Galaxy-scale Bars in Late-type Sloan Digital Sky Survey Galaxies Do Not Influence the Average Accretion Rates of Supermassive Black Holes

We begin by constructing a parent sample of spiral galaxies from which to select our sub-samples of galaxies with and without large-scale bars. Our sample of local galaxies is selected from the seventh data release of the Sloan Digital Sky Survey (hereafter, SDSS-DR7; Abazajian et al. 2009), where we select all spectroscopically targeted $r\lt 17.77$ magnitude galaxies in the redshift range of $z\sim 0.01\mbox{--}0.17$. Following Galloway et al. (2015), the lower redshift limit excludes those galaxies whose angular size significantly exceeds the size of the spectroscopic fiber.

Morphological cuts on the SDSS parent sample are made using visual-classification data gathered from the citizen science project, Galaxy Zoo (Lintott et al. 2008, 2011). Specifically, we harness the second release of the Galaxy Zoo project (hereafter, SDSS-GZ2) that provides detailed morphological statistics on ∼300,000 SDSS galaxies, including inclination angle, existence of spiral arms, bulge dominance, and galactic bars. These statistics are a collation of the responses to a set of hierarchical decision-tree questions, posed to citizen scientists, regarding morphological features that may or may not be present in 3-color images of SDSS galaxies (for details see Willett et al. 2013).

We identified a sample of disk galaxies by selecting all systems in SDSS-GZ2 at $0.01\lesssim z\lesssim 0.17$ that had been visually classified by at least 20 people (i.e., the galaxy had at least 20 responses to the zeroth node question: "Is the galaxy simply smooth and rounded, with no sign of a disk?"), and where the fraction of classifiers identifying disk features (i.e., positive responses to the zeroth node question) was ${f}_{\mathrm{disk}}\geqslant 0.227$. Large-scale bars may be difficult to identify in objects that are highly inclined, hence, we remove likely edge-on systems with the classification fraction threshold ${f}_{\mathrm{Edge} \mbox{-} \mathrm{on}}^{\mathrm{not}}\gt 0.5$. Selecting against edge-on systems will further remove systematic bias against obscured AGNs where the AGN emission is being extinguished by line-of-sight material residing in the host galaxy (e.g., Goulding & Alexander 2009; Lagos et al. 2011; Goulding et al. 2012a), and not necessarily a small-scale dust/gas-rich torus. Performing our stacking analyses at X-ray energies will then allow us to mitigate the effects of the small-scale obscurer. Our chosen cuts on the SDSS-GZ2 are similar to those suggested by Willett et al. (2013) from their in-depth analysis of the entire SDSS-GZ2 data and catalog. After our zeroth order morphological cuts, the SDSS-GZ2 sample contains a robust sample of 96,767 spiral galaxies.

X-ray emission produced due to AGN activity and/or star-forming processes is known to be a function of galaxy stellar mass (e.g., Lehmer et al. 2010, 2016). Hence, to avoid bias and incompleteness, we require our sample to be complete in stellar mass in a given redshift bin. Due to the $r\lt 17.77$ mag selection, the SDSS spectroscopic galaxy sample forms a stellar mass complete sample (Brinchmann et al. 2004). At the low-redshift limit of the survey, SDSS-DR7 is complete to ${M}_{* }\sim {10}^{8}\,{M}_{\odot }$, and allows volume-limited galaxy samples that are mass complete to be constructed to $z\lt 0.22$. To obtain estimates of the stellar mass and star-formation rates (SFR) for the 96,767 spiral galaxies in our SDSS-GZ2 sample, we use the value-added MPA-JHU spectroscopic catalog of Brinchmann et al. (2004). Brinchmann et al. (2004) used the SDSS cmodel photometry and fiber spectroscopy to fit stellar population synthesis templates using a Bayesian methodology to derive the physical properties. Here we use the 50th percentile of the log total stellar mass PDF (i.e., the median estimates of the total stellar masses), the SFR within the fiber, and the scaled total SFR. Median uncertainties are 0.09 dex and 0.14 dex on M_* and SFR, respectively.

In Figure 1, we show the distribution of the ∼10⁵ SDSS-GZ2 spirals with stellar mass estimates in the MPA-JHU catalog. We identify three redshift bins, 0.01–0.05, 0.05–0.09, and 0.09–0.13, where our spiral sample is complete to a given stellar mass threshold (green dashed boxes in Figure 1). These three ${M}_{* }\mbox{--}z$ sub-samples form the basis for our X-ray analyses presented in Section 2.2.

