Constraints on the Thomson optical depth to the Cosmic Microwave Background from the Lyman- α forest

This is the authors' abstract. We don't add key points for this paper.

We present the first constraints on the electron optical depth to reionization, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:msub> <a:mi>τ</a:mi> <a:mi mathvariant="normal">e</a:mi> </a:msub> </a:math> , from the Lyman- <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mi>α</c:mi> </c:math> forest alone for physically motivated reionization models that match the reionization's end point, <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:msub> <d:mi>z</d:mi> <d:mi>end</d:mi> </d:msub> </d:math> , required by the same astrophysical probe, and for symmetric reionization models with fixed duration, <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mrow> <e:mi mathvariant="normal">Δ</e:mi> <e:mi>z</e:mi> </e:mrow> </e:math> , commonly adopted in cosmic microwave background (CMB) reionization analyses. Compared to traditional estimates from the latter, the Lyman- <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mi>α</g:mi> </g:math> forest traces the ionization state of the Intergalactic medium (IGM) through its coupling with the thermal state. We find an explicit mapping between the two by solving the chemistry and temperature evolution equations for hydrogen and helium. Our results yield <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:msub> <h:mi>τ</h:mi> <h:mi mathvariant="normal">e</h:mi> </h:msub> </h:math> = <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"> <j:mrow> <j:mspace width="0.16em"/> <j:mn>0</j:mn> <j:mo>.</j:mo> <j:msubsup> <j:mn>040</j:mn> <j:mrow> <j:mo>−</j:mo> <j:mn>0.018</j:mn> </j:mrow> <j:mrow> <j:mo>+</j:mo> <j:mn>0.042</j:mn> </j:mrow> </j:msubsup> </j:mrow> </j:math> (95% C.L.) and <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"> <l:msub> <l:mi>τ</l:mi> <l:mi mathvariant="normal">e</l:mi> </l:msub> </l:math> = <n:math xmlns:n="http://www.w3.org/1998/Math/MathML"> <n:mrow> <n:mn>0</n:mn> <n:mo>.</n:mo> <n:msubsup> <n:mn>041</n:mn> <n:mrow> <n:mo>−</n:mo> <n:mn>0.017</n:mn> </n:mrow> <n:mrow> <n:mo>+</n:mo> <n:mn>0.028</n:mn> </n:mrow> </n:msubsup> </n:mrow> </n:math> for reionization models with <o:math xmlns:o="http://www.w3.org/1998/Math/MathML"> <o:msub> <o:mi>z</o:mi> <o:mi>end</o:mi> </o:msub> </o:math> and <p:math xmlns:p="http://www.w3.org/1998/Math/MathML"> <p:mrow> <p:mi mathvariant="normal">Δ</p:mi> <p:mi>z</p:mi> </p:mrow> </p:math> fixed, respectively. With mock Lyman- <r:math xmlns:r="http://www.w3.org/1998/Math/MathML"> <r:mi>α</r:mi> </r:math> forest data that mimics the precision of future larger quasar sample datasets, we would potentially obtain tighter <s:math xmlns:s="http://www.w3.org/1998/Math/MathML"> <s:msub> <s:mi>τ</s:mi> <s:mi mathvariant="normal">e</s:mi> </s:msub> </s:math> constraints, paving the way for CMB-independent constraints on the epoch of reionization from a large-scale structure probe.