5 Results of the fits to the galaxy images

Table 3 lists all galaxies with the structural parameters for the disks resulting from all our fits. All parameters are given for J and K, and for H if available. The central surface-brightness values $SB_{\rm c}$ (in mag/square-arcsec) were obtained from the (unconvolved) central flux densities $I_{\rm d}$ of the disks using the photometric calibration. Note that these are the values if the galaxies are seen face on, the inclination is considered in the adopted elliptical geometry and can be calculated from $\cos(i) = Q_{\rm d} = b/a$. The scale lengths $R_{\rm d}$ are given in arcsec and in kpc, using the distances from Table 1. The last columns give the position angles ${\rm PA}_{\rm d} = \Phi_{\rm d}$, and the axis ratios $Q_{\rm d} = b/a$.

Table 4 lists the corresponding structural parameters for the bulges, for J and K, and for H if available. The $SB_{\rm eff}$ numbers were calculated from the $I_{\rm b}$ values via the photometric calibration. The effective radii $R_{\rm b}$ are given again in arcsec and in kpc, using the distances from Table 1. The last columns give the position angles ${\rm PA}_{\rm b} = \Phi_{\rm b}$, the axis ratios $Q_{\rm b} = b/a$, and the bulge exponent $\beta = 1/n$. From the parameter values of $I_{\rm d},\: R_{\rm d}$, it is very easy to calculate the integrated flux for the disks by integration from the centre to infinity. No external truncation radius was used here. In a similar manner the bulge flux was integrated with the values of $I_{\rm b},\: R_{\rm b},\: \beta$ (see Caon et al. 1993). The total flux is simply the sum of the fluxes of disk and bulge. The bulge-disk ratio is the corresponding quotient. The absolute magnitudes were calculated using the distances from Table 1. Table 5 lists all the photometrical parameters from the disk-bulge fits in JHK.

   
5.1 Comparison of the results in JHK

The structural parameters generally have similar values in the different filters JHK. We consider the ratios $R_{\rm d}(J)/R_{\rm d}(K),~R_{\rm b}(J)/R_{\rm b}(K)$, and $\beta(J)/\beta(K)$. There is no significant trend of the corresponding ratios with the values of $R_{\rm d}$ or $\beta$. Only $R_{\rm b}({J})/R_{\rm b}({K})$ shows an increase to low $R_{\rm b}$ values ( $R_{\rm b} < 7''$) which is probably a consequence of the larger errors due to the limited resolution there.

The ratios of the structural parameters are only very weakly dependent on the Hubble type. There is a weak tendency of the ratios of $R_{\rm b}$ to increase, and of the ratios of $\beta$ to decrease with the Hubble types. However, the gradients of the corresponding regressions are very small. The mean value of the quotients and their rms variations are $R_{\rm d}({J})/R_{\rm d}({K}) = 1.01 \pm 0.19$, $R_{\rm b}({J})/R_{\rm b}({K}) = 1.09 \pm 0.26$, $\beta({J})/\beta({K}) = 1.01 \pm 0.16$. This means that $R_{\rm d}, R_{\rm b},\beta$ are practically identical for J and K, the scatter is consistent with our error estimate in Sect. 4.5.

The value of the color index J-K shows a weak increase with Hubble type We neglect this hardly significant gradient and calculate the mean color indices from our model flux integrations to ${J} - {K} = 0.84 \pm 0.18$ and correspondingly ${J} - {H} = 0.71 \pm 0.19$.

   
5.2 Remarks to individual objects

For some of our sample galaxies there exists a large number of papers. The purpose of this section is not to give a review over the most important results of all this research, but to present those aspects which are relevant for our fit and disk/bulge decomposition. All Hubble types used in this paper were taken from Sandage & Bedke (1994).

1. NGC278 is a face-on multiple-armed Sbc galaxy (T=4). On HST images Phillips et al. (1996) could follow the spiral structure to 2-3 arcsec from the centre. The fits of the surface-brightness (SB) distributions in JHK lead to similar results for the structural parameters (Tables 3 and 4). The residuum shows remnants of the spiral arms and of dust filaments, but looks good concerning the fit quality (Fig. 3). The exact distance determination for NGC278 is a problem, since the small radial velocity is not meaningful for that. We use the mean value of the discordant distance values from Tully (14.74 Mpc) and Bottinelli et al. (32.65 Mpc).

