6. Fitting of surface brightness profiles

   

Table 6: Derived photometric parameters

Ident.	$\mu_0^B$	hB	$\mu_0^{B1}$	hB1	$\mu_0^V$	hV	$\mu_0^{V1}$	hV1	$\mu_0^I$	hI	$\mu_0^{I1}$	hI1
		('')		('')		('')		('')		('')		('')
UGC 3755	21.64	12.62			21.25	14.04			20.44	14.51
NGC 2366	22.65	59.75			22.20	59.61			21.42	56.72
UGC 3974	24.52	62.91	23.81	15.22	24.52	79.36	23.32	20.61	22.40	28.03
UGC 4459	24.08	28.69			23.63	28.18
Holmberg I	22.95	33.43			22.72	36.31			22.01	32.65
UGC 5288	21.54	9.16			20.92	8.84			20.12	9.39
Holmberg IX	24.85	49.45	23.45	11.35	24.08	36.75	23.20	8.14	24.18	90.66	23.34	14.46
UGC 5423	21.81	11.91			21.33	12.37			20.90	13.33
UGC 5692	22.47	23.00			21.88	27.58			20.85	31.45
UGC 5918	24.00	27.66			23.48	24.45			22.74	26.74
UGC 6817	23.19	31.06			22.87	32.25			22.41	44.14
NGC 4068	21.84	22.22			21.36	21.91			20.11	19.15
NGC 4144	22.72	42.60	21.08	13.42	22.38	45.95	20.47	13.80	21.52	45.88	19.56	14.07
NGC 4163	21.37	13.91			21.02	15.42			20.21	15.80
P38998	21.50	6.67			20.94	6.50			20.22	6.66
UGC 7298	22.33	7.68			21.95	7.51			20.76	6.25
UGC 7321	24.01	39.85	22.33	8.14	23.32	37.78	21.67	8.35	21.96	29.90	20.50	6.99
IC 3308	21.86	7.11			21.44	7.09			20.65	7.07
UGC 7577	22.74	36.82			22.26	38.00			21.48	42.48
NGC 4449	19.46	29.51	17.72	2.05	19.09	29.79	17.12	1.66	18.39	30.99	16.21	1.41
UGC 7698	23.99	55.42			23.38	46.01			22.65	44.21
IC 3687	22.74	25.05			22.29	24.74			21.59	22.35
IC 4182	21.22	35.51			21.02	38.31			20.33	42.76
UGC 8201	22.28	26.82			22.04	28.09			21.57	31.19
UGC 8308	23.26	16.59			23.26	25.94			22.71	26.75
UGC 8320	22.36	30.17			22.13	32.72			21.39	30.51
UGC 8331	22.59	16.02			22.17	15.70			21.46	14.69
UGC 8508	22.05	15.86			21.67	16.54			20.84	16.35
NGC 5229	22.08	13.61			21.39	12.65			20.27	10.93
Holmberg IV	22.82	25.74			22.37	25.72			21.61	24.06
NGC 5474	22.64	50.53			22.03	45.81			21.09	40.86
NGC 6503	20.05	24.32			19.35	22.57			18.19	22.16
NGC 6946	22.15	142.08	26.10	63.19	21.10	125.55	24.00	41.00	19.41	113.12	22.18	59.82

Figure 5: The model central surface brightnesses (left) and logarithm of the scale lengths (right) in B band versus the absolute B-magnitudes. The filled squares are the measured galaxies, the squares are the galaxies from the article of Vennik et al. (1996), the crosses (+) are the spiral galaxies from the work of Binggeli & Cameron (1993), and the crosses ($\times$) are the spiral galaxies from the work of van der Kruit (1987)

It is well known that surface brightness profiles of dwarf galaxies (both irregular and spheroidal) and also disks of spiral galaxies can be fitted by an exponential intensity law of brightness distribution (de Vaucouleurs 1959)

$$I(r) = I_0*{\rm exp}(-r/h)$$

or, in magnitudes per sq s

$$\mu(r) = \mu_0+1.086*(r/h),$$

where $\mu_0$ is the central surface brightness and h is the exponential scale length. Most of the measured galaxies are well-fitted by an exponential law in the whole profile or in its outer parts. Some galaxy profiles show a prominent surface brightness central peak, which may be formed by the star formation regions near the center of the galaxy. The best result for these cases is given by decomposition of the profiles into contributions from the two exponential components.

