Simulation of Hardness Ratio grids for the ROSAT PSPC

Spectra are modeled for observations with the ROSAT PSPC, using 3 models namely Thermal Bremsstrahlung, Raymond-Smith and an Absorbed Power law. For each model a range of parameters are modeled. Hardness Ratios are calculated for each simulation and a grid of HR1 versus HR2 is produced for each of the three models. Hardness Ratios, from observations which do not have enough spectral counts to ﬁt spectra directly, may be compared with the grid to set limits on observational parameters e.g temperature.


INTRODUCTION
When observations are made in the X-ray it is possible to produce spectra of these objects. Xray spectra of these observations may be modeled and fitted to observations for objects with enough spectral counts (≥ 1000 photons). From these spectra we can derive information about astronomical objects i.e., temperature, amount of neutral hydrogen present, abundances etc. We can also use Hardness Ratios (the X-ray equivalent of optical colours) that compare the photon counts in selected bands of the spectra, to derive information about objects. These are especially important for observations with low counts (≤ 1000) photons. ROSAT Hardness Ratio 1 (HR1) and Hardness Ratio 2 (HR2) are defined as Zimmermann et al. 1992 where the channel numbers 11-41 correspond to the number of photons contained in the energy interval 0.11-0.41 keV. These give us ratios of the soft and hard part of the spectrum.The channels 42-51 are omitted as ROSAT is not very sensitive in this energy range. HRs are especially useful for maximising the extraction of information from the ROSAT data archive and for work on less luminous objects. In this work we simulate spectra for three different spectral models, namely the Absorbed Power law, Raymond-Smith and Thermal Bremsstrahlung for a range of parameters. Hardness ratios are then calculated for these spectra producing a grid of HR1 versus HR2. Using this grid it is then possible to relate observed values of HR1 and HR2 to actual physical parameters.
Astronomical Data Analysis III

SPECTRAL SIMULATIONS
The modeling was done using the EXSAS Zimmermann et al.1992 software analysis system. For the purpose of our simulations we use 100,000 counts. All these simulations use the default detector response matrix and the effective area table for the PSPCb camera on ROSAT.

ABSORBED POWER LAW MODEL
Spectra are simulated for Absorbed Power law models with a range of values of absorbingN H (0.05 -1.5 ×10 20 cm −2 , in steps of 0.05×10 20 cm −2 ) and the Photon Index Γ (from -0.25 through to -4 in steps of 0.25). Hardness Ratios are calculated for these spectra. Figure 1 shows a HR1 versus HR2 plot for the absorbed power law model with values of HR1 ranging from -1 to 1 and HR2 ranging from -0.5 to 0.8.

THERMAL BREMSSTRAHLUNG
Spectra are simulated for Thermal Bremsstrahlung models using the same parameters as for the Raymond-Smith models above. Hardness Ratios are calculated for these spectra. Figures 4 and 5 show HR1 versus HR2 plot for the Thermal Bremsstrahlung model for z=0 and z=0.8 respectively.
Values of HR1 range from -1 to 1 and values of HR2 range from -1 to 0.6.

CALIBRATION
To test the reliability of our grids we use them to derive spectral values from observations with good counts (> 1000 photons) and good spectral fits. We chose one observation corresponding to the Power Law fit and the Raymond-Smith fit. We are currently in the process of doing this for the Thermal Bremsstrahlung model.

Data Reduction
The ROSAT PSPC data were analyzed using the EXSAS/MIDAS data reduction package (Zimmermann 1992), with corrections for bad times and vignetting. Images are created in the 0.11-2.35 keV energy range ,binned in 15 " pixels. A source detection is carried out on the PSPC images which produces a list of sources with a maximum likelihood of ≥ 10. Their coordinates are compared with the target list and only those detections with an offset less than 2 " are accepted. Hardness Ratios are then extracted from these observations and used to derive spectral values using our simulated grids.
Astronomical Data Analysis III

Power law Calibration
The ROSAT PSPC observation of the QSO RX J1333.7+3803 is used to calibrate our power law grid. Dewangan et al.(2002) analyzed this data and found that it is well fitted (reduced χ 2 =0.88) by a power law with spectral index Γ = 2.28 +0.31 −0.27 and with an absorbing hydrogen column density of 0.37 +0. 5 −0.37 ×10 20 cm −2 . Extracting hardness ratios from the PSPC observation we obtain HR1 = -0.52 ± 0.04 and HR2 = 0.04 ± 0.015. Inputing these values into our power law gird we get a value of −2.86 +0.1 −0.3 for the spectral index Γ with an absorbing hydrogen column density of Astronomical Data Analysis III 1.33 +0.8 −0.5 × 10 20 cm −2 . Thus the values returned by the grid method are consistent with the results of a detailed spectral analysis.  Kahabka [2002] simulates hardness ratio grids as a means of distinguishing AGNs from XRBs using hardness ratios. This grid uses 3 values of Γ and 5 values of absorbing N H . The results of Kahabka are found to be consistent with our Grid.

CONCLUSIONS
We have modelled HR grids for three models, namely absorbed power law, Raymond-Smith and thermal bremsstrahlung. These grids have been calibrated against X-ray observations for both the power law and Raymond-Smith models and we are currently in the process of calibrating these models for the thermal bremsstrahlung model. The values returned by our grid are found to be consistent with the results of a detailed spectral analysis. We have produced a tool which allows us to set limits on observational parameters e.g temperature using observations which do not have enough spectral counts to fit spectra directly.