1 Introduction

Extragalactic Science, Cosmology and Galactic Archaeology with the Subaru Prime Focus Spectrograph (PFS)

Abstract

The Subaru Prime Focus Spectrograph (PFS) is a massively-multiplexed fiber-fed optical and near-infrared 3-arm spectrograph (=2400, 380nm, 1.3 degree diameter hexagonal field), offering unique opportunities in survey astronomy. Following a successful external design review the instrument is now under construction with first light anticipated in late 2017. Here we summarize the science case for this unique instrument in terms of provisional plans for a Subaru Strategic Program of 300 nights. We describe plans to constrain the nature of dark energy via a survey of emission line galaxies spanning a comoving volume of 9.3Gpc in the redshift range . In each of 6 independent redshift bins, the cosmological distances will be measured to 3% precision via the baryonic acoustic oscillation scale, and redshift-space distortion measures will be used to constrain structure growth to 6% precision. In the near-field cosmology program, radial velocities and chemical abundances of stars in the Milky Way and M31 will be used to infer the past assembly histories of spiral galaxies and the structure of their dark matter halos. Data will be secured for stars in the Galactic thick-disk, halo and tidal streams as faint as , including stars with to complement the goals of the Gaia mission. A medium-resolution mode with to be implemented in the red arm will allow the measurement of multiple -element abundances and more precise velocities for Galactic stars, elucidating the detailed chemo-dynamical structure and evolution of each of the main stellar components of the Milky Way Galaxy and of its dwarf spheroidal galaxies. The M31 campaign will target red giant branch stars with 21.522.5, obtaining radial velocities and metallicities over an unprecedented area of 65 deg. For the extragalactic program, our simulations suggest the wide wavelength range of PFS will be particularly powerful in probing the galaxy population and its clustering over a wide redshift range. We propose to conduct a color-selected survey of galaxies and AGN over 16 deg to 23.4, yielding a fair sample of galaxies with stellar masses above at . A two-tiered survey of higher redshift Lyman break galaxies and Lyman alpha emitters will quantify the properties of early systems close to the reionization epoch. PFS will also provide unique spectroscopic opportunities beyond these currently-envisaged surveys, particularly in the era of Euclid, LSST and TMT.

Subject headings:
PFS — cosmology — galactic archaeology — galaxy evolution

Subaru PFS] Extragalactic Science, Cosmology and Galactic Archaeology with the Subaru Prime Focus Spectrograph (PFS)

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1. Introduction

There is currently a major expansion in survey imaging capability via the use of CCD and near-infrared detector mosaics on a wide range of ground-based telescopes. Such imaging surveys provide accurate photometric and other data to enable the study of gravitational lensing signals which trace the distribution of dark matter and to conduct census studies of Galactic structures and distant star-forming galaxies. For over a decade it has been recognized that a similar revolution would be provided by a massively-multiplexed spectrograph on a large aperture telescope. Spectra provide precise radial velocities, metallicities and emission line properties for faint and distant sources and enable additional probes of cosmology. The main challenge in realizing this second revolution has been access to a wide field telescope, essential for efficient multi-object spectroscopy of panoramic fields, and the cost of implementing the appropriate instrumentation.

A proposal to construct a Subaru Prime Focus Spectrograph (PFS) emerged following the cancellation in May 2009 of the Gemini-sponsored Wide-Field Multi-Object Spectrometer (WFMOS). WFMOS was envisaged as a facility instrument on the Subaru telescope sharing the optics designed for the new prime focus camera, Hyper Suprime-Cam (HSC). Two teams received Gemini funding for a conceptual design study of WFMOS and, prior to cancellation, a team led by Caltech and the Jet Propulsion Laboratory (JPL) secured preliminary approval. Soon after, however, the Gemini Board indicated they did not have sufficient funding to proceed and the WFMOS project was terminated.

The Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU) at the University of Tokyo submitted a proposal for stimulus funding to the Japanese government in September 2009 using design concepts pioneered in the WFMOS study led by Caltech and JPL. The successful outcome of this proposal in early 2010 initiated the present PFS partnership which now includes Caltech/JPL, Princeton and Johns Hopkins Universities, the Laboratoire d’Astrophysique de Marseille, Academia Sinica Institute of Astronomy & Astrophysics (ASIAA) Taiwan, the University of São Paulo and the Laboratorio Nacional de Astrofísica in Brazil.

In addition to the leadership funding provided by Kavli IPMU, four important milestones have enabled progress and led to the decision to commence construction. Firstly, in January 2011 the Subaru Users Meeting endorsed the PFS project as a next-generation instrument for the Subaru Prime Focus, recognizing the international PFS team and its responsibilities. This decision led to the establishment of a PFS project office at Kavli IPMU in early 2011 and an allocation of funds and manpower by the National Astronomical Observatory of Japan (NAOJ) towards integration, commissioning and survey operations. A second milestone followed the MOU in December 2011 between the Director-General of NAOJ and the Director of Kavli IPMU, that anticipates a Subaru Strategic Program for PFS providing up to 300 nights of observing time for the PFS team in collaboration with the Japanese astronomical community. These developments provided the essential impetus for the science plans and technical requirements defined in this article. The third milestone was a successful Conceptual Design Review (CoDR) held in March 2012 which triggered the decision to commence construction with first light anticipated in 2017. The fourth milestone was a successful Preliminary Design Review (PDR) held in Feb 2013. The CoDR and PDR documentations included a detailed science case for PFS and a list of technical requirements. This article reproduces these for general interest.

Figure 1.— A brief overview of the baseline design of PFS instruments, which consist of components Wide Field Corrector, Field Rotator, Prime Focus Unit, and Fiber Positioner. A Fiber Connector relays light to four identical fixed-format 3-arm twin-dichroic all-Schmidt Spectrographs providing continuous wavelength coverage from 380nm to 1.26m.

This article is not intended to provide a technical description of PFS but a brief overview is helpful (see Fig. 1). Further technical details of the instrument and its current design can be found at http://sumire.ipmu.jp/en/2652 (Sugai et al., 2012). PFS is designed to allow simultaneous low and intermediate-resolution spectroscopy of 2400 astronomical targets over a 1.3 degree diameter hexagonal field. It shares the Wide Field Corrector and associated Field Rotator and Hexapod already constructed for the HSC. An array of 2400 optical fibers is in the Prime Focus Instrument and each fiber tip position is controlled in-plane by a two-stage piezo-electric Fiber Positioner Cobra system. Each fiber can be positioned within a particular patrol region such that these patrol regions fully sample the 1.3 degree field. A Fiber Connector relays light to four identical fixed-format 3-arm twin-dichroic all-Schmidt Spectrographs providing continuous wavelength coverage from 380nm to 1.26m. The blue and red channels will use two Hamamatsu 2K4K edge-buttable fully-depleted CCDs (as in HSC). The near-infrared channel will use a new Teledyne 4RG 4K4K HgCdTe 1.7m cut-off array. We also plan to have a medium resolution mode with for the red channel, which is feasible by using a simple grating/grism exchange mechanism at the red-channel spectrograph.

The present article describes the detailed scientific case for PFS in the context of a Subaru Strategic Program (SSP) of 300 nights of observing time. Since such a program would not be implemented until 2017 at the earliest, the main motivation in formulating the team’s plans at this stage is in providing a list of key science requirements for the technical design. In Sections 24 we describe 3 key components of the science case for PFS that will likely form the basis of the Subaru Strategic Program. For each of these 3 cases we provide a summary, a detailed science justification and survey strategy as well as the flow-down from these to the technical requirements for the instrument. We summarize these science requirements for PFS in more detail in Section 5 and discuss some outstanding issues in Section 6.

2. Cosmology

Summary: PFS will be remarkably powerful in spectroscopic surveys of faint galaxies because of its large multiplex gain and the 8.2 meter aperture of the Subaru telescope. The extended wavelength coverage provided by the red and near-infrared spectrograph arms (650 – 1260 nm) will permit a unique survey of [O ii] emission-line galaxies extending over the redshift range . As large-scale structures remain in the linear regime at high redshift, such a survey will give detailed new information on the cosmological parameters as well as the growth rate of structure formation. This combination will provide a valuable test of alternative models of gravity on large scale which may provide a possible explanation for dark energy. Multi-color data planned to arrive from the HSC imager will be used to select target galaxies for spectroscopy and the expected high throughput should yield a 75% success rate of detecting [O ii] emission at . Herein, we propose to conduct a 100  night cosmological survey over 1400 deg, sampling galaxies within a comoving volume of 9 over . This will complement the lower redshift survey being undertaken by the SDSS BOSS collaboration.

The primary goals of the PFS cosmology survey are to: (1) measure the Hubble expansion rate and the angular diameter distance to 3% fractional accuracies in each of 6 redshift bins over via the baryonic acoustic oscillation (BAO) method, (2) use the distance measurements for determining the dark energy density parameter to about 7% accuracy in each redshift bin, when combined with lower redshift BAO measurements, (3) use the geometrical constraints to determine the curvature parameter to accuracy, and (4) measure the redshift-space distortion (RSD) in order to reconstruct the growth rate of large-scale structure to 6% accuracy since a redshift . These PFS measurements of the large scale galaxy distribution can be combined with complementary weak lensing information from the HSC survey in order to significantly improve the cosmological and structure growth constraints and reduce uncertainties arising from galaxy bias and nonlinear effects that are otherwise major sources of systematic error in spectroscopic surveys.

2.1. Cosmology Objectives

The accelerated expansion of the Universe is the most intriguing problem in cosmology. It either requires the introduction of a mysterious form of energy, “dark energy”, or it could signal a breakdown of Einstein theory of General Relativity on cosmological scales. To distinguish between these and other possibilities requires precise observational constraints on both the expansion history of the universe and the growth rate of large-scale structure.

Measurements of galaxy clustering statistics are one of the most powerful means of addressing the nature of dark energy. The tight coupling between baryons and photons prior to the decoupling epoch of leaves a characteristic imprint on the pattern of galaxy clustering on large scales – the so-called baryonic acoustic oscillation (BAO) scale. As the BAO length scale is precisely constrained to be Mpc from cosmic microwave background (CMB) experiments (Komatsu et al., 2011; Planck 2013 Results XVI, 2013), it offers a standard ruler by which we can infer the angular diameter distance and the Hubble expansion rate from the observed correlation function of the galaxy distribution. The BAO scale is in the linear or weakly-nonlinear density regime and thus provides a robust geometrical test. Furthermore, if uncertainties arising from galaxy bias can be removed or accurately modeled, we can use the amplitude and shape information of the galaxy correlation function in order to constrain cosmological parameters as well as the growth rate of structure formation.

Recognizing this, the main scientific questions we seek to address with the PFS cosmology survey are:

  1. Is the cosmic acceleration caused by dark energy or does it represent a failure of Einstein’s theory of gravity on cosmological length scales?

  2. What is the physics of the early universe that generates the primordial fluctuations as the seed of large-scale structures?

