A New Method to Directly Measure the Jeans Scale of the Intergalactic Medium Using Close Quasar Pairs

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.