Zoom In Zoom Out Reset image size

We distinguish between galaxies with and without bars using the debiased fraction of votes⁷ measured from the SDSS-GZ2 question: "Is there a sign of a bar feature through the center of the galaxy?" (hereafter, ${f}_{\mathrm{bar}}$). We select only spiral galaxies in our ${M}_{* }\mbox{--}z$ samples where the number of votes on the "bar question" was $\geqslant 5$. The average number of "bar question" votes per galaxy for the sample is 13. A naive cut of ${f}_{\mathrm{bar}}\gt 0.5$ provides a bar fraction of only ∼18%. This bar fraction is substantially below the known fraction of local ($D\lt 40$ Mpc) galaxies that contain a bar signature ($\gtrsim 59$%) based on near-IR identification, which is far less susceptible to dust obscuration effects than optical identifications (Eskridge et al. 2000; Menéndez-Delmestre et al. 2007).

Furthermore, a simple analysis of the distribution of ${f}_{\mathrm{bar}}$ for SDSS-GZ2 spiral galaxies, shows it to be roughly exponentially peaked at ${f}_{\mathrm{bar}}\sim 0.0$ with a declining tail toward ${f}_{\mathrm{bar}}\sim 1.0$. The shape of this distribution is likely driven by observational biases, as the true probability distribution of bar versus non-bars in spiral galaxies must be far more bi-modal. Hence, ${f}_{\mathrm{bar}}$ does not directly map to the probability of a bar existing in a particular spiral galaxy.

In order to separate barred galaxies from non-barred galaxies, we use the known nearby bar fraction ($\gtrsim 59$%), and match this to the cumulative distribution of ${f}_{\mathrm{bar}}$ for the SDSS-GZ2 parent spiral sample. A demarcation of ${f}_{\mathrm{bar}}\gtrsim 0.15$ results in a bar fraction of ∼55%. Given small number statistics, and allowing for the possibility of false-positives, we conservatively use a threshold of ${f}_{\mathrm{bar}}\geqslant 0.25$, providing us with a "clean" bar sample (bar fraction of ∼40%).⁸ Similarly, if we adopt a threshold of ${f}_{\mathrm{bar}}\lt 0.1$, we achieve a "clean" non-barred spiral sample with a non-bar fraction of ∼40%. The remaining ∼20% of galaxies in our ${M}_{* }\mbox{--}z$ samples with $0.1\lt {f}_{\mathrm{bar}}\lt 0.25$, in a purely statistical sense, have ambiguous evidence for the presence of a bar. This is further evidenced in Figure 2, where we provide example images used in GalazyZoo2 to classify the galaxies. Sources with ${f}_{\mathrm{bar}}\geqslant 0.25$ seemingly have strong and/or obvious bar structures, while those with $0.1\lt {f}_{\mathrm{bar}}\lt 0.25$ have much weaker and/or difficult to identify bars in their SDSS 3-color images. In Table 1, we provide the number of non-edge-on spiral galaxies in our ${M}_{* }\mbox{--}z$ samples determined to have bars (28,733 galaxies), no bars (28,728 galaxies), and ambiguous evidence for bars (15,474 galaxies).