To address these fundamental questions, the main goals for the PFS cosmology survey are to:

  • Constrain the angular diameter distance and the Hubble expansion rate via the BAO experiment to a precision comparable with, or better than, existing, ongoing or planned BAO surveys.

  • Derive the BAO constraints in a redshift range that is complementary to those probed by the existing or planned BAO surveys on the time scale of the PFS survey.

  • Utilize the unique capabilities of the 8.2m Subaru Telescope and the PFS spectrograph for maximizing cosmological science.

  • Use the shape and amplitude of galaxy correlation function in order to constrain cosmological parameters as well as the growth rate of structure formation.

  • Combine the weak lensing information, delivered from the HSC survey, with the PFS cosmology survey in order to improve the cosmological constraints by calibrating systematic uncertainties that cannot be resolved by either of the PFS and HSC surveys alone.

2.2. PFS Cosmology Survey

Number of fibers 2400 (600 for each spectrograph)
Field of view 1.3 deg (hexagonal – diameter of circumscribed circle)
Field of view area 1.098 deg
Fiber diameter 1.13 diameter at the field center; 1.03 at the edge
Blue arm Red arm IR arm
Wavelength coverage [nm] 380–670 650–1000 970–1260
Spectral resolution 1900 2400 3500
Pixel scale [Å/pix] 0.71 0.85 0.81
Read-out noise [e rms/pix] 3 3 4
Detector type/read-out mode CCD CCD HgCdTe/SUTR
Thermal background [e/pix/sec] None None 0.013
Dark current [e/pix/sec] 0.01
Spectrograph image quality [m rms/axis] 14 14 14
Sky continuum 21.56 mag AB/arcsec @ 1 m at zenith
OH line brightness 16.6 mag AB/arcsec @ band at zenith
Moonlight None (dark time)
Atmospheric extinction Variable; continuum is 0.05 mag/airmass @ m
Instrument throughput Based on the Preliminary Design Review studies
Grating wings Lorentzian with of the true number of lines
Diffuse stray light 2% of the total light reaching the detector
Sky subtraction residuals 2% per pixel
151617

Note. – PFS instrumentation parameters and associated assumptions used for estimating an expected signal-to-noise ratio for an observation of emission-line galaxies.

Table 1Instrumentation parameters

Here we describe the parameters of the PFS cosmology survey that are required to meet the above scientific goals.

Firstly, we will consider which type of galaxies to target with PFS. Given the optical and near infrared wavelength coverage of PFS, [O ii] emission-line galaxies (ELG; [O ii] =3727Å) are particularly useful tracers allowing an efficient survey out to high redshift beyond , a redshift range that is difficult to probe with 4m-class telescopes. Luminous red galaxies (LRGs) are a further potentially-useful tracer of large-scale structure as studied by the SDSS survey, but at they reveal weaker spectral features and are less abundant per unit volume. In the following we focus on ELGs to explore an optimal survey design. We may retain LRGs in future considerations of our survey plans, but their study is not required to meet the PFS cosmology objectives defined above.

Sensitivity of the PFS spectrograph

Figure 2.— Expected signal-to-noise () ratio for measuring the [O ii] emission line as a function of redshift; the blue, green and red curves show the results for the PFS blue, red and IR arms in Table 1, respectively, for an total emission line flux of erg/cm/s. To properly account for the uncertainties, we assumed the instrumentation parameters of the current baseline design listed in Table 1, an observation at the edge of the focal plane, and included the sky emission/absorption and the Galactic dust extinction of and 26 degrees for the zenith angle of the telescope. This computation assumes 15 min total exposure (split into two exposures; ), km/s for the velocity dispersion (the intrinsic line width), and 0.8 for the seeing FWHM. We also accounted for the finite galaxy size relative to the seeing profile and the fiber size, assuming an exponential profile with scale radius 0.3 for the emission-line region (about 3.5 kpc for a galaxy at ). Note that is estimated by the root-sum-square of the spectral pixels (i.e. it is a matched filter combining both doublet members). The current design allows a significant detection of [O ii] emission line over a wide range of redshift, up to with near-equal sensitivities of the red and NIR arms.

To estimate the feasibility of PFS for a wide-field survey of ELGs, we have studied the expected performance of measuring a [O ii] line of a galaxy in our targeted redshift range for a representative exposure time during the dark lunar phase. In doing so, we properly account for the sky emission (continuum plus OH emission lines) and absorption as well as the instrumentation parameters for the current baseline design (as listed in Table 1).

Fig. 2 shows the expected signal-to-noise ratio of the [O ii] line as a function of redshift, measured with each of the blue, red and near-infrared (NIR) arms of PFS. As a working example, here we assume for the total flux of the [O ii] doublet, 15min for the exposure time, 0.8 seeing size and for the Galactic dust extinction, respectively. The galaxy radial profile is assumed to be an exponential disk with a half-light radius of 0.3 (about 3.5 kpc for a galaxy at ). Note that for the galaxy yield forecasts, we use half-light radii from the COSMOS Mock Catalog (Jouvel et al., 2011), and re-compute the fiber aperture correction for each galaxy.18 We have assumed the 15 minute integration is split into 2 sub-exposures for cosmic ray (CR) detection in the CCD channel. The NIR channel will perform CR rejection by processing of the frames acquired during sample-up-the-ramp (SUTR) mode. The cosmology ETC assumes 4 read noise per sub-exposure (appropriate for samples along a 450sec ramp). We will probably not reset the NIR channel in between sub-exposures, so we assume an overall read noise of per pixel for the following study.

In addition to throughput and sky brightness considerations, we have considered several other potential limitations. Their amplitude is difficult to estimate, but they have been important for previous spectrographs and so we make an explicit allowance for them so as to adopt a conservative approach. The systematic sky subtraction residuals and small-angle stray light are very important factors in the study of galaxy spectra where [O ii] is partially blended with a sky line. Diffuse stray light is a concern when [O ii] lies in a cleaner part of the NIR spectrum.

  • Systematic sky subtraction residuals – These are modeled by adding a “noise” term corresponding to some percentage of the sky counts in each spectral pixel. We currently set this to 2% of the brightest of the pixel and its neighbor on either side (equivalent to 1% sky subtraction accuracy on a 4-pixel resolution element).

  • Small-angle stray light – We assign to the grating an effective number of lines that is of the actual number.

  • Diffuse stray light – We take 2% of the OH line flux incident on the detector and uniformly spread it over all pixels. (This may be appropriate for a detector that reflects 10% of the incident radiation, and then there are many surfaces that could potentially reflect this radiation back. Refining this parameter will be a priority since the forecasts degrade rapidly if it gets worse.)

Continuing our conservative approach, we assumed the instrumentation throughput at the edge of the focal plane and 26 degrees for the zenith angle. (The latter corresponds to observations at declination 5S, the southern boundary of the HSC survey region, and hours away from transit.)

Fig. 2 shows that the current design of PFS allows a significant detection of the [O ii] line over a wide range of redshift, up to . Most importantly, the baseline design provides near-equal sensitivity of the red and NIR arms for measuring the [O ii] line for the same exposure time. Hence PFS can execute a cosmological survey very efficiently over a wide range of redshift, provided sufficiently bright ELGs are available for study (see below).

In the following analysis, we set a threshold of (matched filter) for detection of an ELG. In principle, it may be possible to accept less significant detections. However given the uncertainties in the airglow and the early stage of the instrument design, we consider it prudent to leave some margin in .

Target selection of emission-line galaxies

Figure 3.— Left panel: The distribution of objects in the COSMOS Mock Catalog in the color-magnitude diagram. Right: The fraction of objects in each cell that are ELGs with [O ii] doublets detectable at in PFS in min exposures. The third dimension () is not shown on this 2D plot, but allows us to select lower or higher redshift galaxies within the PFS survey range.
Figure 4.— The sensitivity of PFS (green curve; 8.5, s exposures, dark time) to the [O ii] doublet at and 1:1 line ratio, versus the selected targets (red points). Note that the redshift corresponds to the long wavelength end of the NIR arm. Most targets will yield successful redshifts, but some are lost within the atmospheric emission or absorption lines, a few are at , and there is a small number of faint blue nearby objects (lower-left corner) for which we cannot detect [O ii]. Note that the line ratio () and effective radius are re-computed for each galaxy in the COSMOS Mock Catalog, and hence the sensitivity curve drawn does not correspond to an exact boundary between detections and non-detections.

We now address how to optimally select ELGs as suitable targets in the proposed redshift range. We will assume that we can use the multi-color imaging data of the planned HSC survey which will be executed ahead of the PFS survey. The currently-planned HSC survey will reach ( for a point source and 2” aperture), in the 5 passbands over square degrees.

As seen in Fig. 2, if we target ELGs over the wide redshift range , the wide wavelength coverage of red and NIR arms allows a very efficient selection of [OII] emission-line galaxies. A color cut is ideal for selecting galaxies in this redshift range: if an object is blue (), then it likely has no spectral breaks in the and bands – this means the redshift is high enough for the Balmer/4000Å break to have redshifted beyond the band, but the Lyman break has not yet entered the band. Furthermore, implies a blue rest-frame UV slope, which has a strong correlation with the star-formation activity that produces [O ii] emission.

To estimate the efficiency of various target selection algorithms, we used the COSMOS Mock Catalog (Jouvel et al., 2011), where fluxes of various emission lines of each galaxy are estimated based on physical parameters (SFR, stellar mass and metallicity) using the COSMOS 30 passband photometric data and zCOSMOS spectroscopic data. We have chosen the preliminary target selection cuts:

(1)

The HSC depth ( mag AB at 5) is sufficient to find the target galaxies and to provide accurate and colors. The ELGs in the redshift range are primarily selected from the color cut , and the -magnitude cut gives preference to bright objects while reducing low-redshift contamination, as can be seen in Fig. 3. The condition on for fainter magnitudes is designed to tilt the redshift distribution in favor of more objects at . We can further divide the targets into a “bright subsample” () and a “faint subsample” (), with the brighter targets prioritized when we wish to increase the success rate.

In the COSMOS Mock Catalog there are target galaxies available per PFS field-of-view (1.098 deg for the 1.3 FoV diameter). Hence there are a sufficient number of target galaxies compared to the number of fibers (=2400) for the baseline design. The green-solid curve in Fig. 4 shows the redshift dependence of [O ii] flux with for a 15 minutes exposure. To estimate the expected for each galaxy, we employed the same method used in Fig. 2 and also used the galaxy size information and [O ii] doublet ratio available from the COSMOS mock catalog.

Assuming 2400 fibers in the focal plane as in Table 1 and using the results in Fig. 3, we can estimate a success rate of finding [O ii] emission-line galaxies among the target galaxies. We show the redshift and [O ii] flux distributions of the targets in Fig. 4, and the redshift histogram of the successful [O ii] detections in Fig. 5. Of the targets, 74% have successful [O ii] detections, 6% are faint blue local () objects, 6% fail due to an [O ii] feature that falls off the red end of the spectrograph, and the remaining 14% fail due to some combination of too faint [O ii] feature or overlap with an atmospheric emission or absorption complex. To have a sufficiently dense sampling of galaxies to trace large-scale structures in each redshift slice, we will need multiple visits of each field; our BAO forecasts found that 2 visits gave the best constraints.

