Physical parameters of infant disk galaxy constituting the Einstein ring of SPT0418-47

Abstract

SPT0418--47, a star-forming galaxy at $z=4.2$, is strongly lensed into an Einstein Ring with line-of-sight velocities reaching $\simeq \pm 250\,\rm{km\,s^{-1}}$. From models constructed for both the lensing and lensed galaxy, \citet{Rizzo} find that SPT0418--47 is a disk galaxy exhibiting a high degree of rotational support; i.e., a maximum rotational velocity ($V_\rm{rot}$) compared with a dispersion velocity ($\sigma$) of $V_{\rm{rot}}/\sigma \sim 17$. Such a strong degree of rotational support is surprising in view of its high star formation rate of $\sim300\,{\rm M_\odot/yr}$, which ought to generate strong turbulence owing to feedback processes (e.g., radiation, stellar winds and supernovae). Indeed, direct measurements of the velocity fields of unlensed star-forming disk galaxies at $z\sim2$ find $V_{\rm{rot}}/\sigma \sim4$, implying weak rotational support among galaxies that are even older than SPT0418--47. Theoretical simulations suggest that even younger galaxies should have lesser degrees of rotational support.

Here, I use the same high-resolution images as \citet{Rizzo}, comprising spectrally-resolved images of [CII]$\lambda158\,\mu$m emission, and explore also the inclusion of images in dust continuum emission and OH$\lambda119\,\mu$m absorption, to construct a self-consistent model for the lensing galaxy and the lensed galaxy of the SPT0418--47 system. In the process, we found that the dust continuum emission exhibits a somewhat different morphology from the [CII] emission, preventing its use in the construction of a lens model (present lensing algorithms only allow a single model for the lensed galaxy). Comparison of the systemic component of OH absorption and [CII] emission shows agreement in their central velocity, but, unlike [CII], OH does not show evidence of ordered motion and hence cannot be used as lensing constraints. We also demonstrate that the OH molecular outflow identified by \citet{spilker} is confused with absorption by H$_2$O in the Earth's atmosphere, a problem that plagues many of the similarly-identified OH outflows in $z\sim4$ galaxies by these authors. We therefore constrained our lens model primarily using the moment 0 map of [CII], just like \citet{Rizzo}, with additional constraints provided by two sets of multiply-lensed images in [CII] as well as a set of related multiply-lensed images identified from the spectral index map in the dust continuum. In this way, we were able to construct an internally consistent model in which the morphology of the lensed galaxy is best described by an exponential disk, characteristic of disk galaxies in the local universe.

Employing a forward lens modelling approach, we examined in detail how varying the properties of the lensed galaxy such as its velocity field, position angle, inclination affects the predicted [CII] moment maps, thus revealing also the model degeneracies. Good matches between model predictions and the observed maps were found for $V_{\rm{rot}}\simeq 350$--700\,km\,s$^{-1}$ based on inclination angles in the range $20\degr\lesssim i \lesssim 50\degr$. By comparison with the model by \citet{Rizzo} of the lensed galaxy, we also found a shallower rise in its rotation curve at the inner regions. We infer a rise in the rotation curve of the lensed galaxy at its inner regions, peaking at a radius of $1\,$kpc, by comparison with the rise to a maximal rotation velocity of $\sim 300\,$km\,s$^{-1}$ at 0.2\,kpc as inferred by \citet{Rizzo}. Our model for SPT0418--47 requires a uniform velocity dispersion throughout the disk of $75\pm5\,\rm km\,s^{-1}$, implying the $V_{\rm{rot}}/\sigma \sim 7\pm2$ - the range lies at the high end of the range in $V_{\rm rot}/\sigma$ for star-forming galaxies at $z\sim2$ as well as the range predicted by high resolution cosmological simulations, but is much lower than \citet{Rizzo}. Albeit suggesting an unusually high degree of rotational support, our work does not support the sole discovery of a very strongly rotationally supported star-forming galaxy at $z\sim4$.