Characterizing Bars at z~0 in the optical and NIR Implications for the Evolution of Barred

Draft version February 5, 2008
A Preprint typeset using L TEX style emulateapj v. 25/04/01
CHARACTERIZING BARS AT Z ～ 0 IN THE OPTICAL AND NIR: IMPLICATIONS FOR THE EVOLUTION OF BARRED DISKS WITH REDSHIFT
Irina Marinova1 , Shardha Jogee1
marinova@https://www.sodocs.net/doc/7014517747.html,, sj@https://www.sodocs.net/doc/7014517747.html, Draft version February 5, 2008
arXiv:astro-ph/0608039v2 27 Dec 2006
ABSTRACT Critical insights on galaxy evolution stem from the study of bars. With the advent of high redshift HST surveys that trace bars in the rest-frame optical band out to z ～ 1, it becomes increasingly important to provide a reference baseline for bars at z ～ 0 in the optical band. We present results on bars at z ～ 0 in the optical and near-infrared bands, based on 180 spirals in the OSUBSGS survey. (1) The deprojected bar fraction at z ～ 0 is fNIR1 ～ 60% ± 6% in the near-infrared H band, and foptical1 ～ 44% ± 6% in the optical B-band images. The latter likely miss bars obscured by dust and star formation. (2) The results before and after deprojection are similar, which is encouraging for high redshift studies that forego deprojection. (3) Studies of bars at z ～ 0.2–1.0 (lookback times of 3–8 Gyr) have reported an optical bar fraction of foptical2 ～ 30% ± 6%, after applying cuto?s in absolute magnitude (MV <-19.3), bar size (abar ≥ 1.5 kpc), and bar ellipticity (ebar ≥ 0.4) in order to ensure a complete sample, adequate spatial resolution, and reliable bar identi?cation out to z ～ 1. Applying these exact cuto?s in magnitude, bar size, and bar ellipticity to the OSUBSGS data yields a comparable optical B-band bar fraction at z ～ 0 of foptical3 ～ 34% ± 6%. This rules out scenarios where the optical bar fraction in bright disks declines strongly with redshift. (4) We investigate bar strengths at z ～ 0 using the maximum bar ellipticity (ebar ) as a guide. Most (～ 70%) bars have moderate to high ellipticity (0.50 ≤ ebar ≤ 0.75), and only a small fraction (7%–10%) have 0.25 ≤ ebar ≤ 0.40. There is no bimodality in the distribution of ebar . The H-band bar fraction and ebar show no substantial variation across RC3 Hubble types Sa to Scd. (5) RC3 bar types should be used with caution. Many galaxies with RC3 types ‘AB’ turn out to be unbarred and RC3 bar classes ‘B’ and ‘AB’ have a signi?cant overlap in ebar . (6) Most (68% in B and 76% in H) bars have sizes below 5 kpc. Bar and disk sizes correlate, and the ratio (abar /R25 ) lies primarily in the range 0.1 to 0.5. This suggests that the growth of bars and disks is intimately tied. Subject headings: galaxies: fundamental parameters — galaxies: structure — galaxies: kinematics and dynamics — galaxies: evolution
1. introduction
Stellar bars are recognized as the most important internal factor that redistributes the angular momentum of the baryonic and dark matter components of disk galaxies (e.g., Weinberg 1985; Debattista & Sellwood 1998, 2000; Athanassoula 2002; Berentzen, Shlosman, & Jogee 2006), thereby driving their dynamical and secular evolution. Bars e?ciently drive gas from the outer disk to the central few hundred parsecs and are observed to feed central starbursts in local galaxies (Elmegreen 1994; Knapen et al. 1995; Hunt & Malakan 1999; Jogee et al. 1999; Jogee, Scoville, & Kenney 2005). It remains a matter of contention whether large-scale bars relate to AGN activity in galaxies, given the reduction by several orders of magnitude needed in the speci?c angular momentum of gas before it can feed a central black hole, and con?icting observational results (see review by Jogee 2006 and references therein; also Mulchaey & Regan 1997; Knapen et al. 2000; Laine et al. 2002; Laurikainen et al. 2004). In several galaxies, bar-driven gas in?ows appear intimately tied to the formation of disky, high v/σ stellar components in the inner kpc, or ‘pseudobulges’ (Kormendy 1993; Jogee 1999; review by Kormendy & Kennicutt 2004; Jogee, Scoville, & Kenney 2005; Athanassoula 2005). Furthermore, the orbital structure of bars can lead to the ob1 2
served peanut-shaped and boxy bulges in inclined galaxies (Combes et al. 1990; Pfenniger & Norman 1990; Bureau & Athanassoula 2005; Athanassoula 2005; MartinezValpuesta et al. 2006; Debattista et al. 2006). Earlier Hubble Space Telescope (HST ) studies at optical wavelengths (e.g., Abraham et al. 1999) reported a paucity of stellar bars and a sharply declining optical bar fraction at intermediate redshifts z > 0.5. Studies at nearinfrared (NIR) wavelengths also found a low bar fraction, but the authors rightly concluded that the large e?ective point spread functions (PSFs) of the NIR camera only allowed the detection of large bars whose semi-major axes exceeded 0.9′′ , corresponding to 7.2 kpc2 at z ～ 1.0 (Sheth et al. 2003). Recent works based on large optical surveys have now demonstrated the abundance of bars at intermediate redshifts z ～ 0.2–1.0, corresponding to lookback times of 3–8 Gyr (Elmegreen et al. 2004; Jogee et al. 2004; Zheng et al. 2005; Sheth et al. in preparation). The fundamental issue of how robust bars are, and the associated implications for bar-driven evolution in disks over the last 10 Gyr, remains open (e.g., Jogee et al. 2004; Shen & Sellwood 2004; Athanassoula, Lambert, & Dehnen 2005; Bournaud et al. 2005; Berentzen, Shlosman, & Jogee 2006; Berentzen & Shlosman 2006; Martinez-Valpuesta et al. 2006; Debattista et al. 2006). In order to put bars in a cosmological context, it now
Department of Astronomy, University of Texas at Austin, 1 University Station C1400, Austin, TX 78712-0259 We assume in this paper a ?at cosmology with ?M = 1 ? ?Λ = 0.3 and H0 =70 km s?1 Mpc?1 .
1

