1D and 3D Lyman α forest

•  Introduction to Lyα and BAO •  Lyα at SDSS/BOSS •  3D: BAO analysis •  1D: ν mass  

Jean-Marc Le Goff (CEA Saclay, SPP) Rencontres de Moriond , march 2012

Quasars as an IGM probe

2  

Use  quasar  (QSO)  as  a  beam  probe  Intergalac8c  medium  (IGM)                    mostly  ionized  H  some  neutral  H  (H1)  -­‐>  absorp8on    

Lyman-α forest - QSO “continuum” = unabsorbed spectrum - transmitted flux fraction F = flux/continuum : 0<F<1 -­‐  F  =  exp(-­‐τ),              τ∝  nH1            PF(k)  =  b2  PDM(k)  

at  z≈2.5,  Lyα  forest:   Δz  ≈ 0.3            ≈ 350  Mpc/h  

Civ  

Ly  α (H1,  n=2  →  1)

Ly  β (3 →1)

(1+zQSO)x1216    (1+zabs)x1216    

Lyman-­‐α  forest  

λ (ang)

3  

No clustering detected beyond ~1 Mpc/h

1D clustering Measured up to ~20 Mpc/h scales

3D clustering measured up to ~100 Mpc/h scales

BAO scale 3D clustering

o

Num

ber

of z

>2

qua

sar

spec

tra

< 1999 1999-2004 2011 2012

100,000

10,000

1,000

Slosar et al. 2011

History of Lyα forest clustering McDonald et al. 2006

P1D(k) ξ3D(r)

Increasing z 0 100

3000 QSO SDSS-I

BOSS 14,000 QSO

4  

5  

•  at  z  >>  1000  :      baryon-­‐e-­‐  plasma  coupled  to  photons

•  Over-­‐density  (overpressure)  

                           ⇒  acous8c  waves  

•  Z  ∼  1100  recombina8on  :  baryon-­‐photon  decoupling  ⇒  pressure=0  

               ⇒  frozen  wave  has  travelled    

                         s  =  150  Mpc  (commoving)  

•  Peak  at  150  Mpc  in  autocorrela8on  func8on  at  all  z  

                     a  150  Mpc  standard  ruler  •  Geometrical  measurement,  linear  

physics:  low  systema8c  

BAO R2  δρ(R)  

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A 3D survey

6  

A  3D  survey  :  RA,  declina8on  and  z      

⇒  correla8on  transverse  and  along  line-­‐of-­‐sight  

•  transverse  :  Δθ  =  s/D⊥          with  s=150  Mpc  standard  ruler  

     a  measurement  of  DA(z)    same  info  as  SNIa        (DL  =(1+z)2  DA)  

•  radial  :  Δz  =  s  /Dz                a  measurement  of  H(z)  

•  Need  accurate  z  :  i.e.  spectro            photo-­‐z  :  loss  of  stat  by  factor  5  rela8ve  to  cosmic  variance  limit  

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D⊥(z) = (1+ z)DA (z) =cdz'H(z')0

z

∫

Lyman α at BOSS

7  

SDSS III / BOSS

8  

•  SDSS III : BOSS, Marvels (exo-planets), Segue and Apogee (Galaxy)

•  US, Brazil, France, Germany, Korea, Spain, UK •  BAO using LRG and lyα forest of quasars (QSO) •  Telescope 2.5m, 7 deg2 in APO, New Mexico •  Spectrometric survey 10,000 deg2 : LRG and quasars •  data taking 2009-2014

BOSS data taking

9  

1000

Fiber number

λ

CCD plane

3D: BAO analysis

10  

continuum

11  

•  not easy to find continuum with SDSS resolution and S/N •  several methods -  mean shape (from stacking) x (a λ +b) -  idem combined with likelihood using pdf of F (N Busca) -  mean flux regulated PCA continuum (KG.Lee et al. 2011)