Figure 5.— The distribution of successful redshifts ([O ii] detected at ) for the proposed PFS cosmology survey, including breakdown into the two visits. The jagged features in the curves reflect the effect of sampling variance of large-scale structures in the COSMOS field due to the finite survey area (the mock is based on the data of 1.24 square degrees). We refer to the two visits as “Visit A” and “Visit B” (see text for details), respectively, where we preferentially select brighter targets with in Visit A in order to have some flexibility between dark/grey nights.

To obtain a reliable estimate of the number of observable targets, we took into account the fiber allocation efficiency assuming a Poisson distribution of target galaxies on the sky, which should be a good approximation for a given wide redshift coverage. We conservatively assume non-overlapping patrol zones between the different fibers.19 The fiber assignment algorithm is designed to put the easier, i.e. brighter, targets in one of the visits (“Visit A”) and then the harder targets that require better conditions in another (“Visit B”). We divide our targets into two tiers – the bright () and faint () subsamples. The fiber assignment logic within each patrol zone is then:

  • If at least two bright targets are available, one is assigned to Visit A and another to Visit B.

  • If one bright target and at least one faint target are available, then the bright target is observed in Visit A and one of the faint targets is observed in Visit B.

  • If one bright target and no faint targets are available, then the bright target is observed in Visit A and the fiber becomes a sky fiber in Visit B.

  • If more than two bright targets, although unlikely, are available, then the brightest target is observed in Visit A and the next brightest target is observed in Visit B.

  • If no bright targets are available and there are at least two faint targets, then a faint target is observed in both Visits A and B.

  • If no bright targets are available and there is only one faint target, then the fiber becomes a sky fiber in Visit A and the faint target is observed in Visit B.

  • If no targets are available, then the fiber is a sky fiber in both Visits A and B.

This algorithm produces a roughly balanced fraction of sky fibers in the two visits. The predicted allocations of the fibers are:

  • Visit A: 85% bright targets, 6% faint targets, 9% sky.

  • Visit B: 56% bright targets, 33% faint targets, 11% sky.

Thus this leaves about 240 sky fibers in each visit for calibrating the sky spectrum.

Note that the two visits could be scheduled in either order. Since Visit A has the brighter targets, it can achieve a high success fraction under worse conditions than Visit B. We have therefore assumed that Visit B takes place during dark time, whereas Visit A is scheduled on a night of 7 days from the New Moon (but at least away from the moon). The exposure times in both cases are kept at sec. The predicted redshift success rate for a threshold is 75% (Visit A)20 or 73% (Visit B).

An alternative to the baseline (using gray time for Visit A) would be to use dark time only for the cosmology survey, and shorten the exposure time for Visit A, thereby reducing the total number of nights required but using time that may be in high demand by other programs. This trade will be made when we design an integrated observing schedule for PFS.

bias
redshift per field Mpc Mpc
0.59 85 1.9 1.18 0.74 0.25
0.79 358 6.0 1.26 2.23 0.74
0.96 420 5.8 1.34 2.10 0.68
1.09 640 7.8 1.42 2.64 0.87
1.19 491 5.5 1.50 1.78 0.59
2.58 598 3.1 1.62 0.95 0.31
2.71 539 2.7 1.78 0.76 0.25

Note. – The leftmost column shows the redshift range of each slice, and the other columns show the comoving volume (), the number of [OII] galaxies per field (), the mean comoving number density (), the linear bias parameter () and the values of at and for each slice, respectively. The survey volume is for a survey area of square degrees, which is estimated assuming 15 min of open-shutter time per visit, 2 visits per field, 3 min overhead per visit, and 100 clear nights. For comparison, the BOSS BAO survey has the survey parameters: sq. degrees area coverage over , , , and .

Table 2PFS Cosmology Survey Parameters

Survey Strategy

Using the results of target selection in Fig. 5, we have adopted parameters for the PFS cosmology survey summarized in Table 2. Since our primary observable is the galaxy two-point correlation function or the galaxy power spectrum, the key factors that govern the results are the geometrical volume surveyed and the ratio of clustering power to shot noise, . To have a galaxy power spectrum measurement that reaches the sampling variance limit for our volume and is not degraded by shot noise, the number density of galaxies must satisfy at BAO scales. As given by the columns of Table 2, the PFS survey we are proposing has and slightly less than 1 at and , respectively, over the entire target redshift range. With only one visit per field, these numbers are about a factor 2 smaller than in Table 2. On the other hand, if we have more than two visits, the survey area we can cover for a given number of nights becomes smaller. Incorporating multiple visits ensures more flexibility in optimizing the survey, for example in including a mixture of targets in different magnitude ranges.

We have assumed that the bias factor for the ELGs is given by . This specific function was a fit to semi-analytic models (Orsi et al., 2010), but compares very well to real data: e.g. the DEEP2 “main blue” sample has a measured bias of at (Coil et al., 2008).21 We have much less information about clustering of ELGs at redshifts beyond the DEEP2 survey, but H emitters at have a correlation length of Mpc (Sobral et al., 2010), implying a bias of .

The power spectrum measurement accuracy depends also on the area coverage. In order for the PFS survey to have a constraining power on cosmological parameters comparable with the existing or planned BAO surveys, we need a sufficiently large area coverage. We have found that, if about 100 clear nights are allocated to the PFS cosmology survey, it can meet our scientific goals. Hence we assume 100 clear nights for the following analysis, and the total area covered is estimated as

(2)

Here we conservatively assumed 3min overhead for each new pointing, which covers readout, slewing and the time for accurate fiber positioning, and assumed that 8 hours per night are available for observation on source. The comoving volume in each redshift slice is given in Table 2. The total volume is about , a factor 2 larger volume than the SDSS BOSS galaxy survey, which is about . A notable strength of the PFS survey is that it probes large-scale structure in higher redshifts, where the fluctuations are largely in the linear regime and therefore allow a cleaner estimation of cosmological parameters. In fact the genuine cosmological power comes from the volume in Fourier space; the effective volume at each wavenumber is given as , where is the comoving volume. The total number of the Fourier modes usable for constraining cosmology is estimated by integrating the effective volume in Fourier space up to the maximum wavenumber which is determined such that the theoretical model to be compared with the measurement is reliable up to . The larger the redshift, the higher the wavenumber we can use, because the nonlinear scale becomes smaller (higher ). Hence, the proposed PFS survey offers much more than a factor 2 improvement compared to the BOSS constraint (e.g., Anderson et al. 2012). Although Table 2 also gives estimates for the lower redshift slice , which partially overlaps the ongoing BOSS and WiggleZ surveys, the cosmological constraining power of this slice is not as great due to the smaller areal coverage and reduced galaxy number density. However, we consider it important to retain this redshift slice as it can give a useful benchmark in comparison with other surveys such as the BOSS and WiggleZ surveys, particularly for calibrating systematic issues.

Expected cosmological constraints

We now can estimate the power of the PFS cosmology survey in Table 2 for constraining cosmological parameters. To ensure a fair comparison with other surveys, we primarily assess the power of PFS survey in terms of its BAO geometrical constraints.


Geometrical constraints:
The galaxy two-point correlation function is measured as a function of the separation between paired galaxies. The position of each galaxy needs to be inferred from the measured redshift and angular position. Then the separation lengths perpendicular and parallel to the line-of-sight direction from the measured quantities are given as and , where and are the differences between the angular positions and the redshifts of the paired galaxies. For this conversion, we need to assume a reference cosmological model to relate the observables (, ) to the quantities . Thus, the wavenumbers are given as

(3)

The quantities with subscript “ref” are the quantities estimated from the observables assuming a “reference” cosmological model, and the quantities without the subscript are the underlying true values. Since the reference cosmological model assumed generally differs from the underlying true cosmology, it causes an apparent distortion in the two-dimensional pattern of galaxy clustering. In principle, the distortion could be measured using only the anisotropy of clustering statistics (Alcock & Paczynski, 1979), but a more robust measurement can be obtained using features in the power spectrum, particularly if they are at a known scale so that we can measure both and . In particular, the CMB-inferred BAO scale of 150 Mpc gives a powerful standard ruler for this geometrical test (Eisenstein et al., 2005; Percival et al., 2007; Blake et al., 2011; Hu & Haiman, 2003; Seo & Eisenstein, 2003).

The use of this scale without edge effects in a survey field requires the survey to be contiguous on a scale large compared to the BAO length; at our minimum redshift (), 2.5 BAO lengths corresponds to 7.5 degrees on the sky, so we set this as our minimum width. This requirement will be refined further by simulations.

In more detail, the galaxy power spectrum in redshift space is given in the linear regime as

(4)

where is the linear bias parameter, is the linear redshift-space distortion (RSD) parameter, defined as (Kaiser, 1987), is the linear growth rate, is the linear mass power spectrum, and is a parameter to model the residual shot noise. We can use the BAO features in the linear power spectrum as a standard ruler in order to constrain and . The BAO constraints are relatively robust against the galaxy bias uncertainty and the other nonlinearity effects, because none of the systematic effects introduces any particular length scale comparable with the BAO scale. Further, if we can use the shape and amplitude information in the galaxy power spectrum, we can constrain the growth rate as well as other cosmological parameters such as the neutrino mass and the primordial power spectrum parameters (Takada et al., 2006), as we will discuss below.

To make the parameter forecast, we have used the method developed in Seo & Eisenstein (2007). In this method, we include the smearing effect of the BAO features due to the bulk flow of galaxies in large-scale structure (Matsubara, 2008; Taruya et al., 2009; Nishimichi & Taruya, 2011). For the BAO survey of multiple redshift bins, the Fisher information matrix of model parameters can be computed as

(5)

where is the cosine between the wavevector and the line-of-sight direction, ; is the sum over different redshift bins; is the partial derivative of the galaxy power spectrum (Eq. 4) with respect to the -th parameter around the fiducial cosmological model; the effective survey volume and the Lagrangian displacement fields and to model the smearing effect are given as

(6)
(7)
(8)

Here is the comoving volume of the redshift slice centered at ; the present-day Lagrangian displacement field is for (Eisenstein et al., 2007); is the growth rate normalized as ; . The parameter is a parameter to model the reconstruction method of the BAO peaks (see below). In Eq. (5), we take the exponential factor of the smearing effect outside of the derivatives of . This is equivalent to marginalizing over uncertainties in and . The growth rate in or takes into account the smaller smearing effect at higher redshift due to the less evolved large-scale structure. For the parameters, we included the cosmological parameters, the distances in each redshift slice, and the nuisance parameters:

(9)

where , and are parameters of the primordial power spectrum; is the amplitude of the primordial curvature perturbation, and and are the spectral tilt and the running spectral index. The set of cosmological parameters determines the shape of the linear power spectrum. By using the method above, we can estimate the cosmological distance information solely from the BAO peaks, including marginalization over modeling uncertainties in the broad-band shape of the power spectrum. For the -integration, we set and for all the redshift slices, but the exponential factor in Eq. (5) suppresses the information from the nonlinear scales. The Fisher parameter forecasts depend on the fiducial cosmological model, for which we assumed the model consistent with the WMAP 7-year data (Komatsu et al., 2011).

