John Stansberry, Myra Blaylock
Last Updated: 2006 Jan. 18

Abstract

We derive a new absolute calibration of the MIPS 160um band based on observations of asteroids. The calibration strategy relies on near-simultaneous observations at 70 and 160um in all cases, and at 24um for about 1/2 the sample. Photometry in the shorter bands is fit by a Standard Thermal Model (STM). The 160um flux is predicted from those fits and compared with the observed counts in the 160um band to derive the calibration. The calibration based on STM fits is 1050±11 uJy/"²/U160, a 5% increase from the current calibration factor. The formal uncertainty in the new calibration factor is ±1%. The response of the detectors appears to be linear over the flux range 0.1 - 3 Jy. We also used blackbody fits to derive a calibration, but the results are the same as reported here.

Introduction

The 160um channel of MIPS is being calibrated using observations of asteroids. This is in contrast to the MIPS 24 and 70um channels, which rely for their calibration on observations of stars. The 160um channel suffers from a short-wavelength (about 1.6um light) ghost image, which reflects (diffusely) off a surface of the band-pass filter. This short-wavelength light is focused onto the 160um detectors without passing through any other filters, and dominates the signal from the 160um detectors for sources with blue spectral slopes (i.e. stars). Unfortunately the image of the 1.6um light is about 10x brighter than 160um image, and the two images overlap. Hence, stars cannot be used to calibrate the response of the detectors to 160um photons. Thermal emission from main-belt asteroids peaks near 20um, and their (reflected) near-IR brightness is much weaker relative to their 160um brightness than for stars; the image of an asteroid on the 160um array is strongly dominated by the 160um photons, making it possible (in principle) to use asteroids as calibrators.

Calibration Strategy

Unfortunately the spectral energy distributions (SEDs) of asteroids are difficult to predict due to temperature variations across the surface, are time-variable due to rotation and changing distance from the Sun and observer, and are poorly characterized at far-IR wavelengths. Because of these difficulties in predicting the 160um flux from a particular asteroid for a particular observing circumstance, we adopted a calibration strategy that relies on near-simultaneous observations of asteroids at 24, 70 and 160um, and then bootstraps the 160um calibration from the well-understood calibrations at 24 and 70um. Additionally, we have observed many asteroids so that we can use the average properties of the data to derive the calibration, rather than relying on detailed efforts to model the thermal emission of individual asteroids. The emission from asteroids at wavelengths beyond 60um has not been characterized for very many objects (ISO did do a good job on this, but only for a few large asteroids having very weak rotational lightcurves). Because of that, we felt that it was very important to characterize the thermal emission of our calibration targets at both 24 and 70um, and use SEDs fitted to both bands to predict the 160um flux.

Saturation limits introduce a complication in trying to observe any particular asteroid in all 3 MIPS bands. The 24um channel saturates at around 3Jy. For typical asteroid SEDs, this limits the maximum 160um brightness that can be related back to un-saturated 24um observations to a bit under 0.5Jy. Sensitivity and confusion limits at 160um limit the dimmest asteroids that can be used to brighter than about 0.1Jy at 160um. Thus, the dynamic range of the 160um fluxes that can be directly tied to 24um observations is only a factor of 5, from 100mJy to 500mJy. The saturation limit at 70um, 23Jy, does not place any restricion on sources that can be observed at both 70 and 160um (the 160um saturation limit, 3Jy, is about 1/2 of the 160um flux from an asteroid with a 23Jy 70um brightness).

These facts lead us to adopt a 2-tiered observation and calibration strategy:

1. An asteroid is observed nearly simultaneously in 3 (24, 70, 160) or 2 (70 & 160) MIPS bands. This limits any impact from asteroid rotation.
2. We observe asteroids with predicted 24um fluxes < 3Jy in all 3 MIPS bands.
   1. We fit the 24 and 70um photometry with Standard Thermal Model (STM) SEDs to predict the 160um flux.
   2. For all of these "3-color" asteroids, we track the ratio of the observed 70um to the predicted 160um flux (F70/P160).
   3. The mean of F70/P160 we adopt as the "canonical" 70/160 color of our sample. That color has an uncertainty (9%) given by the standard deviation of the individual determinations.
3. For asteroids with predicted 24um fluxes > 3Jy, and predicted 70um fluxes < 18Jy, we observe at 70 and 160um only.
   1. For these "2-color" asteroids, we use the average or "canonical" value of F70/P160 from the 3-color objects to predict the 160um flux based on the observed 70um flux.
4. We plot the observed 160um signal from all objects vs. their predicted 160um fluxes.
5. We fit a line to the observed vs. predicted data to compute the calibration factor relating flux to counts (the slope of the fitted line). The fits were done accounting for both the uncertainties in the measured instrumental units and the uncertainties in the predicted fluxes.