2. NGC628 = M74 is a bright face-on Sc galaxy (T = 5). The distance of NGC628 was individually determined by Sharina et al. (1996) to D = 7.80 Mpc. Our fit results for $R_{\rm d}, R_{\rm b},\beta$ in JHK are similar to each other, however with quite a scatter (Tables 3, 4). The reason is probably the large diameter of the galaxy compared to our field of view ($3\times 3$ arcmin). Nevertheless, the residua of our fit look excellent (Fig. 3). A comparison with the fit results of other authors will be made in the next section.

3. NGC772 = Arp78 is an Sb galaxy with one especially strong spiral arm. Nevertheless the fit of the disk works fairly good and shows very low residua.

4. NGC1023 is one of the few S0 (SB0) galaxies in our sample. It has a very good distance determination (11.11 Mpc) by Ferrarese et al. (2000). The residua show a dipole structure near the centre, probably due to the central nuclear disk (Sil'chenko 1999) which we did not consider in the fit procedure. From our disk-bulge decomposition we obtained a half-light radius of the bulge of 30 to 35'' which is in fairly good agreement with the corresponding bulge radius obtained from stellar velocity dispersion profiles ($\approx$50'', Simien & Prugniel 1997).

5. NGC2196 is a nearly face-on Sa/Sab galaxy. Carollo & Stiavelli (1998) found on HST images the continuation of the R^1/4 density profile of the bulge to less than 1'' radius. We obtained a slope of $\beta = 0.31$ for the whole bulge. The residua of our disk-bulge fit look good. The star near the centre was extracted before the fit.

6. NGC2655 = Arp225 is an Sa galaxy which shows traces of a strong interaction or merger event: faint outer stellar loops, extended HI-envelope (Huchtmeier & Richter 1982). The bulge in NGC2655 is especially large (Table 4). The central dust-structure (Erwin et al. 1996) is probably the reason for the disturbed fit residuum there.

7. NGC2742 is a very regular Sc galaxy of medium inclination. The residuum image (Fig. 3) shows the arms as positive features (white) and the inter-arm regions as negative residuals (black).

8. NGC2775 is an Sa galaxy of low inclination. The nearly perfect residuals show nicely the fine structure of the highly multiple arms (Fig. 3). Corsini et al. (1999) measured the profile of the stellar velocity dispersion of the bulge of NGC2775: their radius of $\approx$50'' coincides well with our value (32'') for the effective radius.

9. NGC2782 = Arp215 is an isolated face-on Sa galaxy showing HI gas plumes extending 5' to the east and 2' to the northwest (Smith 1991), probably formed during a merger event. The eastern plume is associated with a stellar tail of similar size. However, this feature is outside our 3' field of view. The main disk of NGC2782 is fairly undisturbed (Jogee et al. 1998). Our residuum shows some irregularities near the centre, which are probably due to the strong central star-formation region (Boer et al. 1992; Jogee et al. 1998, 1998; Yoshida et al. 1999).

10. NGC2811 is an Sa galaxy of medium inclination. The bulge has a slightly boxy shape which leads to the dipole structure in the residuum.

11. NGC2841 is an Sb galaxy of medium inclination and with regular, flocculent arms. Using the HST Cepheid distances and SN Ia distances Shanks (1997) determined the distance of NGC2841 to 24.9 Mpc. In the central regions there exist a slight rotation of the isophotes' major axis, this is responsible for the double-cone feature in the residuum image (Fig. 4 in on-line version). The reason is probably a weak bar component (Keel 1983; Varela et al. 1996; Afanasiev & Sil'chenko 1999).

12. NGC2855 is an Sa galaxy of low inclination. It is surrounded by faint stellar shells which may be a remnant of an interaction. The filamentary dust arms visible in optical images disappear in the NIR. The residuum looks very good.

13. NGC2964 is an Sc galaxy with strong massive arms. It may form a physical pair with the S0 galaxy NGC2968 at a separation of 6.2' (Sandage & Bedke 1994). However, the spiral pattern is fairly regular.

