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MPE Notes on the Creation of the 1993 January Matrix


[Hasinger and Snowden1992]

Every event is transformed through a long chain of correction procedures from the raw telemetry to calibrated time, position, and amplitude. In particular, the data are corrected for:

  1. ADC nonlinearity,
  2. gain saturation,
  3. temporal gain variations,
  4. small-scale electronic position variations,
  5. spatial gain variations, and
  6. large scale window-position variations (see Chap. 8).
The detector response matrix contains our best current knowledge of the mirror effective areas, the composition of the PSPC entrance window, and a physical model of the characteristics of the counter gas and the proportional counter energy resolution properties. Nevertheless, there are residual systematic uncertainties at the few percent level in almost every element of the above chain. It is also possible that other (unknown) systematic effects have not been included at all. Most of the detailed information originates from extended ground calibrations with monochromatic lines  at nominal gain; important elements were also derived or verified in orbit. Small systematic features in the residuals of PSPC spectral fits have been a well-known problem for some time now, in particular for high signal-to-noise ratio sources. Due in part to the relatively poor energy resolution    of proportional counters, the various possible reasons for such effects are exceedingly difficult to disentangle. One of the major problems in determining a final in-flight calibration is that there exists no bona fide continuum calibration source that has a well defined spectrum in the 0.1-2 keV range, and is suitable for the PSPC (similar to the Crab Nebula for higher energy X-rays).  A sample of bright source spectra of various types has therefore been collected for a better diagnosis.

To date, the pointed observation of the bright BL Lac object Mkn 421 (SEQ Nr. WP700513, PI Thomas, exposure time 33000s, taken in low-gain mode in 1992 May 4-7) comes the closest to the ideal of an in-orbit calibration source.   Mkn 421 has a relatively small galactic tex2html_wrap_inline16951 value of tex2html_wrap_inline16953 H Icm tex2html_wrap_inline16955 , as re-measured recently by J. Lockman (1992, private communication), which turned out to be slightly higher than the value of tex2html_wrap_inline16957 H Icm tex2html_wrap_inline16959 published by [Elvis et al.1989].

In the ROSAT all-sky survey, Mkn 421 was variable and had a count rate of 18-28 counts s tex2html_wrap_inline16961 , but with an apparently constant spectral shape [Fink et al.1991]. Ginga data were taken simultaneously with the ROSAT all-sky survey.  A combined spectral fit to the ROSAT/Ginga data shows very good agreement between the two instruments in the overlapping energy range (1.5-2.4 keV), albeit with relatively poor statistical quality [Fink1992]. The 0.1-10 keV spectrum can be well fit with a slowly curving power law spectrum with a photon index of about 2.45 at low energies and an index of 2.82 at high energies.   Such a convex spectral shape is predicted by inhomogeneous synchrotron models which are fashionable for BL Lac jets. The oxygen absorption trough feature   which was reported from Einstein OGS data of PKS 2155-304,  another bright BL Lac object, would have too small an equivalent width to be observed with the PSPC, if it were present in Mkn 421 at the same strength. During the pointed observation, the source was almost a factor of 10 brighter so that a total of 5 million photons were accumulated for a very high statistical significance spectrum in the 0.1-3 keV range.

We first used this spectrum to better define the residual systematic features in the 92mar11 response matrix. We fixed the tex2html_wrap_inline16963 at the above value and fit a broken power law (BPL) in the energy range 0.2-1.8 keV (power-law indices and break point were allowed to vary). Table 3.4 gives the fractional residuals over the full energy range (0.1-3 keV) defined as: Res = (Data-Model)/Data, Channel 151 = 1.49 keV.

There are three major obvious deviations:

  1. a model deficiency in the range 0.1-0.2 keV. At 0.1 keV this amounts to about 30%, above 0.2 keV this effect has gone away.
  2. a systematic model excess in the window absorption trough above the carbon edge, reaching a maximum of -11% at about (ca. 0.4 keV).
  3. a model deficiency above 1.8 keV. At the nominally highest PSPC photon energy of 2.5 keV, this amounts to 25%. However, with the low-gain data it is possible to reach energies of 3 keV, where the excess is about 40%.

In addition, there is a small ( tex2html_wrap_inline16965 %) ripple in the energy channels 69 and 70. This effect, only apparent in extremely high signal to noise spectra, is due to a sharp feature in the PSPC position dependent gain correction at the Xe-M edge at 672eV. A similar feature is expected at the Ar-L edge at 245eV, but is not easily visible due to the steep falloff of pulse height spectra in this energy range. A change has been made to the PSPC correction procedure which avoids these artifacts for SASS REV1 processing. The Mkn 421 data were reprocessed using this improvement.

The next step was an iterative procedure to minimize these residuals with various trials to change the physical parameters of the proportional counter model (i.e., width parameters, the energy width of the discontinuities at the edges of the counter gas, the amount of electrons lost by drifting back to the window, etc.) within reasonable limits allowed by the ground calibration results and in-flight data. These changes gave a substantial improvement of effect (2) around 0.4keV, from -11% to -4.5%, suggesting that the previously relatively large residuals in this energy range may be due to systematic errors in the ground calibration of the physical counter model parameters.  However, the details of the carbon absorption edge in the PSPC window transmission may also have some effect.

