Rupert Croft

Rupert 

Croft 

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Plan for lecture 1: 

• History : -the first quasar spectra 

-first theoretical models (all wrong) 

-CDM cosmology meets the Lya forest 

• The Lya forest in simulations 

• The Lya forest as cosmological tool: 

•Conclusions 

-the matter power spectrum 

-constraints on neutrino mass 

-baryon oscillations

Plan for lecture 2: 

• Recap : - The physics of the Lya forest 

• Searching for the ionized baryons: CMB-Lya cross 

correlations 

• The Lya forest and the cosmic radiation field 

• Searching the forest for light echoes from dead 

quasars 

• Measuring quasar and galaxy halo masses 

from the Lya forest around them. 

• The future of Lya forest studies


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First optically 

identified 

quasar 

(Maarten 

Schmidt 1965)

Gunn and Peterson (1965)

Energy levels of a Hydrogen atom

We are 

interested in 

the transmitted flux, F: 

wavelength 

F=F observed 

F intrinsic quasar 

spectrum 

F=e -τ 

for H at mean density, 

of the Universe 

τ=10 6 !

Bahcall and Salpeter (1965)

First published high-z QSO spectrum: 

Lynds and Stockton (1966)


Lynds and Stockton (1966) 

Lya 

forest

What is the mean 

density of baryons? 

It is less than 

4 particles per 

cubic meter.

ut from the absorption seen in spectra, the 

number density of neutral H atoms is 10 6 times 

less! 

Why? We think the Hydrogen is still there, but 

How do we detect these neutral atoms?


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How do we detect these neutral atoms?


Lynds and Stockton (1966) 

Lya 

forest

• If we take a spectrum of a quasar, we can see material 

in absorption: 

• Light travelling to us from the quasar gets 

redshifted by the expansion. When the 

wavelength of light gets to the Lyman-alpha 

wavelength, there is a probability that a 

photon will be absorbed by neutral hydrogen 

gas at that redshift. 

Ly-alpha 

emission line 

at quasar 

redshift

What is the physical interpretation of the 

absorption features we see? 

(1966-1994) The original picture: 

discrete small clouds + intercloud medium 


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The width of the clouds in this original model is set 

by thermal (Doppler) broadening and the intrinsic width 

(Lorentzian)because the clouds are physically very 

small in this model

Do these small clouds really exist? 

What are they physically? 

People tried to explain ….

Failed models 


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Ejected from host QSOs 


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Pressure confined clouds 


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Dark matter confined clouds (minihalos) 


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The correct model: 

A fluctuating low density photoionized medium 

•absorption is caused by structures which have 

not yet undergone gravitational collapse 

•broadening is done by Hubble flow 

How did we find this out? 

First models by Bi (1991), Bi Ge & Fang (1992) using 

linear theory. But did not gain wide acceptance 

until advent of numerical simulations. 

e.g. Cen et al (1994), Hernquist et al (1996)

With the simulations we are effectively solving for 

dark 

matter 

dynamics 

Boltzmann 

eqn . 

Poisson 

equation. 

gas 

dynamics

The stars in a simulated universe

The baryons in a simulated universe


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There is no intercloud medium 

-the clouds are the medium 


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absorption level in quasar spectra tells you how much 

neutral hydrogen there is along the line of sight

Simulated spectrum of background quasar. 

F=e -τ 

This Lyman-alpha “forest” can give us a 1D map of the density field.

Baryons trace dark matter well on scales above the 

pressure smoothing scale, ~100 kpc/h 

if we understand how the baryons are distributed, 

we can measure the clustering properties of the 

dark matter from the Lya forest. 

What is the physics involved?

Competition between 

photoionization 

heating 

adiabatic cooling from 

the expansion of the Universe 

drives gas elements 

onto a power-law 

temperature relation 

Hui & Gnedin (1997) 

α∼0.6

For the gas in photoionization equilibrium, 

photo 

ionization 

rate 

(The recombination rate for gas at these 

temperatures is proportional to T -0.7) 

We already know that so the neutral 

hydrogen density and hence optical depth τ: 

(known as the FGPA, Fluctuating Gunn-Peterson Approximation)

or more simply, 

Density of matter 

τ ∝ 

[ 

ρ 

( r)] 

J ( r) 

~ 

1.6 

remember that 

F=e -τ 

(observable quantity) 

also 

Ionizing radiation intensity 

Analyses assume that J(r) is a constant (does not fluctuate 

spatially), so that measuring properties of F will give us 

properties of ρ (such as P(k)) 

We assume this for now - we will drop this assumption tomorrow

Additional physics which could disrupt this simple picture: 

Star formation and supernova winds:

FGPA measured from simulation which includes 

additional physics (star formation, stellar winds etc) 

τ 

It works very well - we can use this knowledge to do cosmology

How do we quantify structure in the Universe? 

