DESI DR1 Lyα 1D power spectrum: The optimal estimator measurement

The one-dimensional power spectrum P1D of Lyα forest offers rich insights into cosmological and astrophysical parameters, including constraints on the sum of neutrino masses, warm dark matter models, and the thermal state of the intergalactic medium. We present the measurement of P1D using the optimal quadratic maximum likelihood estimator applied to over 300,000 Lyα quasars from Data Release 1 (DR1) of the Dark Energy Spectroscopic Instrument (DESI) survey. This sample represents the largest to date for P1D measurements and is larger than the Extended Baryon Oscillation Spectroscopic Survey (eBOSS) by a factor of 1.7. We conduct a meticulous investigation of instrumental and analysis systematics and quantify their impact on P1D. This includes the development of a cross-exposure estimator that eliminates the need to model the pipeline noise and has strong potential for future P1D measurements. We also present new insights into metal contamination through the 1D correlation function. Using a fitting function we measure the evolution of the Lyα forest bias with high precision: bF(z) = (-0.218 ± 0.002) × ((1 + z)/4)2.96±0.06. In a companion validation paper, we substantially extend our previous suite of CCD image simulations to quantify the pipeline's exquisite performance accurately. In another companion paper, we present DR1 P1D measurements using the Fast Fourier Transform (FFT) approach to power spectrum estimation. These two measurements produce a forest bias parameter that differs by 2.2 sigma. However, our model is simplistic, so this disagreement will be investigated in future work.