Global Signals of the First Molecules from the Dark Ages in the Presence of Primordial Magnetic Fields

TL;DR

This work evaluates how primordial magnetic fields (PMFs) modify the thermal history and primordial chemistry during the Dark Ages, focusing on the first molecules $H_2$, $HD$, and $HeH^+$ and their rovibrational populations. By modeling PMFs as Gaussian random fields with symmetric and helical components and integrating a 20-species chemical network under Planck 2020 cosmology, the authors quantify heating via ambipolar diffusion and decaying turbulence and compute the resulting rovibrational populations and line emissions. They find PMFs enhance $H_2$ and $HD$ formation while suppressing $HeH^+$, with the strongest effects on $H_2$ (up to an order of magnitude for non-helical fields with $n_B=-2.9$, $B_0=1$ nG). The study shows that the first-molecule signals manifest as emission in the CMB spectrum, with amplitudes up to about $0.5$ Jy sr$^{-1}$ and strong dependence on $n_B$, $B_0$, and helicity, potentially enabling PMF constraints with future CMB spectrometry missions.

Abstract

We investigate how primordial magnetic fields (PMFs) affect the formation kinetics of the first molecules, H$_2$, HD, and HeH$^+$, as well as the populations of rovibrational levels and the global signals in the rovibrational transitions of H$_2$ and HD. 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 H$_2$ and HD molecules and a decrease in the number density of HeH$^+$ 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 non-helical PMFs with $n_B = -2.9$ and a strength of $\sim 1$~nG, the signal transforms into emission with an amplitude of about $\sim 0.5$~Jy/sr. This signal is comparable in magnitude to other known CMB spectral distortions and falls within the detection capabilities of several proposed missions, including Super-PIXIE, Multi-SIMBAD (4 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 $n_B$, the strength $B_0$, and the helicity of the PMFs. Therefore, the global signals from the first molecules can serve as a potential probe of PMFs.

Figures (7)

• Figure 1: Decreasing PMFs energy density as a result of dissipation processes in the early Universe for different values of power index $n_B$ and for helical (dashed lines) and non-helical (solid lines) PMFs.
• Figure 2: Redshift dependencies of baryonic gas temperature (solid and dashed lines) and CMB temperature (red dashed line) in cosmological models with PMFs. Solid lines correspond to non-helical PMFs and dashed lines correspond to helical PMFs with rms strengths of $B_0 = 0.1$ nG, $B_0 = 0.5$ nG, $B_0 = 1.0$ nG, and $B_0 = 3.0$ nG.
• Figure 3: Relative abundances of atoms, molecules, and their ions at different redshifts in cosmological models with (dashed lines for non-helical and dotted lines for helical PMFs with rms strength $B_0 = 1$ nG and spectral index $n_B=-2.9$) and without PMFs (solid lines).
• Figure 4: Population of ortho- and para-hydrogen molecules in the early Universe in cosmological models with non-helical PMFs of rms strengths $B_0 = 1.0$ nG (dashed lines) and $B_0 = 0.5$ nG (dotted lines) with spectral index $n_B=-2.9$ compared to a cosmological model without PMFs (solid lines).
• Figure 5: Emission signals in the rotational lines of molecules -- H$_2$ (upper row) and HD (bottom row) in a cosmological model with nonhelical PMFs with rms magnitude $B_0 = 1$ nG and spectral index $n_B=-2.9$.