Mon. Not. R. Astron. Soc. 312, 194±206 (2000)

Secular evolution of late-type disc galaxies: formation of bulges and the origin of bar dichotomy

Masafumi Noguchiw Astronomical Institute, Tohoku University, Aoba, Sendai 980-8578, Japan

Accepted 1999 September 21. Received 1999 September 21; in original form 1999 April 8

ABSTRACT Origins of galactic bulges and bars remain elusive, although they constitute fundamental components of disc galaxies. This paper proposes that the secular evolution process driven by the interstellar gas in galactic discs is closely associated with the formation of bulges and bars, and tries to explain the observed variation of these components along the Hubble morphological sequence. The ample interstellar medium serves as a coolant which makes the galactic disc gravitationally unstable and induces fragmentation of the disc. The resulting clumps spiral in to the disc centre because of dynamical friction. Efficiency of this process is governed by the gas-richness of the galactic disc, which is in turn controlled by two parameters: (i) the rapidity of the infall of the halo primordial gas to the disc plane and (ii) the amount of total accreted matter. When these two parameters are appropriately related to the mass and density of the galaxy and the effect of a star formation threshold in the disc is introduced, the gas-driven evolution through disc clumping leads to the appearance of two evolution regimes along the Hubble sequence, separated by the intermediate Hubble type for which the gas-driven mass concentration is minimal. Spiral galaxies of relatively early Hubble type (characterized by large mass and density) experience a rapid clump accumulation to the disc centre in their early evolution phase, which is identified with the formation of a bulge. On the other hand, the evolution of late-type spirals having small mass and density is strongly influenced by the existence of the star formation threshold. The disc in these galaxies becomes gas-rich in a relatively late epoch and experiences a prolonged clump-driven mass accumulation. I argue that this process leads to the formation of not a bulge but a short bar embedded in the galactic disc. The present scenario provides a natural explanation for the well-known bar dichotomy, namely that galactic bars are divided into two major groups on morphological grounds and each group is associated with different Hubble types. Key words: galaxies: evolution ± galaxies: formation ± galaxies: ISM ± galaxies: kinematics and dynamics ± galaxies: spiral ± galaxies: structure.

accretion of the residual primordial gas has built the disc 1 INTRODUCTION components. This simple picture is, however, challenged by One of the most notable structural features of disc galaxies is that recent observations of the Milky Way bulge (McWilliam & Rich they are composed of two distinct components: discs and bulges. 1994) and bulges of other galaxies (Matteucci & Brocato 1990; The origin of this two-component structure remains unclear, Peletier & Balcells 1996; Kormendy 1993). McWilliam & Rich although it constitutes the backbone of disc galaxies. In the (1994) have found that the bulge stars of the Milky Way Galaxy classical picture of galaxy formation (Larson 1976; Gott & Thuan have a larger age spread than formerly considered and show a 1976), bulges have been formed within a relatively short period, as correlation between chemical and kinematical properties (Minniti a result of the collapse of a gaseous protogalaxy, and the later 1996). Peletier & Balcells (1996) have found for their sample of galaxies that the ages of the bulge and inner disc are correlated w E-mail: [email protected] and the difference between them is as small as 30 per cent. These