Further, we assume that we can implement the promising method of Eisenstein et al. (2007) for improving the BAO measurements. Since the peculiar velocity field of galaxies in large-scale structure can be inferred from the measured galaxy distribution, the inferred velocity field allows us to pull back each galaxy to its position at an earlier epoch and then reconstructing the galaxy distribution more in the linear regime. As a result, one can correct to some extent the smearing effect in Eq. (5) and sharpen the BAO peaks in the galaxy power spectrum. Recently, Padmanabhan et al. (2012) implemented this method with real data from the SDSS DR7 LRG catalog, and showed that the reconstruction method can improve the distance error in the BAO scale by a factor of 2. The improvement was equivalent to reducing the nonlinear smoothing scale from to , about a factor 2 reduction in the displacement field. To implement this reconstruction method requires a sufficiently high number density of the sampled galaxies in order to reliably infer the peculiar velocity field from the measured galaxy distribution. Each redshift slice of the PFS survey (see Table 2) satisfies the requirement; the number density of galaxies in each redshift slice is higher than that of both the SDSS DR7 LRGs () and the BOSS LRGs (). Hence we can safely assume that the reconstruction method can be applied to the PFS BAO experiment. In the Fisher matrix calculation, we used for an implementation of the reconstruction method22.

Finally, we have used the CMB information expected from the Planck satellite experiment (Planck 2013 Results XVI, 2013), which gives a precise constraint on the sound horizon scale in order for us to use the BAO scale as a standard ruler. In addition to the cosmological parameters (), we included, in the CMB Fisher matrix, (the optical depth to the last scattering surface) and (the angular diameter distance to the last scattering surface). Then we can compute the Fisher matrix for the BAO experiment by adding the galaxy and CMB Fisher matrices; . The dimension of the Fisher matrix for the PFS survey in combination with the Planck information is (see Eq. 9). When further combined with the SDSS and BOSS BAO information (Eisenstein et al., 2005; Anderson et al., 2012), the dimension of the Fisher matrix increases accordingly.

Figure 6.— Fractional errors in the angular diameter distance and the Hubble expansion rate via the PFS BAO experiment (see Table 2) including marginalization over uncertainties of other parameters. The expected accuracies are compared to the existing and ongoing SDSS and BOSS surveys. The PFS survey will provide geometrical constraints to higher redshift than the SDSS and BOSS surveys, but with comparable precision. The solid curve in each panel shows the fractional difference when changing the dark energy equation of state parameter from the fiducial model to .

Fig. 6 shows the expected accuracies of determining the angular diameter distance and the Hubble expansion rate in each redshift slice with the PFS cosmology survey (Table 2). The errors include marginalization over uncertainties of other parameters. The PFS forecasts can be compared with the accuracies of the existing and ongoing SDSS/BOSS surveys. As can be clearly seen, the PFS cosmology survey can constrain and over a wider range of redshift, yet with similar precision to, the SDSS and BOSS surveys. Even though the PFS area coverage is smaller than that of SDSS or BOSS surveys by a factor of 7 (1400 vs. 10000 sq. degrees), the PFS survey covers a factor 10 and 2 times larger comoving volume than the SDSS and BOSS surveys, respectively.

Cosmological implications:
It is worth noting that the BOSS survey will measure the clustering statistics of the Lyman- forest over (Slosar et al., 2013). PFS thus serves to fill a natural ‘gap’ in-between the galaxy and Lyman- BAO experiments, allowing us to probe the expansion history over the entire range of redshifts, , i.e. through the period where it is believed that the cosmic expansion went from decelerated to accelerated phases. If we model the expansion history as parametrized by the dark energy model () (Linder, 2003) and the curvature parameter (),

(10)

we can propagate the distance measurement errors into the accuracies of estimating the parameters. To be more explicit, we can do this, based on the Fisher information matrix formalism, by projecting the BAO Fisher matrix onto different parameter space:

(11)

Here the new set of parameters is given as , which specifies the cosmic expansion history given by the above equation, and is the sub-matrix computed by inverting the sub-matrix of the inverse of the full BAO matrix, , containing only the parts of the geometrical parameters, . Hence the derived constraints on include marginalization over other parameters such as the galaxy bias and the parameters. Table 3 shows the expected accuracies of the dark energy parameters and the curvature parameter for the PFS survey. Here is the dark energy equation state at the “pivot” redshift, at which the dark energy equation of state is best constrained for a given survey. The quantity is the dark energy figure-of-merit defined in the Dark Energy Task Force Report (Albrecht et al., 2006), which quantifies the ability of a given survey to constrain both and ; , which is proportional to the area of the marginalized constraint ellipse in a sub-space of . Table 3 clearly shows that the PFS BAO can significantly tighten the parameter constraints over the SDSS and BOSS surveys. Most interestingly, the PFS has the potential to constrain the curvature parameter to a precision of 0.3%. If we can detect a non-zero curvature, this would represent a fundamental discovery giving critical constraint into the physics of the early universe, for example insight into different inflation scenarios (Efstathiou, 2003; Contaldi et al., 2003; Freivogel et al., 2006; Kleban & Schillo, 2012; Guth & Nomura, 2012).

Figure 7.— Expected accuracy of reconstructing the dark energy density parameter at each redshift, from the BAO-measured and in Fig. 6. Here we considered the cosmological constant (constant) and the flat universe () as the fiducial model. Adding the PFS BAO constraints to the SDSS and BOSS constraints enables reconstruction of the dark energy density to , and also significantly improves the precision at low redshifts, as the comoving distance at the high redshift arises from an integration of . The solid curve shows the energy density parameter for the fiducial CDM model, while the dashed curve shows the redshift evolution for an early dark energy model in Droan & Robbers (2006), where we employed and for the model parameters (see text for details).
Survey  [eV]
SDSS+BOSS 0.0061 0.076 1.2 11 0.0071 0.188 16
SDSS+BOSS+PFS 0.0051 0.059 0.36 47 0.0030 0.133 11

Note. – The constraints on and are from the BAO distance measurements in Fig. 6, i.e. not including the information on the broad-band shape of the galaxy power spectrum. Note that is the dark energy equation state at the “pivot” redshift, at which the dark energy equation state parameter is best constrained for the given PFS BAO measurements. The constraints on the neutrino mass and are derived by including the broad-band shape information. See the text for details.

Table 3 Forecasted accuracies of cosmological parameters

Nature of dark energy:
The parametrization adopted for the dark energy equation of state samples only a narrow range of dark energy models. Given that there is no well-accepted model for dark energy we seek to interpret our PFS data in a more model-independent way. The wide redshift coverage of the PFS survey, in combination with the SDSS and BOSS surveys, allows us to do this by directly reconstructing the dark energy density as a function of redshift solely based on the geometrical BAO constraints. To illustrate this, we use the Hubble expansion history parametrized in terms of dark energy density parameters in each redshift bins:

(12)

where is the dark energy parameter in the redshift bin centered at . For the combined BAO survey of SDSS, BOSS and PFS, we include the 9 dark energy densities, , given in 9 redshift bins ( redshift bins of the galaxy surveys plus the redshift bin from to ). Then, similarly to the method described around Eq. (11), we can propagate the BAO-measured distance errors into the accuracies of reconstructing the dark energy densities in each redshift bin. Fig. 7 shows the result, where we assumed the cosmological constant, , as the fiducial model. The figure clearly shows that the PFS BAO survey is capable of reconstructing dark energy densities up to high redshift, for a model in which , thereby testing various types of early dark energy models. For comparison, the dashed curve shows the dark energy density parameter for an early dark energy (EDE) model proposed in Doran & Robbers (2006), which gives a more significant contribution to the cosmic expansion at higher redshift than in the cosmological constant:

(13)

where we fixed the parameters to and as the fiducial model. Note that we set the present-day energy density of EDE to be the same as that of the cosmological constant model. The figure clearly shows that PFS can put a more stringent constraint on such an early-dark energy model thanks to its wide redshift coverage, e.g. compared to the BOSS alone. To be more precise, the combined BOSS and PFS geometrical constraints can achieve a precision of even under the conservative setup of our forecasts, while the BOSS alone cannot constrain the parameter well ().

Further, we should emphasize that adding the PFS BAO measurements to the SDSS and BOSS information can significantly improve the reconstruction of dark energy density at low redshift, partly because the SDSS+BOSS BAO alone cannot break degeneracies between parameters () given the distance measurements to the three redshifts (), and also because the angular diameter distances for the PFS redshifts are all sensitive to dark energy densities at low redshift via the integration relation between the angular diameter distance and the Hubble expansion rate. However, we should note that the constraint on the curvature parameter is significantly degraded in this case to from the result in Table 3 because of the larger number of free parameters. Thus the accuracy of the curvature parameter is sensitive to which dark energy model we use for marginalization.

Figure 8.— Marginalized errors in reconstructing the growth rate, , in each redshift slice.

Testing the growth of structure:
We now turn to the utility of measuring the redshift-space distortion (RSD) effect and the broad-band shape of the galaxy power spectrum. If we can reliably model the RSD and the shape of the power spectrum in the weakly nonlinear regime including a possible scale-dependent bias, we can use this information not only to improve the cosmological constraints (Takada et al., 2006), but also to constrain the growth rate which is sensitive to the theory of gravity on cosmological scales. Encouraging progress is being made via many efforts to develop a more accurate model of the redshift-space power spectrum in the weakly nonlinear regime as we discuss below. (Matsubara, 2008; Taruya et al., 2009; Nishimichi & Taruya, 2011; Tang et al., 2011; Hikage et al., 2012a, b).

To estimate the power of the PFS survey, we use the linear theory prediction for the amplitude of the RSD effect, , in Eq. (4), where is defined by the growth rate as . Then we can include the RSD effect in the Fisher matrix formalism by using in each redshift slice instead of treating as parameters (see Eqs. 49). With this implementation, we can break degeneracies between the RSD effect and the galaxy bias uncertainty from the measured anisotropic modulations in the redshift-space galaxy power spectrum. Then we can in turn use the amplitude and shape information of the underlying linear power spectrum.

Fig. 8 shows the expected accuracies of constraining the growth rate, , in each redshift slice via the RSD measurements. The PFS survey can constrain the growth rate in each redshift to a 6% accuracy. In particular, PFS will provide accurate constraints on the growth rate at redshifts beyond , when the cosmic expansion is in its decelerated phase. Such constraint are very important for testing whether dark energy is an illusion caused by an incomplete understanding of General Relativity.

