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Lyman-a quasar spectra
as cosmological probes
MATTEO VIEL
INAF & INFN – Trieste
THEORY: GAS in a LCDM universe
80 % of the baryons at z=3
are in the Lyman-a forest
Bi & Davidsen (1997), Rauch (1998)
baryons as tracer of the dark
matter density field
d IGM ~ d DM at scales larger than the
Jeans length ~ 1 com Mpc
flux = exp(-t) ~ exp(-(dIGM )1.6 T -0.7 )
DATA: high resolution spectrum
Outline
- Where
we were
Mini historical background
- What data we got
The data sets
- How we used them
Theoretical framework
- What we achieved
Results
- Where we are going
Perspectives
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.
Linear matter power spectrum
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
CMB physics
z = 1100
dynamics
Continuum fitting
Lya physics
z<6
dynamics
+
termodynamics
Temperature, metals, noise
Tegmark & Zaldarriaga 2002
CMB + Lyman a
Long lever arm
Constrain spectral index and shape
Relation: P FLUX (k) - P MATTER (k) ??
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…
The data sets-II
SDSS vs LUQAS
McDonald et al. 2005
Kim, MV et al. 2004
SDSS
3035 LOW RESOLUTION LOW S/N
LUQAS
vs
30 HIGH RESOLUTION HIGH S/N
The data sets: the flux power -III
Viel, Hahnelt & Springel 04
z=4.2
z=2.2
McDonald et al. 05
SDSS
Viel et al. 08
Main systematics:
continuum fitting + metal contamination + mean
flux level determination
The interpretation: bias method - I
DERIVED LINEAR DARK MATTER POWER SPECTRUM
1.
LUQAS sample analysed with the effective bias method
z=2.125
z=2.72
Viel, Haehnelt & Springel 04
c2 likelihood code distributed with COSMOMC
The interpretation: full grid of sims - II
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)
+
132 data points
Cosmological parameters
+
e.g. bias
+
Parameters describing
IGM physics
The interpretation: full grid of sims - IIb
McDonald et al. 05
Tens of thousands of models
Monte Carlo Markov Chains
- Cosmology
- Cosmology
- Mean flux
- T=T0 (1+d)g-1
- Reionization
- Metals
- Noise
- Resolution
- Damped Systems
- Physics
- UV background
- Small scales
The interpretation: flux derivatives - III
3. Independent analysis of SDSS power
The flux power spectrum is a smooth function of k and z
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
Flux power
P F (k, z; p) = P F (k, z; p0) +
S i=1,N
Best fit
 P F (k, z; pi)
 pi
(pi - pi0)
p=p
0
p: astrophysical and cosmological parameters
but even resolution and/or box size effects if you want to save CPU time
RESULTS
POWER SPECTRUM AND NEUTRINOS
Results Lyman-a only with full grid: amplitude and slope
c2 likelihood code distributed with COSMOMC
Croft et al. 98,02
Croft et al. 02
Viel et al. 04
McDonald et al. 05
40% uncertainty
28% uncertainty
29% uncertainty
14% uncertainty
McDonald et al. 05
Results Lyman-a only with flux derivatives: correlations
Fitting SDSS data with
GADGET-2
this is SDSS Ly-a
only !!
FLUX DERIVATIVES
SDSS data only
s8 = 0.91 ± 0.07
n = 0.97 ± 0.04
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
Lyman-a forest + Weak Lensing + WMAP 3yrs
AMPLITUDE
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
http://www.astro.caltech.edu/~rjm/cosmos/cosmomc/
VHS+WMAP1
MATTER DENSITY
Lesgourgues, MV, Haehnelt, Massey, 2007, JCAP, 8, 11
SPECTRAL INDEX
Lyman-a forest + Weak Lensing + WMAP 3yrs
Lesgourgues, MV, Haehnelt, Massey, 2007, JCAP, 8, 11
|dn/dlnk| < 0.021
WMAP 5yrs
WMAP5only Dunkley et al. 08
s8 = 0.796 ± 0.036
ns = 0.963 ± 0.015
Wm= 0.258 ± 0.030
h = 71.9 ± 2.7
t= 0.087 ± 0.017
dn/dlnk= -0.037 ± 0.028
WMAP5+BAO+SN Komatsu et al. 08
s8 = 0.817 ± 0.026
ns = 0.960 ± 0.014
h = 70.1 ± 1.3
t = 0.084 ± 0.016
with Lyman-a factor 2 improvements on
the running
Active neutrinos - I
Lesgourgues & Pastor Phys.Rept. 2006, 429, 307
S m n = 0.138 eV
Lyman-a
forest
S m n = 1.38 eV
Active neutrinos - II
Seljak, Slosar, McDonald, 2006, JCAP, 0610, 014
normal
3
1,2
inverted
2
1
3
2s limit
Tight constraints because data
are marginally compatible
Smn (eV) < 0.17 (95 %C.L.)
r < 0.22 (95 % C.L.)
running = -0.015 ± 0.012
Neff = 5.2 (3.2 without Ly a)
CMB + SN + SDSS gal+ SDSS Ly-a
Goobar et al. 06 get upper limits 2-3 times larger……
for forecasting see Gratton, Lewis, Efstathiou 2007
RESULTS
WARM DARK MATTER
Or if you prefer.. How cold is cold dark matter?
