We extend the abundance matching technique ( AMT ) to infer the satellite–subhalo and central–halo mass relations ( MRs ) of local galaxies , as well as the corresponding satellite conditional mass functions .
We use the observed galaxy stellar mass function ( GSMF ) decomposed into centrals and satellites and the \Lambda -CDM distinct halo and subhalo mass functions as inputs .
We explore the effects of defining the subhalo mass , m _ { sub } , at the time of ( sub ) halo accretion ( m _ { sub } ^ { acc } ) versus defining it at the time of observation ( m _ { sub } ^ { obs } ) ; and we test the standard assumption that centrals and satellites follow the same MRs. We show that this assumption leads to predictions in disagreement with observations , specially when m _ { sub } ^ { obs } is used .
Instead , we find that when the satellite–subhalo MRs are constrained by the satellite GSMF , they are always different from the central–halo MR : the smaller the stellar mass , the less massive is the subhalo of satellites as compared to the halo of centrals of the same stellar mass .
This difference is more dramatic when m _ { sub } ^ { obs } is used instead of m _ { sub } ^ { acc } .
On average , for stellar masses lower than \sim 2 \times 10 ^ { 11 } M _ { \odot } , the dark mass of satellites decreased by 60 - 65 \% with respect to their masses at accretion time .
We find that MRs for both definitions of subhalo mass yield satellite conditional mass functions ( CSMF ) in agreement with observations .
Also , when these MRs are used in a halo occupation model , the predicted two–point correlation functions at different stellar mass bins agree with observations .
The average stellar–halo MR is close to the MR of central galaxies alone , and conceptually this average MR is equivalent to abundance matching the cumulative total GSMF to the halo + subhalo mass function ( the standard AMT ) .
We show that the use of m _ { sub } ^ { obs } leads to less uncertain MRs than m _ { sub } ^ { acc } , and discuss some implications of the obtained satellite–subhalo MR. For example , we show that the tension between abundance and dynamics of Milky-Way satellites in the \Lambda -CDM cosmogony gives if the faint-end slope of the GSMF upturns to a value of \sim - 1.6 .