Executive Summary

The 2MASS Calibration Scan data have been used to investigate the internal accuracy of 2MASS photometric calibration with four different nightly zero point offset determination algorithms. The method employed was to consider each calibration field in turn as a test particle and to rederive the nightly zero point offsets excluding the test-field. The test-field observations were then recalibrated using the new nightly calibration fits, and the residuals between the true photometric offsets for the field and the new fits were evaluated. The four algorithms used to fit the new nightly zero point offsets were: 1) constant, 2) linear with time, 3) quadratic with time, and 4) piecewise.

Examination of the residuals for all of calibration fields used in turn indicate the minimum net residuals are achieved using the piecewise fit for the J-band, and the constant fit for H-band and K_s-band.

The overal RMS of the distribution of residuals for all calibration fields provides a measure of the net calibration accuracy for the survey. Using the optimal fitting algorithms described above, the net residuals in the J, H and K_s bands are 0.017, 0.015 and 0.012 mags, respectively.

I. Introduction

Because each 2MASS calibration field was observed between several hundred and several thousand times during the survey, we can use the calibration field measurements themselves as "test-particles" to examine the net calibration accuracy for the survey. We can also investigate different algorithms for determining the best functional form for the nightly zero point offset fits.

Photometric calibration for 2MASS survey observations is accomplished using hourly observations (bi-hourly early in the survey) of one of 35 calibration fields that are distributed along the celestial equator and at declinations near +/-30^o. The instantaneous photometric zero point offset for each calibration scan is determined by taking the mean difference between the "catalog" magnitudes and the instrumental photometry of of 10-50 primary and secondary standard stars in each field, corrected for atmospheric extinction. The photometric zero point offset for any time during the night is determined using fits to the instantaneous offsets from the observations of each calibration field. For the preliminary 2MASS processing, the fits to the nightly zero point offsets were restricted to be linear with time for the J-band, and constant for the night in H and K_s. Survey scans were then calibrated by applying the proper zero point offset for their time of observation and appropriate extinction corrections.

Because their is always an instantaneous measure of the zero point offset for each calibration scan, the offset fit values can be compared to the true offsets to guage the accuracy of the calibration fit. Some preliminary work examining the overall calibration accuracy using the calibration scan residuals is presented in Nightly Photometric Zero Point Uncertainties. John Carpenter has performed an analysis of different calibration fitting algorithms applied to repeated survey observations of the Orion and Chameleon I regions that suggests that better accuracy can be achieved using higher order fits to the nightly offsets than were used during preliminary processing.

This document describes an analysis that uses the complete set of 2MASS calibration data derived from the preliminary processing to estimate the overall calibration accuracy of the survey, and to examine different algorithms for fitting the nightly zero point offsets.

II. Procedure

The inputs for this analysis are the nightly CALMON output summaries, the qDATEh.cal files. Along with the overall nightly calibration nformation, these files contain the mean zero point offset measured using the primary and secondary standard star photometry for each calibration scan. in a given night. Corrected for atmospheric extinction, these define the "true" zero point offset, within the limits of the photometric measurement accuracy. The *.cal files also contain other relevant parameters for each scan such as the airmass, UT times, hour angles, etc..

Using each calibration field in turn as a test field, new nightly zero point fits were made for each night, excluding the measurements of the test field. The zero point offset fits made were

1. constant over the night,
2. linear with time,
3. quadratic with time, and
4. piecewise (piecewise is a linear fit between adjacent calibration scans).

To minimize the impact of measurement errors of individual stars or scans, the nightly fit were made to the average extinction-corrected instantaneous zero point offsets for all six scans of a calibration field that comprise each calibration set. The sophisticated rejection algorithms used by CALMON were not employed in this analysis, so there may still be occasional outliers. The fits were unwieghted, and the linear and quadratic fits were made using simple least-squares polynomial fitting. The piecewise fits were made as linear fits between adjacent calibration sets. The restrictions applied to the data allowed into the analysis are as follows:

• Only previously identified photometric periods were used.
• Obviously, for a given test field, only nights in which the field was observed were considered.
• Only nights for which there were at least 5 other calibration field measurements were used. This insures a reasonable number of points go into the various fits, and a statistically meaningful fit can be achieved.
• Only nights after survey day 427 (980501) were used because secondary standards were available for all fields after that day. This improves the statistical accuracy of the zero point measurement for any given scan.

Once new zero point fits were made for each night, the value of the zero point offset appropriate for the time of each test field observation was determined. The residuals between the average true instantaneous offset for each test cal set, corrected for atmospheric extinction, and the offset determined from the nightly fits were then tabulated (residual = True Offset - Fit). An observation of a test calibration field was used in a given night only if it was bounded by photometric observations of other calibration fields. That is to say, calibration fits were interpolated only, and not extrapolated. The median and RMS for all of the residuals for each calibration field were then determined, and histograms of their distributions were constructed.

III. Results

a. Residuals for each calibration field

The table below gives for each field the number of calibration sets used in the analysis, and the median and RMS residuals for the constant, linear, quadratic and piecewise nightly fits. The number of residual measurements available for each cal field ranged from a minimum of 32 (90330) to a maximum of 343 (90013). Equatorial calibration fields have the largest number of usable observations. All median and RMS values are in magnitudes. Also provided are links to plots showing the histograms of the residuals. In each of the plots the heavy black curve shows the histogram of residuals to the constant zero point fits, the red shaded curve shows the linear fit residuals, the green shaded curve shows the quadratic fit residuals, and the blue curve shows the piecewise fit residuals.

b. Ensemble Residuals

Table 2 below lists the median and RMS of the residuals to the four different fits for the ensemble of all calibration test fields. Also provided are links to the residual distribution histograms.

