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} + c_{1} - c_{2}(*X*-1.0)

where

- c
_{1}is the photometric zeropoint offset (magnitudes) - c
_{2}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, c_{1} - c_{2}*(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.

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

M_{inst} = M_{0,inst} - 2.5*log_{10}(*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, c_{1}, 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.

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 |

K_{s} | 16.54 | 20.03 | 16.40 | 19.89 |

The nightly photometric zero point offset coefficients, c_{1},
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, c_{1}(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 c_{1}(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}-c_{2}*(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:

c_{1}(H,T) = 0.0267 - 0.0021 * T(hr)

c_{1}(K_{s},T) = 0.0699 - 0.0003 * T(hr)

South:

c_{1}(H,T) = 0.0711 + 0.0007 * T(hr)

c_{1}(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 |

Atmospheric extinction coefficients values in each band, c_{2},
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 |

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, c_{1}.
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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