Zoom In Zoom Out Reset image size

Table 1.  Galaxy Sample and X-Ray Stacking Results

						0.5–2 keV				2–7 keV				0.5–7 keV
logM*	z	${f}_{\mathrm{bar}}$	#	${\bar{t}}_{\mathrm{Exp}}$	${\rm{\Sigma }}{t}_{\mathrm{Exp}}$	#	#	${\bar{L}}_{{\rm{X}},\mathrm{AGN}}$	S/N	#	#	${\bar{L}}_{{\rm{X}},\mathrm{AGN}}$	S/N	#	#	${\bar{L}}_{{\rm{X}},\mathrm{AGN}}$	S/N
			SDSS			Det.	Stack	1039		Det.	Stack	1039		Det.	Stack	1039
(M⊙)				(ks)	(ks)			(erg s−1)				(erg s−1)				(erg s−1)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)	(14)	(15)	(16)	(17)	(18)
9.3–11.0	0.01–0.05	>0.25	5958	33.8	2905.8	17	63	${1.56}_{-0.43}^{+0.42}$	10.7	13	67	${2.88}_{-0.65}^{+0.67}$	8.2	18	62	${3.47}_{-1.04}^{+0.97}$	13.5
		0.1–0.25	3486	24.5	770.0	10	21	${1.02}_{-0.62}^{+0.76}$	5.4	10	21	${1.11}_{-0.90}^{+1.31}$	3.3	10	21	${0.59}_{-0.58}^{+1.70}$	6.3
		<0.1	6543	24.7	1444.3	17	57	${1.01}_{-0.83}^{+0.68}$	10.1	14	60	${1.63}_{-0.61}^{+0.80}$	6.9	16	58	${0.48}_{-0.35}^{+2.30}$	12.2
10.0–11.4	0.05–0.09	>0.25	8644	17.0	1448.5	17	60	${3.60}_{-1.65}^{+1.91}$	7.9	13	64	${5.75}_{-4.62}^{+4.00}$	6.1	15	62	${7.66}_{-5.48}^{+4.79}$	10.0
		0.1–0.25	5637	22.0	1035.6	8	37	${4.07}_{-1.23}^{+1.25}$	7.1	7	38	${1.31}_{-2.82}^{+3.79}$	3.8	8	37	${5.33}_{-2.31}^{+3.45}$	8.0
		<0.1	10059	22.1	1552.2	13	54	${2.87}_{-1.04}^{+1.17}$	6.9	12	55	${3.39}_{-2.70}^{+3.06}$	5.0	13	54	${5.04}_{-2.68}^{+3.22}$	8.5
10.5–11.5	0.09–0.13	>0.25	4074	27.3	1090.4	8	27	${8.20}_{-2.78}^{+3.76}$	6.3	6	29	${19.2}_{-5.81}^{+7.81}$	5.5	8	27	${22.1}_{-7.59}^{+10.7}$	8.3
		0.1–0.25	2401	35.9	970.8	3	19	${3.19}_{-1.98}^{+2.48}$	4.7	2	20	${13.2}_{-5.00}^{+6.18}$	5.1	3	19	${11.3}_{-5.50}^{+6.51}$	7.0
		<0.1	3992	33.5	1272.8	7	29	${4.16}_{-1.77}^{+1.89}$	4.6	3	33	${17.2}_{-12.8}^{+10.5}$	5.3	6	30	${1.43}_{-8.70}^{+7.41}$	7.1

Note. (1) Ranges of the logarithm of the stellar mass in units of solar masses; (2) redshift ranges; (3) fraction of citizen scientists voting for the presence of a bar in the SDSS image; (4) number of SDSS-GZ2 galaxies in each bin matched for similar distributions in star-formation rates measured within the SDSS spectroscopic fiber; (5) mean exposure time of all galaxies covered by Chandra ACIS-I observations in units of kiloseconds; (6) total exposure time for all galaxies covered by Chandra ACIS-I observations in units of kiloseconds; (7–10) number of X-ray detected AGNs in the 0.5–2 keV band, number of non-X-ray detected galaxies included in the X-ray stack, star-formation-subtracted stacked (average) X-ray luminosity (in units of ${10}^{39}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$) in the 0.5–2 keV band, signal-to-noise of the X-ray emission in the stack above the stacked local background; (11–14) same as columns 7–9 in the 2–7 keV band; (14–18) same as columns 7–9 in the 0.5–7 keV band.

Download table as:  ASCIITypeset image

Finally, to statistically compare the AGN properties of our ${M}_{* }\mbox{--}z$ samples based on their inferred bar properties, it is important to ensure that the distributions of the first-order galaxy properties (such as SFR; stellar mass) are well matched between the bar/no-bar sub-populations. In Figure 3, we provide the SFR measured within the spectroscopic fiber and the stellar mass distributions of the three ${M}_{* }\mbox{--}z$ samples, separated based on their inferred bar properties. Based on two-sample Kolmogorov–Smirnov (K–S) tests, we find evidence at the >99.99% level that the SFR distributions for the bar and non-bar samples are not drawn from the same distributions ($P\lt {10}^{-7};$ see also Oh et al. 2012). It is further evident from the histograms presented in Figure 3 that, as a function of M_* and z, there is an increasing fraction of barred galaxies with low SFRs over those without bars. It is beyond the scope of this study to provide a full explanation for this phenomenon, though we suggest that it may be easier to visually identify bars in systems that lack significant levels of SF or that star-forming regions may systematically reside at larger radii in barred galaxies (Robichaud et al. 2017).

