ASTRONOMY AND ASTROPHYSICS. The nature of arms in spiral galaxies. III. Azimuthal profiles. M.S. del Río 1,2 and J. Cepa 2,3

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1 Astron. Astrophys. 340, 1 20 (1998) The nature of arms in spiral galaxies III. Azimuthal profiles ASTRONOMY AND ASTROPHYSICS M.S. del Río 1,2 and J. Cepa 2,3 1 Departamento de Astronomía, IFUG, Universidad de Guanajuato, Guanajuato, Mexico 2 Instituto de Astrofísica de Canarias, E La Laguna, Tenerife, Spain 3 Departamento de Astrofísica, Facultad de Física, Universidad de La Laguna, E La Laguna, Tenerife, Spain Received 13 March 1998 / Accepted 24 August 1998 Abstract. In this paper we analyse the structure of a small sample of galaxies using a set of CCD images in standard photometric bands presented in a previous paper (del Río & Cepa 1998a, hereafter Paper II). The galaxies are NGC 157, 753, 895, 4321, 6764, 6814, 6951, 7479 and 7723, and the selected bands were B and I. Seven galaxies are grand design, i.e. they have two long and symmetric arms, second in the classification of Elmegreen & Elmegreen (1987), and are the best laboratories for testing the predictions of the spiral density wave (SDW) theory. Two of the galaxies have intermediate arms, i.e., they are not so well defined. They are selected to compare the results with those found in the grand design spirals. Using the method of analyse the azimuthal flux profiles presented by Cepa (1988) and Beckman & Cepa (1990) (hereafter Paper I) and assuming that star formation is triggered by a spiral density wave, we look for evidence of the existence of a corotation radius, as predicted by the SDW theory. We have determined the corotation radius in all but two grand design galaxies, and, tentatively, in the other four. Galaxies with very weak arms (such as NGC 753 and NGC 6951) or arms which are not well defined (such as NGC 6764 and NGC 7723) present difficulties when employing the azimuthal profile method, but even in these cases, the method is powerful enough to give a good estimate of the value of corotation, which must then be confirmed (or discarded) by other independent methods (del Río & Cepa 1998b, hereafter Paper IV). Key words: galaxies: spiral galaxies: structure 1. Introduction Since Lin and Shu s quantitative development of the spiral density wave theory (SDW) in the 1960s, there have been several attempts to demonstrate its presence in spiral galaxies. The first evidence came from near-infrared observations of spiral galaxies: Adamson (1983) found evidence of spiral arms in the J, H and K bands, in M83. However, the most conclusive and Send offprint requests to: M.S. del Río, sole@cibeles.astro.ugto.mx complete study was that by Elmegreen & Elmegreen (1984), who found that grand design and intermediate arm type (according to Elmegreen & Elmegreen 1987 classification) spirals have density waves in their discs. The present-day dilemma is not the existence of spiral density waves, but the rôle played by these waves in triggering star formation in the spiral arms. Studies of global (i.e., all over the disc) star formation rate per unit area vs. arm type (Elmegreen & Elmegreen 1987; McCall 1987) does not show any trend favouring star formation in grand design with respect to flocculent arm spirals. Also, Schweizer (1976) analysed azimuthal arm profiles of a set of galaxies, looking for asymmetric profiles, which would be a signature of the triggering of star formation by a density wave system: azimuthal profiles in bands tracing star formation (blue bands) should show an asymmetric profile when crossing the arm, with the steeper side on the concave side of the arms for every galactocentric radius of a given galaxy. This phenomena would be due to the presence of a shock caused when molecular clouds moving with differential speeds according to their galactocentric radii encounter the SDW (which itself moves at a constant angular speed). The studies made in this field have in most the cases been based on photographic data of limited quality. Several authors assert that star formation in arms is due to the cumulative effects of the potential well; that is, more gas and dust is located in the arms than in the inner inter-arm regions, thereby giving rise to star formation, so that the star formation efficiency, defined as the quotient between the massive star formation in arms and inter-arms must be very similar (Lees & Lo 1990). However, other authors (Cepa & Beckman 1990a) have demonstrated that this efficiency is highly enhanced in the arms, which suggests that the density waves trigger star formation and compels the gas and dust to enter into a non-linear regime (Kennicutt 1989) where star formation is not linearly dependent on the amount of gas present in the zone. In this study we demonstrate, in a new way, that density waves trigger star formation and we establish the presence of a front that changes from one side to the other in the arms at a radius which we identify as corotation. This radius is calculated by using different and independent methods that are well estab-

