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The Astrophysical Journal, 613:886 ­ 897, 2004 October 1
# 2004. The American Astronomical Society. All rights reserved. Printed in U.S.A.

THE STELLAR DISK THICKNESS OF LOW SURFACE BRIGHTNESS GALAXIES
D. Bizyaev
1,2,3

and S. Kajsin

4

Received 2003 October 23; accepted 2004 June 9

ABSTRACT We present surface photometry results for a sample of 11 edge-on galaxies observed with the 6 m telescope at the Special Astrophysical Observatory, Russia. The photometric scale length, scale height, and central surface brightness of the stellar disks of our sample galaxies are estimated. We show that four galaxies in our sample, which are visually classified as objects of the lowest surface brightness class in the Revised Flat Galaxy Catalog, have bona fide low surface brightness ( LSB) disks. We find from a comparison of photometric scales that the stellar disks of LSB galaxies are thinner than those of high surface brightness ( HSB) galaxies. There is a clear correlation between the central surface brightness of the stellar disk and its vertical-to-radial scale ratio. The masses of spherical subsystems (dark halo + bulge) and the dark halo masses are obtained for the sample galaxies based on the thickness of their stellar disks. The LSB galaxies tend to harbor more massive spherical subsystems than the HSB objects, whereas no systematic difference in the dark halo masses is found between LSB and HSB galaxies. At the same time, the inferred mass-to-luminosity ratio for the LSB disks appears to be systematically higher than for HSB disks. Subject headings: dark matter -- galaxies: spiral -- galaxies: structure g

1. INTRODUCTION Low surface brightness ( LSB) spiral galaxies have been studied extensively in recent years. The main feature that distinguishes them from ``regular,'' high surface brightness ( HSB) galaxies is the roughly 2 mag lower central surface brightness of their stellar disks. They are thought to harbor massive dark halos (de Blok et al. 2003). The LSB rotation curves are shallower in their central parts ( McGaugh et al. 2001), which points to a large dark matter fraction. By observing the thickness of the stellar disk in a galaxy, one can constrain the relative mass of the dark halo (Zasov et al. 1991). Until recently, however, only a few edge-on LSB galaxies have been explored in detail (e.g., UGC 7321, Matthews 2000; IC 5249, van der Kruit et al. 2001). We conducted a study of a small uniform sample of LSB and HSB galaxies observed with the same instrument to compare their structural parameters. Here we present the results of photometric observations in the V and R bands of a sample of 11 edge-on galaxies. The paper is structured as follows. In x 2 we describe the sample of galaxies and observations, in x 3 we discuss the data reduction and present the structural parameters of our galaxies, in x 4 we use the inferred disk thickness to estimate the dark halo mass, x 5 contains a discussion of selection effects and relations between the inferred parameters, and the main results are summarized in x 6. 2. SAMPLE OF GALAXIES AND OBSERVATIONS Our sample is based on the Revised Flat Galaxy Catalog ( RFGC; Karachentsev et al. 1999). All galaxies included in this catalog are highly inclined objects. We selected objects from
1 Physics Department, University of Texas at El Paso, 500 West University Avenue, El Paso, TX 79968. 2 Sternberg Astronomical Institute, University of Moscow, Moscow 119899, Russia; dmbiz@sai.msu.ru. 3 Isaac Newton Institute of Chile, Moscow Branch, Russia. 4 Special Astrophysical Observatory of the Russian Academy of Sciences, pos. Nizhnij Arkhyz 357147, Karachaevo-Cherkessia, Russia; skai@sao.ru.

