Masahiro Takada (IPMU)

Dec 9, 2010 @ NAOJ

• Estimate the power of PFS (its minimum designversion; red-arm) for doing a cosmological survey(especially focused on BAO), compared to competingsurveys of 4m-class telescope• Estimate the feasibility of PFS BAO survey properly
taking into account the PFS instrumentation parameters and thesky background in red wavelengths (working with Jim)
– What is the minimum nights needed for the BAO survey?
– What is the uniqueness of SuMIRe HSC/PFS surveys,
compared to other surveys?

• Space-based survey
1. WFIRST: Dark Energy and Exoplanet Statistics• 1.5m; 144MPx HgCdTe detectors, 200mas, grism; L2• Gravitational lensing, distant supernovae, BAO

2. Explorer Program Augmentation• Ground-based survey
1. LSST: Dark Energy, Dark Matter and the time-variable universe• 8.4m; 3.5 sq. degree FoV; Observe half sky every four days with 6 filters• Gravitational lensing, distant supernovae, imaging BAO

2. Mid-scale innovation program ← PFS?
 HSC survey can play a pioneering role for these ultimate wide-fieldimaging surveys (we can scoop DE science!); URGENT TASK!
 The demand on the wide-field multi-object spectrograph capability
is even more increasing; PFS can play a unique role in 2020’s

Sloan Digital Sky Survey (SDSS-I,II) (2000-2008)

rBAO = DA (z)Δθ obs

Δzobs
rBAO =H(zsurvey )Dark Energy Task Force Report (DETF)€€

Eisenstein et al. (05)€ DA (z)θ obs = rBAO• Measure the single length
 Δzobs
 H(z) = rBAOscale (BAO) from thegalaxy distribution• Not use the clustering
amplitude information to docosmology due to galaxy
bias uncertainties, eventhough much higher signalto-noise ratios in themeasurement• The amplitude uncertainty ismarginalized over to obtain
the distance constraints

×85 Mpc/h

From the Virgo Consortium• Structure formation isdriven by the “invisible”
dark matter distribution• Galaxies are “biased”
tracers of DMdistribution

δg ≠ δ m• There is no sufficiently
accurate theoreticalmodel of galaxy€ formation• Unavoidable uncertainty
if a redshift survey alone
is available (BigBOSS)

see Taruya-san’s talk for details• Now sufficiently
accurate models(simulations +analytic models) areavailable, for dark
matter clustering
Error bars: PFS survey
including nonlineareffects• For dark matter
distribution, if
measured, we can use
the shape andamplitude information
to do cosmology(WL, beyond BAO)

BOSSBigBOSSSuMIRe PFS

Telescope

2.5m

4m @KPNO

8.2 Subaru Tel.

Pre-imaging survey

SDSS

PTF (1.2m) ???

HSC+Redshift

0.2<z<1.7

0.2<z<2+z~3

0.6<z<1.6

Sky coverage

10000 deg^214000-24000deg^2~2000 deg^2Field-of-view

7 deg^27 deg^2

1.8 deg^2

Fiber density (per deg^2) 1437141333

Number of fibers

10005000

2400

Wavelength range

360-1000nm

340-1130nm

600-1100nm (380-1300nm)

Spectral resolution

1600-2600

2300-6000~3000 (2000-4000)

Target galaxies

LRGs

LRGs+[OII] emitters

LRGs + [OII] emitters••

Note: HETDEX (Texas+) is a blind redshift survey targeting Ly-alpha emitters over
1.9<z<3.5 and covering ~400 deg^2 area
Subaru FMOS survey (~50 deg^2): H-alpha survey over 0.5<z<1.7• The imaging data isneeded to findtarget galaxies• Example: BOSS=aspectroscopic
follow-up survey ofLuminous RedGalaxies (LRGs)
constructed fromthe SDSS imagingsurvey

•••Courtesy by A. Nishizawa

Cosmology needs aconnected, wide-areasurveySDSS (i~21) is thelargest, but the
spectroscopic survey isalready on-going(BOSS)
The largest surveys,
without spec. followup, are the data from
CFHT (4m; i~24); ~afew 10’s sq. degrees ofeach field– VVDS, VIPERS (VLTVIRMOS)In 5 years (~2015)…
• Various surveys
planned, aimed atexploring DE
HSC survey (TBD)– Pan-Starrs (1.8m, 3π
survey over 3 years;i~23-24)– DES (4m; 5000 sq.
degrees; i~25), almost
no overlap with SDSS

• Hyper SuprimeCamSurvey (2012-)

Dark Energy Survey (CTIO 4m, Chile; i~25)
Pan-Starrs (PS1) (1.8m, Hawaii; i~23)– ~1500 sq. degrees– grizy (i~26)– Overlap with SDSS,ACT, UKIDSS, …
– Need 10 nights to cover
500 deg^2 with igz(i~25)