2 2 M.S. del Río & J. Cepa: The nature of arms in spiral galaxies. III lished. The first one was introduced by Cepa (1988) and Paper I and is based on the study of different statistical moments in the distribution of flux vs. azimuthal angle for a given radius. The second method, Fourier transforms of bi-dimensional images, was introduced by Kalnajs (1975) as a way of studying H ii regions and spiral arm periodicity. The third method was introduced by Elmegreen, Elmegreen & Montenegro 1992 (hereafter EEM) to enhance the symmetric parts of spiral galaxies (bi-, triand higher symmetries) and to relate qualitatively the gaps found with Lindblad resonances and corotation. In Sect. 2 the selected bands are briefly justified, in Sect. 3 we resume the azimuthal profile method, described in detail by Cepa (1988) and Paper I, and we explain the different features expected depending on the wave strength. In Sect. 4 we show the problem that dust poses to in our analyses and how we have dealt with it. In Sect. 5 we present the analysis of each galaxy, and finally Sect. 6 summarizes the results. 2. Observations and selected passbands We use Johnson B and I-band CCD images of a group of spiral galaxies obtained at the prime focus of the 2.5m Isaac Newton Telescope, at the Observatorio del Roque de los Muchachos, La Palma. A GEC CCD chip was used as a detector, with a conversion factor from ADU to electrons 1. The photosensitive part of the chip ( pixel, with 10 columns of overscan excluded) represents an area of the sky of , i.e. a scale of 0.54 per pixel. The images were reduced using standard routines, with a seeing-limited angular resolution close to 1 arcsec. The observations and data reduction are described in detail in Paper II. In their original form (before deprojection) the orientation is north right, east-top. The bands selected are B and I. The I band was used because it is almost free from radiation from H ii regions and OB stars (Schweizer 1976), and it suffers little extinction from dust. The B band was chosen because arm interarm variations of the B I colour can reveal variations in the mean stellar ages better than the U I colour (the more extreme bands), due to the greater patchiness of the U band and lower detector efficiency. The B band is also less affected by internal extinction and variations in atmospheric transparency than the U band. Thus the B band would represent the younger stellar population, mainly OB stars, and the I band represents older stars (Schweizer 1976). Both bands minimize sky background by avoiding the strong atmospheric emission of [O i]at λ5577 and of OH longward of λ Azimuthal profiles We use the set of parameters defined by Cepa (1988) and Paper I. An azimuthal profile taken at a radial distance ρ from the centre of a galaxy represents the flux distribution, Fi λ, at a certain wavelength, λ, of the points (i =1,,n) located at this radius, in the plane of the galaxy, ordered according to the angle θi λ that each point makes with respect to a defined origin in azimuthal coordinates. This origin of angles was taken as the major axis, i.e., the position-angle axis with angles positive counterclockwise. The radial origin is the centre of each galaxy, taken as the brightest point in the bulge in non-saturated bands, usually U or B. For a particular feature (the arms in our case) characterized by a flux increase at a wavelength λ among the points j = k, k+1,...,l, where l i, k 1 and l n, the following parameters were defined (Cepa 1988; Paper I): l Fj λθλ j j=k θ λ = F λ, (1) l Fj (θ λ j λ θλ) 2 σ λ j=k = D λ (2) and l (θj λ θλ) 3 S λ = where F λ and D λ j=k F λ j D λ σ λ 2 3, (3) l Fj λ (4) j=k F λ l ( ) F λ 2 j j=k F λ. (5) θ λ is the mean azimuthal angle, σ λ, is the FWHM of the particular feature under study and S λ is its skewness (0 if the profile is totally symmetric, positive if the steeper side is before the maximum and negative otherwise, Cepa 1988). For each galaxy, we taken 288 azimuthal profiles (from 1 pixel radius to the end of the frame), in steps of 0.54 (our physical resolution before smoothing the data). From those profiles, we chosen those where arms could be clearly defined, i.e., no so much influenced by bulge neither so weak to be diluted in the outer disk. The bulk of our study is centred on the first and, mainly, third moments of such a distribution, (θ λ and S λ ). The way we choose the limits of a selected feature is slightly different from those of Elmegreen & Elmegreen (1984) and Cepa (1988). Basically, those authors used the minimum flux nearest to the peak position as the level where the disc cuts the profile. To use an objective indicator more related to arm local properties, we choose as zero level the one which clearly represents the arm in the contour maps. In this way we ensure that we are less affected by lower S/N and local flux minima. According to the SDW theory, a non-axisymmetric perturbation induced in a differential rotating disc should produce a quasi-stationary spiral wave that rotates with constant angular speed, Ω p. In a galactic disc, such as those studied in this paper, we can consider the linear velocity, Ω(ρ), of the matter

3 M.S. del Río & J. Cepa: The nature of arms in spiral galaxies. III 3 Table 1. Resumè of distinct possibilities in asymmetry sign of azimuthal profiles and difference mean positions. before CR after CR sense θ sense θ sense θ sense θ S B > 0 S B < 0 S B < 0 S B > 0 Weak Wave θ B θ I > 0 θ B θ I < 0 θ B θ I < 0 θ B θ I > 0 S I > 0 S I < 0 S I < 0 S I > 0 S B > 0 S B < 0 S B < 0 S B > 0 Strong Wave θ B θ I < 0 θ B θ I > 0 θ B θ I > 0 θ B θ I < 0 S I > 0 S I < 0 S I < 0 S I > 0 (stars, gas and dust) to depend on the radius, while the angular velocity of the pattern is approximately constant; i.e., the matter is subjected to differential rotation while the wave rotates as a rigid body. At corotation both angular velocities are equal: Ω p =Ω(ρ). Then, before corotation, the angular velocity of disc matter is higher than the angular velocity of the wave pattern. The contrary happens beyond corotation. If a density wave in some way triggers star formation, we should observe a sudden luminosity increase followed by a smoother fall as the region evolves, in the same direction as that of the movement of the disc matter. The main observable features in the azimuthal profiles due to these events will be a steeper slope on the side where the star formation front is located, together with a bluer colour (Schweizer 1976). This shape of the azimuthal profiles would reverse after the corotation radius. Schweizer did not find any positive result probably because of the noisier photographic photometry and because she examined the profiles by eye instead of using a set of parameters such as described here. In particular, S λ gives an idea of where the steeper side of the profile is (the skewness degree), and θ λ tells us where the mean position of the arm is. Intrinsically, this parameter might not seem very useful compared with the position of the maximum, which would allow us to compare the time shift between the younger arm population (the bluer bands) and the older disc population (the redder bands). However, the position of the maximum can be influenced by the presence of field stars, unresolved dust knots, H ii regions, etc., whereas the mean position depends on every point in the distribution, not just one (as is the case of maxima), and is then less affected by resolution or seeing problems and is much more reliable, in a statistical sense, than the maxima, represented by a single point. Density waves affect gas and stars differently. We will assume for simplicity that wavelengths in the near infrared (J and K) or the very near infrared (I) represent the more evolved stellar population, and that ultraviolet (U) and blue (B) wavelengths mainly represent the younger population (the last 10 8 yr). This can be justified by studying the colours of the arm and interarm disc population in our Galaxy (Schweizer 1976). Density waves produce an increase in the number stars per unit volume. This higher concentration represents an increase of the surface brightness. The less red the observational band, the steeper is the brightness increase. This effect is due not only to Fig. 1. Effect of a density wave on an azimuthal flux profile, proceeding from disc stars, without new star formation. Before CR, counterclockwise sense ( θ ). the newly formed stars in the arm but also to the higher velocity dispersion of the older disc stars, which contribute mainly at longer wavelengths. The effect produced in the gas is very different. Because of the wave, the gas is concentrated (as is the dust) and compressed more and more as it falls deeper into the potential well, but its dispersion velocity is much lower than that of the stars, so the compression is higher. The maximum concentration will be near the minimum of the potential well as in the case of the stars. Depending on the value of this minimum, and the physical characteristics of the interstellar medium, the critical density for a gravitational collapse could be reached a) before the potential minimum, b) near the minimum, or c) is not reached (due to strong cloud magnetic fields, high dispersion velocities, high temperatures, etc.). The strength of the wave can be estimated using the arm amplitude, defined as A I = F I max F I zero F I zero = F max I Fzero I 1, where F I max is the maximum flux in the I band of the feature selected and F I zero is the zero level chosen at each radius. The I band was preferred to the B band because it is mainly representative of the spiral wave, and not of the triggered star formation. In fact, this definition is very similar to

