Dark gaps and resonances in barred galaxies

TL;DR

This study tests whether stellar dark gaps along barred galaxy minor axes trace dynamical resonances. By combining DESI imaging to measure dark-gap radii with Tremaine–Weinberg pattern speeds from MaNGA to obtain $R_{\rm CR}$, and by analyzing the bar speed parameter $\mathcal{R}=R_{\rm CR}/R_{\rm bar}$ across a morphologically diverse sample, the authors show that dark gaps do not correspond to a fixed resonance. Instead, dark-gap locations scale with bar length (via $\mathcal{R}$), while the dip radii in some cases align with corotation or the ultraharmonic resonance depending on ring morphology and whether one or two dips are present. The work reconciles previous conflicting claims by highlighting that resonance associations are not universal but depend on identification method and structural context, offering a nuanced pathway to use dark gaps as resonance proxies in suitably chosen systems. Overall, the results advance our understanding of bar-driven secular evolution and the diagnostic power of dark gaps for probing bar dynamics.

Abstract

Dark gaps, low surface brightness regions along the bar minor axis, are expected to form as a consequence of secular evolution in barred galaxies. Although several studies have proposed links between dark gap locations and dynamical resonances, the results remain inconclusive. Using DESI Legacy Imaging Survey data, we find that approximately 61% of barred galaxies exhibit pronounced dark gaps. We compare the location of dark gaps with resonance radii derived from the Tremaine-Weinberg method applied to MaNGA data for the same galaxies. Our analysis shows that dark gaps do not preferentially form at specific resonances. Instead, their locations correlate with $\mathcal{R}$ $\equiv$ $R_{CR}/R_{Bar}$: slow bars tend to show shorter dark gap radii, while fast bars show longer ones. This trend reflects a tight relation between bar length and dark gap radius. However, when barred galaxies are classified by their ring morphology, certain types exhibit dark gaps that align with specific resonances. Notably, dark gaps located between the inner and outer rings are closely associated with the corotation radius. In galaxies with two dark gaps along the bar minor axis profile, the inner dark gap typically aligns with the ultraharmonic resonance, and the outer dark gap corresponds to the corotation radius. These findings suggest that some morphological types share similar $\mathcal{R}$ values and exhibit dark gaps near specific resonances. Thus, dark gaps may serve as proxies for dynamical resonances only in certain systems. Our findings may help explain the discrepancies observed in earlier studies.

Figures (8)

• Figure 1: (a): Radial surface brightness profiles of the deprojected galaxy MaNGA 8992-6101 are shown for the $g$ (blue), $r$ (green) and $z$ (red) bands. The average of all available bands at each radius is plotted in black and labeled as “m” (master) in the plot. A 3-pixel-wide pseudo-slit is placed along the bar major and minor axes to obtain the mean surface brightness at each radius. The radial profile along the bar major axis is plotted as a thin solid line, while the profile along the bar minor axis is shown as a thick solid line with markers at each radial point. Azimuthally averaged radial profiles are plotted as dash-dotted lines. Vertical line segments with square caps on both ends indicate the radius corresponding to the maximum difference in surface brightness profiles along the bar major and minor axes, $R_{\mathrm{Max}(\Delta \mu)}$. Triangles indicate the dip radius ($R_{\mathrm{Dip}}$) in the radial profile along the bar minor axis for each band. Vertical lines represent the bar radius ($R_{\mathrm{bar}}$, shown as a dotted line), the radius of the maximum difference between radial profiles along the bar major and minor axes ($R_{\mathrm{Max}(\Delta \mu)}$, solid line), and the dip radius along the bar minor axis ($R_{\mathrm{Dip}}$, dashed line). The values of $R_{\mathrm{Max}(\Delta \mu)}$ and $R_{\mathrm{Dip}}$ are displayed at the bottom right of the plot, where the measurements from the “m” (master) profile are used for further analysis. (b): $g$-band image of MaNGA 8992-6101. The yellow solid circle marks $R_{\rm Max(\Delta \mu)}$, while the cyan dashed circle denotes $R_{\rm Dip}$. The black solid bar in the bottom-left corner represents $10"$.
• Figure 2: Radial surface brightness profiles of galaxies, derived by averaging data over all available $g$, $r$, $i$ (if present), and $z$ bands, are shown. Three types of barred galaxies are presented, categorized by the presence of dips along the bar minor axis: (1) no dip, (2) a single dip, and (3) two dips. Thin solid lines represent the radial profiles along the bar major axis, while thick blue lines denote the profiles along the bar minor axis. Azimuthally averaged profiles are indicated by dot-dashed lines. Dips are marked with red triangles in the profile and the $R_{\rm Dip}$ is shown in orange dashed circle in the deprojected image, if any. The maximum differences between the bar major and minor axis profiles are shown as lines with black square caps in the profile and $R_{\mathrm{Max}(\Delta \mu)}$ is shown in black circle in the deprojected image.
• Figure 3: (a) Histogram of the difference between $R_{\mathrm{Max}(\Delta \mu)}$ and $R_{\mathrm{Dip}}$, normalized by the deprojected bar length, for galaxies exhibiting a single dip. The sample is divided into fast and slow bars. (b) Normalized difference between the two dark gap radii and the bar rotation rate, $\mathcal{R}$, which is $R_{\rm CR}/R_{\rm bar}$. Horizontal dashed line divides fast ($\mathcal{R}$$\leq$ 1.4) and slow ($\mathcal{R}$$>$ 1.4) bars. Data points are color-coded by total stellar mass.
• Figure 4: Ratio of dark gap radius to corotation radius. (a): Histogram of $\log(R_{\mathrm{Max}(\Delta \mu)}/R_{\mathrm{CR}})$ for all galaxies. The vertical dashed line indicates where $R_{\mathrm{Max}(\Delta \mu)}$ equals $R_{\mathrm{CR}}$, while the region enclosed by the two dotted lines represents the inferred extent of the inner UHR, estimated using Equation \ref{['eq:resonances']}. (b): Histogram of $\log(R_{\mathrm{Dip}}/R_{\mathrm{CR}})$ for galaxies exhibiting a single dip. (c): Relation between $\log(R_{\mathrm{Max}(\Delta \mu)}/R_{\mathrm{CR}})$ and the rotation rate, $\mathcal{R}$. Spearman’s rank correlation coefficient ($\rho$) and statistical significance (P) are shown in the upper right. A linear fit to the data is displayed as a gray dashed line, with the corresponding equation given in the lower left corner. (d): Relation between $\log(R_{\mathrm{Dip}}/R_{\mathrm{CR}})$ and $\mathcal{R}$ for galaxies with a single dip.
• Figure 5: The distribution of $\log(R_{\mathrm{Max}(\Delta \mu)}/R_{\mathrm{CR}})$ for galaxies grouped by the number of dips in their surface brightness profiles along the bar minor axis: 0 dip (black dashed line), 1 dip (blue solid line), and 2 dips (red solid line). Vertical dotted lines indicate the region of the inner UHR, and the solid line indicates the CR radius. The top-right box shows the results of KS tests between group pairs, including the KS statistic ($D$) and the associated $p$-value ($P$). For example, $D_{01}$ and $P_{01}$ refer to the comparison between the 0-dip and 1-dip groups. The high $D$ value and low $P$ value for $D_{12}$ indicate that the 1-dip and 2-dips groups differ significantly in their distributions.