WFMOS: a tool for probing dark energy

David ParkinsonEDEN in Paris, December 2005

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

– 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 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

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/)

‘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)

‘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.

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.

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

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!

Instrument ComparisonW

FMO

S

WFMOS FoV - Moon and Andromeda

DEIMOS

VIRMOS

FMOS

GMOS

Comparison of MOS fields of view

FLAMES

15 deg ~ 300 Mpc/h at z1

WFMOS

Surveys of Large Scale Structure

WFMOS Efficiency AdvantagesMultiplex-limited case

(density targets > density of fibers)FoV-limited case

(density targets < density of fibers)WFMOS WFMOS

WFMOS major science programs

Measuring the acoustic oscillations

Dark Energy Constraints

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.

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].€

FoM(s) = I(s,θμ )dθμΘ

∫

Procedure

Optimization Procedure

1. Select survey configuration (area coverage, redshift bins, exposure time etc.)

2. Estimate number density of galaxies using LFs.

3. Estimate error on DA(z) and H(z) using scaling relations.

4. Calculate Fisher matrix of parameters, using distance data plus other info (Planck+SDSS).

5. Use Fisher matrix to calculate FoM.6. Monte-carlo markov chain search over survey

configuration parameter space, attempting to minimize determinant.

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.

Scaling Relations

• 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.

€

err(x,x') = err0V0

V

σ rσ r,0

1+neffn

D z0( )2

b02D z( )

2

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟zmz

⎛

⎝ ⎜

⎞

⎠ ⎟γ

z < zm

err(x,x ') = err0V0

V

σ rσ r,0

1+neffn

D z0( )2

b02D z( )

2

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟ z > zm

See paper by Blake, DP, Bassett, Glazebrook, KunzAnd Nichol

Fitting Formulae

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.

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.

Line Emission

Continuum

Error ellipse

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