Large Scale Structure with the Lyman-α Forest

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r

Your Name and Collaborators

Large Scale Structure with

the Lyman-α Forest

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Redshift Surveys

Lo ok ba ck time

(bi llio n y ea rs)

BOSS Lyα forest 160k spectra 2.0 < z < 3.5

BOSS galaxies 1.3M spectra 0.2 < z < 0.7

Overdensity

Underdensity

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Outline

• ^Motivation

• Introducing the Lyman-α forest

• Physics of the Lyman-α forest

• Lyman-α forest as a biased tracer

• Analysing the Lyman-α forest

• Recent results from BOSS

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Motivation I: expanding universe at high-z

Expa ns io n ra te

Redshift

Planck prediction

Acceleration

Deceleration

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Motivation II: small scale clustering

time Ea rl y time

Small scales Large scales

CMB

Photometric Galaxies

CMB Lensing

1 2 Red shi ft 5 1100

21cm?

Lyman-α forest offers a unique window to study

small scale clustering

Combined with CMB, it allows us to study:

• dark matter properties

• neutrino mass

• shape of primordial P(k)

Lyman-α Forest

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Fuerteventura - Sep 21th 2017

Andreu Font-Ribera - Large Scale Structure with the Lyman-α Forest 6

Motivation III: 3D tomography

Cosmic voids 3

Figure 1. A slice through our simulation and a mock reconstructed flux map centered on a large void, with a radius of 9.8 h ¹Mpc. The slice is 22 h ¹Mpc across and 6 h ¹Mpc into the page. (Left) The matter density, in real space. The void center and radius are indicated with a black dot and dashed circle. Positions of halos with M > 10¹² h ¹M are plotted as green dots and positions of halos with M > 3⇥ 10¹¹h ¹M are plotted as yellow dots. These halos would host galaxies at the spectroscopic limits for existing instrumentation.

(Middle left) The matter density, in redshift space. (Middle right) The ‘true’ flux field over the same volume, in redshift space. (Right) A reconstructed flux field from a mock survey (also in redshift space) with average sightline spacing, d_? = 2.5 h ¹Mpc (see text).

parallel direction due to redshift-space distortions (RSDs).

Although the tomographic flux map is a blurred version of the true flux, the void structure is so large that it can still easily be picked out by eye. For reference, the tomographic map is one of the realizations from Stark et al. (2014) with an average sightline spacing of d_? = 2.5 h¹ Mpc, similar to the ongoing survey of Lee et al. (2014a). At the same time, the void is not captured by the galaxy positions. Based on sim- ple abundance matching, (Figure 2) we expect these halos to host galaxies which would just be bright enough for redshift determination with existing facilities. The relative sparsity of such halos highlights the difficulty in finding voids, even large ones, at high redshift using galaxies as tracers.

We compared our void catalog with that produced by a watershed void finder, similar to the ZOBOV code. The watershed method finds the set of connected elements all under some threshold. In ZOBOV the elements are the Voronoi cells in the tessellation of the dark matter particle positions (where the density is estimated from the volume of the Voronoi cell), but in this case, we use the density val- ues on the 2560³ for simplicity. The watershed algorithm on a uniform grid is also straightforward. We find the set of points under the given threshold, and keep a list of the under-threshold points that have not been assigned to a spe- cific watershed. Starting with the minimum value point, we search grid neighbors to see if they are also under the threshold and add them to the current watershed. The search stops when there are no remaining neighbors under the threshold. These points are then removed from the list of unas- signed points and we move on to the next watershed. After we assign all points under the threshold, we discard water- sheds with an e↵ective radius re↵ = (_4⇡³ Vshed)^1/3 less than 2 h ¹Mpc, as we did with the spherical underdensity voids.

Using this method with the same threshold of ⇢ < 0.2 ¯⇢, we found 6364 voids, covering 5% of the simulation volume.

The sets of voids in the spherical underdensity (or SO)

ally inspected the 100 largest voids in the SO catalog, and found matches in the watershed catalog. However, in most cases the watershed void e↵ective radius is 1 – 2 h ¹Mpc smaller, which explains the total volume di↵erence, and the watershed voids typically have complex morphologies. The watershed voids often have an ellipsoidal core, with fingers stretching out into smaller low-density regions. We compared the SO void centers to the watershed void value- weighted centroids ~xshed = P

i ~xi⇢_i ¹/P

i ⇢_i ¹, where the sums are over all the points in the shed, and we weight by the inverse of the density so that the centering is driven by lower-density points. Unfortunately, the non-spherical ge- ometries of the watershed voids tend to drive the centroid away from the center found with the SO method and the centers in the two catalogs tend to disagree by several Mpc.

See Appendix A for more discussion and images of voids. It is reassuring that these two methods for finding voids in the density field qualitatively agree well, but we decided to use the SO void catalog for the remainder of the work due to their simplicity. [CS: should discuss more...]

