Mapping Electron Temperature Variations across a Spiral Arm in NGC 1672

In panels (f)–(h) of Figure 2, we present the electron temperature that is primarily constrained by the [N ii] auroral to strong line ratio. To visualize the correlation with the spiral structure, we split the regions in three bins based on their temperatures. We define the spiral arm by eye guided by the color figure in panel (a). The spiral arm defined on the optical emission line image (magenta curves) is very consistent with where bright molecular clouds live (panel (e), showing the ALMA CO(2−1) peak brightness map; Sun et al. 2018; A. Leroy et al. 2019, in preparation). Figures 2(f)–(h) show that the H ii regions with low temperatures (T_e < 7500 K) preferentially coincide with the eastern spiral arm. Regions with higher temperatures are more likely to appear at the leading side of the spiral arm.

To further investigate possible correlations between ISM physical conditions and the spiral arm, we quantify the dynamical time since the spiral arm passage t_dyn =π/(Ω − Ω_p) where Ω_p is the pattern speed of the two-armed gas spiral and Ω = V_c/R is the angular (circular) rotation rate of material in the disk. This relies on a measure of the rotation curve V_c and an estimate of the pattern speed of the dynamical structure in the disk. We adopt the rotation curve measured from the CO velocity field out to 80'' by P. Lang et al. (2019, in preparation) and then extend this out to the edge of our field of view using the smooth rotation curve model fitted by P. Lang et al. (2019, in preparation).

Our spiral pattern speed estimate is assigned in relation to that of the inner bar structure (as described below) and is chosen to yield a picture in which all H ii regions on the convex side of the arm lie inside the spiral corotation radius and thus downstream of the gas spiral. Our estimate relies on first determining the inner bar pattern speed, which we assign based on the expectation that the bar ends at, or very near to, its corotation radius (Contopoulos 1980; and see, e.g., Elmegreen 1996; Rautiainen et al. 2008; Corsini 2011). We specifically assume R_CR = 1.2 a_B (Athanassoula 1992), where a_B = 80'' is the bar length measured by Herrera-Endoqui et al. (2015; see also Figure 1). This yields Ω_p,B = 25 km s⁻¹ kpc⁻¹. We then estimate our lower spiral speed assuming that the bar and spiral arm are dynamically coupled (i.e., Masset & Tagger 1997; Rautiainen & Salo 1999; Figure 3) and overlap at resonances defined by intersections with the angular frequency curves Ω − κ/m where m is a positive integer and κ is the radial epicyclic frequency in the disk. Given the observed shape of the rotation curve, κ ∼ 2Ω over most of the disk, except toward the center. This places the inner Lindblad resonance of the spiral (where Ω_p = Ω − κ/2) far from the bar corotation radius. We therefore assume that the bar corotation overlaps with the inner ultraharmonic resonance of the two-armed spiral (where Ω_p = Ω − κ/4), which is another possibility suggested by observations (Meidt et al. 2009). This yields the spiral pattern speed Ω_p,S = 12 km s⁻¹ kpc⁻¹, placing all H ii regions inside the spiral corotation radius at approximately 200''.²⁰ We adopt an uncertainty on the measured rotational velocities of ±0.1 V_c due to the inclination uncertainty (P. Lang et al. 2019, in preparation) and let this define the primary uncertainty on the measured timescale t_dyn at all positions, which corresponds to ±3 Myr, on average across the radial zone of interest.

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While a two-pattern-speed scenario is more realistic, we have also derived the dynamical time assuming only a single spiral pattern speed of Ω_p,S = 12 km s⁻¹ kpc⁻¹. The conclusions of this work remain the same.

In Figure 4, we present the dynamical time (t_dyn) in panel (a) and compare in panels (b)–(e) to the strong-line metallicity offset, T_e, n_e, and pressure (n_eT_e). We split the H ii regions into two groups based on their dynamical time. The first group with t_dyn between ±3 Myr²¹ is directly associated with the spiral arm, whereas the second group, with t_dyn greater than 3 Myr, is not. Panels (d)–(e) compare the distributions of the two groups using both histogram and cumulative distribution function. Using a two-side Kolmogorov–Smirnov test, we test the null hypothesis that the two distributions are drawn from the same distributions. The resulting p-values are 8.8 × 10⁻⁴, 4.1 × 10⁻⁴, 0.53, and 0.43 for panels (b)–(e), respectively. Figure 4 demonstrates that the spiral and downstream H ii regions, short and long dynamical time, respectively, are systematically different in electron temperature and strong-line metallicity offset. There is no evidence that the electron density and pressure are systematically different.

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We note that the product of n_e derived from [S ii] and T_e from [N ii] is only an approximation of the ISM pressure given that different ions are excited in different zones within an H ii region and that H ii regions may not be in pressure equilibrium with their surroundings. Deriving n_e from the [S ii] doublet also assumes that the temperature of the [S ii] and [N ii] zones are similar. Also, the [S ii] lines are not very sensitive to n_e in the low-density regime.

Our observations suggest that the H ii regions on the spiral arm have a lower [N ii] temperature than the downstream side. There are several possible reasons for why this occurs. One of the most straightforward explanations is that the lower temperature on the spiral arm is due to the higher metal abundance that causes effective cooling of the nebula. However, at the spatial scale of marginally resolving individual H ii regions and dynamical timescales of a few Myr, variations in [N ii] temperature could also reflect changes in other ISM physical conditions or stellar characteristics.