Observations

87 individual observations of asteroids were made through the 24th MIPS campaign (between December 2003 and September 2005). Of those, 58 resulted in useable detections at 160um. 31 of those observations were 3-color, and 27 were 2-color (70 & 160 only). All observations were made using the photometry AOT. The early observations used a 3x1 raster map at 160um, with the 3 positions along the long dimension of the array (resulting in very skinny mosaics, with little sky around the object). Around campaign 17 we changed to a 1x3 cluster at 160um, which provides a more square-ish mosaic, and a fairly generous sky region completely surrounding the 160um PSF. For these later observations 2 AORs are required: one to take the 24 and 70um data, and a second to take the 160um cluster map. These AORs are associated by a chain-constraint, such that they get executed sequentially without any interruption (to minimize and impacts from asteroid rotation).

All observations were done while tracking the motion of the asteroid. In all cases at 24 and 70um the motion of the target relative to the width of the PSF was negligible during the duration of the observation. At 160um some observations were long enough that some target motion was noticeable. In such cases the data had to be re-mosaicked to account for the motion. (The standard mosaicking procedure generates an image that is stationary in RA-Dec, resulting in the asteroid being streaked even though the telesope was tracking... Don't ask.)

The pointing information for some of the 160um observations is incorrect. This is because the 160um frame table was spuriously tuned such that the 1.6um image from stellar sources was originally thought to be the 160um image. Because the two images are displaced by 10-15", the FITS header information based on the early frame table was incorrect. The main result of this is that photometry on the 160um images cannot reliably be done in an automated fashion using just the pointing information in the FITS headers to find the target in the images.

Predictions

We used predicted fluxes for the asteroids to generate AORs for each campaign. The predictions were generated by Bidushi Bhattacharya (SSC IRAC IST) using the Standard Thermal Model (STM), and albedos and diameters from the IRAS Asteroid Catalog. While the predicted fluxes have reasonable correspondence to the fluxes we observed, we do not use these predictions to generate our 160um calibration.

The "predictions" (which are really extrapolations) used for the calibration are based on either fitting the 24 and 70um photometry, or extrapolating from 70um where we only have data in that band. The fit or extrapolation is used to predict the flux at the effective wavelength of the 160um band (156um).

Data Reduction

The data were reduced using the MIPS Data Analysis Tools (DAT). All the data were post-processed using Karl Gordon's RED_PHOT package, which cleans up the images considerably. RED_PHOT also produces photometry automatically, and we used the RED_PHOT results at 24 and 70um. At 160um we performed the photometry by hand, using me_phot (John Stansberry). This was necessitated by the pointing issues at 160um, mentioned above. Details of the conversion from instrumental units to fluxes are presented in the following table. In addition to allowing the user to select the placement of the photometric aperture, me_phot uses a circular aperture to compute fluxes, rather than the approximately circular aperture utilized for the RED_PHOT photometry. The aperture corrections for the RED_PHOT photometry are small, and the apertures very large relative to the pixel and PSF scales, so the approximation to a circular aperture should be OK. The me_phot aperture correction is huge (a 1.5 pixel object aperture was employed), but was derived using the same methods as employed within me_phot. The uncertainty in the 160um photometry due to the large aperture correction / small object aperture is TBD.

We present the results using all asteroid calibration observations here (i.e. combining the results from the 3-color and 2-color samples). Results for the 2 sub-samples are presented further down, for those who may be interested.

