The DESIRED temperature-metallicity relations in star-forming regions: probing the Galactic radial and azimuthal metallicity distributions

TL;DR

This study establishes two empirical $T_e$–metallicity relations for H II regions, corresponding to homogeneous ($t^2=0$) and temperature-fluctuating ($t^2>0$) nebular temperature structures, and applies them to a large radio sample to map the Milky Way’s radial O/H gradient. The $t^2>0$ calibration yields a nebular gradient in strong agreement with metallicities from young O/B-type stars and Cepheids, while the $t^2=0$ case underestimates abundances by up to ~0.3 dex; the widely used Shaver relation ($t^2=0$, outdated data) produces an excessively steep gradient. Distances are recalibrated in a homogeneous framework, and azimuthal metallicity variations driven by spiral arms are constrained to be below ~0.1 dex within the sampled disk. The results support conventional Galactic chemical evolution with inside-out disc formation and mild infall, and emphasize the importance of accounting for temperature fluctuations when deriving nebular abundances from $T_e$ diagnostics.

Abstract

We analyse a sample of 225 star-forming regions from the DESIRED-E project, each with simultaneous determinations of the electron temperature from ionized nitrogen and oxygen, $T_{\rm e}$([NII]) and $T_{\rm e}$([OIII]), respectively. We derive new empirical relations connecting the gas-phase metallicity to the global electron temperature, $T_{\rm e}$(H$^+$), as determined via radio observations. We establish two calibrations: one assuming a homogeneous temperature distribution ($t^2 = 0$, the ``direct method''), and another accounting for internal temperature fluctuations ($t^2 > 0$). Applying these calibrations to 460 radio observations of Galactic HII~regions spanning Galactocentric distances from $\sim0.1$ to 16 kpc, we determine the radial O/H gradient in the Milky Way under both assumptions. We further compare these nebular gradients to independent metallicity estimates from young O- and B-type stars and Cepheid variables. We find that the $t^2 > 0$ calibration yields a gradient in excellent agreement with stellar-based determinations, whereas the $t^2 = 0$ method underestimates metallicities by up to $\sim$0.3 dex. This discrepancy cannot be reconciled by invoking oxygen depletion onto dust grains or nucleosynthetic processing via the CNO cycle in massive stars. We also find that one widely used relation in the literature, assuming $t^2 = 0$, produces an excessively steep gradient -- likely due to the use of outdated atomic data and pre-CCD observations. Finally, we explore potential azimuthal variations in the Galactic metallicity distribution driven by the presence of the spiral arms, finding no evidence for variations larger than $\sim$0.1 dex with respect to the general radial gradient.

Figures (18)

• Figure 1: BPT diagram Baldwin:81 of the selected nebular optical spectra. The dashed curve represents the empirical demarcation by Kauffmann:03. Objects located above the curve correspond to regions dominated by harder ionizing radiation fields, while those below it are associated with softer, star-formation–driven ionization and other soft ionizing sources.
• Figure 2: Relation between the total O/H abundance ratio, a proxy for the gas-phase metallicity, and the average gas $T_{\rm e}$, equivalent to the $T_{\rm e}$ of ionised hydrogen in the nebula ($T_{\rm e}$(H$^+$)) for our sample objects. The determination is based on equation \ref{['eq:TH_t20']}, which assumes a homogeneous $T_{\rm e}$ structure ($t^2 = 0$), and on the optical observational sample shown in Fig. \ref{['fig:BPT']}. The upper panel shows the positions of the different observed objects along with the corresponding linear fit. $r$ is the Pearson correlation coefficient of the linear fit. As a comparison, the relation from Shaver:83, which is typically used in the literature for radio observations, is shown in red. This latter relation has been plotted only over the temperature range used in the calibration of the original paper ($\sim$6000–11000 K). The lower panel displays the residuals relative to our best linear fit. The shaded gray region indicates the typical fitting uncertainty $1\sigma$, corresponding to +0.05 and $-$0.1.
• Figure 3: Same relation as in Fig. \ref{['fig:metal_tem_t2eq0']}, but assuming an inhomogeneous temperature structure ($t^2>0$) as described in equation \ref{['eq:TH_t2geq0']}. The shaded gray region indicates the typical fitting uncertainty, corresponding to +0.2 and $-$0.1.
• Figure 4: Comparison between the Galactocentric distances determined by Quireza:06 and those obtained in this work for Galactic H II regions (see Section \ref{['Subsec:revis_distances']}). The upper panel shows the object-by-object comparison, while the lower panel displays the differences in percentage. The shaded gray region indicates the typical uncertainty $1\sigma$ confidence interval, corresponding to $+13$ per cent and $-2$ per cent and the blue dashed line represents the median with a value of +6 per cent.
• Figure 5: Analogous comparison to Fig. \ref{['fig:Comparison_Quireza_Rgal']}, but using the data from Wenger:19. The shaded gray region indicates the typical uncertainty $1\sigma$ confidence interval, corresponding to $+4$ per cent and $+1$ per cent and the blue dashed line represents the median with a value of $+2$ per cent.