Zoom In Zoom Out Reset image size

For the purposes of our experiment, it is sufficient to simply ensure that the distributions in galaxy properties are similar for the barred and non-barred stacked samples. Hence, to mitigate these effects, we apply SFR cuts of log SFR/(M_⊙ yr⁻¹) > −1.8, $\gt -1.4$, and $\gt -1.0$ for our ${M}_{* }\mbox{--}z$ redshift bins of 0.01–0.05, 0.05–0.09, and 0.09–0.13, respectively. We find that these cuts are sufficient to simultaneously remove the tensions between the SFR and M_* distributions for the SDSS-GZ2 galaxies included in our X-ray stacking analysis (described in the next section). Comparing the SFR distributions for the barred and non-barred that are covered by Chandra X-ray observations, from two-sample K–S tests we find $P\gtrsim 0.2$ between the $0.01\lt z\lt 0.05$ and $0.05\lt z\lt 0.09$ samples, while we still find some evidence for tension ($P\sim 0.015$) between the samples at $0.09\lt z\lt 0.13$.

While not fully essential for our analyses because we also take care to statistically account for X-ray emission from SF in our stacking analysis, requiring similar distributions in M_* and SFR is still a useful endeavor when comparing the X-ray properties of galaxies as it equally aggregates the contamination to the X-ray emission from SF processes, while also allowing us to (statistically) select sources hosting similar mass BHs (through the ${M}_{* }\mbox{--}{M}_{\mathrm{BH}}$ correlation).

Stacking analyses are based on the principle that objects at known positions, which are not detected individually in imaging at a particular wavelength, may show a significant flux when the observations are averaged together. These aggregate measurements are most accurate when both the multiwavelength properties of the stacked sample are previously well defined and source number statistics are sufficiently high to break through the noise floor, and thus, increase the signal-to-noise and effective depth of the observations. By definition, these stacked signals then have the added effect of averaging over the inherent stochasticity of AGN accretion, which is present in blind selections of AGN samples.

To perform the X-ray stacking of our sample, we used our custom idl-based software stackfast, which is designed specifically for Chandra ACIS data and we briefly describe here (see also Hickox & Markevitch 2007; Hickox et al. 2007, 2009; Chen et al. 2013). stackfast begins with two elements: a master catalog of input sources, and a set of uniformly formatted, reduced, and flare-cleaned Chandra ACIS data products derived from individual Chandra-ACIS observations (ObsIDs). Here we include all ACIS ObsIDs that were publicly available from Cycles 1–16 of the Chandra mission. ObsIDs were reduced using version 4.6 of the ciao software package and by applying v4.6.5 of the caldb calibration files. Events were screened using the grade set 0, 2, 3, 4, 6, and $3\sigma$ background flares were removed using the lc_clean tool. Aspect histograms were constructed using the aspecthist tool available in the chav software package, and convolved with the ACIS chip-map to generate observation exposure maps. For a detailed explanation of the reduction and processing procedure, see Goulding et al. (2012b).

Sources from our master catalog that lie within the field of view of an ObsID are identified, and events/photon information (position, energy, grade, and time) are extracted from a $30^{\prime\prime} \times 30^{\prime\prime}$ box centered on the input source for each associated ObsID. stackfast also determines the effective exposure time at the position of the input source for each ObsID, including the effects of vignetting at large angles from the pointing axis. The result is an output file containing a stackable X-ray event list and list of exposure times for each source in the master catalog, and associated ObsID.

Once the extraction of the stackable database is performed, the next step for stackfast is co-adding a specific subset of sources to yield average background-subtracted X-ray count rates and fluxes in user-defined energy bands. A key consideration is the variable point-spread function (PSF) for Chandra as a function of off-axis angle, which we characterize by the 90% energy-encircled radius⁹ (r₉₀). stackfast extracts photons within r₉₀ and assesses the background on a source-by-source basis, as variations in the PSF also affects background estimates. Local backgrounds are measured by masking high significance (wavdetect threshold 10⁻⁷) sources that may be identified in the $30^{\prime\prime} \times 30^{\prime\prime}$ extraction boxes, and then rescaling the photon counts, in the remaining extraction area at radii larger than $1.3\times {r}_{90}$, to the source extraction area (within r₉₀). These local background measurements are co-added, and used to measure the signal-to-noise of the source stacks.