the faintest surface brightness (SB) class ( IV, according to the RFGC) as candidates for LSB galaxies, and objects from intermediate or high surface brightness classes as reference HSB objects. We narrowed the sample of objects to galaxies large enough for structural studies (major axis size >20 in the RFGC) that fit inside the 3A5field ofviewofour CCDimager. In three observing nights of our program we obtained data for 11 galaxies. Photometric observations were performed with the primefocus camera on the 6 m telescope at the Special Astrophysical Observatory of the Russian Academy of Sciences. This setup provides a plate scale of 0B2 pixelþ1 and good sensitivity for faint regions of galaxies. The data were taken on 2000 April 27, 28, and 30 in the Johnson-Cousins V and R photometric bands. The V-band images were used mostly for calibration purposes, while the R-band images were used for the measurements of structural parameters. For most of the galaxies in our sample we made two to four images shifted by a few pixels in both photometric bands. The Landolt photometric standards ( Landolt 1992) were observed every night. Table 1 summarizes our observations, listing object names, SB class (according to the RFGC), date of the observation, total integration time in every photometric band, number of exposures, and average seeing when the target was observed. 3. DATA REDUCTION AND RESULTS The data were reduced using standard tools in the MIDAS package. The images of galaxies and photometric standards were corrected for the bias and dark current and flat-fielded. The images were then sky subtracted, aligned, and combined. We checked the quality of flat-fielding and sky subtraction by comparing the background level in those parts of the image that are free of foreground stars and are located close to a sample galaxy. The large-scale pattern of the background does not introduce uncertainties above 0.1%. Three galaxies have very bright stars in their fields, which raises the large-scale background fluctuations to 0.2%. 886


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TABLE 1 Summary of th e Obser ving Ru n Date (1999) Apr Apr Apr Apr Apr Apr Apr Apr Apr Apr Apr Apr Apr Apr Apr Apr Apr Apr Apr Apr 27 27 27 27 30 30 30 30 27 27 27 27 28 28 30 28 28 27 27 30 Integration Time (s) 600 1200 700 1000 600 1200 600 1200 1200 900 600 1200 900 900 1200 1800 2900 600 900 1200 Seeing (arcsec) 1.9 2.0 1.6 1.6 3.0 2.4 1.9 1.7 1.8 1.7 2.2 2.0 1.1 1.0 1.7 1.0 1.0 1.8 1.7 1.5 Sky (mag arcsecþ2) 21.37 20.72 20.76 20.38 21.39 20.59 21.49 20.68 21.35 20.48 21.35 20.56 21.37 20.63 20.57 21.46 20.68 21.43 20.50 20.45

887

Name UGC 10111 .......... UGC 11301 .......... UGC 5662 ............ UGC 6080 ............ UGC 6686 ............ UGC 7808 ............ UGC 9138 ............ UGC 9422 ............ UGC 9556 ............ FGC 1273 ............ NGC 4738 ............

SB Class IV III III II III IV I I IV IV I

Band V R V R V R V R V R V R V R R V R V R R

Exposure 1 4 3 4 1 2 1 2 2 3 1 2 2 2 2 4 6 2 2 2

S/N = 3 Level (mag arcsecþ2) 26.58 26.77 25.17 25.81 26.64 26.63 26.46 26.60 26.85 26.45 26.40 26.66 26.48 26.90 26.91 26.51 27.26 26.54 26.59 26.56

Note.--Name of galaxy, SB class (according to the RFGC catalog), photometric band, date of observation, exposure time (total), number of exposures, average seeing, level of sky brightness, and S=N ¼ 3 SB level in combined frames.

Eight and 12 Landolt's stars from three selected areas were available on April 27 and 30, respectively. The residuals for photometric solutions were 0.02 mag for April 27 (in both V and R bands) and 0.04 mag (in both V and R bands) for the night of April 30. The sky brightness level is tabulated in Table 1. The surface brightness corresponding to a 3 level of the background noise in the final combined images is shown in Table 1 as well. The observing conditions were nonphotometric during part of the night on April 28. However, most of our galaxies have the major axis photometric profiles in the R band published by Karachentsev et al. (1992). This enables us to verify the calibration and to adjust it for the nonphotometric night. The mean difference between the surface brightnesses we derived and those published by Karachentsev et al. (1992) is of the order of 0.3 mag. The largest source of discrepancy is the use of different procedures of the major axis profiles extraction. Comparison of the sky brightness in R images can be used to roughly estimate the zero point of calibration for the objects observed on April 28. If we use this method of calibration, the R-band surface brightnesses of UGC 9138 and UGC 9556 would be 0.4 mag lower than those used in this paper. The combined and calibrated images were used to obtain the radial scale length h, vertical scale height z0 , and ``face-on'' central surface brightness of the stellar disk, as well as the bulge-to-disk luminosity ratio Lb =Ld . The images were rotated to align the galactic plane parallel to the horizontal axis. Choosing the rotation angle, we direct our attention to the intermediate regions of galactic disks, where a possible bulge does not reveal itself and the signal-tonoise ratio (S/ N) is high enough. We applied a standard method (van der Kruit & Searle 1981) to derive the structural parameters extracting photometric profiles parallel to the major and minor galactic axes. The radial scale length was obtained from two photometric profiles

