Anomaly distribution in quasar magnitudes: a test of lensing by an hypothetic Supergiant Molecular Cloud in the Galactic halo

Abstract

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 $γ$-rays, coincides with the sky location and extent of the quasar anomaly, and is close to the Northern component of a pair of $γ$-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.