2 behooves us to characterize the frequency and impact of bars by applying the same quantitative methods to large samples at z ～ 0 and at higher redshifts. Spurred by these considerations, we characterize in this paper the frequency and structural properties of bars in the local Universe at optical and NIR wavelengths, by ellipse-?tting the B and H images of the OSU Bright Spiral Galaxy Survey (OSUBSGS; Eskridge et al. 2002) of 180 spirals. The ?rst goal of this study is to provide quantitative characterizations of the bar fraction fbar (de?ned as the fraction of disk galaxies that are barred) and structural properties (sizes, ellipticities, etc.) of bars at z ～ 0, as a function of wavelength, Hubble types, and host galaxy properties. Furthermore, with the advent of high redshift HST surveys, such as the Tadpole ?eld (Tran et al. 2003), the Galaxy Evolution from Morphology and SEDs (GEMS; Rix et al. 2004), the Great Observatories Origins Deep Survey (GOODS; Giavalisco et al. 2004), and COSMOS (Scoville et al. 2006), which trace bars in the rest-frame optical band out to z ～ 1, it becomes increasingly important to provide a reference baseline for bars at z ～ 0 in the optical band. Thus, a second goal of our study is to provide a rest-frame optical z ～ 0 point for bars based on ellipse ?ts, in order to directly compare with studies of intermediate-redshift bars (Jogee et al. 2004; Elmegreen et al. 2004; Zheng et al. 2005; Sheth et al. in preparation) that also use ellipse ?ts. In particular, we use in this paper the same procedure of ellipse ?ts (§ 3.1) and the same quantitative characterizations (§ 3.3) of bars that were applied by Jogee et al. (2004) to bars at intermediate redshifts (z ～ 0.2–1.0) in the GEMS survey. Several studies have used the OSUBSGS to gauge bars in the local Universe (e.g., Eskridge et al. 2000; Block et al. 2002; Whyte et al. 2002; Buta et al. 2005), but they di?er signi?cantly from our study and cannot meet our two goals. Eskridge et al. (2000) visually classi?ed bars in the H band, and in the B band, they used the Third Reference Catalog of Bright Galaxies (de Vaucouleurs et al. 1991; hereafter RC3) visual bar classes. Such visual classi?cations form an invaluable ?rst step, but by de?nition, are subjective and di?cult to compare with results from other studies. Block et al. (2002) and later Buta et al. (2005) applied the gravitational torque Qb method, based on Fourier amplitudes, to H-band images of 163 and 147 OSUBSGS galaxies, respectively. This quantitative method is less subjective than visual classi?cation, but the results of Block et al. (2002) and Buta et al. (2005) cannot be compared to intermediate redshift studies for two reasons. First, the latter studies were based on the HST Advanced Camera for Surveys (ACS) data and trace the restframe optical properties of bars, while Block et al. (2002) and Buta et al. (2005) deal with the rest-frame NIR. Second, it is non-trivial to derive Qb for intermediate-redshift galaxies because of resolution and signal-to-noise limitations. Whyte et al. (2002) ?tted ellipses to B-band images of only 89 of the 180 OSUBSGS galaxies, and do not provide a distribution of bar properties as a function of Hubble type. Our present study complements these existing studies by ellipse ?tting B-band and H-band images of all 180 OSUBSGS galaxies, and performing a comprehensive, statistically signi?cant analysis of barred galaxies in the local Universe. It complements the ongoing analysis (Barazza, Jogee, & Marinova 2006) of local bars based on a sample of 5000 galaxies in the Sloan Digitized Sky Survey (SDSS). The outline of this paper is as follows. § 2 discusses the sample selection based on the OSUBSGS survey (Eskridge et al. 2002). § 3 describes the ellipse-?tting method, the criteria used for identifying bars, and deprojection of images and pro?les to face-on. In § 4.1–4.4, we present results on the bar fraction at z ～ 0, its dependence on Hubble type, the distribution of bar sizes and strengths as characterized by ellipse-?tting, and the variation of bar properties along the Hubble sequence. Results are presented both before and after deprojection to face-on. In § 4.5, we present a ?rst-order comparison of the bar fraction and properties at z ～ 0 from OSUBSGS to those derived at z ～ 0.2–1.0 or lookback times of 3–8 Gyr from GEMS (Jogee et al. 2004) and the Tadpole ?eld (Elmegreen et al. 2004). In § 4.6, we discuss the constraints set by our results for theoretical models addressing the robustness of bars, and the assembly of the Hubble sequence over cosmological times. § 5 presents the summary and conclusions. This paper is the ?rst in a series of three based on the OSUBSGS. Paper II (Marinova et al. in prep) will address the bulge properties and activity of barred and unbarred galaxies in the OSUBSGS sample. In paper III, we will present simulations that arti?cially redshift the rest-frame optical and NIR images of the local OSUBSGS sample out to z ～ 1–2, in order to assess the impact of redshiftdependent systematic e?ects on the recovery rate of bars in surveys conducted by current and future facilities in the optical and IR, such as the planned Wide Field Camera 3 (WFC3) and the James Webb Space Telescopes (JWST).
2. data and sample
The OSUBSGS targets local spiral galaxies that are taken from the RC3 catalog and chosen to represent the bright disk galaxy population in the local universe (Eskridge et al. 2002). The galaxies are selected using the following criteria: RC3 type of S0/a or later, (0≤ T ≤9), MB < 12, D25 < 6′ .5, and ?80? < δ < +50? (Eskridge et al. 2002), and are imaged in the B, V , R, H, J, and K bands. The B and H images of 182 OSUBSGS galaxies are available as part of a public data release (Eskridge et al. 2002). Our starting sample (sample S1) consists of the afore-mentioned 182 OSUBSGS galaxies with B and/or H images. After discarding galaxies (2 galaxies or 1% of sample S1) that do not have images in both the B and H bands, we are left with sample S2 of 180 galaxies imaged in both bands. This constitutes the sample of galaxies to which we ?tted ellipses in order to characterize bars and disks, as outlined in § 3.
3. method for characterizing bars and disks
We adopt the widely used procedure of characterizing bars and disks in galaxies via ellipse ?ts (e.g., Wozniak et al. 1995, Friedli et al. 1996; Regan et al. 1997; Mulchaey & Regan 1997; Jogee et al. 1999, 2002a,b, 2004; Knapen et al. 2000; Laine et al. 2002; Sheth et al. 2003; Elmegreen et al. 2004), as described in detail in § 3.1. Our analysis procedure is schematically illustrated in Figure 1 and described in sections 3.1 to 3.4.

3 3.1. Ellipse Fitting We start with the sample S2 of 180 galaxies imaged in both the B and H bands (Fig. 1). We ?rst remove stars from the B- and H-band images of each galaxy by replacing them with the average of the sky background using a circular aperture. We then ?nd the center of the galaxy using the IRAF routine ‘imcenter’. We determine a maximum galaxy semi-major axis length (amax ) out to which ellipses will be ?tted in each image by ?nding out where the galaxy isophotes reach the sky level. We then use the standard IRAF task ‘ellipse’ to ?t ellipses to each image out to amax . We employ an iterative wrapper developed by Jogee et al. (2004) to run ‘ellipse’ up to to 300 times for each object in order to get a good ?t across the whole galaxy. A successful ?t is one where the routine is able to ?t a ellipse at each radial increment from the center until it reaches amax . When using the iraf task ’ellipse’ for ellipse ?ts, the goodness of the best ?t is measured by four harmonic amplitudes (A3, A4, B3, B4), which describe by how much the actual isophote differs from the best-?tting ellipse (e.g., Jedrzejewski 1987). We have inspected plots of these residuals for representative strongly and weakly barred galaxies (e.g., NGC 4314, NGC 613, NGC 1187, NGC 0210, NGC 1300, NGC 7479, NGC 5701, NGC 4643, NGC 4548, NGC 4450, NGC 3681, NGC 3275, NGC 1703, and NGC 1358). We ?nd that the A3 and B3 residuals are small, typically on the order of a few percent. Values for the A4 and B4 residuals typically range from 2% to 10%, and do not exceed 15%. From the ?nal ?t for each galaxy, we generate radial pro?les of surface brightness (SB), ellipticity (e), and position angle (PA). The ?tted ellipses are over-plotted onto the galaxy images to generate overlays. Examples of the radial plots and overlays are shown in Figures 2, 4, and 5. For each galaxy, an interactive visualization tool (Jogee et al. 2004) is used to display both the radial pro?le and the overlays in order to perform an extra inspection of the ?ts. Of the 180 galaxies in sample S2, 179 (99%) and 169 (94%) were successfully ?tted in the H and B band, respectively. Of the 11 galaxies that could not be ?tted in the B band, ?ve had strong morphological distortions and seem to be interacting; one had a very bright, saturated star with leakage; and ?ve had no clearly de?ned center. The latter ?ve galaxies were all of later Hubble type (Sbc and Sc), and had very ?at or irregular surface brightness pro?les in the B band. Further analyses to characterize inclined, unbarred, and barred disks in § 3.2 were then restricted to the sample S3 of 169 galaxies with successful ?ts in both the B and H bands (Fig. 1). 3.2. Identifying and excluding highly inclined spirals For sample S3, we use the B-band images, rather than the H-band images, to identify and characterize the outer disk because the former are deeper and trace the disk farther out. From the radial pro?les generated by ellipse?tting the B-band image, we measure the ellipticity (edisk ) and PA (PAdisk ) of the outer disk. The outer disk inclination, i, is derived from edisk using cos(i) = (1 - edisk ). Of the 169 galaxies in sample S3, we ?nd 33 (20%) galaxies with disk inclination i > 60? and classify them as ‘inclined’. They are listed in the lower part of Table 1. Figure 2 shows an example of the B-band radial pro?le and ellipse overlays for an inclined galaxy. We only use the ?nal sample S4 (Fig. 1) of 136 moderately inclined (i < 60? ) spirals to further characterize the properties of bars (e.g., size, ellipticity, frequency) and disks in § 3.3–3.4. Such an inclination cuto? is routinely applied in morphological studies because projection e?ects make it very di?cult to reliably trace structural features in a galaxy that is close to edge-on. The exclusion of highly inclined galaxies does not bias the distribution of Hubble types, as shown in Figure 3a, where the Hubble types of samples S3 and S4 are compared. The absolute V -band magnitudes (MV ) of both sample S3 and S4 cover the range -18 to -23, with most galaxies lying in the range MV ～ -20 to -22 (Fig. 3b). 3.3. Characterizing bars and disks before deprojection In § 3.4, we use the deprojected radial pro?les of (SB, e, PA) to characterize the intrinsic properties of bars and disks in sample S4. However, we also decide to ?rst perform the analysis on the observed radial pro?les before deprojecting them to face-on. There are several reasons for this dual approach of deriving bar properties both before and after deprojection. First, it is useful to have bar properties (e.g., frequency, strength as characterized by ellipse?tting, size) prior to deprojection to compare directly to studies at intermediate redshifts (Jogee et al. 2004, Elmegreen et al. 2004, Zheng et al. 2005), where deprojection is not done for several reasons, including the di?culty in accurately measuring the PA of the line of nodes and the inclination of the outer disk in noisy images of distant galaxies. Second, by having bar properties both before and after deprojection, we are able to assess whether deprojection makes a substantial di?erence to the statistical distributions of bar properties. A large di?erence would raise concerns for intermediate redshift studies or even for large nearby studies where deprojection is often not carried out. For sample S4, we use the observed radial pro?les of (SB, e, PA) and the ellipse overlays to classify galaxies as ‘unbarred’ (Fig. 4) or ‘barred’ (Fig. 5), according to the following quantitative criteria. A galaxy is classi?ed as barred if the radial variation of ellipticity and PA follows the behavior that is expected based on the dominant orbits of a barred potential. Speci?cally the following conditions must be satis?ed before a galaxy is deemed to be barred: (1) The ellipticity, e, increases steadily to a global maximum, ebar , greater than 0.25, while the PA value remains constant (within 10? ). This criterion is based on the fact that the main bar-supporting orbits, namely the ‘x1 ’ family of orbits, can be modeled by concentric ellipses with a constant PA as a function of radius in the bar region (Athanassoula 1992a). The requirement that the PA must remain constant in the bar region is important for excluding other spurious elliptical features that may mimic a bar signature in their ellipticity pro?le. (2) Then, at the transition from the bar to the disk region, the ellipticity, e, must drop by at least 0.1, and the PA usually changes. This criterion is justi?ed by the fact that we expect a transition from the highly eccentric x1 orbits near the bar end to the more circular orbits in the disk. We also note that the drop in ellipticity by 0.1 at the transition from bar to disk has been shown to work well in identifying bars (e.g.,

