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5. Changes in Continuum Flux for the Case of $\tau$ Sco

  The above analysis suggests that significant changes over time in the continuum net flux of SWP camera images may result both from changes in the intensity transfer function (ITF) compounded by limitations inherent in the background determination algorithm BCKGRD. To estimate the effects of these problems on the uncalibrated, ripple-uncorrected net fluxes we have taken the net fluxes from the NEWSIPS MXHI files in Table 2 and normalized them to a common effective exposure time. We summed the net fluxes along each of the orders of all pixels with quality flags with values $\nu$ $\ge$ -2 and computed regression lines with time through these order-summed ``continuum" fluxes. Our assumption in this analysis is that the star is not intrinsically variable. Figure 10 shows the slopes of the regression coefficients through these summed fluxes. Noting the segmented decrease with of these fluxes in Figs. 1 and 6, we split repeated the regression fits for data samples in the time intervals 1979.1-1990.5 and 1990.5-1995.7. These fits probably give the more meaningful information because they show the distinct quantitative changes in the behavior of the net fluxes before and after 1990. The relations in Fig. 10 give the slopes in units of fractional change per year in the far-UV continuum fluxes for $\tau$ Sco. For comparison, the slopes are also shown for the B0.5e star $\gamma$ Cas, which has many spectra distributed through the mission. This star's slight variability in the UV does not affect these values appreciably.

If the gross fluxes were perfectly calibrated and background fluxes were precisely extracted, the relations in Fig. 10 would collapse to a single flat line having all zero values. The fact that they are not flat is due to a combination of the flawed background solutions early and midway in the IUE mission and to the ITF calibration for the SWP camera being made only for a single epoch. The ``dip" in these relations in the region $\lambda$1150-1250 represents the initial undercorrection of the background flux we discussed in $\S$3. The low zeropoint from this error leads to excessive net fluxes in this wavelength range early in the mission. Likewise, the sharp minor dip at the order containing Lyman $\alpha$ or the C IV $\lambda$1548-1550 lines are due to enhanced percentage changes from a zeropoint errors when the total flux in the order is dominated by strong absorption lines. On the other hand, the displacement of the late- and early-epoch curves in rate of change is probably due to the change in the ITF properties across the camera beginning in 1990. Reference to the time degradations of SWP low-dispersion fluxes (Garhart 1992, 1997) reveals both some similarities and differences. For example, as in the low-dispersion analyses, the curves in Fig. 10 show local minima in the negative slopes at $\lambda$1450 and $\lambda$2000 and a maximum at $\lambda$1700. The average decline over the mission lifetime (solid line in our figure) also agrees fairly well with the slopes from the low-dispersion analysis. However, we suspect this is coincidental because the changes in the slopes between early- and late-epoch high-dispersion images are themselves fairly large. Reference to the surfaces in Fig. 8 suggests the reason for this coincidental agreement. These surfaces show that the degradation of flux in the nulls is consistently smaller in the lower right section of the surface, both where the short-wavelength end of the low-dispersion spectrum falls and where the maximum of the blaze function of the echelle orders is located. Thus, the collapsed high-dispersion data as represented in Fig. 8 registers an average across the surface in the direction of echelle dispersion which is similar to the more localized low-dispersion values. Finally, we remark that the rise in the curves at $\le$$\lambda$1150 is probably not due to background errors because this region of the camera is well represented by unilluminated background pixels. We believe a more likely alternative is that after 1990 the slopes at the toe of the ITFs steepened for pixels in the short-wavelength region of the SWP camera. This results in an artificial enhancement of the net fluxes in the weak, short-wavelength continua of these orders.