extracted parallel to the major axis and displaced with respect to the galactic midplane. This allows us to minimize the effects of dust absorption, because we avoid the galactic midplane. An average displacement is of the order of 0.7 z0 (see below). If the bulge was present, the central part of the radial photometric profiles (typically, 1 h from the center) is excluded from further analysis. We fit the function f (r) ¼ 2I0 sech2 (z=z0 ) R Rmax exp (þ l =h)rdl to the radial profiles and find mean values 0 of I0 and h. Here, r is the distance to the center, and Rmax is the distance to the edge of the disk. One can assume that Rmax ¼ 4h ( Pohlen et al. 2002; Holley-Bockelmann & Mihos 2001). The integration was made along the line of sight l. Two radial profiles used for the fitting are shown in the middle panels of Figures 1 ­ 11 by the solid lines. Note that each profile was manually cleaned of foreground stars before the fitting. The radial profile drawn through the galactic plane is shown in the middle panels of Figures 1 ­ 11 by the dashed line. As a next step, we draw 10 ­ 14 cuts made parallel to the minor axis of a galaxy and fit each photometric profile with the function f (z) ¼ I sech2 (jz × dzj=z0 ). Here jzj designates the distance to the galactic plane. The ``displacement term'' dz enables us to correct the values of the disk scale height for a possible disorientation of the major axis or disk warp. The resulting value of the scale height z0 and its error were found by averaging the values throughout the disk. Our galaxies show no significant variations of scale height with radius. Hence, we defined the mean scale height with no weights. Fitting the profiles, we convolved the function f (z) with the Gaussian smearing function assuming its FWHM from Table 1. The corresponding vertical profiles are shown in the top frames of Figures 1 ­ 11. They were manually cleaned of the foreground stars and artifacts before the fitting. The value of the disk central surface brightness 0 corrected to the face-on inclination was calculated with the parameters I0 and z0 inferred above, taking into account the photometric


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Fig. 1.--Top: Examples of the vertical profiles of UGC 10111 extracted parallel to its minor axis. Both lines show profiles taken along two vertical cuts closest to the galactic center (see isophotal map in the bottom panel). The 1000 bar indicates the level of S=N ¼ 3. Middle: Radial profiles extracted along the major axis (dashed line) and parallel to it (solid lines). The latter were used to derive the structural parameters of the galaxy. Upper and lower lines are shifted from their real positions by +2 and þ2 mag arcsecþ2, respectively. They are extracted along the upper and lower radial cuts shown on the isophotal map. The 1000 bar indicates the level of S= N ¼ 3. Bottom: Isophotal map of UGC 10111. The isophotes correspond to 20.5, 21, 21.5, 22, 22.5, 23, 23.5, 24, 24.5, 25, and 25.5 mag arcsecþ2 in the R band. The places where the profiles were extracted are shown by lines. All artifacts and stars that could be seen in the picture were cleaned out manually before the structural parameters were found.

Fig. 2.--Same as Fig. 1, but for UGC 11301. The isophotes correspond to 19.5, 20.5, 21, 21.5, 22, 22.5, 23, 23.5, and 24.5 mag arcsecþ2.

calibration equations. The extinction of our Galaxy (according to the LEDA database) is also included in the analysis and listed in Table 2. In order to check how examining only a limited number of brightness profiles (two radial and 10 ­ 14 vertical) affects the inferred values, we derive the same values for each galaxy by extracting the radial profiles (drawn along the major axis) with an increment of 1 pixel from 0.2 zmax to 0.8 zmax in the vertical direction, where zmax is the minor axis of an ellipse encompassing the galaxy to the level of S=N ¼ 3. The vertical profiles in this analysis were drawn with 1 pixel increments taking a step off the disk edge and its center. The resulting structural parameters are similar to those obtained above using only a few photometric profiles. All conclusions of the paper remain unchanged in this case. As was shown by de Grijs et al. (1997), we can neglect inclination corrections for inclinations larger than 86 ­87 .Our V images are deep enough to see obscuration by dust in most of

