3 Analysis

3.1 Ellipse fitting

The main reason for the variations in shape of early-type galaxies is their inclination, but some cases cannot be accounted for by inclination effects and are an indication of intrinsic features, such as triaxiality (Bertola 1981) or gravitational interactions (Binney & Petrou 1985). In order to detect and quantify these effects, we have fitted ellipses to the J, H and $K_{\rm s}$ isophotes, using the task ELLIPSE in the STSDAS package for IRAF. We determine the position angle (PA) of the isophotes, their ellipticity ($\epsilon$), the Fourier amplitudes of the deviation from perfect ellipses (cos 4$\theta$ term, B4), as well as the brightness distribution along the isophotes. The behavior of the position angle is related to the shape of the galaxy. A spheroidal galaxy, independent of its inclination, keeps the direction of the semimajor isophotal axis constant; on the contrary, if the galaxy is triaxial, the position angle can rotate (Mihalas & Binney 1981). Interaction among galaxies can also cause isophotal twisting (Bender & Möllenhoff 1987). The presence of dust in the galaxy is related to the behavior of the ellipticity for different wavelengths, and also to the A3, B3 Fourier coefficients: non-zero values are frequently found in regions of strong extinction (Peletier et al. 1990). The B4 Fourier coefficient measures the deviation of the isophote in relation to a perfect ellipse. Positive values imply disky isophotes, while negative values correspond to boxy isophotes. There is evidence that these deviations from elliptical shapes are associated with different physical structures: disky isophotes reflect an intrinsic disk structure, while boxy ones are seen in massive galaxies, possibly indicating interaction phenomena (Kormendy & Djorgovski 1989).

Figure 1: Isophotal parameters. The vertical line in each graphic represents the region affected by the seeing.

Figure 1: continued.

Figure 1: continued.

Figure 1: continued.

Figure 1: continued.

Figure 1: continued.

The ellipticity, position angle and A3, B3, A4, B4 coefficients as a function of semimajor axis for all galaxies are shown in Fig. 1. The main characteristics of the objects are:

IC 5105: The ellipticity of this galaxy grows from the center up to $\sim$0.3; the position angle of semimajor axis is constant for J and H, showing a fluctuation of $\sim$15$^\circ$ in $K_{\rm s}$. It presents slightly boxy isophotes, especially around 10 $^{\prime\prime}$ ( ${\rm B}4\sim-0.005$).

NGC 596: Presents approximately circular isophotes ( $\epsilon\sim 0.1$), for all radii. The position angle of the external isophotes varies about 40$^\circ$ in relation to the central region.

NGC 636: The ellipticity increases up to $\sim$0.2 in J and $K_{\rm s}$, being slightly higher for $K_{\rm s}$ in the internal regions. The position angle twists more than 30$^\circ$ in J and almost 90$^\circ$ in $K_{\rm s}$. This galaxy shows slightly disky external isophotes ( ${\rm B}4\sim 0.01$).

NGC 720: The ellipticity shows a small amount of growth with radius (from 0.2 to 0.5); its position angle is almost constant, and it shows disky isophotes in the inner ($\sim$10 $^{\prime\prime}$), becoming boxy at the periphery.

NGC 1400: It has low ellipticity isophotes ( $\epsilon\sim 0.1$) through the entire semimajor axis, and the position angle presents low variation.

NGC 1453: The ellipticity of this galaxy grows from about 0.1 to 0.2 from the center. The position angle is nearly constant, increasing by $\sim$10$^\circ$ in the external regions, especially in H and $K_{\bf s}$.

NGC 1600: It shows ellipticity of  0.2. The position angle is nearly constant, and the isophotes are boxy from 6 $^{\prime\prime}$ outward.

NGC 7192: This galaxy presents nearly circular isophotes, which results in the irregular behavior of the position angle values shown in the figure.

NGC 7562: Monotonically increasing ellipticity (0.1 to 0.3) throughout the semimajor axis. The position angle is nearly constant.

NGC 7619: Its ellipticity in the central region is 0.1, reaches a maximum of 0.25 and decreases in the outer regions. The position angle varies slight and monotonically through the radius, and the isophotes are nearly disky.

NGC 7626: Isophotes have low eccentricity ($\sim$0.1). It shows a variation in the position angle ($\sim$50$^\circ$). In general, its isophotes are disky ( $B4\sim 0.01$).

NGC 7796: Ellipticity and position angle are nearly constant; its isophotes tend to be boxy.

3.2 Luminosity profiles

Figure 2: Brightness and color profiles for the galaxies of our sample. The dashed line in each diagram refers to the effective radius in J band. Dotted curves represented with brightness profiles refer to the difference $\Delta \mu$ between profiles and fittings, expanded to a 0.25 mag scale, as indicated to the right of the profiles. The central region of the profile equivalent to the size of the seeing was not plotted. We did not apply deconvolution in these profiles, for the gain in information would not be significant.