During the co-adding process, we exclude sources that lie within $5^{\prime\prime}$ of the pointing position of a particular ObsID because these sources may have been the subject of the proposed observation. The inclusion of these "proposed" sources would introduce a selection bias into the final X-ray stack. Furthermore, we also exclude input sources that are significant X-ray detections, fall on chip-gaps, or are positioned at large off-axis angles $\gt 6^{\prime}$ in a particular ObsID, as background estimation may be inaccurate or severely enhanced due to the large angular size of an X-ray point source ($\sim 5\mbox{--}7\buildrel{\prime\prime}\over{.} 5$ at E ∼1.5–7 keV). The final co-adding procedure is extremely efficient, and thus, readily allows bootstrap realizations to be performed to derive count rate uncertainties on the stacking measurements. In any given X-ray energy band, the final outputs from stackfast are average X-ray count rates within r₉₀, average X-ray backgrounds predicted within r₉₀, hardness ratios, and associated statistical uncertainties from 1000 bootstrap realizations. X-ray count rates are converted to fluxes assuming a power law with slope ${\rm{\Gamma }}=1.8$ and a Chandra ACIS-I response function from Cycle 9 (an average of the collation of observations used throughout our stacking).

Of the 50,794 spiral galaxies in the ${M}_{* }\mbox{--}z$ sub-samples, 468 (∼1%) of the sources are within 6' of the pointing position of at least one Chandra ACIS-I observation, and also are not on chip-gaps or close ($\lt 5^{\prime\prime}$) to the pointing position. There are 101 galaxies that we determine to have significant (3σ) X-ray emission above the estimated local background that is close to the optical position. Each of the X-ray detected sources have centroids within $0\buildrel{\prime\prime}\over{.} 9$ of the optical position, with a median offset of ${\delta }_{{\rm{X}}-{\rm{O}}}\sim 0\buildrel{\prime\prime}\over{.} 26$. This results in a sample of 367 X-ray undetected galaxies that are included as part of our stacking analysis in Section 3.

The majority of BHs residing at galaxy centers are in a low-Eddington state (${\lambda }_{\mathrm{Edd}}={L}_{\mathrm{AGN}}/{L}_{\mathrm{Edd}}\lesssim {10}^{-3}$), and thus, their subsequent AGN emission would fall substantially below the detection threshold of a typical extragalactic survey. Our primary goal is to harness the power of X-ray stacking to ascertain the average X-ray luminosity (in a given energy band) produced due to accretion onto the vast-majority of BHs, not only the BHs accreting above a substantial fraction of Eddington, and subsequently ask how this average accretion rate relates to the existence of a large-scale bar.

Using stackfast, we perform an X-ray stacking analysis (described in Section 2.2) on our spiral galaxy sample based on their perceived bar properties. Given the known scaling relations between the stellar content and the masses of BHs (e.g., McConnell & Ma 2013; Reines & Volonteri 2015), we statistically negate the effects of changing X-ray luminosities and Eddington ratios, due to differing BH mass distributions, by stacking our parent sample in bins complete in both stellar mass and redshift, i.e., the ${M}_{* }\mbox{--}z$ sub-samples that we describe in Section 2. To also ensure that no one stack is biased in sensitivity compared to the other stacks, we used a K–S test to search for evidence of significant differences in the distribution of exposure times for the sources within the stacks. Based on the K–S statistic, we found no evidence for significant differences in the ${t}_{\exp }$ distributions when comparing the ${f}_{\mathrm{bar}}$ samples in a given ${M}_{* }-z$ bin. Furthermore, to prevent bias toward artifically high stacked luminosities due to significant individual detections, we do not include the X-ray bright sources, and defer their analysis to Section 3.2. In Figure 4, we present the results of the X-ray stacks performed in three energy bands (E = 0.5–2, 2–7, 0.5–7 keV) for our three ${M}_{* }\mbox{--}z$ sub-samples separated in bins of ${f}_{\mathrm{bar}}$.