•  However simulations show not so serious: using simplest continuum method ~10% increase of δstat(rBAO) sub percent bias (JMLG et al. 2011)

a BOSS spectrum

Lyβ Lyα

Distortion due to continuum

12  

•  continuum procedure distorts ξ(r) •  but this does not affect BAO peak

•  2 mock spectra sets (A. Font; JMLG)

€

φ(λ) = φ (λrf ,z)(a + bλ)(1+δ)

€

ξ(r) = δ(x)δ(x + r)

T Delubac

Mock data

)-1r (Mpc.h0 20 40 60 80 100 120 140 160

0

0.005

0.01

0.015

Graph

true continuum

fit continuum

0 20 40 60 80 100 120 1400

0.005

Graph

true – fit

rξ(r)

continuum fit mock data

•  analysis in ξ(r)

Weighting and ξ-estimators

13  

€

ˆ ξ (r,µ) =wiw jδ iδ jij

∑wiw jij

∑

LSS

pipeline Var -1

Weight δ according to σ2δ = σ2

pipeline + σ2LSS

σ2LSS(z) determined from data

W= 1/σ2δ

More sophisticated ξ -estimators being studied (A Slosar) N Busca

Error matrix

14  

0 20 40 60 80 100 120 140 160 180 2000

20

40

60

80

100

120

140

160

180

200

-0.2

0

0.2

0.4

0.6

0.8

10

Corr Matrix of

(T Delubac)

•  Bins of ξ(r) are correlated •  Fair agreement between - jackknife : split data in N subsamples - analytical calculation assuming Gaussian distribution and using Wick theorem (A Slosar, N Busca) •  much less correlation than for LRG

Measured correlation

15  

20 40 60 80 100 120 140 160 180 200

0

0.01

0.02

0.03

20 40 60 80 100 120 140 160 180 200

-0.02

-0.01

0

0.01

rξ0(r)

rξ2(r)

15  

•  measure ξ(r,µ) µ=cosθ

•  decompose with Legendre polynoms Pl (µ) -> monopole ξ0(r) and quadrupole ξ2(r)

•  blind analysis

Expected performances

16  

•  for 15 QSO/deg2 and 10,000 deg2 DV=(DA

2/H)1/3 δDv ~ 2% <z>=2.5 with analytical description of P(k) and Fisher matrix (McDonald Eisenstein 2007) •  cross-checked with mock quasar spectra (JMLG et al 2011) •  δDv =2% is an average, significant fluctuations •  DA(z) and H(z) separately ?

1D: neutrino mass analysis

17  

Neutrino mass and Lyman α

18  

•  ν oscillations : Δm122=7.58 10-5 eV2 Δm23

2=2.43 10-3 eV2

•  tritium β decay m(νe) < 2 eV (95% CL) •  0.06 eV < Σ mi < 6 eV

•  Lyman α data go down to Mpc/h scale •  when combined with other cosmological data mν < 0.2 eV (95% CL) (Seljak et al. 2006, SDSS-I data) issue of bias •  safer to use only Lyman α mν < 0.9 eV (95% CL) (Viel et al. 2010) •  important to get large k and z ranges

mν and density fluctuations

19  

•  at high z, ν are relativistic they “free stream” over all scales : δν ≈ 0 •  when z < znr = 1890 (mν /1eV) : ν non relativistic free streaming length large scales

small scales

€

δCDM ∝ a

δCDM ∝ a1−0.6 fν fν =Ων

Ωm

Effect on different scales

20  

€

δCDM ∝ a1−0.6 fν

large scale modes (k < knr) δν ≈ δcdm P(k) not reduced by mν

small scale modes δν ≈ 0

integrated to z=0 -> ΔP(k) = -8fν P(k,mν=0)

(Shoji Komatsu 2011)

kFS

€

aa0

=11+ z

Horizon

aNR

knr

Resulting P(k)

21  

1.4 eV

0.14 eV

k €

P(k,Σmi)P(k,Σmi = 0)

8fν

When mν increases :

knr increases |ΔP/P| = 8 fν increases more effect but limited to smaller scales

shape z dependent

mν = 1 eV

mν = 0.13 eV

z=0

BOSS QSO sample

22  

Z=4.4

Z=2.2

S/N > 2 2.1 < zabs < 4.5 resolution < 85 km/s ~16,000 QSO

mean z HI on spectrum part2 2.5 3 3.5 4 4.5

0

1000

2000

3000

4000

5000

z

NQSO(z)

2 4 3

)Å (!

