The sensitivity functions depend on several factors. The telescope contributes its unobscured geometrical collecting area, the reflectivity of both mirrors, and the fraction of the light which manages to pass through the instrument's entrance aperture. The GHRS optics introduce a finite reflectivity at each surface and transmission at each filter and window, the blaze efficiency and linear dispersion of the gratings. The detectors have an overall quantum efficiency (QE) at each wavelength, spatial gradients related to vignetting or real QE variations, isolated scratches and blemishes, pixel-scale irregularities, finite sampling by the diodes, and diode-to-diode gain variations. As we noted, to simplify this problem, the calibration is broken into several components. The basic function relates flux and count rate measured at the center of the diode array, for a star centered in the LSA, at a range of wavelengths for each grating. The echelle blaze function is quantified separately for each order. Gradients of sensitivity across the diode array are described by vignetting functions which vary with wavelength for each grating or echelle order. The SSA throughput is measured relative to the LSA at several wavelengths, and is assumed to be independent of grating mode. Blemishes are tabulated as departures from the local sensitivity for each grating. Diode response functions are tabulated as detector properties, which depend on threshold settings, but not optical modes. Finally, the pixel to pixel granularity can be identified and suppressed as photometric noise.
Each of these factors that affects the flux measurement has some uncertainty, which we will discuss below.
We used the ultraviolet standard stars BD+28D4211 and µColumbae as our primary flux references. We have also used BD+75D325 and AGK+81D266 on occasion. None of these are known to exhibit significant variability in the ultraviolet. BD+28D4211 is a hot white dwarf that was used for the sensitivity monitors for the low- and medium-dispersion gratings. The corresponding observations for the echelle, and other long-term monitoring programs, were done with the bright late-O super giant µ Col. An example of a Cycle 4 BD+28D4211 observation is in Figure 37.1.
Sensitivity determination is done by comparing an observed spectrum to the reference spectrum for that star. The reference spectrum is the current best estimate of the true flux versus wavelength for a particular star, and therefore represents "truth." The flux scale for the GHRS and other HST instruments has been modified such that observations of the star G191B2B match theoretical models.
37.2.2 Procedures for Determining Sensitivity and Vignetting Functions
A series of observations for the characterization of the post-COSTAR GHRS was made shortly after SMOV, in 1994. A similar series was done early after launch for the pre-COSTAR instrument. To illustrate how these observations were used to determine sensitivity and vignetting, we borrow from GHRS ISR 085, which discusses G140L sensitivity.
The work would be much easier if we could observe a "perfect" star, by which we mean one with a flat or nearly-flat spectrum which is not variable in time and which is largely free of any structure (such as absorption lines). We also wish we had a "perfect" detector to work with, which would be one with a flat response across its face, that response being independent of wavelength, spatial position, or time.
Figure 37.1 shows the first step in this process. The upper frame shows the observed spectrum, C(O), of standard star BD+28 in units of count rate, while the bottom frame shows the reference spectrum, F(R). Please note that this reference spectrum already takes into account the proper white dwarf flux scale, and that no secondary correction is needed.
Small Science Aperture (SSA)
The amount of light seen through the Small Science Aperture (SSA) is sensitive to the centering of the object in the SSA. The baseline SSA sensitivity curve was created by multiplying the baseline LSA sensitivity curve by the SSA to LSA ratio. The process used is discussed in greater detail later in this document.
Effects of Time
Ratios of our regular sensitivity monitoring data to the baseline SMOV data show changes in GHRS Side 1 sensitivity over time since the installation of COSTAR. Each time the monitor was run, the current data was compared to the SMOV BD+28D4211 data at the same wavelength. A ratio and errors were calculated every 10 Å from ~1100 Å to ~1630 Å. While the sensitivity below Lyman- decreased, an apparent increase occurred in sensitivity from ~1200 to 1350 Å, before it declined again. We do not understand this behavior, but it has remained fairly constant with time.
37.2.3 Sensitivity Monitoring
Sensitivity monitoring was done for Side 1 and Side 2 separately. The Side 1 post-COSTAR monitor contained a series of visits of the ultraviolet standard BD+28D4211, done with identical instrumental configuration each time, except that the exposure times were increased at later dates to achieve better signal to noise. The target was acquired into the Large Science Aperture with a 5 x 5 spiral search using mirror N1, followed by a peak-up. The science observations were done with grating G140L in the ACCUM mode at two central wavelengths: 1200 Å and 1500 Å. For the Side 2 observations, BD+28D4211 was acquired into the LSA with a 3 x 3 spiral search using mirror N2, followed by a peak-up. Centering was confirmed by taking an image with the LSA. A series of spectra in the ACCUM mode were taken with gratings G160M (centered at 1200 and 1500 Å), G200M (2000 Å), and G270M (2500 and 3000 Å). This sequence was repeated approximately every three months.
Differences between Successive G140L Time Dependent -Sensitivities
June 14, 1994
August 1, 1994
October 21, 1994
January 14, 1995
April 17, 1995
June 25, 1995
September 17, 1995
January 4, 1996
May 2, 1996
August 30, 1996
November 22, 1996
January 24, 1997
Figure 37.2 shows the Side 1 sensitivity decline and Figure 37.3 shows the decline for Side 2. The Side 1 figure represents fits to the sensitivity monitor ratios for grating G140L. Illustrated are cubic-spline fits to the ratios of an observed spectrum to the one observed during SMOV. These fits are the basis for the time-variable G140L sensitivity files. Figure 37.4 and Figure 37.5 show details of the time variability for the two worst wavelength regions.
