Technical requirements

Survey depth. Using the models of J.S. Dunlop (private communication) we have estimated the K-band magnitude of a passively evolving L* elliptical galaxy as a function of redshift, assuming a formation redshift z=10 (Figure 6.1) and a period of star formation extending to z=3 or terminating at z=5. We find that an L* elliptical galaxy at z=3 in a lambda-dominated cosmology would have a total magnitude in the range K=20-22, depending on the duration of the star-forming phase. Alternatively one can extrapolate the observed K-z diagram for brighter (4L*) elliptical galaxies, as traced by the hosts of luminous radio galaxies (shown as data points on Figure 6.1). To convert to an L* elliptical (assuming, of course, that these follow a similar evolutionary track) one would predict a total magnitude K~21.5 at z=3 (using dK=2.5 log(4)=1.5 mag).

Figure 6.1. Predicted K-z Hubble diagrams for passively evolving L* ellipticals, produced by J.S. Dunlop (based on the models of Jimenez et al. 1999). Both models assume a formation redshift z_f=10. The model shown by the dashed line shows residual star formation to z=3, with a more rapid burst of star formation for the solid line (terminating at z=5). We assume a cosmology with omega_m=0.3, lambda=0.7 and H_o=70. For comparison, the data points illustrate the observed K-z relation for the hosts of powerful radio galaxies (corresponding to 4×L* ellipticals). Note that these data track the faint model predictions with very little dispersion.

However, we need to survey to a considerably fainter point source magnitude depth. Elliptical galaxies are large extended sources and hence aperture correction issues must be taken into account. These effects may have led to a systematic underestimate of the prevalence of large elliptical galaxies at high redshift in previous deep surveys (Dunlop & Gloag, in preparation). A large elliptical galaxy will have a half-light radius of r_1/2~10 kpc, corresponding to ~1 arcsec in a lambda-dominated cosmology (1<z<4). An aperture of radius 3r_1/2, i.e. a 6 arcsec diameter, is required to capture >90% of the light and so provide an accurate total magnitude. Of course the galaxies may transpire not to be this large, but we stress that to prove this we still need to be able to make a meaningful large aperture measurement. The key point is that to establish both the half-light radius and total magnitude of a high-redshift galaxy with confidence requires that meaningful measurements can still be achieved as the aperture is expanded out to a diameter ~6 arcsec.

For median seeing, the point-source depths used throughout this proposal correspond approximately to using a 1 arcsec aperture, as this optimises the S/N. If we detect K=21.5 in a 6 arcsec aperture, then the through-aperture magnitude detected to the same S/N in a 1 arcsec aperture is K=21.5 + 2.5 log(6) = 23.4. However the equivalent point source giving such a through-aperture magnitude is K~22.7. Overall, we see that a survey with a depth corresponding to a point-source limit of K=23 will be able to detect L* passively evolved ellipticals to z=3 (5 sigma) through the necessary range of apertures.

Filter choice. Colour information is also vital for discriminating between objects, and for the determination of photometric redshifts, particularly using the 4000Å break as it moves through the I, J, & H bands over the range 1<z<4 (see Figures 6.2, 6.3). Photometric redshifts need two points longward of the 4000Å break and so should work up to roughly z=3. To effectively separate passive ellipticals from starbursts, we need to be able to detect colours of J-K ~2 and H-K ~1, otherwise the majority of our sample objects may be K-band detections only. By the same reasoning, it is also highly desirable to obtain very deep I-band data to complement the UDS. For an ERO detection, depths of I~27-28 will be required to match the above. SuprimeCam on Subaru would be ideal for such imaging.

Figure 6.2. J-K colours as a function of redshift for the 2 evolution models illustrated in Fig. 6.1.

Figure 6.3. J-H colours as a function of redshift for the 2 evolution models illustrated in Fig. 6.1.

Survey area. Our prime goal is to measure the abundance of high redshift passive ellipticals. A survey of approximately one square degree size is needed for confident statistics. The simplest strategy would be to stack repeated exposures at an identical pointing, resulting in four separated surveys totaling 0.21 sq. degs. However as well as compromising the statistics, this would damage our secondary aim at measuring the clustering amplitude of various populations, which really needs a contiguous area probing ~100Mpc. A contiguous field is also highly desirable for obtaining complementary multiwavelength data in an efficient manner. It may well be best to make such a deep stacked survey on a finely gridded pattern, but the optimum pattern needs further research. For the purposes of modelling, we assume for now that the UDS is a straightforward tile made with four macro-steps, making a filled-in area of area 0.77 sq deg, and mosaic efficiency E_m=0.93".