Global signals of the first molecules from the dark ages in the presence of primordial magnetic fields

We investigate how primordial magnetic fields (PMFs) affect the formation kinetics of the first molecules, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:msub> <a:mrow> <a:mi mathvariant="normal">H</a:mi> </a:mrow> <a:mrow> <a:mn>2</a:mn> </a:mrow> </a:msub> </a:mrow> </a:math> , HD, and <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"> <d:mrow> <d:msup> <d:mrow> <d:mi>HeH</d:mi> </d:mrow> <d:mrow> <d:mo>+</d:mo> </d:mrow> </d:msup> </d:mrow> </d:math> , as well as the populations of rovibrational levels and the global signals in the rovibrational transitions of <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:mrow> <f:msub> <f:mrow> <f:mi mathvariant="normal">H</f:mi> </f:mrow> <f:mrow> <f:mn>2</f:mn> </f:mrow> </f:msub> </f:mrow> </f:math> and HD. For this purpose, we numerically solve a system of differential equations that describes the gas energy balance, the kinetics of the formation of the first molecules, and the populations of their rovibrational levels, taking into account the PMF energy dissipation through ambipolar diffusion and decaying turbulence. We show that PMFs can significantly speed up the formation and destruction of the first molecules, leading to an increase in the number density of <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mrow> <i:msub> <i:mrow> <i:mi mathvariant="normal">H</i:mi> </i:mrow> <i:mrow> <i:mn>2</i:mn> </i:mrow> </i:msub> </i:mrow> </i:math> and HD molecules and a decrease in the number density of <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"> <l:mrow> <l:msup> <l:mrow> <l:mi>HeH</l:mi> </l:mrow> <l:mrow> <l:mo>+</l:mo> </l:mrow> </l:msup> </l:mrow> </l:math> ion molecules compared to the case without PMFs. We demonstrate that more frequent collisions of the gas particles in such models alter the ortho-to-para ratio of hydrogen molecules, making it a potential probe of the thermal history of gas in the early Universe. In contrast to the standard cosmological model, where the global signal from the first molecules appears as an absorption feature in the cosmic microwave background spectrum, cosmological models with PMFs can produce an emission signal. Specifically, for nonhelical PMFs with <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"> <n:msub> <n:mi>n</n:mi> <n:mi>B</n:mi> </n:msub> <n:mo>=</n:mo> <n:mo>−</n:mo> <n:mn>2.9</n:mn> </n:math> and a strength of <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"> <p:mo>∼</p:mo> <p:mn>1</p:mn> <p:mtext> </p:mtext> <p:mtext> </p:mtext> <p:mi>nG</p:mi> </p:math> , the signal transforms into emission with an amplitude of about <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"> <r:mrow> <r:mo>∼</r:mo> <r:mn>0.5</r:mn> <r:mtext> </r:mtext> <r:mtext> </r:mtext> <r:mi>Jy</r:mi> <r:mo>/</r:mo> <r:mi mathvariant="normal">s</r:mi> <r:mi mathvariant="normal">r</r:mi> </r:mrow> </r:math> . This signal is comparable in magnitude to other known cosmic microwave background spectral distortions and falls within the detection capabilities of several proposed missions, including Super-PIXIE, Multi-SIMBAD (four units), and Voyage2050. We show that both the amplitude and the spectral range of the global signals from the first molecules are highly sensitive to the spectral index <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"> <v:msub> <v:mi>n</v:mi> <v:mi>B</v:mi> </v:msub> </v:math> , the strength <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"> <x:msub> <x:mi>B</x:mi> <x:mn>0</x:mn> </x:msub> </x:math> , and the helicity of the PMFs. Therefore, the global signals from the first molecules can serve as a potential probe of PMFs.