q 2000 RAS Late-type disc galaxies 195 results suggest a slower build-up of the bulge components than has by mh, ms, mg and mb respectively. The total mass is denoted by M been hitherto considered, as well as a close relationship between (ˆ mh ‡ ms ‡ mg ‡ mb†. Each galactic component is treated as a bulges and discs. single zone so that any internal structures that might arise in it are There is no convincing theory for bulge formation at present, not treated. though several possibilities are considered. Cosmological simula- Under this simplification, the time evolution of masses in the tions for galaxy formation (Katz 1992) seem to indicate that the respective components is formulated as follows. primordial clumps arising from cold dark matter perturbations dm m MGt t merge to form a bulge when the host galaxy is assembled. Highly g ˆ 2SFR 2 g ‡ exp 2 ; 1† dt t b2 b contrasted to this idea is the secular formation by bar structures. fri  Galactic bars induce inflow of interstellar gas, and the ample gas dms accumulated at the galactic centre provides raw material for the ˆ SFR; 2† dt bulge component (Friedli & Benz 1993). Noguchi (1998, 1999) has suggested the third possibility that the galactic disc in its early and evolution stage fragments into massive subgalactic clumps, which dm m fall to the galactic centre owing to dynamical friction and b ˆ g ; 3† constitute a bulge. dt tfri Bars are another prominent structure ubiquitous in disc where t is the time reckoned from the beginning of gas infall, galaxies. The relation between bulges and bars also remains which is here assumed to be 12 Gyr ago. unclear. Bending instability of galactic bars and the resulting SFR stands for the star formation rate for the whole galaxy, transformation into a box-shape or peanut configuration suggests represented as that bulges in some galaxies originate in bars [see the review by 2 Sellwood & Wilkinson (1993) and references therein]. It is also Sg R 21 SFR ˆ 355 2 M( yr †; 4† known that the morphological properties of bars change system- 103 M( pc 2 104 pc atically along the Hubble sequence and two major classes of bars  are recognized (Elmegreen & Elmegreen 1985). where R is the galaxy radius and Sg denotes the gas surface 2 I develop here a scenario in a partial attempt to shed light on the density in the disc, which is approximated by mg/(pR ). The work origins of bulges and their relationship with galactic bars. This by Kennicutt (1989) suggests that a certain threshold exists for the paper is a sequel to previous papers (Noguchi 1998, 1999) and gas density, below which star formation is effectively inhibited. based on the simple model of disc galaxy evolution developed One plausible interpretation is that the star formation activity is there. A novel point here is that the role of a star formation associated closely with the gravitational instability of the gas disc, threshold is highly emphasized. Section 2 describes the evolution and the threshold corresponds to neutral stability. This interpreta- model briefly. The model results are compared with observations tion seems to be applicable not only to `classical spirals' from Sa and bulge formation in late-type spiral galaxies is discussed in to Sc, but also to later types including low-surface brightness Section 3. Origin of the bar dichotomy, i.e. the existence of the galaxies (van der Hulst et al. 1993). I introduce a threshold for star two classes of galactic bars, is discussed in Section 4, and formation by specifying a minimum velocity dispersion that the Section 5 summarizes the conclusions. gas component of the galactic disc can have. In the present model, the gas disc is assumed to stay at the marginal stability defined by Q ˆ 1, where Q denotes the stability parameter introduced by Toomre (1964). In this state, the surface density of the gas and the 2 THE CLUMP-DRIVEN EVOLUTION MODEL velocity dispersion (or the sound velocity), s, in the gas are FORDISCGALAXIES related by pGSg ˆ sk, where k is the epicyclic frequency The disc galaxy evolution model that serves as a basis for the approximated as k ˆ 2GM=R3†1=2, and G is the gravitational present study has been discussed extensively in Noguchi (1999). I constant. As Sg decreases in the late phase of evolution, s should repeat here those parts of the modelling that are indispensable for also decrease correspondingly to keep the condition that Q ˆ 1. the subsequent treatment. I followed the conventional picture of However, s cannot become less than s min, which is the specified galaxy formation: that the visible part of a galaxy has been formed lower limit of the velocity dispersion. Therefore, star formation from the primordial gas that has collapsed in the gravitational stops at the instant when s reaches s min. The threshold gas potential well of the already virialized dark matter halo. Only surface density is thus determined by Smin ˆ smink=pG. After this the late phase of the galaxy collapse is treated, in which the instant, the amount of gas consumed by star formation is balanced primordial gas accretes nearly perpendicularly to the disc plane by the amount of new gas added to the disc by accretion, so that and does not shrink in the radial direction, owing to sufficient the gas surface density is always kept nearly at the threshold value support from the centrifugal force. In this model, the gas-rich disc (i.e. Sg , Smin). On the other hand, when a sufficient gas supply of a young galaxy is subject to gravitational instability owing to is available, the star formation rate is determined by the current efficient radiative cooling. The resulting clumps drive the gas surface density, i.e. it is `density-dependent'. As a special dynamical evolution of the galaxy. Especially, they suffer from case, setting smin ˆ 0 allows star formation to proceed con- dynamical friction against ambient matter while orbiting in the tinuously depending on the current gas density. disc plane, and sink to the central region of the disc. This inward tfri is the time-scale of the inward motion of clumps caused by motion and the resulting mass accumulation at the galactic centre dynamical friction. I have used the empirical formula derived in is interpreted as the formation of a bulge. These processes are Noguchi (1999) for the dynamical friction time-scale, namely simulated by a multicomponent model, in which the galaxy is 2 20:5 0:67 divided into four components: the halo, the stellar disc, the gas tfri mcl Sd ˆ 0:25 2 : 5† disc and the bulge. The masses of these components are denoted tdyn M M=R   q 2000 RAS, MNRAS 312, 194±206 196 M. Noguchi

3 21=2 Here, tdyn‰; GM=R † Š is the dynamical time of the galaxy, mcl is the mass of the clump, and Sd is the surface density of the total disc, which includes both gas and stars, i.e. Sd ˆ 2 mg ‡ ms†= pR †: The mass of the clump formed is given by p5S3 m ˆ p 0:5l †2S ˆ g ; 6† cl c g k4 2 2 where the critical wavelength lc ˆ 2p Sg†=k . Clump formation is closely related to star formation in the present model. To be consistent with the introduction of a star formation threshold, clump formation is inhibited and t fri is set to be infinity when Sg , Smin. The instantaneous value of tfri is determined by combining equations (5) and (6). Accretion (infall) of the primordial gas is specified by its time-scale, b, and the mass fraction, G, of the total matter that eventually accretes on to the disc. Now equations (1), (2) and (3), combined with the auxiliary equations (4), (5) and (6), complete a set of equations which determine the temporal evolution of the system. These equations have been integrated numerically. starting from the initial condition mg ˆ ms ˆ mb ˆ 0, for various parametrizations of b and G in terms of M and r ; M=R3†. Actually, 12 model families have been constructed. It has turned out that all the continuous model families (i.e. smin ˆ 0) exhibit qualitatively the same dependence of model properties on M and r, including the star Figure 1. The mass fraction, G, and the infall time-scale, b,ofthe formation history, the growth history of each galactic component, primordial gas for the C- and T-families. Solid lines indicate G, whereas the present gas mass fraction, the present SFR, and the present dotted lines give b in units of Gyr. The galaxy density, r, and mass, M, are 21 23 B/D ratio. Also the threshold families (i.e. smin ˆ 3kms ) show given in units of M( pc and M(, respectively. qualitatively the same behaviour among themselves in many respects. Indeed, it seems impossible to distinguish any particular from the most massive and densest galaxies to less massive and family in each group by comparison with the observational data less dense ones, is seen to increase again for these galaxies. This currently available. Therefore, I take in this paper the families c-2- peculiar behaviour of small and diffuse galaxies is caused by the 1 and t-2-1 as typical examples for the two groups of families. introduction of a star formation threshold. In these low-mass and These models (referred to as C-family and T-family, respectively, low-density galaxies, the star formation process is infall-limited. hereafter) have In other words, the consumption of the interstellar gas (i.e. the disc gas) by star formation easily reduces the gas density below the 21=3 21=3 M r threshold and prevents further star formation. After star formation b ˆ min 2:5 2 ; 5 Gyr†; 7† 1011 M( 0:1M( pc 3 is stopped, the gas density starts to rise again owing to the "# persistent infall of the primordial gas from the halo. After a certain and period, the gas density reaches the threshold, initiating the

