Lyman- quasar spectra as cosmological probes

MATTEO VIEL

INAF & INFN – Trieste

80 % of the baryons at z=3 are in the Lyman- forest

baryons as tracer of the dark matter density field

IGM ~ DM at scales larger than the

Jeans length ~ 1 com Mpc

flux = exp(- ~ exp(-(IGM )1.6 T -0.7 )

THEORY: GAS in a CDM universe

Bi & Davidsen (1997), Rauch (1998)

DATA: high resolution spectrum

Outline

- Where we were

- What data we got

- How we used them

- What we achieved

- Where we are going

Mini historical background

The data sets

Theoretical framework

Results

Perspectives

Linear matter power spectrum

Mini historical background

1965: Bahcall & Salpeter, Gunn & Peterson. First extimates of IGM opacity. HI in clusters?1971: A forest of lines seen by Lynds80’s: models of the IGM (gravitational or pressure confinements of clouds)90’s: CDM + median fluctuated IGM (Bi, McGill…) semianalytical models + Hydro sim.

Croft, Weinberg and co-workers (98,99,02): the effective bias method

PF (k) = b2(k) P(k)

28% uncertainty in the power spectrum amplitude

Recovered in velocity space

GOAL: the primordial dark matter power spectrum from the observed flux spectrum

Tegmark & Zaldarriaga 2002

CMB physics z = 1100 dynamics

Lyphysics z < 6 dynamics + termodynamics

CMB + Lyman Long lever arm

Constrain spectral index and shape

Relation: P FLUX (k) - P MATTER (k) ??

Continuum fitting

Temperature, metals, noise

The data sets

The Croft et al. (02) sample: 53 QSO spectra (30 at high res from Keck and 23 low.res)

Tytler et al. (04): 77 low resolution low S/N spectra (KAST spectrograph) at <z>=1.9

The LUQAS sample: Large Uves Quasar Absorption Spectra part of the ESO Large programme by J. Bergeron – 27 high.res and high S/N spectra at <z>=2.125 -- Kim et al. (2004)

The SDSS QSOs (release 1&2): 3300 low. resolution and low S/N QSO spectra z=2.2-4.2. McDonald et al. (2005)

Becker et al. (07) sample: 55 high.res. Spectra spanning z=2-6.4

There is a lot of astrophysics (reionization, metal enrichment, UV background etc.) as well…

3035 LOW RESOLUTION LOW S/N vs 30 HIGH RESOLUTION HIGH S/NSDSS LUQAS

SDSS vs LUQAS

McDonald et al. 2005 Kim, MV et al. 2004

The data sets-II

The data sets: the flux power -III

Main systematics:

continuum fitting + metal contamination + meanflux level determination

McDonald et al. 05SDSS

Viel, Hahnelt & Springel 04

z=2.2

z=4.2

Viel et al. 08

The interpretation: bias method - I

1. LUQAS sample analysed with the effective bias method

Viel, Haehnelt & Springel 04

DER

IVED

LIN

EA

R D

AR

K M

ATTER

PO

WER

SPE

CTR

UM z=2.125 z=2.72

2 likelihood code distributed with COSMOMC

2. SDSS power analysed by forward modelling motivated by the huge amount of data with small statistical errors

+ +

CMB: Spergel et al. (05) Galaxy P(k): Sanchez & Cole (07) Flux Power: McDonald (05)

Cosmological parameters + e.g. bias + Parameters describing IGM physics

132 data points

The interpretation: full grid of sims - II

- Cosmology

- Cosmology

- Mean flux

- T=T0 (1+)-1

- Reionization

- Metals

- Noise- Resolution

- Damped Systems

- Physics- UV background

- Small scales

Tens of thousands of modelsMonte Carlo Markov Chains

McDonald et al. 05The interpretation: full grid of sims - IIb

McDonald et al. 05: fine grid of (calibrated) HPM (quick) simulationsViel & Haehnelt 06: interpolate sparse grid of full hydrodynamical (slow) simulations

Both methods have drawbacks and advantages:

1- McDonald et al. 05 better sample the parameter space2- Viel & Haehnelt 06 rely on hydro simulations, but probably error bars are underestimated