4 Knapen et al. 2000; Laine et al. 2002; Jogee et al. 2002a, 2002b, 2004). What are the limitations of criteria (1) and (2) in identifying bars? We note that the ‘constant PA’ criterion that we use to identify bars may cause us to miss some weak bars at optical wavelengths due to the following reason. In weak bars, the shock loci and corresponding dust lanes on the leading edge of the bar are curved (Athanassoula 1992b). In optical images of weak bars, these curved dust lanes may cause the PA to twist or vary slightly along the bar, thereby preventing the ‘constant PA’ criterion from being met. In the case of very strong bars, the ‘constant PA’ criterion is a good one and isophotal twist is not an issue, because such bars have strong shocks and straight dust lanes along their leading edges (Athanassoula 1992b). In order to gauge how many bars we might be missing because of the ‘constant PA’ criterion, we identify galaxies that show a PA twist accompanied by an ellipticity maximum. It turns out that only a small fraction (～ 7%) of galaxies show this e?ect. We also note that criterion (1) requires the peak ellipticity (ebar ) over the PA plateau to be greater than 0.25 before we call a feature a bar. We picked 0.25 for the practical reason that structures with lower ellipticities are quite round and not always readily distinguishable from disks. Nonetheless, one may be tempted to ask whether we would ?nd more bars if this arbitrary limit of 0.25 were to be lowered, and whether there is a population of lowellipticity (e.g., ebar ～ 0.10–0.25) bars that we might miss. We investigated this question using the OSUBSGS sample, and ?nd that there is no increase in the number of bars if the limiting value for ebar in criterion (1) were to be lowered from 0.25 to 0.10. The reason for this becomes clear later, in Figure 13, which shows that the number of bars already starts to drop rapidly for ellipticities below 0.40, such that by the time we reach ebar of 0.25, we are already probing the tail end of bar distributions. In addition to classifying galaxies as ‘barred’ and ‘unbarred’, we also use the radial pro?les to derive the structural properties of the bar and disk. Speci?cally, for all galaxies, we measure the ellipticity, PA, and semi-major axis of the outer disk (edisk , PAdisk , adisk ). For galaxies classi?ed as ‘barred’, we also measure the maximum ellipticity (ebar ), the PA, and the semi-major axis of the bar. We will discuss in § 4.3 how the maximum bar ellipticity (ebar ) constrains the bar strength. Here, we discuss the question of how to locate the end of the bar in order to measure the bar semi-major axis. There has been some discussion in the literature as to whether the bar end should be de?ned as the radius (abar ) where the bar ellipticity is a maximum, or as the radius where the PA changes abruptly at the transition from the bar to the disk. From a theoretical perspective, several early simulations (e.g., Athanassoula 1992a; O’Neill & Dubinski 2003) show that the de?nition of bar length based on ‘peak ellipticity’ can underestimate the true extent of the bar. Recently, Martinez-Valpuesta, Shlosman, & Heller (2006) have performed a systematic study of the radius (abar ) of maximum bar ellipticity and the bar length. They show that there is a very good correspondence between two independent methods to determine the bar size: ellipse ?tting and orbital analysis. The orbital analysis has involved ?nding the largest (Jacobi) energy x1 orbit in the bar that is still stable. The ellipse ?tting becomes better if the size of the bar is given by the radius where the ellipticity declines by 15% from its maximal value. In his empirical study of bar sizes using ellipse ?ts, Erwin (2005) argues that using the PA signature to de?ne the bar size provides an upper limit, and that the two measures of bar length are very well correlated. However, he ?nds that it is harder to unambiguously measure the bar size from the PA criterion and that the de?nition of bar size based on peak ellipticity is more readily applied consistently to a large number of di?erent galaxy morphologies (Erwin 2005). In this study, we have adopted the ?rst approach. We use the semi major axis (abar ) where the maximum bar ellipticity occurs as a measure of the bar length. We caution that this may underestimate the bar length in some galaxies. However, a visual comparison of abar with the images of our galaxies suggests that abar does a reasonable job in most cases. 3.4. Characterizing bars and disks after deprojection For sample S4, we use the inclination, i, and the PA of the outer disk (determined in § 3.2) to analytically deproject the observed H and B band radial pro?les of (e, PA) to face-on. We perform the analytical deprojection using a code developed by Laine et al. (2002) and used previously in Laine et al. (2002) and Jogee et al. (2002a,b). It should be noted that the deprojection formula used in the code only strictly applies to in?nitesimally thin structures, and may be inaccurate near the galaxy center in the vicinity of the bulge. However, it is a reasonable approximation in the region of interest where large-scale bars reside. Figure 6 shows an example of the deprojected radial pro?les of NGC 4548 in the B and H bands overlaid on the observed pro?les. We note that the process of analytically deprojecting the radial pro?les to face-on after ellipse-?tting the observed (i.e, un-deprojected) images is analogous to the process of ?rst deprojecting the observed images to face-on, and then ellipse-?tting the deprojected images in order to generate face-on radial pro?les. The two methods should yield the same results unless the images are very noisy. We veri?ed this expectation with the following steps. (1) We deproject the images of several galaxies using the Multichannel Image Reconstruction, Image Analysis and Display (MIRIAD) routine ‘deproject’. The routine takes as input the observed image, the galaxy center, the inclination i and PA of the outer disk, and outputs the deprojected image; (2) We then ?t ellipses to these deprojected images using the procedure outlined in § 3.1, and generate face-on radial pro?les of SB, e, and PA; (3) These faceon radial pro?les generated from the deprojected images, are compared with the deprojected radial pro?les derived analytically from the the observed pro?le. There is good agreement in all cases, showing that we are not noise limited. This is illustrated in Figure 7 for the B band image of NGC 4548. The observed and deprojected images are shown in the left panel. In the right panel, three radial pro?les are plotted: the observed radial pro?le derived by ?tting ellipses to the observed image is plotted as stars; the deprojected radial pro?le derived analytically from the ob-

