Weighing dark matter haloes with gravitationally lensed supernovae
  High redshift Type Ia supernovae (SNe Ia) are likely to be gravitationally
lensed by dark matter haloes of galaxies in the foreground. Since SNe Ia have
very small dispersion after light curve shape and colour corrections, their
brightness can be used to measure properties of the dark matter haloes via
gravitational magnification. We use observations of galaxies and SNe Ia within
the Great Observatories Origins Deep Survey (GOODS) to measure the relation
between galaxy luminosity and dark matter halo mass. The relation we
investigate is a scaling law between velocity dispersion and galaxy luminosity
in the B-band. The best-fitting values to this relation (velocity dispersion
normalisation and exponent) are 136 km/s and 0.27. We find the velocity
dispersion normalisation to be less than 190 km/s at the 95 per cent confidence
level. This method provides an independent cross-check of measurements of dark
matter halo properties from galaxy-galaxy lensing studies. Our results agree
with the galaxy-galaxy lensing results, but have much larger uncertainties. The
GOODS sample of SNe Ia is relatively small (we include 24 SNe) and the results
therefore depend on individual SNe Ia. We have investigated a number of
potential systematic effects. Light curve fitting, which affects the inferred
brightness of the SNe Ia, appears to be the most important one. Results
obtained using different light curve fitting procedures differ at the 68.3 per
cent confidence level.