Although we cannot yet recommend the relations given in this diagram for use with datasets for other targets, it is possible that they may be applicable to other early-type main sequence stars, particularly if the exposure times are short as they are for $\tau$ Sco. For example, we have compared these results with coefficients determined from 164 SWP high-dispersion, large-aperture images of the bright B0.5e star $\gamma$ Cas which were taken at regular intervals through the IUE lifetime. A comparison of these, depicted as a dotted line in Fig. 10, with the $\tau$ Sco results demonstrates that the flux decreases in flux with wavelength for images of these two stars are very similar, at least out to the shortest-wavelength orders. We list in Table 1 the values for the dashed and dot-dashed curves ($\tau$ Sco) of Fig. 10. If one represents the fluxes in an echelle order m at epochs 1979.1, 1990.5, and t during the IUE mission as I1979(m), I1990(m), and It(m), respectively, one may use the coefficients C1,t,(m) and C2,t,(m) from Table 1 to adjust the net fluxes of spectra of $\tau$ Sco to a 1979.1 reference frame by using two linear relations. The first is:

I_{m}(t)/I_{m}(1979) ~~=~~ \Delta t~C_{1,t}(m) +1, \end{displaymath} (1)

where the C's are the fractional loss of continuum net flux. After 1990.5 one may correct to the 1979.1 reference frame by a second linear relation:

I_{m}(t)/I_{m}(1990) ~~=~~ \Delta t~C_{2,t}(m) + 1.\end{displaymath} (2)

In these equations $\Delta t$ is the time in years between the observation at a time t and the appropriate earlier reference time, either 1979.1 or 1990.5. The loss of net fluxes relative to 1979.1 can be corrected by means of eqn. 1 for images obtained during 1979-1990. For post-1990 epochs, one first computes in eqn [*] the flux for $\Delta t$ = 10.4 years. This result, Im(1990), is used in eqn 2 along with $\Delta t$ to compute the late-epoch flux Im(t) relative to time 1979.1. Note that application of these corrections to spectra of $\tau$ Sco does not in any way modify or correct spectral line depths. They represent a sensitivity correction for the SWP camera to the NEWSIPS calibration.

Figure 10: Fractional rate of change of continuum fluxes for each order in a sample of 33 SWP high-dispersion spectra of $\tau$ Sco. The three lines indicate early-epoch (dot-dashed) and late-epoch (dashed) echellograms and the image-weighted average of both sets (solid). The dotted line shows the corresponding slopes for 164 large-aperture spectra of the B0.5e star $\gamma$ Cas (not otherwise discussed in this paper) distributed through the timeline of the IUE mission. /td>

Table 1: Degradation Coefficients Cm,i=1,2(t) for $\tau$ Scorpii Spectra
Echelle Order C1,t(m) C2,t(m) Echelle C1,t(m) C2,t(m)
Order #     Order #    
125 -0.00276 0.02965 95 -0.01144 -0.01637
124 0.00069 0.06306 94 -0.01104 -0.01825
123 -0.00659 0.06709 93 -0.01048 -0.01626
122 -0.01625 0.06853 92 -0.01086 -0.01623
121 -0.03167 -0.00221 91 -0.01104 -0.01421
120 -0.03859 -0.06334 90 -0.01046 -0.01536
119 -0.03508 -0.07728 89 -0.01115 -0.02556
118 -0.02928 -0.07593 88 -0.00810 -0.01470
117 -0.02941 -0.07663 87 -0.00784 -0.01432
116 -0.02370 -0.06472 86 -0.00600 -0.01476
115 -0.02087 -0.06070 85 -0.00650 -0.01287
114 -0.02071 -0.06329 84 -0.00579 -0.01207
113 -0.01922 -0.05844 83 -0.00578 -0.00960
112 -0.01435 -0.03760 82 -0.00683 -0.00994
111 -0.01477 -0.03243 81 -0.00693 -0.00951
110 -0.01034 -0.03041 80 -0.00727 -0.00799
109 -0.01000 -0.02317 79 -0.00764 -0.00733
108 -0.00730 -0.02125 78 -0.00779 -0.00693
107 -0.00586 -0.01817 77 -0.00842 -0.00748
106 -0.00684 -0.01986 76 -0.00888 -0.00682
105 -0.00559 -0.01559 75 -0.00863 -0.00681

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