  Although the baryons in the intergalactic medium (IGM) trace dark matter on
Mpc scales, small-scale (~100 kpc) fluctuations are suppressed by pressure
support, analogous to the classical Jeans argument. This Jeans filtering scale
has fundamental cosmological implications: it provides a thermal record of heat
injected by UV photons during reionization events, determines the clumpiness of
the IGM, and sets the minimum mass scale for gravitational collapse, a key
quantity in galaxy formation. Unfortunately, it is extremely challenging to
measure via the standard analysis of purely longitudinal Lyman-alpha forest
spectra, because the thermal Doppler broadening of absorption lines is highly
degenerate with Jeans pressure smoothing. In this work we show that the Jeans
scale can be directly measured by characterizing the coherence of correlated
Lyman-alpha absorption in quasar pairs with separations small enough to resolve
it. We present a novel technique for this purpose, based on the probability
distribution function (PDF) of phase angle differences of homologous
longitudinal Fourier modes in close quasar pair spectra. A Bayesian formalism
is introduced based on the phase angle PDF, and MCMC techniques are used to
characterize the precision of a future Jeans scale measurement, and explore
degeneracies with other thermal parameters governing the IGM. A semi-analytical
model of the IGM is used to generate a grid of 500 thermal models from a dark
matter simulation. Our full parameter study indicates that a realistic sample
of only 20 close quasar pair spectra can pinpoint the Jeans scale to ~ 5%
precision, independent of the parameters governing the temperature-density
relation of the IGM. We show that this new method is insensitive to a battery
of systematics such as continuum fitting errors, imprecise knowledge of the
noise and spectral resolution, and metal-line absorption.