The flux power spectrum is a smooth function of k and z

P F (k, z; p) = P F (k, z; p0) + i=1,N P F (k, z; pi) (pi - pi0)

pi

p = p0

Best fit

Flux power

p: astrophysical and cosmological parameters

but even resolution and/or box size effects if you want to save CPU time

The interpretation: flux derivatives - III

3. Independent analysis of SDSS power

RESULTS

POWER SPECTRUM AND NEUTRINOS

Results Lyman- only with full grid: amplitude and slope

McDonald et al. 05

Croft et al. 98,02 40% uncertaintyCroft et al. 02 28% uncertaintyViel et al. 04 29% uncertaintyMcDonald et al. 05 14% uncertainty

2 likelihood code distributed with COSMOMC

SDSS data only

8 = 0.91 ± 0.07n = 0.97 ± 0.04

Fitting SDSS data with GADGET-2 this is SDSS Ly- only !!

FLUX DERIVATIVES

Results Lyman- only with flux derivatives: correlations

Summary (highlights) of results

1. Tightest constraints to date on neutrino masses and running of the spectral index Seljak, Slosar, McDonald JCAP (2006) 10 014

2. Tightest constraints to date on the coldness of cold dark matter

MV et al., Phys.Rev.Lett. 100 (2008) 041304

Lesgourgues, MV, Haehnelt, Massey, 2007, JCAP, 8, 11

VHS-LUQAS: high res Ly-a from (Viel, Haehnelt, Springel 2004)SDSS-d: re-analysis of low res data SDSS (Viel & Haehnelt 2006)WL: COSMOS-3D survey Weak Lensing (Massey et al. 2007) 1.64 sq degree public available weak lensing COSMOMC module

Lyman- forest + Weak Lensing + WMAP 3yrs

VHS+WMAP1

AM

PLIT

UD

E

SPECTRAL INDEXMATTER DENSITY

http://www.astro.caltech.edu/~rjm/cosmos/cosmomc/

Lesgourgues, MV, Haehnelt, Massey, 2007, JCAP, 8, 11

Lyman- forest + Weak Lensing + WMAP 3yrs

WMAP5only Dunkley et al. 088 = 0.796 ± 0.036ns = 0.963 ± 0.015m= 0.258 ± 0.030h = 71.9 ± 2.7= 0.087 ± 0.017dn/dlnk= -0.037 ± 0.028

WMAP5+BAO+SN Komatsu et al. 08

8 = 0.817 ± 0.026ns = 0.960 ± 0.014h = 70.1 ± 1.3 = 0.084 ± 0.016

with Lyman- factor 2 improvements onthe running

|dn/dlnk| < 0.021

WMAP 5yrs

Lesgourgues & Pastor Phys.Rept. 2006, 429, 307

Lyman-forest

m = 0.138 eV

m = 1.38 eV

Active neutrinos - I

Active neutrinos - II Seljak, Slosar, McDonald, 2006, JCAP, 0610, 014

m (eV) < 0.17 (95 %C.L.) r < 0.22 (95 % C.L.)

running = -0.015 ± 0.012 Neff = 5.2 (3.2 without Ly) CMB + SN + SDSS gal+ SDSS Ly-

normal

inverted

1

2

31,2

3

Goobar et al. 06 get upper limits 2-3 times larger…… for forecasting see Gratton, Lewis, Efstathiou 2007

Tight constraints because dataare marginally compatible

2 limit

RESULTS

WARM DARK MATTER Or if you prefer.. How cold is cold dark matter?

