3 The absolute calibration of NEWSIPS high resolution spectra

For the absolute flux calibration of NEWSIPS high resolution spectra we have followed the method described in Cassatella et al. (1994). Let us indicate with $N(\lambda$) the ripple-corrected high resolution Flux Numbers, normalized to the exposure time. The corresponding absolute flux can be determined from

$$F(\lambda)=C(\lambda)~S^{-1}(\lambda)~N(\lambda)~~{\rm erg~cm^{-2}~s^{-1}~\AA^{-1}}$$ (20)

where $S^{-1}(\lambda)$ is the low resolution inverse sensitivity function appropriate to the camera considered, and $C(\lambda$) is the so-called high resolution calibration function defined as

$$C(\lambda)=n(\lambda)/N(\lambda)$$ (21)

being $n(\lambda$) the net Flux Numbers (i.e., not absolutely calibrated), normalized to the exposure time, derived from low resolution observations of the same target. Because of the time-dependent sensitivity degradation of the cameras, the pairs of low-high resolution spectra used to determine $C(\lambda$) should be obtained close enough in time. Alternatively, both $n(\lambda$) and $N(\lambda$) should be previously corrected for sensitivity degradation. This latter approach, here followed, has the advantage of increasing considerably the number of usable spectra. The correction for sensitivity degradation of high resolution spectra has been made with the same algorithms used for low resolution spectra, as described by Garhart (1992, 1993) and Garhart et al. (1997). This procedure is justified in Paper III, which shows that high resolution spectra obtained even several years apart, once corrected in this way, provide very nearly the same flux repeatability performance as spectra obtained close in time.

The high resolution spectra are first corrected for the blaze function, resampled in 2 Å bins, and normalized to the exposure time in seconds. The spectra are then corrected for sensitivity degradation, for the THDA induced sensitivity variations, and for the camera rise time following the same algorithms used in the NEWSIPS processing of low resolution spectra (see González-Riestra et al. 1999b, Paper IV). Finally, the spectra of each target are averaged together to obtain a mean spectrum $N(\lambda$). To obtain $C(\lambda$), the mean high resolution spectra of a given target are then divided by the mean low resolution spectrum of the same target (which are also corrected for temperature effects, camera rise-time and sensitivity degradation).

3.1 SWP

To determine the high resolution calibration function $C(\lambda$) we have used 28 SWP high resolution spectra of BD+28 4211, 38 of BD+75 325, 27 of HD 60753, 6 of G191 B2B and 13 spectra of CD-38 10980. We find that the repeatability errors on $N(\lambda$) (after all the above mentioned corrections are applied) are typically 3-5%. These small errors confirm the validity of applying the low dispersion degradation rates to high dispersion spectra.

The low resolution net fluxes $n(\lambda$) of the above targets were obtained by averaging many low resolution spectra obtained during the 1990-1991 re-calibration period. The curve $C(\lambda$) for the SWP camera is shown in Fig. 9.

A third order polynomial fit to the data provides:

$$C(\lambda)=A+B~\lambda+C~\lambda^2+D~\lambda^3$$ (22)

where

A = 1349.8538
B = -2.0078566
C = 1.10252585 10^-3
D = -2.0939327 10^-7
with an standard deviation of 6.3. The above equation has been derived from data in the wavelength range 1175 to 1950 Å.

The repeatability error on $C(\lambda$) is 4%, irrespective of wavelength, which we take as the internal error of the high resolution calibration function.

3.2 LWP

To determine $C(\lambda$) for the LWP camera we have used 25 high resolution spectra of BD+28 4211, 37 of BD+75 325, 27 of HD 60753 and 4 spectra of CD-38 10980. The repeatability errors on $N(\lambda$) reach the 4% level at 2400 Å, but do not exceed 2-3% around 2800 Å. Similarly to the case of the SWP camera, these small errors confirm the applicability of the low dispersion sensitivity degradation algorithm to high resolution data. The low resolution net fluxes $n(\lambda$) of the above targets were obtained by averaging many low resolution spectra obtained during the 1990-1991 re-calibration period, extracted with NEWSIPS and corrected for time-dependent sensitivity degradation according to Garhart (1993). The curve $C(\lambda$) for the LWP camera is shown in Fig. 10. A linear fit to the measurements provides:

$$C(\lambda)=251.383956-0.053935103~\lambda$$ (23)

with a standard deviation of 3.49. The repeatability of the $C(\lambda$) function is about 4%. The above equation has been derived from data in the wavelength range 1975 to 3150 Å.

3.3 LWR

To determine $C(\lambda$) we have used a total of 17 high and 23 low resolution spectra of the calibration standards BD+28 4211, BD+75 325, HD 60753 and HD 93521.

We find that the repeatability errors on the net fluxes $N(\lambda$) after the sensitivity degradation correction are of the same order as for the LWP camera, confirming once more the applicability of the low dispersion sensitivity degradation algorithm to high resolution spectra.

The resulting determinations of $C(\lambda$) are reported in the bottom panel of Fig. 10. It is interesting to note that the data points are well fitted by the same analytical representation as for the LWP camera (Eq. 23). The residuals correspond to an rms error on $C(\lambda$) of 5.3. A linear fit would provide about the same residuals (4.5), and the curve would only deviate from that of the LWP by 1.3%. The internal accuracy of the calibration function ranges from 5% below 2300 Å to 3% at longer wavelengths. The wavelength range covered by the LWR high resolution absolute calibration is the same as for the LWP camera.

Note that also Cassatella et al. (1994) found that the $C(\lambda$) curve is the same for LWP and LWR data processed with IUESIPS.

3.4 Examples of application

It is important to compare the fluxes obtained from high resolution spectra using the present method with the fluxes of the calibration standards which define the IUE flux scale (Paper IV). Examples of such a comparison are given in Figs. 11, 12 and 13 referring to the stars HD 60753, BD+28 4211 and BD+75 325 observed with the SWP, LWP and LWR cameras, respectively.

In the above examples, the agreement between high and low resolution fluxes is within the 4% repeatability errors quoted above.

It should be stressed that the present calibration is applicable to both continuum and emission line sources. This is confirmed by line emission measurements in several pairs of low-high resolution spectra of emission line sources. As an example, we show in Fig. 14 a low and a high resolution spectrum of the recurrent nova RS Oph taken very close in time.

Another test made was to verify the accuracy of the absolute calibration in the overlap region around 1950 Å between the SWP and the LWP and LWR cameras. We find that, in this region, the short and long wavelength cameras agree to within 2 to 6% on average. As an example, we show in Fig. 15 the overlap region for two pairs of spectra of HD 60753.

The good match between short and long wavelength high resolution spectra can also be deduced from Fig. 16, which shows a combined SWP-LWP spectrum of the Wolf Rayet star HD 152270.

We note that residual non-linearity effects in the Intensity Transfer Function, especially in the case of underexposed spectra, or spectra near the saturation limit, can occasionally cause a flux mismatch between the short and long wavelength cameras.