IV. 2MASS Data Processing

8. Photometric Calibration

All magnitudes listed in the 2MASS Point and Extended Source Catalogs have been photometrically calibrated using information extracted from observations of Calibration Tiles made during each night of Survey operations (see III.2d). For 2MASS Atlas Images, photometric zero points that allow direct conversion of pixel intensity values to calibrated magnitudes are derived and provided in the "magzp" keyword values in the FITS image headers (see II.4a).

In this section, we describe the process by which instrumental source magnitudes were converted to calibrated magnitudes, and how the nightly photometric calibration transformations were derived. Users do not need to apply these transformations to source data. This page simply documents the transformations that were applied to the data. The absolute calibration of 2MASS photometry is discussed in VI.4.a.

The transformation between instrumental and calibrated 2MASS magnitudes applied to all point and extended sources is:

M_cal = M_inst + c₁ - c₂(X-1.0)

where

• c₁ is the photometric zeropoint offset (magnitudes)
• c₂ is extinction coefficient (magnitudes/airmass)
• X is airmass (sec z)
• M_inst is measured instrumental magnitude of the source, and
• M_cal is the calibrated magnitude of the source.

Each of the coefficients is a function of wavelength. Note that no color coefficients are included in the 2MASS photometric transformations, so all photometry is reported in the natural "2MASS system." The values of the net photometric calibrations, c₁ - c₂*(X-1.0), that apply to the start of each Survey scan are tabulated in the j_zp_ap, h_zp_ap, and k_zp_ap columns of the Scan Information Table.

a. Instrumental Magnitudes

Instrumental magnitudes were measured from the individual frames or Atlas Images using the relation:

M_inst = M_0,inst - 2.5*log₁₀(counts) + K_norm

where

• M_0,inst is the instrumental zero point (magnitudes)
• counts are the integrated, background subtracted counts measured from the images (in digital units), and
• K_norm is the normalization constant used to tie point source photometry to the curve-of-growth-corrected aperture photometry scale.

For pipeline point source photometry, the instrumental zero points were set to fixed values for each detector that resulted in photometric zero point offsets, c₁, that had an average value of approximately zero over the course of the Survey. The instrumental zero points for point source photometry made on the 51 ms "Read_1" and 1.3 s "Read_2" exposures are given in Table 1. The two values for the northern H-band zero points correspond to the original detector array, and the replacement array that was installed in August 1999. The differences between the "Read_1" and "Read_2" zero points reflect the different exposure times.

Table 1 - Instrumental Zero Point Magnitude for Point Source Photometry

	North		South
Band	Read_1	Read_2	Read_1	Read_2
J	17.44	20.93	17.39	20.88
H	17.18/16.85	20.67/20.34	16.93	20.42
Ks	16.54	20.03	16.40	19.89

b. Photometric Zeropoint Evaluation

The nightly photometric zero point offset coefficients, c₁, are a measure of atmospheric transparency. Large (more positive) values indicate higher atmospheric transparency and better effective sensitivity. The plots of zero point offsets versus Julian Day for the full Survey shown in Figure 4 of III.1.c illustrate seasonal variations in the zeropoints. Most pronounced are the transparency drops during the northern and southern summers in each hemisphere, when atmospheric water vapor content is higher. Those plots also show that the H and K_s transparency varies only slowly with time, and was stable at the < 5% level night-to-night. In contrast, the J-band transparency exhibits considerably more scatter over time, and changes by up to ~10% between nights.

The photometric zeropoint offsets, c₁(J,H,K_s), are evaluated for each night's northern and southern data, separately, using the nightly calibration observations (III.2c). The values of c₁(J,H,K_s) are assumed to be a function of time during the night.

For each calibration observation, which consisted of six scans of a calibration field taken in quick succession, the instantaneous zero point offset is given by the average difference between the "true" catalog (M_cat) and extinction-corrected instrumental (<M_inst´=M_inst-c₂*(X-1.0)>) magnitudes for all standards stars measured in each field. The instantaneous offsets are always computed using the standard stars' curve-of-growth-corrected aperture measurements (see IV.4c).

The H and K_s zero point offsets were modeled as linear functions of time using a simple least-squares fit of instantaneous zero point offset versus observation time (T) during the night. Because the J-band zero points exhibited higher frequency and amplitude variations with time, the zero point at any time was taken to be the linear interpolation of the instantaneous offsets of the bracketing calibration observations. This "piecewise" zero point fitting ties the J-band calibrations of each Survey scan to the calibrations observations taken most closely to them in time, allowing response to relatively rapid changes in the transparency. The linear H and K_s and "piecewise" J functional forms were found to produce the smallest photometric zero point residuals in comparative tests of different models of the transparency as described below in IV.8d.

