  We investigate the dependence of the strength of galaxy clustering on
intrinsic luminosity using the Anglo-Australian two degree field galaxy
redshift survey (2dFGRS). The 2dFGRS is over an order of magnitude larger than
previous redshift surveys used to address this issue. We measure the projected
two-point correlation function of galaxies in a series of volume-limited
samples. The projected correlation function is free from any distortion of the
clustering pattern induced by peculiar motions and is well described by a
power-law in pair separation over the range 0.1 < r /h Mpc < 10. The clustering
of L* galaxies in real space is well fit by a correlation length r0 = 4.9 +/-
0.3 /h Mpc and power-law slope gamma = 1.71 +/- 0.06. The clustering amplitude
increases slowly with absolute magnitude for galaxies fainter than M*, but
rises more strongly at higher luminosities. At low luminosities, our results
agree with measurements from the SSRS2 by Benoist et al. However, we find a
weaker dependence of clustering strength on luminosity at the highest
luminosities. The correlation function amplitude increases by a factor of 4.0
between $M_{b_{J}} -5\log_{10}h = -18$ and -22.5, and the most luminous
galaxies are 3.0 times more strongly clustered than L* galaxies. The power-law
slope of the correlation function shows remarkably little variation for samples
spanning a factor of 20 in luminosity. Our measurements are in very good
agreement with the predictions of the hierarchical galaxy formation models of
Benson et al.
