Table 3.

The estimated distances of M31 substructures.

SubstructureSubregionDistance (kpc)[Fe/H] (dex)|$\sigma _{[\mathrm{Fe/H]}}$| (dex)
GSSGSS1|$769.14_{-3.54}^{+0.6}$||$-0.43_{-0.02}^{+0.04}$||$0.70_{-0.01}^{+0.01}$|
 GSS12|$794.40_{-0.05}^{+3.62}$||$-0.20_{-0.06}^{+0.07}$||$0.88_{-0.03}^{+0.03}$|
 GSS2|$812.87_{-0.04}^{+0.06}$||$-0.06_{-0.13}^{+0.18}$||$0.96_{-0.06}^{+0.06}$|
 GSS23|$812.89_{-0.06}^{+0.10}$||$-0.21_{-0.12}^{+0.14}$||$0.92_{-0.06}^{+0.05}$|
 GSS3|$805.47_{-0.07}^{+7.40}$||$-0.09_{-0.11}^{+0.13}$||$0.95_{-0.04}^{+0.05}$|
 GSS34|$835.79_{-0.13}^{+0.32}$||$-0.50_{-0.10}^{+0.12}$||$0.81_{-0.05}^{+0.06}$|
 GSS4|$835.76_{-0.12}^{+0.22}$||$-0.09_{-0.21}^{+0.28}$||$0.95_{-0.09}^{+0.11}$|
Eastern ShellESh1|$774.79_{-2.09}^{+1.48}$||$-0.41_{-0.04}^{+0.05}$||$0.64_{-0.02}^{+0.02}$|
 ESh12|$770.21_{-1.04}^{+0.75}$||$-0.39_{-0.03}^{+0.03}$||$0.66_{-0.02}^{+0.02}$|
 ESh2|$765.62_{-0.01}^{+0.03}$||$-0.38_{-0.04}^{+0.04}$||$0.69_{-0.02}^{+0.02}$|
Western ShellWSh1|$765.66_{-0.06}^{+0.08}$||$-0.49_{-0.06}^{+0.07}$||$0.76_{-0.03}^{+0.03}$|
 WSh12|$772.87_{-0.13}^{+0.21}$||$-0.40_{-0.10}^{+0.10}$||$0.79_{-0.05}^{+0.05}$|
 WSh2|$783.54_{-0.10}^{+0.14}$||$-0.45_{-0.06}^{+0.07}$||$0.78_{-0.03}^{+0.03}$|
NW StreamNW1|$728.72_{-13.08}^{+6.77}$||$-1.30_{-0.04}^{+0.05}$||$0.37_{-0.03}^{+0.03}$|
 NW12|$743.94_{-6.94}^{+0.64}$||$-1.35_{-0.03}^{+0.04}$||$0.38_{-0.02}^{+0.02}$|
 NW2|$744.99_{-19.26}^{+7.38}$||$-1.41_{-0.05}^{+0.05}$||$0.38_{-0.03}^{+0.03}$|
 NW23|$742.89_{-7.81}^{+70.68}$||$-1.38_{-0.09}^{+0.05}$||$0.34_{-0.04}^{+0.03}$|
 NW3|$809.13_{-67.50}^{+19.84}$||$-1.41_{-0.07}^{+0.09}$||$0.31_{-0.03}^{+0.04}$|
Stream CC1|$769.28_{-44.70}^{+7.41}$||$-0.85_{-0.06}^{+0.15}$||$0.57_{-0.04}^{+0.05}$|
 C12|$773.54_{-10.46}^{+6.76}$||$-0.89_{-0.05}^{+0.07}$||$0.58_{-0.03}^{+0.03}$|
 C2|$820.93_{-44.06}^{+10.91}$||$-0.96_{-0.07}^{+0.15}$||$0.64_{-0.03}^{+0.07}$|
 C23|$798.01_{-21.48}^{+23.25}$||$-0.83_{-0.12}^{+0.12}$||$0.68_{-0.04}^{+0.06}$|