• The ultimate imaging
survey, LSST(ugrizy), will comeonline– 6m (effective), i~27,
10 years (2018-?)• The imaging survey
will be done for
HSC survey (TBD) almost all sky (downto i~24th)• Further, Euclid(including NIR;2018-), WFIRST mayhappen• However, nospectroscopic survey,Dark Energy Survey (CTIO 4m, Chile; i~25)
except for PFS, is
Pan-Starrs (PS1) (1.8m, Hawaii; i~23)
LSST (8.4m [6m in effective], Chile; i~27 over 10 years)
planned to follow-up
these imaging gals• BAO survey needs an pre-imagingsurvey with adequate depth that cancover its target redshift range• PFS BAO survey

HSC (i~26)
DES (i~25)
PS1(i~23?)– HSC can give an ideal data set for targeting
galaxies for PFS survey– Minimize systematic errors by observing thesame patch of the sky with the same telescope(HSC/PFS)– Improve cosmological constraints (see later)• BigBOSS survey (may start from 2018-)– The Palomar Transient Factory (PTF; 1.2m)
survey: 12,000 deg^2, R~23.5– PS1 (gi): i~23
– Plan to use PS1(gi)+PTF(R) for targetselection– Very difficult to find target galaxies at z>1– BigBOSS ≈ 0.6<z<1 BAO with 10000 deg^2BigBOSS proposal to NOAO(Oct 1st, 2010)• The DM distribution (=cosmology) needs to be inferred from theobserved galaxy distribution• The measurement errors of P_g(k): sampling variance due to a finite
volume coverage and shot noise due to a finite number of galaxies2
σ(Pg )  2 2 
1 =
1+N k  n g Pg (k)  Pg (k) €4 πk 2 Δk k 2 ΔkNk ≡=V(2π /L) 3 2π 2 survey
Vsurvey : survey volumePg (k) ≈ b 2 Pm (k) in the linear regimen g : mean number density of galaxies• To have the better accuracies, we need a wider survey area, an adequate
density of target galaxies, and/or target galaxies with higher biases€• A reasonable strategy for a choice of target galaxies: ngPg~ a few

RedshiftVolume(h-3 Gpc3)# of galaxies(per field)

Number density(h3 Mpc-3)

biasnP@k=0.1hMpc-1

0.6<z<0.8

0.8

212

3×10-41.5

1.4

0.8<z<1.01.1292

3×10-41.5

1.2

1.0<z<1.2

1.4

495

4×10-41.5

1.3

1.2<z<1.4

1.6

565

4×10-41.5

1.2

1.4<z<1.6

1.7

600

4×10-4

1.5

1.0

Total # of target galaxies per 1.8 sq. degrees=2164• Target galaxies: LRGs + emission-line galaxies over 0.6<z<1.6~1.7– For z<1.4, early-type galaxies favored (LRGs; b_LRG~2, ng~3×10-4 h3Mpc-3)– For z>1.4, emission-line galaxies (OII) (b~1.2-1.5 in Coil et al. for the DEEP2 survey)• PFS allows a uniform sampling of target galaxies over the whole
range of redshifts, with a single exposure! (see below)

From BigBOSS proposal

A fewer density of galaxies
than required for BAO

Fractional error in measuring P(k) at each z, k-bins

Survey Area=2000 sq. degrees• All redshift slices
are equallyimportant• PFS allows a %level precision inP(k) measurement
at each redshift, up
to k~0.3 (where thetheoretical models
are accurateenough)z<0.50.5<z<0.9
0.9<z<1.3z>1.3• Not powerfulenough to surveygalaxies at z>1.2• Also true
BigBOSS (4m) is
not powerful to geta high-S/N
spectrum of galaxy
at such highredshifts (seebelow)

“Geometrical” test alone

A few % accuracies ofH(z) and D_A(z)achieved for eachredshift slice
Complementary toBOSS

Pgg (k) ∝ galaxy − galaxy ∝ b 2 Pm (k) (linear regime)Pγg (k) ∝ shear − galaxy ∝ bPm (k)background gals
(from HSC)

€Survey Area=2000 sq. degrees

halogals with redshifts(from PFS)

• Note that linear bias breaks down even at large BAO scalesPgg (k) ⇐ b ( k ) ⊗ Pm ( k )2• Again, the direct reconstructionof galaxy€ bias is unique forSuMIRe HSC/PFS• Now can use the power
spectrum amplitude information• The growth of matter clustering
is very sensitive to cosmology,
and can be used to test gravity
on cosmological scales

PFS + Planck• Einstein gravity is correct over all the length scales, from solarsystem scales to the horizon scale?