Examination of the plots and statistics shows that the ensemble distributions show no net zero point offsets, indicating that the residual offsets for individual calibration fields are more or less random and sum to zero. The RMS of the distributions provides a measure of the overall accuracy in each band, and indicates the best of the four fits. For J-band, the minimum residual dispersion is achieved for the piecewise fit, and is 0.01685 mags. The minimum dispersion in the H- and K_s-bands are 0.01404 and 0.01170 mags, respectively, and are achieved for the constant nightly fits. In some sense, this is really the worst-case estimate because this procedure rederives the calibration at the maximum time separation from other calibration scans. Normal survey observations are taken closer in time to the adjacent calibration sets than consecutive calibration sets.

IV. Airmass Effects

a. Ensemble Residuals

A concern with the higher-order zero point fits, in particular the piecewise fit, is that small errors in the extinction coefficient on a particular night might bias the calibration of the survey scans adjacent to high airmass calibration observations. The second and third entries in Table 2 address this concern. The second entry lists the median and RMS residual distributions for all of the calibration fields observed at an airmass >1.8. The minimum RMS values are achieved for the quadratic fits in all bands. There are also small offsets in each band that may suggest slight over or underestimates in the extinction corrections for all bands. However, only a few calibration fields were ever observed at very high airmasses during the survey because of their distribution on the sky. Thus, the apparent net biases could be the result of small catalog magnitude biases or time-dependent extinction coefficient errors. This is examined in more detail below.

The third set of entries in Table 2 address the concern that if a piecewise fit is used, and there is an error in the extinction coefficient, then survey scans adjacent to high airmass calibration scans might have a biased calibration applied. These entries show the median and RMS residual statistics for all test calibration scans that were immediately adjacent to calibration sets having an airmass >1.8. The minimum RMS values are achieved for the piecewise fits in J, constant fit in H, and linear fit in K_s, just as in the general case looking at all scans. The dispersion levels with the best fits are only marginally larger than the general case, and the net biases are extremely small and probably insignificant.

b. Residual extinction effects

Figures 1a-1c below show the zero point residuals for each calibration set plotted as a function of the mean airmass of the set. For J-band, the residuals are those with respect to the piecewise fits, and for H and K_s the residuals are with respect to the linear fits. Figure 1a shows all cal sets together, and 1b and 1c show the northern and southern observatory data separately. In these plots, individual cal sets are shown as black crosses, and the red bars shows the mean zero point residuals in 0.1 airmass bins. The vertical error bars on the mean residuals denote the RMS (i.e.population sigma) of the residuals in each bin.

Figure 1a - Zero point residuals for all calibration sets plotted as a function of the mean airmass of the set. Red bars show the mean offsets in 0.1 airmass bins.

Figure 1b - Zero point residuals for Northern calibration sets plotted as a function of the mean airmass of the set. Red bars show the mean offsets in 0.1 airmass bins.

Figure 1c - Zero point residuals for Southern calibration sets plotted as a function of the mean airmass of the set. Red bars show the mean offsets in 0.1 airmass bins.

If the coefficients used during preliminary processing systemmatically under or overcorrected for atmospheric extinction, then we might expect the residuals to increasingly deviate from zero with increasing airmass. The slope of the deviation would provide the correction to the extinction coefficients, in magnitudes/airmass.

A small deviation is seen in the northern J-band residuals, consistent with a correction of 0.05-0.07 mags/airmass. The northern H and K_s residuals appear consistent with no deviation. However, the southern residuals show increasing deviation out to an airmass of ~1.8, and then turn over becoming nearly zero at larger airmasses. The deviation in the southern K_s residuals is small, but the effect is quite pronounced in the J and H bands.

The global calibration analysis suggests that the extinction coefficients vary seasonally. If all calibration fields were observed uniformly all year, then such variations would tend to inflate the dispersion in the residuals evenly. However, because of their distribution on the sky and the calibration scheduling strategy, calibration fields are observed at preferred times and only a small number of fields are ever observed at very large airmasses. For example, of the 35 calibration sets in this analysis observed from Mt. Hopkins with X>1.8, 14 of those sets are field 92202. The second most observed high airmass field from Mt. Hopkins is 92397 with 9 instances. Both of these are relatively low declination "equatorial" fields (~-11^o). Similarly, of the 61 high airmass fields observed from CTIO (X>1.8), 43 are of field 90067 (M67), an "equatorial" field at a declination of +11^o. The second field most often observed from CTIO at high airmass was 90565, with only 10 instances used in this analysis.

The M67 field was observed at high airmass from CTIO preferentially during early January and February and late November, whereas it was observed at lower airmasses more uniformly during the year. Figure 2 shows the southern residuals plotted as a function of airmass, as in Figure 1c, but the sets corresponding to field 90067 are indicated in green. The plot shows clearly that the apparent high airmass turnover in the ensemble residuals is attributable to the observations of field 90067. Because 90067 was observed at high airmasas during specific months, seasonal variations in the extinction coefficients can lead to the unusual structure seen in the residual plot.