 C3|$820.69_{-3.30}^{+0.67}$||$-1.06_{-0.03}^{+0.04}$||$0.54_{-0.02}^{+0.03}$|
Stream DD1|$769.33_{-3.08}^{+0.05}$||$-1.18_{-0.02}^{+0.02}$||$0.49_{-0.02}^{+0.02}$|
 D12|$769.72_{-0.53}^{+2.99}$||$-1.17_{-0.02}^{+0.02}$||$0.50_{-0.02}^{+0.02}$|
 D2|$772.94_{-0.24}^{+18.15}$||$-1.02_{-0.07}^{+0.04}$||$0.56_{-0.02}^{+0.03}$|
 D23|$809.70_{-3.79}^{+7.93}$||$-1.00_{-0.04}^{+0.04}$||$0.57_{-0.02}^{+0.02}$|
 D3|$817.20_{-7.94}^{+10.85}$||$-1.04_{-0.03}^{+0.03}$||$0.53_{-0.01}^{+0.02}$|
SubstructureSubregionDistance (kpc)[Fe/H] (dex)|$\sigma _{[\mathrm{Fe/H]}}$| (dex)
GSSGSS1|$769.14_{-3.54}^{+0.6}$||$-0.43_{-0.02}^{+0.04}$||$0.70_{-0.01}^{+0.01}$|
 GSS12|$794.40_{-0.05}^{+3.62}$||$-0.20_{-0.06}^{+0.07}$||$0.88_{-0.03}^{+0.03}$|
 GSS2|$812.87_{-0.04}^{+0.06}$||$-0.06_{-0.13}^{+0.18}$||$0.96_{-0.06}^{+0.06}$|
 GSS23|$812.89_{-0.06}^{+0.10}$||$-0.21_{-0.12}^{+0.14}$||$0.92_{-0.06}^{+0.05}$|
 GSS3|$805.47_{-0.07}^{+7.40}$||$-0.09_{-0.11}^{+0.13}$||$0.95_{-0.04}^{+0.05}$|
 GSS34|$835.79_{-0.13}^{+0.32}$||$-0.50_{-0.10}^{+0.12}$||$0.81_{-0.05}^{+0.06}$|
 GSS4|$835.76_{-0.12}^{+0.22}$||$-0.09_{-0.21}^{+0.28}$||$0.95_{-0.09}^{+0.11}$|
Eastern ShellESh1|$774.79_{-2.09}^{+1.48}$||$-0.41_{-0.04}^{+0.05}$||$0.64_{-0.02}^{+0.02}$|
 ESh12|$770.21_{-1.04}^{+0.75}$||$-0.39_{-0.03}^{+0.03}$||$0.66_{-0.02}^{+0.02}$|
 ESh2|$765.62_{-0.01}^{+0.03}$||$-0.38_{-0.04}^{+0.04}$||$0.69_{-0.02}^{+0.02}$|
Western ShellWSh1|$765.66_{-0.06}^{+0.08}$||$-0.49_{-0.06}^{+0.07}$||$0.76_{-0.03}^{+0.03}$|
 WSh12|$772.87_{-0.13}^{+0.21}$||$-0.40_{-0.10}^{+0.10}$||$0.79_{-0.05}^{+0.05}$|
 WSh2|$783.54_{-0.10}^{+0.14}$||$-0.45_{-0.06}^{+0.07}$||$0.78_{-0.03}^{+0.03}$|
NW StreamNW1|$728.72_{-13.08}^{+6.77}$||$-1.30_{-0.04}^{+0.05}$||$0.37_{-0.03}^{+0.03}$|
 NW12|$743.94_{-6.94}^{+0.64}$||$-1.35_{-0.03}^{+0.04}$||$0.38_{-0.02}^{+0.02}$|
 NW2|$744.99_{-19.26}^{+7.38}$||$-1.41_{-0.05}^{+0.05}$||$0.38_{-0.03}^{+0.03}$|