Other constraints:
With the growth rate constraints and the information on the shape of the galaxy power spectrum, we can also constrain other interesting parameters, such as the sum of neutrino masses () and the degree of primordial non-Gaussianity (). Primordial non-Gaussianity induces a characteristic scale-dependent biasing effect on the galaxy distribution at very large scales (Dalal et al., 2008) that are well in the linear regime and cannot be explained by other nonlinearity effects. Hence we can use the largest-scale signal of galaxy clustering to explore the signature of the primordial non-Gaussianity. Table 3 shows the expected accuracy of constraining to an accuracy of if systematic errors are under control (see below for discussion on possible systematic errors). The Planck experiment showed a more stringent upper limit on such as (68% C.L.) (Planck 2013 Results XXIV, 2013); PFS is limited by its relatively small area coverage to access the largest-length scales.

On the other hand, the massive neutrinos, as found by terrestrial experiments, suppress the galaxy clustering power on scales smaller than the neutrino free-streaming scale, which imprints a characteristic scale-dependent effect on the galaxy power spectrum (Takada et al., 2006). The amount of the suppression scales with the sum of neutrino mass as at the scales smaller than the neutrino free-streaming scale. Thus the neutrinos of eV, close to the lower bound of the inverted neutrino mass hierarchy, lead to about 6% suppression in the galaxy power spectrum compared to the case without the massive neutrinos. Hence, we can use the measured clustering amplitude to constrain the neutrino mass. However, the achievable precision of neutrino mass depends on the level of our understanding of the nonlinear power spectrum including the galaxy bias uncertainty (Saito et al., 2008, 2009). Here, by assuming that an accurate model of the galaxy power spectrum is available, we estimate the power of PFS to constrain the neutrino mass. To be more precise, we assumed that the following set of parameters, instead of Eq. (9), can model the redshift-space galaxy power spectrum based on the extended perturbation theory based method in combination with numerical simulations:

(14)

In this parameter estimation we did not use the reconstruction method (i.e., we set for the reconstruction parameter in Eq. 8), because the reconstruction method of BAO peaks alters the shape and amplitude of the power spectrum. With this implementation, we can include the shape and amplitude information of the power spectrum for constraining the cosmological parameters, marginalized over uncertainties of the nuisance parameters. Also note that, for the parameter estimation, we included a broader range of cosmological parameters such as the curvature and the dark energy parameters , which also cause a suppression in the growth rate of structure formation as do the massive neutrinos. However, we assumed linear bias parameters for each redshift slice, but instead included parameters to model the residual shot noise contamination, which mimic a scale-dependent bias. As can be found from Table 3, the PFS survey can achieve a precision of 0.13 eV. However, we again note that, even though we included marginalization over other parameters, the neutrino mass constraint is sensitive to the level of our understanding of nonlinearity effects such as nonlinear bias or nonlinear evolution of matter clustering as we will discuss below in § 2.2.5. If we restrict the parameter forecast to the power spectrum information up to , where the linear theory assumption is considered to be valid, the expected constraint of neutrino masses is degraded to . Thus an understanding of the nonlinearity effects is important to obtain a higher-precision, robust constraint on the neutrino mass.

Discussion of other systematic errors

Figure 9.— Nonlinear matter power spectra at different redshifts, , 1 and in the bottom, middle and upper panels, respectively. For illustrative purposes, the power spectrum is divided by the linear power spectrum with BAO features not included. The data points with error bars in each panel are the power spectrum estimated from -body simulations, where the error bars are the expected statistical errors of the power spectrum measurement at each bin, assuming the survey volume of and the comoving number density of . The survey parameters roughly correspond to those for the and 2 slices of the PFS cosmology survey (see Table 2). The solid curve shows the analytical prediction based on the refined perturbation theory (Taruya et al., 2012), which shows a satisfactory agreement with the simulation result, up to a higher wavenumber for higher redshift slices.
Figure 10.— How observational systematic errors affect the selection function of the detected [O ii] emission-line galaxies as a function of redshift, computed by using our exposure time calculator in combination with the COSMOS mock catalog (see Section 2.2.2). Here we assumed the fixed threshold for the [O ii] line detection. As for working examples, we consider the fiber positioning offset by 10  radius from the true centroid), misestimation of PSF FWHM by 0.1, and error in flux calibration. For comparison, we also show the difference between the numbers of detected [O ii] emitters at the center and edge (0.65 degrees in radius) of the focal plane. These observational effects change the number of detected [O ii] emitters.

There remain theoretical and observational systematic errors that may affect our PFS cosmology program. To realize the full potential of the PFS cosmology survey, we must carefully consider and account for these errors.

Uncertainty in the modeling of galaxy power spectrum:
The linear theory of structure formation is not sufficiently accurate to be compared with the measured power spectrum of galaxies even at BAO scales, given the statistical precision of the PFS cosmology survey. In other words, interpreting the the galaxy power spectrum is complicated by non-linear effects such as those relating to large scale structure and the connection between the galaxy and dark matter distributions. An advantage of the PFS cosmology survey is its focus on higher redshift; the rate of evolution in large scale structure, and hence the effect of non-linearities, is reduced at higher redshift. There are promising developments towards an accurate modeling of the galaxy power spectrum based on a suite of high-resolution simulations as well as refined perturbation theory, at BAO scales that are still in the mildly nonlinear regime (Matsubara, 2008; Taruya et al., 2009; Matsubara, 2011; Taruya et al., 2012; Sugiyama & Futamase, 2012). Fig. 9 compares the nonlinear matter power spectra computed from the refined perturbation theory and from -body simulations for different redshift slices, and (Taruya et al., 2012). The figure clearly shows that non-linearities have a reduced effect at higher redshift and also that the refined perturbation theory provides a better match to the simulation results. A gain in the maximum wavenumber () up to which to include the power spectrum information for the cosmological analysis is equivalent to having a larger survey volume; a factor 2 gain in is equivalent to a factor 8 larger survey volume in the sampling variance limited regime23. Thus the PFS survey, in combination with the refined theoretical model, provides a more robust and powerful cosmological result than one based on a survey at lower redshift.

We also stress that there will be many synergistic opportunities enabled by the fact that the PFS survey will be undertaken in the same area of sky as the HSC imaging survey. Weak lensing lensing information from HSC will be very effective in correcting and calibrating systematic effects inherent in the galaxy clustering analysis, nonlinear redshift-space distortion and the galaxy bias uncertainty, up to the slice (Hikage et al., 2012a, b; Nishizawa et al., 2012). The spectroscopic data from the PFS survey can likewise be used to calibrate the photo- errors and the redshift distribution of HSC imaging galaxies, which is one of the major uncertainties in the HSC cosmology analysis. Thus, by combining the HSC imaging and PFS spectroscopic surveys, we can significantly improve the cosmological constraints, making the joint HSC and PFS experiments comparable to a Stage-IV Dark Energy experiment in the parlance of recent US studies.

Observational systematic errors:
The PFS cosmology survey relies on the use of [O ii] emission-line galaxies, detected with greater than a given threshold ( assumed throughout this document). A variety of observational factors will affect the detection efficiency of this line, causing apparent density fluctuations in the observed galaxy distribution. These include

  • Offset of the fibers from its expected position, e.g. due to a systematic error in the astrometric solution and/or imperfect positioning.

  • Variation in the throughput over the field angle (e.g. due to the vignetting).

  • A misestimation in the seeing FWHM. The PSF misestimation causes a biased estimate of the intrinsic [O ii] flux.

  • A flux miscalibration such as an error in the magnitude zero point.

In Fig. 10, we use our exposure time calculator to estimate how the systematic errors mentioned above change the number of detected [O ii] emitters in each redshift bin, where we employed the same threshold . Here we consider some typical values for each of the systematic errors as indicated by the legend. Thus, the systematic errors might alter the number of detected galaxies in each pointing, and the effects generally vary with different pointings, causing apparent density fluctuations of the detected galaxies on the sky.

Thus the systematic errors need to be well corrected in order for us not to obtain a biased constraint on the growth rate or cosmological parameters from the measured power spectrum amplitudes. A calibration of the systematic errors requires an adequate strategy of the PFS cosmology survey; e.g., frequent observations of standard stars, and a large-angle dithering (tiling) offset between different pointings. In particular, we are planning to use, for the calibration, the sample of [O ii] emission-line galaxies taken from the PFS galaxy survey (see Section 4 for details). With its much deeper depth and much higher completeness in the PFS galaxy survey, the sample allows us to understand intrinsic properties of [O ii] emission-line galaxies such as the luminosity function, the line width and the line ratio of [O ii] doublet. We will in turn use the calibration sample of [O ii] emitters in the PFS galaxy survey to estimate the selection function of [O ii] emitters in the PFS cosmology survey as a function of observational conditions and redshift.

2.3. Scientific Requirements for PFS Cosmology Survey

As discussed above, PFS has the unique capability to execute a very powerful cosmology survey across a wide range of redshifts, considerably extending current and planned BAO surveys on m-class telescopes. Here Tables 4 and 5 summarize requirements on the survey parameters and the instrument parameters for the PFS cosmological applications.

Science yield requirements
Distance measurements measurement of and in each of 6 redshift bins
   via BAO (0.8–1.0, 1.0–1.2, 1.2–1.4, 1.4–1.6, 1.6–2.0, and 2.0–2.4)
Dark energy reconstruction measurement of in each of 6 redshift bins via BAO
Curvature Measure to via BAO
Growth of structure measurement of the growth rate of structure in each of 6 bins via RSD
Galaxy catalog requirements
Redshift range ( minimum)
Number density of galaxies deg
of ELGs () or () at /Mpc
Total survey area 1400 deg
Incorrect redshift fraction
Redshift precision, accuracy , ()
Survey geometry Width degrees; 4 contiguously-connected survey regions
Survey implementation requirements
Total nights clear nights
Lunar phase Dark (1 of 2 visits) or age days (other visit)
Imaging survey HSC data to th magnitude AB
Table 4Cosmology Survey Requirements
Wavelength coverage nm (nm minimum)
Number of fibers
Overhead the open-shutter time
Throughput Average (red) or (NIR)
Worst part of band, (red) or (NIR)
(Excludes atmosphere, central obscuration + WFC vignetting, and fiber aperture
effect.)
Fiber aperture factor Encircled energy in fiber is (point source) or (galaxy, )
(Equivalent to 0.8 FWHM seeing + 11 m rms/axis additional aberration
+ 0.12 fiber offset.)
Spectrograph image quality m rms per axis (excluding fiber geometric size, pixel tophat, and
internal defocus due to thickness of red CCD)
Spectral resolution Red: ; NIR: (to resolve out OH lines but limit read noise)
Stray light Near OH lines: Lorentzian wings at amplitude of perfect grating
Diffuse: equivalent to % of total sky brightness spread over detector
Read noise (red) or (NIR) rms per pixel
(If the NIR channel is not reset between exposures, rms is acceptable.)
Sky subtraction accuracy % of sky background per 4-pixel resolution element
Table 5PFS Instrument Requirements for the PFS Cosmology Survey

3. PFS Galactic Archaeology

Summary: The Subaru PFS offers an unprecedented opportunity to investigate the assembly histories of both baryonic and dark matter components of two typical, large galaxies, namely the Milky Way and M31. This will be achieved through the measurements of radial velocities and elemental abundances for a large sample ( a million) of their member stars. We here describe our Galactic Archaeology (GA) science case for a PFS survey designed to incorporate the envisaged medium-resolution (MR) mode, adopting over the spectral range of  Å in the red arm, combined with the baseline low-resolution (LR) mode of in the blue arm. The MR mode will allow the measurement of multiple -element abundances for stars in the Milky Way, elucidating the detailed chemical evolution history for each of the Galactic components. This mode will further enable us to study the global chemo-dynamical evolution and dark-matter distribution of Galactic dwarf spheroidal galaxies, which are the possible remaining building blocks of the Milky Way. This fundamental science is possible only with the -element abundance measurements and more precise radial velocities offered by the planned medium-resolution mode of PFS.