Figure 2: continued.

Figure 2: continued.

With the data obtained with the ELLIPSE routine, we built J, H and $K_{\rm s}$ elliptically averaged brightness profiles along the semimajor axis of the galaxy. In order to find the function that best describes the brightness distribution of the galaxy, we use de Vaucouleurs' (r^1/4) law, as a first approximation. In terms of surface brightness this law has the following analytical expression:

$$\mu(R)=\mu_{\rm e}+8.325\left[\left(\frac{R}{R_{\rm e}}\right)^{\frac{1}{4}}-1\right],$$ (2)

where $R_{\rm e}$ (effective radius) is the radius containing one half of the luminosity of the galaxy, and $\mu_{\rm e}$ (effective brightness) is the superficial brightness at $R=R_{\rm e}$. There have been several studies on the "universality'' of the r^1/4 law, and especially on the insertion of one free parameter in this law - a shape parameter. This is made in Sérsic's law (Caon et al. 1993; D'Onofrio et al. 1994), which has the form:

$$\mu(R)=\mu_{\rm e}+2.5b_n\left[\left(\frac{R}{R_{\rm e}}\right)^{\frac{1}{n}}-1\right].$$ (3)

where b_n=0.868n-0.142, so that $\mu_{\rm e}$ and $R_{\rm e}$ keep the same physical meaning as in the de Vaucouleurs law. Having one more free parameter, Sérsic's law naturally should be more successful in fitting observed profiles of early-type galaxies (Saraiva et al. 1999). For a sample of early-type galaxies, Caon et al. (1993) analyzed the physical meaning of the parameter n in the B band, and found that n correlates with the effective radius, in the sense that galaxies with higher n values tend to have higher effective radii. This is an indication that the shape parameter in Sérsic's law has a real physical meaning. Thus, for those profiles that did not fit the de Vaucouleurs law, we applied Sérsic's law. Note that we do not apply Sérsic's law in all profiles, because Sérsic's law is more sensible to the observational errors in the outer regions, and could introduce false structural parameters.

   

Table 2: Fitting parameters of brightness profiles. Objects with the symbol (*) have fittings of comparatively minor quality. Galaxies separated by a line at the end of table were fitted with Sérsic's law.

Galaxy	Band	$\mu_{\rm e}$(mag arcsec-2)	$R_{\rm e}$(arcsec)	$R_{\rm e}$(kpc)	n
IC 5105	J	$21.01\pm0.04$	$19.33\pm0.40$	$10.55\pm0.21$	4
	H	$20.38\pm0.03$	$20.81\pm0.44$	$11.36\pm0.24$	"
	$K_{\rm s}$	$20.01\pm0.05$	$18.12\pm0.55$	$9.89\pm0.30$	"
NGC 596	J	$20.22\pm0.03$	$13.81\pm0,22$	$2.77\pm0.05$	"
	H	$19.34\pm0.03$	$11.62\pm0.19$	$2.33\pm0.04$	"
	$K_{\rm s}$	$19.27\pm0.03$	$12.14\pm0.22$	$2.43\pm0.05$	"
NGC 636	J	$20.41\pm0.06$	$12.78\pm0.38$	$2.49\pm0.07$	"
	$K_{\rm s}$	$19.77\pm0.07$	$13.86\pm0.55$	$2.71\pm0.11$	"
NGC 1400	J	$19.84\pm0.04$	$21.23\pm0.44$	$1.03\pm0.02$	"
	H	$19.31\pm0.02$	$23.64\pm0.31$	$1.15\pm0.01$	"
	$K_{\rm s}$	$19.10\pm0.04$	$22.37\pm0.47$	$1.09\pm0.02$	"
NGC 1453*	J	$20.63\pm0.05$	$17.70\pm0.52$	$7.22\pm0.21$	"
	H	$19.70\pm0.04$	$14.07\pm0.34$	$5.74\pm0.14$	"
	$K_{\rm s}$	$19.47\pm0.05$	$13.61\pm0.38$	$5.55\pm0.15$	"
NGC 7192	J	$20.99\pm0.04$	$16.90\pm0.35$	$4.79\pm0.09$	"
	H	$20.38\pm0.02$	$16.20\pm0.20$	$4.60\pm0.06$	"
	$K_{\rm s}$	$20.38\pm0.02$	$17.96\pm0.22$	$5.09\pm0.06$	"
NGC 7562	J	$21.09\pm0,03$	$22.95\pm0.46$	$8.90\pm0.18$	"
	H	$20.47\pm0.04$	$22.27\pm0.54$	$8.64\pm0.21$	"
	$K_{\rm s}$	$20.37\pm0.03$	$22.63\pm0.42$	$8.78\pm0.17$	"
NGC 7619	J	$20.29\pm0.03$	$15.37\pm0.29$	$6.25\pm0.12$	"
	H	$19.53\pm0.05$	$13.21\pm0.33$	$5.37\pm0.13$	"
	$K_{\rm s}$	$19.61\pm0.02$	$16.13\pm0.22$	$6.56\pm0.09$	"
NGC 7626	J	$21.10\pm0.04$	$19.76\pm0.46$	$7.22\pm0.17$	"
	$K_{\rm s}$	$20.07\pm0.04$	$17.27\pm0.36$	$6.31\pm0.13$	"
NGC 7796*	J	$20.74\pm0.04$	$16.31\pm0.40$	$5.38\pm0.13$	"
	H	$19.99\pm0,04$	$14.83\pm0.52$	$4.88\pm0.17$	"
	$K_{\rm s}$	$19.34\pm0.14$	$10.68\pm0.80$	$3.52\pm0.26$	"
NGC 720*	J	$19.34\pm0.12$	$16.88\pm1.37$	$2.95\pm0.24$	$1.80\pm0.32$
	H	$18.70\pm0.12$	$16.84\pm1.36$	$2.95\pm0.24$	$1.82\pm0.32$
	$K_{\rm s}$	$18.49\pm0.12$	$16.00\pm1.25$	$2.80\pm0.12$	$1.77\pm0.30$
NGC 1600	J	$19.97\pm0.15$	$14.62\pm1.33$	$7.16\pm0.65$	$1.65\pm0.51$
	H	$19.11\pm0.15$	$12.64\pm1.05$	$6.19\pm0.52$	$1.45\pm0.41$
	$K_{\rm s}$	$18.84\pm0.16$	$11.70\pm0.95$	$5.73\pm0.46$	$1.34\pm0.38$