The [N ii] temperature in an H ii region can be changed by the pressure of the nebula. In the latest mappings v photoionization models by Kewley et al. (2019), the authors construct model grids as functions of metal abundance, pressure, and ionization parameter. At solar and supersolar metallicities of their plane-parallel models, pressure correlates positively with [N ii] temperature (panel (b) of Figure 5). From $\mathrm{log}(P/k)$ of 5 to 6 cm⁻³ K, the [N ii] temperature increases from approximately 4000 to 5000 K for twice-solar metallicity models. At half-solar metallicity, the positive correlation only starts at an extreme pressure of $\mathrm{log}(P/k)\gt 7\,{\mathrm{cm}}^{-3}\,{\rm{K}}$. Our H ii regions are at approximately 0.8 solar metallicity and $\mathrm{log}(P/k)=5\,{\mathrm{cm}}^{-3}\,{\rm{K}}$; it is thus unlikely that the pressure can substantially change the [N ii] temperature. Moreover, if one attributes the temperature variation purely due to pressure variation, this would imply that the spiral arm H ii regions have lower pressure than those in the inter-arm regions. This is not supported by the data (n_eT_e; panel (e) of Figure 4) and also contradicts the expectation of higher pressure in the spiral arm due to higher gas and star formation rate surface densities.

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Another possible driver of the temperature variations is the aging of the ionizing source. As a stellar population ages, evolution of the spectral energy distribution alters the ionization structure of the H ii region and hence the measured electron temperature. To understand this effect, we derive [N ii] temperatures at different ages from the mappings iii models by Levesque et al. (2010; see panel (e) of Figure 5). For the instantaneous burst models,²² a systematic decrease in [N ii] temperature of up to 2000 K is apparent for the first 10 Myr of the stellar evolution for the models with metallicities above 0.4 solar. If star formation occurs only on the spiral arm, then as stars age and drift off the spiral arm, we would expect the temperature of the H ii regions to decrease, leading to lower temperatures on the downstream side. This is opposite to the observation where the H ii regions on the spiral arm have lower temperatures than those on the downstream side. The reality is likely more complex given that the dynamical time of some of our regions is much longer than the typical lifetime of H ii regions (up to 30 Myr versus a few Myr), which suggests that many downstream H ii regions are inconsistent with being formed on the spiral arm. It is unlikely that the aging effect alone could produce the observed temperature variations.

Of the three possibilities discussed above, the most likely cause of the observed temperature variations is the higher ISM metallicity on the spiral arm than the downstream side. The T_e measurements would thus confirm the finding from the strong-line method (panels (b)–(d) in Figure 2). That is, the inverse correlation between strong-line metallicity and T_e reflects simply metal cooling of the nebula.

To quantify the absolute abundance variation from the T_e measurements is nontrivial. The [O iii]λ4363 auroral line and the [O ii]λλ3726,3729 strong lines fall outside the MUSE passband, so it is not possible to directly constrain the oxygen abundance. Alternatively, we can compare the observationally derived T_e to the mappings v models by Kewley et al. (2019). The median T_e is 7294 K for the spiral arm regions and 7980 K for the downstream regions (Figure 4(c)). This corresponds to 0.81 and 0.77 solar metallicity,²³ respectively, using the models of $\mathrm{log}(P/k)$ of 5 cm⁻³ K and ionization parameter of 10⁷ cm s⁻¹. The abundance difference of 0.04 dex is larger than the 0.01–0.02 dex from the strong-line method (Figure 4(b)). However, given the calibration uncertainty of the strong-line method, particularly for high-metallicity regions, and the simple geometry and sparse metallicity sampling of the models, we consider that the two estimates are not inconsistent.

Despite that a quantitative statement to an accuracy of a few times 0.01 dex is not yet feasible, it is clear that qualitatively H ii regions on the spiral arm have higher oxygen abundance than those at the downstream side. Such a signature has been reported in a number of nearby spiral galaxies using different strong-line methods (Sánchez-Menguiano et al. 2016; Ho et al. 2017, 2018; Vogt et al. 2017). In Ho et al. (2017), the authors argue that the decrease in metallicity is due to mixing triggered by a spiral density wave. Prior to density wave passage, chemical inhomogeneity (between star-forming and non-star-forming sites) was established due to inefficient mixing, when materials travel in the inter-arm region. The passage of the spiral density wave drives large-scale mixing with the surrounding lower-metallicity gas, resulting in the low metallicity and high temperature in the downstream H ii regions. It remains unclear why such a signature is only observed in some galaxies, and even more puzzling why sometimes only seen in one spiral arm (e.g., this study; also see Kreckel et al. 2019). It could be that right combinations of dynamical time, star formation, and gas surface densities are required to drive large metallicity variations. Dynamical properties of spiral arms may also be important (e.g., short- versus long-lived arms, material arm versus density wave), and the mixing processes could be more complicated than that proposed in Ho et al. (2017). Simulations of the dynamical effect of spiral arms on star formation and chemical mixing and also observations of multiple temperature-sensitive lines (e.g., the CHAOS Project; Berg et al. 2015; Croxall et al. 2015, 2016) and resolved stellar populations with the Hubble Space Telescope could be possible ways forward.