Abstract

I present a study of the sizes (semimajor axes) of bars in disc galaxies, combining a detailed R-band study of 65 S0-Sb galaxies with the B-band measurements of 70 Sb-Sd galaxies from Martin (1995). As has been noted before with smaller samples, bars in early-type (S0-Sb) galaxies are clearly larger than bars in late-type (Sc-Sd) galaxies; this is true both for relative sizes (bar length as fraction of isophotal radius R25 or exponential disc scalelength h) and absolute sizes (kpc). S0-Sab bars extend to ~1–10 kpc (mean ~ 3.3 kpc), ~0.2–0.8R25 (mean ~ 0.38R25) and ~0.5–2.5h (mean ~ 1.4h). Late-type bars extend to only ~0.5–3.5 kpc, ~0.05–0.35R25 and 0.2–1.5h; their mean sizes are ~1.5 kpc, ~ 0.14R25 and ~0.6h. Sb galaxies resemble earlier-type galaxies in terms of bar size relative to h; their smaller R25-relative sizes may be a side effect of higher star formation, which increases R25 but not h. Sbc galaxies form a transition between the early- and late-type regimes. For S0-Sbc galaxies, bar size correlates well with disc size (both R25 and h); these correlations are stronger than the known correlation with MB. All correlations appear to be weaker or absent for late-type galaxies; in particular, there seems to be no correlation between bar size and either h or MB for Sc-Sd galaxies.

Because bar size scales with disc size and galaxy magnitude for most Hubble types, studies of bar evolution with redshift should select samples with similar distributions of disc size or magnitude (extrapolated to present-day values); otherwise, bar frequencies and sizes could be mis-estimated. Because early-type galaxies tend to have larger bars, resolution-limited studies will preferentially find bars in early-type galaxies (assuming no significant differential evolution in bar sizes). I show that the bars detected in Hubble Space Telescope (HST) near-infrared(IR) images at z~ 1 by Sheth et al. have absolute sizes consistent with those in bright, nearby S0-Sb galaxies. I also compare the sizes of real bars with those produced in simulations and discuss some possible implications for scenarios of secular evolution along the Hubble sequence. Simulations often produce bars as large as (or larger than) those seen in S0-Sb galaxies, but rarely any as small as those in Sc-Sd galaxies.

1 Introduction

Observations indicate that ~70 per cent of all disc galaxies are barred to one degree or another (e.g. Eskridge et al. 2000; Erwin, in preparation). There is considerable debate about the origin and influence of bars, and also about their strengths, something for which there is still no agreed-upon measurement, though many have been suggested (e.g. Martin 1995; Seigar & James 1998; Chapelon, Contini & Davoust 1999; Buta & Block 2001). Curiously, somewhat less attention has been given to the question of bar sizes, perhaps because this seems, on the face of it, easier to measure: even though there are no agreed-upon methods of measuring bar sizes either (see the discussions in Athanassoula & Misiriotis 2002; Aguerri, Debattista & Corsini 2003).

Is bar size actually important? There are, I would argue, several reasons why bar size is interesting, beyond a basic, natural historian's curiosity (‘Just how big or small are they, anyway?’). To begin with, the size of a bar is a first approximation to how much of its host galaxy can be affected by the dynamical influence of the bar: a larger bar can obviously affect more of the galaxy than a smaller bar. In addition to the well-known effects of bars on gas flow, Weinberg & Katz (2002) and Holley-Bockelmann, Weinberg & Katz (2005) argued that bars can also restructure dark-matter haloes, flattening out the steep central cusps, that are produced in cosmological simulations but apparently not seen in real galaxies (but see Sellwood 2003; Athanassoula 2004). Larger bars could then mean larger dark-matter cores. Holley-Bockelmann et al. also argued that tidally induced bars could be significantly larger than the ‘classical’N-body bars, which form via disc instabilities, so bar size may provide clues to past merger histories. More generally, bar size is an obvious way of testing the accuracy of different bar-formation and bar-evolution models (e.g. Valenzuela & Klypin 2003). For example, Bournaud & Combes (2002) recently outlined a scenario of galaxy evolution involving multiple rounds of bar formation, self-destruction and resurrection due to gas accretion; they predict a trend of bar size with Hubble type, where galaxies with larger bulges (i.e. earlier Hubble types) have shorter bars. N-body simulations also suggest that bar size depends on angular momentum exchange between the bar and the bulge, the outer disc and the halo. Because the relative masses of these components, as well as how kinematically hot they are, can affect how much angular momentum is exchanged (e.g. Athanassoula 2003), bar size could be a useful probe of halo mass and kinematics. Finally, several studies have suggested that longer bars are correlated with higher star formation activity, at least in late-type galaxies (e.g. Martinet & Friedli 1997; Chapelon et al. 1999).

The first systematic investigation of bar sizes was made by Kormendy (1979), who found that bar size correlated with galaxy blue luminosity. Subsequently, Elmegreen & Elmegreen (1985, hereafter EE85) showed that bars in early-type disc galaxies tended to be larger, relative to the optical disc diameter D25, than bars in later Hubble types (see also Regan & Elmegreen 1997). They also found a dichotomy in bar structure: early-type galaxies typically have bars with shallow (‘flat’) profiles and truncations (as noted by Kormendy 1982), while late-type galaxies tend to have bars with steep exponential profiles. More recent studies using CCDs or near-infrared(IR) images include those of Chapelon et al. (1999), Laine et al. (2002), and Laurikainen and collaborators (Laurikainen & Salo 2002; Laurikainen, Salo & Rautiainen 2002); in general, these have supported the findings of Kormendy and EE85.

Because a number of these studies have focused on particular subtypes of galaxies, the results are not as general or unbiased as they might otherwise be. For example, Chapelon et al. (1999) studied primarily a large sample of starburst galaxies, while the studies of Laine et al. (2002) and Laurikainen et al. (2002) were aimed at Seyfert and other ‘active’ galaxies. Chapelon et al. noted that bar sizes for their late-type (starburst) galaxies tended to be larger than those of the normal late-type galaxies of Martin (1995); similarly, Laurikainen et al. found that Seyferts tended to have larger bars than non-Seyferts. Except for the pioneering studies of Kormendy and EE85, bars in the earliest disc galaxies (i.e. S0 galaxies) have been ignored or represented by only a handful of examples. Finally, there has also been a tendency to overlook so-called ‘weak’ (i.e. SAB) bars: the samples of Kormendy and EE85 are almost entirely SB galaxies and bar sizes were measured by Laurikainen et al. only for galaxies with relatively high m= 2 Fourier bar amplitudes.

Thus, there is still considerable room for improving our understanding of bar sizes in the general population of disc galaxies, especially for S0 galaxies and weak bars. The relevance of bar size distributions for galaxy evolution was recently highlighted by Sheth et al. (2003), who discussed the visibility of bars as a function of redshift and resolution. Put simply, large bars (size in kpc) are easier to detect at high redshift than small bars; if the average bar is small enough, it will be undetectable at high z. Failure to account for this possibility can produce spurious changes in bar fraction with redshift. (We might also like to know if the average bar size has changed significantly between, say, z= 1 and now, which presupposes a good understanding of local bar sizes.)

In this paper, I take a detailed look at the question of bar sizes along the Hubble sequence in the local Universe. The main part of this study uses a diameter-limited sample of nearby, early-type (S0-Sb) disc galaxies with both strong (SB) and weak (SAB) bars. I measure the bar lengths and compare them with the overall size of the galaxy, using both the 25th-magnitude radius (R25) and the exponential scalelengths of the outer discs. These are combined with the measurements of Martin (1995), which also include both SB and SAB bars and are primarily of later Hubble types (Sbc-Sd).

2 Samples

I use two samples of galaxies in this paper. The first is a sample of early-type (S0-Sb) galaxies, using recent R-band imaging for both bar-size and exponential disc scalelength measurements; both sets of measurements are presented here. To extend this study to later Hubble types, I have drawn on a second sample, that of Martin (1995). This consists primarily of Sb-Sd galaxies, with bar-size measurements made from blue photographic prints.

The early-type galaxy sample is an expanded version of that presented in Erwin & Sparke (2003); I will refer to their original sample as the ‘WIYN Sample’ (because most of the observations were made with the 3.5-m WIYN Telescope).1 The WIYN Sample consists of all optically barred (SB + SAB) S0-Sa galaxies from the Uppsala General Catalog (UGC) (Nilson 1973), that met the following criteria: declination >10°, heliocentric radial velocity ≤2000 km s−1, major axis diameter ≥2 arcmin and ratio of major to minor axis a/b ≤ 2 (corresponding to i ≲ 60°). Galaxy types and axis measurements (at the 25 mag arcsec−2 level in B) were taken from de Vaucouleurs et al. (1991, hereafter RC3); radial velocities are from the NASA/Infrared Processing and Analysis Center. Extragalactic Database (NED). The size restriction and the use of the UGC means that the sample is biased in favour of bright, high surface brightness galaxies. The sample had a total of 38 galaxies; I subsequently eliminated four galaxies where bars were either absent, ambiguous, or too difficult to measure (see the Appendix), leaving a total of 34 S0-Sa galaxies.

There is some evidence that Hubble types in clusters (in the Virgo cluster, at least) do not agree with Hubble types of isolated field galaxies (van den Bergh 1976). Koopman & Kenney (1998) found that Virgo Sa-Sab galaxies had central light concentrations more like those of isolated Sb-Sc field galaxies. Accordingly, Erwin & Sparke (2003) excluded Virgo galaxies from their sample. Because the case for S0 galaxies is unclear (Koopman & Kenney noted that their sample was strongly incomplete for S0 galaxies, and the few S0 galaxies they studied did not differ significantly between the field and Virgo: see their fig. 1) and because information on bar sizes in S0 galaxies is particularly lacking, I have added bar measurements for eight of the 10 barred S0 galaxies in Virgo that meet the criteria given above, except for the redshift limit. (The redshift limit was intended to set a distance limit of ~30 Mpc for the field galaxies; if it were applied to the Virgo cluster, which lies well within that distance, it would improperly exclude cluster galaxies with high peculiar velocities.)

To make the coverage of Hubble types more complete, I have also added galaxies from an ongoing study of barred Sab and Sb galaxies (Erwin, Vega Beltrán & Beckman, in preparation). The selection criteria are identical, aside from the difference in Hubble type, leading to a total of nine Sab and 18 Sb galaxies; two of each type appear to be unbarred and are not considered further (see the Appendix).

The final early-type sample thus has a total of 65 strongly and weakly barred S0-Sb galaxies. All of these galaxies, grouped by Hubble type, are listed in Table 1, along with the parameters of their bars and outer discs.

Table 1

Bar and disc measurements for S0-Sb galaxies.

Table 1

Bar and disc measurements for S0-Sb galaxies.