3.1. Galactic Archaeology Objectives

Our understanding of how galaxies like the Milky Way and M31 formed and evolved in the expanding Universe remains limited. The current paradigm of cosmic structure formation based on the CDM model proposes that galaxy formation is driven by hierarchical assembly of dark matter halos, starting from sub-galactic scales. The repeated merging and overall clustering of many small dark halos over cosmic time forms a larger, galaxy-sized halo. The associated cooling and collapse of baryonic matter confined in the dark halos at each stage of the hierarchy forms the visible galaxies, with the morphology of the final galaxy set by the physics of star formation and of the merging process. Indeed, mergers are predicted to play a key role in the creation of stellar halos, bulges, thick disks and even some parts of thin disks.

However, CDM models have encountered several fundamental difficulties in explaining observations on galactic scales; the model predicts an excess of small scale clustering power than observed. One of the most serious issues is the prediction of many more subhalos in a Milky Way-sized system than the modest number of visible satellites. This discrepancy can only be reconciled if the vast majority of small halos are dark. Our understanding of the star formation process on these small scales, which correspond to dwarf satellite galaxies, remains limited, so there may well be a large population of dark satellites. They would then only reveal their presence through their dynamical effects on visible systems. Alternatively, the assumption that CDM is collisionless may not be correct (Ostriker & Steinhardt, 2003, see Fig. 11 for the predictions of various dark matter models). The merging history of the ‘building blocks’ of galaxies is determined by the power spectrum, i.e. by the nature of dark matter, and this we plan to investigate through the study of the stellar populations in both the Milky Way and M31.

Figure 11.— An illustration of how the number of objects of a given type depends on their present day mass for different dark matter models (Ostriker & Steinhardt, 2003) including Collisionless Cold dark matter (CCDM), Strongly Self-Interacting dark matter (SIDM), Warm dark matter (WDM), Repulsive dark matter (RDM), Fuzzy dark matter (FDM), Self-Annihilating dark matter (SADM), Decaying dark matter (DDM) and Massive Black Holes (BH). Observations on small scales are key to distinguishing these.

Our primary science goal with Subaru/PFS is thus to constrain the assembly process of dark matter halos on Galactic scales, and in particular test the predictions of CDM, by dedicated observations of old stars nearby, formed at high look-back times. Resolved ancient stars in the Milky Way, M31 and other Local Group galaxies are ideal targets because they offer us our most detailed views of galactic structure and evolution through their kinematics and chemical abundances (Freeman & Bland-Hawthorn, 2002). Kinematics of stars reflect past galaxy collapse and/or merging events. Their distribution in phase space as defined by integrals of motion such as angular momentum remains basically unchanged (e.g., see Fig. 12 and Helmi & de Zeeuw, 2000). The chemical abundances of stars reflect their past star-formation history and chemical evolution, possibly in association with the dynamical state of proto-galactic clouds such as their collision and merging (e.g., De Silva et al., 2007; Nissen & Schuster, 2010). All of these processes are predicted to be controlled by hierarchical clustering of CDM via self-gravity on galactic and sub-galactic scales (e.g., Bullock & Johnston, 2005; Cooper et al., 2010; Font et al., 2011). Thus, to assess what CDM models predict, it is essential to derive the spatial distribution of dark matter subhalos in the Galaxy and M31 through their dynamical effects on visible stellar systems. Stars are indeed ideal tracers of a background gravitational field dominated by dark matter.

To make progress we propose to obtain spectra for about a million stars in the Milky Way and M31, as one component within the framework of the proposed PFS Subaru Strategic Program. These spectroscopic studies will be in strong synergy with the upcoming astrometric satellite, Gaia, that will provide very precise measurements of distances and proper motions for Galactic stars, and with the HSC survey which will provide the essential large imaging data set. Therefore, PFS, in combination with Gaia and HSC, will provide us with unique data in the area of near-field cosmology. With these data we hope to gain an ultimate understanding of the nature of dark matter and the associated galaxy formation processes.

Figure 12.— Top: Model distribution of tidal streams in a Milky Way-like galaxy in spatial coordinates where the different colors represent different satellites (from Freeman & Bland-Hawthorn, 2002). These stream-like features disappear after several dynamical times. Bottom: Model distribution of nearby stars in the integrals of motion space, i.e., vs. and vs. , based on numerical simulations of satellites falling into the Milky Way (from Helmi & de Zeeuw, 2000). The different colors represent different satellites. Shown is the final distribution of stars after 12 Gyr within about 6 kpc from the Sun, after convolution with the errors expected for Gaia. It is clear that each of the progenitor galaxies can be traced via the current phase space distribution.

The main questions we seek to address in our dedicated Galactic Archaeology (GA) survey are summarized as follows.

  1. What is the merging history of the Milky Way? – addressing the role and nature of dark matter in galaxy formation.

  2. How did the old Galactic components (thick disk and stellar halo) form? – addressing baryonic physics at early epochs.

  3. How does M31 differ from the Milky Way? – contrast merging and baryonic processes on small scales in two systems.

3.2. Science goals with the planned medium-resolution mode

The implementation of the planned MR mode of in the red arm will allow us to investigate further important aspects in the GA science case. We describe here the two main science goals in GA with the MR mode: -element to iron abundance ratios and precision radial velocities.

Alpha elements

The planned MR mode will enable us to unravel the temporal chemical evolution of building blocks of the Galactic halo and thick disk, in addition to surviving Galactic satellites, through their elemental abundances. In addition to iron, the -elements observable in the wavelength range (nm) provide the ratios [XFe] with XMg, Si, Ca, Ti (Fig. 13). These abundance ratios depend sensitively on the relative contributions of core collapse (Type II) supernovae, from short-lived massive stars (masses greater than ) and Type Ia SNe, which explode on longer timescales. Stars formed from gas that was enriched predominantly by Type II SNe show a high [Fe] ratio, reflecting the yields of core-collapse SNe; such ‘high-alpha’ stars will be expected to form early in the enrichment process, on timescales of 10 years after the onset of star formation, a typical life time of the SN progenitors. Further, more massive progenitors produce higher -element abundances (see Fig. 14 for the case of oxygen, one of the -elements). On the other hand, Type Ia SNe produce very significant iron on longer timescales, typically years after the birth of the progenitor stars (with ); stars formed out of gas that has been enriched by Type Ia SNe show a low [Fe] ratio. Thus, the plot of [Fe] vs. [Fe/H] shows a high [Fe] plateau at low [Fe/H] where short-lived Type II SNe dominate then a turndown at higher [Fe/H] – but fixed delay time (Gyrs) – when Type Ia SNe start to explode and contribute iron. For example, a system with lower star formation rate (SFR) shows the turndown in [Fe] vs. [Fe/H] at lower [Fe/H]. Also, if the initial mass function (IMF) of core-collapse progenitors were biased to more massive stars, the [Fe] ‘plateau’ would have a higher value; a change of IMF slope of over the progenitor mass range of 10 to 100  predicts a difference in [Fe] of at least 0.3, which is thus detectable if this ratio is measured to better than 0.2 dex (Wyse & Gilmore, 1992).

Figure 13.— Alpha-elements (Mg and Ca) in four nearby dwarf spheroidal galaxies: Sgr, Fnx, Scl and Carina. The small black symbols denote the abundances of local MW disk and halo stars (from Tolstoy et al., 2009). PFS will measure the -element abundances for a much large number of stars in the Galactic halo, thick disk and their substructures, in addition to member stars across the radial extent of dSphs, identified by their kinematical and spatial distributions.

Figure 14.— Mass of ejecta from Type II SN in the form of oxygen (an -element; upper four curves) and iron (lower three curves) yields as a function of progenitor mass (from Gibson, 1998). Note that a higher oxygen yield is ejected from a more massive progenitor, while the iron yield is approximately constant.

Therefore, in addition to the overall metallicity (provided by our low-resolution (LR) survey) which reflects the integrated star formation and chemical evolution up to that star’s birth, the measurements of [Fe] ratios provided by the MR mode will enable us to identify substructures through chemical ‘tagging’ with elemental abundance patterns, establish timescales of enrichment and star formation and constrain the IMF, for each of the major stellar components of the Milky Way and surviving satellite galaxies. Indeed, this is what Galactic Archaeology should ultimately pursue as a goal, based on coordinated observation of higher-resolution stellar spectra.

It is also worth emphasizing that Subaru/PFS will offer us a very large FoV that is ideal for exploring Milky Way dwarf spheroidal (dSph) galaxies, such as Fornax, Ursa Minor and Sextans, out to their tidal radii. In order to measure the enrichment histories of these systems, it is essential to measure their [/Fe] distributions across large spatial areas, whereas present samples with elemental abundance measurements are limited to the stars in the inner regions (e.g., Kirby et al., 2009, 2010). PFS’s spectral coverage, resolution, and field of view will make it the most powerful instrument to study the putative building blocks of the Milky Way halo and to study star formation at the smallest scales.

Precision radial velocities

The red-arm MR mode provides us with more precise radial velocities of stars than the original spectrograph design can achieve. The MR mode will provide velocities with errors km s rather than 5–10 km s with the LR mode. This improvement for radial velocity measurements is essential for isolating cold kinematic substructures in the halo and thick disk. These substructures possibly originate from building blocks of the Milky Way such as dSphs, with adiabatic evolution in phase space ’cooling’ their internal kinematics. Arguably even more importantly, the MR mode will enable us to separate and measure the internal kinematics of Galactic dSphs (having velocity dispersion typically km s) over much larger spatial areas—out to their tidal radii—than previous spectroscopic studies have explored with comprehensive sampling.

Figure 15.— Contours of line of sight velocity dispersion of stars in the meridional plane for models of dSphs, where major and minor axes are normalized by a stellar scale length. Solid and dashed lines show NFW and cored dark-halo models, respectively (from Hayashi & Chiba, 2012). Top: spherically symmetric model for both dark halo and luminous stellar components, with their axial ratios denoted as and , respectively. Middle: . Bottom: . Note that the 2D distribution of velocity dispersion depends sensitively on shapes and profiles of both dark halo and luminous stellar components. PFS, with its large FoV, will play an essential role in these velocity measurements.