14. NGC2985 is an Sab spiral with very regular, tight arms. The fit procedure worked very good, the corresponding low residuum is shown in Fig. 4 (in on-line version).

15. NGC3147 is an Sb spiral of low inclination ( $Q_{\rm disk} = 0.84$, ${\rm PA}_{\rm disk} = 150^{\circ}$). The bulge has a similar axis ratio, but appears at a very different position angle ${\rm PA}_{\rm bulge} = 88^{\circ}$. Since it is not plausible that the different orientations of the (projected) major axes of disk and bulge are due to a different plane of symmetry, the bulge must be triaxial. NGC3147 is one of the rare examples with such a feature. Most triaxial bulges seen on visual images are artefacts of dust absorption and disappear in the NIR.

16. NGC3162 is an Sbc spiral of low inclination. One arm is prominent, the other one much weaker. This could be a consequence of an interaction. Nevertheless we obtained a good fit with good residua (Fig. 4 in on-line version).

17. NGC3169 is an Sb spiral of medium inclination, it forms a pair with NGC3166 at 7.7' angular distance. There exist signs of interaction (warps; Sandage & Bedke 1994). The strong dust lane is still visible in the J image, especially in the residuum (Fig. 4 in on-line version).

18. NGC3198 is an Sc spiral of fairly high inclination, showing numerous HII regions (Corradi et al. 1991). In the HST key project the Cepheid distance of NGC3198 was determined to 14.5 Mpc (Kelson et al. 1999).

19. NGC3338 is an Sbc spiral of medium inclination, it has thin and well ordered arms. Correspondingly the fit procedure yielded a very low residuum (Fig. 4 in on-line version).

20. NGC3359 is a nearly face-on SBc spiral with a fairly weak bar and practically no bulge. Thus our disk/bulge fit treats the bar as a bulge of high ellipticity (see the $Q_{\rm b}$ in Table 2) and works still satisfying (Fig. 4). However, the residuum is asymmetric due to the slightly banana-shaped light distribution in the bar.

21. NGC3368 = M96 is an Sab spiral of low inclination. It is the brightest galaxy in a group of galaxies in Leo (e.g. Schneider 1989). Our field of view is a bit too small for this object. Due to a complex substructure and isophote twist in the central region, our fit yields only fairly good residua (may be double bar, see Jungwiert et al. 1997). In the HST key project the Cepheid distance of NGC3368 was determined to 11.2 Mpc (Tanvir et al. 1999; Gibson et al. 2000).

22. NGC3430 is a fairly regular Sbc spiral with thin arms and with medium inclination. The fits yielded excellent residua (Fig. 5 in on-line version).

23. NGC3626 is an Sa spiral of medium inclination. Ciri et al. (1995) found that the gas in this galaxy is counter-rotating to the stars. This is probably the remnant of a merging or accretion event. NGC3626 shows a prominent dust lane (ring) around the central bulge. The fit residuum shows the corresponding substructure there.

24. NGC3675 is an Sb spiral of fairly high inclination. The circular dust near the centre (very good detectable in a ${\rm Pa}_{\alpha}$snapshot image of the HST, Böker et al. 1999) leads to some problems with the fit there; this is visible in the residuum (Fig. 5 in on-line version). Eskridge et al. (2000) classify NGC3675 as strongly barred from their analysis of NIR images in the H filter. We found a bulge component with the same position angle as the disk and somewhat rounder in projection ( $Q_{\rm b} = 0.61$, $Q_{\rm d} = 0.43$), but no signature of a bar.

25. NGC3705 is a regular Sb spiral of medium inclination and with thin outer arms. A bright star $\approx$9'' NW of the centre disturbs the residuum. This star was masked for the fitting procedure.

26. NGC3726 is an Sbc spiral of medium inclination. It has a small weak bar (Martin 1995). Nevertheless the fit was satisfying and lead to good residua (Fig. 5 in on-line version).

27. NGC3810 is an Sc spiral of low inclination. It is characterized by a fairly sudden decrease of surface brightness between inner and outer arms, without a change of position angle. However, the fit did not pose any problems.

28. NGC3898 is an Sa spiral of medium inclination with multiple thin arms. Carollo & Stiavelli (1998) found on HST images the continuation of the R^1/4 density profile of the bulge to less than 1'' radius.