Figure 2 compares our measured 160um photometry of asteroids to our predicted 160um fluxes based on STM fits and extrapolations from 24 and 70um observations of those objects. The figure also shows lines for the previously determined calibration factor (1000 uJy/"²/U160), a fit that is forced to pass through the point F160 = P160 = 0, and a fit which is not constrained to pass through [0,0]. The fit constrained to pass through [0,0] gives a calibration factor of 1047&plumn;6 uJy/"²/U160. The unconstrained fit gives a calibration factor of 1063&plumn;8 uJy/"²/U160. These formal uncertainties in the fitted slopes (i.e. the calibration factors) are about 1%, so the difference between these calibration factors and the older one are significant at the several-sigma level. We adopt 1050 uJy/"²/U160 as the new calibration factor, a 5% increase over the historical one. The formal uncertainty on the intercept is 5 mJy, so the intecept (-14 mJy) is formally different from zero at the 3-sigma level. However, at the lowest fluxes where MIPS is sensitive at 160um (about 100 mJy), the impact of the non-zero intercept is at most 10%, and is smaller at higher fluxes. Here the fits are performed (and data plotted) using just the measurement uncertainties for the individual 160um observations, rather than RSS'ing those with the 20% calibration uncertainty. Below, figures and fits include that 20% calibration uncertainty. Excluding the absolute calibration uncertainty should be more correct, but doing so weights the observations of bright objects considerably more because they are detected at high signal-to-noise. The plot shows that the response of the detectors is linear over the flux range 0.1 - 3 Jy.

Fig. 2 Observed 160um flux vs. predicted flux for 49 asteroids. The black plus signs show the data for objects with data at 24, 70 and 160um; the grey symbols are for objects observed only at 70 and 160um. The 3 lines are for the previously determined calibration factor (dashed thin line), a fit to these data constrained to go through the point F160 = P160 = 0 (dotted line), and an unconstrained fit to these data (thick dash-dot line). Corresponding calibration factors are given in the legend. The predicted fluxes are based on STM fits to the 24 and 70um data (for the 27 objects shown that have data at 24, 70 and 160um), and on extrapolation from 70um data (for the 22 brighter objects with only 70 and 160um data). Derivation of the 70:160 color used for the extrapolation is described in detail below. Linear fits to the data plotted in black give a calibration factor of 1047 uJy/"2/U160 if the point [0,0] is included, and a factor of 1063 uJy/"2/U160 if it isn't included.

We fit the observed 24 and 70um fluxes for 31 asteroid observations with the Standard Thermal Model, and used those fits to predict the 160um flux we should have observed. The figures below summarize the results. We used the previously-determined 160um calibration factor of 1000 uJy/"²/U160 in constructing these plots. Figure 3 shows the relationship between the observed and STM-predicted 160um fluxes. Lines show the previously determined 160um calibration (see Table 1), and 2 linear fits to the data. One fit includes the point F160 = P160 = 0 (labeled "Fit0" in the legend), and the other does not include that point. The fits to this subset of the data give calibration factors lower than the historical value. However, because of the very limited dynamic range of this subset of the data, these calibration factors are not particularly important. Also, the formal uncertainty in the slope is about 7%, and the intecept is uncertain by about 14 mJy, so both fits and the historical calibration are statistically consistent with one another.

Fig. 3 The observed 160um flux vs. the predicted flux based on STM fits to the 24 and 70um data. Observations with low SNR at 160um are in red. The photometry has recently been completely re-reduced: previous values which have appeared in some slides are shown as circles, and the newer, improved values as plusses. Observed flux errors are computed as the RSS of the error determined from the image and the 20% uncertainty on the previously determined calibration factor (1000 uJy/"2/U160). Errors on the predicted flux are determined by fitting STM to the 0.7-sigma deviant observed flux values, and using those models to predict the range of 160um fluxes that are consistent with the shorter-wavelength observations. Linear fits to the data plotted in black give a calibration factor of 991 uJy/"2/U160 if the point [0,0] is included, and a factor of 938 uJy/"2/U160 if it isn't included.

Figure 4 presents the same data as Figure 3, but as the observed/predicted flux ratio. The significant improvment made in the recent re-reduction of all the data is quite noticeable as the tighter clustering of the plus symbols relative to that of the open circles.

Fig. 4 The ratio of observed to predicted 160um flux based on blackbody fits to the 24 and 70um data. Observations with low SNR at 160um are in red. Basically the same as Figure 3. Circles reflect old photometry results. Plusses give the results based on the newer, completely re-reduced photometry.

