A New Measurement of the Mean Transmitted Flux in the Lyman-alpha and Lyman-beta Forest

We present new measurements of the mean transmitted flux in the hydrogen Ly$\alpha$ and a relative transmitted flux measurement in Ly$\beta$ using 27,008 quasar spectra from the Fourteenth Data Release (DR14) of the Extended Baryon Oscillation Spectroscopic Survey (eBOSS). Individual spectra are first combined into 16 composites with mean redshifts in the range of $2.8<z<4.9$. We then apply Markov Chain Monte Carlo (MCMC) inference to produce a piecewise fit of the effective ${\tau }_{\mathrm{L}\mathrm{y}\alpha }$ (corrected for metal lines and optically thick absorption) assuming a spline point distribution. We also perform a relative $\mathrm{\Delta }{\tau }_{\mathrm{L}\mathrm{y}\beta }$ measurement with the same data set, finding $\mathrm{\Delta }{\tau }_{\mathrm{L}\mathrm{y}\beta }<0.35$ at $z<4.8$. The 6-8 $\mathrm{\%}$ precision measurements in the rest frame 1075-1150 Å at $z<4.0$ and 10-12 $\mathrm{\%}$ precision measurements in the same region at $z>4.0$ on ${\tau }_{\mathrm{L}\mathrm{y}\alpha }$, and our determinations of $\mathrm{\Delta }{\tau }_{\mathrm{L}\mathrm{y}\beta }$, are dominated by systematic errors, likely arising from bias and uncertainties in estimates of the quasar continuum. Our ${\tau }_{\mathrm{L}\mathrm{y}\alpha }$ values show a smooth increase by a factor of 5 over the redshift range $z=2.4-4.4$.