The sample that best complements mine is that of Martin (1995): it is large and drawn from ordinary, optically barred galaxies (including both SB and SAB classes), contains both observed and deprojected bar lengths, and is almost entirely Sb or later in Hubble type. To make the match between samples as close as possible, I applied the same selection criteria to Martin's galaxies: SB or SAB bar classification, major axis ≥2 arcmin, axis ratio ≤2 and radial velocity ≤2000 km s−1. Martin argued that deprojection was unreliable for Magellanic galaxies (Sm and Im), so I follow him in excluding those types. I also removed three Virgo galaxies (NGC 4303, 4321 and 4394) and eliminated NGC 4395, which is classed as SA in RC3; for the three galaxies in common between the samples (see Section 3.4), I retain my measurements. This leaves a total of 75 galaxies from his sample, still large enough for a good comparison; the bulk of these (70) are Sb-Sd. To these I added distances and total blue magnitudes, mostly from Lyon-Meudon Extragalactic Database (LEDA; see Appendix A4 for details). Although the underlying sample selection was different (Martin's galaxies were taken from the Sandage-Bedke 1988 atlas), the relative numbers of different Hubble types are consistent with local populations. For example, my sample has 24 S0/a-Sab galaxies compared with 56 Sbc-Scd galaxies in Martin's sample; the ratio of late to early types (2.3) is similar to that found in RC3 for galaxies with D25 ≥ 2.0 arcmin and a/b ≤ 2.0 (480 Sbc-Scd galaxies versus 199 S0/a-Sab, for a ratio of 2.4). This suggests that the combined set provides a reasonable picture of bar sizes for the Hubble sequence down to Sd (Martin's sample has very few Sdm or Sm galaxies), at least for bright galaxies (median MB=−19.5 for my S0-Sb galaxies and −19.8 for Martin's Sb-Sd; see Fig. 1).

Figure 1

Absolute blue magnitudes for galaxies from the two samples as a function of Hubble type. Galaxies from my sample are shown with open circles, while galaxies from Martin (1995) meeting the same selection criteria are shown with filled diamonds; mean values for each Hubble type are indicated by the large boxes.

Figure 1

Absolute blue magnitudes for galaxies from the two samples as a function of Hubble type. Galaxies from my sample are shown with open circles, while galaxies from Martin (1995) meeting the same selection criteria are shown with filled diamonds; mean values for each Hubble type are indicated by the large boxes.

For the early-type galaxies, the measurements of bar size and shape and of disc sizes are discussed in Sections 3.1–3.3. In Section 3.4, I discuss how the published bar sizes of Martin (1995) can best be compared with my measurements and how I obtained disc scalelengths for Martin's galaxies.

3 Observations and Measurements

Observations of the original WIYN Sample (S0-Sa galaxies) are presented and discussed in detail by Erwin & Sparke (2003). All but two of the galaxies were observed in B and R with the 3.5-m WIYN Telescope at Kitt Peak, Arizona, between 1995 December and 1998 March. Images for NGC 936 and 4314 were taken from the Barred and Ringed Spirals (BARS) Project observations (Lourenso & Beckman 2001); in a few cases, additional images from other sources were used for outer-disc or bar measurements (see the Appendix for details).

Images of the barred Virgo S0 galaxies and the Sab-Sb galaxies are from a variety of sources, including: the WIYN Telescope (1995 March to 1998 March); the 2.4-m MDM Telescope at Kitt Peak, courtesy of Paul Schechter (1996 March); the 2.5-m Nordic Optical Telescope (NOT) in La Palma (2001 April and 2002 April); and the Isaac Newton Group archive (images from both the 1-m Jacobus Kapteyn Telescope and the 2.5-m Isaac Newton Telescope, INT). The outer-disc scalelengths for several galaxies were measured using images taken with the INT in 2004 March; these observations will be described in more detail in Erwin, Pohlen, & Beckman (in preparation). I also used observations from the BARS Project (for NGC 4151 and 4596) and r- or R-band images from the sample of Frei et al. (1996) for a number of galaxies. Specific details for individual galaxies are discussed in the Appendix.

Except where noted in the Appendix (cases where dust severely distorted bar isophotes in the optical images), all bar and outer-disc scalelength measurements were made with R-band or equivalent images. For Sab and Sb galaxies, these measurements were usually checked against measurements made with near-IR images; the agreement was generally very good.

Parameters for these galaxies are listed in Table 1. Most distances are from LEDA (exceptions are discussed in the Appendix); the latter are based on redshifts corrected for Virgocentric infall, as listed in LEDA, and assuming H0= 75 km s−1 kpc−1. For Virgo galaxies, I assumed a default distance to the Virgo cluster of 15.3 Mpc (Freedman et al. 2001), except for NGC 4754, for which a surface-brightness fluctuation measurement by Tonry et al. (2001) is available. Note that distance measurements and their uncertainties only affect the absolute sizes of bars; relative bar sizes are distance-independent.

3.1 Measuring the sizes of bars

There is no standard way to measure the length of a bar, either for real galaxies or for simulations. Methods that have been used for real galaxies include:

  1. visual estimation directly from images (e.g. Kormendy 1979; Martin 1995);

  2. fitting ellipses to the galaxy isophotes, with bar length usually determined from a maximum in the ellipticity (e.g. Wozniak & Pierce 1991; Wozniak et al. 1995; Jungwiert, Combes & Axon 1997; Laine et al. 2002; Sheth et al. 2003);

  3. various measurements based on Fourier analysis of the galaxy image, using either the bar-interbar luminosity contrast (e.g. Ohta, Hamabe & Wakamatsu 1990; Aguerri et al. 2000) or the phase angle (e.g. Quillen, Frogel & Gonzalez 1994); and

  4. measurements using the major-axis profile of the bar (e.g. Seigar & James 1998; Chapelon et al. 1999).

There is similar variation in how bars are measured even when the galaxy is readily accessible, i.e. in N-body simulations: compare, for example, Debattista & Sellwood (2000), Athanassoula & Misiriotis (2002) and Valenzuela & Klypin (2003). As Athanassoula & Misiriotis demonstrate, different methods applied to the same (model) galaxies can lead to variations of ~15–35 per cent in measured length.2

After some experimentation, I settled on two measurements, an approach I also used for the outer and inner bars of double-barred galaxies (Erwin 2004). These can be thought of as lower and upper limits on the bar size. The lower-limit measurement is aε, the semimajor axis of maximum ellipticity in the bar region, which is useful primarily because it is common and reproducible. In some cases, there is no clear ellipticity peak associated with the bar; but a corresponding extremum in the position angles (PA) can often be found, which serves the same purpose; examples include NGC 2880 and 4143 (see Erwin & Sparke 2003). It is important to stress that I identify aε with the maximum in ellipticity (or maximum deviation in PA) closest to the end of the bar, but still inside the bar. In some cases, particularly when there are strong dust lanes and/or star formation, the inner isophotes can become highly distorted and more elliptical than the bar proper: examples include NGC 2787, IC 676 and NGC 4691 (Erwin & Sparke 2003).3 In other cases, the bar merges so smoothly into spiral arms further out that the ‘obvious’ maximum in ellipticity occurs well outside the bar and is due to spiral arms or a ring. Examples of this include NGC 3185 and 7743 (Erwin & Sparke 2003); another good example, albeit a galaxy not in this study, is NGC 4303 (see the discussion in Erwin 2004).

Despite the relative simplicity and common use of aε, there is good reason to believe that it underestimates the true length of the bar. This has been pointed out by several authors (Wozniak et al. 1995; Laurikainen et al. 2002; Erwin & Sparke 2003) and Athanassoula & Misiriotis (2002) found that it generally provided the smallest estimates of bar length in their N-body simulations. Thus, there is a need for a second (‘upper-limit’) measurement, which I refer to as the ‘length’ of the bar Lbar. This is based on the approach of Erwin & Sparke (2003), where the bar length was defined as the minimum of two ellipse-fit measures: the first minimum in ellipticity outside the peak ellipticity of the bar (amin), or the point at which the PAs of the fitted ellipses differ by =10° from the PA of the bar. To their definition, I have added a qualification: if the bar is surrounded by a ring or spiral arms and the size of the ring (or arms, where they intersect the bar) is smaller than either amin or a10, then I adopt the ring/spiral size. This is because chance combinations of orientation and projection acting on the ring or spirals can lead to ellipse-fit profiles that place amin and a10 well outside the bar. Because there is no indication in any of these galaxies that the bar extends beyond the ring or surrounding spirals, it makes sense to use the latter as an upper limit on bar size. Table 1 lists aε, amin, a10 and the adopted Lbar for each galaxy; if Lbar is smaller than either amin or a10, then this means that Lbar was derived using rings or spiral arms.

The Lbar measurement is perhaps less consistent and accurate than aε (it is prone to strongly overestimate bar length in face-on galaxies lacking rings or spiral arms), but may give a better measure of the the ‘true’ length of the bar: that is, where the bar distortion finally gives way to the outer disc or spiral structure. The only galaxy where it clearly fails is NGC 4203, which is face-on and lacking in any spiral arms or rings, so that amin= 46 arcsec even though aε= 13 arcsec; consequently, I exclude that galaxy from statistics using Lbar.

In practice, the two measurements are extremely well correlated (Fig. 2); the Pearson and Spearman correlation coefficients are r= 0.96 and rs= 0.95, respectively.4 The mean (deprojected) ratio of aε/Lbar is 0.80. This is not too far from the mean ratio (0.73) of sizes for the Lb/a and Lphase measurements of Athanassoula & Misiriotis (2002), which suggests that those two N-body bar measurements are a good match to aε and Lbar (see Section 5.2).

Figure 2

Correlation between two deprojected measurements of bar semimajor axis [semimajor axis at maximum isophotal ellipticity (aε) and bar length (Lbar; see text for definition)] for S0-Sb galaxies. The dashed line indicates the mean ratio of the two measurements: Lbar= 1.25 aε.

Figure 2

Correlation between two deprojected measurements of bar semimajor axis [semimajor axis at maximum isophotal ellipticity (aε) and bar length (Lbar; see text for definition)] for S0-Sb galaxies. The dashed line indicates the mean ratio of the two measurements: Lbar= 1.25 aε.

The PAs of the bars are also needed, because I use them to deproject bar sizes. As shown by Erwin & Sparke (2003), ellipse fits are a problematic source for bar PAs. Their table 5 lists 11 large-scale bars whose PAs differ from those given by the ellipse fits by more than 5°; see their figs 5 and 6 for examples. Thus, bar PAs are always checked against the images, and the PA determined from the isophotes and unsharp masking is preferred to the ellipse-fit PA if the two differ by more than a couple of degrees.

