Weak lensing magnification of Type Ia Supernovae from the Pantheon
  sample
  Using data from the Pantheon SN Ia compilation and the Sloan Digital Sky
Survey (SDSS), we propose an estimator for weak lensing convergence
incorporating positional and photometric data of foreground galaxies. The
correlation between this and the Hubble diagram residuals of the supernovae is
$3.7\sigma$, consistent with weak lensing magnification due to dark matter
halos centered on galaxies. We additionally constrain the properties of the
galactic haloes, such as the mass-to-light ratio $\Gamma$ and radial profile of
the halo matter density $\rho(r)$. We derive a new relationship for the
additional r.m.s. scatter in magnitudes caused by lensing, finding $\sigma_{\rm
lens} = (0.06 \pm 0.017) (d_{\rm M}(z)/ d_{\rm M}(z=1))^{3/2}$ where $d_{\rm
M}(z)$ is the comoving distance to redshift $z$. We therefore find that the
scatter in flux caused by lensing will be of a similar size as the intrinsic
scatter (after standardisation of the magnitude) of modern SN Ia surveys by $z
\sim 1.2$, which is closer than generally assumed. We propose a modification of
the distance modulus estimator for SN Ia to incorporate lensing, which we
anticipate will improve the accuracy of cosmological parameter estimation using
high-redshift SN Ia data.
