VI. Analysis of the 2MASS Second Incremental Release Catalogs

6. PSC Reference Field Characteristics

a. Global Statistics for the PSC

Introduction

These statistics are based on 12,800 queries to the local database for equal area tiles. The statistics are as follows. We made a cut at signal-to-noise ratio (S/N) = 30. For each of the high and low S/N subsamples we computed at each band:

• Means of quoted and ²
• Standard deviation about mean for these
• Rank value such that 1% are below value ( and ²) [Not shown]
• Rank value such that 1% are above value ( and ²)
• Number in bin (divide by 3.22 to get number per square degree)

The figures below are Aitoff projections of isovalue maps in galactic coordinates for each of these quantities.

Details

The coordinate space was divided into 160 bins in galactic longitude and 80 bins in x=cos(colatitude). The distribution in each quantity was binned and summed to get the cumulative distribution function along with the sample statistics. The rendering was done using the VTK package. The data blanking facility was not working, so cells with no data are shown as red. There are some edge artifacts where the bins in galactic coordinates very poorly sample the Second Incremental Data Release areas.

Number density of sources

Figures 1 and 2 show true number density, not number per bin, with linear and logarithmic contour levels, respectively. There are no surprises here. The gaps in coverage give the illusion of structure in the plane.

Figure 1	Figure 2

Quoted Error

Shown in Figures 3, 4, and 5, and 15, 16, and 17 are the mean plots for each 2MASS band for high S/N sources and low S/N sources, respectively. Overall, the error appears very uniform north to south. The error is better in the south than in the north at K_s. This is subtle and only obvious for the high S/N sources. The northern error is more variable than the south. There is a large error feature in the Galactic plane at H (galactic longitude l of about 245°). We are not sure if this is real, or some sort of numerical artifact. For low S/N sources, the trend reverses, which may be an artifact of source density confusion in the plane; only high S/N sources are recovered.

Shown in Figures 6, 7, and 8, and 18, 19, and 20 are the standard deviation plots. The Galactic plane is a smaller variance about the mean at J and larger at K_s (again, H is distorted by the big error bump).

Shown in Figures 9, 10, and 11, and 21, 22, and 23 are the 1% tail value. These show, not surprisingly, that the error values in the Galactic plane have a heavy tail (again, H is distorted by the high error feature, or analysis bug)

Shown in Figures 12, 13, and 14, and 24, 25, and 26 are the number per bin value. At low S/N, one sees the lower recovery fraction in the plane of the Galactic disk.

High signal-to-noise ratio data (S/N>30)
J	H	Ks
Figure 3	Figure 4	Figure 5
Figure 6	Figure 7	Figure 8
Figure 9	Figure 10	Figure 11
Figure 12	Figure 13	Figure 14

Low signal-to-noise ratio data (S/N<30)
J	H	Ks
Figure 15	Figure 16	Figure 17
Figure 18	Figure 19	Figure 20
Figure 21	Figure 22	Figure 23
Figure 24	Figure 25	Figure 26

The tables below show the "Top 10" fields ranked by mean quoted error. All but the top few in some cases are nominal and are included to provide a baseline. The field with galactic longitude and latitude 254.25°< l <254.5° and -1.4° < b <0° is large at both J and K_s, but only contains 7 sources.

High S/N at J					Low S/N at J
l1(°)	l2(°)	b1(°)	b2(°)	j_sigma_hi_mean	l1(°)	l2(°)	b1(°)	b2(°)	j_sigma_lo_mean
254.25	256.5	-1.43254	0	0.087	184.5	186.75	-40.5416	-38.6822	0.143
290.25	292.5	-44.427	-42.4542	0.05	348.75	351	-50.805	-48.5904	0.136
267.75	270	67.6684	71.8051	0.046	58.5	60.75	-67.6684	-64.1581	0.136
42.75	45	1.43254	2.86598	0.0447592	240.75	243	-31.6682	-30	0.135
355.5	357.75	1.43254	2.86598	0.0445452	51.75	54	26.7437	28.3594	0.134
45	47.25	0	1.43254	0.0439315	254.25	256.5	-1.43254	0	0.1224
114.75	117	-53.1301	-50.805	0.0433333	36	38.25	36.8699	38.6822	0.118167
51.75	54	26.7437	28.3594	0.043	101.25	103.5	-20.4873	-18.9656	0.1145
330.75	333	-2.86598	-1.43254	0.0429486	141.75	144	61.045	64.1581	0.1135
135	137.25	0	1.43254	0.0420386	137.25	139.5	64.1581	67.6684	0.112773