our galaxies. Although dust is not seen in the galaxy FGC 1273, its bulge has a high degree of symmetry. Because its edge-on disk is very thin, we assume that its inclination angle is 90 .For all other galaxies we can estimate the inclination angle of the galactic plane from the shape and position of their dust layers and the asymmetric position of their centers of brightness with respect to external isophotes. The value of the inclination is shown in Table 3; its typical error is 0N7. Based on those values , we applied no additional correction for non ­ edge-on inclination to the photometric parameters derived above. Assuming the inferred disk parameters, we subtracted the disk and extracted the bulge images from the central parts of our galaxies. Then the central parts of two radial profiles mentioned above, as well as the vertical profiles extracted along the minor axis, were áused to estimate the bulge parameters. The King ö profile, 0 1 × (r=ak )2 þ3=2 , as well as the exponential one, L b 0 exp ( þ r=ae ), were used to fit the bulge volume luminosity L b density distribution. Here 0 denotes the central volume lumiL nosity density. The bulge scales ak and ae could be different in b b the vertical and radial directions (i.e., for oblate bulges). The inner parts of the vertical profiles were excluded from the analysis. Bulges of most galaxies in our sample are best fitted by the King profile. The only exception is UGC 9556, the bulge of which is best fitted by the exponential profile. Because the central part of the latter galaxy is oblate, we suggest that it probably has two disks: an HSB disk encompassed by a more


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Fig. 3.--Same as Fig. 1, but for UGC 5662. The isophotes correspond to 20.5, 21, 21.5, 22, 22.5, 23, 23.5, and 24 mag arcsecþ2.

Fig. 4.--Same as Fig. 1, but for UGC 6080. The isophotes correspond to 20.5, 21, 21.5, 22, 22.5, 23, 23.5, 24, 24.5, and 25.5 mag arcsecþ2.

extended LSB disk. We consider its LSB disk throughout the paper. According to the RFGC, UGC 9556 may have a lens in its central part. On the other hand, its type was defined as a galaxy with a bar (SB?c) in the UGC catalog ( Nilson 1973). Moreover, UGC 9556 has an asymmetry of bright isophotes close to the galactic plane, which points toward a possible bar shielded by dust whose nearer side is seen. Indeed , photometric identification of bars in edge-on galaxies can rarely be conclusive. With the help of the parameters obtained, we infer the bulgeto-disk luminosity ratio Lb =Ld . The main results of the fitting are shown in Table 3. The values of h and z0 are converted to the spatial units according to the adopted distances to the galaxies D. Table 3 also shows R magnitudes and colors (VþR) derived for our objects. The magnitudes were obtained by integrating background-subtracted images of the galaxies within elliptical diaphragms. Major and minor axes of the diaphragms correspond to the sizes from the RFGC, which are quite similar to the galaxies' dimensions at S=N ¼ 3 level. The distribution of 0 (see Table 3) indicates the presence of two subsamples: galaxies with 0 greater than 23.5 mag arcsecþ2, which we define as LSB galaxies, and galaxies with a higher surface brightness, which are designated as HSB galaxies in this paper. Hence, our sample consists of four LSB and seven HSB galaxies. Note that all galaxies in the faintest RFGC SB class were classified here as LSB objects. Although our sample of objects enables us to compare the structural parameters of LSB and HSB disks, the sample is very limited. We incorporated one more sample of edge-on

galaxies whose photometric parameters have been published by Barteldrees & Dettmar (1994). They made use of similar red photometric band and technique to extract the photometric parameters. We utilize their data together with ours throughout the paper in order to increase the available sample of HSB galaxies. As it will be seen, the sample of Barteldrees & Dettmar also includes one object that can be classified as an LSB galaxy. 4. LSB VERSUS HSB: THE VERTICAL SCALE HEIGHT OF THE GALACTIC DISK AS A NEW FEATURE TO COMPARE As was shown in Bizyaev (2000), Bizyaev & Mitronova (2002), and Reshetnikov et al. (2003), the galaxies of lower surface brightness tend to have smaller z0 =h ratios. However, this conclusion was based on studies of mostly HSB galaxies. Now, we can incorporate our LSB subsample and consider the relation between z0 =h and the central surface brightness 0 .The objects from our sample are denoted by squares in Figure 12. The open squares show the HSB subsample, whereas the filled ones designate LSB galaxies. The galaxies taken from Barteldrees & Dettmar (1994) are shown by crosses. Furthermore, the near-infrared Ks -band sample of edgeon galaxies from Bizyaev & Mitronova (2002) (hereafter referred to as the 2MASS sample) is available for comparison. Here we must take into account the systematic difference in the brightness and z0 =h between the R and K photometric bands.