5 served pro?le is plotted as squares; and the face-on radial pro?le derived by ?tting ellipses to the deprojected image is plotted as triangles. There is good agreement between the squares and the triangles. The deprojected pro?les provide an accurate characterization of the ‘intrinsic’ or face-on properties of disks and bars. For all galaxies in S4, we therefore use the analytically deprojected B and H radial pro?les to classify galaxies as ‘barred’ or ‘unbarred’, according to the criteria outlined in § 3.3. We also re-measure the bar ellipticity (ebar ), semi-major axis (abar ), and disk size adisk from the deprojected radial pro?le. In the rest of this paper, many of these deprojected quantities will be compared to those derived before deprojection (§ 3.3) in order to gauge the impact of deprojection.
4. results and discussions
4.1. The optical and NIR bar fraction at z ～ 0 Table 2 and Figure 8 show the bar fraction (de?ned as the fraction of spiral galaxies that are barred) for the B and H bands, both before (§ 3.3) and after deprojection (§ 3.4). The results are based on sample S4 of 136 moderately inclined (i < 60? ) spirals (§ 3.2). The sample is dominated by galaxies with MV ～ -20 to -22. We ?nd a deprojected bar fraction of 60% in the H band and a lower fraction of 44% in the B-band images, which likely miss bars obscured by dust and star formation. Our results that 60% of spirals are barred in the infrared con?rms the preponderance of bars among spirals in the local Universe. Our H-band bar fraction of ～ 60% is in agreement with the NIR bar fraction of 59% (Menendez-Delmestre et al. 2006) based on 2MASS. It is also consistent, within a margin of 12%, with the results of Eskridge et al. (2000), who visually inspected the OSUBSGS H-band images and reported an overall H-band bar fraction of 72%, with 56% of spirals hosting ‘strong’ bars and 16% hosting ‘weak’ bars. Why is there a 12% deviation? The Eskridge et al. (2000) paper does not give ‘barred’ or ‘unbarred’ classi?cations for individual galaxies, so we can not make a case by case comparison with that study. However, in a subsequent paper, Eskridge et al. (2002) give visual classi?cations of individual galaxies as barred or unbarred, and classify barred systems as ‘SB’ (strongly barred) and ‘SAB’ (weakly barred). We ?nd that our classi?cations as barred or unbarred disagree on 25 galaxies in the B band (～ 18% of sample S4), and 23 galaxies in the H band (～ 17% of sample S4). Of the galaxies in the B band and H band where we di?er, we ?nd that the majority (15 of the 25 galaxies in the B band, and 11 of the 23 galaxies in the H band) are classi?ed as ‘SAB’ (weakly barred) by Eskridge et al. (2002). We conclude that, as might be intuitively expected, the di?erences between visual and quantitative classi?cations of bars are strongest for systems that visually appear as ‘weakly barred’. How does our study compare with other quantitative studies? We ?nd that our reported H-band bar fraction of 60% agrees with that of Laurikainen et al. (2004), who used Fourier modes and the Qb method for 158 galaxies in the OSUBSGS sample and 22 2MASS galaxies. Laurikainen et al. (2004) ?nd a NIR bar fraction of 62% for galaxies with i < 60? . We present a more detailed comparison of our bar ellipticity and fraction with other studies
in § 4.3. Another important result is that deprojection does not make any signi?cant changes to the global bar fraction, when dealing with the fairly large OSUBSGS sample. As shown by Table 2 and Figure 8, the B- and H-band bar fractions are 45% and 58% before deprojection, and change by only a factor of 0.97 and 1.03, respectively, after deprojection. We suggest several reasons for the small impact of projection e?ects. First, this study uses only moderately inclined (i < 60? ) galaxies where projection e?ects are less severe than in highly inclined systems. Second, projection e?ects produce large changes in the morphology of a galaxy only when the disk inclination, i, is signi?cant and the di?erence in PA between the bar and the disk major axes is close to 90? . From a statistical point of view, these two conditions are unlikely to occur simultaneously in a dominant fraction of the sample. These arguments are supported by Figures 9a and 9b, which show that the galaxy classes assigned prior to deprojection are in no way biased by the galaxy inclination, i: both barred and unbarred galaxies span a similar range in i. Furthermore, even the bar ellipticity ebar measured before deprojection is uncorrelated with i (Figs. 9c and 9d). The fact that the bar fraction in large samples is similar before and after deprojection is encouraging for large studies of bars at intermediate redshift (e.g., Jogee et al. 2004, Elmegreen et al. 2004, Zheng et al. 2005), where deprojection is not done because of the di?culty in accurately measuring the PA of the line of nodes and the inclination of the outer disk in noisy images of distant galaxies. 4.2. Sizes of bars and disks at z ～ 0 As outlined in § 3.1, we use the semi major axis abar , where the bar ellipticity is a maximum, as a measure of the bar length. We caution that this may underestimate the bar length in some galaxies. However, a visual comparison of abar with the images of our galaxies suggests that abar does a reasonable job in most cases. The distributions of bar sizes or semi-major axes (abar ) before and after deprojection are shown for the B and H bands in Figure 10. Some bars do appear larger after deprojection, but from a statistical point of view, deprojection does not have a substantial e?ect on the bar size distribution. For example, the mean bar size in the H band before deprojection is 3.4 kpc and after deprojection it is 4.0 kpc. Sizes of large-scale bars in the local Universe lie in the range ～ 1 to 14 kpc, with most (68% in B and 76% in H ) bars having abar ≤ 5 kpc, and ～ 50% of them clustering with abar in the range 2 to 5 kpc. If such a distribution of bar sizes is present at a redshift z ～ 1, where 1′′ corresponds to 8.0 kpc, then only observations ′′ with angular resolutions superior to 0. 3 can adequately resolve the majority of bars. This is relevant for assessing the relative e?ectiveness of current NIR capabilities, such as NICMOS, and those of future planned missions, such as WFC3, in detecting high redshift bars in the NIR band over wide ?elds. In Figure 11, we plot the bar size versus the disk size before and after deprojection. The bar size is measured from the H band, whose low extinction enables more accurate measurement than in the optical. The disk is measured from the B-band image, which is deeper than the H band

6 and traces the disk further out (§ 3.2). Both before and after deprojection, we ?nd that bar and disk sizes are correlated with an average slope of ～ 0.9, albeit with a large scatter of several kpc in bar size at a given disk size. Figure 12 shows the observed bar semi-major axis distribution normalized to R25 (the radius in arcseconds of the isophote, where the surface brightness equals 25 mag arcsec?2 ) of the disk. R25 values are obtained from the Nearby Bright Galaxies Catalogue (Tully 1988; hereafter NBG), except for NGC 6753, 6782, 5078, 6907, 7814, and ESO 142-19, which are from the RC3. The ratio (abar /R25 ) lies primarily in the range 0.1 to 0.5 in both the H and B bands (Fig. 12). Only a minority of galaxies have larger values out to 0.95. These results are consistent with several smaller earlier studies. Laine et al. (2002) ?nd that the sizes of primary bars correlate with the host galaxy sizes and the (abar /R25 ) ratio lies primarily in the range 0.1 to 0.5. Menendez-Delmestre et al. (2004) ?nd an average (abar /R25 ) ratio of 0.35, on the basis of ellipse ?ts of 134 2MASS galaxies. In his study of bar lengths, based on ellipse ?ts of R-band images of 65 local early-type S0-Sab galaxies, Erwin (2005) ?nds a similar mean (abar /R25 ) ratio of 0.38 and reports a correlation between bar size and disk size. What do these results imply? From a theoretical standpoint, the size of the bar (abar ) depends on the concentration of matter in the disk and the distribution of resonant material that can absorb angular momentum from the bar (Athanassoula 2003). Furthermore, the prevalence of chaotic orbits between the 4:1 and the corotation resonance (CR) would naturally lead bars to end somewhere between the two resonances. If bars end very near the CR as is found observationally (e.g., Merri?eld & Kuijken 1995; Debattista et al. 2002; Aguerri et al. 2003), then our result that (abar /R25 ) is generally well below 1.0 suggests that the CR of disk galaxies lies well inside their R25 radius. Furthermore, the correlation between bar and disk sizes and the narrow range in (abar /R25 ) suggests that the growths of the bar and disk may be intimately tied. 4.3. Distribution of bar strengths as characterized by ebar at z ～ 0 The term ‘bar strength’ is not well de?ned in the literature. Various measures of bar strength are used and each measure has some bene?ts and trade-o?s. These measures include the Qb method (Block et al. 2002; Buta et al. 2003; Buta et al. 2005), the maximum ellipticity of the bar, bar/interbar contrasts, Fourier decomposition techniques (Elmegreen & Elmegreen 1985; Elmegreen et al. 1996), and visual estimates of strength (e.g., Martin 1995; Eskridge et al. 2000, 2002) gauged via eyeball inspection of images. The Qb method (Block et al. 2002; Buta et al. 2003; Buta et al. 2005) directly measures the gravitational torque exerted by the bar, but it measures the torque at only one point along the bar. The Qb method depends on the scale height of the disk and the ability to derive a reliable model for the potential using images. It is hard to apply this method to a large number of intermediate redshift galaxies due to resolution and signalto-noise limitations. In the bar/interbar contrast method used by Elmegreen & Elmegreen (1985) and Elmegreen et al. (1996), the bar strength is characterized by the ratio of the peak surface brightness in the bar region to the minimum surface brightness in the interbar region. The Fourier decomposition method also used by Elmegreen & Elmegreen (1985) and Elmegreen et al. (1996) is similar to the Qb method. It characterizes bar strength by measuring the relative amplitudes of the Fourier components of the bar. The maximum amplitude of the m=2 mode determines the strength of a bar. In studies where ellipse ?ts are used to characterize bars, the maximum ellipticity of the bar (ebar ) is used as a measure of bar strength (e.g., Athanassoula 1992a; Martin 1995; Wozniak et al. 1995; Jogee et al. 1999, 2002a,b; Knapen et al. 2000; Laine et al. 2002). One advantage of this approach is that the bar ellipticity can be estimated without making any assumptions about the mass to light ratio of the galaxy or its scale height. It can also be applied to local galaxies as well as galaxies out to intermediate redshifts (z ～ 0.2–1.0 ; Jogee et al. 2004, Elmegreen et al. 2004). There are also several theoretical reasons that support the use of the maximum bar ellipticity as a measure of bar strength. Shen & Sellwood (2004) compare bar strength in N-body simulations, as characterized by the m = 2 Fourier components and the peak ellipticity. They ?nd that the ellipticity is very well correlated to bar strength estimator A, where A is the relative amplitude of the bisymmetric (m = 2) Fourier component of the mass density averaged over a certain inner radial range where the bar dominates. In addition, from an observational standpoint, Laurikainen et al. (2002) ?nd that, on average, the gravitational torque, Qb , and ebar are correlated for ebar ≤ 0.6. For higher ebar values, the relation appears to ?atten out although the small number of galaxies precludes a ?rm conclusion. Nonetheless, if we deem that a measure of bar strength should give an indication of the gas in?ow rate that a bar drives via gravitational torques, then the maximum ellipticity of the bar (ebar ) is only a partial measure of the bar strength. Both the mass and shape of the bar in?uence the magnitude of the gravitational torque at each point along the bar. The peak bar ellipticity describes the shape of the bar, but does not directly measure its mass or luminosity. While bearing this caveat in mind, we use the maximum bar ellipticity ebar as a partial measure of the bar strength in this study. Figure 13 shows the observed and deprojected distributions of bar strength as characterized by ebar from ellipse?ts in the B (Figs. 13a,c) and H bands (Figs. 13b,d). It is striking that only a very small proportion (7% in B; 10% in H) of bars are very weak with 0.25 ≤ ebar ≤ 0.40, while the majority of bars (70% in B; 71% in H) have moderate to high strengths as characterized by ebar , with 0.50 ≤ ebar ≤ 0.75. This point is further illustrated in Figure 14, which is a generalized plot of the fraction of disks with ‘strong’ and ‘weak’ bars. It shows how the fraction of spiral galaxies that host bars with ellipticities (ebar > e1 ) changes as we vary e1 . As we increase e1 from 0.35 to 0.45, 0.55, and 0.75, the deprojected bar fraction in the B band falls from 43% to 39%, 34%, and 7%, respectively. Correspondingly, the bar fraction in the H band falls from 59% to 47%, 30%, and 1%, respectively. The ?attening