 NW23|$742.89_{-7.81}^{+70.68}$||$-1.38_{-0.09}^{+0.05}$||$0.34_{-0.04}^{+0.03}$|
 NW3|$809.13_{-67.50}^{+19.84}$||$-1.41_{-0.07}^{+0.09}$||$0.31_{-0.03}^{+0.04}$|
Stream CC1|$769.28_{-44.70}^{+7.41}$||$-0.85_{-0.06}^{+0.15}$||$0.57_{-0.04}^{+0.05}$|
 C12|$773.54_{-10.46}^{+6.76}$||$-0.89_{-0.05}^{+0.07}$||$0.58_{-0.03}^{+0.03}$|
 C2|$820.93_{-44.06}^{+10.91}$||$-0.96_{-0.07}^{+0.15}$||$0.64_{-0.03}^{+0.07}$|
 C23|$798.01_{-21.48}^{+23.25}$||$-0.83_{-0.12}^{+0.12}$||$0.68_{-0.04}^{+0.06}$|
 C3|$820.69_{-3.30}^{+0.67}$||$-1.06_{-0.03}^{+0.04}$||$0.54_{-0.02}^{+0.03}$|
Stream DD1|$769.33_{-3.08}^{+0.05}$||$-1.18_{-0.02}^{+0.02}$||$0.49_{-0.02}^{+0.02}$|
 D12|$769.72_{-0.53}^{+2.99}$||$-1.17_{-0.02}^{+0.02}$||$0.50_{-0.02}^{+0.02}$|
 D2|$772.94_{-0.24}^{+18.15}$||$-1.02_{-0.07}^{+0.04}$||$0.56_{-0.02}^{+0.03}$|
 D23|$809.70_{-3.79}^{+7.93}$||$-1.00_{-0.04}^{+0.04}$||$0.57_{-0.02}^{+0.02}$|
 D3|$817.20_{-7.94}^{+10.85}$||$-1.04_{-0.03}^{+0.03}$||$0.53_{-0.01}^{+0.02}$|
Table 3.

The estimated distances of M31 substructures.

SubstructureSubregionDistance (kpc)[Fe/H] (dex)|$\sigma _{[\mathrm{Fe/H]}}$| (dex)
GSSGSS1|$769.14_{-3.54}^{+0.6}$||$-0.43_{-0.02}^{+0.04}$||$0.70_{-0.01}^{+0.01}$|
 GSS12|$794.40_{-0.05}^{+3.62}$||$-0.20_{-0.06}^{+0.07}$||$0.88_{-0.03}^{+0.03}$|
 GSS2|$812.87_{-0.04}^{+0.06}$||$-0.06_{-0.13}^{+0.18}$||$0.96_{-0.06}^{+0.06}$|
 GSS23|$812.89_{-0.06}^{+0.10}$||$-0.21_{-0.12}^{+0.14}$||$0.92_{-0.06}^{+0.05}$|
 GSS3|$805.47_{-0.07}^{+7.40}$||$-0.09_{-0.11}^{+0.13}$||$0.95_{-0.04}^{+0.05}$|
 GSS34|$835.79_{-0.13}^{+0.32}$||$-0.50_{-0.10}^{+0.12}$||$0.81_{-0.05}^{+0.06}$|
 GSS4|$835.76_{-0.12}^{+0.22}$||$-0.09_{-0.21}^{+0.28}$||$0.95_{-0.09}^{+0.11}$|
Eastern ShellESh1|$774.79_{-2.09}^{+1.48}$||$-0.41_{-0.04}^{+0.05}$||$0.64_{-0.02}^{+0.02}$|
 ESh12|$770.21_{-1.04}^{+0.75}$||$-0.39_{-0.03}^{+0.03}$||$0.66_{-0.02}^{+0.02}$|
 ESh2|$765.62_{-0.01}^{+0.03}$||$-0.38_{-0.04}^{+0.04}$||$0.69_{-0.02}^{+0.02}$|
