Starlight Sensitivity Calculation

The sensitivity of ACIS to starlight is computed using realistic stellar atmosphere emission. The models of Kurucz (1991) have been used as the input spectrum for a range of temperatures. In all cases dwarf stellar gravity values have been assumed. The form of the computations is to integrate the radiation flux times the blocking filter transmission and the CCD optical detection efficiency over the full energy range and compare this to the same spectrum put through a standard V filter, for example, with a unit efficiency detector of one square centimeter. Putting this into an equation we have
 

where the OF refers to the optical flux, the quantity F_star($\lambda$) is the flux computed using the Kurucz model spectrum for a star at temperature T, as a function of wavelength; T_bf($\lambda$) is the transmission of the filter at wavelength $\lambda$; QE_CCD($\lambda$) is the quantum detection efficiency for photons at wavelength $\lambda$, and A_tel($\lambda$) is the area of the AXAF telescope for visible light at a wavelength $\lambda$. The telescope area was taken as the geometrical area, 1029 cm², times a function describing the fraction of the diffracted light that falls into one pixel with the telescope axis at the center of the pixel. This function was computed by the expressions found in Born and Wolfe . (See Appendix C for details.) The value of OF was then multiplied by 3.3 to include the exposure time.

The integral above was computed using standard numerical integration techniques. Although stellar atmosphere data exists for many more temperatures than computed here, the variation with temperature appears to be slowly varying, so that adding more points seems unnecessary.

The effect of optical contamination is to introduce photoelectrons which are unrelated to X-ray interactions. Thus if the X-ray frame bias is calculated without the star's optical light the X-ray photon energy will be miscalculated due to these additional electrons. If accurate X-ray photon energies are important to the analysis, then the observer should refrain from observing stars brighter than a certain limit. The results of the computation (assuming that one electron per pixel is the threshold for concern) are shown in Table 5.4. Observing with shorter integration times (by using subframe readout or continuous clocking), or willingness to tolerate greater uncertainty in the X-ray energies will move the threshold toward brighter stars.
 
 

Table 5.4: Stellar Magnitude required to produce one photoelectron per 3.3 second frame in the central pixel at the focus of AXAF for a range of stellar temperatures

Stellar Temperature (K)	BI Chip in S-Array	FI Chip in I-Array
	(V-magnitude)	(V-magnitude)
4000	8.1	2.87
5000	7.93	2.44
6500	7.73	1.79
10000	7.66	1.17
20000	7.6	0.97

Since many observations of bright stars will be performed with the objective gratings in place, the optical transmission of samples of the grating facets were measured as a function of wavelength. The results of these measurements are illustrated in Appendix C. The transmission curves were used in the integral above to compute the limiting magnitude with the grating in place. The HEG and MEG gratings were taken to cover 33% and 67% of the mirror area respectively, the MEG covering the outer two shells and the HEG covering the inner two shells. Table 5.5 gives the corresponding limit for optical contamination when the gratings are in place.
 
 

Table 5.5: Stellar Magnitude required to produce one photoelectron per 3.3 second frame in the central pixel at the focus of AXAF for a range of stellar temperatures with MEG/HEG grating in place 

Stellar Temperature (K)	BI Chip in S-Array	FI Chip in I-Array
	(V-magnitude)	(V-magnitude)
4000	2.13	-1.52
5000	1.49	-2.16
6500	1.04	-2.62
10000	0.41	-3.27
20000	0.21	-3.48

Table 5.4 shows that most observations proposed using ACIS will not suffer from optical light contamination, since the optical emission for most X-ray emitting objects are fainter than these limiting magnitudes. Only those observations in which bright stars fall within the ACIS array will a background signal be produced and only when the image is nearly on-axis. (The off-axis PSF grows rapidly, spreading the optical light over many more pixels, and hence reducing the number of optical photoelectrons per pixel.)

The optical photoelectron signal will behave differently from a signal induced by X-rays in that the photon level will build up linearly with time for stars brighter than the limiting ones in Table 5.4. X-rays, on the other hand will produce discrete packets of electrons in a pixel that either appear or are zero; they do not increase the charge in a pixel in a linear manner with accumulation time.^5.1

Even if contamination is present, it can be removed just as a bias offset can be removed, but at the cost of an increase in the noise level in the detected electrons generated by the fluctuations in the light signal. For spectroscopic observations, the grating will attenuate the optical light by a factor of about thirty-three, or increase the magnitude limit by 3.8 magnitudes. Only the very brightest stars should be a problem when the gratings are in place.