Figure 5 shows the ratio of our measured 70um flux to the predicted 160um flux for all asteroids observed at 24 and 70um, and provides the basis for extending the calibration to brighter objects. The mean 70:160um color of the STM models is 3.748, while the scatter of the individual determinations indicates a 1-sigma uncertainty in that color 0.092 (only 2.4%). Thus we should be able to very confidently predict 160um asteroid fluxes from 70um data alone, at least in the statistical sense required by our calibration strategy. When RSS'd with the 10% uncertainty in the absolute calibration at 70um, we can use a 70um observation (alone) to predict the 160um flux of an asteroid to better than 11%. This is a significant improvement over the uncertainty on the 160um calibration (20%) that we are currently carrying.

Fig. 5 Asteroid 70um to 160um color derived from our blackbody fits to the 24 and 70um observations. The error bars include the uncertainties in the measured 70um fluxes and those on the predicted 160um fluxes (see caption to Fig. 5). Based on these 31 asteroids, the 1-sigma variation in the 70 to 160um color is 0.092.

About half of the asteroids we observed have only 70 and 160um data, because they would have saturated the 24um array. For these 2-color targets, we use the 70 to 160um color derived above to predict thier 160um flux. As noted earlier, the uncertainty in that color due to variations in the temperature of asteroids is only about 2.4%. Figure 6 shows our results for the 27 2-color targets. These data, which do have significant dynamic range, indicate that an upward revision of the 160um calibration factor is be called for. When the data are fit with a line constrained to pass through the point [0,0] the resulting calibration factor is 1068 uJy/"²/U160, whereas without that constraint the factor is 1103 uJy/"²/U160. The formal uncertainties in these calibration factors are about 5%. The fits exclude 5 observations which had low SNR, or where the measured 160um flux deviates from the predicted flux by more than 50%. These deviant points (in red in figure 5) all lie well above the trend indicated by all the other data. The reason for these departures is TBD, although the predicted flux for the 2 brightest targets are flirting with the 3Jy 160um saturation limit.

Fig. 6 Observed vs. predicted 160um flux for asteroids observed only at 70 and 160um. Most are brighter than those in the 3-color sample, although a few faint ones were observed this way early in the calibration program. Errors on the observed flux are computed as the RSS of the error determined from the image and the 20% uncertainty on the previously determined calibration factor (1000 uJy/"2/U160). Errors on the predicted flux are the RSS of the uncertainty in the observed 70um flux (including its 10% absolute calibration uncertainty) and the uncertainty in the 70 to 160um color computed from the 3-color asteroid sample. Linear fits to the data plotted in black give a calibration factor of 1068&pusmn;57 uJy/"2/U160 if the point [0,0] is included, and a factor of 1103±87 uJy/"2/U160 if it isn't included.

Earlier efforts to fit 24 and 70um photometry with the STM revealed a systematic underprediction of the 70um flux, and imperfect fits to a few of the 24um observations as well. (see slides 8 and 10 from the Sept. 2005 Calibration Workshop at UA. The causes of those problems were traced to a too-coarse grid of model parameters in the 24um case, and in the 70um case to the fact that the earlier STM fits were performed with the beaming parameter constrained to be equal to the canonical value of 0.756 (see Lebofsky et al., 1989). While not mentioned earlier, our implementation of the STM requires the model to fit both the thermal fluxes and the visible brightness of the object, which we compute based on its absolute magnitude (from Horizons) and the circumstances of the observation. Our earlier systematic problem in fitting the 70um photometry simultaneously with the 24um and visible brightness, was due to the fact that the canonical beaming parameter is canonically wrong: we find a considerably lower value based on our fits to the calibration data. The figures below show the quality of the fits we now achieve to the 24 and 70um photometry, and result from the fits done to the 3-color sample above.

Fig. 7 Our STM model fits to the 24um photometry from the 3-color sample of asteroids. The quality of the fits is significantly better than before.

Fig. 8 Our STM model fits to the 70um photometry from the 3-color sample of asteroids. The quality of the fits is significantly better than before, and the systematic under-prediction of the 70um flux has been eliminated by allowing the beaming paramter to vary.