7 of the curve around e1 ～ 0.40 shows that the majority of bars have ebar above this value. This has implications for theoretical models that address the robustness of bars, and we refer the reader to § 4.6 for a discussion. How do our results on bar strength as characterized by the maximum bar ellipticity ebar from ellipse-?tting compare with those of Buta et al. (2005) who use the Qb parameter? At ?rst glance, the results may seem contradictory: they conclude that 40% of the galaxies in the OSUBSGS H band have ‘weakly barred’ or unbarred states (Qb ≤ 0.1), whereas we ?nd that only 6% of galaxies have ‘weak’ bars with 0.25 ≤ ebar ≤ 0.4 in the H band after deprojection. However, it should be noted that Buta et al. (2005) group unbarred and weakly barred galaxies together. Their cited fraction of 40% for weak and unbarred states is, in fact, fully consistent with the fraction (46%) that we ?nd when we group together unbarred galaxies (40%) and ‘weakly barred’ galaxies (6%). How do the bar classes and bar strengths from ellipse?ts, as derived by our quantitative method (§ 3.3), compare with the RC3 bar classes based on visual inspection of optical B images (de Vaucouleurs et al. 1991)? The three RC3 visual bar classes, ‘A’, ‘AB’, and ‘B’ denote ‘unbarred’, ‘weakly barred’, and ‘strongly barred’ disks, respectively. Of the 42, 47, and 46 galaxies in our sample that have an RC3 bar class of ‘A’, ‘B’, and ‘AB’, respectively, our quantitative characterization (§ 3.3) shows that 5%, 85%, and 41% host bars in B-band images and 19%, 87%, and 65% host bars in H-band images. Clearly, only a small fraction (41% or 19/46) of galaxies with RC3 bar class ‘AB’ qualify as barred in B-band images, according to our quantitative criteria (§ 3.3). We visually inspected the remaining 27 galaxies that fail to qualify in order to investigate why they do not. We found that for 17 of them, we could not identify a bar feature in the B-band image, even by eye. For the remaining 10, we could visually see a somewhat elongated feature, but it does not satisfy the ellipticity and PA criteria outlined in § 3.3. Another interesting point highlighted by Figure 15 is that while the mean bar strength (as characterized by ebar ) is higher for RC3 visual class ‘B’ than for class ‘AB’, the two classes have signi?cant overlap in the range ebar ～ 0.5–0.7. Thus, RC3 bar types should be used with caution and may be misleading. It is also noteworthy that Figure 13 shows no evidence for bimodality in the distribution of bar strength, as characterized by ebar from ellipse ?ts, in the B or H bands, in agreement with Buta et al. (2005). What about the bimodality claimed in earlier studies by Abraham & Merri?eld (2000) and Whyte et al. (2002)? Both of these studies used the parameter fbar to characterize the ellipticity of the most elliptical feature of a galaxy, and measure fbar for both barred and unbarred galaxies. They report no bimodality in fbar among barred galaxies, which is consistent with our ?ndings that ebar shows no bimodality among barred galaxies. The only bimodality that they report in fbar is between barred and unbarred galaxies. It is unclear how robust this bimodality is since Whyte et al. (2002) report a bimodality that is much weaker than the one seen by Abraham & Merri?eld (2000). The authors assigned this weakening to the larger sample size used by Whyte et al. (2002). At any rate, we cannot make any direct comparison with their bimodality results involving unbarred galaxies, since we measure ebar in barred galaxies, but not in unbarred galaxies. The reason for this selective measurement is rooted in our rigorous approach for identifying a bar. In the study of Abraham & Merri?eld (2000) and Whyte et al. (2002), a bar is simply considered as the innermost feature whose isophote has the highest ellipticity. In contrast, we use a rigorous approach for identifying a bar: we call a feature a bar only if its radial variation of ellipticity and PA follows the behavior expected based on the dominant orbits of a barred potential, as outlined in § 3.3. We measure the maximum bar ellipticity ebar only for those features that qualify as a bar. 4.4. Bar fraction and ellipticity as a function of Hubble type at z ～ 0 Figure 16 shows how the fraction of barred disks varies across di?erent Hubble types in sample S4. The Hubble types are taken from RC3 and the bins represent S0, Sa/Sab, Sb/Sbc, Sc/Sd, and Sd/Sm. We ?rst note that the bar fraction in di?erent RC3 Hubble types does not change signi?cantly after deprojection, whether in the B (Fig. 16a vs. 16d) or H (Fig 16b vs. 16e) band images. This is again encouraging for large studies of bars at intermediate redshift (e.g., Jogee et al. 2004, Elmegreen et al. 2004, Zheng et al. 2005), where deprojection is not done for the reasons outlined in § 4.1. In the B band, we ?nd that the bar fraction is lower with respect to the H band by ～ 1.2–1.5 in Sas to Scs, and by ～ 2.5 in Sds/Sms (Fig. 16c,f). This is consistent with higher obscuration in dusty, gas-rich late types. Eskridge et al. (2000) also ?nd that the increase in bar fraction from the B to H band is most signi?cant for late-type galaxies. How does the bar fraction vary across RC3 Hubble types? The number of galaxies involved are too small in the S0 and Sd/Sm bins for robust number statistics and we therefore restrict our analysis to types Sa to Scd. We conclude that the H-band bar fraction (Fig 16e) remains ～ 60% across RC3 Hubble types Sa to Scd. Our quantitative result based on 136 galaxies is consistent with the results based on ellipse ?ts of a much smaller sample (58 galaxies) by Knapen, Shlosman,& Peletier (2000), as well as with the qualitative results of Eskridge et al. (2000), who also report a constant NIR bar fraction as a function of RC3 Hubble types, based on visual inspection. The large H-band bar fraction of ～ 60% across di?erent Hubble types implies that bars are ubiquitous in spirals across the entire Hubble sequence. Further implications are discussed in § 4.6. How does the bar strength, as characterized by ebar from ellipse-?tting, vary as a function of RC3 Hubble type? In the H band, the bar strength ebar lies in the range 0.35–0.80, and shows no systematic variation across Hubble types Sa to Scd, either before (Fig. 17a) or after (Fig. 17b) deprojection. We note, however, that Buta et al. (2004) and Laurikainen et al. (2004) ?nd that the Qb and Qg parameters tend to have lower values toward earliertype galaxies. In order to understand this discrepancy, we ?rst note that the Qb and Qg parameters measure the bar strength relative to the axisymmetric components, such as the disk and bulge. The lower Qb and Qg values in early type galaxies could re?ect the fact that such galaxies have

