The absolute calibration of MIPS data proceeds in three steps. First, we have determined the best possible calibration of our flux standards at 10.6 µm using other instrumentation. Second, we use ''standard'' stellar spectral energy distributions normalized to 10.6 µm to extrapolate from that wavelength to the MIPS bands. Additional calibration tasks using asteroids were developed at 160 µm to cope with the ~1.2 µm light leak (see section 7.2.6). Finally, for the 70 and 160 µm germanium arrays, stimulator flashes provide continuous tracking of responsivity changes since the last observation of a calibration source. Calibration sources are observed at the beginning and end of each MIPS observing campaign to allow the removal of any second-order changes in the calibration of the germanium detectors.
An Anchor at 10.6 µm
The most accurate absolute calibration near 10 µm is that of Rieke et al. (1985, AJ, 90, 900). This work became the basis for the calibration of IRAS at 12 µm, so the IRAS catalogs propagate it to many stars. However, the fundamental calibrators are best represented in the original paper. Rieke et al. found that calibrations based on extrapolation of A-star spectra disagreed systematically from those obtained in a number of other ways. If we discard the A-star estimates (as was also done by Rieke et al.) but include the other indirect methods that they also discarded, we arrive at fluxes for the three fundamental calibrators in their system as listed in Table 4.2. A more recent absolute measurement of a Boo is in agreement with the work of Rieke et al. but has substantially larger errors (Witteborn et al. 1999, AJ, 117, 2552). Although not among the Rieke et al. fundamental calibrators, we also include their estimate for Vega, based on intercomparison with the other calibrators.
Table 4.2: Flux densities (Jy) of primary MIPS calibrators at 10.6 µm; rms error of 2% in final adopted value (see text).
Rieke et al.
Cohen et al.
M. Cohen and co-workers have published a series of papers presenting calibrated spectral energy distributions of stars, all based upon extrapolated spectra of Vega and Sirius. They use improved models for the atmospheres of these stars, which remove the discrepancies noted earlier by Rieke et al. While their work provides calibrated composite spectra for the stars, here we use only their monochromatic flux densities at 10.6 µm. In Table 4.2, we compare the Cohen et al. and Rieke et al. flux calibrations for the three Rieke et al. fundamental calibrators and Vega. Cohen et al. estimate an overall uncertainty of 3% in their results (Cohen et al. 1996, AJ, 112, 2274). The Cohen values in Table 4.2 reflect a 0.6% upward revision of their fluxes, as suggested by a recent revision in the calibration of Vega at V (Megessier, 1997, Proc. IAU Symp. 189, p. 153), with an accompanying downward revision of their uncertainty to ~2.5%.
The most important result in Table 4.2 is that the two calibration approaches are in excellent agreement for all three calibrators (and Vega). Since the quoted errors for both groups are nearly identical, it is appropriate to take the straight average of the fluxes from the two approaches, and to assign an rms error of 2% to the result.
Extrapolation to the MIPS Bands
To guard against systematic errors, we use three independent methods to extrapolate the calibration to the MIPS bands: 1) Solar Analog method; 2) extrapolation with A star atmospheric models; and 3) extrapolation with semi-empirical models of red giants. Additional tasks at 160 µm use asteroids; see below.
Johnson introduced a method of absolute calibration in which direct comparisons of the Sun and calibrated blackbody sources are transferred to a network of ''solar analog'' stars of type similar to the Sun. The flux offset between the Sun and these stars is assumed to be equal to their brightness difference at some readily measured wavelength (e.g., V band). This method has been used by Campins et al. (1985, AJ, 90, 896) and further references can be found there.
One unique aspect of the application of this method to MIPS is that it is the only feasible ''direct'' calibration, in which the data can be referred back to a comparison with a calibrated laboratory source at or near the wavelength of interest, without relying on spectral extrapolation. Calibration using the solar-type stars is accomplished by using the empirical fit to the measured solar spectrum Engelke 1992, AJ, 104, 1248) to extrapolate solar-type spectra through the MIPS bands. Because of the small differences in stellar temperature, and the minimal line blanketing in the far infrared, the Engelke approximation should be very accurate.
A-Star Model Atmospheres
A-type stars are popular for extrapolating calibrations because it is believed that their atmospheres are relatively straightforward to model. They are probably the most reliable way to extend the MIPS calibration by comparison with theory. A large number of A-stars can be easily measured at 70 µm, and many more (excepting Sirius, which will saturate) can be measured at 24 µm.