High S/N at H					Low S/N at H
l1(°)	l2(°)	b1(°)	b2(°)	h_sigma_hi_mean	l1(°)	l2(°)	b1(°)	b2(°)	h_sigma_lo_mean
254.25	256.5	-1.43254	0	0.194	348.75	351	-50.805	-48.5904	0.209
42.75	45	1.43254	2.86598	0.0552654	254.25	256.5	-1.43254	0	0.1718
252	254.25	64.1581	67.6684	0.053	308.25	310.5	-44.427	-42.4542	0.153
45	47.25	0	1.43254	0.0509786	36	38.25	36.8699	38.6822	0.150583
4.5	6.75	58.2117	61.045	0.0509545	294.75	297	-53.1301	-50.805	0.146
51.75	54	26.7437	28.3594	0.0495	153	155.25	36.8699	38.6822	0.142429
191.25	193.5	36.8699	38.6822	0.0492357	306	308.25	53.1301	55.5885	0.141667
58.5	60.75	-22.0243	-20.4873	0.0490068	159.75	162	17.4576	18.9656	0.1416
60.75	63	-18.9656	-17.4576	0.0483095	353.25	355.5	42.4542	44.427	0.138909
67.5	69.75	15.962	17.4576	0.048191	150.75	153	11.537	13.0029	0.133948

High S/N at Ks					Low S/N at Ks
l1(°)	l2(°)	b1(°)	b2(°)	k_sigma_hi_mean	l1(°)	l2(°)	b1(°)	b2(°)	k_sigma_lo_mean
153	155.25	36.8699	38.6822	0.049	290.25	292.5	30	31.6682	0.197333
193.5	195.75	40.5416	42.4542	0.0478305	58.5	60.75	-67.6684	-64.1581	0.170333
45	47.25	0	1.43254	0.0471634	342	344.25	46.4688	48.5904	0.16
45	47.25	33.367	35.0996	0.046	159.75	162	17.4576	18.9656	0.1554
42.75	45	1.43254	2.86598	0.0459062	112.5	114.75	30	31.6682	0.155286
171	173.25	-5.73917	-4.30122	0.0458865	36	38.25	36.8699	38.6822	0.139917
47.25	49.5	35.0996	36.8699	0.045579	87.75	90	44.427	46.4688	0.138476
45	47.25	35.0996	36.8699	0.0453898	119.25	121.5	-53.1301	-50.805	0.138167
189	191.25	40.5416	42.4542	0.0453732	308.25	310.5	-44.427	-42.4542	0.1374
60.75	63	-20.4873	-18.9656	0.0451757	108	110.25	-25.1507	-23.5782	0.134939

Chi-Square ²

Shown in Figures 27, 28, and 29, and 39, 40, and 41 are the mean ² plots for each 2MASS band for high S/N sources and low S/N sources, respectively, which are consistent with a value of 1 in all bands, except for the higher values realized in the Galactic plane.

Shown in Figures 30, 31, and 32, and 42, 43, and 44 are the standard deviation ² plots. We see larger variance in the Galactic plane and for K_s in the north. In general, the large variance regions indicate errors not included in the extraction error model.

Shown in Figures 33, 34, and 35, and 45, 46, and 47 are the 1% tail ² value plots. There is a slightly odd, unexplained feature in the Galactic plane.

Shown in Figures 36, 37, and 38, and 48, 49, and 50 are the number per bin ² value. There is a similar dip at low S/N near the Galactic plane, as seen in the quoted error plots above.