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Fig. 5.--Same as Fig. 1, but for UGC 6686. The isophotes correspond to 20.5, 21, 21.5, 22, 22.5, 23, 23.5, 24, 24.5, and 25.5 mag arcsecþ2.

Fig. 6.--Same as Fig. 1, but for UGC 7808. The isophotes correspond to 20.5, 21, 21.5, 22, 22.5, 23, 23.5, 24, 24.5, and 25.5 mag arcsecþ2.

As noticed by Zasov et al. (2002), the ratio of scales z0 =h is 1.4 times less for the stellar disk in K than for the stellar disk in R. This can be explained by stronger dust extinction in the R band and was well illustrated by Xilouris et al. (1998). We corrected z0 =h for the 2MASS galaxies taken from Bizyaev & Mitronova (2002) according to this value. The typical color R þ K ¼ 2:1 mag inferred for late-type face-on spirals by de Jong (1996) was added to the central surface brightnesses of the 2MASS galaxies as well. The final correction we applied was the addition of the internal extinction to the 2MASS central surface brightness, because it is low in the infrared band and nonnegligible in the R band. The value of this correction, 1.2 mag, is chosen so that the 2MASS sample coincides with our HSB objects in Figure 12. Figure 12 shows all three samples together; the 2MASS objects are denoted by the triangles. A trend is seen in Figure 12: an average difference of 2 mag in 0 leads to a factor of 1.5 change in the ratio of scales. At the same time, there is no clear correlation found when h and z0 are plotted against 0 separately. The correlation of 0 versus h was shown by Graham (2001), but that conclusion was based on mostly early-type spiral galaxies. We also incorporate general galactic properties taken from the LEDA database into the analysis: absolute B magnitude Babs, maximum of the rotation curve Vmax , and H i index. The latter index denotes the difference between the B magnitude and the H i magnitude. We found that LSB and HSB subsamples do not differ systematically in Babs , Vmax ,and H i index. There is no

correlation found between the values of 0 and z0 =h on the one hand and Babs , Vmax , and H i index on the other hand. In Figure 13 one can see a relation of the Tully-Fisher type, where the values of the radial scale length are well correlated with the maximum rotational velocity Vmax. According to Zwaan et al. (1995), Sprayberry et al. (1995), and Chung et al. (2002), LSB and HSB spiral galaxies follow the same TullyFisher relation, and our Figure 13 is in good agreement with this, which argues that we did not make a mistake deriving the spatial values. Thus, in their investigation of the galaxy UGC 7808, de Grijs & van der Kruit (1996) inferred a shorter scale height value (in kpc) because of the lower adopted distance to the galaxy. Figure 13 shows that our value of the scale length for the galaxy, 13.55 kpc, places the galaxy very close to the general dependence in Figure 13, whereas the scale length of 1.9 ­ 2.7 kpc taken from de Grijs & van der Kruit (1996) would place this object far off. At the same time, the angular values of the scale lengths found in the present work and in the cited one are very similar. Following Zasov et al. (2002), we calculated the ratio of the total mass Mt inside the optical radius to the luminosity of the galactic disk in the B band LB . We suppose that Mt ¼ 2 Gþ1 4hVmax , where G is the gravitational constant and the 4h radius encompasses the whole galaxy. The value of LB is obtained from the absolute B magnitude, which was taken from the LEDA and corrected for the internal galactic absorption. The values of Mt =LB are plotted against the ratio z0 =h in Figure 14.


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Fig. 7.--Same as Fig. 1, but for UGC 9138. The isophotes correspond to 20.5, 21, 21.5, 22, 22.5, 23, 23.5, 24, 24.5, 25, and 26 mag arcsecþ2.

Fig. 8.--Same as Fig. 1, but for UGC 9422. The isophotes correspond to 20.5, 21, 21.5, 22, 22.5, 23, 23.5, 24, 24.5, 25, and 25.5 mag arcsecþ2.