1050 1100 1150 1200 1250 1300 1350 1400 14500

0.5

1

1.5

2

2.5

3

2.1<z<2.3

2.3<z<2.5

2.5<z<2.7

2.7<z<2.9

2.9<z<3.1

3.1<z<3.3

3.3<z<3.5

3.5<z<3.7

3.7<z<3.9

3.9<z<4.1

4.1<z<4.3

4.3<z<4.5

z=2.2

z=4.4

we measure z, when multiplied by c -> km/s 1 Ang ≈ 70 km/s

Power spectra

23  

Pk (data) – Pk (noise) W2(k,R,λ)

average over 100 realizations

W2(k,R,λ) = exp [-( k R )2] x [sin ( k Δλ / 2 ) / ( k Δλ / 2 )]2

Spectrograph resolution (LSF)

binning

Spectro resolution Noise

k*P(k)/π

k (km/s)-1

1/ RMS of difference between individual exposures

(in forest)

2/ Correction to error from coaddition

€

RMS F k (λi) − Fk+1(λi)

σ k (λi)2 +σ k+1(λi)

2

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

3/ Correction wrt flux C1(Exp. RMS) x C2(λ) x C3(f, λ)

Compatible with correction estimated from side bands (flux rms vs. pipeline σf)

Pixel noise known to ~1%

Correction to pipeline noise

24  

OI 5577 A +9%

25

Correction from arc lamps (3650 < λ < 5800A) or sky lines (λ > 5500 A)

PS

F (p

ixel

)

PS

F (p

ixel

)

fiber #

HgI 3650 A HgI 5461A

+2% +8%

PS

F (k

m/s

)

fiber #

flat ~9% correction (sky lines) λ = 5577 A to λ = 6300 A

fiber #

sky line pipeline

arc lamp pipeline

arc lamp pipeline

hPullEntries 500

Mean 1.001

RMS 0.02571

/ ndf 2! 44.36 / 12

Constant 4.64! 73.09

Mean 0.002! 1.001

Sigma 0.00101! 0.02383

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.20

10

20

30

40

50

60

70

80

90hPull

Entries 500

Mean 1.001

RMS 0.02571

/ ndf 2! 44.36 / 12

Constant 4.64! 73.09

Mean 0.002! 1.001

Sigma 0.00101! 0.02383

pull

HgI 5461 Ang

Correction to pipeline resolution

25  

-1k (km/s)

-310

-210

!

P(k

)*k/

-210

-110

4.3<z<4.5

4.1<z<4.3

3.9<z<4.1

3.7<z<3.9

3.5<z<3.7

3.3<z<3.5

3.1<z<3.3

2.9<z<3.1

2.7<z<2.9

2.5<z<2.7

2.3<z<2.5

2.1<z<2.3

Power spectra

26  

•  syst <= stat at small z, syst << stat at high z •  both FFT and likelihood analysis

Borde, Palanque Delabrouille, Yeche (JMLG)

k (km/s)-1

k*P(k)/π

z=4.4

z=2.2

Conclusions

27  

BAO •  BOSS Lya analysis well advanced •  unblinding to be discussed today in SLC: signal ? •  taking data up to July 2014 •  LRG paper being circulated inside BOSS a beautiful BAO signal

neutrino mass •  Analysis of 1D P(k) nearly finished •  Hydro simulations with J. Lesgourgues •  Extraction of Σmi, using only Lyα data and M. Viel larger z level arm than SDSS-I •  Other science: DLA, proximity effect, …