Our present investigations of the dark-matter distribution in dSphs are mostly limited to the inner regions, where abundant member stars are available from spectroscopic observations even with a small FoV (e.g., Walker et al., 2009). Recently, Walker & Peñarrubia (2011) develop a method for measuring the slopes of mass profiles in the inner regions of dSphs and conclude that the Fornax and Sculptor dSphs have ‘cores’ of constant dark-matter density. This technique relies upon the existence and identification of chemodynamically distinct sub-populations of member stars, each defined by spatial distribution, kinematics and metallicity. This motivates the PFS survey of these and other dSphs, to obtain the necessary velocity and metallicity data to apply their method. Further, most existing mass models of dSphs are based on the simple assumption of spherical symmetry, and in order to derive more detailed, realistic spatial distributions of their dark halos, such as their global shape and mass, we require line-of-sight velocity data for stars over much larger areas, and full two-dimensional coverage (not just major/minor axes), as demonstrated by recent mass models (e.g., see Fig. 15 and Hayashi & Chiba, 2012). It is also of great importance to have velocity data out to the tidal radii of dSphs, thereby enabling us to estimate the true total mass of a dark halo (through the abrupt change of the velocity dispersion profile in the edge) and detecting any effects of Galactic tides in their outskirts.

The advent of the large FoV and fiber multiplexing of Subaru/PFS is tremendously advantageous in selecting member stars of dSphs from background/foreground field stars out to their tidal radii (Fig. 16). It is worth noting here that since the probability of finding true member stars in the outer parts of dSphs is generally small, a pre-imaging survey of target dSphs using HSC with a newly developed narrow-band filter (NB515 filter with CW = 5145 Å and BW = 80 Å, which is similar to the DDO51 filter24) will be very useful for efficiently distinguishing red-giant branch (RGB) stars in dSphs from foreground dwarf stars. Our experiments using Suprime Cam with a proto-type NB515 filter suggest that the number of RGB candidates within a fiducial RGB locus of a color-magnitude diagram for observed stars, after NB515-imaging selection, is narrowed down to about 50 % of that without using this NB filter (Tanaka et al. 2013 in preparation). Thus, the combination of HSC and PFS will allow us to explore this important dark-matter science; dSphs are the ideal sites for studying the nature of dark matter because these galaxies are largely dark-matter dominated and their past star formation is not likely to have modified the dark-matter distribution. Furthermore, this selection of member stars in dSphs is essential for the measurement of their -element abundances with the same MR mode out to large radii, thereby enabling us to characterize the global chemo-dynamical evolution of dSphs.

Figure 16.— Proposed Subaru/PFS pointings (red circles) for the wide-field velocity measurements of some Galactic dSphs (Fornax, Sculptor and Sextans) reaching their tidal radii (dotted lines). Note that previous velocity measurements were limited only to the central parts (black circles) (adapted from Walker et al., 2009).
Survey Mode Mag. Range Exposures No. Fields Survey Time Comments
(mag) (sec) (nights)
Bright time:
The Milky Way MR+LR(blue) 2700 208 20 Thick disk: ,
The Milky Way MR+LR(blue) 2700 46 5 Thick disk: ,
Grey time:
dSph MR+LR(blue) 7200 28 7 Fnx, Scl, LeoI, UMi & Dra
The Milky Way MR+LR(blue) 7200 40 10 Halo: , & 270
The Milky Way LR 7200 48 12 Outer disk:
The Milky Way LR 7200 24 6 ‘Field of Streams’
Dark time:
dSph MR+LR(blue) 7200 8 2 Sextans
M31 halo LR 18000 50 31 HSC sample
dIrr LR 18000 4 3 NGC6822, IC10 & WLM
Total 456 96
Table 6Summary of Galactic Archaeology Survey

3.3. GA survey plan

Now that the MR mode will allow us to address GA science subjects beyond what is achievable with the LR mode as described above, we summarize our survey plan in Table 6. The primary targets are stars in the Milky Way and dSphs using both the MR and LR modes and bright red giant stars in a wide area of M31’s halo with the LR mode.

The Milky Way and dSphs

As detailed in Section 3.4, the MR mode will enable us to obtain the ratios [XFe] with XMg, Si, Ca, Ti with precisions of of [XFe] dex for spectra with SN of about 60 per resolution element. Primary Milky Way targets in our dedicated large survey using this higher-resolution mode will be bright stars with mag, which are observable even in bright time; exposure times of 2700 sec are needed to obtain sufficiently accurate [XFe] ratios. The MR mode will be further dedicated to the survey of fainter Milky Way stars, in addition to member stars of dSphs with mag in grey/dark time, for which we require exposure times of 7200 sec. Thus, this mode will offer us an efficient usage of allocated PFS nights including some bright/grey time.

The LR PFS survey of radial velocities combined with Gaia astrometry data will provide six-dimensional phase-space information for Galactic stars, with which it is possible to identify individual progenitors as building blocks of the Milky Way, in the form of kinematically distinct clumps in phase space (Helmi & de Zeeuw, 2000; Gómez et al., 2010). With [/Fe] ratios of these stars obtained from our MR spectroscopy, it will be possible to set important limits on the star formation and chemical evolution histories in each building block of the Milky Way halo. Furthermore, the [/Fe] ratios are excellent discriminators of the thick disk from the thin disk, with which one can set important limits on the formation scenario of the thick disk by investigating its rotational and orbital properties as a function of [Fe/H] (Lee et al., 2011). We will also quantify the velocity distribution of the thick disk as a function of spatial coordinates and the asymmetry/symmetry of its dynamical properties, providing constraints on the role of dynamical heating by CDM subhalos and/or visible satellites in thick disk formation (e.g., Hayashi & Chiba, 2006). To address these issues, we focus on three regions sensitive to azimuthal streaming velocity (disk rotation) at the halo/disk interface: and , where each block includes a sufficient number of targets (e.g., as many as 2000 stars per PFS FoV, including more than 500 F/G turnoff stars with mag) to derive the spatial dependence of the velocity distribution. Full spatial motions of these stars, in synergy with Gaia, and their [/Fe] ratios from the MR mode of PFS will allow us to gain new insights into the origin of the thick disk as well as the star formation history of halo progenitors. In addition, taking advantage of the wide FoV of PFS, we will also target other Milky Way samples and obtain the distribution of [/Fe] ratios for selected bright stream stars ( mag), so that their star-formation history is constrained and compared to other regions. This survey requires in total PFS pointings ( sq. degree), for each of which 2700 sec of exposure is required.

Figure 17.— Spatial distribution of simulated tidal debris of a merging dwarf galaxy associated with the Monoceros stream (adapted from Peñarrubia et al., 2005). The Sun is placed at  kpc. Red triangles and squares denote positions of previously detected stream stars. Note that mag limit for G5V stars is largely incomplete in probing these tidal debris compared with mag limit.

In addition to these survey regions using the MR mode, we plan to observe Milky Way stars as faint as mag, with the LR mode, in the regions of the outer disk near and in the ‘Field of Streams’, to clarify the chemo-dynamical nature and origin of these substructures. In particular, outer disk regions including the so-called Monoceros stream are expected to contain abundant tidal debris from a merging dwarf galaxy (e.g. Peñarrubia et al., 2005) which can be probed by observing G5V stars as faint as mag with Subaru/PFS; a mag limit, practical for 4m telescope projects, would be largely incomplete in probing these merger remnants (see Fig. 17).

Our proposed survey regions are summarized in Fig. 18. We note the number of sample stars required in each survey mode, i.e. for thick disk, stellar halo and outer disk, follows the justification of the required sample size described in Section 3.2.

Figure 18.— Proposed survey fields in the thick disk, stellar halo, and outer disk regions of the Milky Way in the galactic coordinate system.

As described in the previous section, the MR mode in Subaru/PFS will be essential to determine the global chemo-dynamical state of Galactic dSphs across their radial extent. We will use the MR mode for most of these dSphs in grey time, where we will observe member stars as faint as mag with 7200 sec of exposure for each PFS pointing. We require four PFS pointings for those dSph with large tidal radii (Fornax, Sculptor and UMi: see Fig. 16) and one PFS pointing for each of LeoI and Draco. Since repeat velocity measurements are necessary for identifying binary effects, we require at least 28 PFS pointings in total for these dSphs. Sextans has a large tidal radius ( arcmin), for which we need many PFS pointings. To efficiently execute this observing run, we will request dark time in spring for this particular target. For a sample of Local Group dIrr galaxies, we will target RGB stars down to mag (in the summer/fall season) using the LR mode and in order to obtain SN as large as 20 at Å, we require dark time and 5 hr exposures per pointing for these stars .

The Gaia intermediate data release is expected by the time the PFS GA survey commences. Gaia and ground-based imaging surveys, such as Pan-Starrs, VST, and Skymapper, are likely to find many streams and ultra-faint dwarf galaxies. The MR mode of PFS will uniquely provide the resolution and field of view necessary for follow-up spectroscopy of these new-found structures.

Figure 19.— Proposed PFS pointings along the minor axis of M31’s halo ( pointings), in which several stellar streams are included. The map of RGB stars is taken from Richardson et al. (2011).

The M31 halo

The primary targets in the M31 survey are bright red giants with mag, i.e., stars around the tip of the RGB with 20.5 selected along the minor axis of the galaxy (Fig. 19). Pre-imaging observations and selection of the candidate halo giants will be provided by an HSC imaging survey and we will utilize a newly developed narrow-band filter, NB515, to assist in removing foreground Galactic dwarfs. A survey along the minor axis will enable us to derive the chemodynamical properties of the general M31 halo as well as to study in detail several stellar streams, including a cold stream-like feature in the north-west part of the halo, part of which corresponds to Stream F discovered by previous Subaru observations (Tanaka et al., 2010). The distribution of stars along these M31 streams will be especially useful in constraining the number of orbiting dark matter subhalos, which are predicted to induce detectable density variations along the stream through dynamical disturbances (Carlberg et al., 2011). A careful subtraction of foreground Milky Way stars through spectroscopic observations will be crucial for constraining the number of orbiting CDM subhalos in Andromeda and comparing with theoretical predictions.

PFS will measure radial velocities and metal abundances for M31 halo stars to set important constraints on their intrinsic chemo-dynamical properties. Spectroscopic metallicities derived for individual stars will represent a major advance over those derived photometrically or by stacking spectra. To estimate the number of RGB stars in the M31 halo per PFS field, we follow the recent observations with Keck/DEIMOS by Gilbert et al. (2012), in which the pre-selection of candidate RGB targets using the DDO51 filter was made. At a projected distance of 80 kpc from the M31 center, we expect objects per PFS field (including significant foreground/background contamination even after NB515 pre-selection), among which about 100 secure RGB stars of the M31 halo can be extracted. We propose to observe sq. degrees ( pointings) as shown in Fig. 19. In order to obtain spectra with S/N per resolution element at Å, 5 hr exposures are required at mag. Thus, 30 nights are required for this component of the survey.