4 4 M.S. del Río & J. Cepa: The nature of arms in spiral galaxies. III a low-amplitude well, or physical conditions of the interstellar medium do not favour star formation, the mean position in B could be delayed with respect to the mean I position. So we can find a positive asymmetry in B (after the minimum is reached the star formation is triggered), a positive or zero asymmetry in I (star formation is not very intense, and the asymmetry in I would come only from the subsequent evolution of the scarce newly formed stars in the I band) and a positive mean position difference. So in a weak wave Fig. 2. Effect of a density wave on an azimuthal flux profile, proceeding from newly formed stars. Before CR and θ sense. Fig. 3. Effect of a weak density wave on the B profiles (continuous line) and I profiles (dotted line). Before CR and θ sense. S B > 0; S I > 0 and θ B θ I > 0. If the potential well is deep, or the ISM is near critical values for star formation, star formation is triggered before and will presumably be more intense. The evolution of newly formed stars will contribute to the I band, increasing the tail profiles and its asymmetry. This shifts the I-band mean position, so we can measure a higher positive asymmetry in B (triggering is more intense), a positive asymmetry in I, because the number of newly formed stars is greater, and a negative or zero difference in mean position. So in a strong wave S B > 0; S I > 0 and θ B θ I < 0. In the case of a clockwise rotating galaxy ( θ ), the signs are changed. After corotation, the disc matter speed is lower than the wave speed, Ω p > Ω(ρ), and every sign also changes. 4. The dust problem Fig. 4. Effect of a strong density wave on the B profiles (continuous line) and I profiles (dotted line). Before CR and θ sense. that of Elmegreen & Elmegreen (1984). Both differ only by a single unit. Once the gravitational collapse is reached, a delay of 10 7 yr. (Elmegreen & Lada 1977) is expected for the radiation from newly formed stars to be seen through the molecular clouds and to reach the main sequence. This delay would cause a shift between the arm s mean position in different bands, when combined with the position of the star formation front with respect to the potential well. When gravitational collapse has terminated, stars with strong emission in U and B (i.e., O to F stars) are formed. Let us suppose that we are observing a galaxy rotating in a counterclockwise sense ( θ ), and that we measure its azimuthal profile before corotation, so that the disc matter encounters the density wave. The steeper side of profiles is then located before the maximum, i.e., the asymmetry is positive in B and I. However, θ B θ I depends on the strength of the potential well. If it is Dust is mixed with gas, so that the higher the gas density, the higher must be the dust density. When dust particles pass through an arm they are evaporated due to the effect of intense radiation from young stars. After the passage of the wave, dust is formed again in a continuous process with maximum concentration just before the encounter with another arm, where the cycle is repeated. It has been shown observationally that dust lanes occur on the concave sides of arms (before corotation) and far from the maxima in optical bands. In some cases (such as NGC 4321, see Cepa et al. 1992) dust lanes can be seen crossing the arms from the concave to the convex side, in a zone that corresponds to corotation. Generally, the presence of dust might enhance or generate asymmetries (usually in the bluer bands) so it is necessary to check whether the azimuthal profile measured includes dust lanes or not, and when it does, this has to be taken into account when analysing the data. Dust extinction is more important in the B than in the I band, so the difference mean position might be affected too but in different ways if the potential is weak or strong. In the first case (θ B θ I ) dust > (θ B θ I ), where (θ B θ I ) dust is the difference in the means contaminated by dust, which are what we measure, while (θ B θ I ) is the difference in the means that we should measure, in the same region, in the absence of dust. In the second case it could be that (θ B θ I ) dust 0 instead of (θ B θ I ) < 0 ( θ sense) or (θ B θ I ) > 0 ( θ sense), so the effect of dust is more hazardous when the potential well is strong, because it could invert the difference sign.

5 M.S. del Río & J. Cepa: The nature of arms in spiral galaxies. III 5 Fig. 5. NGC 157, in B band. The grey scale is in mag/ 2. Fig. 7. NGC 157. mean and maxima positions (top) and Skewness (bottom) Fig. 8. NGC 157. Maxima (dotted line) and media (thick line) positions vs. radius in B and I bands. Fig. 6. NGC 157, in B band. Low level corresponds to 0.5 count/sec., increments are 0.5 count/sec (10 levels). Triangles mark the mean position of the studied feature. Whenever possible, we have studied an arm without dust lanes, or that with the least dust in each galaxy. When this was not possible, we have analysed the results obtained with care and have compared them with other independent methods. 5. The galaxies 5.1. NGC 157 This is an isolated galaxy (the closest galaxy, NGC 255, is more than 3 distant) and is moderately face-on (i 50 ) with two well defined arms and several secondary branches (Fig. 5). The first impression of this galaxy is that its surface is covered by luminous spiral-arm segments mixed with dust lanes. The most prominent dust lane is located on the concave side of north arm (which originates on the eastern side and twists to the north). The south arm has a secondary branch, at R 27 that branch out from it and extend to the outer disc. At R 35 it has a bifurcation produced partially by the strong dust lane between sub-arms. For these reasons we have studied only the north arm, which has its dust lane on one side, and which crosses the arm only once. Both arms are very bright, with an azimuthal extension of near 360 around the nucleus. At R 60 they become almost circular, and disappear in the disc at R 70, where the OLR could be located. So our analysis extends from R 20 to R 60. From our data (Paper II) it turns out that the bulge has colours characteristic of an old population (B V ), while the arms are bluer (B V ). The north