The luminosity profiles of the galaxies of our sample were well fitted by the r^1/4 law, except those of NGC 720 and NGC 1600, which fit Sérsic's law. Figure 2 presents the brightness profiles and the best-fitted law for J band; the fittings were made after removing the region affected by seeing. In Fig. 2, the dotted lines represent the difference between observed and fitted profiles, expanded on a scale of 0.25 mag. The profiles in H and $K_{\rm s}$ show similar characteristics for all the sample galaxies. The parameters $R_{\rm e}$ and $\mu_{\rm e}$ are listed in Table 2.

3.3 Integrated magnitudes

   

Table 3: Integrated magnitudes and isophotal radii. Objects whose bands are marked by (*) had its observed profiles extrapolated up to the isophotal brightness. The last columns show the integrated magnitude up to a radius of isophotal limit 1 mag brighter than the isophotal magnitude.

Galaxy	Band	m(0.2$\cdot$$R_{\rm e}$)	m(0.5$\cdot$$R_{\rm e}$)	m($R_{\rm e}$)	$m_{\rm iso}$	$R_{\rm iso}$ ( $^{\prime\prime}$)	$M_{\rm iso}$	$\Delta \mu$(mag/arcsec2)	$R^*_{\rm iso} (\hbox{$^{\prime\prime}$ })$	$m^*_{\rm iso}$
IC 5105	J*	11.32	10.51	10.07	9.99	34.44	-24.53	0.1	18.57	9.57
	H*	10.53	9.74	9.33	9.27	30.32	-25.25	0.4	21.41	8.91
	$K_{\rm s}$	10.53	9.67	9.24	9.08	28.36	-25.44	-	17.59	8.87
NGC 596	J*	11.43	10.38	9.86	9.52	30.02	-22.83	0.2	19.60	9.25
	H*	10.99	9.91	9.37	8.93	29.25	-23.42	0.1	19.45	8.65
	$K_{\rm s}$	10.80	9.73	9.19	8.81	25.82	-23.54	-	16.95	8.48
NGC 636	J	11.71	10.71	10.23	9.93	25.71	-22.36	-	17.02	9.65
	$K_{\rm s}$	10.80	9.86	9.41	9.18	24.02	-23.11	-	15.59	8.86
NGC 720	J*	10.89	9.69	9.15	8.69	52.36	-23.37	0.7	34.64	8.47
	H*	10.22	9.03	8.48	8.04	53.14	-24.02	0.5	36.62	7.82
	$K_{\rm s}*$	10.15	8.93	8.38	7.97	45.70	-24.09	0.5	30.45	7.77
NGC 1400	J	10.43	9.68	9.30	9.05	50.06	-20.22	-	35.74	8.87
	H*	9.67	8.95	8.60	8.36	60.08	-20.91	0.1	40.20	8.21
	$K_{\rm s}$	9.58	8.84	8.49	8.26	50.98	-21.01	-	33.29	8.09
NGC 1453	J*	11.02	10.21	9.80	9.55	35.45	-24.34	0.3	20.97	8.88
	H	10.67	9.75	9.29	8.96	30.79	-24.93	-	20.28	8.23
	$K_{\rm s}$	10.54	9.60	9.14	8.84	26.69	-25.05	-	17.08	8.11
NGC 1600	J*	12.15	10.77	10.11	9.70	32.63	-24.59	0.7	22.88	9.45
	H*	11.73	10.27	9.55	9.10	27.98	-25.19	0.7	22.67	8.78
	$K_{\rm s}*$	11.67	10.19	9.44	9.01	22.59	-25.28	0.2	19.08	8.62
NGC 7192	J*	11.53	10.58	10.07	9.86	26.77	-23.24	0.2	16.72	9.55
	H*	11.06	10.11	9.60	9.34	26.82	-23.76	0.3	16.88	8.96
	$K_{\rm s}$	10.73	9.83	9.36	9.22	23.99	-23.88	-	14.91	8.87
NGC 7562	J*	10.92	10.11	9.70	9.56	32.09	-24.22	0.5	21.53	9.22
	H	10.39	9.57	9.16	9.01	33.18	-24.77	-	22.17	8.72
	$K_{\rm s}*$	10.24	9.43	9.01	8.88	30.31	-24.90	0.2	19.41	8.51
NGC 7619	J*	11.20	10.26	9.80	9.51	32.39	-24.38	0.5	21.05	9.26
	H*	10.83	9.83	9.35	9.00	30.96	-24.89	0.3	20.12	8.77
	$K_{\rm s}*$	10.35	9.46	9.02	8.77	29.93	-25.12	0.1	19.63	8.47
NGC 7626	J*	11.26	10.39	9.92	9.72	29.47	-23.93	0.6	19.45	9.27
	$K_{\rm s}*$	10.64	9.75	9.25	9.05	25.63	-24.60	0.1	16.68	8.62
NGC 7796	J	11.37	10.49	10.00	9.78	27.50	-24.51	-	18.47	9.51
	H*	10.88	9.94	9.43	9.17	27.02	-25.12	0.6	18.43	8.91
	$K_{\rm s}*$	10.95	10.06	9.48	9.06	21.77	-25.23	0.1	15.97	8.64