• One way to describe fluctuations 

statistically is to decompose them into 

Fourier modes (3 dimensional plane 

waves). 

• If we Fourier transform the Universe, 

we can get the density contrast at 

a point in space from a superposition 

of Fourier modes: 

Fourier amplitude 

for plane wave with 3d 

wavevector k 

(wavelength of mode 

is λ=2π/k)

• The variance of the mode amplitudes is known as the 

power spectrum: 

• P(k) tells you how large the fluctuations are for a 

given scale (for wavenumber k).

Here is the galaxy power spectrum, but what is the 

matter power spectrum? 

Surveys of different 

types of galaxies have 

different power spectra

People assume that on large scales, 

P galaxies (k) = b P matter (k) 

but what is b? Unknown “biasing” 

relation - cannot yet be predicted from 

first principles or using simulations. 

~ 

However we know that for the lyman-alpha forest 

we can predict the “biasing relation”: 

observed 

quantity 

τ ∝ 

[ ρ ( r)] 

J ( r) 

1.6 

matter density 

so we can use lyman alpha forest measurements 

to estimate P matter (k)

We measure clustering in 1 dimension, along a 

sightline. How is this related to 3D clustering? 

(Kaiser and 

Peacock 1991) 

3D 

power spectrum

First application, to a single quasar spectrum 

(RC et al, 1998) 

From the lyman alpha flux 

power spectrum 

to the matter power 

spectrum

SDSS 

quasar spectrum 

low quality spectra are still useful

Sloan Digital 

Sky Survey 

Data Release 1 

Bright quasars: 

= -27 

Mpc/h

flux power spectrum from 

3400 SDSS spectra 

McDonald et al (2006)

Why are measurements of matter clustering 

from the lya forest useful? 

Spergel 

et al (2003) 

The power spectrum of matter fluctuations constrains 

cosmology – but the WMAP and galaxy data can only probe large scales

From Max Tegmark’s webpage

Applications of Lyman alpha forest 

measurements. 

First - constraining the neutrino mass…

Massive neutrinos suppress the clustering of matter on small scales 

if they make up some fraction of the total matter density. 

Eisenstein 

and Hu (1998) 

This is because they are light enough that they were relativistic in the 

early Universe when they decoupled from the rest of matter.

The Lyman alpha forest works well 

to constrain the neutrino mass because it 

measures clustering on small scales: 

A simulation 

test 

which 

included 

massive 

neutrino 

particles 

(10 eV) 

(RC, Hu and Dave’ (1999))

Constraints on 

neutrino mass 

from combination 

of CMB and 

Lyman-alpha 

data 

These are 

from 1999 

current constraints 

are better 

~ 1 eV

Lya clustering can also 

constrain warm dark matter 

candidates, and rule 

out sterile neutrinos.

Even better 

limits from 

Viel et al (2007)

The Lya forest power spectrum can 

constrain inflationary parameters, like the 

scalar spectral index and the roll: 

From Seljak et al (2005)

The Lya forest will also be used in the 

future to constrain dark energy. 


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size of the 

sound horizon 

at matter-radiation 

equality 

WMAP 

Spergel et al 


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Baryon acoustic oscillations make a 

standard ruler 


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SDSS Galaxies z~0.3 

CMB z~1100 

Percival et al (2007) 

The Lyman alpha forest could do this at z~3

Need a survey 

with a huge volume 

and many spectra…

Predictions by McDonald and Eisenstein (2007) 

BOSS 

will measure 

acoustic scale 

to 1% at z=3 

(compare to 

~5% precision 

of present 

measurement at 

z~0.3)

Conclusions for part I 

• The lyman alpha forest arises in a 

fluctuating photoionized intergalactic medium, 

not from gravitationally collapsed objects. 

• Understanding this simple physics means 

that it provides one dimensional maps of the 

density field. 

• This can be used to do cosmology: 

-by measuring P(k) on smaller 

scales than is possible with 

the CMB and galaxy surveys 

• Upcoming surveys will enable us to 

move to even larger scales.

Rupert Croft

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