Anomaly distribution in quasar magnitudes: a test of lensing by an
  hypothetic Supergiant Molecular Cloud in the Galactic halo
  An anomaly in the distribution of quasar magnitudes based on the SDSS survey,
has been recently reported by Longo (2012). The angular size of this anomaly is
of the order of $\rm \pm 15^o$ on the sky. A low surface brightness smooth
structure in $\gamma$-rays, coincides with the sky location and extent of the
quasar anomaly, and is close to the Northern component of a pair of
$\gamma$-ray bubbles discovered in the \sl Fermi Gamma-ray Space Telescope \rm
survey. Molecular clouds are thought to be illuminated by cosmic rays. I test
the hypothesis that the magnitude anomaly in the quasar distribution, is due to
a lensing effect by an hypothetic Supergiant Molecular Cloud (SGMC) in the
Galactic halo.A series of grid lens models are built by assuming firstly that a
SGMC is a lattice with clumps of $\rm 10^{-3} M_\odot$, 10 AU in size, and
assuming various filling factors of the cloud, and secondly a fractal
structure. Local amplifications are calculated for these lenses by using the
public software LensTool, and the single plane approximation. A complex network
of caustics due to the clumpy structure is present. Our best single plane lens
model capable of explaining Longo's effect, \sl at least in sparse regions, \rm
requires a mass $\rm (1.5-4.1) \times 10^{10} ~M_\odot$ within $\rm 8.7 \times
8.7 \times (5-8.6) kpc^3$ at a lens plane distance of 20 kpc. It is constructed
from a molecular cloud building block of $5 \times 10^5 M_\odot$ within a scale
of 30 pc expanded by fractal scaling with dimension $D = 1.8-2$ up to 5-8.6 kpc
for the SGMC. If such a Supergiant Molecular Cloud were demonstrated, it might
be part of a lens explanation for the luminous anomaly discovered in quasars
and in red galaxies. The mass budget may be varied by changing the cloud depth
and the fractal dimension.