29. NGC4051 is an Sbc spiral of medium inclination. It is a well investigated Seyfert galaxy. The light contribution of the active nuclues was not considered in the fit, a corresponding tiny residuum can be seen in Fig. 5 (in on-line version).

30. NGC4254 = M99 is a face-on Sc grand design spiral in the Virgo cluster. The western m=1 mode arm is not fully covered by our field of view. Since the galaxy does not show any other peculiar features in NIR, the fit procedure lead to good results.

31. NGC4303 = M61 is a face-on Sc spiral in the Virgo cluster. It has a weak bar in NS direction (RC3: Type SAB(rs)) which caused no problems for the disk-bulge fit. However, a star forming ring of $\approx$6'' diameter (Colina et al. 1997; Colina & Arribas 1999) produces a clear corresponding signature in the residuum image (Fig. 6 in on-line version).

32. NGC4414 is a multi-armed flocculent Sc spiral of medium inclination in the Virgo cluster. We obtained good fit residua. In the HST key project the Cepheid distance of NGC4414 was determined to 19.1 Mpc (Turner et al. 1998).

33. NGC4450 a Virgo cluster galaxy, is an Sab spiral of medium inclination with soft spiral arms. The galaxy shows an inner structure with a slight different position angle ( $\Delta {\rm PA} \approx 5^{\circ}$) compared to the disk. This may be interpreted as a lens or bar (Rubin et al. 1997; Eskridge et al. 2000). Nevertheless, our fit lead to good results.

34. NGC4501 = M88 is a prominent Sbc spiral in the Virgo subcluster around NGC4486. On red HST images Carollo et al. (1998) could follow the spiral structure of NGC4501 down to the nucleus. Due to the medium high inclination of this galaxy a reasonable fit with our limited field of view was still possible. The arm structure is very regular; we obtained very good residua.

35. NGC4535 is a large face-on SBc galaxy with two strong arms in the Virgo cluster. Nevertheless, we obtained quite reliable fit results, only the small central bar lead to some problems with the residuum there. In the HST key project the Cepheid distance of NGC4535 was determined to 16.6 Mpc (Macri et al. 1999; Sakai et al. 2000).

36. NGC4725 is an Sb/SBb spiral of medium inclination. The neglect of the small bar in our fit resulted in a corresponding residual feature (Fig. 6). In the HST key project the Cepheid distance of NGC4725 was determined to 13.0 Mpc (Gibson et al. 1999; Sakai et al. 2000).

37. NGC4826 = M64 is an Sab spiral of medium high inclination. The galaxy shows two counter-rotating gas disks (ionized gas and neutral hydrogen) in the outer region, pointing towards an accretion event (e.g. Braun et al. 1994; Rubin 1994). The strong dust lane (bad eye galaxy, e.g. Walterbos et al. 1994) is still visible even in the NIR, leading to some problems with the fit.

38. NGC5248 is an Sbc spiral of medium inclination. The outer arms have very low surface brightness and are outside our field of view. NGC5248 has a central ring of star formation of $\approx$12'' diameter (Storchi-Bergmann et al. 1996). Inside this ring a tiny nuclear spiral was discovered (Laine et al. 1999). These nuclear structures produce a corresponding residuum pattern as result of our disk-bulge fit (Fig. 6 in on-line version).

39. NGC5364 is a very regular Sc spiral of medium inclination. The regular spirals always give excellent fit results and low residua (Fig. 6 in on-line version).

40. NGC5371 is an Sb/SBb spiral of low inclination. The faint bar (e.g. Martin 1995) is no problem for our fit (Fig. 6 in on-line version).

   
5.3 Comparison with previous papers

Although there exist quite a number of papers about disk-bulge decompositions in the literature (see Sect. 1), it is not easy to compare the results. The reasons are that different authors use different detectors/filters, different methods, and different parametrizations of the SB distribution. The choice of a fixed or variable $\beta = 1/n$is also of great importance for the results.

  

Table 6: Disk- and bulge parameters of NGC628 from studies of different authors in different filters

Only for two galaxies of our sample (NGC628 and NGC2841) there exist several studies in the literature measuring the SB distribution in optical or NIR colors.