Finally, the inclination and line of nodes of the galaxy discs need to be determined. The easiest approach is to use the RC3 axis ratios and PAs and assume that the outer disc is circular. Unfortunately, this is by no means the most accurate way, especially for early-type barred galaxies. This is because the RC3 axis ratios sometimes reflect bar-related features such as inner rings, lenses and outer rings, which are more common in early-type disc galaxies and are not always intrinsically circular (Buta 1986; Buta 1995). So I determined the outer disc orientation, where possible, using kinematic information (e.g. H i maps) and/or isophotes at diameters larger than D25. For the WIYN Sample galaxies, I use the values from Erwin & Sparke (2003), which were determined using this approach (certain exceptions based on more recent data are mentioned in the Appendix). Details for the Virgo S0 and the Sab-Sb galaxies are given in the Appendix.

3.2 Measuring the shapes of bars

Another way to define a bar is by its ‘strength’. This too lacks an obvious, universally agreed-upon definition. The simplest way to measure the strength of a bar is to measure its shape, usually reduced to measuring its ‘ellipticity’. For theorists, this often means the ellipticity of the bar itself (e.g. that of a Ferrers ellipsoid), but for observers (lacking the ability to unambiguously isolate the bar from other galactic components) it usually means measuring the semiminor axis of the isophote defined by the bar length (usually aε) and comparing it with the semimajor axis. This is approximately the method used by Martin (1995) to define bar strengths and also by Shlosman, Peletier & Knapen (2000) and Laine et al. (2002) for fitted ellipses defining bars. For comparison, if no other reason, it makes sense to do the same.

A more complex approach, which attempts to estimate the non-axisymmetric gravitational influence of the bar, is that of Buta & Block (2001). Unfortunately, this generally requires near-IR images and assumes that the entire galaxy is flat with a constant scaleheight. For bars in late-type galaxies, where the bulge is small or even absent, this is probably reasonable; but for early-type galaxies, large bulges (and possibly multiple disc components with different thicknesses) make this a questionable assumption. (More recently, Laurikainen et al. 2004 have an included a spherical bulge component in the modeling process, which alleviates some of the problems.) Happily, Laurikainen et al. (2002) find that the bar strength measured this way correlates quite well with bar ellipticity.

3.3 Measuring the sizes of discs

Galaxies come in many sizes and what might be a large bar in one galaxy would be small in another. Thus, although absolute measurements of bars size (in kpc) are useful, we also need some kind of relative measurement. What should we compare bar sizes with?

The simplest approach is to follow EE85 and Martin (1995): compare the bar size to the optical disc size D25, which is available for all the galaxies. Because I measure bar semimajor axes, I use R25=D25/2 for the disc size. To be consistent with Martin's measurements, I use the D0 values from RC3, which are corrected for inclination (usually a very small effect) and for Galactic extinction.

Another useful measurement is the exponential scalelength of the disc. Combes & Elmegreen (1993) argued that bars in late-type galaxies should extend to approximately one disc scalelength, and Laine et al. (2002) suggested that the correlation they observed between bar size (aε) and D25 implied that bars ‘extend to a fixed number of radial scalelengths in the disc’. Bar sizes in terms of disc scalelengths are also much easier to compare with simulations, because exponential scalelengths for N-body discs are easily measured.

For those galaxies in which an outer exponential disc can be identified, I derive its slope by fitting the region outside the bar, using an azimuthally averaged surface-brightness profile.5 This is the classic approach of ‘marking the disc’ by eye. In principle, more accurate scalelengths might be derived by performing a bulge-disc decomposition, so that the contribution of bulge light to the outer disc profile is accounted for. However, I do not attempt this because many of these galaxies are strongly barred and/or contain luminous central structures apart from the bulge (secondary bars, inner discs, or nuclear rings). In extreme cases, these non-bulge components can dominate the interior light (Erwin et al. 2003) and attempting to fit them with, e.g. a de Vaucouleurs or Sérsic profile, could assign too much light at large radii to the ‘bulge’ and distort the disc fit. Because I am deliberately fitting only the region outside the bar, the effect of bulge light in most cases is minimized. In any event, de Jong (1996) found that the change in derived scalelength between marking the disc and more sophisticated decomposition techniques was typically only a few per cent. A comparison of my disc scalelengths with those of Baggett, Baggett & Anderson (1998; hereafter BBA98), which were obtained via bulge-disc decompositions, shows a similarly small variation (see Section 3.4). Details for unusual cases are provided in the Appendix, along with notes for galaxies where severely non-exponential outer discs prevented determining an exponential scalelength.

Another reason for fitting the outer disc only is shown in Fig. 3. Although it is sometimes argued that bars vanish from the surface-brightness profile when it is averaged, leaving behind only the underlying exponential disc (e.g. EE85; Ohta et al. 1990), this is not always true: the bar can sometimes appear as a clear, significant excess above the (outer) exponential profile (see also de Jong 1996). None the less, if we exclude the bar region and any excess just outside it, we can still distinguish an unambiguous outer exponential profile in such galaxies (see Erwin, Pohlen, & Beckman, in preparation, for details).

Figure 3

Azimuthally averaged R-band profile for NGC 4151. The vertical, short-dashed lines indicate deprojected bar-size measurements aε and Lbar; the diagonal, long-dashed line is an exponential fit to the disc region outside the bar (r > 145 arcsec, excluding the ring excess at r~ 200–260 arcsec). Note the excess light at r~ 40–100 arcsec, which is primarily due to the bar.

Figure 3

Azimuthally averaged R-band profile for NGC 4151. The vertical, short-dashed lines indicate deprojected bar-size measurements aε and Lbar; the diagonal, long-dashed line is an exponential fit to the disc region outside the bar (r > 145 arcsec, excluding the ring excess at r~ 200–260 arcsec). Note the excess light at r~ 40–100 arcsec, which is primarily due to the bar.

However, in other galaxies, the outer disc does not have a single exponential profile. For 16 galaxies, the profile outside the bar is what Freeman (1970) termed a ‘Type II’ profile in which it is divided into two (usually) exponential zones: a shallow inner zone and a steeper outer zone (see Fig. 4 for an example). In such cases, it is not at all clear which of the two zones (if either) should be considered the ‘true’ outer disc. In at least some cases (e.g. NGC 2859, 3412, 2962, 5701 and 6654), the inner zone is extremely narrow and/or shallow in slope, or even increasing in brightness with radius. The simplest solution is to ignore these more extreme ‘outer’ Type II profiles. (Five other galaxies have Type II profiles with a deficit inside the bar, so there is still a single exponential profile outside the bar; these are similar to profiles produced in some N-body simulations, e.g. Valenzuela & Klypin 2003).

Figure 4

As for Fig. 3, but showing the profile of NGC 3945, which has two exponential zones outside the bar (an example of a Freeman Type II profile). Because there is no single, well-defined exponential zone in such galaxies, I do not compute bar sizes relative to disc scalelengths for them.

Figure 4

As for Fig. 3, but showing the profile of NGC 3945, which has two exponential zones outside the bar (an example of a Freeman Type II profile). Because there is no single, well-defined exponential zone in such galaxies, I do not compute bar sizes relative to disc scalelengths for them.

There are additional galaxies where the surface brightness profile at large radii is shallower than that of disc immediately outside the bar; these are the ‘Type III’ or ‘anti-truncation’ profiles discussed in Erwin, Beckman & Pohlen (2005). Because these galaxies do have an extended, well-defined exponential zone outside the bar, I include their scalelength measurements. The presence of extended light at large radius may contribute to a subtle selection effect, which I discuss in Section 4.1.

3.4 Comparing measurements: early- and late-type galaxies

The bar sizes of the S0-Sb galaxies are measured using a combination of ellipse fits and direct inspection of R-band images, supplemented by near-IR images when dust is strong. On the other hand, the bar sizes of Martin (1995) are based on measurements made on blue photographic prints. How consistent are these measurements? Also, which of my two measurements (aε and Lbar) is a better match to Martin's single bar-size measurement?

Unfortunately, there are almost no galaxies in common between the two samples, even among the Sb subset (the three shared galaxies are NGC 3351, 3485 and 4725, where Martin finds a= 46, 18 and 109 arcsec, respectively; these values are only slightly smaller than my aε= 52, 23 and 118 arcsec). This makes it difficult to tell which of the two, aε and Lbar, is a better match to Martin's visual estimates. Fortunately, Martin compared his measurements with the visual bar-size measurements of Kormendy (1979) and there are numerous overlaps between Kormendy's sample and mine.6 In Fig. 5, I compare aε and Lbar measurements with those of Kormendy for galaxies in common. Kormendy's measurements generally sit inbetween aε and Lbar; in fact, the best agreement is with the mean of aε and Lbar, which I will refer to as Lavg. Because Martin found excellent agreement between Kormendy's measurements and his for galaxies in common between their samples, this suggests that Lavg is a reasonable match to Martin's bar lengths. (The results discussed later do not change significantly if I compare Martin's measurements with aε instead.)

Figure 5

Comparison of observed (i.e. projected) bar size measurements between this study and Kormendy (1979): aε values are shown with filled circles, Lbar with open boxes.

Figure 5

Comparison of observed (i.e. projected) bar size measurements between this study and Kormendy (1979): aε values are shown with filled circles, Lbar with open boxes.

The disc scalelengths for the galaxies from Martin (1995), when available, are taken from BBA98. This is the only study with large numbers of scalelengths that overlaps significantly with both the early-type galaxies in my sample and the later-type galaxies in Martin's sample. The BBA98 fits differ from mine in using major-axis cuts from V-band photographic images and in using bulge-disc decompositions with an optional ‘hole’ in the disc. Because the ‘bulge’ component (i.e. the central excess over the exponential disc, which BBA98 model with a de Vaucouleurs profile) in late-type galaxies is generally smaller and less luminous than in earlier types, the effect on the disc fit is reduced.

The optional hole in the BBA98 disc model, which is intended to account for Type II profiles, introduces a new problem, however: it forces the bulge component to account for all the inner light (including, e.g. the inner part of the disc and the bar). Because the bulge model is not truncated, it ends up contributing more light at large radii than the true bulge probably does and can thus distort the disc fit. The ‘disc with hole’ fits also obviously indicate possible Type II profiles, which, as noted in Section 3.3, are problematic for estimating scalelengths. However, because they use major-axis cuts rather than azimuthally averaged profiles, at least some of their Type II profiles turn out to be Type I when azimuthally averaged. This generally happens when the bar is oriented at an intermediate angle or perpendicular to the major-axis cut, and probably signals the transition between the outer disc and, for example, a lens in which the bar is embedded (e.g. NGC 2787; see Erwin, Pohlen, & Beckman, in preparation, and also Ohta et al. 1990).

To evaluate how well the BBA98 disc scalelengths compare with mine, Fig. 6 plots scalelengths for galaxies in common between this study and BBA98. There is a fair amount of scatter, but the agreement is generally good if I reject BBA98 scalelengths when the hole radius is more than twice the scalelength. This criterion would also reject six of the nine Type II profiles from my sample that are also in BBA98 (not plotted), so I use the BBA98 scalelengths only when their fit has no hole or a hole with radius <2 h.

