John Stansberry, Myra Blaylock
Last Updated: 2005 Dec. 13

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) or a blackbody. 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 TBD. The calibration based on blackbody fits is 1075±11 uJy/"²/U160, and represents a 7.5% increase from the current calibration factor. The response of the detectors appears to be linear over the flux range 0.1 - 3 Jy.

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 model SEDs (Blackbody and Standard Thermal Model) 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 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 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).

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" used for the calibration are based on either fitting the 24 and 70um photometry for objects, 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 approximate 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 subsamples are presented further down, for those who may be interested.

  Standard Thermal Model Fits

STM results are TBD, and will be presented in Figure 1.

  Blackbody Fits

Figure 2 compares our measured 160um photometry of asteroids to our predicted 160um fluxes based on blackbody 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 to these data which is forced to pass through the point [0,0], and a fit which is not constrained to pass through [0,0]. The plot shows that the response of the detectors is linear over the flux range 0.1 - 3 Jy. The formal uncertainties in the fitted slopes (i.e. the calibration factors) are about 1%, so the differences in the calibration factors is significant. The formal uncertainties on the intercept is 9 mJy, so the intecept is statistically consistent with zero. Here the fits are performed (and data plotted) using just the measurement uncertainties for the individual observations, rather than RSS'ing those with the 20% calibration uncertainty. Below, figures and fits include that 20% calibration uncertainty. This method should be more correct, but weights the observations of bright objects considerably more because they are detected at high signal-to-noise.

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 blackbody 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.

  Blackbody Fits

We fit the observed 24 and 70um fluxes for 31 asteroid observations with blackbodies, 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 blackbody-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 formal uncertainty in the slope is about 4%, and the intecept is uncertain by about 10mJy, so both fits and the previously determined calibration are consistent with one another, based on these data.

Fig. 3 The observed 160um flux vs. the predicted flux based on blackbody 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 blackbodies to the 0.7-sigma deviant observed flux values, and using those blackbodies 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 1050 uJy/"2/U160 if the point [0,0] is included, and a factor of 972 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.

Figures 5 & 6 provide the basis for extending the calibration to brighter objects. Figure 5 shows the blackbody temperatures derived from our fits to the 24 and 70um photometry. The temperatures of all the asteroids observed at 24 and 70um are clustered around 266 K, with a range of only 240 - 300 K. Because both the 70 and 160um bands are well longward of the blackbody peak of even the warmest asteroid we've observed (at 230 K the blackbody peak is as 22um), the variation in temperature seen in this figure does not result in very much variation in the 70um to 160um color.

Fig. 5 Blackbody temperatures based on our fits to the 24 and 70um photometry for 31 asteroid observations. The error bars are the range computed by using the 0.7-sigma deviant 24 and 70um fluxes, and fitting blackbodies to those. The errors are dominated by the 10% uncertainty in the 70um absolute calibration. The legend gives the weighted-average blackbody temperature, and the 1-sigma range. Horizontal lines across the plot display those same values.

Figure 6 shows the ratio of our measured 70um flux to the predicted 160um flux for all asteroids observed at 24 and 70um. The error bars on individual measuremnts are large relative to the scatter of the points, probably indicating that we over-estimate the uncertainty on our predicted 160um fluxes. The scatter of the individual determinations indicates a 1-sigma uncertainty in the 70 to 160um color of 0.092. This translates into an uncertainty on 160um fluxes predicted solely by extrapolation from 70um of 2.4%. 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. 6 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.

  Blackbody Fits

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 7 shows our results for the 27 2-color targets. These data indicate that a small upward revision of the 160um calibration factor may be called for. When the data are fit with a line constrained to pass through the point [0,0] the resulting calibration factor is 1108 uJy/"²/U160, whereas without that constraint the factor is 1139 uJy/"²/U160. The formal uncertainties in these calibration factors are about 5%, based on these data. The fits exclude 6 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. 7 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 1108 uJy/"2/U160 if the point [0,0] is included, and a factor of 1139 uJy/"2/U160 if it isn't included.