Western ShellWSh1|$765.66_{-0.06}^{+0.08}$||$-0.49_{-0.06}^{+0.07}$||$0.76_{-0.03}^{+0.03}$|
 WSh12|$772.87_{-0.13}^{+0.21}$||$-0.40_{-0.10}^{+0.10}$||$0.79_{-0.05}^{+0.05}$|
 WSh2|$783.54_{-0.10}^{+0.14}$||$-0.45_{-0.06}^{+0.07}$||$0.78_{-0.03}^{+0.03}$|
NW StreamNW1|$728.72_{-13.08}^{+6.77}$||$-1.30_{-0.04}^{+0.05}$||$0.37_{-0.03}^{+0.03}$|
 NW12|$743.94_{-6.94}^{+0.64}$||$-1.35_{-0.03}^{+0.04}$||$0.38_{-0.02}^{+0.02}$|
 NW2|$744.99_{-19.26}^{+7.38}$||$-1.41_{-0.05}^{+0.05}$||$0.38_{-0.03}^{+0.03}$|
 NW23|$742.89_{-7.81}^{+70.68}$||$-1.38_{-0.09}^{+0.05}$||$0.34_{-0.04}^{+0.03}$|
 NW3|$809.13_{-67.50}^{+19.84}$||$-1.41_{-0.07}^{+0.09}$||$0.31_{-0.03}^{+0.04}$|
Stream CC1|$769.28_{-44.70}^{+7.41}$||$-0.85_{-0.06}^{+0.15}$||$0.57_{-0.04}^{+0.05}$|
 C12|$773.54_{-10.46}^{+6.76}$||$-0.89_{-0.05}^{+0.07}$||$0.58_{-0.03}^{+0.03}$|
 C2|$820.93_{-44.06}^{+10.91}$||$-0.96_{-0.07}^{+0.15}$||$0.64_{-0.03}^{+0.07}$|
 C23|$798.01_{-21.48}^{+23.25}$||$-0.83_{-0.12}^{+0.12}$||$0.68_{-0.04}^{+0.06}$|
 C3|$820.69_{-3.30}^{+0.67}$||$-1.06_{-0.03}^{+0.04}$||$0.54_{-0.02}^{+0.03}$|
Stream DD1|$769.33_{-3.08}^{+0.05}$||$-1.18_{-0.02}^{+0.02}$||$0.49_{-0.02}^{+0.02}$|
 D12|$769.72_{-0.53}^{+2.99}$||$-1.17_{-0.02}^{+0.02}$||$0.50_{-0.02}^{+0.02}$|
 D2|$772.94_{-0.24}^{+18.15}$||$-1.02_{-0.07}^{+0.04}$||$0.56_{-0.02}^{+0.03}$|
 D23|$809.70_{-3.79}^{+7.93}$||$-1.00_{-0.04}^{+0.04}$||$0.57_{-0.02}^{+0.02}$|
 D3|$817.20_{-7.94}^{+10.85}$||$-1.04_{-0.03}^{+0.03}$||$0.53_{-0.01}^{+0.02}$|
SubstructureSubregionDistance (kpc)[Fe/H] (dex)|$\sigma _{[\mathrm{Fe/H]}}$| (dex)
GSSGSS1|$769.14_{-3.54}^{+0.6}$||$-0.43_{-0.02}^{+0.04}$||$0.70_{-0.01}^{+0.01}$|
 GSS12|$794.40_{-0.05}^{+3.62}$||$-0.20_{-0.06}^{+0.07}$||$0.88_{-0.03}^{+0.03}$|
 GSS2|$812.87_{-0.04}^{+0.06}$||$-0.06_{-0.13}^{+0.18}$||$0.96_{-0.06}^{+0.06}$|
 GSS23|$812.89_{-0.06}^{+0.10}$||$-0.21_{-0.12}^{+0.14}$||$0.92_{-0.06}^{+0.05}$|
 GSS3|$805.47_{-0.07}^{+7.40}$||$-0.09_{-0.11}^{+0.13}$||$0.95_{-0.04}^{+0.05}$|
