VI. Analysis of the Release Catalogs

2. Photometric Sensitivity

The photometric sensitivity achieved for any observation of a 2MASS Tile was governed by atmospheric conditions at the time of the measurement, including transparency, emissive backgrounds, and image quality (or seeing), and the effects of confusion noise, due to astronomical source backgrounds. The confusion limits scale with source density, and thus follow fixed patterns on the sky. However, the limits imposed by atmospheric conditions led to significant variations on a Tile-by-Tile basis as well as systematic trends on the sky. In this section, we describe how the photometric sensitivity limits, due to atmospheric terms, were estimated for each 2MASS Tile. These estimates do not take into account confusion in high source density regions. The effects of confusion on photometric sensitivity are discussed in Section VI.7.

The nightly calibration field observations made during the Survey provided a means to measure directly empirical relationships between the achieved photometric sensitivity and the atmospheric conditions. These relationships were used to estimate the achieved sensitivity for for all scans of Tiles acquired during the Survey. We define the magnitude at which a signal to noise-ratio (SNR) of 10 is achieved, M₁₀, to be the metric by which we track photometric sensitivity in the following discussion. For reference, the 2MASS Level 1 Science Requirements specified that M₁₀ be achieved for magnitudes no fainter than J=15.8, H=15.1 and K_s=14.3 mag, in the absence of confusion.

a. Backgrounds and Seeing

i. Measuring Photometric Sensitivity from Repeated Calibration Field Measurements

Each 2MASS Calibration Observation (III.2.d) consisted of six scans of one of the 8.5´×1° Calibration Fields made in rapid succession. As a routine part of data processing and quality assurance, the extracted source lists from each set of six scans were positionally correlated, and the the mean and root variance brightness was determined for each object in the merged source lists. In Figure 1 is shown representative photometric repeatability made from the merged scans of one Mt. Hopkins observation of the A2409 Calibration Field on the night of 1997 November 16 UT. This figure shows the measured root variance (_J,H,Ks) versus mean magnitude for each merged source in the field. Black crosses represent sources detected at least five times in the six scans, and the red points are sources detected less than five times. Marked in green are the trimmed average and RMS root variances for all stars detected 5 times in 0.5 magnitude-wide bins. J, H and K_s repeatabilities are shown in the top, middle and bottom panels, respectively. The dashed horizontal lines in each panel show the SNR=10 level, the value where root variances are 10% of the brightness (0.1086 mag). For reference, the dashed blue vertical lines show the magnitudes in each band for which the Survey measurements are required to have a SNR10.

The point at which the loci of root variances for all sources crosses the SNR=10 line is the direct measurement of the M₁₀ photometric sensitivity metric. In this example shown in Figure 1, M₁₀ is achieved at J~16.1, H~15.5 and K_s~15.0 mag, so these measurements easily surpass the sensitivity requirements for the Survey. The SNR=10 crossing-point magnitudes, M₁₀, were compiled for all calibration observations made during the Survey. This dataset was used to derive empirical relationships between the achieved sensitivity and atmospheric backgrounds and image quality (seeing) levels.

Figure 1

ii. The Photometric Sensitivity Parameter (PSP)

Figures 2 and 3 show how the measured SNR=10 level, M₁₀, varied with the mean sky background levels (BG), measured on the individual calibration scan image frames in DN (digital numbers), for the northern and southern observatories, respectively. In these and the following figures, J-band data are shown in blue, H-band in green and K_s-band in red. For reference, the Survey requirement SNR=10 limits are shown for each band by the horizontal lines in the appropriate colors.

The measured value of M₁₀ is generally proportional to BG^1.5. This is the relationship expected for Poisson statistics in sky-background-limited measurements: SNR scales as BG^-0.5. Most of the calibration scan data taken during the Survey satisfy the sensitivity requirements. However, most of the scans with mean background levels above ~2500 DN are below the sensitivity limits in H and K_s. Furthermore, there is considerable vertical spread in the M₁₀ vs. BG distributions, and even some lower background data have sensitivities below the requirements. Some of this spread is caused intrinsic variations in the sky backgrounds values, since the mean background over six calibration scans is shown. However, most of the scatter arises because measurements at a given background level were taken in a wide range of seeing conditions.

Figures 4 and 5 show M₁₀ as a function of the mean seeing shape parameter for all calibration observations from Mt. Hopkins and CTIO, respectively. The seeing shape parameter (SH) is an empirical characterization of the point spread function (see IV.5a) that is derived during scan data processing. The shape is used to monitor the seeing as a function of time within a scan, for the purpose of PSF selection for point source profile-fit photometry (IV.4b) and for definition of the stellar ridgelines for extended source star/galaxy discrimination (IV.5a). Shape is related to image full-width-at-half-maximum intensity (FWHM) via the relation:

FWHM(´´) = 3.13*SH - 0.46

The achieved SNR for data in all bands from both observatories shows an approximately linear dependence on seeing shape. A much broader range of seeing conditions were encountered at the Mt. Hopkins site than at CTIO, which is also illustrated by the time-histories of the SH parameters from the two observatories shown in Figure 2 of III.1.c. Thus, the dependence of sensitivity on seeing is easier to see in the northern data. However, the limited instances of poorer seeing at Cerro Tololo do reveal the trends.