1Rµν − gµν R + Λgµν = 8πGTµν
2(Curvature of space-time = Matter)• The observed cosmic acceleration may be a signature of themodification in gravity law on cosmological scales€• Einstein gravity should be tested by data
• To do this, we need both the geometrical test (BAO, SN) and thestructure formation probes (P(k), WL, clusters)• SuMIRe HSC/PFS can test both DE and gravity (very unique!)BOSS

PFS (+BOSS)SuMIRe (HSC+PFS+BOSS)

Redshift

0.2<z<0.65

0.6<z<1.60<z<1.6

Sky coverage

10000 deg^22000 deg^22000 deg^2σ(w_constant)

0.083

0.0460.018

DETF FoM

1333192

Growh: σ(γ)--~0.03σ(Σm_nu) [eV]--~0.06eVσ(f_NL)--~10(GR: γ≈0.55)••••Planck priors assumed
SuMIRe PFS: BAO alone (geometrical test alone)
SuMIRe HSC+PFS: WL + cluster counts + BAO + galaxy clustering
Te forecasts above is somewhat conservative (taking into account various
systematic errors)– Allows to constrain gravity theory on cosmological scales, neutrino masses andprimordial non-Gaussianity• Combining HSC andPFS improves the darkenergy FoM by a factorof 6, compared to thatfrom either of HSC orPFS alone• Note 2000 deg^2 (evenmore improved if alarger survey area isavailable)• σ(w_const)=0.02:
equivalent to Stage-IV
DE experiment

Q: What is the number of minimum nights tocarry out the PFS BAO survey?

• The minimum PFS BAO survey is done over 0.6<z<1.7,
corresponding to the red wavelength range, 6000<λ<10000A• Sky is bright in the red wavelengths• Need to estimate the sky background correctly, taking into
account the PFS spectrograph parameters (resolving power,pixel scale, fiber size and so on)Working with Jim, Michael and Iwata-san (Jim has always been correctin his calculations; I made a factor mistake in the unit conversion)• Higher resolving
power has a more
window ofwavelengths wheresky is very low• Relevant for high-z
galaxy hunting withPFS, and also forTMT• The accurate modelof sky spectrum isvery useful for NIR
astronomy

Assuming 15min exposure

f>5×10-17 erg/s/cm^2100Ly et al.2006(1.171< z<1.203)
Hippelein et al.2003(1.175< z<1.21)
COSMOS(1.171< z<1.203)
SDF(1.171< z<1.203)!(logL)(logL-1Mpc-3)

10-1• Use theluminosity
function of [OII]
emitters, derived
from the narrowband imaging
surveys

10-2

10-3

10-4

10-5

40

41

42
logL([Oll])(erg/s)

4344

• If targeting [OII]
emitters withf_obs>5×10-17 erg/s/cm^2, a sufficientnumber density ofthe targets,required for BAO,
seems available upto z~1.6• 15min exposure
time is enough perfieldQ: What is the number of minimum nights tocarry out the PFS BAO survey?
• A: To cover 2000 deg^2 with PFS, we need#=€2000deg 22

 1.5deg 8[hours/night] × 60[min/hour]π × 2  15min/pointing + 40sec/60sec(overhead)≈ 37nights• Assumed a single visit to each field (about 100% success rate of targetselection)• PFS is so powerful instrument to allow a very quick BAO experiment
up to z~1.6• A further PFS BAO extension because more imaging survey data are
available in PFS timeline: DES, Pan-Starrs, HSC shallow survey (giz,each 5min, i~25: 10nights=500 sq. degrees)Continuum detection possible
with PFS BAO survey?
iAB=22
exposure time=15min

iAB=22Texp=15minexposure time=15min
iAB=22continuum

iAB=23iAB=24σ(sky)[OII]=0.5×10-16 erg/s/cm^2

texp=1hours

Note: my estimate on sky continuum is larger than real

Red galaxies
texp=1hours

We can use our sky model to estimate an exposure
time needed for the continuum detection• SuMIRe HSC/PFS are very unique even in TMT/LSST era• Combining HSC-lensing and PFS galaxy clustering allows a very robust
test of cosmology against various systematic errors: e.g., a directreconstruction of scale-dependent galaxy bias
– A similar-level constraining power to Stage-IV survey ($1B experiments)– Enables us to constrain both DE and gravity with the same data sets (inaddition, neutrino masses, inflation and primordial non-Gaussianity)• PFS is so powerful instrument to carry out BAO survey– ~37 nights needed to cover 2000 deg^2– If 2 visits per field are needed, we still need just ~75 nights• Tasks to be studied:– Estimate the usefulness of even higher redshift BAO survey with NIR (up toz~2.5) and blue (z~3) arms
– A more optimal survey design needs to be realized: e.g. a part of BAO survey
includes a deeper spectroscopic survey to construct a mag.-limited redshiftsample for LSST and Euclid