3 Data analysis

   
3.1 Surface photometry

Surface photometry was performed with the ellipse task within the IRAF STSDAS. ISOPHOTE package. The ellipse task matches elliptical isophotes to galaxy light intensity. The technique employed is described in Jedrzejewski (1987). It consists on an iterative method that fits ellipses to the intensity of the images at a given semi-major axis. Once the isophote is fitted, the semi-major axis is changed (increased or decreased). This task was run interactively always starting from the same semi-major axis (the one corresponding to 3 arcsec to avoid the part of the galaxy profile dominated by seeing). First, we proceeded outwards until we reached twice the Kron radius (Kron 1980) and then inwards. Intensities were converted into surface brightnesses and plotted against the semi-major axes of the isophotes. No correction for inclination (i) was attempted before fitting the profiles due to the great variety of uncertainties that the determination of i involves. These surface brightness profiles, together with the bulge-disk adjustments explained in the Sect. 3.2, are available via anonymous ftp at the site 147.96.22.14.

Along with the surface brightness profiles, the method mentioned above also provides the ellipticity $\epsilon$ and position angle PA of each isophote. For each image, mean $\epsilon$ and PA were calculated with the values of the isophotes between 23 and 24 magarcsec^-2 and are listed in Table 2. Since the outer isophotes of many of our galaxies were distorted by different structures, such as bars, rings, spiral arms, bright HII regions, some of these averages were corrupted, so a visual inspection of each image was carried out in order to exclude from the averaging the distorted zones and get more indicative values.

   
3.2 Bulge-disk decomposition. The method

Traditionally, galaxy light distributions have been studied through the decomposition in distinct components (Kent 1985; de Jong 1996b; Vitores et al. 1996a; Baggett et al. 1998; among others). Most methods are based on the assumption of specific functions. Ideally, these functions should have a physical background, being connected with the formation and evolution of galaxies. Unfortunately this is a very hard task so authors commonly use empirically derived functions.

Light distributions of spiral galaxies are commonly modeled using two components: a central concentration of luminosity (the bulge) and an outer plane structure (the disk). This simple scheme can be far from the real component mixture of the galaxy. Features such as bars, rings or bright starbursts affect dramatically the light distribution and make bulge-disk decomposition a nearly impossible task. These features are supposed to be more frequent in late Hubble type galaxies and extremely relevant in starburst galaxies, becoming dominant at high-redshifts.

Bulge-disk decomposition can be undertaken using several techniques and fitting functions. Several authors are now using the entire galaxy image to perform two dimensional fittings of the flux (see, e.g., de Jong 1996b); this technique is better for galaxies with peculiar structures such as bars or rings, which are masqueraded in the azimuthally averaged plots.

We have carried out the morphology study of the sample using one-dimensional surface brightness profiles. These profiles were checked visually in order to exclude from the fitting algorithm those regions dominated by artifacts, which are revealed through bumps and dips in the radial profiles. Besides, the algorithm only utilizes the points with $\mu$ lower than the detection threshold, which was measured as the surface brightness corresponding to the standard deviation of the sky; the values of this threshold ranged from 24 to 26 magarcsec^-2, depending on the observation campaign. Some of the galaxies showed very irregular morphologies and extremely perturbed profiles due to interaction companions or starbursts; consequently, these galaxies were excluded from this bulge-disk study.

A great variety of fitting functions are available in the literature. Some authors adjust exponential laws to both bulge and disk or other more complicated functions. We have attempted the decompositions using the empirical bulge law established by de Vaucouleurs (1948):

$$\mu=\mu_{\rm e}+8.33\times \left( \left( \frac{r}{r_{\rm e}} \right)^{1/4} - 1 \right)$$ (1)

and the classical exponential law for the disk (Freeman 1970):

$$\mu=\mu_0+1.09\times \left( \frac{r}{d_{\rm L}} \right)$$ (2)

where $\mu$ stands for the surface brightness, r for the radius, $r_{\rm e}$ for the bulge effective radius (that containing inside half of the total light of the bulge component), $\mu_{\rm e}$ the bulge effective surface brightness, $d_{\rm L}$ and $\mu_0$ the disk scale length and central surface brightness. The choice of the classical r^1/4 and exponential fitting functions allows us to compare our results with the Gunn r study and with most of the data found in the literature.