Figure 6

Comparison of exponential disc scalelengths for galaxies in common between this study and Baggett et al. (1998; BBA98). Different symbols indicate different types of fits from Baggett et al.: filled circles are standard discs (no holes), small hollow circles are fits using discs with holes having radii <2 times disc scalelength h and large hollow circles are fits with large holes (rhole > 2 h). The agreement is generally good except when the BBA98 fits have large holes.

Figure 6

Comparison of exponential disc scalelengths for galaxies in common between this study and Baggett et al. (1998; BBA98). Different symbols indicate different types of fits from Baggett et al.: filled circles are standard discs (no holes), small hollow circles are fits using discs with holes having radii <2 times disc scalelength h and large hollow circles are fits with large holes (rhole > 2 h). The agreement is generally good except when the BBA98 fits have large holes.

The comparison in Fig. 6 is also useful as a test of how well scalelengths measured directly from the profile (‘marking the disc’) compare with those derived from a bulge-disc decomposition, as performed by BBA98. Except for cases where BBA98 used very large holes in their discs (large open symbols), the agreement is rather good. There is a very weak systematic trend: my scalelengths are on average 4 per cent larger than the BBA98 scalelengths. However, because the relative scatter (absolute value) is 17 per cent, this is not a very significant difference.

Fig. 7 shows the run of R25/h versus Hubble type for the combined samples. In general, the early-type galaxies have R25~ 3h, while Sb and later-type galaxies have R25~ 4h, presumably because their discs have more younger stars and are thus bluer and brighter. As I will show in Section 4.1, this has some implications for relative bar sizes.

Figure 7

Isophotal disc size (R25) in terms of the exponential scalelength h, as a function of Hubble type. Galaxies from my sample are shown with open circles, while galaxies from Martin (1995) meeting the same selection criteria are shown with filled diamonds; mean values for each Hubble type are indicated by the large boxes.

Figure 7

Isophotal disc size (R25) in terms of the exponential scalelength h, as a function of Hubble type. Galaxies from my sample are shown with open circles, while galaxies from Martin (1995) meeting the same selection criteria are shown with filled diamonds; mean values for each Hubble type are indicated by the large boxes.

4 Bars Sizes, Strengths and Hubble Type

In this section, I look at how bar sizes, in absolute and relative terms, vary with Hubble type and with bar strength. I also investigate whether and to what degree the size of bars correlates with galaxy size and luminosity, and with bar strength. I begin by discussing the S0-Sb bars from my sample in isolation, both because my sample is more consistent and complete than that of Martin (1995) and because I measured two bar sizes (aε and Lbar) versus Martin's single measurement. I then add in the later types of Martin's sample and look at the run of bar sizes along the Hubble sequence from S0-Sd, and finally examine how bar size relates to bar strength.

4.1 Bars in early-type galaxies

Fig. 8 shows absolute bars sizes as a function of Hubble type for the S0-Sb galaxies; Figs 9 and 10 show the run of bar sizes relative to R25 and the disc scalelength h. Table 2 shows mean bar sizes for different galaxy types, and Tables 3 and 4 show the strength of different correlations between bar sizes and galaxy properties.

Figure 8

Deprojected sizes of S0-Sb bars in absolute terms (semimajor axis in kpc), using maximum-ellipticity length aε (top) and Lbar (bottom). Virgo cluster S0 galaxies are indicated by hollow circles, with filled circles for field galaxies. The mean values for each Hubble type are indicated by the large boxes.

Figure 8

Deprojected sizes of S0-Sb bars in absolute terms (semimajor axis in kpc), using maximum-ellipticity length aε (top) and Lbar (bottom). Virgo cluster S0 galaxies are indicated by hollow circles, with filled circles for field galaxies. The mean values for each Hubble type are indicated by the large boxes.

Figure 9

As for Fig. 8, but now showing sizes of bars relative to disc radius R25.

Figure 9

As for Fig. 8, but now showing sizes of bars relative to disc radius R25.

Figure 10

As for Fig. 8, but now showing sizes of bars relative to the outer-disc exponential scalelength h.

Figure 10

As for Fig. 8, but now showing sizes of bars relative to the outer-disc exponential scalelength h.

Table 2

Mean bar sizes for S0-Sb galaxies.

Table 2

Mean bar sizes for S0-Sb galaxies.

Table 3

Correlations for S0-Sb galaxies.

Table 3

Correlations for S0-Sb galaxies.

Table 4

Correlations for S0-Sb galaxies with measured scalelengths.

Table 4

Correlations for S0-Sb galaxies with measured scalelengths.

Bar and disc sizes are well correlated for these galaxies; the correlations between bar sizes and outer-disc scalelength are equally good. In fact, when only those galaxies with measured scalelengths are considered (Table 4), the strongest correlation is with the disc scalelength (this may be biased by the Sb galaxies; see below). There is also a correlation between bar size and blue luminosity, as first noted by Kormendy (1979); however, it is clearly not as strong as the correlations with h and R25. This is reasonable, because bars are disc phenomena and MB can include variable contributions from the bulge; in addition, it may be more affected by variations in star formation and dust extinction.

The correlation between bar size and scalelength is strongest for Sb galaxies (Table 4), but the correlations with R25 and MB are noticeably weaker. The Sb galaxies are also odd in having bars that are smaller in absolute and R25-relative size (Figs 8 and 9): yet almost the same size relative to the disc scalelength (Fig. 10).

This curious situation may partly be due to higher levels of recent star formation in the Sb and later galaxies, which makes their discs brighter and thus larger (in blue isophotal size) for a given scalelength (see Fig. 7). For the Sb galaxies in my sample, R25/h= 3.9 ± 1.1 (3.9 ± 1.0 if Sb galaxies from Martin 1995 are included), versus 3.2 ± 0.9 for the S0-Sab galaxies. For the combined Sb-Sd galaxies, the mean size is R25/h= 4.3 ± 1.7. Kolmogorov-Smirnov (K-S) tests suggest that there is indeed a significant difference in relative disc size between early and late types, starting with the Sb galaxies: the Sb-Sd R25/h ratios are inconsistent with those of S0-Sab galaxies (P= 0.012).

Thus, my selection criterion of D25 ≥ 2.0 arcmin means that the Sb subsample includes galaxies with smaller h (and thus bars with smaller absolute sizes) than the earlier Hubble types: the mean h= 2.5 ± 1.7 kpc for Sb galaxies versus 3.0 ± 1.6 kpc for S0-Sab galaxies. If the star formation in Sb and later galaxies is also more variable than in earlier types, then the weaker correlations of Sb bar size with R25 and MB make sense as well.

An additional possible effect is the existence of galaxies with excess light at larger radii, relative to the outward projection of the exponential disc profile. These are the Type III profiles of Erwin et al. (2005) and they are, in this sample at least, especially common in both Sb galaxies and S0 galaxies (31 and 32 per cent, respectively, of those Hubble types, compared with 13 per cent of the S0/a-Sab galaxies). Again, if we assume that bar size scales most strongly with inner-disc h, then a diameter-limited selection will preferentially include S0 and Sb galaxies with smaller disc scalelengths and smaller bars, when compared with S0/a-Sab galaxies in the same sample.

Table 2does show a slight tendency for both S0 and Sb bars to be smaller in size relative to disc scalelength, but this is not statistically significant: for example, a K-S test gives P= 76–87 per cent that Sb and S0/a-Sab bar sizes relative to h come from the same parent population. Therefore, despite what Figs 8 and 9 seem to suggest, it is not clear that S0 and Sb bars are really smaller than the bars in S0/a-Sab galaxies. If size relative to disc scalelength is the most reliable measuring stick, then there is no significant difference in bar size over the range S0-Sb.

Although most of the galaxies in my sample are from the field, I did include eight S0 galaxies from the Virgo cluster. Do Virgo S0 galaxies have different bar properties from field S0 galaxies? The Virgo lenticulars do tend to have slightly larger bars than the field S0 galaxies (e.g. mean aε/R25= 0.41 ± 0.15 versus 0.28 ± 0.09; mean aε/h= 1.25 ± 0.49 versus 1.06 ± 0.39). However, none of these differences is statistically significant: K-S tests give probabilities of 9–88 per cent for the field and Virgo S0 bar sizes being drawn from the same parent population.

4.2 Bar sizes in later-type galaxies and the Hubble sequence

When galaxies from the sample of (Martin 1995, see Section 3.4) are added to the S0-Sb galaxies, the Hubble sequence coverage extends down to Sd galaxies. Figs 11–13 and Table 5 show bar sizes for this combined set of galaxies. As noted by earlier studies (EE85; Martin 1995; Laurikainen et al. 2002), there is a clear tendency for bars in later Hubble types to be smaller; this is true using both relative-size measurements and absolute sizes.

Figure 11

Sizes of S0-Sdm bars in absolute terms (kpc), combining my sample (circles) with galaxies from Martin (1995) meeting the same selection criteria (diamonds). All bar lengths are deprojected; as explained in the text, I use the average of aε and Lbar for galaxies in my sample as the best match to Martin's bar measurements. Mean values for each Hubble type (using galaxies from my sample only for S0-Sb) are indicated by the large boxes.

Figure 11

Sizes of S0-Sdm bars in absolute terms (kpc), combining my sample (circles) with galaxies from Martin (1995) meeting the same selection criteria (diamonds). All bar lengths are deprojected; as explained in the text, I use the average of aε and Lbar for galaxies in my sample as the best match to Martin's bar measurements. Mean values for each Hubble type (using galaxies from my sample only for S0-Sb) are indicated by the large boxes.

Figure 12

As for Fig. 11, but now showing size of bars relative to disc radius R25.

Figure 12

As for Fig. 11, but now showing size of bars relative to disc radius R25.

Figure 13

As for Fig. 11, but now showing size of bars relative to the outer-disc exponential scalelength h.

Figure 13

As for Fig. 11, but now showing size of bars relative to the outer-disc exponential scalelength h.

Table 5

Mean bar size (Lavg) for S0-Sd galaxies.

Table 5

Mean bar size (Lavg) for S0-Sd galaxies.

Crudely speaking, one can divide the Hubble sequence into two zones, plus a transition region. Bars in S0-Sb galaxies are clearly larger than bars in late-type (Sc-Sd) galaxies. On average, the early-type bars are ≈ 2.2–2.7 times as large as late-type bars. The K-S probabilities that S0-Sb bars come from the same parent population as Sc-Sd bars are 7.9 × 10−11 for Lavg in kpc, 3.3 × 10−15 for Lavg/R25 and 5.1 × 10−6 for Lavg/h; so the result is quite robust (to put it mildly). It is worth mentioning that Martin (1995) noted that some bars in his sample could not be measured because ‘the inner parts of the disc were overexposed’. This indicates a possible bias against very small bars in Martin's final set of measurements, which apply to later-type galaxies, so the difference could be even greater.

