WFMOS: a tool for probing dark energy

1. WFMOS: a tool for probing dark energy David Parkinson EDEN in Paris, December 2005

2. BAO as a standard ruler • Acoustic Oscillations are imprinted into the matter power spectra. • Fundamental wavelength fixed at recombination • Can be used as a ‘standard ruler’ to probe geometry and dark energy

3. WFMOS is also a very broadly capable facility instrument: • Studies of large-scale structure • Formation and evolution of galaxies at high redshift • The growth of structure • AGN physics at high redshift • The relation between galaxies and the IGM at high redshift • Stellar pops in LG galaxies • Dark matter distributions via kinematics of LG galaxies • The structure of the LMC disk • Milky Way halo survey at MS • Population III and the dSph’s • Milky Way interstellar medium • Studies of high-velocity clouds • Kuiper Belt objects WFMOS Science • WFMOS has two flagship science programs: • Acoustic oscillations  What is the dark energy? • Galactic archeology  How do galaxies form? (See KAOS Purple Book - http://www.noao.edu/kaos/)

4. ‘Archival’ Science • Additional science from survey data… • Constrain dark energy from cluster counts and Alcock-Paczsynki test • Spectroscopically identify thousands of SNe Ia • Test reciprocity relation dA/dL = (1+z)2 to constrain GR and photon conservation (axion-photon interactions) • Accurately measure luminosity functions & star-formation rate densities with redshift & environment • Constrain shape of primordial power spectrum to 2% and thus mass of the neutrino to 0.1eV (2)

5. ‘Community’ Science • Science from other WFMOS observations… • Detailed studies of local low-luminosity galaxies, down to Mr~-11 (r~24) in the Coma Cluster • High redshift (z>4) studies of galaxies and QSOs selected from multi-color photometry • Observations of M31 and M33 to provide kinematical and abundance information in the bulges and disks • Simultaneously observing QSOs and galaxies (in the same fields) to quantify the relation between the IGM and the large-scale structures as traced by galaxies.

6. WFMOS History • WFMOS is a proposed second-generation Gemini instrument that emerged from the ‘Aspen’ process. • Before that, it was the KAOS conceptual instrument (see http://www.noao.edu/kaos/). • Originally intended for Gemini, the potential technical, financial, observational and strategic advantages of building WFMOS for Subaru, sharing Gemini & Subaru resources, has since been recognized. • The WFMOS feasibility study has lead to a RfP for two competing concept studies, for review Oct/Nov 2006.

7. Target Specifications for WFMOS • Top-level design performance guidelines for WFMOS… • Wavelength range: 0.39–1.0 µm • Field of view: ~1.5 deg diameter • Spatial sampling: ~1 arcsec fiber entrance • Spectral resolution: 1000–40,000 • One-shot coverage: ~0.4 µm (at low resolution) • Simultaneous targets: 4000–5000

8. Advantages of WFMOS • What differentiates WFMOS from other instruments? • Large field area: the FoV of WFMOS is 10x larger than that of any other 8m multi-object spectrograph. • Multiplex: multiplex gain of WFMOS is 5x that of any other 8m MOS (though fiber density is relatively low compared to multi-slit instruments). • Limiting magnitude: with nod & shuffle designed-in, WFMOS is not limited by sky-subtraction systematics when compared to multi-slit instruments. • WFMOS can deliver of order 20,000 spectra per night!

9. Instrument Comparison WFMOS

10. WFMOS FMOS FLAMES

11. WFMOS FoV - Moon and Andromeda

12. Surveys of Large Scale Structure 15 deg ~ 300 Mpc/h at z1 Comparison of MOS fields of view WFMOS FLAMES FMOS DEIMOS VIRMOS GMOS

13. WFMOS Efficiency Advantages Multiplex-limited case (density targets > density of fibers) FoV-limited case (density targets < density of fibers) WFMOS WFMOS

14. WFMOS major science programs

15. Measuring the acoustic oscillations

16. Dark Energy Constraints

17. Optimisation • The Unique Selling Point of BAO is that they act as standard rulers and can probe the dark energy. • Our goal is to get the best possible constraints on the dark energy. • How do we optimize the survey to do this? • Constraining equation of state, w, and its evolution in time is seen as the primary goal.

18. IPSO • Even selecting some parameterization of w (e.g. w(a)=w0+waz/(1+z)) the errors on w of our survey still depends on the fiducial cosmology. • Integrated Parameter Survey Optimization (Bassett 2004; Bassett, Parkinson and Nichol 2005) The Figure of Merit is the integral of the performance (I) over the cosmological parameters. • D-optimality: performance (I) is measured as the determinant of the Fisher matrix of the dark energy parameters (w0, wa) [using Linder expansion w(a)=w0+(1-a)wa].

19. Procedure

20. Optimization Procedure • Select survey configuration (area coverage, redshift bins, exposure time etc.) • Estimate number density of galaxies using LFs. • Estimate error on DA(z) and H(z) using scaling relations. • Calculate Fisher matrix of parameters, using distance data plus other info (Planck+SDSS). • Use Fisher matrix to calculate FoM. • Monte-carlo markov chain search over survey configuration parameter space, attempting to minimize determinant.

21. Survey Parameters • Time: split between the high and low redshift regions. Total time = 1500 hours (expected observing time over three years). • Area: different areas assigned to high and low redshift regions. • Exposure time and number of pointings: generated from area and time. • Redshift binning: Redshift regions broken down into a number of bins.

22. Scaling Relations See paper by Blake, DP, Bassett, Glazebrook, Kunz And Nichol • It is computationally intensive to find full error covariances for power spectrum (requires FFTs). • Computed errors on x and x’ for a grid of survey parameters and derived fitting formula. • For photo-z surveys, assumed Gaussian photometric error r.

23. Fitting Formulae

24. Monte-carlo Markov Chain • We conduct an MCMC search through the parameter space, accepting or rejecting surveys depending on the figure of merit. • To find the optimum survey, have to search over large parameter space (>10 different parameters). • Lots of degenerate minima! • We “heat” and “cool” the chains, attempting to guarantee we reach the global minima.

25. Design Objectives • Using these techniques we can optimize: • The observational area in the low and high redshift regimes • The number of redshift bins in each regime • The redshifts of the bins • The number of spectroscopic fibres • The gain in information from pushing into the redshift desert.

26. Line Emission

27. Continuum

28. Error ellipse

29. Summary • WFMOS is a next generation Multi-Object Spectrograph currently in the design phase. • It will be developed as part of a Subaru-Gemini partnership. • It will dominate seeing-limited survey spectroscopy. • It will enable flagship high-impact science programs, such as the dark energy. • Using IPSO the survey will be optimised to extract information about the dark energy