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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
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
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
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.
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.