Color gradients

The color variation in a galaxy can be quantified using a color gradient parameter, i.e.,\

 

i.e., change in color per decade in radius. We describe below the procedure for obtaining this parameter. We then present the color gradients that we obtain for the radio and control samples and compare them with those obtained by others for similar samples. We show that in principle the scale lengths should provide the same information as the color gradients but that the former are more robust indicators of color variation.

The change in color per decade in radius is almost linear in most cases and the color gradient, e.g. , is obtained by fitting a straight line to the color profile between an inner radius and an outer radius . The choice of and has been described in Chapter . is at a radial distance of 1.5 times the FWHM of the PSF while is the point along the major axis at which the error on the mean surface brightness of the fitted ellipse reaches 0.1 magnitude. The additional caveat is .

When two small galaxies (angular diameter ;SPMlt;15'') and a quasar host are excluded, we find that the mean color gradients for the two samples in magnitudes per decade in radius are:

and

The distribution of gradients is shown in Figure .

We find that the numbers that we obtain are larger than those obtained by other authors. For a sample of normal ellipticals (with dusty galaxies excluded) Peletier et al. (1990) had obtained a color gradient of -0.1. Zirbel (1996) had obtained a value of -0.15 for a sample of radio galaxies.

 

Results for the samples

Figure  shows that their are important difference between the radio and control samples with respect to the scale length ratio. One can especially see that a larger proportion of radio galaxies become bluer towards the center. However, such a distinction can not be made on the basis of color gradients. In the case of radio galaxies as well as the control sample galaxies we find that a majority have a negative color gradient i.e., they become redder as one approaches the center. This is in confirmation with color gradients in galaxies in general ( Sandage and Visvanathan, 1978). A comparative distribution of color gradients for the two samples is given in Table .

A few properties related to color gradients hold true for both the samples:

• For optically brighter galaxies there is a hint that the color gradient increases linearly with brightness (Figure ). This is consistent with elliptical galaxy formation models based purely on dissipation (Carlberg, 1984). As clouds collapse and give rise to galaxies, larger galaxies (larger scale length) are also seen to possess larger color gradients. However, the correlation coefficients indicate that this dependence is not significant, the best correlation being that between in B for radio galaxies: the correlation coefficient is -0.31 with a significance level of 98%. The plots for the radio and control samples are shown in Figures  and .
• For fainter galaxies a larger scatter is seen in the color gradient (Figure ). Such a behavior has been noted before ( Vader et al., 1988). It has been suggested that dwarf ellipticals which are closer to disk galaxies are likely to show larger scatter.

 

 

Color gradients and scale length ratios

Color gradients and scale length ratios are both indicative of the change in color with distance from the center. We present below a relation between the two quantities so that one can be obtained from the other.

Let and denote the B and R profiles of the galaxy in Figure . We can then write,

 

and

 

where, , m is a constant and and are the bulge scale lengths in .

The surface brightness profile of a de Vaucouleurs galaxy is a straight line in the plane. Equations  and  provide the slopes of surface brightness profiles ( and ). One can also obtain these values by considering two points, ( ) and ( ), on the respective straight lines representing the surface brightness profiles in the plane. One can then obtain a relation between the scale length ratio and the color variation by equating the ratio of the slopes (of the surface brightness profiles) obtained by the two methods:

 

where, .

The change in color can also be obtained from the color gradient as follows:

Thus,

 

Using the value of from Equation  in Equation  and since is small, we have,

which further gives us:

Thus, for galaxies that obey de Vaucouleurs' law the color gradient can be obtained directly using the fitted bulge scale lengths. We show in Table  the color gradients obtained from the color profile as well as that obtained from the scale lengths. The conventional color gradient does not greatly distinguish between the radio and control samples, although here too the control sample does have a higher proportion of objects becoming redder towards the center. When we turn to the color gradients as obtained from the scale lengths, we see that the radio and the control sample are clearly separated into two different categories. The scale lengths indicate that a large fraction ( ) of the control sample galaxies become redder towards the center while a large proportion ( ) of the radio galaxies are seen to become bluer towards the center.

Since identical processing has been carried out for the radio and control samples, it is unlikely that a bias in selection or procedure leads to the significant difference between the two samples as indicated by the scale lengths.

