Exploring the Voids: Luminosity Functions and Magnetic Field
  We present semi-analytical models for magnetisation of the void
inter-galactic medium (IGM) by outflows from void galaxies. The number density
of dark matter haloes in an under-dense region (i.e., void) is obtained using
the excursion set method extended for such low density environment. The star
formation in such haloes has been estimated, taking account of the negative
feedback by supernovae. The galaxy formation/evolution model is tuned to
provide the $r$-band luminosity function, the stellar mass function and also
the color of void galaxies as obtained from recent observations. This star
formation model is used to study possible outflows from void galaxies driven by
the hot thermal gas and cosmic ray pressures. These outflows drag the magnetic
fields present in those galaxies to the void IGM. We show that such a model can
magnetise $\sim 30\%$ of the void IGM with the magnetic field strength of
$10^{-12}-10^{-10}$ G while considering only magnetic flux freezing condition.
Along with this, the megapersec size of individual outflows can explain the
non-detection of GeV photons in TeV blazars that put a lower limit of
$10^{-16}$ G for void IGM magnetic field with a Mpc coherent length scale.
