LATEX TikZposter ANALYTICAL HALO MODEL OF GALACTIC CONFORMITY Isha Pahwa and Aseem Paranjape Inter-University Centre for Astronomy and Astrophysics, Pune University Campus-Ganeshkhind, Pune - 411007 ipahwa@iucaa.in ANALYTICAL HALO MODEL OF GALACTIC CONFORMITY Isha Pahwa and Aseem Paranjape Inter-University Centre for Astronomy and Astrophysics, Pune University Campus-Ganeshkhind, Pune - 411007 ipahwa@iucaa.in Galactic Conformity is the observation that satellite galaxies in groups whose central galaxy is quenched (or red) are preferentially quenched, even when the groups are restricted to reside in dark matter halos of the same mass. We develop a model to include the effects of ‘Galactic conformity’ within halo occupation distribution (HOD) framework. This effect has been modelled via the correlation of galaxy colors in a group with the concentration of the common parent dark matter halo. Standard HOD Framework • fcen(> L|m) - The fraction of m-halos (i.e., halos with masses in the range (m, m + dm)) that have a central galaxy brighter than the luminosity threshold L. • Nsat(> L|m) - The number of satellites brighter than L in each m-halo with a central brighter than L (assumed to be Poisson distributed with mean). fcen(> L|m) = 1 2  1 + erf log(m/Mmin) σlog m  , Nsat(> L|m) = m −M0 M1 α , [Zehavi et al 2011] with {Mmin, σlog m, α, M1, M0} being functions of the threshold L. We deﬁne the following quantities that are ﬁxed by the HOD: Nsat(> L|m) ≡fcen(> L|m)¯Nsat(> L|m) ; fcen(L|m) ≡−∂fcen(> L|m)/∂L , Nsat(Lm) ≡−∂Nsat(> L|m)/∂L ; ¯Nsat(L|m) ≡Nsat(L|m)/fcen(> L|m) . Color-selcted HOD •Given p(red|Mr) = 0.423 −0.175 (Mr + 19.5) and [Paranjape et al 2015] p(red|sat, Mr) = 1.0 −0.33  1 + tanh Mr+20.25 2.1  , one can calculate p(red|cen) from equation p(red|L) = p(red|cen, L) ¯p(cen|L) + p(red|sat, L) ¯p(sat|L) , where ¯p(sat|L) = R dm n(m) Nsat(L|m) R dm n(m) [fcen(L|m) + Nsat(L|m)] • The HOD split by galaxy colour - frcen(L|m) ≡p(red|cen, L)fcen(L|m) , Nrsat(L|m) ≡p(red|sat, L)Nsat(L|m) , ¯Nrsat(L|m) ≡Nrsat(L|m)/fcen(> L|m) = p(red|sat, L)¯Nsat(L|m) . frcen(L|m)dL is the differential fraction of m-halos with red L-centrals and ¯Nrsat(L|m)dL is the mean differential number of red L-satellites in m-halos with centrals (of any colour) brighter than L. Red fractions as a function of luminosity −22.0 −21.5 −21.0 −20.5 −20.0 −19.5 −19.0 Mr 0.0 0.2 0.4 0.6 0.8 1.0 red fraction satellites all centrals psat HOD with galactic conformity • We introduce conformity between the central and satellite colors in a group using the model of Paranjape et al 2015 which correlates the red fraction of a given galaxy type with the parent halo concentration, i.e., a concentration-dependence of the red fraction of satel- lites/centrals at ﬁxed luminosity and halo mass by making galaxies in high (low) concentration halos preferentially red (blue). • Given the fact that distribution of halo concentration c at ﬁxed halo mass is approximately Lognormal with mean ¯c(m) ≡e⟨ln c|m ⟩and logarithmic scatter σln c, we deﬁne s ≡ln(c/¯c)/σln c . The distribution of s is approximately a standard Gaussian (zero mean and unit variance), independent of halo mass. The conditional red fraction now depends on the parent halo concentration and is given as p(red|sat/cen, s) = (1 −ρ) p(red|sat/cen) + ρ Θ(s −sr,sat/cen) , where sr,sat/cen gives the dividing line between high and low concentrations in each case as sr,sat/cen = √ 2 erfc−1 [2 p(red|sat/cen)] . • “group quenching efﬁciency", ρ ∈[0, 1]. • The color selected HOD with conformity - frcen(L|m, s) ≡p(red|cen, s)fcen(L|m) , Nrsat(L|m, s) ≡p(red|sat, s)Nsat(L|m) and ¯Nrsat(L|m, s) ≡Nrsat(L|m, s)/fcen(> L|m) = p(red|sat, s)¯Nsat(L|m) . 1-halo conformity • Difference in the red fractions of satellites with red and blue centrals of similar halo mass represented by red and blue colors. −22.0 −21.5 −21.0 −20.5 −20.0 −19.5 −19.0 Mr 0.0 0.2 0.4 0.6 0.8 1.0 satellite red fraction ½ =0:01 ½ =0:65 ½ =0:90 Correlation funct