Integrated magnitudes were calculated with the IRAF task PHOT. Table 3 shows the integrated magnitudes from the aperture photometry, which was performed for 0.2, 0.5 and 1.0 effective radii and for the isophotal radius. The isophotal radius ( $R_{\rm iso}$) is defined as the semimajor axis of the ellipse fitted to a specific limit brightness, called the isophotal brightness. The adopted isophotal brightness values were 22.0, 21.5 and 21.0 mag arcsec^-2 for J, H and $K_{\rm s}$ respectively (Hunt et al. 1999).

To determine the isophotal radius, we calculated, in the fitted profiles, the radius corresponding to the isophotal brightness. When profiles did not reach the isophotal brightness, what was true for most profiles (marked by "*"), we extrapolated the fitted profile. Table 3 shows the isophotal radii and, for the objects for which extrapolation was used, the difference between the weaker points of the observed profile and the isophotal brightness. We see that the maximum difference between the limit brightness and the isophotal brightness is about 0.7 mag arcsec^-2. So, if we add 1 mag to the isophotal magnitudes adopted, all integrated magnitudes would be obtained without extrapolation. These data (m $^*_{\rm iso}$ and $R^*_{\rm iso}$) are shown in the last two columns of Table 3. This table also shows the absolute magnitudes, which were calculated using the distances given in Table 1 and corrected for galactic extinction by Schlegel et al. (1998).

3.4 Colors and color gradients

We constructed, through the brightness profiles, the corresponding color profiles. They are represented in Fig. 2, below the brightness profiles. We can see that color gradients are very small, and probably accounted for the observational uncertainties for most of the profiles, albeit showing a systematic tendency to bluer colors in the external region. In some cases, different color profiles do not have the same tendency for the same galaxy (IC 5105 and NGC 1400 present a J-H color tending to redder for the external region, contrary to the other colors; NGC 596 and NGC 7619 present a similar effect for the $H-K_{\rm s}$ band; galaxy NGC 636 presents a redder $J-K_{\rm s}$ profile in the external regions). These small near-IR color gradients may reflect the fact that the stellar population that dominates the near-infrared colors is distributed homogeneously throughout the galaxy.

Integrated color were determined from subtraction of the integrated isophotal magnitudes. We present in Fig. 5 a flux ratio diagram from these data, obtained applying 10 $^{-0.4({\rm color})}$ to the isophotal colors of the galaxies. This figure also presents the representative region of the sample of E/S0 galaxies from Frogel et al. (1978), whose J/H colors are redder than the average of those observed for our sample. The galaxies NGC 7192, NGC 7562 and NGC 7619 present a very blue J/H color, suggesting that an earlier stellar population may be present in these galaxies (see Sect. 5).