This didn't change the shape and magnitude of the residuals at low and high energies. For each of the effects (1) and (3), there are at least two different physical explanations for which we lack calibration data to address at this point. Naturally, combinations each of the effects below could be, and probably are, responsible for the residuals:

    1. The excess at low energies could be due to a few % smaller value for the window thickness compared to the preflight calibration. In this case the net effective area at lower energies would be larger than expected. Indeed, some of the detailed studies done on calibration data of the white dwarf HZ 43 point in this direction (Fleming, private communication). The window thickness calibration is based on measurements averaged over the entire window at only four energies, the lowest of which was 0.18keV. The transmission of the window at 0.1 keV is therefore not well constrained.  
    2. A similar effect could be produced by an offset of 3-5eV (less than half a channel) in the pulse height versus energy relation at low energies, which could be produced by the on-board electronics (ADC, pulse shaper, peak detector, etc.). There is no information about this offset from the flight-model calibration. The fact that most pulse height spectra rise very steeply in the energy range 0.1-0.15keV exaggerates any such uncertainty by a large factor.
    1. The excess at high energies could be due to a larger mirror reflectivity above the Au-M edge at 2keV compared to the theoretical predictions.  Indeed there are at least two incompatible models for the optical constants of gold in the energy range 2-3 keV.
    2. A similar effect could be again due to an uncertainty in the gain (channel versus energy) curve. The effect of gain saturation has only been reasonably measured at the nominal gain and above, and then only reliably up to 1.7 keV. A gain saturation effect which is less severe than extrapolated (by about 2-3% in absolute channels, or about 10% of the predicted gain saturation effect) could easily explain the findings. Again, because of the steep decrease of all spectra in this energy range, the effect in the residuals is amplified by a large factor.

Since we have no further calibration information at this time which would allow us to distinguish between these different possibilities and to refine our physical understanding of the situation, we took the brutal and somewhat distasteful approach of simply fudging the response matrix values with the residuals to the Mkn 421 fit, i.e., multiply every entry in the matrix with the factor (Fig. 3.15):


The response matrix created this way, 93jan12, has been tested on our sample of bright sources. In general the fits achieved were better (note: later tests showed the 92mar11 matric to be better for data collected during high-gain-state observations). For more details see Tab. 3.5.

The improvement in the fit to the low-gain spectrum of HZ 43 was particularly spectacular. While the fit with the previous matrix had very severe discrepancies at low energies, an acceptable tex2html_wrap_inline16967 was obtained by fixing all shape parameters (temperature, gravity) to the best currently available multiwavelength model (Fleming, private communication) and only allowing the normalization to vary. Such a good fit could unfortunately not be achieved for the high-gain spectrum of HZ 43, indicating a residual gain-dependent shape of the response curve. See also [Napiwotzki et al.1993], who require a factor 1.77 to fit the amplitude of the HZ 43 spectrum.)

Using the 93jan12 matrix, the Crab Nebula  data appear to be systematically shifted to a lower energy, compared to the model (also true using the 92mar11 matrix). Indeed, after reprocessing the Crab data with a 5% lower gain, we achieved an almost perfect fit to the Crab data in the energy range 0.4-2 keV. The most straightforward explanation for the discrepancy is a rate-dependent gain effect in the PSPC. While for most observations this should have no effect, it is unfortunately significant for bright and hard calibration targets (like the Crab).     Ground re-calibrations showed that the rate-gain saturation effect is to small to account for the observed gain shift in the Crab spectrum (see also Sect. 3.2.2).

In the course of our matrix optimization attempts we have identified a number of uncertainties or lack of knowledge about the following calibration items:

ADC offset
window thickness
shape of the window transmission near the carbon edge
actual energy of the window carbon edge
Gold reflectivity above 2 keV
gain saturation at high energies and low gain
shape of the low-energy response function at low gain
rate-gain effect

While for (a) and (b) we cannot obtain further calibration data for the flight models, the effects (c)-(h) are relatively independent of the specific counter and therefore can be re-calibrated on ground using the engineering model PSPC. (a) can also be studied using the engineering model in order to obtain information about the possible magnitude of this effect. We have therefore planned a number of additional ground calibration tests with the engineering model of the PSPC, partially at the PANTER facility and partially in a synchrotron laboratory. Data were collected at the PANTER facility in early 1994 but have not yet been collected at synchrotron facility. We do not anticipate a new response matrix for some time.

While we have always attempted to improve our knowledge of the PSPC performance and to push down the uncertainties asfar as possible, we advise ROSAT observers to include systematic errors of about 2 percent (in quadrature) in their PSPC spectral fits and to be cautious about the interpretation of narrow spectral features, particularly those of small equivalent width as well as possible high-energy excesses.  It is also strongly recommended to rebin the spectra into no more than the 34 energy bins defined by SASS (see the ROSAT Data Products Guide).

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