need the arf filter and the fitting parameters become less position dependent.
The authors are grateful to Prof. K. Makishima in correcting the manuscript, and to N. Iyomoto for preparation of the figures.
Ishida, M. et al. 1994, ASCANews Letter No.2
Tashiro, M. et al. 1995, ASCANews Letter No.3
Serlemitsos, P.J. et al. 1995, PASJ 47, 105
Tsusaka, Y. et al. 1995, Appl. Opt. 34, 4848
Kunieda, H. et al. 1996, ASCANews Letter No.4
Ohashi, T. et al. 1996, PASJ 48, 157
Makishima, K. et al. 1996, PASJ 48, 171
Toor, A and Seward, F. D. 1974, Astron. J. 79, 995
Figure 1 Positions of the Crab observations, plotted in the GIS2 DETX-DETY coordinate. Small circles correspond to pointings in 1993 April, and large circles represent those of other observations. The radii of the inner and outer circles are 10' and 20', respectively. The 1 CCD nominal position is shown in the figure. Positions of the optical axes are marked with S2 and S3 for GIS2 and GIS3, respectively.
Figure 2 a & b The Crab spectra taken in 1994, fitted with the power-law model using latest RMF and ARF. (a) GIS2, (b) GIS3.
Figure 3 a & b The arf filter. (a) GIS2, (b) GIS3.
Figure 4 a & b Results of the fit to the Crab spectra obtained in 1994, using the latest RMF and ARF modified with the arf filter. (a) GIS2 (b) GIS3.
Figure 5 a, b, & c The best-fit parameters of the Crab spectra corresponding to different observing positions. The latest RMF and ARF are used, together with the arf filter. Open circles and filled squares correspond to GIS2 and GIS3, respectively.
(a) Photon index . (b) Column density . (c) The 2--10 keV flux after a dead-time correction.
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