G ˆ 0:12 log M=M(† 2 1:00: 8† formation of the next generation of stars. It should be cautioned that this result does not necessarily mean bursting behaviour of the Fig. 1 plots G and b on the (r, M) plane for the C- and T-families. whole galaxy. The present multicomponent model does not make G is an increasing function of M, while b decreases as r or M. allowance for the spatial dependence of any physical processes Fig. 2 shows the time variation of the star formation rate for and treats each galactic component as a single structureless zone. the grid of models for the T-family. As evident from this figure, It is likely that, depending on the size of the galaxy, such a burst- the infall time-scale, b, is the most influential parameter in like change in the SFR in individual local regions is averaged determining the star formation history. As b decreases, the peak spatially to give a much smoother variation in the total SFR. More value of the specific SFR increases, and is attained at an earlier massive and denser galaxies also enter this infall-limited regime in time epoch. However, the decline of the SFR after the peak is their late evolutionary phase, but the bulk of star formation in steeper, leading to a smaller value of the specific SFR at the these galaxies takes place in the density-dependent regime in early present epoch. This systematic variation seems to agree with the epochs. observationally inferred change in the star formation history along the Hubble sequence, with a smaller b representing an earlier Hubble type (Sandage 1986). Moreover, the largest value of the 3 NATURE OF LATE-TYPE BULGES 21 peak SFR is about 100 M( yr (it is realized in the most massive I now discuss the bulge formation characteristics of the multi- and densest model), which does not contradict the observed range, 21 component evolution models. 4±75M( yr , for a sample of high-redshift galaxies (Steidel et al. 1996). 3.1 The important role of the star formation threshold It is seen that for galaxies with very small M and r, the SFR shows a discontinuous burst-like time variation for most of the In a previous paper (Noguchi 1999), the difference between the calculated period. Also, the specific SFR, which first decreases continuous and threshold models was not stressed. In the present

q 2000 RAS, MNRAS 312, 194±206 Late-type disc galaxies 197

Figure 2. The specific star formation rate (i.e. the star formation rate per unit galaxy mass) plotted against time for a subset of models in the T-family. Only a quarter of the calculated models are chosen for display. To facilitate the comparison with Fig. 1, the two numerals in each panel give log r (left) and log M 23 (right) of the galaxy, where r and M are given in units of M( pc and M(, respectively. study, however, it is vital to note the effect of introducing a In the continuous models, the gas is consumed continuously, threshold on the long-term disc galaxy evolution. The importance depending on the current gas density, as long as there is a gas of the star formation threshold is demonstrated dramatically in component. In this family, the infall time-scale of the gas (b)is Fig. 3, which shows the bulge-to-total mass ratio at the present lengthened as the density and/or mass of the galaxy decreases. At epoch for two model families, the C-family and T-family, which the same time, the mass fraction of the total accreted gas (G) are identical to each other except for the absence or presence of a decreases. These two factors combine to decrease the peak gas threshold. In the continuous C-family, the B/T ratio decreases mass fraction during the whole evolution period for smaller M monotonically toward the lower left direction, i.e. as the mass or and/or r. Therefore, the clumping of the disc component is internal density of the galaxy decreases. In contrast to this, the suppressed, leading to less effective bulge formation. This is the threshold T-family exhibits a more complicated behaviour. The reason for the monotonic decrease of the B/T toward the lower left B/T ratio initially decreases to the lower left direction, but finally direction. starts to increase again. In other words, there is a valley (which is When a threshold for star formation is introduced (solid lines), called the Scd valley, for a reason which will become evident the late evolution of the galactic disc becomes infall-limited; shortly) in the contour map of the B/T ratio, which divides the namely the star formation consumes the same amount of the gas as galactic parameter space into two regions. added to the disc component by the infall. Therefore, the gas mass The reason for the appearance of this valley becomes clear by fraction stays constant in late evolution phases, as seen in Fig. 4. examining the time evolution of the individual models. Fig. 4 The important point here is that this constant value, i.e. the shows the time variation of the fraction of the gas for the models threshold gas fraction, becomes larger and lasts for a longer period included in the C-family (dotted lines) and T-family (solid lines). as the galaxy becomes less massive and/or less dense. This q 2000 RAS, MNRAS 312, 194±206 198 M. Noguchi