[Color gradient details using two methods] Number of galaxies with negative and positive color gradient for the two samples as obtained from (1) their color profiles and (2) their bulge scale lengths. A negative color gradient is indicative of the galaxy having a redder center compared to its outer regions.  

Color gradient From color profile From scale lengths

Radio Control Radio Control

;SPMlt;0 20 24 9 20

;SPMgt;0 7 6 18 10

Indeterminate 3 0 3 0

Preference for scale lengths

We have seen above that while the color gradients do not seem to distinguish between radio galaxies and the control sample to a great extent, the results obtained from the fitted scale lengths clearly bring out the difference very vividly. We examine here the reasons behind this.

Obtaining the color gradient involves fitting a straight line to the B-R profile. As a result, small variations, especially small 'kinks' close to the center, cannot affect the fit. The profiles show that the radio galaxies are more 'kinky', but the straight line fits miss that fact. In principle these small changes can be crucial. Also, the magnitude of the color gradient is of the order of the errors on the color profile, especially in the outer region.

The procedure for obtaining the scale lengths does not suffer from the above defects. We obtain scale lengths by fitting an empirical formula separately to the B and R band profiles. As discussed earlier, the obtained are well within acceptable limits in most cases and thus indicative of good fits. The added advantage of using the effective radius for such a comparison is that it provides a single descriptor for large scale trends in the distribution of light.

 

Discussion

It is clear from the preceding discussion that in our sample the control galaxies seem to behave as expected, the radio galaxies show a larger scatter in the scale length ratio. A few galaxies show evidence of large reddening as one approaches the center while a majority show a tendency of bluer colors towards the center. We interpret these effects as being due to dust and star formation respectively.

Following earlier studies made using reddening-free color indices, it was assumed that the color gradient in a galaxy is a result of the metallicity gradient (combined with age gradient) alone. Though metallicity is indeed the main cause of color gradients, there are other factors like dust (Wise and Silva, 1996) and star formation that can affect the color gradient and hence the scale lengths. The effect of dust and star formation are in general complimentary in that dust tends to redden whereas star formation leads to bluer colors. If a galaxy is without dust or young stars or has dust that is well mixed with stars, . Given below are three simple-minded dust and star formation scenarios that affect .

1. Young stars being formed in the central but extended region of the galaxy: In such a case there will be excess blue light from the center and the radius of the aperture enclosing half of the blue light will be smaller than the corresponding radius for the red light, thus reducing the .
2. Extended dust in the outer regions: Excess dust in the outer region will cause larger amount of blue light to be absorbed there which is equivalent of a red excess. As a result, as in the case above, the radius of the aperture enclosing half of the blue light will be smaller than the corresponding radius for the red light, thus leading to a smaller .
3. Dust in the inner region: Blue light will be more absorbed near the center, as a result of which the blue surface brightness will appear to rise slower than the red light towards the center, increasing .

The following calculation shows the quantitative effect of dust in changing the scale length of a galaxy.

If the opacity , then the change in magnitude due to absorption . If the dust affects only the shorter wavelengths (e.g. B band) then absorption is equivalent to the change in color, . This change occurs near the center of the galaxy, typically over a decade of radius. The resulting color gradient, for , as given by Equation  is

The equivalent change in scale lengths is i.e., .

Since the effect of dust is not easily discernible authors often prefer to publish scale lengths for a single filter even when data are available in more than one. Dust alone does not seem to be sufficient in giving rise to the color gradients, but substantial amounts of it can certainly lead to reddening. In particular for the radio galaxies that have we do find evidence of dust in the color maps (Chapter ). Thus the scale length ratio is also a good indicator of dust.

[Details of excess near center in the radio and control samples] Details of the excess emission found near the center in radio galaxies and the control sample.  

Radio Control Interpretation

% cases % cases

1 30 27 Dust near the center

2 17 7 Weak excess emission

3 13 10 Excess emission + dust

4 17 0 Excess emission + dust. Dust more dominant.

5 3 0 Excess emission + dust. Excess more dominant.

6 3 6 Excess emission + dust. Excess more dominant.

7 3+4+5+6 36 16 Excess emission + dust

8 2+3+4+5+6 53 23 Excess emission

9 1+3+4+5+6 66 43 Dust