However, where does the transition take place and how abrupt is it?Figs 11 and 12 make it appear that Sb and Sbc galaxies are a continuation of later-type galaxies: in particular, they have some very small bars (Lavg ≲ 1 kpc and ≲ 0.2 R25) not found in earlier types. However, this continuity may be partly an illusion. As discussed in the previous section, the combination of large R25/h values for Sb galaxies (mean = 3.9 ± 1.0) and diameter-limited selection leads to the inclusion of Sb galaxies with smaller disc scalelengths than is the case for the earlier Hubble types; because bar size correlates with scalelength for these galaxies, this leads to the inclusion of Sb bars with smaller absolute and R25-relative sizes. This is partly the case for Sbc galaxies as well: their mean R25/h is 4.9 ± 2.5, in comparison with 4.1 ± 1.4 for the Sc-Sd galaxies (there is little variation in R25/h among the latter types; see Fig. 7).

So once again the best picture is probably achieved by looking at bar sizes relative to the disc scalelength (Fig. 13). This shows that Sb bars are distinct from Sc-Sd bars and that they are largely indistinguishable from bars in earlier Hubble types, as I argued in the previous section. The transition point between the early- and late-type regimes is thus the Sbc galaxies: their average bar sizes are intermediate, but they include both bars as large as those in earlier types and bars shorter than 0.5 h, common in Sc-Sd galaxies but absent in the early types.

An additional, significant difference between bars in early- and late-type galaxies is the weakness or absence of correlations between bar size and other galaxy properties for the late-type galaxies. Table 6 compares the various correlations between bar size and other galaxy properties. In all cases, the later galaxy types have weaker bar-size correlations: in fact, for Sc-Sd galaxies, the correlation with MB is no longer statistically significant and there is apparently no correlation between bar size and disc scalelength!

Table 6

Correlations between bar size Lavg and galaxy properties for S0-Sd galaxies.

Table 6

Correlations between bar size Lavg and galaxy properties for S0-Sd galaxies.

It is interesting (and perhaps suspicious) that these differences are primarily between galaxies in my sample (Sb and earlier) and the later types of Martin's (1995) sample. Because the two samples have bar (and disc scalelength) measurements from different sources, some of the dichotomy could be due to varying measurement techniques or biases. However, at least some of it is probably real. Table 7 repeats the correlation analysis using only galaxies from Martin: including galaxies with V > 2000 km s−1 in order to boost the number of Sb galaxies. The table shows the same trends as Table 6, including the strong correlation of bar size with disc scalelength for Sb galaxies. This suggests that the pronounced absence of almost any correlations in Sc-Sd galaxies between bar size and disc size or galaxy luminosity is probably real. As I show in the next section, this result appears to be due, at least in part, to the fact that SB and SAB bars have distinctive sizes in late-type galaxies.

Table 7

Correlations between bar size Lavg and galaxy properties: galaxies from Martin (1995) only.

Table 7

Correlations between bar size Lavg and galaxy properties: galaxies from Martin (1995) only.

4.3 Bar size and bar strength

Strongly barred early-type galaxies (that is, S0-Sb galaxies with an RC3 bar classification of SB) typically have bar sizes roughly the same as those of early-type SAB galaxies (Table 2). The average SB bar is only ~10–35 per cent larger than the average SAB bar for size in kpc or relative to R25 and 2–3 per cent smaller when size relative to disc scalelength is used. K-S tests give probabilities of 11–94 per cent (depending on how the size is measured) that the SB and SAB lengths come from the same parent distributions.

The parameter that does differ significantly between SB and SAB bars in early-type galaxies is, not surprisingly, the deprojected ellipticity (0.49 ± 0.13 for SB, 0.36 ± 0.15 for SAB), with a K-S test giving only a 0.6 per cent probability of the same parent distribution. Interestingly, this is not as true for the observed ellipticities: the mean ellipticity is still higher for SB galaxies (0.47 ± 0.15 versus 0.39 ± 0.14 for SAB), but the K-S probability is now 22 per cent.

Deprojected ellipticity does correlate with bar size for S0-Sb galaxies, but only weakly: rs= 0.46 and 0.42 (P= 1.2 × 10−4 and 4.5 × 10−4) for aε/R25 and aε in kpc, respectively. These correlations are weaker when Lbar is used: rs= 0.25 and 0.29 (P= 0.041 and 0.021) for Lbar/R25 and Lbar in kpc, respectively. (The correlations for bar size relative to disc scalelength are weaker still: rs= 0.09 and P= 0.64 for Lbar/h.) This generally agrees with Fbar size underestimates full bar lengthChapelon et al. (1999) and Laurikainen et al. (2002), who found very little correlation between deprojected ellipticity or bar axis ratio and bar size for their early-type spirals. It is also consistent with the correlation reported by Laine et al. (2002), who used aε for bar sizes: especially because the latter authors' samples included some Sc galaxies, for which the correlation is stronger (see below).

In late-type galaxies, SB bars are more elliptical than SAB bars (deprojected ellipticity 0.64 ± 0.18 versus 0.40 ± 0.20), just as for the early-type galaxies.7 However, there is also a dramatic difference in bar size between late-type strong (SB) and weak (SAB) bars. On average, SB bars in Sc-Sd galaxies are almost twice the size of SAB bars (Table 5); a K-S test shows that this difference is significant at the 99.9 per cent level for bar size relative to R25 (the significance is 99.2 per cent for absolute sizes and 94 per cent for sizes relative to h). Because SB bars are also more elliptical than SAB bars, we should expect a strong correlation between bar size and deprojected ellipticity for the late-type bars, and this is indeed the case. For Lavg/R25 versus deprojected ellipticity, rs= 0.73 (P= 9.4 × 10−9) for Sc-Sd bars, compared with only 0.36 (P= 0.0021) for the S0-Sb bars. A similar result was found by Martinet & Friedli (1997) for a late-type (Sbc-Scd) subset of Martin's galaxies and by Chapelon et al. (1999) for their ‘normal’ (i.e. non-starbursting) Sbc and later-type galaxies.

There is some evidence for a stronger correlation between bar size and R25 (and perhaps also MB) when only late-type SB bars are considered: the Spearman correlation coefficient is 0.73 with a probability of P= 0.0013 for Lavg versus R25. In contrast, for SAB late-type galaxies, rs is only 0.29 with P= 0.21. A similar disparity exists for correlations between relative bar size and MB, though they are not statistically significant for the main sample; when all of Martin's Sc-Sd galaxies are included, the coefficients are -0.68 (P= 4.5 × 10−4) for SB bars versus −0.48 (P= 0.0019) for SAB bars.

Thus, it appears that there may be a dichotomy between SB and SAB bars in the late-type galaxies, with SB bars perhaps retaining some of the characteristics (larger size, stronger correlation with R25 and MB) of both SB and SAB bars in early-type galaxies. It should be noted that there are about twice as many SAB as SB bars in the Sc-Sd galaxies studied here; thus, the overall weakness or absence of bar-size correlations for Sc-Sd galaxies is partly a combination of poor correlation for the SAB bars and the dichotomy in sizes between SB and SAB bars. However, even when Sc-Sd bars are analysed independently in SB and SAB categories, there is still no correlation between bar size and exponential disc scalelength.

5 Discussion

5.1 Biases, sample incompleteness and the absolute sizes of bars

All the bars studied in this paper are in galaxies classified as barred (SB or SAB) in RC3. Because RC3 classifications are based on blue photographic plates, there is the possibility that some bars have been missed, for two reasons. First, as has been recognized for some time, bars can be hidden in optical images due to dust and star formation. This is probably not a large effect, if SAB galaxies are included in the ‘barred’ category: Eskridge et al. (2000) found that the total (SB + SAB) bar fraction goes from 65 ± 3 per cent when using B-band images to 73 ± 3 per cent when using H-band images. However, they also found that a significant number of optically weak (SAB) galaxies (68 per cent) become SB when classified in the IR, which suggests that many optically weak bars are really ‘disguised’ strong bars.

The second potential bias is the possibility that small bars have been missed due to resolution (and possibly saturation) effects. Recent CCD and near-IR observations have uncovered large numbers of small, inner bars embedded inside large bars; most of these went unnoticed in earlier photographic surveys (see Erwin 2004). Some galaxies classed as unbarred turn out to have nuclear bars small enough to have been missed in low-resolution or nuclear-saturated photographic images (e.g. Buta 1991; Buta & Crocker 1991; Scorza et al. 1998). So the samples may be missing precisely those galaxies with the smallest bars.

An additional bias affects the absolute sizes (lengths in kpc). The samples studied here tend to exclude small, faint galaxies. The mean (and median) luminosity is MB=−19.3 for the S0 galaxies, −19.6 for the S0/a-Sb galaxies in my sample and −19.8 for the Sb-Sd galaxies taken from Martin's (1995) sample. This can be compared with the mean luminosities for cluster S0 galaxies (MB=−18.9) and spirals (MB=−18.2), from Jerjen & Tammann (1997): clearly, the bars studied here come from galaxies on the bright ends of the distributions. As we have seen, bar size generally scales with disc size and with galaxy luminosity; thus, smaller galaxies will have smaller bars. This means that the absolute-size distributions presented here (e.g. Figs 8 and 11) are biased towards larger bars and the mean sizes are probably overestimates for the complete galaxy population.

5.2 Bar sizes and simulations

The only reasonable way to compare the sizes of real bars with those produced in N-body simulations is to use sizes relative to the disc scalelength. In principle, one can calculate sizes relative to R25 as well, but this requires estimating mass-to-light ratios and the star-formation history (e.g. Michel-Dansac & Wozniak 2004) and is thus prone to more uncertainties. In this section, I survey some recent N-body studies in an attempt to see how well or poorly they do at reproducing the relative sizes of real bars. I make no attempt to be comprehensive, and I am necessarily limited to those studies that provide both bar sizes and some indication of disc scalelength in the region outside the bar (either as measured by the authors or via inspection of surface density profiles).

Table 8 summarizes results from eight different papers. In each case, I have included as many models from each study as possible, though in some cases additional models are left out because there were no bar or disc sizes for them. One thing is immediately apparent: simulations tend to produce large bars. Indeed, several simulations produce bars that are either at the upper end of the local distribution, or are larger than any seen in nearby galaxies. Except for two of the earlier simulations, no N-body bars are as small as typical Sc-Sd bars. (Ironically, one of these is the ‘early-type’ model CS2 of Combes & Elmegreen 1993, which produced a shorter bar than their ‘late-type’ model CSE.)

Table 8

Relative bar sizes from N-body simulations.

Table 8

Relative bar sizes from N-body simulations.

