We are proposing to use the 2dF to make a simultaneous QSO and galaxy redshift survey across two declination strips, one in the South Galactic Pole and one in an equatorial region at the North Galactic Cap. The Southern strip will be in the same area of sky as the Durham/UKST B<17 galaxy redshift survey. QSOs will be selected by the ultra-violet excess (UVX) method and the key to the success of this proposal is the large amount of deep U plate material which we have already obtained with the UK Schmidt Telescope. We shall observe 120 - 130 UVX QSO candidates per fibre field to B=21. The area surveyed in each strip will be 75° × 5° and the resulting catalogue will contain 30000 z<2·2 QSOs. Combined with large area galaxy redshift surveys, it will form the most comprehensive picture of the large-scale structure of the Universe in a given area of sky, with the QSOs probing the structure up to scale lengths of 1000h Mpc (comparable to the scales studied by COBE) and the galaxies at B<20 forming a more detailed picture of the topology on scales up to 500h Mpc.
(a) The Non - Linear Regime: (r < 10h
At small scales we will obtain information about the development of the non-linear regime of QSO clustering in the redshift range 0·5<z<2·2. Since the Ellingson et al. (1991) result suggests that optical QSOs randomly sample the optical galaxy distribution, this means that we will also be investigating the evolution of the galaxy correlation function at these depths. In this range of redshifts, an unbiased, = 1, CDM model predicts that there will be substantial evolution of the correlation function, , at small scales (see Fig. 2 ), whereas a biased CDM model predicts much less evolution in (as measured in comoving coordintes). Even by combining all 700 QSOs in the existing deep (B<21) surveys (Durham/AAT+ESO/AAT+CFHT, see Shanks & Boyle 1994), at present there are only 40 QSO pairs with r<10h Mpc. From this data the suggestion is that the QSO clustering amplitude seems more consistent with comoving evolution, although the data allows only a rough correlation function amplitude to be measured for r < 10h Mpc on the assumption of an underlying -1·8 power-law (see Fig. 3 ). With 2000 r < 10h Mpc QSO pairs available in the proposed survey, this will make possible an accurate measurement of both the amplitude (± 10%) and the slope (± 0·1) of the correlation function over the whole redshift range 0·5<z<2·2. Further, at scales < 2h Mpc present QSO samples contain no QSO pairs. With a sample of 30000 QSOs we estimate (assuming for the QSO sample) that we should find QSO pairs at these scales. At this scale we might expect clustering to be stable in proper coordinates, in which case it may follow a different evolution with z. Also on these < 2h Mpc scales the 3-D QSO clustering evolution results can be directly compared to those obtained from deep 2-D analyses of galaxy clustering (Roche et al 1993). By comparing the results for over the entire 0 < r < 10h Mpc range with the predictions from cosmological N-body and hydrodynamic simulations we shall be able to discriminate between not just biased and unbiased CDM but also HDM, baryonic and low models.
(b) The Intermediate Linear Regime: (10 < r < 30h
Here we will determine the form of the QSO correlation function at the scales where it is most sensitive to the primordial mass spectrum. At these scales the correlation function is claimed to show excess power over what is expected for a standard CDM model, on the basis of the projected APM correlation function (Maddox et al. 1991) and, at a less significant level, on the basis of the IRAS redshift survey correlation function. In this range of scales, QSO surveys are becoming highly competitive with galaxy redshift surveys in terms of the statistical accuracy of the correlation function since they are effectively a very sparse sampled dataset (Kaiser 1987) with each QSO bringing almost completely independent correlation function information. Currently the QSO correlation function errors in this range are ± 0·15 from the 700 QSOs in the Durham/AAT+ESO+CFHT surveys and show insignificant excess power over that expected for CDM (see Mo & Fang 1993). However, a correlation function as flat as the APM result is also not significantly excluded. In the proposed 30000 QSO survey this error will reduce to ± 0·02 and we will be able to discriminate between the APM and the standard CDM correlation function slopes at the level (see Fig. 4 ). This is a powerful example of what will be possible with a QSO correlation function measured to this accuracy in this intermediate regime. In Fig. 4 we also show the different correlation function shapes expected for a canonical CDM power spectrum form with primordial index running between 0·5 < n < 1·5, the range favoured by consideration of the COBE results and inflation theory. With errors as low as ± 0·02, the proposed 2dF QSO survey therefore provides the unique opportunity to obtain an independent determination of the index of the primordial fluctuation power spectrum to ± 0·2.