Zoom In Zoom Out Reset image size

Detailed Chandra studies of nearby star-forming and passive galaxies have shown that in the absence of AGN activity, the X-ray emission from hot diffuse gas, young high-mass X-ray binaries, and older low-mass X-ray binaries correlates with the SFR and M_*, respectively (e.g., Gilfanov 2004; Revnivtsev et al. 2007). This X-ray emission produced due to X-ray binaries (${L}_{{\rm{X}},\mathrm{SF}}$) is an obvious source of contamination in our total X-ray stacked luminosity (${L}_{{\rm{X}},\mathrm{tot}}$). We estimate and statistically remove ${L}_{{\rm{X}},\mathrm{SF}}$ from ${L}_{{\rm{X}},\mathrm{tot}}$ by calculating the log-mean SFR and M_* of the stacked galaxy sample and invoking the local relations of Lehmer et al. (2010) and Pereira-Santaella et al. (2011). Specifically, in the 0.5–2 keV band, we use Equation (4) presented in Pereira-Santaella et al. (2011), and in the 2–7 keV band, we use the SFR-dependent relation log ${L}_{{\rm{X}}}=39.46+0.76$log SFR presented in Lehmer et al. (2010), and linearly combine both ${L}_{{\rm{X}},\mathrm{SF}}$ predictions in the 0.5–7 keV. Both Lehmer et al. (2010) and Pereira-Santaella et al. (2011) invoke a Kroupa (2001) initial mass function to compute M_* and SFRs in their models, this is consistent with assumptions used for the SDSS M_* and SFR measurements taken from Brinchmann et al. (2004). After subtraction of the average ${L}_{{\rm{X}},\mathrm{SF}}$ in the relevant bands, we produce clean average X-ray luminosities due to BH accretion¹⁰ (${L}_{{\rm{X}},\mathrm{AGN}}={L}_{{\rm{X}},\mathrm{tot}}-{L}_{{\rm{X}},\mathrm{SF}}$). We observe average X-ray luminosities of ${L}_{{\rm{X}},\mathrm{AGN}}\sim (0.1\mbox{--}2)\times {10}^{40}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$ for the stacked samples. The stacks have typical S/Ns of ∼5–10 calculated using the stacked counts within the r₉₀ region, and the predicted counts within r₉₀ using stacked local backgrounds (see Section 2.2. These results are presented in Table 1 for the three energy ranges considered here.

In Figure 4, we show that within a given redshift bin there is no significant difference (at the 90% level) between the average ${L}_{{\rm{X}},\mathrm{AGN}}$ for barred (${f}_{\mathrm{bar}}\gt 0.25$), non-barred (${f}_{\mathrm{bar}}\lt 0.1$), and ambiguously barred (${f}_{\mathrm{bar}}=0.1\mbox{--}0.25$) spiral galaxies in SDSS-GZ2. We further tested this result by selecting a sample of galaxies over the full redshift range, $0.01\lt z\lt 0.13$, within a relatively small stellar mass range of ${M}_{* }\sim (3\mbox{--}10)\times {10}^{10}\,{M}_{\odot }$, and performed an additional stacking analysis. This sample included 58 barred, 36 ambiguously barred, and 72 non-barred galaxies. We again found no statistical difference between the average ${L}_{{\rm{X}},\mathrm{AGN}}$ in any of the three energy ranges. Additionally, if ${N}_{{\rm{H}}}$ were playing a significant role in our findings, then we would expect such a result to manifest in the hardest energy band. However, we find no significant difference between bars and non-barred galaxies in any of the three X-ray energy ranges, suggesting that our result is independent of obscuration effects.

While independent of the presence of a bar, we also find in Figure 4 a trend of increasing ${L}_{{\rm{X}},\mathrm{AGN}}$ with z. While the ${f}_{\mathrm{bar}}$ samples within a particular redshift bin are matched in SFR and M_*, they are systematically different between the redshift bins. Galaxies at higher-z have systematically higher M_* in our sample due to the limiting magnitude of SDSS. Due to the known relation between M_* and ${M}_{\mathrm{BH}}$, a systematically larger M_* at a given z will produce a higher average ${L}_{{\rm{X}},\mathrm{AGN}}$ in each redshift bin.¹¹ We show in the upper panel of Figure 4 that when ${L}_{{\rm{X}},\mathrm{AGN}}$ is normalized by average M_* between the redshift bins, the resultant specific accretion rate is independent of redshift in each energy range. Thus, we can robustly conclude that there is no obvious positive effect between the average X-ray luminosity associated with BH accretion and the presence of a large-scale bar in nearby spiral galaxies.