Holley-Bockelmann et al. (2005) argued that when bars are triggered by satellite interactions, rather than disc instabilities, ‘the length of the bar will depend on the mass and distance of the satellite.… The typical bar induced by this process will be much larger than those formed through internal disc instabilities’. Their final bar size of aε/h~ 2.6 is indeed rather large: only two of the galaxies in my sample and one of Martin's have bars that large (Figs 10 and 13). The aε/h~ 4 bar that they report for their B5 simulation (no profiles shown) is clearly excessive. None the less, the fact that the bar size in their simulations depends on the details of the galaxy-satellite interaction is intriguing, because it suggests that bar sizes in real galaxies might provide clues to the interaction/merger histories of their host galaxies. The absence of real bars with aε/h > 3 could then indicate an upper limit on past bar-forming interactions.

Taking this argument further, one could ask if the larger bars of early-type galaxies indicate a stronger role for interactions in their formation. In this vein, Noguchi (1996) argued that bars in early-type galaxies, with their ‘flat’ major-axis profiles, are better produced by interactions than by spontaneous disc instabilities; the latter, he suggests, are responsible for late-type bars. When combined with the argument of Holley-Bockelmann et al. (2005), we seem to get a consistent picture: the differing characteristics of bars in early- and late-type galaxies indicate a greater role for interactions in the evolution of early-type galaxies. There is at least some observational evidence for this: Elmegreen, Elmegreen & Bellin (1990) reported that, for early-type (Sa-Sb) galaxies, the SB fraction was higher in binary-galaxy systems than in groups or the field; for late-type galaxies, there was no trend with environment. This fits neatly into scenarios where evolution into or along the Hubble sequence is determined primarily by the number and strength of interactions and mergers; for example, recent simulations support the idea that the bulges and thick discs characteristic of early-type galaxies have grown through satellite accretion (e.g. Walker, Mihos & Hernquist 1996; Aguerri, Balcells & Peletier 2001). Unfortunately, as Table 8 shows, both Berentzen et al. (1998) and Athanassoula & Misiriotis (2002) were able to produce extremely large bars via disc instabilities. Because flat bar profiles can also be produced this way (e.g. Sparke & Sellwood 1987; Combes & Elmegreen 1993; Athanassoula & Misiriotis 2002), it appears that satellite interaction may not be a unique explanation for early-type bars.

Athanassoula & Misiriotis (2002) and Athanassoula (2003) have emphasized the importance of angular momentum transfer in regulating the size of bars, based on their analysis of N-body simulations. Put simply, bar length is ultimately limited by the corotation radius; if a bar slows down, the corotation radius moves further out in the disc and the bar can grow in length. A bar slows if it can lose angular momentum, primarily via resonances, to particles in the outer disc, the halo and the bulge (if present). In principle, then, larger bars indicate galaxies where the bar was able to lose more angular momentum. This might explain the generally large bars of early-type galaxies, because these galaxies are more likely to have significant bulges, which can act as angular momentum sinks for the bar. This might also explain why model B of Valenzuela & Klypin (2003) produces a relatively small bar because, in that model, the halo (also an angular momentum sink) is less massive relative to the disc than in the A1/A2 models. However, this still does not explain why late-type bars are as small as they are, because even the ‘bulge-less’N-body simulations (e.g. model MD of Athanassoula & Misiriotis 2002) produce bars at least a scalelength in radius.

5.3 Some implications for secular evolution

In the past decade, an increasingly popular idea has been that bars can drive long-term (‘secular’) evolution of disc galaxies, perhaps even helping to determine the present-day Hubble sequence. The general argument is that bars, through gas inflow and vertical buckling, create or amplify bulges, thus shifting a galaxy from smaller to larger bulge/disc ratio (e.g. from being an Sc galaxy to being an Sb or Sa galaxy). In addition, it is suggested that the increasing central mass concentration produced by bar-driven gas inflow can end up turning the bar into a bulge. This is because a sufficiently strong central mass concentration can apparently destroy a bar, producing an axisymmetric, bulge-like remnant (Hasan & Norman 1990; Hasan, Pfenniger & Norman 1993; Norman, Sellwood & Hasan 1996; Berentzen et al. 1998).

A recent elaboration on the scenario of secular evolution via bar dissolution, with specific predictions for bar sizes, is that of Bournaud & Combes (2002). They posit multiple rounds of a sequence where bars form, weaken or are destroyed via mass inflow and then reform due to gas accretion by the disc (see also Sellwood & Moore 1999). In their simulations, later (i.e. second, third, or even fourth!) bars are progressively shorter than earlier bars. The implication is that early-type spirals (and S0 galaxies), whose larger bulges are built out of multiple rounds of bar formation and bar-driven inflow, should have smaller bars. Unfortunately, this is clearly incompatible with the Hubble sequence as we see it today.8

However, secular changes in bar size may still be relevant if we drop the idea of bar destruction. Most of the N-body bars mentioned in the previous section have sizes measured near the end of the simulation and can thus be considered ‘mature’ bars. However, in almost all N-body simulations, bars lose angular momentum, slow down and increase in length as time goes by: older bars are longer than younger bars. The growth is usually fairly mild, but can sometimes be dramatic: for example, Valenzuela & Klypin (2003) mention that the bar in their A2 simulation triples in absolute length (from 1.5 to 4.5–5 kpc) between t= 3 and 6 Gyr. Because the disc scalelength varies by ≲ 20 per cent, the relative size of the bar also triples, from ~0.4 h to ~1.2 h. This neatly spans the range in typical relative sizes between Sc-Sd galaxies and Sa-Sb galaxies (Table 5 and Fig. 13). Could the difference in bar sizes between early- and late-type galaxies, or the scatter in sizes for a given region of the Hubble sequence, be at least partly a matter of bar age? This might also explain the lack of a correlation between bar size and other galaxy properties, especially disc scalelength, for the late-type galaxies (Section 4.2), if disc scalelength primarily affects or determines the final size of a bar. Bars in Sc-Sd galaxies would then be young and/or still growing rapidly and thus less likely to show correlations with disc size.

This idea (younger, shorter and fast-growing bars in Sc-Sd galaxies; older and longer bars in early-type galaxies) is also consistent with the simulations and arguments of Friedli & Benz (1995) and Martin & Friedli (1997). They combined N-body simulations with gas and star formation, and noted that ‘young’ bars (<500 Myr old in their simulations) had star formation concentrated along the bar major axis, something observed in at least some SBc galaxies, while older bars tended to have star formation confined to the nucleus, the ends of the bars and an inner ring/spiral surrounding the bar, a pattern more often seen in early-type galaxies. Based on this, they suggested that barred Sc galaxies could evolve into barred Sb galaxies. (The fact that subsequent star formation is generally restricted to the ends of the bar and an inner ring might also indicate that star formation helps transform late-type ‘exponential’ bars into early-type ‘flat’ bars, by preferentially adding stars near the ends of the bar.) It would be interesting to see if there is a correlation between star-formation patterns and bar sizes in, for example, Sbc-Sd galaxies: are smaller bars in fact more likely to have ‘young’ star-formation patterns? There is actually a hint of this in the sample of Martin & Friedli (1997): they classified 11 bars into three categories (A, B, C) based on the distribution of H ii regions and then associated these categories with increasing age, based on their simulations. The mean relative bar sizes of the three groups are, in order of increasing age, Lavg/R25= 0.19, 0.28 and 0.32, which does agree with the scenario; however, the sample is really too small for this to be a valid test.

A problem with this idea is the fact that, in the few simulations where gas has been included and bar length at different times is reported (e.g. Berentzen et al. 1998; Immeli et al. 2004), the bar does not grow significantly; it may even shrink slightly. This may be because the bar gains angular momentum from the gas inflow it drives, thus keeping its pattern speed constant or increasing and keeping corotation at a small radius. This would seem to mean that bars in Sc-Sd galaxies, which generally have abundant gas, should not grow significantly; this might even help explain why their bars are generally small! It may be that once enough of the gas within corotation has been exhausted (e.g. converted to stars), the bars can grow; however, whether this is possible and whether the bars can grow large enough awaits further simulation. (Both of the studies mentioned above produced bars larger than those of typical early-type galaxies, so it is not clear how relevant they are to late-type bars.)

The alternative to these scenarios of secular evolution is that there is something fundamentally different between early- and late-type disc galaxies, which is reflected in their different bar properties. It would be fruitful to examine more carefully why some simulations produce larger bars than others (see, for example, the discussions in Athanassoula 2003; Valenzuela & Klypin 2003) and whether there are any parameters (e.g. relative halo mass, halo structure and kinematics and, in particular, gas content) that can reliably produce the small bars of late-type galaxies.

On a separate note, it is interesting to compare the field and Virgo S0 galaxies in my sample. A popular scenario for creating cluster S0 galaxies is ram-pressure stripping of spirals that fall into a cluster and encounter its intracluster medium at high speed (e.g. Quilis, Moore & Bower 2000). If removal of the gas of a spiral galaxy (and subsequent aging of its stellar population without new star formation) is all that happens, then we might expect other properties, such as bar size, to remain unchanged. Because the most numerous bright spiral types are Sbc and Sc (e.g. Eskridge et al. 2002), we should on average see smaller bars in cluster S0 galaxies (if conversion of infalling spirals is the primary formation mechanism). However, as I showed in Section 4.1, Virgo cluster S0 galaxies tend, if anything, to have larger bars than field S0 galaxies and their bars are certainly consistent with the general field S0-Sb population. This suggests that cluster S0 galaxies are probably not just stripped and aged spirals, or else that they are preferentially formed from early-type spirals. Quilis et al. note that other mechanisms may be needed to produce larger bulges and thicker discs in stripped spirals in order to make the end products more like S0 galaxies; such mechanisms must also, it seems, ensure that cluster S0 galaxies end up with large bars.

5.4 Finding bars at high redshift

Although the samples analysed here do not extend to very faint magnitudes, there is no evidence for any trend in relative bar size with magnitude or R25 (Fig. 14). This suggests that smaller and fainter galaxies should follow the general bar-size-luminosity and bar-size-disc-size correlations found here, at least for Hubble types earlier than Sc. So, if high-z galaxy samples include significant numbers of faint galaxies, they will probably include bars that are small in absolute (kpc) terms and thus difficult to detect.

Figure 14

Relative bar size aε/R25 versus disc size (top) and galaxy luminosity (bottom) for S0-Sb galaxies. Relative bar size shows no correlation with either galaxy size or luminosity; this suggests that galaxies smaller and/or less luminous than the sample probably have a similar range of relative bar sizes.

Figure 14

Relative bar size aε/R25 versus disc size (top) and galaxy luminosity (bottom) for S0-Sb galaxies. Relative bar size shows no correlation with either galaxy size or luminosity; this suggests that galaxies smaller and/or less luminous than the sample probably have a similar range of relative bar sizes.

