Here I give a brief pedagogical description of the results of Blanton et al. (2003g). The basic result is that color and luminosity are the galaxy properties (of those which we have considered) that are related to environment most independently of the others.
Blanton et al. (2003c) present the joint bivariate distributions of a number of optical galaxy properties, such as color, luminosity, surface brightness, profile shape, and local overdensity. There exists a pedagogical description of those results.
First let us review the properties we are going to be considering:
Here, just consider the joint distribution of color and absolute magnitude:
Here we show the one-dimensional distributions on the diagonal and the
bivariate distributions on the off-diagonals. The greyscale is a
square root stretch and the contours enclose 33%, 68%, 95% and 99% of
the number density (from high to low). Several scientifically
interesting features appear, including the clear red and blue
sequences. It is bivariate plots like this that form the basis of the
results in Blanton et al
(2003c).
We can also consider all of the bivariate distributions between the properties:
The details of this plot are discussed in Blanton et al. (2003c). For now just
note that the relationships are complex and interesting. Many of the
trends have been known for many years, but here we see them at high
signal to noise.
Hogg et al. (2003b) discuss the application of the local environmental indicator described by Eisenstein (2003) to the SDSS. The mean of the indicator for many galaxies corresponds to the mean three-dimensional overdensity field smoothed with a Gaussian with sigma of 1 Mpc/h.
For example, consider the dependence of overdensity on luminosity. We can take galaxies within 0.5 magnitudes of a specific luminosity and calculate the mean overdensity for such galaxies. The result of doing so at all luminosities for our sample yields the following plot:
Clearly the overdensity which a galaxy is in is strongly related to
its luminosity.
We can go further, however. We can look at the bivariate dependence of mean overdensity on luminosity and color simultaneously:
Here the diagonal plots show the
dependence on each parameter alone, while the off-diagonal plots show
the dependence jointly on the two parameters as a contour plot (shaded
such that higher mean overdensities are darker. This result is the focus
of Hogg et
al. (2003b). Interestingly, there is a clustered population of low
luminosity, red galaxies, a strong dependence of environment on
luminosity for bright galaxies, and a strong dependence of environment
on color for blue galaxies.
One might note that we do not extend to very low luminosity. This is because the low luminosity galaxies are at low redshift, and the deprojection operator fails to work well when the edges of the survey are too close.
Of course, we can look at the dependence on mean density of all the properties:
We discuss these plots in detail in
Blanton et al. (2003g). They reveal dependence on Sersic index
and surface brightness as well as color and luminosity.
Is this dependence independent of color and luminosity? In the paper, we argue that there is not much residual dependence on Sersic index once the dependence on color and luminosity is accounted for. The easiest way to see this result is to divide the galaxies into bins of luminosity and look at the joint dependence of density on color and each of the other properties. Consider the figure:
Each row corresponds to a different
range of luminosities. At high luminosity (at the bottom) there is a
strong dependence of environment on surface brightness and Sersic
index, in the sense that lower surface brightness, less concentrated
galaxies are in denser regions. This dependence is weaker at lower
luminosities, and it is still in the sense that less concentrated
galaxies are in denser regions.
The basic result is the following: at fixed luminosity and color, there is not a strong relationship between density and either Sersic index or surface brightness. To the extent that such a relationship exists, at very high concentration or surface brightness the density decreases.