6 6 M.S. del Río & J. Cepa: The nature of arms in spiral galaxies. III Fig. 9. NGC 157. I-band amplitude arm is well fitted by a logarithmic spiral (Pearson coefficients of 0.98 for the B and I bands) which leads to a pitch angle of 21 for the inner part (20 < R < 60 ), in reasonable agreement with Kennicutt (1981). Around 40 < R < 45 the dust lane crosses the arm from the concave to the convex side, with an estimated relative extinction of A V 0.49 mag. This extinction is calculated assuming that the same flux as that in a small surrounding arm zone should be observed. The difference in mean position is positive until R 40, and negative or zero beyond 40. The two points (R =43.2 and R =44.4 ) with θ B θ I > 0 after this sign change corresponds to the neighbourhood of an H ii region that distorts azimuthal profiles, and that can be readily identified in the contour maps (Paper II). The skewness degree is clearly positive in B before R 40 and negative afterwards, while S I 0 in this range of radii. The arm amplitude is moderately weak, A I < 2 before R 40 and A I > 3 after that. With all these data we can conclude that in NGC 157 the density wave is moderately weak, but very effective; corotation is located at R 40, where the asymmetry changes its sign. This radius is confirmed because the dust lanes cross over from the concave to the convex side. This leads to the additional conclusion that the galaxy is trailing. Also, at the corotation radius the arms are broken (this is a quite common phenomenon, because the corotation radius is a critical region which poses difficulties for density waves to cross it). Presumably, the OLR is located around R 70, where both arms disappear, in good agreement with EEM, who found OLR/CR According to Table 1, it is a counterclockwise rotating galaxy with a weak trailing wave. For the distance used by Ryder et al. (1998) our CR value corresponds to 4 kpc. This value intersects with the theoretical rotation curve at Ω pt 38 km s 1 kpc 1, and with an observational value of Ω pt 42 km s 1 kpc 1, which are in good agreement with the value of Sempere & Rozas (1997) of Ω 40 km s 1 kpc 1. These authors have considered resonances through velocity fields studies. With their method there are uncertainties in the pattern speed, but eventually such data Fig. 10. NGC 753, in B band. The grey scale is in mag/ 2. Fig. 11. NGC 753, in B band. Low level corresponds to 0.2 count/sec., increments are 0.35 count/sec (11 levels). Triangles mark the mean position of the studied feature. might be used in conjunction with our method to further refine the resonance estimate. Those differences, that are not very significant due to the flatness of the rotation curve in the neighboroughood of CR, will probably minimized taking the most recent data from Ryder et al. (1998), rather than the old data from Afanasiev et al. (1988) used to fit their model.

7 M.S. del Río & J. Cepa: The nature of arms in spiral galaxies. III 7 Fig. 13. NGC 753. Maxima (dotted line) and media (thick line) positions vs. radius in B and I bands. Fig. 12. NGC 753. mean and maxima positions (top) and Skewness (bottom) 5.2. NGC 753 This apparently small galaxy is the biggest one in the sample, and is also the most distant (about 2.5 times the median distance). It is moderately face-on (i 45 ) with multiple and large spiral arms: two very strong and tight arms extending around 180, and three weaker and larger arms, continuing from the former and sub-dividing into several branches. It has a small companion, NGC 759, which could be causing this opening and breaking in the outer arms. The main feature in the arm analysed here (the one that originates on the eastern side and twists to the south-west, which we called the west arm ) is an elbow in the mean and maxima positions, near R 30, where the curve becomes stepless and the pitch angle therefore changes from 13 (tightly wound arms) to 42. This elbow obliges us to use two fits, one from the beginning to R 30 and the other from 30 to 50. In this way, the fit is much better and allows us to deduce in a qualitative way that the inner arms are tighter than the outer ones. At this radius the arm is broken into three sub-arms. The first of these turns on over the nucleus and merges into the other arm. The second one, continuing the main arm, is open, with a pitch angle of 42, reaching a radius of 70, but is too weak for our study, so for optimum S/N to apply our method of analysis, this arm reaches only 50. The elbow is observed also in the other arm, which is not analysed here. The third sub-arm is just a bridge that is closed over the main arm. All these features can be seen in Fig 10. Fig. 14. NGC 753. I-band amplitude The B and I mean positions coincide everywhere except at 30 < R < 40, the zone where the arm (really both main arms) is broken. Neither does the asymmetry have a clear sign, but instead oscillates about zero in the I band and perhaps change twice in the B band. All these features are seen more clearly if we pass a five-point median filter through both the asymmetry in the B band and the mean position difference. According to Pasha (1985), NGC 753 is trailing, so that, from the shape of the arms, it rotates in a clockwise sense. So if asymmetry is assumed to be positive from R 30 till the end, corotation could be located here, where the arms are broken and the pitch angle changes. The arm amplitude is small, with A I < 2 in almost the entire arm, and is never A I > 3. All these characteristics imply that the wave density is weak (see, for example, typical I-band contrasts in Elmegreen & Elmegreen 1984). This galaxy is one of the cases where the azimuthal profile method alone cannot assert where the corotation radius actually is, but we need further evidence to support this tentative measurement, such as the one used in Paper IV NGC 895 This is a pure non-barred spiral galaxy with two very blue (B V 0.2) long and somewhat loosely bound arms. The small