As an example, we show in Table 6 all available scale lengths for disk and bulge of NGC628, normalized in arcsec. The blue disk scale lengths of the different authors coincide fairly well, apart from the value of Simien & de Vaucouleurs (1986). The differing numbers of Bagget et al. (1998) are due to their different choice of the fit parameters (inner-truncated disk). The red scale length values of Natali et al. (1992) tend to shorter values.

In a recent observational run (Feb. 2000) we used the Calar Alto 2.2 m telescope with a focal reducer (field of view 16', 0.53''/pix) for an UBVRI imaging of NGC628. The structural parameters have been obtained by the methods described in this paper. The large field of view reduces the sky-subtraction problems to a minimum. Our results for $R_{\rm d}, R_{\rm b},\beta$ show the behaviour already described in Möllenhoff et al. (1999): the disk scale length decreases from U to I and JHK. However, there is quite a scatter between the NIR values. The large diameter of NGC628 has the consequence that only minor errors in the sky determination lead to strong variations of the $R_{\rm d}$-values. The reason for the longer scale length in the blue colors is probably that the stars in the outer regions are younger and have lower metalicity (de Jong 1996c). Nevertheless, the residua of our fit look excellent (Fig. 3). The results of Natali et al. (1992) also show the tendency of a decreasing scale length to redder colors, however less marked. The difference to the results of Möllenhoff (2000) may be due to the fact, that Natali et al. truncated the innermost region and considered only a disk fit.

The bulge of NGC628 behaves just vice versa (Table 6): the half-light radius $R_{\rm b}$ increases from blue to red (apart from the not very reliable value in K). The slope decreases as well from blue to red, i.e. in blue colors the bulge is smaller and steeper outsid $R_{\rm b}$. This is probably a population effect as well (Möllenhoff et al. 1999).

  

Table 7: Disk- and bulge parameters of NGC4450 from NIR studies of different authors

Concerning the comparison of whole samples of different authors for better statistics, the data situation is not very satisfying. Only a minority of the different samples have enough galaxies in common. From the old era of photographic plates there exists the big sample of Grosbøl (1985, R POSS plates, disk scale lengths obtained from ellipse fits) which has 29 galaxies in common with ours. The quotient $R_{\rm d} / R_{{\rm d-Grosbol}}$ has a mean value of 0.90 with a scatter of $\pm 0.33$. With Boroson (1981, major- and minor-axis profiles, 1-dim disk-bulge decomposition) we have 7 galaxies in common. The mean values and scatter are $R_{\rm d}/R_{\rm d-Boroson} = 0.85 \pm 0.43$ and $R_{\rm b}/R_{\rm b-Boroson} = 1.30 \pm 0.67$. Although the scatter is quite big, all three quotients reflect the findings that the disk scale lengths are larger in blue colors, the bulge effective radii behave vice versa (de Jong 1996b,c; Möllenhoff et al. 1999). Other studies with photographic plates (e.g. Simien & de Vaucouleurs 1986; Kodaira et al. 1986; Schombert & Bothun 1987) contain only very few galaxies of our sample.

Figure 7: (a-d) Correlation of disk parameters with Hubble types and with other disk parameters. The different colors are marked with different symbols ($\circ = J$, + = H, $\times = K$). In each plot the solid line represents the linear regression through all corresponding points, the dotted lines represent the $1\sigma$-deviations. Neither the disk scale-lengths (a) nor the central SB values (b) show any systematic dependency on the Hubble types. However, there exist fairly strong correlations among the disk parameters themselves: Large disks have a lower central surface brightness (c), and large disks have a higher absolute luminosity in NIR (d)

Figure 8: (a-d) Correlation of bulge parameters, symbols and lines as in Fig. 4. While the bulge effective radii show a weak dependency on Hubble types (a), this is not true for ${\rm SB}_{\rm eff}$, which only shows a big scatter (b). On the other hand, large bulges have a lower ${\rm SB}_{\rm eff}$ (c) and a higher absolute luminosity (d)