8 stronger axisymmetric components, which make the relative strength of the bar lower, even if the bar was as strong or stronger intrinsically than those in later-type galaxies. 4.5. Comparison of optical properties of bars at z ～ 0 and at z ～ 0.2–1.0 Studies of bars at z ～ 0.2–1.0 (lookback times of 3–8 Gyr) based on HST ACS observations in the Tadpole ?eld (Elmegreen et al. 2004), the GEMS and GOODS ?elds (Jogee et al. 2004), and COSMOS surveys (Sheth et al. in preparation) trace bars in the rest-frame optical. The reddest ACS ?lter F850LP has a pivot wavelength of 9103 ?, while the value for the F814W ?lter is 8064 ?. Over A A the redshift range z ～ 0.2–1.0, the rest-frame wavelength traced by the F850LP ?lter ranges from 7586 ? to 4550 ?, A A which corresponds to the rest-frame optical R/I to V /B bands. In order to avoid the pernicious e?ects of bandpass shifting, it is essential that ACS studies of bars at z ～ 0.2–1.0 compare their rest-frame optical results to the optical bar fraction at z ～ 0, rather than to the NIR bar fraction at z ～ 0. If the NIR z ～ 0 point is used for comparison (e.g, Menendez-Delmestre et al. 2006), it will lead to ?awed conclusions because the NIR z ～ 0 bar fraction (60% ± 6%) is signi?cantly larger than the optical z ～ 0 bar fraction (44% ± 6%), as reported in § 4.1. We therefore use the OSUBSGS optical bar fraction at z ～ 0 in the discussion below. In the study of bars at z ～ 0.2–1.0, Jogee et al. (2004) ellipse ?tted a sample of 1590 galaxies at z ～ 0.2–1.0, drawn from 25% of the GEMS survey area. Then they applied essential cuto?s in absolute magnitude, bar size, and bar ellipticity in order to ensure a complete sample, high spatial resolution, and reliable bar identi?cation out to z ～ 1. In particular, in order to ensure that the sample of spiral galaxies is fairly complete out to z ～ 0.9, an absolute magnitude cuto? of MV < ?19.3 had to be applied. Secondly, at z > 0.5 (where 1′′ corresponds to scales > 6.2 kpc), the study could not e?ciently resolve very small bars with semi-major axes a < 1.5 kpc, in agreement with Lisker et al. (2006). Thus, a cuto? of abar ≥ 1.5 kpc is implicitly applied. Finally, the study only considered bars with moderate ellipticity ebar ≥ 0.4 because at intermediate redshifts, it becomes di?cult to unambiguously identify and characterize bars with lower ellipticities. This is not a dramatic cuto? as most bars have ebar ≥ 0.4 (Fig. 13). After applying these cuto?s in absolute magnitude (MV <-19.3), bar size (abar ≥ 1.5 kpc), and bar ellipticity (ebar ≥ 0.4), Jogee et al. (2004) ?nd a rest-frame optical bar fraction of foptical2 ～ 30% ± 6% z ～ 0.2–1.0. A constant and similar optical bar fraction (23% to 40%) out to z ～ 1 is also reported by Elmegreen et al. (2004). In order to get a valid optical bar fraction for comparison at z ～ 0, we must apply the exact same cuto?s to the OSUBSGS optical data. We start with observed bar properties prior to deprojection from OSUBSGS because no deprojection was applied in any of the intermediate redshift studies (Jogee et al. 2004; Elmegreen et al. 2004; Zheng et al. 2005). With a cuto? of MV <-19.3, the optical B-band bar fraction at z ～ 0 drops from 45% (61/136) to 43% (45/104). Applying a further cuto? of abar ≥ 1.5 kpc makes it drop to 36% (37/104). Finally, a third cuto? of ebar ≥ 0.4 reduces the optical B-band bar fraction to 34% (35/104). Thus, after the same cuto?s in absolute magnitude (MV <-19.3), bar size (abar ≥ 1.5 kpc), and bar ellipticity (ebar ≥ 0.4) are applied, a very good agreement ensues between the GEMS optical bar fraction at z ～ 0.2–1.0 (foptical2 ～ 30% ± 6%) and the OSUBSGS optical B-band bar fraction at z ～ 0 (foptical3 ～ 34% ± 6%). This agreement strongly suggests that the optical bar fraction in bright disks does not decline strongly with redshift. Such a decline would cause foptical2 ? foptical3 because the observed bar fraction would be lowered both by the intrinsic decline, and by systematic e?ects at intermediate redshifts, such as cosmological dimming, the loss of spatial resolution, and lower signal-to-noise. However, our ?nding allows for models where the optical bar fraction is either constant, or rises with redshift. In the latter class of models, one can arrive at comparable values of foptical2 and foptical3 only if the intrinsic increase in bar fraction with redshift produced by the model is compensated for by the ‘loss’ of bars due to systematic e?ects, such as cosmological dimming, and low signal-tonoise. In a forthcoming paper, we will assess the impact of such redshift-dependent systematic e?ects by arti?cially redshifting the OSUBSGS sample to z ～ 1, and repeating the bar characterizations. This will enable us to distinguish between the two classes of models. 4.6. Constraints on the robustness and evolution of bars The robustness and lifetime of bars de?ne some of the most fundamental issues in the evolution of bars, their impact on disk galaxies (§ 1) and the assembly of the Hubble sequence. In general terms, the evolution of a bar depends on the exchange of angular momentum between the stars in the bar and the other components of a galaxy, namely, the dark matter (DM) halo and the baryons (gas and stars) in the bulge and disk. Important factors in?uencing the bar include the triaxiality of the DM halo in which it lies (e.g., Berentzen, Shlosman, & Jogee 2006); the amount of angular momentum that the DM halo can absorb (Athanassoula 2003); the central mass concentrations (CMCs) present in the inner few hundred pc (e.g., Shen & Sellwood 2004; Athanassoula et al. 2005; MartinezValpuesta et al. 2006; Debattista et al. 2006); and the distribution and amount of gas in the disk (e.g, Shlosman & Noguchi 1993; Bournaud et al. 2002, 2005; Debattista et al. 2006). In this section, we compare our empirical results to di?erent simulations in order to constrain theoretical scenarios. We note, however, that most simulations do not yet fully incorporate the e?ects of star formation and feedback, which can impact the evolution of the disk in important ways. Dubinski (1994) showed that the triaxiality of DM halos is diluted by baryonic dissipation. Recent simulations by Berentzen, Shlosman, & Jogee (2006) ?nd that bars embedded in triaxial non-rotating DM halos can only survive if the inner halo ellipticity is washed out. Otherwise, the interaction between the bar and the DM halo induces chaotic orbits and destroys the bar. In the present paper, our ?ndings that the majority (60%) of spirals are barred in the infrared (§ 4.1), and that these bars have primarily moderate to high strengths, as characterized by the maximum bar ellipticity ebar (0.50 ≤ ebar ≤ 0.80; § 4.3),

9 suggest that DM halos of most present-day spirals are close to axisymmetric, with a maximum equatorial axial ratio of ～ 0.9 in potential. These limits may change slightly if one allows the DM halo to have a ?gure of rotation. These results are consistent with Kazantzidis et al. (2004), who ?nd that in the very early stages of disk formation, the settling of the dissipative baryonic component within a triaxial halo strongly dilutes the triaxiality to such values. Berentzen & Shlosman (2006) also report that a growing disk is responsible for washing out the halo prolateness (in the disk plane) and for diluting its ?atness over a period of time comparable to the disk growth. The CMC typically refers to the mass present within the inner hundred or few hundred pc. A large or more centrally concentrated CMC can weaken a bar amplitude by changing the orbital structure of a barred potential and inducing chaotic orbits. Most recent simulations (e.g., Athanassoula et al. 2005; Shen & Sellwood 2004; MartinezValpuesta et al. 2006; Debattista et al. 2006) ?nd that bars are more robust than previously thought: in order to produce any signi?cant reduction in bar strength, the ratio XCMC ～ (MCMC /Mdisk ), where MCMC is the mass of the CMC in the inner few hundred pc, and Mdisk is the disk mass, must be very large, at least 10%. Such large values are only of academic interest and are not realized in present-day galaxies, as we discuss below. In present-day galaxies, the components that contribute to the CMC in the inner few hundred pc consist of supermassive black holes (SMBHs) central dense stellar clusters, gaseous concentrations, and the inner parts of bulges. SMBHs have typical masses in the range 106 –109 M⊙ and tend to scale as 0.001 of the bulge mass; gaseous concentrations range from 107 –109 M⊙ in the central 500 to 1000 pc radius (e.g., Jogee et al. 2005); and central dense stellar clusters typically have masses in the range 106 –108 M⊙ . These components typically lead to XCMC values that are much lower than 10%. This suggests that CMCs that exist in present-day galaxies are not large enough to produce any signi?cant reduction in bar strength. Our results are consistent with these expectations and with simulations that support robust bars. We found that the majority (～ 71%–80%) of bars have moderate to high strengths, as characterized by ebar from ellipse?tting (0.50 ≤ ebar ≤ 0.80). We also found that the bar fraction (～ 60%) and mean bar strength, as characterized by ellipse ?ts (ebar ～ 0.5), is relatively constant across RC3 Hubble types Sa to Scd (§ 4.4), although the latter encompasses a wide range of gas mass fractions, CMC masses, and CMC components. Gas can a?ect the formation and evolution of a bar in di?erent ways, depending on its distribution and clumpiness. In the case of an unbarred disk, the accretion of cold gas makes the disk more massive, dynamically colder, and therefore more bar unstable (e.g., Bournaud et al. 2002). However, in the case of very gas-rich disks, the gas can become clumpy, and the e?ect of dynamical friction on massive gas clumps at low radii can heat the disk and prevent it from forming the bar (e.g., Shlosman & Noguchi 1993). In the case of a disk that is already barred, the bar exerts gravitational torques that drive gas located outside the corotation resonance (CR) outward, and drive gas located between the CR and inner Lindblad resonance (ILR) inward. Most simulations to date (e.g., Debattista et al. 2006; Berentzen & Shlosman in preparation; Curir et al. 2006) suggest that gas in?ows in present-day galaxies do not readily destroy bars. For instance, simulations (e.g., Debattista et al. 2006), can only destroy the bar when there are large gas in?ows that build a very massive, soft CMC, of order 20% of the mass of the total baryonic (gas and stars) disk. Furthermore, the simulations also suggest that gas which sinks into the center can become bar supporting if it forms stars. As discussed above, CMCs as large as 10% or 20% are not realized in presentday galaxies and the simulations therefore imply that gas in?ows in present-day galaxies do not readily destroy bars. In the very early Universe, if extreme gas in?ows and extreme CMCs are realized, the evolution of bars might be di?erent. We note that simulations of bar-driven gas in?ow by Bournaud et al. (2005) yield widely di?erent predictions from those discussed above. The simulations of Bournaud et al. (2005) appear to destroy a bar even with a gas mass fraction (GMF) that is as low as 5% to 7%. Here, the GMF is de?ned as the ratio of gas mass to the total mass of the stellar disk. A GMF of order 5% is easily met in presentday galaxies and these simulations would suggest, therefore, that strong bars in present-day galaxies are easily destroyed by bar-driven gas in?ows (Bournaud et al. 2005). There is clearly a stark di?erence between the predictions of these simulations and the ones outlined in the previous paragraph. Part of the reason why the simulations yield such di?erent results might lie in the way the DM halo is modeled and the assumed ratio of DM halo mass to disk mass. The DM halo is live and dominates over the disk mass in Debattista et al. (2006), while it is rigid and less massive than the disk in Bournaud et al. (2005). What do our observational results suggest? We found that at z ～ 0, only a small fraction (～ 7%–10%) of bars are very weak (0.25 ≤ ebar ≤ 0.40), while the majority (～ 71%–80%) of bars have moderate to high strengths (as characterized by the maximum bar ellipticity ebar ), with 0.50 ≤ ebar ≤ 0.80. We also do not see any sign of bimodality in bar strength, as characterized by ebar from ellipse ?ts. Finally, we found that the bar fraction (～ 60%) and mean bar ellipticity (ebar ～ 0.5) is relatively constant across RC3 Hubble types Sa to Scd (§ 4.4), despite the wide variation in GMFs. Our results are easily reconciled with scenarios where bars in present-day moderately gasrich galaxies remain strong under the e?ect of bar-driven gas in?ows. Our results do not necessarily rule out models where bars are easily destroyed by bar-driven gas in?ows. They do, however, imply that if such an easy destruction occurs, then there must be a very e?cient mechanism that not only regenerates bars on a short timescale (e.g., Block et al. 2002; Bournaud et al. 2002), but is also very well tuned to the bar destruction rate so that it can reproduce the observed constant optical bar fraction in bright galaxies over the last 8 Gyr (Jogee et al. 2004; Elmegreen et al. 2004; § 4.5).
5. summary and conclusions
With the advent of high redshift HST surveys, such as the Tadpole Field, GEMS, GOODS, and COSMOS, which trace bars in the rest-frame optical band out to z ～ 1,