Figure 3. The mass ratio of the bulge and the total stellar component at the present epoch for two model families. The ordinate indicates the mass, M, of the 23 galaxy inside the optical radius in units of M(, whereas the abscissa indicates the density, r, within the optical radius in units of M( pc . The mass ratio is defined by B=T ; mb= mb ‡ ms†, where mb and ms are masses of the bulge and the stellar disc, respectively. The solid lines give contours of log(B/T). The C- family is a set of continuously star-forming models while the star formation threshold is introduced in the T-family. Other model parameters are the same for the two families. The shaded region in the right panel indicates a minimum for the B/T ratio. Dashed lines denote contours for the surface density of the 2 4 3 2 22 galaxy, S ; M=R , with S ˆ 10 ,10 and 10 (M( pc ) from upper to lower lines. variation of the threshold gas mass fraction brings about two the qualitative behaviour of the models and observational data in regimes of bulge formation, leading to a bimodal distribution of the following. the B/T ratio. In galaxies with large mass and density, most of the Fig. 5 compares the model B/T ratios of the T-family with the bulge is formed when the gas mass fraction attains a peak value in photometric observations by Whitmore (1984). Whitmore's data the early evolution epoch and hence the clumping activity is are presented in the same way as in Noguchi (1999). It is highest. Therefore, the final B/T ratio is correlated with the peak recognized in Fig. 5 that, in the region above the Scd valley, the mg/M for these galaxies, and increases toward higher galaxy mass model B/T increases as the galaxy mass increases at a fixed galaxy and density, in the same way as in the continuous C-family. On the density, and at a fixed galaxy mass it increases with the density, in other hand, the evolution of a galaxy with small mass and density agreement with the observation. is greatly modified. Such a galaxy builds up its bulge in late The filled squares in Fig. 5 denote very late spirals with the evolution phases when the gas mass fraction reaches the threshold Hubble parameter t . 6 (i.e. later than Scd), mostly taken from value, which is at the same time the largest value during the whole the sample studied by van der Kruit (1987). No photometric data period. The bulge formation efficiency in this regime is therefore are available regarding the B/T ratio of these galaxies (except correlated with the threshold value of mg/M, which increases NGC 3495). Out of these five galaxies, four are located below the toward smaller mass and density of the galaxy. Scd valley. On the other hand, all other galaxies indicated by open circles (i.e. with the observed B/T value) are earlier than Scd t , 6† and most of them lie above the Scd valley. Although there is no galaxy that has exactly the Scd type in the sample plotted 3.2 Confrontation with observations here, it is easy to guess that the valley in the theoretical B/T It is difficult at present to compare the theoretical B/D ratios with contour map corresponds approximately to the locations of Scd the observational ones in a completely quantitative manner. On the galaxies, as its name says. Fig. 5 demonstrates clearly that the observational side, there is considerable dispute about the appro- T-family explains the observed variation of the B/T as a function of priate decomposition technique of the light profile into the bulge the galaxy mass and density for the morphological types earlier and disc. The measured B/D ratio changes by up to one order of than Scd, at least qualitatively. magnitude depending upon whether the bulge component is The situation regarding later morphological types could be represented by the r1/4 profile or the exponential law (de Jong clarified by comparison with the photometric data of de Jong 1996; Andredakis, Peletier & Balcells 1995). The difficulty on the (1996). Fig. 6 gives a schematic representation of the de Jong data. theoretical side is caused primarily by the one-zone nature of the Some of his observations are made in the near-infrared K band, present multicomponent galaxy model. The spatial structure of which is a more faithful indicator of the stellar mass in the galactic each galactic component is neglected, which makes a quantitative components than the B band. The top panel shows that the prediction difficult. The most serious limitation is that I was absolute magnitude of the bulge component decreases as the forced to specify one single infall time-scale in each evolution Hubble type moves from Sa/0 t ˆ 0† to Scd t ˆ 6† as we naively model. Actually, this quantity is likely to depend on the expect. However, the bulge luminosity stays nearly constant for galactocentric radius in a single galaxy, with slower infall later types up to Im t ˆ 10†. On the other hand, the absolute occurring in the outer parts (Matteucci & FrancËois 1989; Lacey luminosity of the disc component is seen to decrease almost mono- & Fall 1985; Larson 1976). Therefore, attention is paid mainly to tonically as the Hubble type becomes later. These behaviours

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Figure 4. Time evolution of the mass fraction of the interstellar gas, mg/M, for the models in the T-family (solid) and C-family (dotted). Only a quarter of the calculated models are chosen for display. All the panels are located in increasing order of galaxy mass and density from the lower left corner to facilitate easy comparison with Fig. 1. The galaxy density and mass in logarithmic units are indicated in the upper right corner of each panel in the same way as in Fig. 2. combine to give rise to a complicated variation of the B/D ratio, average. The combined effect of these variations is the appearance which decreases from t ˆ 1tot ˆ 6 but increases afterward, as of a minimum for the model B/D ratio at log S , 2:3 (the arrow). the bottom panel shows. The Scd valley is indicated by an arrow in All other threshold model families show qualitatively the same this panel. behaviour (i.e. the inflection of the B/D curve), although details A similar diagram for the T-family is given in Fig. 7. Here, the depend upon the adopted parametrization for the infall time-scale 2 22 surface density of the galaxy, S ˆ M=R (in units of M( pc ), is (b) and the mass fraction of accreted matter (G). On the other used as a substitute for the Hubble parameter, t, because Whitmore hand, all the continuous families fail to produce the observed (1984)'s principal component analysis has found this quantity to variation of B/D along the whole Hubble sequence. An example is be the most strongly correlated with B/T and hence the Hubble shown in Fig. 8, which is the same as Fig. 7, but for the C-family. type. (The tightness of this correlation is hinted at in the right It has been confirmed at this point that the clumpy evolution panel of Fig. 3, which shows the surface density contours by model of disc galaxies can explain the systematic variation of the dashed lines, together with the B/T contours.) The upper and bulge-to-disc ratio along the Hubble sequence, by including the middle panels in Fig. 7 plot the masses of the bulge and disc effect of the star formation threshold, which is suggested strongly components in units of M(. The bottom panel plots the mass ratio by observations of nearby galaxies (Kennicutt 1989; van der Hulst of these two components. All the three panels show strikingly et al. 1993). Especially important is that the model can reproduce similar behaviour to the corresponding panels in Fig. 6. The model the existence of significant bulge components in galaxies of very bulge mass decreases from log S , 4to,2.3, but stays nearly late types, which contradicts common sense but is suggested by constant for smaller surface densities. On the other hand, the recent photometric observations. Nevetheless, the terminology of model disc mass decreases monotonically as S decreases, on `bulge' for these central components in very late spirals may not q 2000 RAS, MNRAS 312, 194±206 200 M. Noguchi