Profile parameters estimation for UGC 4459 in I band has not been made because there is not any significant part of the profile which followed to exponential law of brightness distribution.

Finally, one galaxy of our sample, namely the late type spiral NGC 6946, is well decomposed into bulge and exponential disk components. Among the most commonly used bulge fitting functions is the "r^1/4 law'' proposed by de Vaucouleurs (1948). This is written as

$$I(r)/I_{\rm e} = 10^{-3.33*((r/r_{\rm e})^{1/4}-1)}$$

or, in magnitudes per sq s

$$\mu(r) = \mu_{\rm e}+8.33*((r/r_{\rm e})^{1/4}-1),$$

where $r_{\rm e}$ is the effective radius that contains half of the total luminosity, and $\mu_{\rm e}$ is the effective surface brightness at this radius.

The exponential fits to the surface brightness profiles were done by a least-squares fitting procedure. Decomposition of profiles into two components was performed using the algorithm by Kormendy (1977). The rms deviation of the derived model profiles from the original ones does not exceed 0.02 mag.

The results of the fitting are presented in Table 6. The columns of the table are:

Column 1: galaxy name.

Columns 2 and 3: best-fitting parameters of the exponential disk in B filter (the central surface brightness $\mu_0$ (mag/sq s) and exponential scale length h (arcsec)).

Columns 4 and 5: best-fitting parameters of the second exponential disk in B filter, or, for NGC 6946 are best-fitting bulge parameters (effective surface brightness $\mu_{\rm e}$ (mag/sq s) and effective radius $r_{\rm e}$ (arcsec)).

Columns 6, 7, 8 and 9: same as 2, 3, 4 and 5, but in V filter.

Columns 10, 11, 12 and 13: same as 2, 3, 4 and 5, but in I filter.

The central surface brightnesses in the table are not corrected for galactic absorption.

In Fig. 5 the absolute B-magnitudes for the measured galaxies are shown versus the model central surface brightnesses ( $\mu_0^{\rm c}$) in B band (left) and scale lengths in kpc (right). All the magnitudes are corrected for galactic absorption. For comparison, these distributions for spiral galaxies studied by Binggeli & Cameron (1993) and van der Kruit (1987), and also for dwarf and low surface brightness galaxies (LSB) from Vennik et al. (1996) are given in the figure. As seen from Fig. 5 the absolute B-magnitudes of the studied galaxies span over a wide range from $-12^{\rm m}$to $-20.5^{\rm m}$ and the exponential disk central surface brightnesses are distributed mostly in the range from 21 to 24.5 mag/sq s, except some bright spiral galaxies, the central surface brightnesses of which are higher. The mean value of the central SB in B band is about 22.4 $\pm$ 0.8 for the measured galaxies (and the mean value in V band is about 22.1 $\pm$ 0.9 and in I band is about 21.3 $\pm$ 0.9). Near the same area is occupied in the figure by the nearby dwarf galaxies studied in the paper by Vennik et al. (1996). Some distant LSB galaxies from this work have higher absolute B-magnitudes and lower central surface brightnesses. The plotted spiral galaxies are on average of higher absolute magnitudes and also of higher central SB. Note that absolute magnitudes are only slightly correlated with central surface brightnesses for the galaxies plotted in the Fig. 5. On the contrary, the disk scale lengths in B band are closely correlated with absolute B-magnitudes. The scale lengths are distributed over a wide range, $-0.7 <\log h <+0.7$ and the area of nearby dwarf galaxies and the area of bright spiral (and LSB) galaxies are well-separated in the figure. The mean scale length value for the measured nearby dwarf galaxies is about 0.68 $\pm$ 0.40 kpc in B band.