\begin{table}%ta1 \par \caption{\label{table.the42s.mu}USNO-B1 stars towards $\sigma$~Orionis with $\mu_{\rm USNO-B1} > 40$~mas~a$^{-1}$, $J_{\rm 2MASS} < 15.5$~mag, and $N_{\rm USNO-B1} > 3$: coordinates, magnitudes, and proper motions.} \small%\centering \par \begin{tabular}{c ccc c ccc c ccc} \hline \hline \noalign{\smallskip} & \multicolumn{3}{c}{2MASS} & & \multicolumn{3}{c}{USNO-B1} & & \multicolumn{3}{c}{This work} \\ \noalign{\smallskip} No. & $\alpha^{J2000}$ & $\delta^{J2000}$ & $J$ & & $\mu_\alpha \cos{\delta}$ & $\mu_\delta$ & $N$ & & $\mu_\alpha \cos{\delta}$ & $\mu_\delta$ & $N$ \\ & & & [mag] & & [mas~a$^{-1}$] & [mas~a$^{-1}$] & & & [mas~a$^{-1}$] & [mas~a$^{-1}$] & \\ \hline 01 & 084.595001 & --03.064613 & 14.59~$\pm$~0.03 & & +18 &--40 & 5 & & +19.2~$\pm$~1.0 &--36.3~$\pm$~1.7 & 9 \\ % 02 & 084.425714 & --03.025405 & 14.53~$\pm$~0.03 & &--82 &--62 & 5 & &--54.0~$\pm$~1.9 &--62.7~$\pm$~1.2 & 8 \\ % (***02) 03 & 084.826136 & --03.013852 & 13.07~$\pm$~0.02 & & +10 &--50 & 5 & & +11.4~$\pm$~1.1 &--46.1~$\pm$~0.9 & 8 \\ % 04 & 084.539224 & --03.003337 & 14.26~$\pm$~0.03 & & +30 & +28 & 5 & & +11.0~$\pm$~1.2 & +3.9~$\pm$~1.3 & 8 \\ % (***04) 05 & 084.948355 & --02.983131 & 10.36~$\pm$~0.03 & & +42 &--14 & 5 & & +47.6~$\pm$~1.1 &--17.5~$\pm$~0.9 & 9 \\ % J05394761-0258593 06 & 084.850070 & --02.963510 & 11.26~$\pm$~0.03 & & +32 & +80 & 5 & & +34.3~$\pm$~0.5 & +82.8~$\pm$~1.0 & 9 \\ % SO411068 07 & 084.850866 & --02.924599 & 11.79~$\pm$~0.03 & & +14 &--54 & 5 & & +14.0~$\pm$~0.7 &--59.5~$\pm$~0.5 & 9 \\ % SO441143 08 & 084.642299 & --02.859457 & 15.18~$\pm$~0.04 & & +54 &--52 & 4 & & +44.3~$\pm$~1.5 &--61.9~$\pm$~0.7 & 7 \\ % (J=15.181mag) 09 & 084.244956 & --02.819184 & 13.62~$\pm$~0.04 & & +6 & +70 & 4 & & --9.4~$\pm$~1.6 &--22.9~$\pm$~1.6 & 9 \\ % (***09) 10 & 084.369333 & --02.779688 & 14.81~$\pm$~0.03 & &--28 &--36 & 5 & &--29.9~$\pm$~0.7 &--37.9~$\pm$~1.2 & 7 \\ % [KJN2005] 38 11 & 084.706846 & --02.757468 & 13.15~$\pm$~0.03 & &--54 &--24 & 5 & &--55.3~$\pm$~0.9 &--23.1~$\pm$~1.8 & 8 \\ % [SWW2004] J053849.560-024526.94 12 & 084.533024 & --02.752464 & 15.33~$\pm$~0.05 & & +20 &--36 & 4 & & --7.5~$\pm$~1.8 &--72.0~$\pm$~1.6 & 7 \\ % (***12) 13 & 084.485297 & --02.732624 & 13.04~$\pm$~0.03 & & +20 &--40 & 5 & & +20.2~$\pm$~1.1 &--41.5~$\pm$~0.9 & 8 \\ % [SWW2004] J053756.467-024357.36 14 & 085.152776 & --02.729698 & 11.54~$\pm$~0.03 & & +50 & +10 & 4 & & +43.9~$\pm$~0.9 & +0.3~$\pm$~1.0 & 9 \\ % J05403667-0243469 15 & 085.098384 & --02.718792 & 11.37~$\pm$~0.03 & & +62 &--96 & 5 & & +63.8~$\pm$~1.2 &--89.4~$\pm$~1.5 & 10 \\ % SO430116 16 & 084.730988 & --02.691593 & 12.17~$\pm$~0.03 & & +96 & +8 & 5 & & +96.6~$\pm$~0.9 & +11.8~$\pm$~0.7 & 9 \\ % [SWW2004] J053855.425-024129.68, [SFR2008] S38 (***16) 17 & 084.270844 & --02.684343 & 14.37~$\pm$~0.03 & & +6 &--42 & 5 & & +3.5~$\pm$~1.0 &--43.3~$\pm$~1.0 & 7 \\ % [SWW2004] J053705.004-024103.43 18 & 084.523630 & --02.672057 & 12.77~$\pm$~0.03 & &--20 &--40 & 4 & & +24.3~$\pm$~1.2 &--74.4~$\pm$~1.3 & 8 \\ % [SWW2004] J053805.676-024019.36, [SFR2008] S50 (***18) 19 & 085.122689 & --02.651908 & 13.98~$\pm$~0.03 & &--12 &--46 & 5 & & --8.9~$\pm$~1.2 &--43.5~$\pm$~0.5 & 8 \\ % 20 & 084.472224 & --02.602508 & 14.94~$\pm$~0.05 & & +38 & +30 & 5 & & --2.6~$\pm$~1.3 &--20.2~$\pm$~0.9 & 8 \\ % (***20) 21 & 085.032746 & --02.598684 & 14.65~$\pm$~0.04 & & +6 &--40 & 5 & & --9.1~$\pm$~0.7 &--30.0~$\pm$~1.9 & 8 \\ % (***21) 22 & 084.346086 & --02.546276 & 14.18~$\pm$~0.04 & &--42 & +0 & 5 & &--20.0~$\pm$~0.7 &--22.2~$\pm$~0.6 & 8 \\ % [SWW2004] J053723.067-023246.38 (***22) 23 & 084.257197 & --02.544301 & 15.29~$\pm$~0.07 & & +40 &--18 & 4 & & +40.0~$\pm$~0.7 &--40.2~$\pm$~1.1 & 8 \\ % (J=15.293mag) 24 & 084.379406 & --02.528789 & 10.46~$\pm$~0.03 & & +50 &--282 & 5 & & +49.9~$\pm$~0.4 &--282.0~$\pm$~0.8 & 9 \\ % G 99-20 25 & 085.175498 & --02.516978 & 14.17~$\pm$~0.03 & &--30 &--34 & 5 & &--28.8~$\pm$~1.0 &--32.9~$\pm$~1.0 & 8 \\ % 26 & 084.815180 & --02.499121 & 9.81~$\pm$~0.03 & & +0 &--42 & 5 & & --0.6~$\pm$~1.1 &--39.9~$\pm$~0.6 & 9 \\ % J05391564-0229568 27 & 084.622984 & --02.479908 & 14.87~$\pm$~0.03 & & +32 & +46 & 5 & & +33.9~$\pm$~1.4 & +36.9~$\pm$~1.0 & 8 \\ % 28 & 084.353969 & --02.476976 & 12.75~$\pm$~0.02 & &--10 &--40 & 5 & & --9.9~$\pm$~0.4 &--38.5~$\pm$~0.8 & 8 \\ % 29 & 085.159839 & --02.451720 & 14.02~$\pm$~0.03 & & +78 &--104 & 4 & & +70.7~$\pm$~1.1 &--115.3~$\pm$~1.2 & 7 \\ % 30 & 084.665077 & --02.447131 & 11.22~$\pm$~0.03 & & +46 &--18 & 5 & & +48.4~$\pm$~0.9 &--25.8~$\pm$~0.6 & 10 \\ % SO120908 31 & 084.774245 & --02.437633 & 14.34~$\pm$~0.03 & & --6 &--40 & 5 & & --5.0~$\pm$~0.3 &--43.4~$\pm$~0.6 & 7 \\ % [KJN2005] 30 / [SE2004] 42 32 & 084.462951 & --02.435409 & 14.92~$\pm$~0.04 & &+240 &--210 & 4 & & --5.8~$\pm$~0.5 &--13.0~$\pm$~1.3 & 7 \\ % Mayrit 999306 / [BZR99] S Ori 23 (faint; i=17.135mag,J=14.921mag) 33 & 084.806169 & --02.397745 & 13.95~$\pm$~0.03 & & +50 & +22 & 5 & & +54.1~$\pm$~0.5 & +25.1~$\pm$~0.4 & 8 \\ % [KJN2005] 12 34\tablefootmark{a}& 084.362205 & --02.365031 & 11.41~$\pm$~0.02 & &--18 & +44 & 5 & &--23.9~$\pm$~1.1 & +44.6~$\pm$~1.5 & 10 \\ % SO241003 (rho=2.8arcsec,theta=128deg,DZ=2.9mag,DH=3.6mag,no-K) 35 & 084.999408 & --02.339369 & 14.59~$\pm$~0.03 & & +44 & +12 & 5 & & +44.3~$\pm$~0.5 & +11.6~$\pm$~0.6 & 8 \\ % 36 & 085.004221 & --02.333267 & 13.10~$\pm$~0.03 & &--12 & +48 & 4 & & --7.0~$\pm$~0.6 & --5.9~$\pm$~0.3 & 7 \\ % Mayrit 1493050 (faint; i=15.307mag,J=13.096mag) 37 & 084.923889 & --02.329536 & 14.22~$\pm$~0.03 & & +20 &--36 & 5 & & +25.5~$\pm$~0.8 &--32.8~$\pm$~0.8 & 8 \\ % [SWW2004] J053941.738-021946.22 38 & 084.720246 & --02.324637 & 14.23~$\pm$~0.03 & & +70 &--108 & 5 & & +8.9~$\pm$~0.7 & --1.4~$\pm$~0.8 & 8 \\ % (***37) 39 & 084.355084 & --02.267993 & 13.80~$\pm$~0.04 & &--34 &--54 & 5 & &--34.1~$\pm$~0.2 &--56.0~$\pm$~0.3 & 7 \\ % [SWW2004] J053725.220-021604.56 40 & 084.543043 & --02.233226 & 13.47~$\pm$~0.03 & &+104 & --6 & 5 & & +96.4~$\pm$~0.4 & --6.3~$\pm$~0.6 & 8 \\ % [SE2004] 57, [KJN2005] 7 41\tablefootmark{b}& 084.969042 & --02.192280 & 14.85~$\pm$~0.04 & & +54 &--82 & 4 & & +59.8~$\pm$~1.2 &--80.7~$\pm$~1.1 & 8 \\ % [SE2004] 112 (rho=2.4arcsec,theta~177deg,DZ=3.0mag,DKs=2.9mag) 42\tablefootmark{c}& 084.560575 & --02.170903 & 12.48~$\pm$~0.03 & &--52 &--32 & 4 & & +2.4~$\pm$~0.5 & +6.3~$\pm$~0.5 & 8 \\ \hline \end{tabular} \tablefoot{\tablefoottext{a}{Star No.~34 is a close binary, only resolved by UKIDSS ($\rho \sim 2.8$~arcsec, $\theta \sim 128$~deg, $\Delta Z \sim \Delta K \sim 3$~mag).}\\ \tablefoottext{b}{Star No.~41 is a close binary, only resolved by UKIDSS ($\rho \sim 2.4$~arcsec, $\theta \sim 177$~deg, $\Delta Z \sim \Delta K \sim 3$~mag).}\\ \tablefoottext{c}{The USNO-B1 proper motion values of star No.~42 actually correspond to a faint source at 4.5~arcsec to the southwest of the tabulated coordinates (see Sect.~\ref{section.binaries}).}} \end{table}