As part of our stacking analysis, we used forced photometry to additionally detect (${\rm{S}}/{\rm{N}}\gtrsim 5$) 101 (out of the 468 optical galaxies) X-ray point-sources that were spatially coincident (median offset of $0\mathop{.}\limits^{\prime\prime }26$) with the optical nuclear position of the galaxies. While each X-ray source is presumed to be an AGN, X-ray emission from circumnuclear star formation could still contribute to the measured X-ray flux. Hence, we remove this contamination following the same procedure used in the stacks. The X-ray detected AGNs in our sample have derived luminosities of ${L}_{{\rm{X}},0.5\mbox{--}7\mathrm{keV}}\sim 9\times {10}^{38}$–$5\times {10}^{43}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$, similar to X-ray luminous AGNs identified in detailed studies of local ($D\lesssim 50$ Mpc) galaxies (e.g., LaMassa et al. 2011).

We use the X-ray detected sources to further validate our stacking results found in the previous section by producing an average stack that includes both the detected and undetected X-ray sources. We exclude the 16 AGNs with ${L}_{{\rm{X}},0.5\mbox{--}7\mathrm{keV}}\gt {10}^{42}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$, which form the higher luminosity tail of the AGN distribution in these sources, and then stack all (X-ray detected and undetected) sources observed with sufficient depth to detect an AGN if it were to have had ${L}_{{\rm{X}}}\gt {10}^{42}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$. This has the added effect of removing sources from the stack with extremely shallow X-ray observations. With the inclusion of the detected sources, we observed marginally higher (∼0.17–0.26 dex) ${L}_{{\rm{X}},\mathrm{AGN}}$ in the stacked luminosities when compared to the measurements presented in Table 1. However, crucially, we still found no significant difference in the average ${L}_{{\rm{X}},\mathrm{AGN}}$ between the ${f}_{\mathrm{bar}}$ sub-samples when including the X-ray detected sources.

We find that the detected X-ray AGN luminosities are, in general, at or above the stacked luminosities, suggesting that the stacks are measuring the peak of the luminosity distribution of the overall population, and the detected sources are populating a high-Eddington tail of the accretion rate distribution. In Figure 5, we present the specific accretion rate (${L}_{{\rm{X}}}/{M}_{* }$) distributions for the X-ray detected (at 0.5–7 keV) barred, ambiguous, and unbarred SDSS-GZ2 galaxies. Consistent with our finding of no dependence of average accretion rate on the presence of a bar, we also show that there is no difference between the specific accretion rates between barred and non-barred galaxies for the X-ray detected AGNs either (two-sample KS reveals $P\sim 0.73$).

Zoom In Zoom Out Reset image size

Differences between fueling of BHs due to the presence of a bar may only become apparent when considering the most rapidly growing BHs in the sample. Hence, we further investigated whether increasing thresholds in X-ray luminosity, i.e., higher accretion rates, would produce differences in the tails of the specific accretion rate distributions for the galaxies in our sample. Applying cuts in X-ray luminosity of ${L}_{{\rm{X}}}\gt {10}^{41}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$ and ${L}_{{\rm{X}}}\gt {10}^{42}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$, we find that the peak of the distributions for barred and non-barred galaxies shifts toward higher specific accretion rates. However, we show in Figure 5 that these peaks and the overall distributions remain statistically the same between the barred and non-barred systems, irrespective of the L_X cuts. There is extremely marginal evidence for an upturn at the highest specific accretion rates probed by our sample (${L}_{{\rm{X}}}/{M}_{* }\gt {10}^{32}\,\mathrm{erg}\,{{\rm{s}}}^{-1}\,{M}_{\odot }^{-1}$) for the barred galaxies, though this is within the statistical uncertainties of the sample.

Taken together, we find no statistical evidence for a difference in the specific accretion rate distributions of BHs present in barred or non-barred galaxies. Thus, even over long ∼Gyr timescales, a large-scale bar appears to have no effect on the growth of the central BH in a spiral galaxy.