The 2dF QSO redshift survey - IV. The QSO power spectrum from the 10k catalogue

We present a power spectrum analysis of the 10k catalogue from the 2dF QSO Redshift Survey. Although the Survey currently has a patchy angular selection function, we use the Virgo Consortium's Hubble Volume simulation to demonstrate that we are able to make a useful first measurement of the power spectrum over a wide range of scales. We compare the redshift-space power spectra of QSOs with those measured for galaxies and Abell clusters at low redshift and find that they show similar shapes in their overlap range, 50-150 h(-1) Mpc, with P-QSO(k) proportional to k(-1.3). The amplitude of the QSO power spectrum at z approximate to 1.4 is almost comparable to that of galaxies at the present day if Omega(m) = 0.3 and Omega(Lambda) = 0.7 (the Lambda cosmology), and a factor of approximate to 3 lower if Omega(m) = 1 (the EdS cosmology) is assumed. The amplitude of the QSO power spectrum is a factor of approximate to 10 lower than that measured for Abell clusters at the present day. At larger scales, the QSO power spectra continue to rise robustly to approximate to 400 h(-1) Mpc, implying more power at large scales than in the APM galaxy power spectrum measured by Baugh & Efstathiou. We split the QSO sample into two redshift bins and find little evolution in the amplitude of the power spectrum, consistent with the result for the QSO correlation function. In models with Omega(m) greater than or similar to 0.1 this represents evidence for a QSO-mass bias that evolves as a function of time. We compare the QSO power spectra with cold dark matter (CDM) models to obtain a constraint on the shape parameter, Gamma. For two choices of cosmology (Omega(m) = 1, Omega(Lambda) = 0 and Omega(m) = 0.3, Omega(Lambda) = 0.7), we find that the best-fitting model has Gamma approximate to 0.1 +/- 0.1. In addition, we have shown that a power spectrum analysis of the Hubble Volume ACDM mock QSO catalogues with Gamma = 0.17 as input produces a result that is statistically consistent with the data. The analysis of the mock catalogues also indicates that the above results for Gamma are unlikely to be dominated by systematic effects, owing to the current catalogue window. We conclude that the form of the QSO power spectrum shows large-scale power significantly in excess of the standard CDM prediction, similar to that seen in local galaxy surveys at intermediate scales.