Lyman-a and Warm Dark Matter - I
LCDM
30 comoving Mpc/h z=3
In general
k FS ~ 5 Tv/Tx (m x/1keV) Mpc-1
WDM
0.5 keV
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
Set by relativistic degrees of freedom at decoupling
MV, Lesgourgues, Haehnelt, Matarrese, Riotto, PRD, 2005, 71, 063534
Lyman-a and Warm Dark Matter - II
P(k) = A kn T2 (k)
[P (k)
WDM/P
LCDM
(k)
10 eV
CDM ]1/2
Light gravitino contributing
to a fraction of dark matter
100 eV
1/3
T
x
Tn
=
10.75
g (T D)
1/3
Warm dark matter
MV, Lesgourgues, Haehnelt, Matarrese, Riotto, PRD, 2005, 71, 063534
Lyman-a and Warm Dark Matter - III
MV et al., Phys.Rev.Lett. 100 (2008) 041304
SDSS + HIRES data
(SDSS still very constraining!)
Tightest constraints on mass of
WDM particles to date:
m WDM > 4 keV (early decoupled
thermal relics)
m sterile > 28 keV (standard DodelsonWidrow mechanism)
SDSS range
Completely new small scale regime
Little room for standard warm dark matter scenarios……
… the cosmic web is likely to be quite “cold”
COLD
(a bit) WARM sterile 10 keV
NEW RESULTS
for
SIMPLER STATISTICS ?
Fitting the flux probability distribution function
Bolton, MV, Kim, Haehnelt, Carswell (08)
T=T0(1+d)
g-1
Inverted
equation of state
g<1 means voids are
hotter than mean
density regions
Flux probability
distribution
function
Fitting the flux probability distribution function-II
Bolton, MV, Kim, Haehnelt, Carswell (08)
SUMMARY
- Lyman-a 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 (s8 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
Low resolution SDSS like spectra
High resolution UVES like spectra
<F> = exp (- t eff)
Power spectrum of
F/<F>
Systematics II: Thermal state
T = T0 ( 1 + d) g-1
Thermal histories
Flux power fractional differences
Statistical SDSS errors on flux power
Systematics III: Numerical modelling HPM simulations
equation of motion for gas element
if T = T0 ( 1 + d) g-1
Gnedin & Hui 1998
Other similar techniques agree with the statement above
Meiksin & White 2001
Systematics IV: Numerical modelling HPM simulations
Full hydro 200^3 part.
HPM NGRID=600
HPM NGRID=400
FLUX POWER
MV, Haehnelt, Springel (2006)
Systematics V: UV fluctuations and Metals
UV fluctuations from Lyman Break Galaxies
Ratio of Flux power
McDonald, Seljak, Cen, Ostriker 2004
Metal contribution
Ratio of Flux power
Kim, MV, Haehnelt, Carswell, Cristiani (2004)
Lyman-a and Warm Dark Matter - IV
WDM
LCWDM
(gravitinos)
MATTER
FLUX
neutrinos
FLUX
FLUX
m WDM > 550 eV thermal
> 2keV sterile neutrino
Viel et al. (2005)from high-res
z=2.1 sample
m WDM > 1.5-2 keV thermal
> 10-14 keV sterile neutrino
Seljak, Makarov, McDonald, Trac, PhysRevLett, 2006, 97, 191303
MV, Lesgourgues, Haehnelt, Matarrese, Riotto, PhysRevLett, 2006, 97, 071301
Active neutrinos -II
WDM
neutrinos
Smn (eV) < 1 eV (95 % C.L.)
WMAP1 + 2dF + LYa
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-a and Warm Dark Matter - III
WARM DARK MATTER
WDMGRAVITINO
0.5 keV
(light)
a sets the transition scale
f
x
is W x/ W DM
m < 16 eV (2s)
L
SUSY
< 260 TeV
MV, Lesgourgues, Haehnelt, Matarrese, Riotto, PRD, 2005, 71, 063534