During the performance of bulge-disk decomposition, special care should be taken when dealing with the inner parts of the galaxy profile, since these zones are affected by atmospheric seeing. Most authors exclude from the fit the part of the galaxy dominated by seeing (e.g., Baggett et al. 1998; Schombert & Bothun 1987; Chatzichristou 1999). To account for this effect, we used in the fitting procedure a seeing-convolved formula for the light profile in the inner parts of the galaxy (Pritchet & Kline 1981). This procedure copes with the uncomfortable r^1/4 bulge law, that tends to infinity as r approaches 0. Assuming radial symmetry and a Gaussian description of the PSF, the seeing convolved profile can be expressed as:

 

$$I_{\rm c}(r)=\sigma^{-2}{\rm e}^{-r^2/2\sigma^2}\int_{0}^{\infty}I(x)\,I_0(xr/\sigma^2)\,{\rm e}^{-x^2/2\sigma^2}x\,{\rm d}x$$ (3)

where $I_{\rm c}(r)$ is the seeing-convolved intensity, $\sigma$ the dispersion of the seeing Gaussian PSF, I(x) the sum of the bulge and disk intensities and I₀ the zero-order modified Bessel function of the first kind. Seeing dispersions were measured on several field stars for each image; the averaged seeing value was $1\hbox{$.\!\!^{\prime\prime}$ }5\pm0\hbox{$.\!\!^{\prime\prime}$ }4$, ranging from $0\hbox{$.\!\!^{\prime\prime}$ }9$ to $2\hbox{$.\!\!^{\prime\prime}$ }0$.

The main problem involved with seeing is the determination of the seeing-dominated zone of the profile, where Eq. (3) has to be used. This parameter was set free until a best fit was achieved.

The decomposition procedure followed to obtain the bulge and disk parameters is the following:

• All the fitting subroutines need a first guess for the bulge and disk parameters $\mu_{\rm e}$, $r_{\rm e}$, $\mu_0$ and $d_{\rm L}$. To calculate them we separated the bulge and disk dominated regions; the first one should be located in the centroid of the galaxy (with the most central zones dominated by seeing) and should be linear in a surface brightness versus r^1/4 plot; the zone dominated by the disk must be in the outer parts of the galaxy and should be linear in a $\mu$ versus r plot. This decomposition provided a first estimate for the bulge and disk parameters;
• The next step is to fit the two components simultaneously. This was done using a $\chi^2$ minimization performed with the simplex method. Before this minimization, we proved several solutions in the parameter space around the data acquired in the first step in order to avoid local minima of the $\chi^2$ function. The simplex algorithm needs five sets of initial parameters that were built with the best of the previous values, varying them randomly;
• One final step was performed in order to calculate the best set of fitting parameters and their corresponding errors. Each data value in the surface brightness profile was varied randomly according to a Gaussian distribution; the sigma of this Gaussian was the standard deviation of the point calculated with the ellipse task. Each new profile was refitted using the simplex method. This process was repeated 1000 times. Then those fits with values of the function $\chi^2$ between the lowest value $\chi^2_{\rm min}$ and 3 times $\chi^2_{\rm min}$, were selected from the 1000 iterations. The final set of parameters were the averaged values of the latest and the errors corresponded to the standard deviations of these fits.

Equal weights were used for all the points during the fits. The outermost points of the profiles have larger errors due to the uncertainties in the determination of the sky, artifacts, etc. This should lead to assign greater weights to the innermost points, as some authors do in the literature (Baggett et al. 1998; Chatzichristou 1999; Hunt et al. 1999). However, in our profiles there were more points in the inner parts of the plots than in the outer ones; when weights were introduced in the fitting algorithm, wrong estimates of the parameters (the bulge parameters are the most affected ones) occurred; therefore, the equi-weighting scheme was chosen.

The method described above was tested in several artificial galaxies. They were built with known and representative bulge and disk parameters. We chose typical profiles for this test, including: (a) those with well-defined bulge and disk, (b) with a dominant disk, (c) with a dominant bulge, (d) a nearly linear profile (fitted with a disk by our method) and (e) a curved profile (identified as a bulge by our method). The artificial profiles were convolved with a common seeing value of $1\hbox{$.\!\!^{\prime\prime}$ }5$; the zone where this convolution was made was set randomly inside the typical interval of the true fits. Standard values of noise were added to the profile, based on real data. In Table 1 some of the input and output bulge and disk parameters are shown. The initial parameters seem to be well recovered by our technique; the largest differences correspond to profiles where the disk dominates although there is some contribution of a bulge component (test number 2, corresponding to a late-type spiral); these profiles were identified as an isolate disk by our method. Discrepancies were also present when one of the components is dominant (examples number 4 or 7, corresponding to a late-type spiral and an early-type galaxy, respectively); in this case, the parameters of the other component do not contribute much to the total profile and our method of decomposition does not recover the initial values (the errors of the B/D ratio are specially affected and are not shown in the result table - they are substituted by three dots -), although this fact is irrelevant. We took special care with these types of profile during morphological classification based on bulge-disk decomposition.

