The IRIS$^{2+}$ inversion tool: recovering the radiative losses and the thermodynamics in the lower solar atmosphere

TL;DR

IRIS$^{2+}$ introduces a fast, data-driven inversion tool to recover the thermodynamic state ($T$, $v_{los}$, $v_{turb}$, $n_e$) and the integrated radiative losses (IRL) in the lower solar atmosphere from IRIS multi-line observations. Built on a large repository of ~135k RP–RMA–IRL triplets inverted with STiC, the method uses a $k$-nearest-neighbor search ($k=1$) to map observed profiles to representative atmospheres, enabling rapid inferences from photosphere to top of chromosphere. Comparisons with STiC demonstrate broad agreement in IRL and thermodynamics across many datasets, with depth-dependent differences arising from line sensitivity and database coverage; the approach offers substantial speed gains (minutes per raster) and an accessible, Python-based tool for large-scale chromospheric heating studies. The work also discusses the calculation of radiative losses (including and excluding certain species) and highlights the importance of line weighting, recommending expansion of the RP–RMA–IRL database and exploration of scalable search methods to improve coverage and precision.

Abstract

We introduce an improved and fast inversion tool that is able to provide the thermodynamics of the solar atmosphere from the photosphere to the top of the chromosphere, as well as the integrated radiative losses in the chromosphere for data observed by the Interface Region Imaging Spectrograph (IRIS). This NASA mission has been observing the Sun and providing, among other kinds of data, multi-line spectral observations sensitive to changes in the lower solar atmosphere since 2013. In this paper, we explain the new inversion tool IRIS$^{2+}$ based on the IRIS$^{2+}$ database, which is based on 135,472 synthetic representative profiles (RP), each of them consisting of 6 chromospheric lines and 6 photospheric lines, their corresponding representative model atmospheres (RMA), and the integrated radiative losses (IRL) associated with these atmospheres. A nearest neighbor (k-nn) model algorithm is trained with the synthetic representative profiles to predict the closest RP in the database to the one observed, at which point IRIS$^{2+}$ assigns the RMA and the IRL to the location of that observed profile. We have compared the results obtained by IRIS$^{2+}$ with results obtained from the state-of-the-art inversion code STiC, which is also used to build the IRIS$^{2+}$ database. We find that the thermodynamics and the IRL obtained with both methods are comparable in most cases. Therefore, IRIS$^{2+}$ is a fast and reliable inversion tool that provides approximate values of the thermodynamic state and the radiative losses in the lower solar atmosphere for a large variety of solar scenes observed with IRIS.

Figures (23)

• Figure 1: Left: location of the 550 datasets selected to build the IRIS$^{2+}$ database. Right: distribution of the observation date of these datasets during the years of the IRIS mission (which was launched in 2013).
• Figure 2: Screenshot of the interactive IRIS$^{2+}$ inspection tool. In the first and second columns the map images show from top to bottom, left to right: the specific intensity in $\mu erg~cm^{-2}~s^{-1}~sr^{-1}~Hz^{-1}$ at the wavelength ($\AA$) selected in one of the spectral plots shown in the third column (first 8 plot panels from the top); the integrated radiative loss (IRL) in $kW~m^{-2}$; the T in $kK$; the $v_{los}$ in $km~s^{-1}$; the $v_{turb}$ in $km~s^{-1}$; and the $n_e$ in $cm^{-3}$. These thermodynamic variables show the value at the optical depth ($log(\tau)$) determined by the positions in the thermodynamic plots displayed in the last four panels in the third column. The spectral plots show the observed spectral profile (blue) and the synthetic spectral profile found by IRIS$^{2+}$ (orange) that best fits it. The specific intensity shown in the first top panel can be toggled to show either the observed intensity, as it is in the current figure, or the synthetic intensity corresponding to the synthetic best fit profiles at that particular wavelength. Similarly, the IRL panel can be toggled to show the $\chi^2$ map. In all cases, the value below the cursor these cases is shown in the bottom right corner of the window.
• Figure 3: First row: Integrated slit-reconstructed intensity map around C II 1334 Å, Mg II k$_3$, Ti$\;$ 2785.46 $\AA$, and 2832.04 $\AA$, roughly corresponding to the high chromosphere, mid chromosphere, the high photosphere, and the continuum photosphere, respectively. Second to the fith row: Total contribution (second row) and partial contribution from the main ions (H, Mg II, and Ca II in the third, fourth, and fifth rows respectively) to the integrated radiative losses in three regions in the lower solar atmosphere (first, second, and third columns respectively) and the total integrated radiative loss (fourth column).
• Figure 4: The first 5 IRIS observations used for the comparison between STiC and IRIS$^{2+}$. The first column shows the intensity in the photosphere, the mid chromosphere, and high chromosphere as observed in the core of Fe I 2827.33, Mg II k, and C II 1334 Å respectively. The images show the specific intensity in $\mu erg~cm^{-2}~s^{-1}~sr^{-1}~Hz^{-1}$ in these wavelengths.
• Figure 5: Same as figure \ref{['fig:intmap_1']} for the last 5 IRIS observations used for the comparison between STiC and IRIS$^{2+}$.