Modeling the anomaly of surface number densities of galaxies on the
  Galactic extinction map due to their FIR emission contamination
  The most widely used Galactic extinction map (Schlegel, Finkbeiner, & Davis
1998, SFD) is constructed assuming that the observed FIR fluxes entirely come
from the Galactic dust. According to the earlier suggestion by Yahata et al.
(2007), we consider how far-infrared (FIR) emission of galaxies affects the SFD
map. We first compute the surface number density of SDSS DR7 galaxies as a
function of the $r$-band extinction, $A_{r,\rm SFD}$. We confirm that the
surface densities of those galaxies positively correlate with $A_{r,\rm SFD}$
for $A_{r,\rm SFD}<0.1$, as first discovered by Yahata et al. (2007) for SDSS
DR4 galaxies. Next we construct an analytic model to compute the surface
density of galaxies taking account of the contamination of their FIR emission.
We adopt a log-normal probability distribution for the ratio of $100\mu {\rm
m}$ and $r$-band luminosities of each galaxy, $y \equiv (\nu L)_{100\mu {\rm
m}}/(\nu L)_r$. Then we search for the mean and r.m.s values of $y$ that fit
the observed anomaly using the analytic model. The required values to reproduce
the anomaly are roughly consistent with those measured from the stacking
analysis of SDSS galaxies (Kashiwagi, Yahata, & Suto 2013). Due to the
limitation of our statistical modeling, we are not yet able to remove the FIR
contamination of galaxies from the extinction map. Nevertheless the agreement
with the model prediction suggests that the FIR emission of galaxies is mainly
responsible for the observed anomaly. While the corresponding systematic error
in the Galactic extinction map is 0.1 to 1mmag, it is directly correlated with
galaxy clustering, and thus needs to be carefully examined in precision
cosmology.