The notation in Figure 14 is the same as that in Figure 12. As noticed by Zasov et al. (1991), the ratio of scales z0 =h indicates the total mass of the spherical component of a galaxy expressed in its disk mass Ms =Md . The relation between z0 =h and Ms =Md obtained from numerical modeling (N-body simulations) was published by Mikhailova et al. (2001) and is shown in Figure 15. We made use of that dependence to evaluate the model values of Ms =Md for our galaxies. Here we must clarify that we distinguish between spherical and disk subsystems throughout this paper. By the term ``spherical subsystem'' we refer to both a stellar bulge and a dark halo, even if their shapes are not spherical but oblate (see discussion in x 5.5). In general, ``spherical subsystem'' means a nondisk component, whether stellar or not. The disk in our understanding is the galactic stellar disk, which for our objects consists mostly of stars. Later in this paper we also evaluate the ratio of dark-to-luminous masses. The dark mass refers to the dark halo, whereas the luminous mass refers to the stellar bulge and disk. Then we take into account that Mt ¼ Ms × Md and LB ¼ Md =(M =L), where M/L denotes the B-band stellar mass-to-light ratio in the disk. Hence Mt =LB ¼ (Ms =Md × 1)(M =L). We see that the model value of Mt =LB depends on the adopted M/L. The three lines in Figure 14 present the model values of Mt =LB , which were calculated based on Figure 15 with M/L values of 1, 5, and 15, respectively. As shown in Figure 14, most of the galaxies have M/L values between 3 and 10. The M/L in

Figure 14 corresponds to the distance along the horizontal axis toward the curve of M =L ¼ 1. Thevalue of thestellar mass-tolight ratio is systematically higher for our LSB galaxies than for HSB galaxies. This conclusion contradicts the bluer color of LSB galaxies found by de Blok et al. (1995), who give lower values for their M/L, but the bulge-dominated LSB galaxies have colors comparable with HSB galaxies ( Beijersbergen et al. 1999). The dereddened colors from both our LSB and HSB subsamples are almost the same (Table 3). On the other hand, LSB spirals have low metallicity, as a rule. This might give the comparable colors, whereas the stellar disk's M/L has a higher value in the LSB spirals. Another reasonable explanation might be an excess of dark matter in the disks of bulge-dominated LSB spirals. Large LSB galaxies have, on average, twice the mass in their gaseous components ( Romanishin et al. 1982) as HSB galaxies. Our LSB subsample has almost twice the H i index of the HSB subsample. However, this difference is not enough to explain the systematic difference in M/L in Figure 14, since the gas component does not dominate by mass in our galaxies. The mass of the dark halo Mh can be estimated from the relation shown in Figure 15. The dark-to-luminous ratio is (Md × Mb )=Mh ¼ (1 × Mb =Md )(Md =Mh ), where Mb and Md denote the masses of the bulge and the dark halo, respectively. On the other hand, Ms =Md ¼ (Mh × Mb )=Md , hence,


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Fig. 9.--Same as Fig. 1, but for UGC 9556. The isophotes correspond to 20.5, 21, 21.5, 22, 22.5, 23, 23.5, 24, 24.5, 25, 26, and 26.7 mag arcsecþ2. The diagonal feature in the bottom panel is a remainder of a bright satellite track.

Fig. 10.--Same as Fig. 1, but for FGC 1273. The isophotes correspond to 20.5, 21, 21.5, 22, 22.5, 23, 23.5, 24, 24.5, 25, and 25.5 mag arcsecþ2.

Mh =Md ¼ Ms =Md þ Mb =Md . Combining previous equations, we obtain Mh M s =M d þ M b =M d ¼ : Md × Mb 1 × M b =M d Ï 1÷

The values of Mb =Md can be estimated from observations making a rough assumption that the bulge-to-disk luminosity ratio follows the bulge-to-disk mass ratio, Mb =Md ¼ Lb =Ld (we consider in x 5 how our conclusions might change for real galaxies where M/L is different for bulges and disks). At the same time, Ms =Md can be estimated from Figure 15. The ratio of dark-to-luminous mass Mh =(Md × Mb ) for our galaxies is shown in Figure 16. Surprisingly, there is no systematic difference between the values of dark-to-luminous mass ratio for galaxies with different central surface brightnesses (see Fig. 16). It is generally assumed that the LSB galaxies are dark matter dominated, but those conclusions were based on studies of bulgeless galaxies. Our sample, however, comprises mostly galaxies possessing nonnegligible bulges. We can also compare masses of the spherical subsystem Ms (i.e., the sum of the bulge and the halo) in our galaxies. In Figure 17 we present how the spherical-to-disk mass ratio Ms =Md depends on the disk central surface brightness. We used the same notation as in Figures 12 and 14. Figure 17 indicates that the LSB galaxies do not have more massive dark matter halos. Instead, they have more massive spherical subsystems.