10 it becomes increasingly important to provide a reference baseline for bars at z ～ 0 in the optical band. Motivated by these considerations, we characterize the frequency and structural properties of bars at z ～ 0 in the optical and NIR bands, by ellipse-?tting the B and H images of 180 spirals in the OSUBSGS (Eskridge et al. 2002), and applying quantitative criteria in order to identify and characterize bars. We determine the inclination of the outer disk and exclude highly inclined (i > 60? ) galaxies to derive a sample S4 of 136 moderately inclined spirals. For this sample, we derive bar properties both before and after deprojection to face-on. Our study complements existing work on OSUBSGS based on Fourier amplitudes (Block et al. 2002; Buta et al. 2005) and visual classi?cation (Eskridge et al. 2000), and it can be compared with studies (Jogee et al. 2004; Elmegreen et al. 2004; Zheng et al. 2005) of intermediate redshift (z ～ 0.2–1.0) bars employing the same ellipse-?tting methodology. Our results are summarized below. (1) The optical and NIR bar fraction at z ～ 0: For our sample, which is dominated by galaxies with MV ～ 20 to -22, we ?nd a deprojected bar fraction at z ～ 0 of fNIR1 ～ 60% ± 6% in the near-infrared H band, and foptical1 ～ 44% ± 6% in the optical B-band images. The latter likely miss bars obscured by dust and star formation. Deprojection does not make any signi?cant changes to the global B- and H- band bar fractions, which are 45% and 58% before deprojection, and change by only a factor of 0.97 and 1.03, respectively, after deprojection. This is encouraging for large studies of bars at intermediate redshift (e.g., Jogee et al. 2004, Elmegreen et al. 2004, Zheng et al. 2005), where deprojection is not performed. (2) Comparison of optical properties of bars at z ～ 0 and at intermediate redshifts: Studies of bars at z ～ 0.2–1.0 (lookback times of 3–8 Gyr) based on HST ACS observations in the Tadpole ?eld, the GEMS and GOODS ?elds, and COSMOS surveys trace bars in the rest-frame optical. R/I to V /B bands (7586 ? to 4550 ?). Therefore, in order A A to avoid the pernicious e?ects of bandpass shifting, it is essential that ACS studies of bars at z ～ 0.2–1.0 compare their rest-frame optical results to the optical bar fraction at z ～ 0, rather than to the signi?cantly higher NIR bar fraction at z ～ 0. Furthermore, at z ～ 0.2–1.0, it is essential to apply cuto?s in absolute magnitude, bar size, and bar ellipticity in order to ensure a complete sample, adequate spatial resolution, and reliable bar identi?cation. After applying cuto?s in absolute magnitude (MV <-19.3), bar size (abar ≥ 1.5 kpc), and bar ellipticity (ebar ≥ 0.4), Jogee et al. (2004) found a rest-frame optical bar fraction of foptical2 ～ 30% ± 6% at z ～ 0.2–1.0. A constant and similar optical bar fraction (23% to 40%) out to z ～ 1 is also reported by Elmegreen et al. (2004). In order to derive the equivalent optical bar fraction for comparison at z ～ 0, we applied the exact same cuto?s to the OSUBSGS optical data. With a cut o? of MV <-19.3, the optical bar fraction z ～ 0 drops from 45% (61/136) to 43%. Applying a further cuto? of abar ≥ 1.5 kpc makes it drop to 36%. Finally, a third cuto? of ebar ≥ 0.4 reduces optical B-band bar fraction at z ～ 0 to foptical3～ 34% ± 6%. The result that foptical2 is comparable to foptical3 rules out scenarios where the optical bar fraction in bright disks declines strongly with redshift. It allows for models where the optical bar fraction is either constant, or rises with redshift. (3) Distribution of bar strengths z ～ 0 as characterized by ellipse-?tting: In this study, we use the maximum bar ellipticity ebar from ellipse-?ts as a partial measure of the bar strength. Only a very small proportion (7% in B; 10% in H) of bars are very weak as characterized by ebar from ellipse ?ts (0.25 ≤ ebar ≤ 0.40), while the majority of bars (70% in B; 71% in H) have moderate to high ellipticities (0.50 ≤ ebar ≤ 0.75). We ?nd no evidence for bimodality in the distribution of bar strength, as characterized by ebar in the B or H bands, in agreement with Buta et al. (2005). (4) Bar fraction and strength, as characterized by ellipse-?tting, as a function of RC3 Hubble type at z ～ 0: The deprojected bar fraction is 60% in H and 44% in B, con?rming the ubiquity of local bars. In the B band, the bar fraction is lower with respect to the H band by ～ 1.2– 1.5 for Hubble types S0s to Scs, and by ～ 2.5 for Sds/Sms. This is consistent with the higher obscuration in dusty, gas-rich late types. The bar fraction and bar strength, as characterized by ebar , in the H band shows no systematic variation across Hubble types Sa to Scd. (5) Comparison with RC3 visual bar classes: Of the 42, 47, and 46 galaxies in our sample that have an RC3 visual bar class of ‘A’ (unbarred), ‘B’ (strongly barred), and ‘AB’ (weakly barred), respectively, our quantitative characterization (§ 3.3) shows that 5%, 85%, and 41% host bars in B-band images and 19%, 87%, and 65% host bars in Hband images. Thus, quantitative characterization of bars di?ers signi?cantly from RC3 bar classes for the RC3 bar class ‘AB’. Furthermore, the mean bar strength, as characterized by the maximum bar ellipticity ebar , is higher for RC3 visual class ‘B’ than for class ‘AB’, but the two classes have signi?cant overlap in the range ebar ～ 0.5–0.7. Thus, RC3 bar types should be used with caution and may be misleading. (6) Sizes of bars and disks at z ～ 0: The sizes or semimajor axes abar of large-scale bars in the local Universe lie in the range ～ 1 to 14 kpc, with the majority of bars (68% in B and 76% in H) having abar ≤ 5 kpc. Bar and disk sizes are correlated with an average slope of ～ 0.9, albeit with a large scatter of several kpc in bar size at a given disk size. The ratio (abar /R25 ) lies primarily in the range 0.1 to 0.5, with only a minority of galaxies having larger values out to 0.95. The correlation between bar and disk sizes, and the narrow range in abar /R25 suggests that the growths of the bar and disk may be intimately tied. The fact that (abar /R25 ) is generally well below 1.0 suggests that the CR of disk galaxies lies well inside their R25 radius, assuming that bars end near the CR. (7) Constraints on the robustness of bars: Our ?ndings that the majority (60%) of spirals are barred in the infrared and that most (～ 71%–80%) of these bars have primarily moderate to high ellipticities (0.50 ≤ ebar ≤ 0.80) suggest that DM halos of present-day spirals have at most a mild triaxiality, with a maximum equatorial axis ratio b/a ～ 0.9 in the potential. We also found that the bar fraction and mean bar strength (as characterized by the maximum bar ellipticity ebar ) are relatively constant across Hubble types Sa to Scd, and there is no bimodality in ebar . Taken together, our results are easily reconciled with scenarios where bars in present-day galaxies are relatively

