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 Lynds 80’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 P F (k) = b 2 (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 Ly  physics 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 =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 = Kim et al. (2004) The SDSS QSOs (release 1&2): 3300 low. resolution and low S/N QSO spectra z= 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/N SDSSLUQAS SDSS vs LUQAS McDonald et al Kim, MV et al The data sets-II

The data sets: the flux power -III Main systematics: continuum fitting + metal contamination + mean flux level determination McDonald et al. 05 SDSS 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 DERIVED LINEAR DARK MATTER POWER SPECTRUM 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 - Mean flux - T=T 0 (1+  )  -1 - Reionization - Metals - Noise - Resolution - Damped Systems - Physics - UV background - Small scales Tens of thousands of models Monte Carlo Markov Chains McDonald et al. 05 The interpretation: full grid of sims - IIb

McDonald et al. 05: fine grid of (calibrated) HPM (quick) simulations Viel & 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 space 2- 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; p 0 ) +   i=1,N  P F (k, z; p i ) (p i - p i 0 )  p i p = p 0 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% uncertainty Croft et al % uncertainty Viel et al % uncertainty McDonald et al % uncertainty  2 likelihood code distributed with COSMOMC

SDSS data only  8 = 0.91 ± 0.07 n = 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) Tightest constraints to date on the coldness of cold dark matter MV et al., Phys.Rev.Lett. 100 (2008)

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 AMPLITUDE SPECTRAL INDEXMATTER DENSITY

Lesgourgues, MV, Haehnelt, Massey, 2007, JCAP, 8, 11 Lyman-  forest + Weak Lensing + WMAP 3yrs WMAP5only Dunkley et al. 08  8 = ± n s = ±  m = ± h = 71.9 ± 2.7  = ± dn/dlnk= ± WMAP5+BAO+SN Komatsu et al. 08  8 = ± n s = ± h = 70.1 ± 1.3  = ± with Lyman-  factor 2 improvements on the running |dn/dlnk| < WMAP 5yrs

Lesgourgues & Pastor Phys.Rept. 2006, 429, 307 Lyman-   forest  m = 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 = ± Neff = 5.2 (3.2 without Ly  ) CMB + SN + SDSS gal+ SDSS Ly-  normal inverted ,2 3 Goobar et al. 06 get upper limits 2-3 times larger…… for forecasting see Gratton, Lewis, Efstathiou 2007 Tight constraints because data are marginally compatible 2  limit

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

Lyman-  and Warm Dark Matter - I  CDM WDM 0.5 keV 30 comoving Mpc/h z=3 MV, Lesgourgues, Haehnelt, Matarrese, Riotto, PRD, 2005, 71, k FS ~ 5 T v /T x (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, [P (k) WDM /P (k) CDM ] 1/2 P(k) = A k n T 2 (k) T x = T g (T D ) 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) Tightest constraints on mass of WDM 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 for SIMPLER STATISTICS ?

Fitting the flux probability distribution function Bolton, MV, Kim, Haehnelt, Carswell (08) T=T 0 (1+  )  -1 Flux probability distribution function Inverted equation of state  <1 means voids are hotter 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 = exp (-  eff ) Power spectrum of F/ Low resolution SDSS like spectra High resolution UVES like spectra

Systematics II: Thermal state T = T 0 ( 1 +  )  Statistical SDSS errors on flux power Thermal histories Flux power fractional differences

Gnedin & Hui 1998 equation of motion for gas element if T = T 0 ( 1 +  )  Other similar techniques agree with the statement above Meiksin & White 2001 Systematics III: Numerical modelling HPM simulations

Systematics IV: Numerical modelling HPM simulations Full hydro 200^3 part. HPM NGRID=600 HPM NGRID=400 FLUX POWER 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

m WDM > 550 eV thermal > 2keV sterile neutrino WDM  CWDM (gravitinos) neutrinos Lyman-  and Warm Dark Matter - IV Viel et al. (2005)from high-res z=2.1 sample Seljak, Makarov, McDonald, Trac, PhysRevLett, 2006, 97, m WDM > keV thermal > keV sterile neutrino MATTER FLUX FLUX MV, Lesgourgues, Haehnelt, Matarrese, Riotto, PhysRevLett, 2006, 97,

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, WARM DARK MATTER (light) GRAVITINO  sets the transition scale f x is  x /  DM m < 16 eV (2  )  SUSY < 260 TeV