A measurement of the Ly β forest power spectrum and its cross with the Ly α forest in X-Shooter XQ-100

The Ly α forest is the large-scale structure probe for which we appear to have modelling control to the highest wavenumbers. This makes the Ly α forest of great interest for constraining the waness/fuzziness of dark matter and the timing of reionization processes. However, the standard statistic, the Ly α forest power spectrum, is unable to strongly constrain the intergalactic medium (IGM) temperature-density relation, and this inability further limits how well other high-wavenumber-sensitive parameters can be constrained. With the aim of breaking these degeneracies, we measure the power spectrum of the Ly β forest and its cross-correlation with the coeval Ly α forest using the 100 spectra of z = 3.5-4.5 quasars in the VLT/X-Shooter XQ-100 Legacy Survey, motivated by the Ly β transition's smaller absorption cross-section that makes it sensitive to somewhat higher densities relative to the Ly α transition. Our inferences from this measurement for the IGM temperature-density relation appear to latch consistently on to the recent tight lower redshift Ly α forest constraints. The z = 3.4-4.7 trends we find using the Ly α-Ly β cross-correlation show a flattening of the slope of the temperature-density relation with decreasing redshift. This is the trend anticipated from ongoing He ii reionization and there being sufficient time to reach the asymptotic temperature-density slope after hydrogen reionization completes. Furtheore, our measurements provide a consistency check on IGM models that explain the Ly α forest, with the cross-correlation being imne to systematics that are uncorrelated between the two forests, such as metal line contamination.