11 robust against the range in gas mass fractions, gas in?ows, and CMC components present across Hubble types Sa to Scd. Our results do not necessarily rule out models where bars are easily destroyed by bar-driven gas in?ows. They do, however, imply that if such an easy destruction occurs, then there must be a very e?cient mechanism that not only regenerates bars on a short timescale, but is also very well tuned to the bar destruction rate so that it can reproduce the observed constant optical bar fraction in bright galaxies over the last 8 Gyr. S.J. and I.M. acknowledge support from NSF grant AST-0607748, NASA LTSA grant NAG5-13063, as well as HST grants G0-1048 and G0-10395 from STScI, which is operated by AURA, Inc., for NASA, under NAS5-26555. The Ohio State University Bright Spiral Galaxy Survey, was funded by grants AST-9217716 and AST-9617006 from the United States National Science Foundation, with additional support from the Ohio State University. We thank Pat Shopbell, Peter Teuben, and Stuart Vogel for their assistance with the Zodiac and MIRIAD packages; Seppo Laine for sharing his deprojection code from Laine et al. (2002); and James Davies for help with IRAF and IGI visualization routines. We also thank Paul Eskridge, Ron Buta, Fabio Barazza, Debbie Elmegreen, Isaac Shlosman, Ingo Berentzen, Seppo Laine, Juntai Shen, Victor Debattista, Lia Athanassoula, Francoise Combes, Frederic Bournaud, Jerry Sellwood, and Johan Knapen for useful discussions.
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Fig. 1.— Analysis steps for characterizing bars and disks at z ～ 0 from OSUBSGS: Our procedure of characterizing bars and disks in OSUBSGS galaxies via ellipse ?ts is schematically illustrated in this ?gure and described in detail in § 3.1–3.4. For the B and H-band images of the 180 galaxies in sample S2, we remove stars, ?nd an accurate center, and determine the maximum semi-major axis of the galaxy, amax , where the galaxy isophotes reach the sky level. We ?t ellipses out to amax to the B and H images of each galaxy, generate radial pro?les of e, PA, and SB, and overlay the ellipses on the galaxy image for inspection. Successful ?ts are found in both bands for 169 galaxies (sample S3). For sample S3, we use the B-band radial pro?les to characterize the inclination i and PA of the outer disk. We exclude 33 galaxies with i > 60? to generate sample S4 of 136 moderately inclined galaxies. For sample S4, we deproject the B and H radial pro?les using the outer disk i and PA, and use the deprojected pro?les to characterize the properties of barred and unbarred disks. For completeness, we also perform this characterization on the the observed pro?les before deprojection.

13
Fig. 2.— Ellipse ?ts to the B-band image of an inclined (i > 60? ) galaxy: The left panel made of 3 images shows the ellipses ?tted to the B-band image of NGC 3877. The top image shows only the galaxy. The scale is shown on the top image in arcseconds, where 1′′ = 86 pc. The middle and bottom images show the ellipses overlaid on the galaxy, with greyscale stretches chosen to emphasize the inner (middle image) and outer (bottom image) regions of the galaxy. Note that ellipses are ?tted out to the sky level in the image. The right panel shows the radial pro?les of surface brightness (SB), ellipticity (e), and position angle (PA) versus semi-major axis (a) derived from the ellipse ?ts. The pro?les show evidence for some structure in the inner regions, but at a > 100′′ , the e settles to a high value of 0.8, while the PA also settles to a constant value. This is the signature of an inclined disk with i > 60? .

14
Fig. 3.— Distribution of Hubble types and absolute magnitudes: Left: The distributions of RC3 Hubble types are shown for the sample S4 (solid line) of 169 galaxies that include inclined systems, and for the sample S3 (dotted line) produced by excluding 33 galaxies with high inclination (i > 60? ). This exclusion does not signi?cantly a?ect the Hubble type distribution of the sample. Right: The distributions of absolute V -band magnitudes for sample S4 (solid line) and S3 (dotted line) are similar as well.

15
Fig. 4.— Example of ellipse ?ts for the unbarred galaxy NGC 2775: Left and middle panels: They show the ellipse-?ts overlayed on the B- and H-band images of the unbarred galaxy NGC 2775. The scales of the B and H images are shown in the top image panels for each band. 1′′ corresponds to 86 pc at the galaxy distance of 17 Mpc. Within each panel, there are 3 images with di?erent greyscale stretches that are chosen to emphasize the inner (middle image) and outer (bottom image) regions of the galaxy. Note that ellipses are ?tted out to the sky level in the image. Right panel: This shows the radial pro?les of (SB, e, and PA) for the B (stars) and H (squares) bands, derived from the ellipse ?ts prior to deprojection. The pro?les do not show any characteristic bar signatures, such as a smooth rise in e to a maximum above 0.25, concurrent with a PA plateau. The e remains below 0.25 across the galaxy. There is no signature of large-scale structure, such as spiral arms or a bar.

16
Fig. 5.— Example of ellipse ?ts for the barred galaxy NGC 4643: Left and middle panels: They show the ellipse-?ts overlayed on the B- and H-band images of the barred galaxy NGC 4643. The scales of the B and H images are shown in the top image panels for each band. 1′′ corresponds to 130 pc at the galaxy distance of 26 Mpc. Within each panel, there are 3 images with di?erent greyscale stretches that are chosen to emphasize the inner (middle image) and outer (bottom image) regions of the galaxy. Note that ellipses are ?tted out to the sky level in the image. Right panel: This shows the radial pro?les of (SB, e, and PA) for the B (stars) and H (squares) bands, derived from the ellipse ?ts and prior to deprojection. The pro?les show a clear bar signature. Between 15′′ and 40′′ , the e rises smoothly to a global maximum of 0.5, while the PA remains roughly constant. The e then drops to ～ 0.1, and the PA changes at the transition from the bar to the disk region.

17
Fig. 6.— Example of observed and deprojected radial pro?les for NGC 4548: For galaxies in sample S4, we use the inclination i and the PA of the outer disk (from § 3.2) to analytically deproject the observed H- and B-band radial pro?les of (e, PA) to face-on. The case for NGC 4548 is illustrated here. The left panel shows the observed (stars) and deprojected (squares) radial pro?les in the B band. The right panel shows the observed and deprojected radial pro?les in the H band. After deprojection, as expected, the outer disk e is nearly zero in the B band. Note also that the bar size is slightly di?erent and the bar appears somewhat stronger in both bands after deprojection.

18
Fig. 7.— Comparison of the face-on radial pro?le generated via two di?erent methods: For the B-band image of NGC 4548, this ?gure compares the face-on radial pro?les of e and PA generated via two di?erent methods. In the ?rst method, ellipses are ?tted to the observed image (left panel) to generate the observed radial pro?le (plotted as stars in the right panel), which is then analytically deprojected to produce the face-on pro?le (plotted as squares in the right panel). In the second method, the observed image is deprojected with MIRIAD and the resulting deprojected image (middle panel) is ?tted with ellipses to generate the second face-on pro?le (plotted as triangles in the right panel). Note the good agreement between the squares and triangles.

19
Fig. 8.— The optical and NIR bar fraction at z ～ 0 from OSUBSGS: We show the fraction of spirals that are barred in the B and H bands, based on ellipse ?ts of 136 moderately inclined galaxies (sample S4), followed by quantitative characterization of the resulting radial pro?les of (e, SB, PA). Top row: The observed bar fraction before deprojection is 45% in the B band (left) and 58% in the H band (right). Bottom row: The deprojected bar fraction is 44% in the B band (left) and 60% in the H band (right).

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Fig. 9.— Verifying that bar properties measured prior to deprojection are not biased by galaxy inclination: Top tow: The histograms show the distributions of inclination i for galaxies that were classi?ed as ‘barred’ or ‘unbarred’, prior to deprojection, in the B band (left) and H band (right). Note that there is no correlation with i. Bottom row: The measured bar ellipticity ebar in the B band (left) and H band (right), prior to deprojection, are plotted against the galaxy inclination i. Note that there is no correlation between ebar and i.