with or without an additional exponential component. The second group includes the bulges fitted by a double exponential profile. The third group comprises the bulges fitted by a single exponential profile. These three groups are associated with galaxies of different types. R1=4 ‡ exponential bulges are limited to types earlier than Sbc t ˆ 4†, whereas the double exponential bulges are hosted by galaxies later than Sb t ˆ 3† but earlier than ,Sd t , 7†. The switch from the R1=4 ‡ exponential to double exponential bulges occurs at Sb. Single exponential bulges do not appear to favour particular galaxy types. R1=4 ‡ exponential bulges are more luminous than double exponential ones with respect to the total galaxy luminosity. The latter typically contribute several per cent of the total galaxy light. The luminosity change from the R1=4 ‡ exponential bulges to the double exponential ones is continuous, and corresponds to the systematic decrease of the B/D ratio from Sa/0 to Scd revealed by other observations (see Fig. 6). The nature of the single exponential bulges is not so clear. The most surprising point is that these bulges are very luminous, contributing a large fraction of the total galaxy light, if the result by Carollo et al. (1998) is taken at face value. This may come partly from their particular method of profile fitting, however. Suppose that the total surface brightness profile is nearly exponential at all galactocentric radii, but the slope in the inner part is slightly steeper than that in the outer part. Then, fitting the inner part by an exponential function Figure 5. The model B/T mass ratio (in logarithmic units, solid contours) for the T-family compared with the photometrically derived luminosity as Carollolo et al. (1998) did leads to a large scalelength, which is ratio of Whitmore (1984) (open circles). The ordinate indicates the mass, almost identical to that of the outer part, and the calculated M, of the galaxy inside the optical radius in units of M(, whereas the luminosity of the `bulge' component will constitute a large abscissa indicates the density, r, within the optical radius in units of fraction of the total luminosity. Therefore, the abnormally large 23 M( pc . The area of each circle is proportional to the B/T ratio for the luminosities of the single exponential bulges may not necessarily corresponding galaxy. The mass and density of a Whitmore galaxy have measure their true luminosity but might merely tell us that the 2 23 been calculated by M ˆ GR25V25 and r ˆ MR25 , where R25 is the radius central concentration is very weak, so that the density slope does 22 at which the surface brightness in the B band is 25 mag arcsec and V25 is not increase significantly toward the galactic centre. If this is the the rotational velocity at R25. All the Whitmore galaxies except NGC 3495 case, some outer cut-off radius should be specified for the `bulge' are earlier than Scd t , 6†. Filled squares denote spiral galaxies later than component and the resulting bulge luminosity will be reduced Scd. NGC 3495 is included in Whitmore (1984), and other four galaxies were taken from the sample studied by van der Kruit (1987). For the latter considerably. Anyway, the use of the term `bulge' in these cases is misleading. Existence of single exponential bulges in early galaxy galaxies, V25 was replaced by W20 listed in RC3 (de Vaucouleurs et al. 1991) and corrected for the inclination given in table 1 of van der Kruit types t & 5† is another mystery, for which no convincing

(1987). The morphological type is also based on RC3. R25 was replaced by explanation is available at present. 4.5h, where h is the disc scalelength given in table 2 of van der Kruit The present multicomponent models are incapable of predicting (1987), and converted into the physical scale assuming a Hubble constant the structure of the bulge components formed by disc clumps. 21 21 of 50 km s Mpc , consistent with Whitmore (1984). Dashed lines Nevertheless, the existence of more disc-like bulges in late-type denote contours for the surface density of the galaxy, S ; M=R2, with 1/4 4 3 2 22 spirals suggests that those bulges lacking R components are ˆ ( S 10 ,10 and 10 (M pc ) from upper to lower. indeed the product of secular evolution of clumpy galactic discs. The `classical' R1/4 bulges, on the other hand, may have been formed from pregalactic clumps such as those envisaged in the be adequate. In relation to this, the current observational status hierarchical clustering picture of structure formation (Katz 1992). concerning late-type bulges is briefly summarized below, and their possible association with bars is discussed in Section 4.