The important point is that (in the absence of any evolutionary effects) the absolute size of bars and thus their detectability depend on the size, luminosity and Hubble types of the galaxies being studied. Thus, a proper measure of bar fractions as a function of redshift requires careful sample selection: the low- and high-redshift samples must contain galaxies with a similar distribution of disc sizes or absolute magnitudes. The latter is probably easier to achieve, but evolutionary corrections will almost certainly need to be applied. Disc isophotal size will probably also evolve with redshift, in ways perhaps less easy to model. (Recall the subtle bias introduced by an isophotal size limit in my sample, leading to an Sb subsample with smaller scalelengths and absolute bar sizes than the S0-Sab bars; see Section 4.1.) The best sample-matching might therefore be in terms of disc scalelengths: assuming, of course, that they do not evolve significantly.

Recently, van den Bergh et al. (2002) analysed the detectability of bars and spiral structure with redshift by artificially redshifting and resampling B-band images from the Ohio State University Bright Spiral Galaxy Survey (BSGS; Eskridge et al. 2002) to match z= 0.7Hubble Deep Field (HDF) exposures. They argued that most of the strong bars in the BSGS galaxies would still be detectable at z= 0.7; the apparent absence of such bars in real HDF galaxies at z~ 0.7 (e.g. van den Bergh et al. 2000) is then, they suggest, a genuine effect. However, lurking behind this is the assumption that the BSGS is a reasonable match to high-zHDF galaxies. As their Fig. 2 shows, the BSGS does live up to its name: the magnitude distribution peaks at MB≈−20.2 and essentially all of the galaxies are brighter than the mean magnitude (−18.2) of local spirals found by Jerjen & Tammann (1997). Van den Bergh et al. noted that deep HST images, such as the HDF, will sample significantly fainter galaxies, even in the absence of luminosity evolution. This means that (assuming no bar evolution) the average bar in the HDF sample will probably be smaller (in kpc) than the average BSGS bar and therefore harder to detect (see the discussion of bar-size detectability versus redshift in Sheth et al. 2003).

In striking contrast to the apparent absence of optical bars at high z in the HDF, Sheth et al. (2003) found at least four barred galaxies with z~ 1 in the HDF by using Near Infrared Camera and Multi-Object Spectrometer (NICMOS) images, which suggests that bandshifting effects are important. More recent studies based on higher-resolution Advanced camera for Surveys imaging (Elmegreen, Elmegreen & Hirst 2004; Jogee et al. 2004) find comparable fractions of bars at low and high z; this is eloquent confirmation of the parallel importance of resolution, as Sheth et al. also emphasized.

Sheth et al. reported an average bar semimajor axis of 6 kpc for their high-z, NICMOS-detected bars and argued that this was unusually large when compared with local galaxies: specifically, when compared with the Berkeley Illinois Maryland Association Survey of Nearby Galaxies (BIMA SONG) sample.9 However, are the bars they found really so large? The BIMA SONG galaxies are dominated by intermediate and late types (21 of its 29 barred galaxies are Sbc or later) and thus should include mostly smaller bars. In Fig. 15, I plot the semimajor axes of their high-z bars in the context of the entire Hubble sequence. The high-z bar sizes are based on my inspection of their NICMOS ellipse fits, with Lavg= the average of aε and a10. In general, I find smaller values of aε than they do (2.4–6.5 kpc, versus their 4–8 kpc), probably because they use the absolute peak in ellipticity, which can be due to spiral arms outside the bar itself. Because these bar sizes are observed (i.e. no deprojection was attempted), I compare them with the observed sizes of local bars. Fig. 15 shows that the high-z bars Sheth et al. found are unusually large only in the context of late-type spirals; they are large but plausible for early-type spirals.

Figure 15

As for Fig. 11, but now showing observed (i.e. not deprojected) bar sizes. Sizes for the four high-z bars of Sheth et al. (2003) are indicated by dashed lines.

Figure 15

As for Fig. 11, but now showing observed (i.e. not deprojected) bar sizes. Sizes for the four high-z bars of Sheth et al. (2003) are indicated by dashed lines.

The mean Lavg of the high-z bars is 4.7 kpc, very close to the NICMOS3 detection limit Sheth et al. suggest for z~ 1. One might then ask, following Sheth et al., whether finding the number of bars of that size (e.g. two with Lavg > 4.7 kpc) in high-z spirals is at all meaningful in the context of local galaxies. In Fig. 15, there are six out of 113 local barred spirals with projected Lavg > 4.7 kpc. This translates to six out of ~160 local spirals of all bar classes (assuming that ~70 per cent of local spirals with D25 ≥ 2.0 arcmin and a/b ≤ 2.0 have RC3 classifications of SB or SAB; Erwin, in preparation) for a local frequency of ≈4 ± 2 per cent. Sheth et al. found their four barred galaxies in a sample of 95 disc-like galaxies with z > 0.7; they noted that the total number would drop to 31 (and three barred galaxies) if the magnitude cut-off of Abraham et al. (1999) was used. Regardless of how the parent sample is defined, the frequency of large bars at high-z (2/95 = 2 ± 1 per cent or 2/31 = 6 ± 4 per cent) appears consistent with the local frequency. Of course, this analysis assumes the parent samples are comparable, which is probably not true. For example, the faintest of their high-z barred galaxies has H≈ 26, which they suggest corresponds to rest-frame MB≈−16. This is fainter than any of the galaxies in my sample, Martin's (1995) sample, or the BIMA SONG sample.

Finally, I note that the much larger (though currently incomplete) sample of z= 0.7–1.0 disc galaxies studied by Jogee et al. (2004) seems to have typical bar semimajor axes ~3 kpc, very close to the average S0-Sb bar sizes in my sample (Table 2). Again, this suggests that bar sizes at z~ 1 were similar to bar sizes in the local universe and that high-z studies will naturally select against the small bars characteristic of late-type spirals.

6 Summary

I have presented a study of bar sizes in disc galaxies, using a sample of 65 nearby S0-Sb galaxies as well as the published bar sizes for 70 nearby Sb-Sd galaxies from Martin (1995). The main results are summarized as follows.

  1. Bars in early-type (S0-Sb) galaxies have mean absolute sizes (semimajor axis) of ~3.3 kpc and mean relative sizes of ~0.38R25 and ~1.4h (where h is the exponential disc scalelength).

  2. For these galaxies, the sizes of bars relative to disc scalelength are roughly constant with Hubble type. The Sb galaxies in my sample appear to have smaller bars relative to R25 in comparison with the S0-Sab galaxies because the Sb galaxies have, on average, larger values of R25/h. A diameter-limited selection criterion then leads to smaller average scalelengths for these galaxies and thus bars with smaller average absolute sizes (~2.5 kpc) as well.

  3. As has been noted earlier, bars in early-type (S0-Sb) galaxies are larger than those in late-type (Sc-Sd) galaxies. This is true regardless of how bar size is measured; bar size relative to disc scalelength appears to be the most robust measurement and the least vulnerable to selection effects. On average, early-type bars are ~2.5 times larger than late-type bars, which have mean sizes of ~1.5 kpc, 0.14R25 and 0.6h. Sbc galaxies have bars intermediate in size between the early and late types.

  4. Early-type bars show strong correlations of bar size with R25 and h; these correlations are stronger than the known correlation of bar size with MB. However, late-type bars as a whole show only weak correlations of bar size with R25 and MB, and no correlation with h at all.

  5. Strong (SB) and weak (SAB) bars in early-type galaxies differ primarily in ellipticity; they are very similar in size. However, late-type galaxies exhibit a real dichotomy: SB bars in Sc-Sd galaxies are on average twice the size of SAB bars, and the SB bars have stronger correlations of bar size with R25 and MB.

  6. Comparison with a number of recent N-body studies suggests that simulations usually produce relatively large bars (bar size ≳1.5 h), including some bars larger than those seen in real galaxies. The small bars typical of late-type galaxies (bar size ~0.6h) are rare in simulations.

  7. Comparison with local bars shows that the recently discovered z~ 1 bars of Sheth et al. (2003) have sizes typical of those in early-type (S0-Sb) galaxies. Because bar size scales with disc size (and, less strongly, with MB) for all but the latest Hubble types and because smaller bars are harder to detect at high redshift, attempts to compare bar frequencies at different redshifts must be careful to use similar samples of galaxies: ideally samples with similar disc scalelengths.

Acknowledgments

I am grateful to Paul Schechter for observations made at the MDM Telescope, to Hans Deeg for observations made at the INT and especially to Juan Carlos Vega Beltrán for his help in obtaining observations at the NOT; I also thank Johan Knapen for a K-band image of NGC 4725. I enjoyed helpful and interesting conversations with a number of people, including Andrew Cardwell, Ignacio Trujillo, Alister Graham, Alfonso López Aguerri, Michael Pohlen, John Beckman, Victor Debattista and Octavio Valenzuela. Kartik Sheth, Karin Menendez-Delmestre, Witold Maciejewski and Lia Athanassoula provided insightful comments on early drafts, and Seppo Laine was quite helpful at clarifying some of the complexities of deprojecting ellipses. Finally, I thank the referee, Eija Laurikainen, for a careful reading and several suggestions that improved the paper.

This research is (partially) based on data from the Isaac Newton group (ING) Archive and on observations made with both the Isaac Newton Group of Telescopes, operated on behalf of the UK Particle Physics and Astronomy Research Council (PPARC) and the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO) on the island of La Palma, and the NOT, operated on the island of La Palma jointly by Denmark, Finland, Iceland, Norway and Sweden. Both the ING and NOT are part of the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias. I also used images from the BARS database, for which time was awarded by the Comité Científico Internacional of the Canary Islands Observatories.

This research made use of the NED, which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with NASA. It also made use of the LEDA (part of HyperLeda at ).

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1
The WIYN Observatory is a joint facility of the University of Wisconsin-Madison, Indiana University, Yale University and the National Optical Astronomy Observatories.
2
Based on the mean and standard deviations from their table 1.
3
This can happen even in the near-IR: Laurikainen & Salo (2002) report an unusually small aε= 18 arcsec for NGC 4691, from ellipse fits to TwoMicron All Sky Survey images.
4
As a reminder, the Pearson coefficient measures the strength of linear correlations and the Spearman coefficient measures general correlations and is usually considered more robust against outliers; see, e.g. Press et al. (1996).
5
That is, a profile obtained with concentric, similar ellipses using the ‘Outer disc’ PA and ellipticity from Table 1.
6
There is not enough information about bar orientation in Kormendy's Table 1 to allow reliable deprojections of his bar sizes; in addition, his sample is limited to SB galaxies.
7
This discussion omits the SBc galaxy NGC 2835, for which Martin (1995) lists a deprojected axis ratio of 1.0.
8
At least some of the difference may be due to the particular mode of accretion used by Bournaud & Combes (2002), such that alternate accretion scenarios might produce more realistic distributions of bar sizes (Bournaud, private communication.)
9
Note that they discuss all sizes and plot their ellipse fits, in terms of diameters.