The interplay of seeing, sky backgrounds and photometric sensitivity is illustrated in Figure 6 in which the mean seeing shape for northern K_s calibration observations is shown as a function of the mean K_s frame backgrounds. The different colors in this figure encode data with different ranges of measured sensitivity, M₁₀. Photometry made under conditions with the best seeing and lowest backgrounds has the highest sensitivity (i.e., largest value of M₁₀). Under the best conditions, SNR=10 was achieved at nearly K_s~15 mag. The sensitivity degrades in a systematic fashion with higher backgrounds and poorer image quality. While the mean seeing and background levels for the Calibration observations are not correlated overall, there is a well-defined relationship between the seeing and background for data confined to a narrow range in sensitivity. Fitting the value of shape as function of background for successive, narrow intervals of M₁₀ and averaging the slopes from each fit established that SH is proportional to BG^-0.29, for fixed sensitivity.

Based on this relationship, a Photometric Sensitivity Parameter (PSP) was defined that predicts the magnitude at which SNR=10 for any value of mean seeing shape and frame background within a 2MASS scan measurement. PSP is defined as:

PSP = SH*BG^+0.29

The values of M₁₀ for all northern and southern calibration observations, respectively, are shown plotted as a function of PSP in Figures 7 and 8. Northern H-band data taken after 1999 August, when the H-band detector array was replaced (III.1.b), are shown by the magenta points in Figure 7. They are offset from the older H-band data because of the different sensitivity of the two H-band detectors.

The linear relationships between M₁₀ and PSP allowed predicting the achieved H and K_s photometric sensitivity of a scan taken under a given set of atmospheric background and seeing conditions to within ~0.1 mag. The residual scatter about the linear relationships is slightly larger in the J-band, ~0.2 mag, because, under the lowest background conditions, 2MASS J-band data was only marginally background-noise-limited. This prediction was the basis for photometric sensitivity quality scoring assigned to each Survey scan during the nightly Quality Assurance process (IV.10.b).

The PSP values derived for each Tile in the All-Sky Release are given in the j_psp, h_psp, and k_psp columns in the Scan Information Table.

Figure 2 Figure 3 Figure 4 Figure 5

Figure 6 Figure 7 Figure 8

Figures 9, 10 and 11 show all-sky maps of the J, H and K_s PSP values computed for all Tiles in the All-Sky Release, respectively. These maps (and those shown in Figures 12--17) are cartesian equatorial projections with 0^h right ascension in the center and RA increasing right to left. The north celestial pole is at the top and the south pole is at the bottom. The sense of the grey scale is that lighter levels correspond to higher sensitivity, darker to lower sensitivity. The range of PSP values corresponding to the full grey-scale levels in each map are indicated in the figure legends, as are the approximate range of sensitivity (in magnitudes) to which they correspond. These maps exhibit the following characteristics:

A significant level of variation in the PSP values Tile-to-Tile, because adjacent Tiles were sometimes observed at very different times under different conditions
J-band shows systematically lower PSP values (higher sensitivity) in data taken from CTIO, because of the much better seeing encountered at that site
H-band PSP values are consistent between the hemispheres, but have larger values (lower sensitivity) in Tiles near the both celestial poles, because of increased levels of atmospheric OH airglow background emission
The K_s PSP values show a seasonal trend with lower values in the respective hemisphere's late winter-to-early spring skies, primarily because of the lower thermal background levels resulting from lower temperatures

Figure 9 - J-band PSP - Range: 3.5 to 8.5 (~1.0 mag) Figure 10 - H-band PSP - Range: 6.0 to 12.5 (~1.3 mag) Figure 11 - K_s-band PSP - Range: 7.0 to 12.5 (~1.1 mag)

c. Atmospheric Transparency

Under the same background and seeing conditions, photometric sensitivity (measured in magnitudes) could still vary between observations because of differences in atmospheric transparency. The sensitivity variation (measured in magnitudes) due to transparency differences is directly proportional to the difference in photometric zero point offsets derived from the nightly Calibration solutions, as described in IV.8. Since the instrumental zero points applied to the measurements were defined such that the mean of the photometric zero point offsets over the full survey would be approximately zero, then the relative contribution to the sensitivity from atmospheric transparency for any given measurement is equal to the photometric zero point offset.

Figures 12, 13 and 14 show sky maps of the photometric calibration zero point offsets, in magnitudes, that were applied to each Tile in the 2MASS All-Sky Data Release. The ranges listed for each map correspond to the full magnitude scale of the image grey scale. The sense of the grey scale is that lighter is higher sensitivity, darker is lower sensitivity.

Systematic seasonal transparency variations are seen in all bands. Observations made in late winter-to-early spring in both hemispheres were the most sensitive (highest zero-point offsets = best transparency). However, Tile-to-Tile variations can be significant. These seasonal trends are easily seen in the time histories of the derived zero-point offsets from each observatory shown in Figure 4 of III.1.c.