4 INTERPRETATION OF THE BAR 3.3 Observed diversity in galactic bulges DICHOTOMY The Hubble Space Telescope has cast new light not only on distant Granted that a significant bulge exists in very late spirals, what galaxies but also on the very central parts of relatively nearby does it mean? Surely those galaxies with type designation ,8±10 galaxies. Recent observations of 40 spiral galaxies by Carollo, have been classified as late because they have a negligible bulge? Stiavelli & Mack (1998) using WFPC2 have revealed complicated Here I would like to propose that these `bulges' are actually bars. morphological features in the galactic bulges (see also Phillips This issue is closely related to what we call `bar dichotomy'. It has et al. 1996). They have fitted the surface density profile in the long been known that the morphological properties of galactic inner ,20 arcsec (corresponding typically to a 1-kpc radius for the bars change systematically along the Hubble sequence. Most sample galaxies) with analytical functions, and classified the well- galactic bars can be divided roughly into two large groups on fitted bulges into three categories. The first distinctive group morphological grounds (Elmegreen & Elmegreen 1985). Bars of comprises those bulges fitted well by the de Vaucouleurs R1/4 law, early-type galaxies are in general large relative to the optical size

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Figure 6. Variation of the bulge and disc components along the Hubble sequence for the sample of de Jong (1996). The shaded regions indicate a rough boundary for the distribution of the sample galaxies. The Hubble type is coded following de Vaucouleurs (1974)'s quantification, t. t ˆ 0 for Sa/0, 1 for Sa, 3 for Sb, 5 for Sc, 7 for Sd, and so on. The top panel plots the near-infrared K-band absolute magnitude of the decomposed bulge component, while the middle panel is a similar plot for the decomposed disc component. The bottom panel shows the luminosity ratio in the K band of the bulge and disc components. The Scd valley is indicated by an arrow. of the host galaxy and their surface brightness profile along the its type to an earlier one as the bar grows. For several reasons, I major axis is nearly flat (flat bars). Bars in late-type galaxies tend argue against the bar-induced formation of galactic bulges. First, to be shorter and usually have a steeply decreasing surface the gas-rich discs in early evolutionary phases of disc galaxies are brightness outward along the major axis (exponential bars). Spiral generally unfavourable to bar formation (Shlosman & Noguchi arms outside the bar radius are usually of grand design with two 1993). The clumps formed in the disc efficiently scatter stellar prominent arms in early-type disc galaxies, whereas late-type orbits. This dynamical heating damps the bar instability in the galaxies often have multiple arms outside the bar. stellar disc component. Secondly, bar-driven bulge formation will One possible interpretation has been proposed that this change lead to a bulge that is younger than the bar. However, no with the Hubble type represents an evolutionary sequence (e.g. convincing example of younger bulges seems to have been Friedli & Benz 1993). Namely, the bars in late-type galaxies reported in the literature so far. The other factor that makes the represent an earlier stage of the bar evolution, and they evolve into bar-induced evolution scenario unappealing is the difference in a larger and stronger bar as time elapses. The inward flow of gas the host galaxy properties. For example, the mass fraction of the triggered by the gravitational torque of the bar will lead to the luminous part (within the optical radius) is smaller for galaxies of growth of the bulge component, so that the galaxy itself changes later types (Section 2). It is therefore doubtful that a late-type q 2000 RAS, MNRAS 312, 194±206 202 M. Noguchi

Figure 7. Variation of the bulge (top) and disc (middle) masses along the surface density of the galaxy for the T-family. The disc mass md ; ms. The masses 2 are given in units of M( and the surface density is defined by S ; M=R , where the mass, M, is in units of M(, and the optical radius, R, is in units of pc. The bottom panel shows the bulge-to-disc mass ratio, B=D ; mb=md. Note the appearance of the Scd valley (arrow) in the bottom panel. barred galaxy evolves into an earlier one that has a larger fraction distribution of the disc and dark matter halo components within of luminous matter. the galaxy. I propose here a completely different interpretation of the bar dichotomy. The key point here is to note that the transition of 4.1 Different fates of disc clumps depending on their masses bar properties mentioned above occurs roughly at Scd type (Elmegreen & Elmegreen 1985), i.e. at the same position as the The clumps formed in the gas-rich disc component in an evolving minimum of the B/D ratio hinted observationally in the de Jong disc galaxy will be subject to various destructive forces, including (1996) data. I do not take this coincidence to be an accidental one. tidal forces from the galactic potential and energy injection from I argue here that the exponential bars in galaxies later than Scd are internal star formation processes. Actually, the strong concentra- actually their `bulge' component deformed by the bar instability, tion of the gas clouds into narrow spiral arms observed in nearby whereas the flat bars in galaxies earlier than Scd originate in their galaxies points to relatively short lifetimes for those clouds. For disc component, which suffered from the bar instability. As example, the giant molecular clouds (GMC), with masses of 6 discussed below, theoretical and observational evidence suggests ,10 M(, are considered to have a lifetime shorter than a few that two different factors are cooperating in creating the bar times 108 yr (see Kwan & Valdes 1987, and references therein), dichotomy in late-type spiral galaxies. They are (i) the robustness perhaps because of energy deposition by young massive stars born of the clumps formed in the disc and (ii) the relative mass in them. The present model generally develops clumps with

q 2000 RAS, MNRAS 312, 194±206 Late-type disc galaxies 203

Figure 8. Same as Fig. 7, but for the C-family. Note the monotonic decrease of B/D as the surface density decreases.