Lyman- and Warm Dark Matter - I

CDMWDM 0.5 keV

30 comoving Mpc/h z=3

MV, Lesgourgues, Haehnelt, Matarrese, Riotto, PRD, 2005, 71, 063534

k FS ~ 5 Tv/Tx (m x/1keV) Mpc-1

In general

Set by relativistic degrees of freedom at decoupling

See Colombi, Dodelson, Widrow, 1996 Colin, Avila-Reese, Valenzuela 2000 Bode, Ostriker, Turok 2001 Abazajian, Fuller, Patel 2001 Wang & White 2007 Colin, Avila-Reese, Valenzuela 2008

Lyman- and Warm Dark Matter - II

CDM

MV, Lesgourgues, Haehnelt, Matarrese, Riotto, PRD, 2005, 71, 063534

[P (k) WDM/P (k) CDM ]1/2

P(k) = A kn T2 (k)

T x 10.75 =T g (T D)

1/3

1/3

Light gravitino contributing to a fraction of dark matter

Warm dark matter

10 eV

100 eV

MV et al., Phys.Rev.Lett. 100 (2008) 041304

Tightest constraints on mass ofWDM particles to date:

m WDM > 4 keV (early decoupled thermal relics)

m sterile > 28 keV (standard Dodelson-Widrow mechanism)

SDSS + HIRES data

(SDSS still very constraining!)

SDSS range Completely new small scale regime

Lyman- and Warm Dark Matter - III

COLD (a bit) WARM sterile 10 keV

Little room for standard warm dark matter scenarios…… … the cosmic web is likely to be quite “cold”

NEW RESULTS forSIMPLER STATISTICS ?

Fitting the flux probability distribution function

Bolton, MV, Kim, Haehnelt, Carswell (08)

T=T0(1+) -1

Flux probabilitydistributionfunction

Invertedequation of state <1 means voids arehotter than mean density regions

Fitting the flux probability distribution function-II

Bolton, MV, Kim, Haehnelt, Carswell (08)

SUMMARY- Lyman- forest is an important cosmological probe at a unique range of scales and redshifts

- Current limitations are theoretical (more reliable simulations are needed for example for neutrino species) and statistical errors are smaller than systematic ones

- Need to fit all the IGM statistics at once (mean flux + flux pdf + flux power + flux bispectrum + … ) -Tension with the CMB is partly lifted (8 went a bit up). Still very constraining for what happens at those scales:

running (inflation), neutrinos, warm dark matter candidates …

SYSTEMATICS

Systematics I: Mean flux

Effective optical depth

<F> = exp (- eff) Power spectrum of F/<F>

Low resolution SDSS like spectra

High resolution UVES like spectra

Systematics II: Thermal state

T = T0 ( 1 + )

Statistical SDSS errors on flux power

Thermal histories Flux power fractional differences

Gnedin & Hui 1998

equation of motion for gas element

if T = T0 ( 1 + )

Other similar techniques agree with the statement aboveMeiksin & White 2001

Systematics III: Numerical modelling HPM simulations

Systematics IV: Numerical modelling HPM simulations

Full hydro 200^3 part. HPM NGRID=600 HPM NGRID=400F

LUX

PO

WE

R

MV, Haehnelt, Springel (2006)

UV fluctuations from Lyman Break Galaxies Metal contribution

Systematics V: UV fluctuations and Metals

McDonald, Seljak, Cen, Ostriker 2004 Kim, MV, Haehnelt, Carswell, Cristiani (2004)

Ratio of Flux power Ratio of Flux power

m WDM > 550 eV thermal > 2keV sterile neutrino

WDM CWDM(gravitinos)

neutrinos

Lyman- and Warm Dark Matter - IV

Viel et al. (2005)from high-resz=2.1 sample

Seljak, Makarov, McDonald, Trac, PhysRevLett, 2006, 97, 191303

m WDM > 1.5-2 keV thermal > 10-14 keV sterile neutrino

MATTER FLUX

FLUX FLUX

MV, Lesgourgues, Haehnelt, Matarrese, Riotto, PhysRevLett, 2006, 97, 071301

Active neutrinos -II

m (eV) < 1 eV (95 % C.L.) WMAP1 + 2dF + LY

WDM neutrinos

Good agreement with the latest Tegmark et al. results…..

Fitting the mean flux evolution –I

Faucher-Giguere et al. (07)

McDonald et al. (05)

Lyman- and Warm Dark Matter - III

WDM 0.5 keV

MV, Lesgourgues, Haehnelt, Matarrese, Riotto, PRD, 2005, 71, 063534

WARM DARK MATTER (light) GRAVITINO

sets the transition scale f x is x/

DM

m < 16 eV (2)

SUSY < 260 TeV