Unified Spectrospatial Forward Models: Spatially Continuous Maps of Weak Emission Lines in the Rosette Nebula with SDSS-V LVM

Abstract

Analyses of IFU data are typically performed on a per-spaxel basis, with each spectrum modelled independently. For low signal-to-noise (S/N) features such as weak emission lines, estimating properties is difficult and imprecise. Arbitrary binning schemes boost S/N at the cost of resolution, and risk introducing biases. We present a general forward-modelling approach that assumes spectra close on the sky are more similar than distant ones, and so can be modelled jointly. These "spectrospatial" models exploit spatial correlation to provide robust inferences, while simultaneously providing continuous predictions of line properties like strength and kinematics across the sky. Instrumental and calibration systematics are straightforward to include and infer. The model provides a natural trade-off between spatial resolution and S/N in a data-driven way. We apply this to Sloan Digital Sky Survey V (SDSS-V) Local Volume Mapper (LVM) data of the Rosette Nebula, producing continuous maps of fluxes and kinematics for Balmer, nebular, and auroral lines, as well as weak C II and N II recombination lines, demonstrating the approach across three orders of magnitude in S/N, including in the very low-S/N regime. The method recovers identical morphologies across different lines tracing similar ionisation volumes, at varying resolutions set by the S/N. We additionally provide a general framework for building and fitting such models in JAX, suitable for many applications. The implementation is fast and memory efficient, scales to large data volumes as in LVM, and can be deployed on hardware accelerators.

Figures (11)

• Figure 1: Diagram of the spectrospatial framework. The observed spectrum in spaxel $i$ is generated from a parametric function $g(\lambda; \boldsymbol{\theta}_i)$, where the parameters $\boldsymbol{\theta}_i$ are split into two groups: those that are continuous functions of sky position ${\bf x}_i$ (the $\psi_\mu$), and those that are not (the $\xi_\nu$). The continuous components $\psi_\mu({\bf x})$ are drawn from (transformed) Gaussian processes, while the non-continuous components $\xi_\nu(\cdot)$ are independent per-spaxel $i$, per-pointing $j$, or per-spectrograph $k$. The diagram assumes each $\xi_\nu$ is per-spaxel ($i$) for simplicity. In this paper, we use this framework to model individual emission lines, where $g$ is a Gaussian line profile plus a constant continuum component. In general, $g$ could be any parametric function, and could represent multiple lines or even the full spectrum.
• Figure 2: Flux intensity maps for the chosen strong emission lines, in units of $10^{-12} \, \mathrm{erg \, s^{-1} \, cm^{-2}}$. The lines are ordered by increasing wavelength from left to right, top to bottom. The maps cover a contiguous region of the Rosette Nebula, from 19 LVM pointings or "tiles". These maps show the flux continuously across the sky, rather than just at the fibre positions. No interpolation is performed; the values are computed directly from the model $F({\bf x})$ inferred from the data, on a dense grid of sky locations. The strength of the lines varies by about one order of magnitude, with H$\alpha$ being the strongest, and H$\gamma$ the weakest.
• Figure 3: Similar to Figure \ref{['fig:flux_9lines']}, but for the auroral lines [O$\;$] $\lambda$4363, [N$\;$] $\lambda$5755, [S$\;$] $\lambda$6312, and [O$\;$] $\lambda$7319. The weakest of these is [O$\;$] $\lambda$4363, which is around 1000 times weaker than H$\alpha$.
• Figure 4: Similar to Figure \ref{['fig:flux_9lines']}, but for six He$\;$ recombination lines.
• Figure 5: Similar to Figure \ref{['fig:flux_9lines']}, but for C$\;$$\lambda$4267, N$\;$$\lambda$5680, C$\;$$\lambda$6578 and C$\;$$\lambda$7236. Note that C$\;$$\lambda$6578 and C$\;$$\lambda$7236 have both recombination and permitted contributions due to fluorescence. All these lines are at least 1000 times weaker than H$\alpha$. These maps suffer from some artefacts due to their very low S/N, but the spatial structure of the nebula is still resolved.