Figure 12 - J-band Zero Point - Range: -0.3 to +0.3 mag Figure 13 - H-band Zero Point - Range: -0.15 to +0.11 mag Figure 14 - K_s-band Zero Point - Range: -0.12 to +0.12 mag

d. Net Achieved Sensitivity

The net sensitivity achieved for each 2MASS Tile is given by the combination of transparency and background/seeing terms. Linear fits of the measured values of M₁₀, corrected for photometric zero point, as a function of PSP lead to this simple relation between total, net sensitivity and observing conditions:

M₁₀ = M₀ + a×PSP + ZP

where M₀ and a are the intercept and slopes of the linear fits. These are given for each band at each observatory in Table 1. The two values for the northern H-band coefficients correspond to the original and replacement H-band arrays used at Mt. Hopkins. The linear fits are overlayed on the data points for each band in Figures 7 and 8.

Table 1 - M₁₀ vs. PSP Linear Fit Coefficients
North South

Band M₀ a M₀ a

J 17.690 -0.2229 17.609 -0.2210

H 17.215 -0.1922 17.325 -0.2262

H-new 17.028 -0.2035

K_s 16.524 -0.1960 16.880 -0.2405

**Table 1 - M₁₀ vs. PSP Linear Fit Coefficients**
	North	South
Band	M₀	a	M₀	a
J	17.690	-0.2229	17.609	-0.2210
H	17.215	-0.1922	17.325	-0.2262
H-new	17.028	-0.2035
K_s	16.524	-0.1960	16.880	-0.2405

The relation above was used to derive the estimated magnitude at which each Survey Tile achieved SNR=10. The values of the estimated magnitude at which SNR=10 was achieved were derived using the above relationship, and are given for each Tile in the j_msnr10, h_msnr10, and k_msnr10 columns in the Scan Information Table. These values were used to produce the J, H and K_s effective sensitivity maps for all Tiles in the All-Sky Release that are shown in Figures 15, 16 and 17. The magnitude ranges corresponding to the full grey-scale ranges in the maps are given in the Figure legends.

These maps represent the predicted photometric sensitivity achieved by the 2MASS observations, based solely on the atmospheric conditions measured from the Survey data themselves. These estimates do not take into consideration the effect of confusion noise which also degrades sensitivity. The impact of confusion noise in high source density regions is discussed at length in VI.7.

Histograms of the J, H and K_s M₁₀ values derived for all Tiles in the All-Sky Release using the measured PSP values and applied photometric zero point offsets are shown in Figure 18. Tile observations taken from Mt. Hopkins and CTIO are shown separately in this figure. The statistics of the M₁₀ distributions for the whole sky are summarized in Table 2. The average magnitudes at which SNR=10 are achieved are 0.5--0.6 mag fainter than the Survey's Level 1 Requirements in the J- and K_s-bands, and 0.3 mag fainter in the H-band. There are a small number of Tiles from both observatories that fall below the required H-band limit of 15.1 mag. Most of these Tiles lie near the celestial poles, and the loss of sensitivity was a result of the high levels of atmospheric OH airglow emission encountered during scans of the polar Tiles that were necessarily taken at relatively high airmasses.

Table 2 - M₁₀ Statistics for Tiles in the All-Sky Data Release
Band Min Max Mean Std.Dev.

J 15.787 16.951 16.422 0.135

H 14.821 16.044 15.484 0.175

K_s 14.264 15.340 14.808 0.162

**Table 2 - M₁₀ Statistics for Tiles in the All-Sky Data Release**
Band	Min	Max	Mean	Std.Dev.
J	15.787	16.951	16.422	0.135
H	14.821	16.044	15.484	0.175
K_s	14.264	15.340	14.808	0.162

Figure 15 - J-band M₁₀ - Range: 15.8 to 16.9 mag Figure 16 - H-band M₁₀ - Range: 14.8 to 16.0 mag Figure 17 - K_s-band M₁₀ - Range: 14.3 to 15.3 mag

Figure 18

[Last Updated: 2005 October 12; by R. Cutri & L. Cambresy]

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Figure 9 - J-band PSP - Range: 3.5 to 8.5 (~1.0 mag)	Figure 10 - H-band PSP - Range: 6.0 to 12.5 (~1.3 mag)	Figure 11 - K_s-band PSP - Range: 7.0 to 12.5 (~1.1 mag)


Figure 12 - J-band Zero Point - Range: -0.3 to +0.3 mag	Figure 13 - H-band Zero Point - Range: -0.15 to +0.11 mag	Figure 14 - K_s-band Zero Point - Range: -0.12 to +0.12 mag


Figure 15 - J-band M₁₀ - Range: 15.8 to 16.9 mag	Figure 16 - H-band M₁₀ - Range: 14.8 to 16.0 mag	Figure 17 - K_s-band M₁₀ - Range: 14.3 to 15.3 mag