Figure 37.2: Side 1 Sensitivity Decline
Figure 37.3: Side 2 Sensitivity Since COSTAR
In Figure 37.3, the five panels are for central wavelengths of 1200 Å, 1500 Å, 2000 Å, 2500 Å, and 3000 Å. Each point represents the ratio of the median counts measured over 20 Å relative to the counts measured on 30 April 1994 over the same 20 Å (the first data point). The error on individual data points is 1%. Time is represented in days using the date we consider COSTAR to have aligned and focussed for GHRS (February 4, 1994) as the zero-point. The vertical dashed lines represent one-year intervals.
An example of the improvement possible from using the time-dependent files is shown in Figure 37.6. In this figure, the top plot is flux-corrected with an appropriate time-variable sensitivity file; the bottom plot is the same data calibrated by the pipeline (PODPS).
Figure 37.4: Time Variability for GHRS G140L Below Ly-
Figure 37.5: GHRS G140L Change in Sensitivity Monitor Ratio
Figure 37.6: Ratio of Monitor Data to Reference Star
37.2.4 Calibrated Flux Quality
Absolute and Relative Fluxes
The foregoing discussion of the process used to create the components of the flux calibration illustrates some of the factors that influence the quality and reproducibility of flux calibrations in GHRS observations. You want to know how precise and accurate the flux values are, and that varies by -situation.
Now suppose that the same instrumental setup is used throughout (grating and wavelength do not change) but that different stars are being compared. If the stars have similar spectra, then the previous situation pertains. If the spectra differ significantly, then the convolution of that spectrum with the sensitivity and vignetting functions will introduce additional uncertainty. Near the center of the spectrum these effects will be minimal and the intercomparability should be to within 1 to 2%.
In Figure 37.7, the circles are observations of µ Col-all five data points are based on a single SSA ACQ/PEAKUP. The crosses are for Lup; the first and last points are from a single ACQ/PEAKUP and the cluster of three points near 1950 Å is from another. The diamonds are for AGK+81D266; each point is based on an individual ACQ/PEAKUP. The solid line is a straight line fit to the µ Col and Lup data.
Figure 37.7: Ratio of Count Rates for Post-COSTAR SSA to LSA
Sensitivity Changes Over Time-Scales of Months to Years
We noted earlier the evidence for changes in GHRS sensitivity with time since the first servicing mission. Corrections for the effects of these changes have been incorporated into CDBS so that you should get back the appropriate sensitivity reference file for the time an individual observation was taken.
The largest effects are seen for grating G140L, especially below Lyman-. From the monitoring data, a ratio and errors were calculated every 10 Å from ~1100 Å to ~1630 Å. While the sensitivity below Lyman- decreased, an apparent increase occurred in sensitivity from ~1200 to 1350 Å, before it declined again. We do not understand this behavior, but it has remained fairly constant with time. In addition to rederiving the baseline post-COSTAR G140L sensitivity, we have also created time-dependent G140L curves for the date of each sensitivity monitor based on the ratio of the counts from the monitor to the SMOV baseline data. Observers will need to interpolate between sensitivity curves to get a correction appropriate for the date of their observations. The derivation of these Side 1 changes is described in GHRS ISR 085.
The results of the Side 2 GHRS medium-resolution sensitivity monitor suggest that since COSTAR was installed, the GHRS sensitivity changes between 1200 Å and 3000 Å do not exceed about 5%. We find evidence for a time-dependence of the sensitivity with a decline rate of about 2% per year. As an example we showed in Figure. 37.3 count rate ratios of BD+28D4211 obtained since COSTAR installation, focus, and alignment and referenced to the beginning of Cycle 4. (Details for the Cycle 4 observations are in GHRS ISR 071). The sensitivity files used by calhrs reflect the state at the beginning of Cycle 4. The changes seen for Side 2 are described in GHRS ISR 089.
Note that the calibrated science data in the .c1h file take into account the different throughput for point sources of the LSA and SSA before and after the installation of COSTAR. Therefore a star observed before and after the installation of COSTAR will have the same flux although its count rate will be lower before COSTAR.
Decreasing Counts During an Orbit
A series of short-exposure spectra of a star over many orbits in ACCUM mode appeared to show a regular decline of the observed counts of roughly 10% over the course of each orbit. This is described in GHRS ISR 073, together with some possible explanations. The best guess is that this phenomenon is due to telescope "breathing." This effect can contribute to flux uncertainty, obviously.
Correction for Extended Sources
When calhrs photometrically calibrates your observations, it assumes you have observed a point source, and adjusts the flux in your spectrum to account for light loss due to the PSF outside of the aperture, i.e., it returns the flux you would have seen if all of the flux from your point source fell within the aperture. Therefore, the absolute fluxes of point sources measured through the LSA and SSA should be the same. Of course, the count rates will be lower for the SSA observation but calhrs will automatically apply a different sensitivity function to the SSA observation to account for the light loss. The properties of the GHRS apertures are presented in Table 37.3.
calhrs always assumes a point source is observed and it effectively applies a correction factor for the light lost outside the aperture. If you observed an extended source, then your source does not fill the aperture as does a point source and the flux calibration from calhrs will be inappropriate. To obtain a rough estimate of the specific intensity multiply the observed flux by 0.95±0.02 for observations taken through the LSA and divide by the area of the aperture in square arcseconds. This assumes that the extended source completely and evenly fills the aperture. For pre-COSTAR observations, the correction factor is 0.725 (see GHRS ISR 061 for details).
The absolute fluxes for extended sources obtained with calhrs are incorrect.
Properties of GHRS Apertures
Clear Aperture (mm)
Correction for Background Counts
The background level, or dark current for both GHRS detectors was very low: typically about 0.01 counts per second per diode when well away from the South Atlantic Anomaly. However, for very faint objects the dark level could dominate the signal, and accurate correction for the background is vital.
2 More properly this is the inverse sensitivity. We will ignore the distinction here.
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