masses much larger than those of the giant molecular clouds we noted that Mcl,max increases as the galaxy mass increases. A observe today. The fate of these extremely massive clumps is not weaker dependence on the density, r, is also seen. From this clear because they are absent from nearby (i.e. present-day) figure, it is inferred that the clumps in a more massive and/or galaxies. Nevertheless, a simple dimensional argument suggests denser galaxy are more robust against destruction by star that more massive clumps are more robust against internal star formation. It is not clear what cloud mass demarcates disruption formation. The observations of the Milky Way molecular clouds and survival. Judging from the observation that the GMCs in the suggest that the cloud mass, m, and radius, r, obey a power law Milky Way are suffering from efficient disruption, the lower limit k 7 correlation, m / r , where k ˆ 2±3 (Leisawitz 1990). Assume for their survival will be around 10 M(. The whole domain in that the energy released from a single star formation event in a Fig. 9 is divided into two parts labelled `clumpy' and `turbulent' 7 given gas cloud, Esn, is proportional to the cloud mass, and the by the line with Mcl;max ˆ 10 M(. It is interesting that this border ease with which the cloud is disrupted is measured by the ratio line lies close to the Scd valley, which divides relatively early f ; Epot=Esn, where Epot is the potential energy of the cloud. spirals and very late ones in the (r, M) plane. In the clumpy 7 For the mass±radius relation observed in the Milky Way, domain (with Mcl;max . 10 M(), where relatively early spirals f / m0:5±0:67, meaning that a more massive cloud is more difficult are located, the clumps forming in the disc survive disruption and to disrupt. reach the galactic centre keeping their identity. Such a clumpy Fig. 9 overlays the contours for the maximum clump mass configuration will inhibit formation of a bar, which requires a fine during the evolution, Mcl,max, on the contours of the final B/T.Itis alignment of elongated stellar orbits over a large radial range. q 2000 RAS, MNRAS 312, 194±206 204 M. Noguchi

visible components. Although this ambiguity is causing a debate about whether the galactic discs are maximal or not (Courteau & Rix 1999, and references therein), the trend seems to be established rather firmly that the mass fraction of the visible matter relative to the total galaxy matter within the optical radius decreases with decreasing galaxy luminosity or mass (see Section 2). It is, however, not trivial to decide what radius should be used to define the size of a disc galaxy in comparing the global structure of different galaxies. Conventional use of R25 may not be justified for low surface brightness (LSB) galaxies, for which the disc component starting from a much lower central surface

brightness than Freeman (1970)'s canonical value, mB;0 ˆ 21:65 mag arcsec22; is observed to extend to very faint levels below mB ˆ 25 in the outer parts. An alternative choice is to use a fixed multiple of the exponential scalelength, h, of the disc. The survey by de Blok & McGaugh (1997) has revealed that the mass fraction of the luminous matter (including the gas) within r , 5h is a decreasing function of m B,0 and an increasing function of Vmax, the maximum rotational velocity for r , 5h. Because m B,0 increases while Vmax decreases for later Hubble types (de Jong 1996; Brosche 1971), the observations of the high surface brightness galaxies and de Blok & McGaugh (1997)'s result for LSB galaxies together suggest a continuous decrease of the baryonic mass fraction as the galaxy type becomes later, Figure 9. The final bulge-to-total mass ratio, B/T (solid lines), and the irrespective of the definition of the visible galaxy size. It should maximum mass of the clumps during the whole evolution period, M cl,max be noted that the arguments in this subsection are essentially (in units of M(, dotted lines), plotted on the (r, M) plane, where the galaxy 23 density, r, and mass, M, are given in units of M( pc and M(, unaffected by whether we use R25 or 5h in defining the galaxy respectively. The entire parameter plane is divided into two regions size. 7 labelled `clumpy' and `turbulent' by the line Mcl;max ˆ 10 M(. See the There is another important structural difference between late text for details. spirals and earlier ones. The compilation by Rubin et al. (1985) of a large number of spiral galaxy rotation curves for the range Sa±Sc already shows that later spirals tend to have a more slowly Individual massive clumps will destroy such coherence by causing rising curve near the centre, indicating weaker concentration of irregularity in the galactic gravitational field. Of course, the the mass. The extremity of this systematic trend is provided by the clumps will finally lose their identity and make a single system by rotation curves of the LSB galaxies, which rise almost linearly tidal disruption or mutual merging. Owing to effective dynamical from the galactic centre in general and are still increasing at the heating by the clumps, the end product is not a bar but a globally outermost measured point in some cases (de Blok & McGaugh axisymmetric (even spheroidal) configuration dominated by 1997). random motions, which we call a bulge. A bar in these relatively Bars are known to form when the rotationally supported disc early galaxies will be created later from the fully grown disc component occupies a certain fraction of the total mass within the component, as discussed in Section 4.2. disc radius (Ostriker & Peebles 1973; Hohl 1976; Athanassoula & On the other hand, the disc located in the `turbulent' region will Sellwood 1986). Therefore, early-type spirals have favourable have a smooth texture at any epoch, because the clumps in this conditions to form a bar from the entire disc component, leading region are easily disrupted and continuously turned into less possibly to the formation of long flat bars in Elmegreen & massive fragments. In this case, the evolution of the galactic disc Elmegreen (1985). On the other hand, a late-type spiral is will be more akin to that of the type of star-forming viscous disc dominated by dark matter everywhere. Therefore, the disc in very investigated by Saio & Yoshii (1990) and others. Reduction in the late spirals cannot be bar-unstable in general. However, the inner scattering forces from the clumps will lead to the formation of a part of these galaxies is a little more delicate. Although the central flat mass component that is dynamically cold and is dominance of the dark matter halo is strong, its central concen- supported mainly by rotation. As argued below, such a `bulge' is tration is generally weak as evidenced by the slow rise of the very sensitive to bar-forming instabilities. rotation curve in the central part. Therefore, if a certain amount of matter is gathered at the centre, the central part becomes self- gravitating easily and vulnerable to the bar instability. The clumpy 4.2 Different parts of the galaxy susceptible to the bar evolution behaves as expected by building a large mass instability accumulation (pseudo-bulge). The final product in this case is a The answer to the question of why the flat and exponential bars short bar embedded in a bulgeless galaxy, corresponding to the have such different sizes relative to the disc radius (at least a factor exponential bars in Elmegreen & Elmegreen (1985). of 2 according to Elmegreen & Elmegreen 1985) can be sought in The origin of the bar dichotomy inferred from above arguments the different mass structure of their host galaxies. Mass is summarized as follows. In spiral galaxies earlier than ,Scd, the decomposition of a given galaxy into distinct components based clumps formed in the disc spiral in to the inner galactic part, on the observational data is not unique in general, mainly because maintaining their identity. This mass accumulation, even if it is there is a large uncertainty in the mass-to-luminosity ratio of the strong, does not lead to bar formation owing to the destructive

