Decaying Neutrinos and Structure Formation
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**Session 13 -- Large Scale Structure**
*Oral presentation, Monday, 10:30-12:00, Zellerbach Playhouse Room*

## [13.02] Decaying Neutrinos and Structure Formation

*Philip Maloney, Mark Giroux (JILA)*
We examine the Hogan-Rees photoionization instability (Hogan 1992,
*Nature* **359**, 40) in the context of an $\Omega=1$
universe dominated by massive ($m_\nu\approx 30$ eV) decaying
neutrinos. In a medium with a smoothly distributed source of ionizing
radiation, the photoionization and heating rates on scales larger than the
photon mean free path are independent of the local gas density. Thus,
underdense regions receive more energy per particle and heat up
faster; this nonadiabatic temperature change produces a pressure term
which drives the growth of fluctuations.

Hogan (1992) showed that in a static medium this instability produces
exponential growth, with growth rates which can be much larger than
the expansion rate in the expanding universe. We have found that on
small scales (comoving wavenumber $k > k_m$, where $k_m$ corresponds
to $\lambda\sim 10^{-2}$ Mpc present-day), the growth remains
exponential in an expanding universe. The instability growth rate is
independent of scale for $k > k_m$, and declines rapidly with increasing
scale, so the characteristic mass produced by the instability will
correspond to $k\sim k_m$. For a neutrino energy above the Lyman limit
$\Delta E$ $(\approx m_\nu/2-13.6$ eV) of a few eV and a decay
lifetime $T\sim 10^{24}$
seconds, fluctuations at the Poisson level on the scale $k_m$ can grow
to non-linearity between $z\sim 70$ (when Compton cooling inhibits
the instability) and $z\sim 20$ (when the intergalactic medium becomes
ionized).

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