3 Amplitude correlations

The top two panels in Fig. 3 show the distribution of amplitudes as a function of redshift and luminosity for the UVX sample. The most striking thing about these figures is the marked drop in amplitude towards low redshift and luminosity. This is illustrated more clearly in the top two panels of Fig. 4, where the data is binned in intervals of 0.5 in redshift and unit absolute magnitude, and the mean plotted with $\sqrt{N}$ error bars. The fall towards low redshift and luminosity is highly significanti (a 3-$\sigma$ effect), although it is not clear from these data alone whether it is primarily a luminosity or redshift effect. The correlation coeffecient for the top left panel of Fig. 3 with z < 0.5 is 0.46, and for the top right panel with M_B > -22 is -0.67, confirming the reality of the correlation. There is also some evidence for a decrease in amplitude for the most luminous quasars ( M_B < -25), and an even weaker decline for high redshift objects. Correlation coefficients for all the data in the top two panels are 0.12 and -0.10 for left and right panels respectively, emphasising the weakness of the effect. This is another manifestation of the well known degeneracy between redshift and luminosity. This point will be investigated further below by dividing the data into sub-samples.

Figure 3: The top two panels show plots of amplitude versus redshft and absolute magnitude for quasars selected solely on the basis of ultra-violet excess. The bottom two panels are similar plots for quasars selected on the basis of variability

Figure 4: Plots based on the same data as for Fig. 3, but binned in redshift intervals of 0.5 and unit absolute magnitude intervals. The error bars show the uncertainty in the position of the mean

The bottom two panels in Figs. 3 and 4 show similar plots for the VAR sample. The greater redshift range allowed by variability selection still shows little trend of amplitude with redshift, but the decrease in amplitude for luminous quasars is shown to continue to greater luminosities, although the effect is inevitably lessened by the absence of quasars with $\delta m < 0.35$.

It has been mentioned above that there is a degeneracy between redshift and luminosity. This results from the fact that in a magnitude limited sample high redshift quasars tend to be high luminosity objects, and vice versa. Thus a trend with one parameter will be mimicked by a trend with the other, and the true relation will be hard to disentangle. This degeneracy can in principle be broken byi binning the data in redshift and luminosity, and the result of doing this is shown in Figs. 5 and 6. The VAR sample was used as it covers a wider range of luminosity and redshift, making binning feasible. The left hand panel of Fig. 6 shows amplitude as a function of luminosity in two redshift bins, z < 1.5 and z > 1.5. Data for the two redshift ranges overlap nicely, and clearly show a decrease in the relation between amplitude and luminosity. The right hand panel shows amplitude as a function of redshift in two luminosity bins. In this case there is some evidence for an increase in the relation at low redshift, but it is essentially flat beyond z = 0.5for both luminosity ranges. It is however worth noting that the less luminous quasars have larger amplitudes, as expected from the data in the left hand panel. It would thus appear that while for M_B > -25amplitude does indeed decrease with luminosity, it does not change with redshift for z > 0.5.

Figure 5: Plots of amplitude versus redshift and absolute magnitude for the variability detected sample (VAR). The top two panels show amplitude versus absolute magnitude for two redshift ranges, and the bottom two panels show amplitude versus redshift for two absolute magnitude ranges

Figure 6: Plots based on the same data as for Fig. 5, but binned in unit absolute magnitude intervals and redshift intervals of 0.5. The left hand panel shows the relation between amplitude and absolute magnitude for quasars with z < 1.5 (small dots) and z > 1.5 (large dots). The right hand panel shows the relation between amplitude and redshift for quasars with MB > -25 (small dots) and MB < -25 (large dots). The error bars show the uncertainty in the position of the mean

Examination of Fig. 3, especially the bottom panels, suggests that there may be population of low luminosity and/or low redshift quasars distinct from the parent population. This is particularly evident in the bottom left hand panel of Fig. 3, which is uniformly populated between amplitudes of 1.1 and 1.8 up to a redshift of 2 at which point there is a sharp cut-off with no amplitudes greater than 1.1 at higher redshift. To investigate this population with better statistics all variables with $\delta m > 1.1$ in the measured area of field 287 were observed on the 3.6 m at La Silla to confirm their identification as quasars and measure redshifts. This became the AMP sample. Figure 7 shows amplitude as a function of both redshift and luminosity, and it will be seen that there is indeed a cut-off in redshift at $z \sim 2$and $M_{B} \sim -25$. It is clear that this cut-off must in fact be related to luminosity. If it were a redshift cut-off there is no reason why such objects should not be seen with greater luminosity. On the other hand if it were a luminosity cut-off, then this combined with a magnitude limit will indeed produce an effective cut-off in redshift.

Figure 7: Plots of amplitude versus redshift and absolute magnitude for the most variable quasars in the sample