In summary, for all the GA survey targeting the Milky Way, dSphs and the M31 halo, we require a total of 96 nights.

Figure 20.— Spectrum of a red giant star in the Sculptor dSph, with Å. This has been obtained by slightly degrading a Keck/DEIMOS spectrum with Å. This spectral region contains many weak metal lines as well as significant Ca II triplet lines.

3.4. Estimation of stellar atmospheric parameters from MR spectra

This medium-resolution survey at will yield stellar spectra similar to those provided by the Keck/DEIMOS instrument, with which we have sufficient experience and well-calibrated techniques to measure multi-element abundances and quantify their uncertainties (Kirby et al., 2008, 2010). MR spectra with 1.3 Å to 1.5 Å FWHM in the red spectral region (7,000 Å  9,000 Å, see Fig. 20) yield multiple abundance dimensions, such as [Fe/H] and [/Fe], as well as other stellar atmospheric parameters, as clearly demonstrated by E. Kirby and his collaborators using Keck/DEIMOS data (Kirby et al., 2008, 2009). The method makes use of a large grid of stellar synthetic spectra parametrized by effective temperature (), surface gravity (), metallicity ([Fe/H]), and -element abundance [/Fe]). The atmospheric parameters and metal abundances are then derived with the fitting to an observed PFS spectrum. This spectral modeling method for the determination of metallicities is advantageous compared to an empirical spectrophotometric one, such as the Ca II infrared triplet method, where the latter is affected by the assumed ratio of [Ca/Fe] and limited to the calibrated range of metallicity. Furthermore, this method enables us to obtain individual abundances of -elements in addition to Fe, namely Mg, Si, Ca, and Ti, which characterize the yields of massive stars that exploded as Type II SNe.

Figure 21.— Left: Comparison of [Mg/Fe] ratios derived from PFS-LR spectra ( Å) to those of the original DEIMOS data ( Å; where the former spectra are made by degrading the resolution of the latter ones), for 400 red giant stars in the Sculptor dSph.. Right: The same comparison but for PFS-MR spectra ( Å). These panels indicate that the expected errors in [Mg/Fe] derived from PFS-LR spectra ( dex) are too large to distinguish field halo stars with [Mg/Fe] dex from disk stars and/or recently accreted stars with [Mg/Fe]. On the other hand, PFS-MR provides the [Mg/Fe] measurement precision required for this determination.

Fig. 21 shows the feasibility of deriving [Fe/H] and [Mg/Fe] from PFS-MR spectra of Å, in comparison with Å(LR mode). It is clear from these figures that the uncertainty in [Mg/Fe] derived from PFS-MR spectra should be of order dex (taking into account an error of [Mg/Fe] dex in DEIMOS) and is thus small enough to distinguish field halo stars with [Mg/Fe] dex from disk stars and/or recently accreted stars with [Mg/Fe]. Our simulations using DEIMOS data also suggest that this precision of multi-element abundances is possible with hour exposures for bright stars of in bright time and hour exposures for stars as faint as in grey/dark time.

Mode Requirements & Comments
LR For the Milky Way stars () and M31 halo ()
(2000-3000) Velocity precision of 5–10 km s
[Fe/H] to dex, no other elements measurable
3800 Å to 1 m incl. Ca II HK, Ca I, Mgb/MgH, CaT
fibers, stars
MR For the Milky Way stars ( in bright and in grey/dark time)
(5000) Velocity precision of 3 km s
[Fe/H] to dex, [X/Fe] (X=Mg, Si, Ca, Ti) to dex
7100 to 8850 Å incl. CaT and -element lines
fibers, stars
Table 7Summary of Galactic Archaeology Requirements

3.5. Instrument requirements for MR GA survey

For the MR mode, a spectral resolution at least as high as Å and S/N per resolution element over the wavelength range 7,100 Å to 8,850 Å will allow us to determine [X/Fe], with XMg, Si, Ca, Ti, to a precision of dex. The resolution of the LR mode ( Å, ) yields [X/Fe] dex, insufficient to distinguish field halo stars, with [X/Fe], from disk and tidal stream stars with [X/Fe] (see Fig. 21). A MR capability for PFS, such as described here, is necessary to achieve the science goals proposed in this document.

We also note that in order to determine radial velocities with accuracy of km s, a resolving power of (i.e. that of the planned MR mode) is required with a wide wavelength coverage, in particular for the red region where highest SN ratios are expected.

The Galactic Archaeology requirements are summarized in Table 7.

In addition to the dedicated GA survey described here, there are a number of other important questions that may be addressed with both LR and MR modes of PFS. These include: (1) chemo-dynamical properties of the Galactic bulge/bar and the transition(s) between the bulge, inner disk and halo components in the Milky Way, (2) kinematics of the outer parts of halo globular clusters in the Milky Way, and (3) identification and analysis of globular clusters in M31. These studies of these issues can be carried out through PI-led programs.

4. PFS Galaxy Evolution Survey

Summary: The goal of the PFS Galaxy Evolution Survey is to follow the growth of the full panoply of modern-day galaxies from cosmic dawn to the present. While we know some of the basic physical processes that drive galaxy evolution (dark matter halo merging, gas accretion, star formation and associated energy release, galaxy merging, black hole accretion and associated energy release), how and when they operate, and their relative importance, remain unknown. We will use the unprecedented wavelength coverage of PFS, in particular from to m, to explore the redshift desert between when the star formation rate density and black hole growth were at their peak. Using Ly  emission, we will trace the growth of galaxies and black holes all the way to the epoch of reionization, . Thanks to deep broad- and narrow-band imaging enabled by the HSC survey, we will be able to study these young galaxies with unprecedented statistics using PFS. We propose a 100 night survey covering 16 deg with these main components: (i) A color-selected galaxy survey of 500,000 galaxies using 785,000 fiber-hours over 16 deg from to to a limiting magnitude of mag, with a component limited to mag, and a magnitude-limited component covering 2.6 deg; (ii) A survey of bright dropout galaxies and Ly  emitters over , using 247,000 fiber-hours; (iii) A survey of color-selected quasars from , using a total of 1600 fiber hours in this survey and 21,000 fiber hours in the BAO survey.

The most important requirements for our science are the following:

  1. The multiplexing capability of PFS is a critical component of our survey design, allowing us to observe hundreds of thousands of objects.

  2. The sensitivity in the NIR is most crucial to our redshift success. We assume that in 3 hrs of integration we can measure continuum redshifts from the 4000Å break down to AB mag. We find that this is achievable with the default instrument configuration, at an effective in the NIR arm, if the scattered light going down each fiber is no more than a few percent of the sky brightness; the nominal requirement is 0.5%.

  3. We assume that in a 3 hr integration we can achieve line detections of erg s cm at effective resolution for the full spectral band in the blue and red arms and 75% of the NIR arm, including systematic errors in sky subtraction (see §4.3).

4.1. Extragalaxy Science Objectives

The Sloan Digital Sky Survey has provided us with a detailed understanding of the optical properties and large-scale distribution of present-day galaxies. Large redshift surveys such as zCOSMOS (Lilly et al., 2009), DEEP2 (Cooper et al., 2006), and VVDS (Le Fèvre et al., 2005) have studied areas of square degrees at ; at this epoch galaxies had similar morphologies, luminosity ranges, and environmental characteristics as they do today. However, the bulk of the stellar and black hole mass was assembled at (Fig. 22), when the universe was a very different place. We want to understand how galaxies and gas are distributed relative to dark matter halos at these epochs, how each of these components interact (via merging, cooling flows, star formation, energy feedback, and reionization), and whether star formation proceeded in a fundamentally different way at that crucial epoch of mass assembly. To date there are spectroscopic samples of only a few thousand blue, star-forming galaxies with , covering deg (e.g., Steidel et al., 2010). Particularly difficult to study is the so-called redshift desert , since no strong and reliable redshift indicators fall in the optical bandpass. Even with the current generation of multi-object near-infrared spectrographs, it will not be possible to survey the solid angles proposed here, which allow us to tie together galaxy evolution with the large-scale environment. The PFS spectrograph, with a wavelength coverage of 0.38-1.26 m, is specifically designed to explore the redshift desert over volumes comparable to the SDSS at low redshift. We propose the first large-area spectroscopic survey of roughly half a million galaxies in the redshift range , when the bulk of stellar mass was assembled.

While the bulk of the stellar mass in galaxies was assembled between , the star formation rate density likely peaked at even earlier times (Fig. 22), and so to get a full picture of galaxy evolution we must study the earliest cosmic epochs as well. The wide wavelength coverage of PFS allows us to observe galaxies from to the redshift frontier of (Fig. 22) within the same survey design. It is prohibitive to perform a rest-frame optical continuum selection at . Instead we will target high-redshift Lyman break galaxies (LBGs) and Ly  emitters (LAEs) at . We will obtain unprecedented numbers of spectra of both populations, particularly at , to probe the epoch of reionization. With these samples we will chart the evolution of star formation rate, metallicity, galaxy density, and large-scale structure as a function of redshift. We will probe the epoch when the star formation of early galaxies changed the ionization state of the intergalactic medium (IGM) in what is called cosmic reionization. The large area of the PFS spectrograph allows us to survey wide enough areas on the sky to study the topology of ionized bubbles in the IGM at this epoch ( Mpc) as well as to conduct a census of young galaxies at . We will have a sample two orders of magnitude larger than those that came before.

Figure 22.— Left: The differential build-up of stellar mass as a function of redshift using both a logarithmic (left) and linear (middle) stretch. The data are from Behroozi et al. (2013), and is in units of [yr/Mpc]. Right: Expected number of clusters with   per deg survey volume with the stated depths. The estimates use the “lightcone” simulations of Sehgal et al. (2010) and populate halos with galaxies using the halo occupation distribution model from Tinker & Wetzel (2010).

It is now recognized that all massive galaxies contain supermassive black holes (SMBHs) in their centers, with masses ranging from  . The evolution of black hole growth with cosmic time resembles that of the star-formation activity. The steep drop-off of both at points to a link between supermassive black hole growth and galaxy formation. Moreover, the masses of SMBHs are correlated with those of their host bulges in the present-day Universe, suggesting that they evolved together (e.g., Kormendy & Richstone, 1995; Magorrian et al., 1998; Marconi & Hunt, 2003). A full understanding of galaxy evolution requires study of the accretion history of SMBHs. We will target color-selected quasars that are three magnitudes fainter than the SDSS to a redshift of and study their clustering properties, the evolution of BH mass density with cosmic time, and evolution in the metal content and ionization state of the inter-galactic medium.

We propose to study galaxy formation and cosmic reionization from to seamlessly. We will conduct the first spectroscopic census of young galaxies at