Systematic Continuum Errors in the Lyman-Alpha Forest and The Measured Temperature-Density Relation

Continuum fitting uncertainties are a major source of error in estimates of the temperature-density relation (usually parametrized as a power-law, $T \propto \Delta^{\gamma - 1}$) of the inter-galactic medium (IGM) through the flux probability distribution function (PDF) of the Lyman-$\alpha$ forest. Using a simple order-of-magnitude calculation, we show that few percent-level systematic errors in the placement of the quasar continuum due to e.g. a uniform low-absorption Gunn-Peterson component, could lead to errors in $\gamma$ of order unity. This is quantified further using a simple semi-analytic model of the Lya forest flux PDF. We find that under-(over-)estimates in the continuum level can lead to a lower (higher) measured value of $\gamma$. Within current observational uncertainties, continuum biases double the error in $\gamma$ from $\sigma_{\gamma} \approx 0.1$ to $\sigma_{\gamma} \approx 0.2$ within our model. We argue that steps need to be taken to directly estimate the level of continuum bias in order to make recent claims of an inverted \tdr\ more robust.