Appendix

APPENDIX A: Notes on Individual Galaxies

Unless otherwise noted, all disc scalelengths were measured using the azimuthally averaged profile outside the bar region. If no clear, exponential profile could be determined, then no fit was performed. Specific exceptions and cases where the non-exponentiality can be traced to specific morphological features (or observational problems) are subsequently listed. Galaxies that met the sample selection criteria but that are not included in the final set of measurements are indicated by names enclosed by brackets, or else listed at the end of each subsample.

A1 The WIYN Sample (field S0-Sa)

For most of these galaxies, the relevant details (including sources for the distance measurements) are discussed in Erwin & Sparke (2003). Here, I provide additional notes, primarily on measurements of outer disc scalelengths.

NGC 936. Type II outer-disc profile.

NGC 2859. Strong outer ring produces extreme Type II profile.

NGC 2880. Outer profile is non-exponential, flattening at large radii (probably dominated by bulge light). The inclination is based on the region of maximum ellipticity, where the disc appears to dominate (r~ 50 arcsec), but no clear slope can be determined.

NGC 2962. Type II outer-disc profile.

NGC 3412. Type II outer-disc profile.

NGC 3489. Bar measurements are from an unpublished William Herschel Telescope (WHT)-Isaac Newton Group Red Imaging Device H-band image, due to strong dust extinction in the optical.

NGC 3729. The outer-disc scalelength and revised outer-disc orientation are from a Sloan r-band image obtained with the INT Wide Field Camera (WFC; Erwin et al., in preparation), because the WIYN images were taken during full moon.

NGC 3945. Strong outer ring produces extreme Type II profile; the inclination has been updated using a high-quality r-band image from the WFC of the 2.5-m INT (INT-WFC, La Palma; Erwin et al., in preparation).

NGC 4143. The outer-disc scalelength is from a Sloan r-band image obtained with the INT-WFC (Erwin et al., in preparation).

NGC 4203. Type II outer-disc profile. The length Lbar of the bar, based on the ellipticity minimum, is undoubtedly an overestimate; because this galaxy is nearly face-on and lacks spiral arms, the ellipse-fit measurements amin and a10 are misleading or undefined.

NGC 4245. Outer disc orientation and scalelength measurements are from a Sloan r-band image obtained with the INT-WFC (Erwin et al., in preparation).

NGC 4665. Type II outer-disc profile.

The following galaxies in the WIYN Sample were eliminated because they appeared to lack bars, or because they were too dusty and highly inclined for accurate measurements of their bars (for details, see Erwin & Sparke 2003): NGC 2655, 2685, 3032 and 4310.

A2 Virgo S0

NGC 4267. All measurements are from NOT R-band images; bar measurements agree very well with the H-band measurements of Jungwiert et al. (1997).

NGC 4340. All measurements are from MDM R-band images (bar measurements agree very well with J- and K-band measurements from BARS Project images), except for the outer-disc scalelength, which is from the R-band image of Frei et al. (1996).

NGC 4371. Bar measurements are from WIYN R-band images measurements, but the outer-disc inclination and scalelength are from deeper INT-WFC r-band images (Erwin et al., in preparation).

[NGC 4435]. Bcause this galaxy is apparently interacting with its neighbour NGC 4438 and possibly edge-on as well (e.g. Kenney et al. 1995), I excluded it from the sample.

NGC 4477. All measurements are from the R-band image of Frei et al. (1996).

[NGC 4531]. This galaxy has a dusty inner spiral, but no evidence for a bar, despite its SB0 classification.

NGC 4596. All measurements are from BARS Project R-band images (taken with the Prime Focus Camera of the INT), except for the outer-disc orientation and inclination, which are from a deeper I-band image.

NGC 4608. All measurements are from NOT R-band images.

NGC 4612. All measurements are from MDM R-band images; these agree well with measurements made using the R-band image of Frei et al. (1996).

NGC 4754. All measurements from WIYN R-band images, except that the outer-disc scalelength was determined from the R-band image of Frei et al. (1996), due to strong background variations in the WIYN image.

A3 Field Sab-Sb

Unless otherwise noted, bar and disc measurements for these galaxies were made using R-band images from the NOT, supplemented in some cases by J and Ks images from the WHT.

[NGC 278]. Both optical and near-IR images indicate that this SAB galaxy is not actually barred (e.g. Eskridge et al. 2000).

[NGC 2146]. This galaxy is severely distorted and almost certainly interacting; near-IR images suggest there is probably no bar.

NGC 2712. Bar measurements are from near-IR images, due to strong dust extinction in the R-band. The outer-disc scalelength is from an archival R-band INT-WFC image; disc orientation is from H i kinematics (Krumm & Shane 1982).

NGC 3351. Bar measurements are from the r-band image of Frei et al. (1996); the outer-disc profile is Type II. Distance is from HST Cepheid measurements (Freedman et al. 2001).

NGC 3368. Because the (outer) bar is very dusty in the optical, measurements were made using the K-band image of Möllenhoff & Heidt (2001). The outer-disc PA and inclination are from WIYN R-band images, which agree well with measurements made using the Frei et al. (1996),R-band image and with kinematic line of nodes from both the H i study of Schneider (1989), as quoted in Sakamoto et al. (1999), and the near-nuclear 2D spectroscopy of Sil'chenko et al. (2003). Type II outer-disc profile.

[NGC 3455]. Inspection of R-band and NICMOS2 F160W images strongly suggests that this SAB galaxy is not actually barred.

NGC 3504. Bar measurements are from a BARS Project I-band image from the NOT (no R-band images are available). Outer disc orientation is from Grosbøl (1985) and Kenney, Carlstrom & Young (1993). Although the inclination is uncertain, deprojection is not a major issue given that the bar is almost aligned with the outer-disc major axis.

NGC 3982. Type II outer-disc profile. Bar measurements are from a NICMOS2 F160W image; outer-disc PA is from Sánchez-Portal et al. (2000).

NGC 4102. Type II outer-disc profile. Bar measurements are from a NICMOS3 F160W image.

NGC 4151. Bar measurements and outer-disc scalelength are from a BARS Project R-band image (taken with the INT Prime Focus Camera). Outer disc orientation and inclination from the H i kinematics (Bosma, Ekers & Lequeux 1977; Pedlar et al. 1992).

NGC 4319. Bar measurements are from archival Jacob Kapteyn Telescope R-band images, obtained from the Isaac Newton Group Archive, and from an unpublished WHT J-band image. Outer disc orientation and inclination is from Grosbøl (1985).

NGC 4725. The large-scale bar in this galaxy is peculiar and somewhat difficult to measure, because it twists sharply with radius (it is similar to NGC 3185 and 5377 in this respect). None the less, there is a clear ellipticity maximum very close to the inner ring (which itself defines Lbar); this agrees fairly well with the measurements of Martin (1995) and Chapelon et al. (1999). Although the galaxy is somewhat dusty, the R-band bar measurements agree very well with measurements made with a K-band image kindly provided by Johan Knapen. The outer disc scalelength is from the r-band image of Frei et al. (1996); distance is from HST Cepheid measurements (Freedman et al. 2001). The ellipticity of the outer disc is uncertain, due to the presence of two strong spiral arms, so the inclination is based on inverting the Tully-Fisher relation using the H-band magnitude of Gavazzi & Boselli (1996), the H i width W20 from RC3, the Cepheid distance and the H-band Tully-Fisher relation as given in (Binney & Merrifield 1998, p. 425).

[NGC 4941].Greusard et al. (2000) argued that this galaxy has a nuclear bar but no large-scale bar, based on their near-IR images; on the other hand, Eskridge et al. (2002) classified it as SAB using lower-resolution H-band images, so it is not clear whether this is a single- or double-barred galaxy.

NGC 5740. Bar measurements are from near-IR images, due to strong dust extinction in the R-band. The outer-disc scalelength, from fits to r < 100 arcsec (this is another Type III profile, so the disc beyond that radius has a shallower slope) agrees beautifully with Courteau's (1996)r-band h= 18.3 arcsec.

NGC 5806. The bar presence is uncertain, at least in the R-band, though there is a clear ellipticity peak. The outer surface-brightness profile is Type III; the disc scalelength is from the extended exponential region (r~ 55–100 arcsec) outside the bar. This scalelength matches the r-band scalelength (28.8 arcsec) of Courteau (1996) quite well, though not the V-band major-axis scalelength (15 arcsec) of BBA98.

NGC 5832.aε is taken from a minimum in the PA.

NGC 5957.aε is taken from a maximum in the PA.

NGC 6012. There are several ellipticity maxima in the ellipse fits within the bar; in this case, aε is taken from the extremal value of the PA. The outer disc orientation is from the R-band image; because the outer ellipticity is uncertain, the inclination is based on inverting the Tully-Fisher relation, using the H-band magnitude of de Jong & van der Kruit (1994), the H i width W20 from RC3, the LEDA distance and the H-band Tully-Fisher relation as given in Binney & Merrifield (1998 p. 425). The outer-disc scalelength was measured from an INT-WFC r-band image (Erwin et al., in preparation).

NGC 7177. Bar and disc measurements are from an archival INT-WFC R-band image. The outer-disc scalelength is from the r= 35–60 arcsec region and agrees very well with measurements by de Jong & van der Kruit (1994) and Graham (2001). Outside this region, the profile flattens; this is another Type III profile.

UGC 3685. The outer-disc scalelength was measured from an INT-WFC r-band image (Erwin et al., in preparation). The outer-disc inclination is from Kornreich, Haynes & Lovelace (1998), with the PA from H i kinematics Kornreich et al. (2000).

A4 Data for galaxies from Martin (1995)

For the galaxies of Martin (1995), I took total blue magnitudes (Btc) from LEDA. Distances are mostly from LEDA as well, using the velocities corrected for Virgo-centric motion and H0= 75 km s−1 Mpc−1, except for cases where more accurate distances were available. These were mainly HST Cepheid distances from Freedman et al. (2001), which I used for NGC 925, 1365, 3198 and 5457. In two cases, I used distances to galaxies in the same group as one of Martin's galaxies: NGC 4236 is in the same group as NGC 2403 (M81), which has an HST Cepheid distance, while NGC 5236 is in the same group as NGC 5253 (D= 4.2 Mpc from Cepheids; Saha et al. 1995) and NGC 5128 (D= 4.2 Mpc from surface-brightness fluctuations; Tonry et al. 2001).

Some of the galaxies in Table 1 of Martin (1995) have incorrect numerical Hubble types (T) listed, though the full RC3 types are correct: NGC 1156, 1288, 1433, 3614, 4214, 4304, 5350 and IC 1953. Finally, ‘NGC 4891’ is really NGC 4397 and ‘New1’ is MCG-01-03-085 (also listed as ‘Shapley-Ames 1’ in NED).

Author notes

Max-Planck-Institut für extraterrestrische Physik, Giessenbachstrasse, D-85748 Garching, Germany.
Guest investigator of the UK Astronomy Data Centre.