 

 

Table 1: Bulge-disk decomposition test data

Profile type	$\quad \mu_{\rm e}$	$\quad r_{\rm e}$	$\quad \mu_0$	$\quad d_{\rm L}$	$\quad B/D$
(1)	(2)	(3)	(4)	(5)	(6)
a	19.50	0.90	21.60	5.50	0.67
	$19.47\pm 0.77$	$0.88\pm 0.58$	$21.53\pm 0.81$	$5.30\pm 0.93$	$0.66\pm 0.36$
b	26.00	13.80	21.50	4.60	0.51
	$25.34\pm 0.23$	$5.95\pm 4.17$	$21.32\pm 0.41$	$4.54\pm 1.42$	$0.15\pm 0.33$
c	23.30	5.30	21.80	6.90	0.54
	$23.30\pm 0.34$	$5.31\pm 1.82$	$21.84\pm 0.62$	$7.10\pm 3.30$	$0.52\pm 0.27$
d	31.20	4.60	18.70	1.30	0.00
	$26.76\pm 0.04$	$1.60\pm 0.99$	$18.71\pm 0.01$	$1.30\pm 0.02$	$0.00\pm 0.01$
d	24.10	4.40	19.20	2.40	0.13
	$23.30\pm 0.48$	$2.06\pm 0.83$	$19.16\pm 0.04$	$2.42\pm 0.04$	$0.05\pm 0.02$
e	20.80	3.40	21.60	6.80	1.88
	$20.80\pm 0.13$	$3.40\pm 0.39$	$21.62\pm 0.74$	$6.94\pm 2.81$	1.84$\pm$0.51
e	21.50	3.50	22.90	4.90	6.68
	$21.55\pm 0.16$	$3.60\pm 0.48$	$23.13\pm 4.90$	$5.22\pm 1.17$	$7.35\pm\ldots$

Results for the test of the bulge-disk decomposition procedure on seven artificial galaxies. Input parameters are in the first row and output results and their corresponding errors in the second one. Columns: (1) Profile type as explained in the text. (2) Effective surface brightness of the bulge in magarcsec-2. (3) Effective radius of the bulge in arcsec. (4) Typical surface brightness of the disk in magarcsec-2. (5) Exponential scale of the disk in arcsec. (6) Bulge-to-disk ratio.

One of the main problems during profile fitting is the fact that the hypersurface in the four parameters space ( $\mu_{\rm e},~r_{\rm e},~\mu_0,~d_{\rm L}$) has many local minima. The minimization method must be able to determine the real absolute minimum, whose parameters must have physical meaning. To achieve this, all the initial parameters were varied randomly before attempting the fit; we also used several fractional convergence tolerances in each individual fit and boundaries on each parameter were taken in order to avoid solutions with no physical meaning.

With the four parameters of the disk-bulge decomposition, the bulge-to-disk luminosity ratio was calculated as follows:

$$\frac{B}{D}=\frac{L_B}{L_D}=3.607 \left ( \frac{r_{\rm e}}{d_{\rm L}}\right )^{2} 10^{(-0.4(\mu_{\rm e}-\mu_0))}.$$ (4)

All the data referring to bulge-disk decomposition, along with mean ellipticities and position angles calculated as explained in Sect. 3.1, are shown in Table 2. Some galaxies were unsuitable to perform bulge-disk decomposition due to very perturbed profiles or bad-quality of the images. These galaxies have no data of the bulge and disk parameters. Other galaxies were fitted with only one component; bulge-to-disk ratios for these objects have very large errors and no physical meaning so they are not shown in Table 2. Position angles were only measured in those galaxies with ellipticities greater than 0.05 (for rounder isophotes, estimation of the PA is meaningless); two galaxies with $\epsilon=0.06$, but very large error values, have not PA measurement, either.

  

Table 2: Bulge and disk parameters, bulge-to-disk ratio, ellipticity and position angle of the UCM Survey galaxies

 

Table 2: continued

 

Table 2: continued

 

Table 2: continued

(1) UCM name. (2) Effective surface brightness of the bulge in magarcsec^-2. (3) Scale of the bulge in arcsec. (4) Characteristic surface brightness of the disk in magarcsec^-2. (5) Exponential disk scale in arcsec. (6) Bulge-to-disk ratio. (7) Ellipticity of the galaxy calculated as an average of the ellipticities of the isophotes between 23 and 24 magarcsec^-2. (8) Position angle in degrees measured counterclockwise from the North axis and calculated as an average of the previously detailed isophotes.

