A differentiable and optimizable 3D model for interpretation of observed spectral data cubes

Abstract

Molecular spectral cubes of prestellar cores encode the information on the physical and chemical properties of these objects along the line of sight. To retrieve this information, we need an interpretable model that reproduces the observed spectra. We designed a differentiable 3D geometrical model that produces synthetic observations from the parameterized density and velocity fields, and that can be efficiently optimized to reproduce the real data cubes. The model has been applied to p-NH2D and N2D+ spectral cubes in the prestellar core L1544. The optimized model suggests that to reproduce the observed velocity difference between p-NH2D and N2D+ in L1544, an asymmetric structure in density and velocity is necessary.

Figures (14)

• Figure 1: Sketch of the methods employed. Given a set of parameters (1), we generate a 3D model (2) that contains the velocity field along the LOS and the number density information for $p$-NH2D (3) and N2D+ (4). With this 3D data information, we can utilize their known spectral emission features (5 and 6) to compute the emission and absorption in each velocity channel, thereby generating a set of modeled PPV spectral cubes for each species (7). We compare the generated PPV with the observed one (8), computing a loss function (9) that will be used to modify the parameters in order to minimize the loss (10). The cycle is repeated until the loss is minimized.
• Figure 2: First and second rows are the observed and modelled intensity maps for some of the brightest selected velocity channels of $p$-NH2D. The values are normalized to the same global maximum value of the PPV cube. The cyan cross is the position of the center as found by the optimizer, described by the $x_{\rm c}$ and $z_{\rm c}$ parameters (slightly different for each molecule, see Fig. \ref{['fig:maps1']}). The third row is the difference between the optimized and observed maps. The last row represents the density probability distribution of the difference maps.
• Figure 3: Same as Fig. \ref{['fig:maps0']} but for N2D+.
• Figure 4: Three-dimensional schematic representation of the velocity vector fields (blue cones for $p$-NH2D and red for N2D+) and density isocontours (the colorscale in viridis is arbitrarily chosen to show the shape of the oblated spheroid). We include the position of the observer at $y=-1$ and the rotation axes, i.e., the yaw axis (rotation axis of $\vartheta_{\rm y}$). Note that the velocity difference is asymmetric, and the red cones closer to the observer overlap the blue ones. For the observer, the object appears as in Figs. \ref{['fig:maps0']} and \ref{['fig:maps1']}. Also, consider that the cones are reported to show the global properties of the vector field, but the observed velocity depends on the corresponding emitting density. To this aim, we report in Appendix \ref{['sect:slices']} the velocity and density slices at $x=0$ and $z=0$ (Fig. \ref{['fig:slice_xz']}), with the corresponding velocity difference (Fig. \ref{['fig:slice_dv']}).
• Figure 5: Comparison between observed (blue) and measured spectra (orange) of some selected pixels for $p$-NH2D. The offset indicated in the "pos" box is in pixel units with respect to the central position, i.e., (0, 0) corresponds to (8, 8) within the 16$\times$16 pixel map. The intensity is the units of the observed PPV, normalized to their absolute maximum.