8 8 M.S. del Río & J. Cepa: The nature of arms in spiral galaxies. III Fig. 15. NGC 895, in B band. The grey scale is in mag/ 2. Fig. 17. NGC 895. mean and maxima positions (top) and Skewness (bottom) Fig. 18. NGC 895. Maxima (dotted line) and media (thick line) positions vs. radius in B and I bands. Fig. 16. NGC 895, in B band. Low level corresponds to 0.4 count/sec., increments are 0.4 count/sec (10 levels). Triangles mark the mean position of the studied feature. bulge is slightly elongated perpendicularly to the major axis with moderately red colours (B V ). Thin dust lines can be seen on the concave side of each arm. The strongest arm is the west one (south-west-north), which we study from R 20 to R 100, where it disappears into the disc. The logarithmic fit to the mean position is the best one in the sample (with correlation coefficients higher than 0.995). The possible break at R for both arms is an optical effect and is not reflected in mean-maximum position diagrams (Fig. 15). The pitch angle calculated with the fit is 27, slightly higher that found by Kennicutt (1981) but in excellent agreement with that found via Fourier transforms (Paper IV), which take into account both arms as a whole, not only the brightest part. The asymmetry in B shows two main tendencies; the first, before R 75, where on average it is negative, and after that, where it is also on average positive. The I-band asymmetry has a similar qualitative behaviour. The difference in mean position also has two tendencies, θ B θ I < 0 before 60 70, 0 further out. In the neighboroughood of these changes the arm flux also decays. The amplitude grows slowly until R 75, after which we can see peaks of relative amplitude 6 over a brief space. So in this highly symmetric galaxy we can see a trailing, moderately strong wave, with corotation located at R 75, where the asymmetry sign changes from negative to positive values; the difference of mean positions also roughly changes at this position from negative values to values close to zero, and the amplitude in the B band decays, due to the

9 M.S. del Río & J. Cepa: The nature of arms in spiral galaxies. III 9 Fig. 19. NGC 895. I-band amplitude scarce star formation after it. So we conclude that corotation is located at R 75. The relatively strong star formation before corotation and its later decay are an indication that star formation depends not only on wave amplitude but also on the physical conditions of the interstellar medium, which could be quite different before and after corotation, in the outer parts of the disc NGC 4321 This is the well known but complex M100 galaxy. In its circumnuclear region Cepa & Beckman (1990b) found an internal spiral emitting in Hα and N ii, delimited by two ILRs. Because of the apparently high degree of symmetry, we have studied both arms. The analysis begins at R 64, rather far away from the bar, and extends to R 120, where arm intensity is almost the same as that of the disc. The north arm (east-north-west) has fewer star formation regions than the south (west-southeast) one, so that, although the mean position in both bands can be very well fitted (the correlation coefficient of the spiral fits > 0.99), the maxima have relatively high dispersion. Both arms present a star formation burst in opposite directions (173 for the N-arm and 12 for the S-arm). Both bursts are shown as a plateau in the mean-position vs. radius graphs. The burst in the N-arm is located at 95 < R < 105 and the S-arm burst is located at 80 < R < 90. The south arm presents a similar asymmetry in B and I; itis positive before R 80 until 95, where S B suddenly becomes negative and quickly oscillates around zero, while S I increases slowly, approaching zero, but without clearly positive values. The north arm, less clearly defined, shows only one relevant sign change in asymmetry in the B band at R 78 and none in the I band, where S I is always on average negative. It should be noted that NGC 4321 has a companion, NGC 4322, that is linked to the southern arm through a weak light bridge that makes up a bifurcated spiral arm at R (Paper II). In fact, the south arm studied here corresponds, out to 95, to the brightest arm, which branches off from the main, weaker, arm at 90 < R < 95. From R 95 the Fig. 20. NGC 4321, in B band. The grey scale is in mag/ 2. studied arm once again predominates undistorted by NGC A more detailed study of the images in every band shows that dust lanes cross the secondary southern arm at R 90 95, while in the main arm, which has a little elbowing probably due to the companion galaxy, the dust lane crosses over again to the concave side, so this is a trailing arm with a different pattern speed, an idea supported by Fourier decomposition of the spiral arms (Paper IV). The processes described here are not evident in the northern arm. These effects could explain the unusual features (compared with other galaxies in the sample), such as the double sign change in asymmetry. From the azimuthal profile analyses we can conclude that the corotation radius is at R 80 in both arms, and from the winding sense and asymmetry sign we can conclude that it is a trailing galaxy. The corotation radius is in good agreement with those deduced from fitting ILRs by Cepa & Beckman (1990b), from crossing dust lanes at 90 (Cepa et al. 1992), and a much lower number of H ii regions beyond this radius (Cepa & de Pablos 1998). The plateau observed at in mean position corresponds to the south arm bifurcation towards NGC 4322; when we return to the main arm, the mean position follows the former behaviour. Through A I we can see that the wave amplitude in the north arm is bigger after corotation (80 ), so, the wave is weak before CR and strong later (in excellent agreement with the

10 10 M.S. del Río & J. Cepa: The nature of arms in spiral galaxies. III Fig. 22. NGC mean and maxima positions of the North-arm (top) and the South-arm (bottom) Fig. 21. NGC 4321, in B band. Low level corresponds to 0.5 count/sec., increments are 0.5 count/sec (10 levels). Triangles and squares mark the mean position of the studied feature. observed difference in mean position in the B and I bands). Information about the south arm is a bit confused. We think that after corotation the spiral wave could be reinforced by tidal interaction with NGC NGC 6764 This is the first of the two arm class 5 galaxies in this sample. The bright and active nucleus dominates the galaxy, where little more recent star formation is found. The nucleus and the two star formation bursts in the bar end have moderately blue colours (B V and B I 2.6 3), whereas the remainder is moderately red (B V and B I 4 4.2), without clear differences between the arm and inter-arm in the colour maps (Paper II). The arms, which are very faint compared to the near bar, are very difficult to analyse using the azimuthal profile method. The south arm (originating on the west side of the bar) blends into the disc just when leaving the bar. The north arm (originating on the east side of the bar) is slightly more luminous and continuous than the south one and shows an H ii region at its tip at R 52. We have analysed it from R 37, where a star Fig. 23. NGC Skewness of the North-arm (top) and the Southarm (bottom) formation zone is found, until R 54, where the arm is indistinguishable from the disc. Moreover, arms are almost circular (see the deprojected images in Paper IV), so azimuthal profiles do not cut the arms transversely, but rather almost tangentially. This indicates a priori that the arms are not logarithmic spirals, a clear difference with respect to all grand design galaxies studied here. The mean position in the B and I bands shows three clearly different zones. The first one, larger in I than in B, corresponds to the end of the bar, with constant angular position 200. The second one, which corresponds to the arm,