As an example, Figure 1 and Figure 2 show the the photometric zeropoint offset solutions for the night of 1999 November 11 UT in the north and south, respectively. The green points show the average value of M_cat-M_inst´ for all standards in a single calibration scan plotted as a function of time (in UT hours), with J-band on the top, H-band in the middle, and K_s on the bottom. Each cluster of green points represents the six scans in a calibration observation. The annotations below each set of points give, from top-to-bottom, the airmass at the beginning of the calibration observations, the field name, the starting scan number and instantaneous zero point offset measured from the set of six scans. Various fits to the instantaneous zero points as a function of time are shown on the plots; the dashed lines are best fits to constant zero points, the solid lines in the H and K_s panels are the linear fits with time, the "x"'s represent the piecewise, linear interpolations between each calibration observations. In the J-band plots, the solid lines represent a quadratic fit to the zero points. The red, green and blue error bars, found in the upper left corner of each plot, represent the RMS residuals to the constant, linear and polynomial (J only) fits. Residuals cannot be measured for the J-band "piecewise" fits. The H and K_s zero point offsets are given as a function of time for each hemisphere on this night by:

North:
c₁(H,T) =       0.0267 - 0.0021 * T(hr)
c₁(K_s,T) =     0.0699 - 0.0003 * T(hr)

South:
c₁(H,T) =       0.0711 + 0.0007 * T(hr)
c₁(K_s,T) =     0.0834 + 0.0005 * T(hr)

The RMS residuals to the H and K_s fits are 0.0057 and 0.0051 mag in the north, and 0.0026 and 0.0037 mag in the south.

Figure 1	Figure 2

c. Extinction Coefficients

Atmospheric extinction coefficients values in each band, c₂, were taken from a look-up table indexed by observatory and month during the Survey.

The monthly average extinction coefficients were derived prior to the final 2MASS data processing as a part of the global chi-squared minimization procedure used to develop the optimal magnitudes for the 2MASS secondary standard star network (III.2d). This procedure, described by Nikolaev et al. (2000, AJ, 120, 3340), used the set of between 600 and 3500 measurements of each standard star from the preliminary data processing to derive a set of photometric solutions to each night's calibration data that minimizes the overall variance of the solutions for all observations. To derive the monthly average extinction coefficients, the residual differences between the calibrated and instrumental magnitudes for each standard star were first calculated without the extinction term. Then for each month during the Survey, the distribution of residuals for all measurements were fit with a straight line as a function of airmass. This is illustrated in Figures 3, 4, and 5 which show the J, H and K_s residual distributions by month for all calibration observations made at the southern observatory in 1999. Each point in these figures is the residual for an individual standard star measurement, and lines are the best fits of the residuals versus airmass. The slopes of the lines are the mean atmospheric extinction coefficients for each month.

Table 2 contains the mean extinction coefficients for each band measured for each month of the Survey at the two observatories. The uncertainties listed for each value are the errors on the slopes derived from the linear fits of the residuals versus airmass.

Table 2 - Atmospheric Extinction Coefficients as a Function of Month (mag/airmass).

The mean monthly extinction coefficients from Table 2 are plotted as a function of time in Figures 6 and 7 for the northern and southern observatories, respectively. Both sites show seasonal variations in the extinction coefficients, with J and H extinction at a minimum in the respective winters. The Mt. Hopkins K_s extinction exhibits more month-to-month variation than that at CTIO.

Figure 3	Figure 4	Figure 5

Figure 6	Figure 7

d. Calibration Uncertainties

The "combined" photometric uncertainties quoted in the 2MASS All-Sky Release Point Catalogs, j_msigcom, h_msigcom, and k_msigcom, have incorporated the contribution of the photometric calibration uncertainties.

The RMS residuals to the nightly H and K_s zero point offset linear fits provide a measure of the accuracy of each night's calibration solutions. In Figure 8 are shown the distributions of these residuals for the northern and southern nightly calibration solutions during the Survey. The mean residuals are 0.006 and 0.005 mag for the north and south, respectively, and there are a few nights with residuals above 0.01 mag. However, these residuals do not really capture what is the uncertainty in the calibration on a random measurement in the Survey. Moreover, the J-band "piecewise" zero point offset fits do not even provide a direct measure of the residuals.

A more conservative estimation of the calibration errors is provided by an analysis that uses each calibration field in turn as a test particle, and recomputes each night's photometric solution without the measurements of that field. "Piecewise" zero point offset fits are used for J, and linear fits with time are used for H and K_s. The zero point offset that would be applied to each field's measurements according to the new fits is then compared to the "true" zero point offset (ZP_true) for the field computed using the differences between the instrumental and "true" magnitudes of the standards in that field. This technique actually computes a worst-case error because the test-particle calibration field observations are twice as far away in time from the bracketing calibration observations than any Survey observations would be from their bracketing calibrations. Figure 9 shows the distributions of zero point differences computed for all of the calibration fields used in turn on all of the Survey nights. The distributions are approximately Gaussian and have RMS residual values of 0.011, 0.007 and 0.007 mag in J, H and K_s, respectively. These are the characteristic calibration uncertainties that are added in quadrature with the measurement and other error terms in the j_msigcom, h_msigcom, and k_msigcom values for each source in the PSC.

This analysis was also used to determine the optimal fitting functions for the nightly photometric zero point offsets, c₁. The procedure was carried out in each band using a constant, linear, quadratic and piecewise fits to the zero point offsets on each night. The minimum scatter in the residuals between fits and "true" zero point offsets were produced using the linear fits in H and K_s and "piecewise" fits in J.

Figure 8	Figure 9

[Last Update: 2005 October 12; by R. Cutri, S. Wheelock and S. Nikolaev]

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