(c) The Fully Linear Regime: (30 < r < 1000h
At these very large scales, the QSOs are clearly superior to galaxies as probes of large scale structure by virtue of both their sparse sampling and their flat n(z) distribution. This regime, between the APM and the COBE scales is still highly controversial. Although many basic models such as standard CDM predict that is close to zero on these scales, many previous methods of probing large-scale structure have suggested significant power in this range e.g. bulk motions, Abell clusters, bright B galaxy counts (the `local hole'), the possible 100h Mpc scale cell structure in galaxy redshift surveys such as CfA, Durham/UKST and the claimed 128h Mpc periodicity in the faint galaxy redshift survey of Broadhurst et al. (1990). However, even if such features are real they are only expected to have very low amplitude, < 0·05, as measured by the correlation function. At h Mpc the correlation function from the 700 Durham/AAT+ESO/AAT+CFHT QSOs has errors at the ± 0·05 level and is only showing some tentative evidence of weak features, eg. a possible anti-correlation at the = -0·05 level at h Mpc (see Fig. 4 ). We have used simulations to determine the likely error on at these scales in the proposed survey. These show that the error at r 100h Mpc will reduce from ± 0·05 to ± 0·003. This means that features even at the = 0·02 level could be detected at . No other method of probing large scale structure can reach these levels of precision in the same exposure time.
(b) QSO geometric measurement of
With the 50-fold increase number of QSO pairs at small separations in the proposed QSO survey, an even more powerful geometric test for the cosmological constant will be available to us. The test, suggested by Phillipps (1994), after Alcock & Pacynski (1979), comprises a comparison of the extent of small scale QSO clustering in the redshift and angular directions. Under the reasonable assumption that the QSO small-scale clustering will be spherically symmetric at least in the average, the extent of the QSO correlation function should be the same in both directions. However, the distance between a pair of QSOs measured in the line of sight from the redshifts has a different dependence on the cosmological parameters from the distance measured in the angular direction. By demanding that these two distances are in the average the same, a powerful cosmological test emerges. Now in the case of models the difference between the 2 extents is only small for values of in the range 0 < < 0·5 (see Fig. 6 ). However, the difference in extents for models with 0 can be much more significant. For example, in the interesting case of a zero spatial curvature model with and 0 the result is strikingly different from the conventional case. The current constraints on from this method are poor, since there are only 40 correlated QSO pairs with r < 10h Mpc. However in the proposed survey the number of pairs would rise to and then, according to Phillipps (1994), there is the possibility of an almost exact determination of from this method. Redshift measurement errors and random small-scale peculiar velocities are not a problem for this method, since their effects are small if the extents are measured over 10h comoving Mpc. Of course, it should also be noted that if the result is consistent with and 0 < < 0·5 then this will be a non-negligible test of the GR theory that relates the angular and redshift distance measurements.
Most of the examples given above discuss the measurement of QSO clustering using the correlation function, primarily for ease of comparison with existing analyses. However, we will also make extensive use of other statistics to measure QSO clustering e.g. power spectrum, higher order (3-point, 4-point) correlation functions, counts in cells etc. to extract the maximum information content from the proposed survey.
From this survey we will also be able to determine the space density and evolution of intrinsically rare classes of QSO e.g. Broad Absorption Line (BAL) QSOs, damped Ly QSOs and QSOs with strong metal absorption line systems. Based on a BAL QSO fraction of 5-10%, we expect to identify over 1500 BAL QSOs in this survey. This is sufficient to derive an accurate picture of their space density and evolution at z<2·2, and will provide vital clues to the physical nature of such systems. We will also identify QSOs with 1·9<z<2·2, the redshift range over which we will be able to identify candidate damped Ly systems. Assuming that 2-5% of QSOs exhibit damped Ly (Pettini, private comm.), we will identify 100-250 such systems in the survey, providing valuable data towards an accurate determination of the space density of the galactic disks at thought to be responsible for the damped Ly lines. Similar information should be derived for the significant number of strong metal-line absorption systems which will also be identified in this survey. With over 6000 bright (B<19·5) QSOs ( /2dF field) in the final sample, the survey will also provide an invaluable source of material for future, more detailed, spectroscopic campaigns of QSOs and their absorption line systems.
In passing, we note that the survey will also yield astrophysically important information on other classes of astronomical objects. Based on the Durham/AAT UVX survey (Boyle et al. 1990), we expect to find over 1500 hot white dwarfs and distant (r>50kpc) blue horizontal branch stars. The white dwarfs can be used to provide an accurate measure of their scale-height (Boyle 1989), possibly even as a function of spectroscopic class, and the horizontal branch stars are important tracers of the dynamics of the outer halo of our galaxy (Sommer-Larsen & Christiansen 1986).References:
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