11 M.S. del Río & J. Cepa: The nature of arms in spiral galaxies. III 11 Fig. 26. NGC 6764, in B band. The grey scale is in mag/ 2. Fig. 24. NGC Maxima (dotted line) and media (thick line) positions vs. radius in B and I bands. The North-arm (top) and the Southarm (bottom). Fig. 25. NGC I-band amplitude. The North-arm (left) and the South-arm (right). is larger in B than in I, with a smooth slope. The last one is due to a conspicuous H ii region, and produces a jump in angular position. There is not much difference between the mean and maximum positions, so that the profiles should be quite symmetric. In fact, the symmetry is very close to zero (except near the H ii region) and shows a slight tendency from negative towards positive values, with the changeover around R 45. The difference between the mean and maximum positions shows a similar tendency, from zero negative to zero positive mean values, with the changeover occurring around 45. The relative amplitude is very low, which confirms the idea that the wave, if present, is very weak (the arms are hardly seen in the I band) and inefficient. If we consider that our results are consistent with S B and S I being negative and θ B θ I < 0 before 45 and positive later, we might have a trailing galaxy, in agreement with Pasha (1985), with corotation at R 45 and with an extremely weak wave. However, star forming activity is too scarce Fig. 27. NGC 6764, in B band. Low level corresponds to 0.07 count/sec., increments are 0.07 count/sec (10 levels). Triangles mark the mean position of the studied feature. to allow us to obtain a clear conclusion from the statistical study of the azimuthal flux distribution, so in this case our conclusions are provisional and must be contrasted with other methods in order to become more definite. The method of analysing the azimuthal profiles is more powerful when the arms are well defined than when they are intermediate, because it is based on the hypothesis that star formation is triggered by a density wave which has also organized the background population of the disc. When there is no such wave, as seems to be the case in this galaxy, whose red arms are hardly visible in the I image, it is not possible to measure the asymmetry of the profiles, because star formation is probably due

12 12 M.S. del Río & J. Cepa: The nature of arms in spiral galaxies. III Fig. 30. NGC I-band amplitude Fig. 28. NGC mean and maxima positions (top) and Skewness (bottom) Fig. 29. NGC Maxima (dotted line) and media (thick line) positions vs. radius in B and I bands. to stochastical rather than organized processes, such as those produced for a density wave. Nevertheless, an extremely weak wave seems to be present in this galaxy and is probably induced by the active bar NGC 6814 This is a Seyfert 1 galaxy (Ulrich 1971) whose nuclear region dominates the disc. CO was detected by first time in 1986 by Blitz et al., in a narrow line of 100km s 1. An intrinsically low-luminosity active nucleus suggests a small narrow line region (NLR). The spectroscopy history of this galaxy indicates long-term ( few years) large-scale flux variations, the nuclear spectrum of NGC 6814 varies from Seyfert 1 to one closely resembling a Seyfert on a time scale of months to a few years (Sekiguchi & Menzies 1990). When our data were taken (1990) the object was still in a very faint state (Winkler 1992). The arms are very patchy with some conspicuous blue knots in the weak spiral structure (B V 0.5) with little evidence of Fig. 31. NGC 6814, in B band. The grey scale is in mag/ 2. dust. The galaxy is the most face-on in the sample (i 7 only). The two main arms originating in the bulge bifurcate very soon several times. Hence, it is difficult to know which main arm corresponds to each external branch. The brightest arm components complete approximately a full revolution around the bulge, until R 49. Beyond this point, there is a sudden decay in luminosity, and the arms end at R 65, where they cannot be distinguished from the disc. The dust in this galaxy seems to be present mainly on the convex side of the arms. The multiple arm pattern in this galaxy complicate the analysis. Only three arms exceed R 40, and only one (southeast-north) is continuous enough for study using the azimuthal profile method over a wide range (27 < R < 54 ). Although mean positions in the B and I bands show a smooth behaviour, a more detailed view of the mean position vs. radius (Fig. 28a top) shows a slight discontinuity at R 45, where the slope changes significantly. In fact, the fit to two separate regions (from 27 to 45 and from 45 to 54 ) provides

13 M.S. del Río & J. Cepa: The nature of arms in spiral galaxies. III 13 Fig. 34. NGC Maxima (dotted line) and media (thick line) positions vs. radius in B and I bands. Fig. 32. NGC 6814, in B band. Low level corresponds to 0.4 count/sec., increments are 0.4 count/sec (10 levels). Triangles mark the mean position of the studied feature. Fig. 35. NGC I-band amplitude Fig. 33. NGC mean and maxima positions (top) and Skewness (bottom) a more accurate pitch angle than a single fit. The first region contains the most intense stellar formation. Another important difference between the two regions is the pitch angle. For the inner part, the arms are more tightly wound (i ) than the outer ones (i 32 ). This feature can be easily seen in the m =4component of the Fourier transform (Paper IV). The difference in the mean position graph shows that θ B θ I > 0, with some negative values before R 45. In the B I colour map (Paper II) the arms disappear beyond R 45. Asymmetry is very similar in the B and I bands and is negative before R 45 and positive beyond. All these features point to R 45 as the corotation radius. A difference θ B θ I > 0 before corotation would be an indication of a strong wave, while θ B θ I > 0 after corotation would indicate a weak wave. Both cases correspond to a clockwise rotating galaxy (Table 1). If corotation is located at R 45, as the change in the pitch angle and the lower luminosity beyond this radius, the change in the sign of the asymmetry, all indicate, then this galaxy is rotating in a clockwise sense. Also, when θ B θ I > 0 before corotation, this is an indication that the wave is strong, whereas when θ B θ I > 0 after corotation, the wave is presumably weak. Both classes correspond to a clockwise rotating galaxy. Hence, according to these results and the arm shapes, NGC 6814 is a leading galaxy, with a strong wave before corotation and a weak wave after it. NGC 6814 has no conspicuous companion in the POSS plates that could excite with its interaction the leading arms. This is an exception to Pasha s sample, where trailing arms are more numerous, and all leading arms present a close companion with signs of interaction.