q 2000 RAS, MNRAS 312, 194±206 Late-type disc galaxies 205 action of individual clumps. Instead a roughly axisymmetric bulge relation to the formation of bulges and bars in these galaxies. This will be formed at the galactic centre. This process may also scenario states that the gas-rich discs of young disc galaxies steepen the inner rotation curve as actually observed in a number produce massive clumps because of gravitational instability, and of early-type spirals (Rubin et al. 1985). The infall of the these clumps spiral in to the galactic centre owing to dynamical primordial gas from the halo to the disc plane is still continuing friction, leading to the formation of a bulge. The dominant after the completion of the bulge, because the infall time-scale is parameters that determine the efficiency of this process are the considered to be larger in the outer parts (though such a spatial time-scale of gas infall to the disc plane and the mass fraction of variation is not taken into account in the multicomponent models the baryonic component, which are in turn related systematically presented in Section 2). At some epoch when the disc mass to the mass and density of the galaxy. exceeds the critical value, the bar instability is triggered, involving Assuming a reasonable mapping of the galaxy mass and density a wide region of the disc component. to the Hubble type, this scenario predicts a complicated behaviour On the other hand, spiral galaxies later than ,Scd generally have of the bulge formation efficiency along the Hubble sequence. As asmallG so that the resulting disc is stable. However, the existence the galaxy becomes of later-type, the bulge-to-disc ratio at the of the star formation threshold and the resulting gas-richness of the present epoch initially decreases. However, at about Scd type, this disc bring about efficient transport of the disc matter to the inner ratio starts to increase again toward later types. The existence of a region. This mass accumulation leads to the formation of a threshold interstellar gas density for star formation to occur is concentrated disc-like component (a secondary disc or a pseudo- responsible for this upturn. Namely, the star formation in very late bulge). Because the clumpiness of this component is subdued owing spirals is always limited by the supply of new interstellar gas to the fragility of less massive clumps contained within, it is prone through infall from the halo, leading to a high level of gas content, to the bar instability under sufficient mass accumulation. The which favours clump-driven bulge formation. resulting bar will be significantly smaller than the disc. This The existence of a minimum for the bulge-to-disc ratio at Scd scenario naturally explains several aspects of the bar dichotomy: (i) type seems to be hinted by recent observational data, though the flat bars have a larger relative size with respect to the optical radius terminology of `bulge' for the central light concentration in than exponential bars (Elmegreen & Elmegreen 1985); (ii) the flat extremely late spirals is problematic. Instead, it is proposed that bars are always associated with a distinct bulge, whereas the these `bulges' (or pseudo-bulges) manifest themselves as a short exponential bars lack appreciable bulges (Elmegreen et al. 1996). bar in the galactic centre, owing to bar instability. The observed frequency of barred galaxies in different Hubble Interestingly enough, past observations have found that galactic types also seems to fit in with this scenario. The statistical analysis bars change their morphological features (especially the bar size) of the RC3 catalogue (de Vaucouleurs et al. 1991) by Odewahn around Scd. The clumpy evolution scenario naturally explains this (1996) indicates that the barred galaxy fraction decreases from Sa bar dichotomy as follows. The bars in galaxies later than Scd have (,55 per cent) to Sc (,30 per cent), and then from Sc to later evolved from the central concentration of the disc matter created types it rises again, up to ,80 per cent for Im. A similar change by the clump-driven inflow. The whole disc in these galaxies for the RSA catalogue (Sandage & Tammann 1981) is reported in cannot form a bar because it is not sufficiently massive. On the Sellwood & Wilkinson (1993). The change of the bar frequency other hand, the bars in earlier spirals result from the bar instability from Sa to Sc may be caused by the systematic variation of the of the entire galactic disc, which occupies a large fraction of the baryonic matter fraction (G in the present study) along this total galaxy matter. The central mass component in this case sequence. Actually, G is likely to have a dispersion around the cannot form a bar but evolves into an axisymmetric bulge because mean at a fixed Hubble type. If the mean value decreases from Sa the massive and robust clumps impede the bar formation process. to Sc, as is plausible from observations (Section 2), and only those The systematic difference in bar length (relative to the galaxy systems having G exceeding the fixed threshold evolve into a optical size) for the two types of bars is thus explained easily in barred galaxy (as confirmed numerically for a wide class of terms of the different galactic regions transformed into a bar. rotationally supported discs), the observed decrease of the bar incidence from Sa to Sc is easily understood. On the other hand, ACKNOWLEDGMENTS the remarkable increase of the bar incidence toward extremely late types is consistent with the rise of the secular mass accumulation The author thanks the referee, Dr R. Durisen, for helpful effect for this morphological range. comments on the manuscript. 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