How Bar Fraction Depends on Baryon Fraction

Bars are elongated features in disk galaxies. At low redshifts, 30%–40% of disk galaxies have bars, depending on the details of classification, bar fraction is observed to correlate with various global properties of galaxies, such as stellar mass, star formation rates (color), and gas content (e.g., Masters et al. 2011; Cervantes Sodi 2017; Géron et al. 2021). Simulations of bars show how their evolution depends on stellar mass and the dark matter halo, (e.g., Debattista & Sellwood 2000; Athanassoula 2003; Rosas-Guevara et al. 2022) suggesting that bars should grow more quickly and end up stronger in heavier discs.

Cervantes Sodi (2017) have previously showed how the bar fraction depends on both the stellar mass and estimated total baryon fraction. That work used the 70% sample from the Arecibo Legacy Fast ALFA survey (ALFALFA; Haynes et al. 2018) alongside visual inspection of color-identified disk galaxies in the Sloan Digital Sky Survey (SDSS) Legacy Imaging (York et al. 2000) to find bars. Here we present similar results using disk galaxy identification and bar classifications from Galaxy Zoo 2 (GZ2; Willett et al. 2013), and the final data release from ALFALFA. This allows us to re-examine the correlation between observed bar fraction and its estimation in a larger sample and use quantitative crowd-sourced morphology for discs and bars.

We use galaxy morphologies from GZ2 (Willett et al. 2013; Hart et al. 2016) and stellar masses and inclinations based on SDSS photometry (via the NASA-Sloan Atlas catalog; NSA; Blanton et al. 2011). H i masses and rotation widths come from ALFALFA (Haynes et al. 2018), which limits to gas rich galaxies with H i detections, since we need both H i mass measurements and rotation widths. This gives 12,854 galaxies out of which we use a volume-limited sample of 6428 "not edge-on" disk galaxies in which bars can be observed (i.e., ${p}_{\mathrm{features}}\geqslant 0.27$ and p_notedgeon ≥ 0.68 and limiting to M_⋆ > 10⁹  M_⊙ and z ≤ 0.06, motivated by Figure A4 in Kruk et al. 2018). The top two panels of Figure 1 show histograms of stellar masses and baryon masses for this sample.

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We estimate both the baryonic and dynamical mass of the galaxies to calculate the baryon fraction, M_baryon = M_gas + M_*/M_dyn. Neutral hydrogen (H i) is the dominant gas phase by mass: we estimate M_gas = 1.4 M_H I using the standard conversion factor to account for molecular hydrogen, and helium (e.g., see Cervantes Sodi 2017).

H i rotation widths probe the outer velocities in a disk galaxy, giving us an estimate of the dynamical mass via

$$\begin{eqnarray}&&{M}_{\mathrm{dyn}}=\displaystyle \frac{{R}_{{\rm{H}}\,{\rm\small{I}}}{V}_{\mathrm{rot}}^{2}}{G},\end{eqnarray} \tag{ 1 }$$

where the physical rotation speed is ${V}_{\mathrm{rot}}=W/2\sin \,i$ with W being the H i line width, and the inclination angle i is found from the axial ratio assuming q₀ = 0.13 for the intrinsic axial ratio (Giovanelli et al. 1994). The radius of the H i disk, R_H I, comes from its scaling with H i mass (Broeils & Rhee 1997),

$$\begin{eqnarray}&&\mathrm{log}{M}_{{\rm{H}}\,{\rm\small{I}}}=1.96\mathrm{log}(2{R}_{{\rm{H}}\,{\rm\small{I}}})+6.52.\end{eqnarray} \tag{ 2 }$$

Using GZ2, we define a galaxy to be strongly barred if the weighted and debiased fraction of positive votes for "bar", or p_bar ≥ 0.5; and weakly barred for 0.2 < p_bar < 0.5. See Géron et al. (2021) for a justification of this choice based on the Galaxy Zoo analysis of DECaLS imaging which included a "weak bar" option; (Masters et al. 2011) also made similar arguments.

In the lower panels of Figure 1 we show our results. Figure 1(c) shows bar fractions against stellar mass. The strong bar fraction (blue line) increases with stellar mass, particularly for galaxies with $\mathrm{log}\,{M}_{\star }/{M}_{\odot }\gt 9.7$. The weak bar fraction (orange line) instead is higher for lower mass galaxies. This results in a total bar fraction (green line) with peaks at both lower and higher stellar masses, similar to that found in Géron et al. (2021). Our results also agree with those in Cervantes Sodi (2017), however we find the opposite trend to Erwin (2018) who used a nearby galaxy sample based on the S4G survey.

Figure 1(d) shows bar fraction against our estimate of baryon fraction. We observe an increase in the strong bar fraction toward higher baryon fractions, while the weak bar fraction shows at best a mild trend. The total bar fraction increases from 30% to almost 60% as the baryon fraction increases. This appears to be a slightly stronger trend than Cervantes Sodi (2017), perhaps because their partly color based selection for discs removed some of the highest baryon fraction (reddest) discs.

We examine the correlations between bar fraction and both stellar mass and baryonic mass fraction. Using galaxy morphologies from GZ2 and gas (H i) measurements from ALFALFA, we find that the strong bar fraction displays an increasing trend with respect to both stellar mass and baryonic mass fraction. The weak bar fraction shows a mildly decreasing trend with stellar mass and a mildly increasing trend with baryonic mass fraction.

These results agree with most previous work, but are the first using the full ALFALFA sample with the GZ2 morphologies. Our results are in agreement with simulations/theory of bar formation (e.g., Combes & Sanders 1981) which show that at lower baryonic mass fractions, thus higher dark matter halo to disk ratio, there are fewer bars overall, mostly as a result of the longer formation time for the bar instability in those galaxies.

This publication uses data from Sloan Digital Sky Survey, ALFALFA (Arecibo) and generated via the Zooniverse.org platform.

Facilities: Arecibo - Arecibo observatory, SDSS - .

Software: astropy (Astropy Collaboration et al. 2018).