14 14 M.S. del Río & J. Cepa: The nature of arms in spiral galaxies. III Fig. 36. NGC 6951, in B band. The grey scale is in mag/ 2. Fig. 38. NGC mean and maxima positions (top) and Skewness (bottom) Fig. 39. NGC Maxima (dotted line) and media (thick line) positions vs. radius in B and I bands. Fig. 37. NGC 6951, in B band. Low level corresponds to 0.2 count/sec., increments are 0.2 count/sec (10 levels). Triangles mark the mean position of the studied feature NCG 6951 This galaxy shows important dust lanes, one of which originates in the nucleus and is the companion of the west arm (south-westnorth). The arms are relatively short, no more than 180, and end approximately at R 100, at least for the more symmetric part, with some sporadic star formation further away. This galaxy presents the weakest arms in our grand design sample. We have studied the west arm, which is the most intense and continuous, from R 48, far away from the bar, until R 90, where the arms become circular. A small discontinuity around R 70 can be seen in mean positions, both in the B and I bands, which are noisier from this radius outwards, where the intensity decreases. The maxima and media are very similar. This implies that star formation is neither violent nor patchy but bright due to the density wave. The logarithmic fit shows very open arms (i 40 ) but is very noisy with errors 1 2. The mean position difference has two clearly defined zones. Before R 70, θ B θ I < 0, and after R 70 θ B θ I > 0. This should correspond, if we assume R 70 as the corotation radius, to a spiral with an inner strong and a weak outer wave, but with different senses of rotation. This is because the dust follows the inner arm part. In the arm being studied (the west one) the presence of dust is important until R 70. Since it is located on the concave side of the arm, we can expect a shift in the star formation front which could produce θ B θ I < 0 instead of θ B θ I > 0. Also, there is no conspicuous dust beyond 70, so that the difference of the means is not altered. We

15 M.S. del Río & J. Cepa: The nature of arms in spiral galaxies. III 15 Fig. 40. NGC I-band amplitude can conclude, then, that the wave is strong before R 70, weak after R 70 and rotates in a clockwise sense. The wave intensity also changes at this radius, as also happens in other galaxies in the sample, all of which is coincident with corotation. In this galaxy it is not easy to analyse asymmetries because the results are very sensitive to the zero level. This is the only case in the sample where this occurs and is probably due to the weakness of the arms. The arm amplitude is moderately strong (A I 4.5) until R 70, where it decreases to less than 3. So, without unambiguous clues from the asymmetry and relying only on differences in mean positions, we cannot distinguish between trailing and leading spirals; we can, however, consider both cases, and choose the most reasonable of the following hypotheses: a) Corotation is at the end of the bar. This hypothesis, combined with the presence of dust lanes on the concave side of the arm, implies that the spiral is leading. In this case, from θ B θ I we could deduce that the wave produces little star formation before R 70, and that, beyond this point, waves trigger stronger star formation. But this is contrary to what is observed. b) Corotation is further away from the bar, so that the position of the dust lanes implies that the wave is trailing. The mean position difference indicates that, if we assume that corotation is at R 70, the density wave is relatively strong. In fact, the I amplitude supports this idea, although star formation does not seem to be triggered to any great extent. This indicates that the spiral wave is not an efficient trigger of star formation, presumably because of the physical conditions of the ISM. The second hypothesis seems the more plausible, and does not contradict observation. So, it is most likely is that NGC 6951 is a trailing galaxy with corotation at R 70. This is a clear example of dust having a strong effect when the wave is strong NGC 7479 This is a barred galaxy, identified as a starburst by Young & Devereux (1991), with an asymmetrical two-arm spi- Fig. 41. NGC 7479, in B band. The grey scale is in mag/ 2. Fig. 42. NGC 7479, in B band. Low level corresponds to 0.3 count/sec., increments are 0.3 count/sec (10 levels). Triangles mark the mean position of the studied feature. ral and many symptoms of interaction. It has a luminous nuclear region which is classified to be a LINER (Keel 1983) and as type Hii by Filipenko & Sargent (1985). The nucleus is compact at 10µm (Telesco et al. 1993) with IRAS colours between those of Seyfert and Starburst galaxies (Roche et al. 1991). However, NGC is relatively isolated (Tully 1989), with nearest neighbor 2 away ( 1 Mpc projected), so it is unlikely that a nearby galaxy has caused its present, shortlived asymmetric appearance. The appearance of the galaxy would however be consistent with a recent merger with a low-mass companion (Mihos & Hernquist 1994). Quillen et al.

