Appendix A: Stellar variability and the IRAS flux densities

As discussed in Sect. 2.2 (click here), the flux densities obtained from co-addition of the IRAS data generally agree well with those in the PSC with, however, some notable exceptions, as shown in Fig. 1 (click here). Several stars have flux densities which are in disagreement at a level well outside that expected from noise. In this Appendix we investigate whether these disagreements can be explained by stellar variability, using the data for Cyg as an example. The ephemerides listed in the GCVS give a variation of about mag at V between maximum and minimum light, a period of  d and the epoch of zero phase which is closest to the IRAS launch date of JD 2445404.4.

The colors of Cyg, calculated from the IRAS PSC flux densities (see Table A2), are photospheric, despite the strong circumstellar CO emission (discussed in Sect. 5 (click here)). On the other hand, model IRAS colors calculated from the mass loss rate given by the CO lines (several 10^-7  y^-1), assuming a normal gas to dust ratio and silicate grains (the star is an SiO maser; e.g. Patel et al. 1992), are well displaced from photospheric values. This discrepancy does not mean that the circumstellar envelope is dust-free, however; the ratio of the 12  to 2  flux densities is well in excess of the photospheric value for a temperature of 2400 K (Haniff et al. 1995), demonstrating the presence of an appropriate amount of circumstellar dust.

We therefore re-examined the raw IRAS data for this star. The individual IRAS 12 , 25 , and 60  observations for Cyg are listed in Table A1. Column 1 gives the Julian date of the observations computed from the "Satellite Operation Plan'' number attached to each scan and from the mission chronology provided by the Explanatory Supplement. Column 2 lists the phase. Next are the flux density, the offset between the scan center and the stellar position, and the detector number for the 12 m data. The final columns contain the 25 m and 60 m flux densities and the [12] - [25] and [25] - [60] colors calculated from combinations of the observed flux densities. The colors calculated from the flux densities derived from individual scans locate Cyg in Region B of the color-color diagram.

 

F12 offset det F25 F60 [12]-[25] [25]-[60]

(Jy) (') (Jy) (Jy)

5452.8 0.12 1860.6 0.40 48 643.5 99.4 0.41 -0.15

540.2 0.22 0.04

5453.7 0.12 1778.6 -1.01 23 533.2 97.7 0.25 0.04

1880.7 1.23 51 92.6 0.19 -0.02

5466.1 0.15 1157.5 -1.79 28 626.6 86.5 0.89 -0.27

1975.0 0.63 48 525.0 99.8 0.37 -0.11

0.70 -0.08

0.18 0.08

5466.2 0.15 1624.5 -0.03 53 520.7 98.7 0.32 0.08

583.0 0.45 -0.05

5639.7 0.58 1248.7 -0.22 30 456.3 72.6 0.47 -0.11

422.1 0.38 -0.03

5639.8 0.58 1172.5 -0.52 24 433.5 69.5 0.48 -0.11

1266.5 1.72 49 0.40

5640.3 0.58 1184.6 -0.04 24 404.9 70.8 0.39 -0.01

5640.6 0.58 1249.0 0.13 27 383.0 74.7 0.28 0.11

1214.4 1.75 51 0.31

Table A1 shows that there are occasionally large discrepancies between the flux densities measured by different detectors at the same time; see, for example, the 12 m flux densities observed at JD 2445466.1. The low flux density is probably due to the large offset between the stellar and detector center positions; such discrepant observations are usually filtered out in the IRAS data processing. Real variability is also apparent. The data were obtained at two epochs, near maximum and minimum phase, and the flux densities at all four wavelengths are systematically higher for the first set of observations than the second. The mean flux densities for these two epochs are listed in Table A2; the differences are = 32% at 12 m, 26% at 25 m, 25% at 60 m and 31% at 100 m.

 

Observed (averages) F12 F25 F60 F100

(Jy) (Jy) (Jy) (Jy)

max 1804 568 96 20

min 1223 420 72 14

PSC 1688 459 81 18 Calculated

Phase F12 F25 F60 F100

(Jy) (Jy) (Jy) (Jy)

max 1486 576 86 20

min 1108 486 79 17

Can these variations be attributed to the stellar variability? The huge variations in Mira variables at visible wavelengths are due largely to the changing photospheric temperature; the variation in the bolometric magnitude is much smaller, about a factor of 2 (e.g. Petit 1982; Hoffmeister et al. 1985). Because of the variation in stellar effective temperature, the star reaches maximum light later at longer wavelengths in the visible and near infrared (e.g. Le Bertre 1992). In particular, the variation at visible wavelengths leads the total light variation by about 0.1 of a period. The two groups of observations in Table A1 were thus made close to maximum and minimum luminosity.

We modeled the object as a star with a circumstellar envelope and varied the luminosity of the model star. The envelope contains silicate grains, has a dust loss rate of   y^-1 and is assumed to have the same outflow speed as the gas (9.5 ). The star is assumed to be a black body of temperature 2400 K and luminosity 3000  at minimum, and 2800 K and 6000  at maximum. The resulting model flux densities are listed in Table A2 and are reasonably close to the observed values (note that the discrepancy at 12 m may be caused in part by the saturation of the detectors at these flux densities exceeding 1000 Jy). The variation in the IRAS flux densities can thus be fully explained by the stellar variability.

These results show that caution is required in the interpretation of IRAS data for variable stars; colors must be calculated from data taken at the same epoch, as should models of the circumstellar envelope. Variability introduces a significant amount of scatter into the IRAS colors, especially [12] - [25], which as a result does not provide the clean measure of the stellar mass loss rate which the models predict (see, for example, the discussion by Habing 1996).