3.3 Light concentration indices

In order to characterize galaxies morphologically, we need a measure of the degree of concentration of light towards the central or the outermost regions of the object. Traditionally, this has been performed through the calculation of the bulge-to-disk ratio B/D mentioned in the previous section. The methodology and degree of fidelity of the bulge-disk decomposition are trustful just for galaxy profiles where only these two components are present and no special features are found (Schombert & Bothun 1987). As was already mentioned, some of our galaxies are dominated by bright features (mainly bars, spiral arms and bright starbursts) and it seems better to improve their morphological classification using concentration indices not based in previous component fits.

We have calculated for the whole sample three concentration indices in the same way that Vitores et al. (1996a) did for the Gunn r bandpass:

• c₃₁, defined by de Vaucouleurs (1977) as the ratio between the radius containing 75% of the light of the galaxy (r₇₅) and the radius with 25% of the galaxy luminosity (r₂₅):
  

  $$c_{31}={r_{75} \over r_{25}}\cdot$$ (5)

  
  
  The calculation was performed integrating the flux of the galaxy in contiguous isophotes until 25 and 75% of the total flux were reached. The radii used in Eq. (5) are equivalent radii, calculated as the square root of the product of the semi-major and semi-minor axes. This index was found to correlate well with morphological type, decreasing from early to late-type galaxies (Gavazzi et al. 1990);
• c₄₂, defined by Kent (1985) as:
  

  $$c_{42}=5\,{{\rm log}\left ( r_{80} \over r_{20} \right )}$$ (6)

  
  
  where r₈₀ and r₂₀ are the equivalent radii containing 80 and 20% of the total flux of the galaxy, respectively. These radii were calculated as the ones for c₃₁;
• $c_{\rm in}(\alpha)$, as defined in Doi et al. (1993):
  

  $$c_{\rm in}(\alpha)=\frac{\int_{0}^{\alpha r(\mu_{\rm L})}r\,I(r){\rm d}r}{\int_{0}^{ r(\mu_{\rm L})}r\,I(r){\rm d}r}$$ (7)

  
  

  where $\mu_{\rm L}$ is the detection threshold (set to 24.5 magarcsec^-2, mean value in our images) and $\alpha$ a parameter $0<\alpha<1$, appropriately chosen (it was set to 0.3, optimal value as described in Doi et al. 1993).

Mean surface brightnesses, radii (calculated as the semi-major axis of the isophote) and magnitudes inside the 24.5 magarcsec^-2 isophote, effective radii (see Paper I) and mean surface brightnesses inside the effective isophote have also been calculated.

All these parameters are listed in Table 3. It was not possible to obtain reliable parameters for two objects, since their images were of very bad quality.

3.4 Asymmetry parameter

An asymmetry parameter A was computed for each galaxy according to the definition established by Abraham et al. (1996). Each image was first smoothed with a Gaussian kernel of $\sigma=1$ pixel. After smoothing, it was rotated 180${\rm ^o}$ around the center of the object (this center was determined as the average of the inner isophotes of the galaxy). Finally, the rotated image was subtracted from the original. The parameter A was calculated as:

$$A=\frac{\Sigma \vert(I_0-I_{180})\vert}{2\Sigma \vert I_0\vert}$$ (8)

where the sum runs over all the pixels, I₀ is the intensity of the original smoothed image and I₁₈₀ the intensity of the rotated one. Since the absolute value of the flux of the self-subtracted image is used, the uncertainty in the sky value adds a positive A signal. This effect was corrected calculating the parameter A for a region of the sky of the same size of the galaxy aperture and then subtracting it from the one calculated for the galaxy. This coefficient is shown in Table 3.

  

Table 3: Luminosity parameters for the UCM galaxies

 

Table 3: continued

 

Table 3: continued

 

Table 3: continued

(1) UCM name. (2) c₃₁ index as defined by de Vaucouleurs (1977). Mean error is $\sim$1%. (3) c₄₂ index calculated after Kent (1985). Mean error is $\sim$2%. (4) $c_{\rm in}$ as defined by Doi et al. (1993). Mean error is $\sim$6%. (5) Johnson B magnitude measured inside the 24.5 magarcsec^-2isophote. Mean error is 0.06$^{\rm m}$. (6) Radius of the 24.5 magarcsec^-2 isophote in kpc. Mean error is $\sim$11%. (7) Mean surface brightness inside the 24.5 magarcsec^-2isophote. Mean error is $\sim$ 0.06$^{\rm m}$. (8) Mean effective surface brightness. Mean error is $\sim$0.02$^{\rm m}$. (9) Asymmetry coefficient calculated as in Abraham et al. (1996). Mean error is $\sim$2%.