Figure 9: (a-d) Correlations of the bulge exponent $\beta = 1/n$, symbols and lines as in Fig. 4. The bulge exponent $\beta = 1/n$ increases with the Hubble types, the late types have profiles which decrease faster in the outer radii (a). The NIR absolute luminosity of the bulges decreases with $\beta$ (b). The central SB of the bulges shows a strong anti-correlation with $\beta$ (c). The small bulges have larger $\beta$ values (d)

Figure 10: (a-d) The correlations between disk- and bulge-parameters are only fairly weak (symbols and lines as in Fig. 4). The bulge-disk ratio decreases with Hubble type (a) as well as with $\beta$ (b). The effective SB of the bulges correlates with the central SB of the disks, however with a big scatter (c). There exists a weak correlation between bulge- and disk-radii (d)

Figure 11: (a-d) Distribution of the absolute luminosities over Hubble types (symbols and lines as in Fig. 4). Total B luminosties over the Hubble types (a). The NIR absolute total luminosities of the sample galaxies decrease with Hubble types (b). While the NIR absolute luminosities of the disks only show a fairly big scatter (c), the absolute luminosities of the bulges correlate strongly with Hubble types: late spirals have fainter bulges (d)

Baggett et al. (1998) present the results of a 1-dim profile decomposition of a large sample of galaxies, based on digitized photographic plates (Kodaira et al. 1990). They use a combination of a de Vaucouleurs law for the bulge and an inner-truncated exponential disk (Kormendy 1977a). We have 31 galaxies in common with Baggett et al. The results show quite a scatter ( $R_{\rm d}/R_{\rm d-Baggett} = 1.20 \pm 0.59$ and $R_{\rm b}/R_{\rm b-Baggett} = 1.31 \pm 1.87$) which is probably a consequence of the different choice of fit parameters.

The more modern CCD studies should generally be of better quality due to the better photometric calibration of the CCD detectors. However, we oftenly face again the problem of disjunct samples (e.g. Kent 1985; Prieto et al. 1992; Courteau 1996; Pompei & Natali 1997; Lu 1998). Héraudau & Simien (1996) presented CCD photometry in V and I of 234 spiral galaxies. We have 17 object in common with them. However, they determined the effective or half-light radii for the whole galaxies, without separation of disks and bulges. For a comparison we calculate the effective radii of our disks (J filter) according to $R_{\rm eff} = R_{\rm d}*1.6716$ (see Eq. (6)) and compare them with the $R_{\rm eff}$-values of Héraudau & Simien (I filter). The quotient $R_{\rm eff} / R_{\rm eff-HS}$ has a mean value of $1.11 \pm 0.55$. Here the influence of strong bulge contributions disturbs the comparison. If we restrict ourselves to those galaxies with bulge/disk-ratios < 0.3 (10 objects in common) we obtain $0.91 \pm 0.23$ for the mean quotient of the effective radii, i.e. a better agreement.

There exist not yet many NIR studies on disk-bulge decompositions. With de Jong (1996a,b,c) we have only two galaxies in common (NGC3162 and 4450), with Moriondo et al. (1998) four galaxies (NGC2775, 2841, 3898, 4450). Table 7 displays all NIR results for NGC4450. While the disk scale-lengths $R_{\rm d}$ are fairly similar, the bulge half-light radii $R_{\rm b}$ are quite different. They are very sensitive on the choice of the slope $\beta$. If one compares the models with similar $\beta$, the coincidence is more satisfying. This is also valid for the comparison of our model parameters of NGC2775 and NGC3898 with those of Moriondo et al. (not shown here).

Andredakis et al. (1995) studied the SB profiles for a K-band sample of 30 spirals of fairly high inclination. They used a different fit method, where a 1-dim cut is swept azimuthally by $360^{\circ}$ over the galaxy. They found that a variable $\beta = 1/n$ is advantageous for bulge fits. This was also supported by Seigar & James (1998), who studied of 45 spirals in J, K with 1-dim disk-bulge fits. Khosroshahi et al. (2000a,b) used the K sample of Andredakis et al. to fit 2-dim SB functions with a variable $\beta = 1/n$. Héraudau et al. (1996) obtained NIR images of 31 southern spirals and made a disk-bulge decomposition of 6 objects, together with kinematical models (Héraudau & Simien 1997). All these papers have no galaxies in common with our sample, but it is interesting to compare these results with ours statistically.