Planetary brightness and flux density calculations

The calibration of the temperature and flux density scales for the JCMT antenna ultimately rests on accurate knowledge of the brightness temperatures of the planets as a function of frequency. The main planets used are: Mars, Jupiter, Saturn, Uranus, and Neptune. Brightness and flux values are not provided for Mercury, Venus, or Pluto/Charon. Mars is used as the primary calibrator; that is, the brightness temperatures of all other planets are referred to the brightness temperature of Mars. Since Mars is a solid body, it is relatively secure to use a model of its brightness temperature as a function of date. This information can then be used to calibrate observations of the other planets.

Once the brightness temperatures are known, it becomes possible to calculate the flux density received at the Earth from a given planet, corrected for the apparent size of the planet and the beam size of the JCMT at the frequency being used. This is done by FLUXES and FLUXNOW.

Historically, FLUXES was developed for use with the bolometer UKT14. For each of the presently available UKT14 filters the brightness temperature and total flux density of the planet is calculated, along with the flux density visible to a 65mm aperture (the standard detector width) - shown in the tables under the heading Flux in beam. The latter is calculated from the beam width given in the final column - if you have reason to believe that the beam width is different, or you have used a different aperture, you will have to re-do the calculation.

The planetary brightness temperatures used are obtained from the measurements of Griffin et al. (1986, Icarus, 65, 244), Orton et al. (1986, Icarus, 67, 289), and Griffin & Orton (1993, Icarus, 105, 537). The errors in brightness temperatures are the rms internal errors of the observations.

From MJD 46040 until MJD 50000 (i.e. JD 2450000.5, corresponding to 1995 October 10), FLUXES uses $\lambda350\mu$m Martian brightness temperatures $T_b$ derived from the model described by Wright (1976, Ap.J., 210, 250). This uses an adjusted model of the thermal behaviour of Mars' surface and geometric factors to predict the flux received at the Earth and the whole-disk brightness temperature at 40-day intervals. The model does not include the effects of dust storms and the Martian polar cap. At all other times, the model has a maximum uncertainty of within $\pm5$% . Since the results for Mars are derived from models, no errors are quoted in the output of FLUXES.

Before MJD 46040 and, more importantly, since MJD 50000, FLUXES uses a modification of Wright's rotating cratered asteroid program (Wright, E.L., 1995; private communication to H.E. Matthews). This reproduces 82% of the $T_b$ values in Table 6 of Wright (1976) exactly (where they are rounded to the nearest Kelvin), while the other 18% differ by only $\pm1$ K. A low-precision formula by Van Flandern and Pulkinnen, (1979, Ap.J.Supp., 41, 391) was used to compute the geometric factors (Mars-Sun distance $R$, Martian declinations of the Sun and the Earth $D_S$ and $D_E$, and the difference in Martian right ascensions between the Earth and the Sun $A_S - A_E$) far into the future.

Figure: Martian brightness temperatures

The values of $T_b$ for Mars are calculated for the entire date range at intervals of 40 days. FLUXES interpolates between the nearest two values to obtain the value for the requested date and time. Figure shows the variation of disk-averaged Martian $\lambda350$-$\mu$m brightness temperatures over a period of 25.2 years, beginning in late 1975, calculated using a rotating cratered asteroid model, and corrected for the microwave background. The differences between this model and the full model by Wright (1976) over the range for which data is available is shown dotted below, where the solid horizontal line is 0 K T$_b$ difference.

Over the interval for which both the original Wright model and the simplified model are valid, the differences in brightness temperatures have an rms error of 0.13 K (i.e. negligible) after removing a constant offset of -2.56 K, assumed due to the microwave background.