Fluctuations in the high-redshift Lyman-Werner and Lyα radiation backgrounds

We use a new method to model fluctuations of the LymanWerner (LW) and Lya radiation backgrounds at high redshift. At these early epochs the backgrounds are symptoms of a universe newly lit with its first stars. LW photons (11.513.6 eV) are of particular interest because they dissociate molecular hydrogen, the primary coolant in the first minihaloes. By using a variation of the halo model, we efficiently generate power spectra for any choice of radiation background. We find that the LW power spectrum typically traces the matter power spectrum at large scales but turns over at the scale corresponding to the effective horizon of LW photons [similar to 100 comoving Mpc (cMpc)], unless the sources are extremely rare. The series of horizons that characterize the Lya flux profile shape the fluctuations of that background in a similar fashion, though those imprints are washed out once one considers fluctuations in the brightness temperature of the 21-cm signal. The Lya background strongly affects the redshifted 21-cm signal at just about the time the LW background begins to dissociate H2, so measuring that backgrounds properties will reveal important information about the transition from early Population III stars to more normal stars. Around this time we find that fluctuations in the LW background are weak; the fractional standard deviation is less than similar to 0.5 on scales ?10 cMpc, only rising to be of the order of unity on scales ?1 cMpc. This should not lead to substantial spatial fluctuations in H2 content, except at the earliest times. Even then, most haloes form far from other sources, so the transition from star formation in low-mass to high-mass haloes is rather homogeneous across the universe.