Solar carbon abundance from 3D non-LTE modelling of the diagnostic lines of the CH molecule

TL;DR

This work trains 3D NLTE radiative transfer on solar CH lines to derive the solar carbon abundance with optical and infrared diagnostics. By leveraging 3D radiation-hydrodynamics atmospheres (M3DIS and STAGGER) and an updated CH molecule model, the authors show that 3D NLTE modeling reproduces the center-to-limb variation of CH lines and yields a solar carbon abundance of $A(C)=8.52\pm0.07$ dex, with NLTE corrections being small for CH lines ($\sim$0.01 dex). The analysis contrasts with 1D LTE and some 1D NLTE results, which misrepresent CLV and produce biased abundances; cross-checks with neutrino flux and solar wind data support the robustness of the 3D NLTE CH-derived abundance. The study also reveals that <3D> averages and granulation effects have molecule-dependent impacts, and it releases the CH model and line lists for public use, underscoring the broader importance of 3D NLTE treatments for molecular diagnostics in stellar atmospheres.

Abstract

Context. The spectral lines of the CH molecule are a key carbon (C) abundance diagnostic in FGKM-type stars. These lines are detectable in metal-rich and, in contrast to atomic C lines, also in metal-poor late-type stars. However, only 3D LTE analyses of the CH lines have been performed so far. Aims. We test the formation of CH lines in the solar spectrum, using for the first time, 3D Non-LTE (NLTE) models. We also aim to derive the solar photospheric abundance of C, using the diagnostic transitions in the optical (4218 - 4356 Å) and infrared (33025 - 37944 Å). Methods. We use the updated NLTE model molecule from Popa et al. (2023) and different solar 3D radiation-hydrodynamics model atmospheres. The models are contrasted against new spatially-resolved optical solar spectra, and the center-to-limb variation (CLV) of CH lines is studied. Results. The 1D LTE and 1D NLTE models fail to describe the line CLV, and lead to underestimated solar C abundances. The 3D NLTE modelling of diagnostic lines in the optical and IR yields a carbon abundance of A(C)=$8.52\pm0.07$ dex. The estimate is in agreement with recent results based on neutrino fluxes measured by Borexino. Conclusions. 3D NLTE modelling and tests on spatially-resolved solar data are essential to derive robust solar abundances. The analysis presented here focuses on CH, but we expect that similar effects will be present for other molecules of astrophysical interest.

Figures (25)

• Figure 1: A view of the solar disk by the Helioseismic and Magnetic Imager nasa_sun_image. Overlayed are concentric rings showing viewing positions of constant $\mu$-angle, while the green scale shows corresponding relative radii. We also show the finite fiber size of 32.5 of the IAG instrument SchaferRoyen2020.
• Figure 2: Comparison of synthetic and observed solar G-band intensity at wavelength $4306.8\pm$15 at different positions across the solar disc (different rows). The synthetic G-band has been convolved with the SST photometric filter transmission function CarlssonStein2004. The G-band observations were acquired with the Swedish 1-m Solar Telescope (SST, Scharmer2003a) on La Palma in 2003-2004 Berger2004Lin2005. For more detailed information on these observations we refer the reader to https://www.isf.astro.su.se/data1/gallery/. We show the disc center $\mu=1$ at the bottom and two angles approaching the limb $\mu=0.92, \mu=0.55$ above. The black and white levels of the observations were adjusted to account for the different processing of the individual measurements.
• Figure 3: Grotrian diagram of the CH molecule.
• Figure 4: Temperature structure as a function of optical depth of employed solar models. All 11 downsampled M3DIS snapshot are presented as a density plot in the background. The solid black line shows the average of the snapshots over surfaces of equal $\tau_{500}$. Overplotted as red dashed line is the corresponding structure of the 1D MARCS model.
• Figure 5: CH LTE number densities converted to absolute CH abundance, $\log_{10}(N_{\rm CH}/N_{\rm H}) + 12$, as a function of optical depth. All 11 downsampled M3DIS snapshots are presented as a density plot in the background. The solid black line shows the average of all 3D snapshots over surfaces of equal $\tau_{500}$. Overplotted as red dashed line is the corresponding structure of the 1D MARCS model.