The Deuterium Abundance Towards Q1009+2956

We present a measurement of the deuterium to hydrogen ratio (D/H) in a metal-poor absorption system at redshift $z=2.504$ towards the QSO 1009+2956. We apply the new method of Burles & Tytler (1997) to robustly determine D/H in high resolution \Lya forest spectra, and include a constraint on the neutral hydrogen column density determined from the Lyman continuum optical depth in low resolution spectra. We introduce six separate models to measure D/H and to assess the systematic dependence on the assumed underlying parameters. We find that the deuterium absorption feature contains a small amount of contamination from unrelated \ion{H}{1}. Including the effects of the contamination, we calculate the 67% confidence interval of D/H in this absorption system, log (D/H) $= -4.40 ^{+0.06}_{-0.08}$. This measurement agrees with the low measurement by Burles & Tytler (1997) towards Q1937--1009, and the combined value gives the best determination of primordial D/H, log (D/H)$_p = -4.47 ^{+0.030}_{-0.035}$ or D/H $= 3.39 \pm 0.25 \times 10^{-5}$. Predictions from standard big bang nucleosynthesis (SBBN) give the cosmological baryon to photon ratio, $\eta = 5.1 \pm 0.3 \times 10^{-10}$, and the baryon density in units of the critical density, $\Omega_b h^2 = 0.019 \pm 0.001$, where $H_0 = 100 h$ \kms Mpc$^{-1}$. The measured value of (D/H)$_p$ implies that the primordial abundances of both $^4$He and $^7$Li are high, and consistent with some recent studies. Our two low measurements of primordial D/H also place strong constraints on inhomogeneous models of big bang nucleosynthesis.