Probing dark matter clustering using the Lyman- forest

Pat McDonald

(CITA)

COSMO06, Sep. 28, 2006

The Lyman- forest is the Ly absorption by neutral hydrogen in the intergalactic medium (IGM) observed in the spectra of high

redshift quasars

A probe of (relatively small-scale) large-scale structure

SDSS quasar spectrum

Ly-alpha forest

simulation of the IGM (25 Mpc/h, neutral hydrogen) (R. Cen)

z = 3.7 quasar

Absorption by gas at redshift z appears in a quasar spectrum at wavelength

Scales of various LSS probes

(figure by Max Tegmark)

WMAP CMB map

WMAP CMB power spectrum

SDSS Galaxies - for the LyaF we are looking in between (not literally - at high redshift)

SDSS galaxy power spectrum (Tegmark et al. 2004)

CFHTLS cosmic shear correlation function (Hoekstra et al. 2005)

Keck-HIRES Quasar Spectrum

• Neutral hydrogen• Lyman- absorption at

< 1216 (1+zq) Å

• Metal absorption small but everywhere

• Continuum fluctuations significant on large scales

• From Rauch & Sargent or Cowie

QSO spectrum at z=3

transmitted flux fraction

HIRES Spectra

Z~2

Z~3

Z~4

LyaF power from SDSS (McDonald et al. 2006) 2(k) = π-1 k P(k)

(0.01 s/km ~ 1 h/Mpc)

• Colors correspond to redshift bins centered at z = 2.2, 2.4, …, 4.2 (from bottom to top)

• 1041<rest<1185 Å • Computed using optimal weighting• Noise subtraction

• Resolution correction

• Background subtraction using regions with rest>1268 Å

• Error bars from bootstrap resampling

• Code tested on semi-realistic mock spectra

• HIRES/VLT data probes smaller scales

What is the LyaF good for?• ~100 kpc/h scales

– Warm dark matter• Gravitinos• Sterile neutrinos• “Dark matter from decays” (Kaplinghat)

– Primordial black holes

• ~1 Mpc/h scales– Inflation: running spectral index– Light neutrino masses– “Late forming dark matter in theories of neutrino dark energy”? (Weiner)

• >10 Mpc/h scales– Dark energy & curvature: baryonic acoustic oscillations

(future, McDonald & Eisenstein 2006)

SDSS LyaF Data3300 spectra with zqso>2.3

redshift distribution of quasars

1.4 million pixels in the forest

redshift distribution of Ly forest pixels

SDSS quasar spectra

• Resolution typically 160 km/s (FWHM)

• Pixel size 70 km/s

• We use spectra with S/N>1, with a typical S/N≈4 (per pixel)

• This is an unusually good one

Compute statistics of the transmitted

flux fraction, F(z)=exp(-), i.e., the spectrum after dividing by an estimate of the quasar continuum

• Use rest wavelength range 1041<rest<1185 Å

• Mean absorption ‹F(z)›• Power spectrum of fluctuations around

the mean F(z) = F(z)/ ‹F(z)›-1

LyaF power from SDSS (McDonald et al. 2006) 2(k) = π-1 k P(k)

(0.01 s/km ~ 1 h/Mpc)

• Colors correspond to redshift bins centered at z = 2.2, 2.4, …, 4.2 (from bottom to top)

• 1041<rest<1185 Å • Computed using optimal weighting• Noise subtraction

• Resolution correction

• Background subtraction using regions with rest>1268 Å

• Error bars from bootstrap resampling

• Code tested on semi-realistic mock spectra

• HIRES/VLT data probes smaller scales

Ly-alpha forest as a Ly-alpha forest as a tracer of mass/dark tracer of mass/dark mattermatter

Basic model: neutral hydrogen (HI) density is determined by Basic model: neutral hydrogen (HI) density is determined by ionization equilibrium between recombination of e and p and ionization equilibrium between recombination of e and p and HI ionization by a nearly uniform UV background, this gives HI ionization by a nearly uniform UV background, this gives

Recombination coefficient depends on gas temperatureRecombination coefficient depends on gas temperature

Neutral hydrogen traces overall gas distribution, which traces Neutral hydrogen traces overall gas distribution, which traces dark matter on large scales, with additional pressure effects dark matter on large scales, with additional pressure effects on small scales (parametrized by the filtering scale kon small scales (parametrized by the filtering scale kFF))

Best fitted model

2 ≈ 185.6 for 161 d.o.f.

• A single model fits the data over a wide range of redshift and scale

• Wiggles from SiIII-Ly cross-correlation

• Helped some by HIRES data

Linear Power Spectrum Constraint(for LCDM-like power spectrum)

1, 2, and 3-sigma error contours for the amplitude and slope of the linear power spectrum at z=3.0 and k=0.009 s/km

Basic linear power spectrum constraint from the LyaF:

Comprehensive cosmological parameter paper:Seljak, Slosar, & McDonald

astro-ph/0604335

• CMB: WMAP3, Boomerang-2k2, CBI, VSA, ACBAR

• Galaxies: SDSS-main, SDSS-LRG (BAO), 2dF

• SN: SNLS, Riess et al.

• LyaF: SDSS, HIRES

WMAP vs. LyaF (vanilla 6 parameters)Linear amp. & slope constraints at z=3, k=0.009 s/km

• Green: LyaF• Red: WMAP• Black: WMAP,

SDSS-main, SN• Yellow: All• Blue: Viel et al.

(2004) independent LyaF

WMAP vs. LyaF (including running)Linear amp. & slope constraints at z=3, k=0.009 s/km

• Green: LyaF• Red: WMAP• Black: WMAP,

SDSS-main, SN• Yellow: All• Blue: Viel et al.

(2004) independent LyaF

Warm Dark Matter constraintsSeljak, Makarov, McDonald, & Trac, astro-ph/0602430

• Free-streaming erases power on small scales.

• Simulate the LyaF power for different sterile neutrino masses:

• 6.5 keV, 10 keV, 14 keV and 20 keV

• (1.3, 1.8, 2.4, 3.1 keV for traditional WDM)

• At higher z, linear signal largely preserved

The measured 1D power spectrum is equal to the 3D power spectrum integrated over the transverse k’s. This means that the 1D power is sensitive to smaller scales than one would guess from k_parallel.

Black: CDM, Red: WDM

• Easy to see by eye… and we have almost 50000 chunks of this length.

Warm Dark Matter constraintsSeljak, Makarov, McDonald, & Trac, astro-ph/0602430

• Flux power spectrum• 3000+ SDSS spectra• HIRES data probes smaller

scales 2(k) = π-1 k P(k)

• 0.01 s/km ~ 1 h/Mpc

• Colors correspond to redshift bins centered at z = 2.2, 2.4, …, 4.2 (from bottom to top)

WDM constraints

• ~Model independent: 50% power suppression scale restricted to k>18 h/Mpc (Gaussian rms smoothing ~<45 kpc/h)

• Thermal relic (gravitino): mass>2.5 keV

• Sterile neutrino: mass>14 keV

• Agreement with other main LyaF group led by Viel (>~11 keV)

PBH dark matter constraintsAfshordi, McDonald, & Spergel (2003)

• Linear theory power.

• Primordial black hole dark matter leads to extra white noise power, increasing with increasing mass of the holes.

PBH dark matter constraintsAfshordi, McDonald, & Spergel (2003)

• Simulated LyaF power for different masses.

• Found M~<20000 M_sun

• These results were pre-SDSS.

• Working on improving them by ~ an order of magnitude.