Concepto

Since 77-type 1 galaxies correlate with early type galaxies, ellipticals and SOs, and 77-type 2-4

galaxies correlate with late type galaxies, spirals and irregulars, the luminosity-surface bright­ ness correlation appears to relate to the morphology of the galaxy, de Jong & Lacey (2000) use

the Fall & Efstathiou (1980) disk galaxy formation model to predict the BBD. This assumes a dissipational collapse of a gas cloud to form a disk, with angular momentum conserved. Disks are supported by the rotation of the disk. Disks have constant (complete) dissipation but a range of angular momenta. Faint, low surface brightness disks have high angular momentum, and bright, high surface brightness disks have low angular momentum.

Wyse & Jones (1984) discuss the relationships between the rotational parameter {vjor) to surface brightness and absolute magnitude. The rotational parameter is defined as the ratio of maximum rotational velocity to mean velocity dispersion within half the de Vaucouleurs radius. Brighter and lower surface brightness galaxies tend to have lower rotational parameters, although the correlation is stronger in surface brightness. They argue that dissipation is the key to understanding this correlation since dissipation increases both the surface brightness and the importance of rotational velocities, de Zeeuw & Franx (1991) discuss the dynamics of elliptical galaxies and point out that only the centres will have had time to come into dynamical equilibrium, since the dynamical timescale in the outer parts of elliptical galaxies is similar to the Hubble time (3 > 10^ yrs). Thus elliptical galaxies can be thought of as

systems with constant angular momentum but different amounts of dissipation. Fainter, high surface brightness ellipticals have smaller dynamical time scales, since the dynamical time is proportional to (r^/^/M^/^), where r is radius, and M is the enclosed mass. Smaller ellipticals will have dissipated more, and be closer to equilibrium. Larger, lower surface brightness ellipticals have had much less dissipation and are further from equilibrium.

Zhang & Wyse (2000) have used these models to discuss the formation of the Hubble sequence for spiral galaxies. They suggest that disks form first, through the dissipational evolution discussed above. Bulges then form from bar instabilities. This gives the variety of bulge-to-disk ratios seen throughout spiral galaxies.

As one moves from 77-type 1 to 77-type 4, the faint end slope a steepens significantly. 77-type

Is represent a distribution that may be better represented by a double Gaussian for the bright population, 77-type 2s have a ~ —0.8, 77-type 2s have a ~ —1.2 whereas 77-type 4 galaxies have

a faint end slope a — —1.45. The population becomes intrinsically fainter with each 77-type

too, although the shape of the functions is such that M* can actually get brighter. We will discuss the Schechter parameters more in the context of the luminosity function.

Chapter 5: The BBD as a Function of Spectral Type. 164 Î i I Nwwvl# / mog U oqrulude /

Figure 5.13: The 2dFGRS Bivariate Brightness Distribution as a function of spectral type, all produced via the SWML method. The top left hand plot shows the BBD for ry-type 1 galaxies,

the top right plot shows the BBD for r/-type 2 galaxies, the bottom left hand plot shows the BBD for 77-type 3 galaxies and the bottom right hand plot shows the BBD for 77-type 4

galaxies. The contour lines for the BBDs are set at 1 .0 x 1 0“ ^, 1 .0 x 10“'*, 2.5 x 10“^, 5.0 x 10“'*,

7.5 X 10“'*, 1.0 X 10“3, 1.25 X 10“ 3, 1.5 x 10“%, 1.75 x 10“^ 2.0 x 10“ %, and 2.25 x 10“% galaxies

Chapter 5: The BBD as a Function of Spectral Type. 165

5.3.2 C om parison w ith o th e r O bservers

In Table 5.2 we have also listed the parameters obtained by Choloniewski (1985) for elliptical and lenticular galaxies and de Jong & Lacey (2000) for Sb-Sdm spirals. The Choloniewski (1985) data are a sample of 233 galaxies from Sadler (1984), with ruest < 14, D{ESO) > 1% and can be compared to 77-type 1 BBD. ruestis the estimated total brightness and D{ESO) is

the maximal isophotal diameter. The data are in the B-band and the parameters have been converted to Hg = 100 kms“ *Mpc“ *. We have converted the absolute magnitude and half light radii values to the absolute magnitude and effective surface brightness parameters using Eqn 2.22. Choloniewski uses Eqn 5.5 to express the luminosity-scalesize correlation:

log r = aM + h (5.5)

The conversions from a, b and the width ar^ to pe and cr^ are given as:

f3^ — 1 5a

//* = ( ! - 5a)M* - 5b 4- 38.567

cffji — 5<jj.g (5.6)

The Choloniewski (1985) BBF gives a j3^ value close to the SWML value; a fiat distribution. However the value of and //* are very dijfferent to either the empirical or the SWML values. The value of a that Choloniewski finds is much steeper (a = —1.35) although M* agrees well with the empirical method result.

The de Jong & Lacey sample was also converted to absolute magnitude and effective surface

brightness parameters and has been converted from the I-band, see § 2.7.3. In Chapter 2, we compared it to the preliminary 2dFCRS BBD and found that while and p* corresponded,

the gradient was significantly steeper. The increased gradient in the de Jong & Lacey sample could be due to contamination by ellipticals/SOs in the Cross et al. (2001) sample or the colour-luminosity correlation seen by e.g. Marzke et al. 1997, Blanton et al. (2001), Brown et al. (2001), and the colour-surface brightness correlation, Brown et al. (2001). This is discussed in § 2.7.3. However, we can now use the 77-type 3 BBD to test whether contamination

by ellipticals is the reason for the discrepancy. The 77-type 3 sample is mainly composed of

Sb-Scd galaxies (see Madgwick et al. 2001) and so it is a straight forward comparison to de Jong & Lacey. The only difference, apart from the selection boundaries which are dealt with by the methodology, is the colour. Again we find that the de Jong & Lacey (2000) sample has a much larger The values of /i* and lie between the values for the empirical method and the SWML method, so give a good match. However M* is significantly brighter and a

significantly flatter. Blanton et al. (2001) finds no significant change in a with filter for the SDSS luminosity function and finds a = —1.25 in the Sloan i* filter. Since the de Jong & Lacey (2000) sample is quite bright, this effect could be due to a more complicated luminosity function, which starts off flat before rapidly steepening.

Chapter 5: The BBD as a Function of Spectral Type. 166

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Figure 5.14: The top left hand corner shows the LF for 77-type 1 galaxies, the top right shows

the LF for 77-type 2 galaxies, the bottom left shows the LF for 77-type 3 galaxies and the bottom

right 77-type 4 galaxies. In each the red lines show the LFs produced via the empirical method

and the blue lines via the SWML method, with the Schechter function fits shown as the solid curves. The dotted curves show the Madgwick et al. (2001) Schecter function fits.