We present the effective temperatures ( T _ { eff } ) , metallicities , and colours in SDSS , 2MASS , and WISE filters , of a sample of 3834 late-K and early-M dwarfs selected from the Sloan Digital Sky Survey APOGEE spectroscopic survey ASPCAP catalog .
We confirm that ASPCAP T _ { eff } values between 3550 K < T _ { eff } < 4200 K are accurate to \sim 100 K compared to interferometric T _ { eff } values .
In that same T _ { eff } range , ASPCAP metallicities are accurate to 0.18 dex between -1.0 < [ M/H ] < 0.2 .
For these cool dwarfs , nearly every colour is sensitive to both T _ { eff } and metallicity .
Notably , we find that g - r is not a good indicator of metallicity for near-solar metallicity early-M dwarfs .
We confirm that J - K _ { S } colour is strongly dependent on metallicity , and find that W 1 - W 2 colour is a promising metallicity indicator .
Comparison of the late-K and early-M dwarf colours , metallicities , and T _ { eff } to those from three different model grids shows reasonable agreement in r - z and J - K _ { S } colours , but poor agreement in u - g , g - r , and W 1 - W 2 .
Comparison of the metallicities of the KM dwarf sample to those from previous colour-metallicity relations reveals a lack of consensus in photometric metallicity indicators for late-K and early-M dwarfs .
We also present empirical relations for T _ { eff } as a function of r - z colour combined with either [ M/H ] or W 1 - W 2 colour , and for [ M/H ] as a function of r - z and W 1 - W 2 colour .
These relations yield T _ { eff } to \sim 100 K and [ M/H ] to \sim 0.18 dex precision with colours alone , for T _ { eff } in the range of 3550–4200 K and [ M/H ] in the range of - 0.5–0.2 .