The foundation for this approach is accurate atmospheric models, such as those available for Sirius and Vega. Vega itself cannot be used as a calibrator because of its bright debris disk, and a comparison among the measurements of a number of stars will be necessary to identify those without any contamination by disk excesses. Fortunately, enough A-type and solar type stars are available to allow us to reject sources with disk-induced far-IR excesses by simple comparison with the median fluxes of the ensemble of sources.
Red giants generally have very complex atmospheres and are not favored for extrapolation of calibrations. However, in the far-infrared, their spectra appear to exhibit simple Rayleigh-Jeans-like behavior, as shown by the extensive set of composite spectra assembled by Cohen and co-workers. Thus, the brightest red giants play a critical role in the calibration in the far infrared. Unfortunately these sources saturate the 24 µm array. To cross-calibrate the bright giants with the shorter-wavelength A and G star calibration, it is necessary to observe a group of fainter red giants at 24 µm, and then assume that their spectra are identical to the bright giant spectra for stars of identical spectral type.
160 µm Light Leak and Calibrations
During IOC/SV, 160 µm signals from K stars were detected to be about a factor of five stronger than expected. Review of the instrument design revealed a weakness in the stray light control resulting in a short-wavelength (1-1.6 µm) light leak in this band. As a result, there was a reworking of the calibration plans for this waveband. Asteroids are now used as the primary celestial 160 µm calibrators.
Asteroids are observed at both 70 and 160 µm (with some also observed at 24 µm), and so the 70 µm channel provides a link to 160 µm via asteroid models. This is similar to the IRAS 100 µm calibration strategy. Secondary calibrators at 160 µm include leak-subtracted stars, debris disks, extended targets such as galaxies and planetary nebulae, and ISO surveys.
For many types of observations, this light leak does not impact the data at all. Stars fainter than mJ ~ 5.5 mag will not be detectable in the leak above the confusion level. No compact extragalactic sources have mJ brighter than 5.5 mag. The leak signal for a star of mJ = -0.5 mag is equivalent to ~ 2.5 Jy at 160 µm. The parameter to consider for any given target is the 160 µm /2 µm flux density ratio. For a Rayleigh-Jeans source, this ratio is 0.0001. Anything with a ratio larger than 0.004 will produce uncorrupted data, so most objects will not be affected. Sources with 160 µm fluxes more than a factor of 40 above that of a Rayleigh-Jeans source from 1 - 1.6 µm will have leak signals <10% at 160 µm. Galactic programs on star formation, ISM, etc., will likely be impacted.
It has been demonstrated that observations of bright point sources strongly impacted by the leak (stars) can be corrected to a high level using an empirical stellar PSF and careful deconvolution (see, e.g., Stapelfeldt et al. 2004, ApJS, 154, 458). Best results will be obtained with observations for which proper planning and data acquisition was made to allow a good characterization of the leak signature for the object brightness and color. For example, plan to obtain identical observations of ''calibrator'' stars of similar type and brightness to your target stars, but without long-wavelength excesses.
For stellar observations, the strongest signal apparent in a 160 µm observation is likely to be the leak itself. Tests were performed using HD 163588, a K2III star that is routinely observed at 70 µm and has also been observed at 160 µm. Similar results are obtained for HD 36673 (Arneb), an F0Ib star, and for HD 87901 (Regulus), a B7V star. The leak is 15±7 times as bright as the photosphere of a star. Example images are presented in Data Features and Artifacts.
Using normal stars as calibrators imposes severe requirements on the understanding of near-infrared filter leaks. Leaks were measured by comparing the beam profiles of observations of asteroids and stars. If there had been filter leaks, the stellar point spread function would have included spatial frequencies appropriate to the near-infrared Airy pattern of the telescope, frequencies which physically cannot be associated with a true far-infrared signal. Because the ratio of near-infrared to far-infrared flux is much lower for asteroids than for stars, near-IR filter leaks are negligible for the asteroids. Therefore, a careful comparison of PSFs can reveal filter leaks and allow us to measure them. Spatial power spectra of the PSFs can clearly separate the two frequency components if they are present. This method is described by Kirby et al. (1994, AJ, 107, 2226).