### I. A table which shows the astrometry anomaly :

We use compare positions of brighter objects from SDSS and 2MASS (JHK catalog), and between SDSS and NOMAD (astrometric catalog from USNO). For a few locations on the sky, it appears that there are some differences in position beyond the nominal spec of less than 100 mas accuracy per coordinate. Our way to show that differences is to calculate in arcsecond what we call the "Delta". The Delta is the distance between the positions of the stars in SDSS vs 2MASS. Matches for objects separated by more than 0.6 arcsec have been excluded from the averages. Beyond this, no outlier rejection has been performed.

We can also calculate the average contribution in Delta of RA and DEC separately.

Having chosen some part of the sky in coordinates (RA, DEC), we can get in each picture some information, like the average of Delta in this area of the sky ( AVR(Delta) ), the standard deviation of Delta (SIGMA(Delta)), or the average of the contribution of right ascension and declination (which are AVR(DeltaRA) and AVR(DeltaDEC)).

Each area compared is about 1 square degree in size.

We have not done a comprehensive comparison of the whole of the SDSS footprint vs. the other catalogs.

We conclude that there are a few areas on the sky where either the SDSS or one of the comparison catalogs is off by more than the standard quoted error of 100 mas per coordinate.

### II. The SQL we used in website http://openskyquery.net/Sky/skysite/ :

Here is an exemple for (Ra,Dec) = (180,10)

SELECT o.objId, o.ra,

o.dec, o.r, o.type,

t.objId, t.ra, t.dec, o.g, o.r, o.i, t.j_m, t.h_m

FROM

SDSS:PhotoPrimary o, TWOMASS:PhotoPrimary t

WHERE XMATCH(o, t) < 0.1 AND

Region('CIRCLE J2000 180 10 29.5') AND

o.type = 6

### III. The way to do the Selection :

#### 1. The use of awk :

We can use with this query the following awk code to obtain Delta :

awk -F, ' NR>1 {print \$2,",", sqrt((\$2-\$7)*(\$2-\$7)*cos(\$3*3.14159/180)*cos(\$3*3.14159/180)+(\$3-\$8)*(\$3-\$8))*3600.0;}' data.csv > data_delta.csv

To obtain only the contribution of Ra, we can use :

awk -F, ' NR>1 {print \$2,",", sqrt((\$2-\$7)*(\$2-\$7)*cos(\$3*3.14159/180)*cos(\$3*3.14159/180))*3600.0;}' data.csv > data_deltaRA.csv

And the following to get the contribution of Dec :

awk -F, ' NR>1 {print \$2,",", sqrt((\$3-\$8)*(\$3-\$8))*3600.0;}' data.csv > data_deltaDEC.csv

#### 2. The results of averages and standart deviation :

Firstly, we cut the stars with Delta > 0.6 (because they are outliers and are not linked with our astrometry problem) :

awk -F, '\$2 < 0.6 {print;}' data_delta.csv > clean_delta.csv

Then, we can use Excel to calculate both average and standart deviation.

#### 3. Our results show that there are a few instances where SDSS and 2MASS disagree by more than the nominal of 0.1 arcsec/coordinate. The delta(RA) values have been corrected for cos(DEC). There are fewer instances where SDSS and NOMAD differ by more than the spec, however, one should note that the basic SDSS astrometric calibration used the UCAC catalog as a reference in computing its astrometric solution. Thus, SDSS, UCAC and NOMAD are not independent astrometric catalogs.

We highlight those areas of overlap between SDSS and 2MASS where seems that when AVR(Delta) > 0.23 in red in the table.

 STRIPE RA DEC AVR(Delta) SIGMA(Delta) AVR(DeltaRA) AVR(DeltaDEC) AVR(Delta)-Nomad AVR(DeltaRA) AVR(DeltaDEC) (deg) (deg) (arcsec) (arcsec) (arcsec) (arcsec) (arcsec) (arcsec) (arcsec) 1188 225.9559042 56.98013139 0.194 0.126 0.042 -0.033 1188 264.7419681 64.43645654 0.151 0.126 0.005 0.025 1188 287.3997103 63.26341684 0.236 0.127 -0.100 0.098 0.224 0.102 -0.086 1188 306.2138751 58.97310519 0.204 0.116 0.014 0.118 1188 320.0438116 52.62969748 0.207 0.122 0.023 0.082 1188 330.0970633 45.10372779 0.160 0.126 -0.001 -0.003 1260 18.2428094 18.78702952 0.215 0.137 0.024 -0.064 1260 19.55515186 28.71491245 0.287 0.150 0.129 -0.165 0.299 0.207 -0.145 1260 21.14557734 38.62744541 0.177 0.127 -0.015 0.003 1260 23.25128998 48.51146966 0.225 0.142 -0.128 -0.091 1260 26.38611505 58.33829694 0.334 0.100 -0.148 0.262 0.222 0.103 -0.002 1260 31.94278132 68.02907252 0.263 0.115 -0.106 0.171 0.181 0.005 0.023 1260 45.27525281 77.26698364 0.246 0.121 -0.043 0.167 0.159 0.017 -0.017 1260 96.19431975 83.61873228 0.239 0.133 -0.061 0.106 0.210 0.007 -0.094 1300 59.98168844 51.62104928 0.217 0.126 -0.065 0.104 1300 72.54559713 58.619552 0.290 0.133 -0.142 0.134 0.232 0.086 -0.099 1300 90.38627883 63.8437677 0.328 0.102 -0.224 0.178 0.137 0.024 -0.005 1300 113.566800 66.09084647 0.311 0.116 -0.104 0.213 0.167 0.038 -0.023 1220 292.183761 78.09942726 0.211 0.140 -0.062 -0.021 1220 326.3612711 72.62666558 0.173 0.125 0.044 -0.057 1220 341.8681607 64.3233318 0.142 0.120 0.027 -0.014 1220 349.9007666 55.15929513 0.172 0.134 -0.057 -0.011 1220 354.8711739 45.66743628 0.152 0.118 -0.042 0.000 1220 358.3799125 36.02327954 0.190 0.122 0.092 -0.014 14 180 10 0.236 0.138 -0.129 -0.012 0.200 0.074 -0.122 32 230 45 0.192 0.126 -0.056 -0.004 37 135 55 0.178 0.126 0.046 -0.030