16 16 M.S. del Río & J. Cepa: The nature of arms in spiral galaxies. III Fig. 43. NGC mean and maxima positions (top) and Skewness (bottom) Fig. 44. NGC Maxima (dotted line) and media (thick line) positions vs. radius in B and I bands. (1995) located CR at 45 (assuming CR at the end of the bar), that leads to Ω p 100 km s 1 kpc 1, much more than found by Sempere, Combes & Casoli (1995), with Ω p 30 km s 1 kpc 1, also with a mass model from a red image. The Hα spectroscopy suggests the presence of large, bright H ii regions along the bar (Hua et al. 1980). The nuclear region and bar are formed by and old stellar population (B V ) in the bulge, B V in the star formation zones of the bar, very similar to that of the west arm, and B V 0.7 elsewhere (including the bar). Dust lanes are visible on the concave side of the inner part of the spiral arms. At the end of the huge bar ( 100 ) two large arms originate. One of these bifurcates when leaving the bar, but this is an artefact of the dust lane which is present from the nuclear region to the end of the east arm. The west arm, which is much more regular, is also accompanied by a dust lane, which is shorter than that associated with the east arm ending near the supernova remnant SN 1990V, at R 60. This arm will be the object of our study, although it is not a typical logarithmic spiral arm. In the B-band image (Paper II), two sudden changes in pitch angle can be clearly seen. The first one is just when departing from the bar (more pronounced that in the east arm). The second one is just before the beginning the star formation necklace at R 85. This is not a purely optical effect since both changes persist after deprojecting the image (Paper IV). Our analysis extends from R 55, which approximately marks the bar end, out to R 100, where the arms become circular and the profiles no longer cut across them any. Maximum positions have strong dispersion, both in the B and I bands, because in the west arm there are plenty of star formation bursts. The mean positions are much smoother and are monotonically rising, and are more similar to an Archimedean than a logarithmic spiral, as shown by a better fitting, as far as R 85, where a change in slope is present in both bands. This change coincides with a break in the arms that cannot be due to a dust lane. All these things indicate that there is a physical discontinuity in the spiral structure of NGC Since two fits are much better than just one, we have found i 43 for the inner part (from 55 to 85 ), and i 17 for the outer part (from 85 to 100 ). But, while dust lane is present, there is a mismatch of 2 between B (i 44 ) and I (i 42 ) bands; in other words, the blue arm is more open than the I arms. This is probably caused by the dust lane, which affect B mean positions more than I mean positions. After R 85 there is not so much dust, and pitch angles match within the errors. Otherwise, if the change in pitch angle were not due to dust lanes, it would be necessary to assume that density wave is leading (see below). Mean position differences show the typical behaviour of a clockwise rotating galaxy, with a thick dust lane as far as R 75. From this point, differences become significantly negative and noisy. At R 75 there is a flux minimum in both bands. Differences close to zero are usually produced by strong waves. This is the case up to R 75, and could be from 85 onwards, but they are too noisy to show a clear result. Asymmetries show a very regular behaviour. Close to R 60 there is a change in sign, from positive to negative, in both the B and I bands. This distance is only 0.4 kpc higher than what Duval & Monet (1985) give as the bar end and corotation. If corotation were located there, then this galaxy has S B and S I > 0 before and < 0 after corotation, with θ B θ I < 0. This corresponds to a strong wave (asymmetry is very clear in the I band) rotating in counterclockwise sense; that is, it is a leading spiral. This was the incorrect conclusion found by Paper I and was caused by the assumption that corotation was at the end of the bar, and because only profiles to R 80 were available. Nevertheless, nowadays there exists a greater range of dynamical evidence (Athanassoula 1992) that bars do not always end at corotation but can finish before, even at inner Lindblad resonances. NGC 4321 is a clear example of a barred galaxy where the bar does not end at corotation (Cepa & Beckman 1990b, Sempere et al and this work). If we accept that NGC 7479 is a leading galaxy, then there is no explanation for a second sign change at R 85, where both (S B and S I ) become positive again. This leads to a differ-

17 M.S. del Río & J. Cepa: The nature of arms in spiral galaxies. III 17 Fig. 45. NGC I-band amplitude ent interpretation, which is that corotation is located in a wide fringe between R 75 and 85 (better determined by asymmetry than by mean difference). This can explain the second sign change. The difference mean position sign implies that the wave is strong. The galaxy then rotates in a clockwise sense and is therefore trailing, as found by Pasha & Smirnov (1982) and Pasha (1985). The first asymmetry sign change could be due to the strong influence of the end of the bar, or to the possibility that the bar actually ends at R 60 instead of at R 56 as Pasha & Smirnov (1982) claim. Given the shape of this galaxy, it is not easy to determine the location of the end of the bar precisely. So, the change in pitch angle, in asymmetry sign and arm breaking are located at the same position as that of the corotation radius, which in this galaxy is clearly determined by S λ at R 85. The wave is very strong before corotation, as can be seen in the difference of mean positions vs. radius and A I vs. radius, and is moderately strong later. The asymmetry sign, together with the arm shape, indicates that this is a trailing spiral. Fig. 46. NGC 7723, in B band. The grey scale is in mag/ NGC 7723 This is the second arm class 5 galaxy in the sample. It is an intermediate barred galaxy, with wide arms, which are difficult to distinguish from interarms. Unlike NGC 6764, the other class 5 galaxy, it has an extensive disc beyond the end of the arms. This galaxy has a companion, NGC 7727, a peculiar Sa, located 40 NW from it, with a radial velocity difference of only 3 km s 1. However, the multiple arm pattern seen in the outer part of the disc is probably not due to the interaction, because it is quite symmetric, and not only in the companion direction. From each bar tip two arms originate; one closes over the bulge and the other opens to the outer regions. These inner arms are so closed that they look like an almost complete ring around the bar. We call these secondary arms and their bifurcations, while we call the most external arms main or principal arms. These are the object of our study. In this case, both arms are Fig. 47. NGC 7723, in B band. Low level corresponds to 0.4 count/sec., increments are 0.4 count/sec (10 levels). Triangles and squares mark the mean position of the studied feature. rather well defined and allow us to analyse their azimuthal profiles. Our study begins at R 16, where bar is still important, and ends at R 35 for the north arm (west-north-east) and at R 40 for the south arm (east-south-west). In both mean vs. radius plots the bar is present out to R 24 on the west side and to R 22 on the east side. Its angular position is very well defined in the north arm (θ 226 ), while in the south arm it varies by 20, from θ i 50 to θ f 30. That is because in the extreme west the bar is straight as far as its end, where a main arm originates, while at the opposite extreme