 GSS34|$835.79_{-0.13}^{+0.32}$||$-0.50_{-0.10}^{+0.12}$||$0.81_{-0.05}^{+0.06}$|
 GSS4|$835.76_{-0.12}^{+0.22}$||$-0.09_{-0.21}^{+0.28}$||$0.95_{-0.09}^{+0.11}$|
Eastern ShellESh1|$774.79_{-2.09}^{+1.48}$||$-0.41_{-0.04}^{+0.05}$||$0.64_{-0.02}^{+0.02}$|
 ESh12|$770.21_{-1.04}^{+0.75}$||$-0.39_{-0.03}^{+0.03}$||$0.66_{-0.02}^{+0.02}$|
 ESh2|$765.62_{-0.01}^{+0.03}$||$-0.38_{-0.04}^{+0.04}$||$0.69_{-0.02}^{+0.02}$|
Western ShellWSh1|$765.66_{-0.06}^{+0.08}$||$-0.49_{-0.06}^{+0.07}$||$0.76_{-0.03}^{+0.03}$|
 WSh12|$772.87_{-0.13}^{+0.21}$||$-0.40_{-0.10}^{+0.10}$||$0.79_{-0.05}^{+0.05}$|
 WSh2|$783.54_{-0.10}^{+0.14}$||$-0.45_{-0.06}^{+0.07}$||$0.78_{-0.03}^{+0.03}$|
NW StreamNW1|$728.72_{-13.08}^{+6.77}$||$-1.30_{-0.04}^{+0.05}$||$0.37_{-0.03}^{+0.03}$|
 NW12|$743.94_{-6.94}^{+0.64}$||$-1.35_{-0.03}^{+0.04}$||$0.38_{-0.02}^{+0.02}$|
 NW2|$744.99_{-19.26}^{+7.38}$||$-1.41_{-0.05}^{+0.05}$||$0.38_{-0.03}^{+0.03}$|
 NW23|$742.89_{-7.81}^{+70.68}$||$-1.38_{-0.09}^{+0.05}$||$0.34_{-0.04}^{+0.03}$|
 NW3|$809.13_{-67.50}^{+19.84}$||$-1.41_{-0.07}^{+0.09}$||$0.31_{-0.03}^{+0.04}$|
Stream CC1|$769.28_{-44.70}^{+7.41}$||$-0.85_{-0.06}^{+0.15}$||$0.57_{-0.04}^{+0.05}$|
 C12|$773.54_{-10.46}^{+6.76}$||$-0.89_{-0.05}^{+0.07}$||$0.58_{-0.03}^{+0.03}$|
 C2|$820.93_{-44.06}^{+10.91}$||$-0.96_{-0.07}^{+0.15}$||$0.64_{-0.03}^{+0.07}$|
 C23|$798.01_{-21.48}^{+23.25}$||$-0.83_{-0.12}^{+0.12}$||$0.68_{-0.04}^{+0.06}$|
 C3|$820.69_{-3.30}^{+0.67}$||$-1.06_{-0.03}^{+0.04}$||$0.54_{-0.02}^{+0.03}$|
Stream DD1|$769.33_{-3.08}^{+0.05}$||$-1.18_{-0.02}^{+0.02}$||$0.49_{-0.02}^{+0.02}$|
 D12|$769.72_{-0.53}^{+2.99}$||$-1.17_{-0.02}^{+0.02}$||$0.50_{-0.02}^{+0.02}$|
 D2|$772.94_{-0.24}^{+18.15}$||$-1.02_{-0.07}^{+0.04}$||$0.56_{-0.02}^{+0.03}$|
 D23|$809.70_{-3.79}^{+7.93}$||$-1.00_{-0.04}^{+0.04}$||$0.57_{-0.02}^{+0.02}$|
 D3|$817.20_{-7.94}^{+10.85}$||$-1.04_{-0.03}^{+0.03}$||$0.53_{-0.01}^{+0.02}$|
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