High signal-to-noise ratio data (S/N>30)
J	H	Ks
Figure 27	Figure 28	Figure 29
Figure 30	Figure 31	Figure 32
Figure 33	Figure 34	Figure 35
Figure 36	Figure 37	Figure 38

Low signal-to-noise ratio data (S/N<30)
J	H	Ks
Figure 39	Figure 40	Figure 41
Figure 42	Figure 43	Figure 44
Figure 45	Figure 46	Figure 47
Figure 48	Figure 49	Figure 50

Signal-to-Noise Ratio

Shown in Figures 51, 52, and 53, and are plots for each 2MASS band for sources with S/N > 7. Shown in Figures 54, 55, and 56, and are plots for each 2MASS band for sources with S/N > 10. Shown in Figures 57, 58, and 59, and are plots for each 2MASS band for sources with S/N > 20. The effect of differing sensitivity between the bands is clear: a small fraction of sources below S/N=7 at J, larger number at H, and even larger at K_s. At K_s, the Galactic plane is clearly "avoided" at these small S/N. Some trends of north vs. south are evident at K_s, especially at S/N < 7. There is a hint of this at S/N < 10 and S/N< 20 as well, but only at K_s.

Shown in Figures 60, 61, and 62, and are plots for each 2MASS band for sources with S/N > 30. We were a bit surprised that 93% of the sources have S/N below 30 at K_s!

	J	H	Ks
SNR < 7
	Figure 51	Figure 52	Figure 53
SNR < 10
	Figure 54	Figure 55	Figure 56
SNR < 20
	Figure 57	Figure 58	Figure 59
SNR < 30
	Figure 60	Figure 61	Figure 62

Global Color Statistics

The goal of this analysis is to look for color changes over the entire sky. This can be accomplished through a narrow cut near the peak in the color-color plane and then compute the statistics in the distribution of J-K_s. Figure 63 shows the color-color (Hess) diagram with color cut 0.30Figure 64 shows the distribution in J-K_s for an out-of-plane Galactic field (l=35°, b=35°). As anticipated, the J-K_s trend follows close to the reddening vector and is, therefore, sensitive to extinction. There is evidence for a color drift of about 1.5% toward the north celestial pole, and evidence for small biases in the northern declination bands.

Figure 63	Figure 64

In Figures 65, 66, and 67 are shown the mean in, the standard deviation in, and the number, respectively, of high S/N sources for J-K_s. In Figures 68, 69, and 70 are shown the 20%, 50%, and 80% fraction, respectively, of high S/N sources for J-K_s. In Figures 71, 72, and 73 are shown the mean, 50% fraction, and 60% enclosed width, respectively, of low S/N sources for J-K_s.

Figure 65	Figure 66	Figure 67
Figure 68	Figure 69	Figure 70
Figure 71	Figure 72	Figure 73

We have more closely examined the H-band behavior on the color statistics in Figures 74-97. We compare the J-K_s maps with the H-K_s maps, to show the H-band behavior relative to J and K_s. We also show the pattern orthogonal to J-K_s on the standard two-color plane (J-H, H-K_s), which should be approximately reddening independent. At the spatial scale shown in the figures, there is only weak evidence of slightly poorer H-band stability. The "reddening-free" flux ratio shows a weak dependence at higher galactic latitude. There is clearly a smaller range in this variable towards the plane, but it will be difficult to deconvolve the S/N and sensitivity selection effects from both reddening and population differences.

	J-Ks	H-Ks	(J-H)-(H-Ks)
High SNR: mean
	Figure 74	Figure 75	Figure 76
High SNR: std. dev.
	Figure 77	Figure 78	Figure 79
High SNR: fraction 50%
	Figure 80	Figure 81	Figure 82
High SNR: width 60%
	Figure 83	Figure 84	Figure 85
Low SNR: mean
	Figure 86	Figure 87	Figure 88
Low SNR: std. dev.
	Figure 89	Figure 90	Figure 91
Low SNR: fraction 50%
	Figure 92	Figure 93	Figure 94
Low SNR: width 60%
	Figure 95	Figure 96	Figure 97

Summary

Overall, the data appear to meet the Level 1 specifications on average. Regions with sources with anomalously large error are given in the tables in the "Quoted Errors" subsection, above. The top offender has only seven sources; excluding this one, there are no terrible fields. K_s-band had noticeably higher excursions in the north in quoted error for high S/N sources (excluding the plane).

[Last Updated: 1999 Dec 27 by M. Weinberg. Modified 2000 Sep 13 by S. Van Dyk.]