This supports a result by Graham (2002) that not all LSB galaxies are dark matter dominated objects. Nevertheless, our result does not contradict previous conclusions, since the dark matter halo and the spherical subsystem become identical for bulgeless galaxies. Differentiation between the bulge and the halo allows us to demonstrate that there are large LSB galaxies dominated by dark matter halos as well as LSB galaxies with halos less massive than their disks. 5. DISCUSSION 5.1. The Sample Selection There is no systematic difference in the obtained values of 0 among our sample galaxies of I ­ III SB class (also noticed by Bizyaev 2000). On the other hand, most galaxies of IV SB class are apparently bona fide LSB galaxies. They constitute a small part of all RFGC objects (3%). As noticed by McGaugh et al. (1995), there is a significant fraction of LSB galaxies with a large bulge-to-disk ratio. Bulges of LSB and HSB systems are indistinguishable ( Beijersbergen et al. 1999), yet their disks are different. Hence, we must distinguish between LSB galaxies with bulges and without bulges and take this into account when studying properties of dark halos in LSB galaxies. Our paper does not attempt to present a statistically complete study of LSB spiral galaxies with large bulges. Instead, we compare two samples of objects of opposite properties. To


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formulae in x 3. Let us consider how the non-90 inclination of the disk plane affects 0 and z0 =h. If the inclination angle is less than 90, the scale height z0 calculated in x 3 will be overestimated. At the same time, the scale length h is much less affected by the value of the inclination angle. On the other hand, the value of z0 was taken into account when the central surface brightness was calculated. While overestimating the ratio z0 =h, we underestimate the disk central surface brightness ( hence, its numerical value will be larger). This means that a non-90 inclination of the disk shifts the data points in Figure 12 toward the upper right corner. Hence, the systematic errors due to inclination may only scatter the dependence shown in Figure 12 ( for example, for the 2MASS galaxies) and do not explain a good correlation. The second effect that has to be considered is the internal dust absorption in galaxies. According to Xilouris et al. (1999), the scale length in dusty disks appears higher because of the scattering and absorption effects. On the other hand, the dust absorption decreases the derived central surface brightness. In our case it would shift the data points in Figure 12 from the upper left corner to the lower right corner and form a dependence similar to that seen in Figure 12. Nevertheless, we decreased the influence of dust by avoiding the dust layer when extracting the radial profiles. This allowed us to minimize the dust absorption. Furthermore, one can see that the infrared and optical subsamples follow a dependence similar to that seen in Figure 12. This argues that the internal absorption has little effect on the difference between LSB and HSB photometric parameters and that Figure 12 has a physical meaning. 5.3. Internal Absorption in Galactic Disks and the Ratios Ms =Md and Mh =(Mb × Md )
Fig. 11.--Same as Fig. 1, but for NGC 4738. The isophotes correspond to 20.5, 21, 21.5, 22, 22.5, 23, 23.5, 24, 24.5, 25, and 25.5 mag arcsecþ2.

make statistically reliable conclusions, the sample has to be extended. 5.2. Selection Effects Figure 12 presents a correlation between 0 and z0 =h. Indeed, the values of 0 and z0 =h have not been obtained independently from each other, as can be concluded from the

As noted in x 4, the disk thickness is different when it is estimated in different photometric bands. All the considered relations between the mass of a dark halo, stellar disk, and spherical component are made using the data taken in the R band. On the other hand, the infrared ratios of photometric scales z0 =h are less than the optical ratios. The infrared values are preferable because of the lower dust absorption, so we could decrease all our ratios z0 =h by a factor of 1.4. As shown in Figures 14 and 15, a proportional decrease of the scale ratio affects Figure