3 VOIDS AT z = 2.5

In Figure 3, we show the cumulative number density of voids vs. the void radius. As expected, there are many more small voids and voids are generally smaller at z = 2.5 than at z ' 0 (c.f. Figure 1 of Ceccarelli et al. 2006 or Figure 7 of Lavaux

& Wandelt 2012). While voids with radii of 7 h ¹Mpc are common for low-redshift studies, we have only 126 voids with r > 7 h ¹Mpc, which cover two percent of the simulation volume. We note, however, that it is difficult to compare halo sizes across works using di↵erent void-finding methods and working at di↵erent redshifts. For instance, we could increase the number of r > 7 h ¹Mpc voids by simply in- creasing the average target value in our SO void finder. For

CLAMATO (Lee et al. 2016): high-density survey over tiny area

We can map the cosmic web at high redshift (z > 2)

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Outline

• ^Motivation

• Introducing the Lyman-α forest

• Physics of the Lyman-α forest

• Lyman-α forest as a biased tracer

• Analysing the Lyman-α forest

• Recent results from BOSS

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Introducing the Lyman-α forest

z=3.56

z=2.95

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Introducing the Lyman-α forest

Lyman-α video by Andrew Pontzen

https://www.youtube.com/watch?v=6Bn7Ka0Tjjw

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Introducing the Lyman-α forest

CLAMATO video by KG Lee

https://www.youtube.com/watch?v=TVHlGDxYlQk

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Outline

• ^Motivation

• Introducing the Lyman-α forest

• Physics of the Lyman-α forest

• Lyman-α forest as a biased tracer

• Analysing the Lyman-α forest

• Recent results from BOSS

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Physics of the Lyman-α forest

Rauch 1998, Meiksin 2009, McQuinn 2015

Let us ignore Helium today

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Physics of the Lyman-α forest

Let us simplify the model to have a better intuition

We can describe the gas/baryons as a fluctuating field around its mean density

Temperature - density relation (good approximation at low densities)

equation of state of gas

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Physics of the Lyman-α forest

Peculiar velocities of the gas change absorption features

Coherent velocities change absorption position

Random velocities caused by gas temperature broaden lines

McDonald 2003

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Physics of the Lyman-α forest

We can simulate it very well using hydrodynamic simulations

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Outline

• ^Motivation

• Introducing the Lyman-α forest

• Physics of the Lyman-α forest

• Lyman-α forest as a biased tracer

• Analysing the Lyman-α forest

• Recent results from BOSS

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Lyman-α forest as a biased tracer

What do we mean by bias? It can get confusing…

Consider an observable 𝝉 tracing density fluctuations If you like configuration space

If you prefer Fourier space

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Lyman-α forest as a biased tracer

Taylor expansion on powers of density fluctuations

McDonald 2006

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Lyman-α forest as a biased tracer

EXAM: What is the bias of the following tracers?

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Lyman-α forest as a biased tracer

Linear redshift space distortions (RSD) in galaxy clustering The volume is deformed in redshift space

Density of galaxies is modified by velocity gradient

In Fourier space, and assuming linear perturbation theory

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Lyman-α forest as a biased tracer

Same applies for linear RSD in optical depth

How about the Lyman-α forest?

And in Fourier space

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Fuerteventura - Sep 21th 2017

Andreu Font-Ribera - Large Scale Structure with the Lyman-α Forest 22

Lyman-α forest as a biased tracer

Just like galaxies, the Forest is a tracer of the density field

2 Galaxy Power spectrum

h ^g (k) _g (k 0)i = (2⇡) ^{3 D} (k + k 0) P ^g (k) (12) Kaiser formula

P _g (k) = b ² _g 1 + _g µ ² _k ² P (k) (13)

g = f

b _g (14)

✓ S N

◆ 2 g

= N _k P _g ² (k)

g 2 (k) (15)

g 2 (k) = 2 P _g (k) + n _g ¹ ² (16)

II. LY↵ CLUSTERING

First done by [1], we will use terminology from [2].

Ly↵ forest trace total density

F (x) = F [⇢(x)] (17)

Definition of galaxy overdensity

F (x) = ¯ F (1 + _F (x)) (18)

Redshift space distortions

F [⇢, ⌘] = F [⇢ = 0, ⌘ = 0] + @F

@⇢ ^⇢ + @F

@⌘ ⌘ + ... (19)

Fourier space bias

F (k) = b ^F _⇢ + b ^F _⌘ f µ ² _k _⇢ (k) = b _F 1 + _F µ ² _k _⇢ (k) (20) Ly↵ forest Power spectrum

h ^F (k) _F (k 0)i = (2⇡) ^{3 D} (k + k 0) P ^F (k) (21) Kaiser formula

P _F (k) = b ² _F 1 + _F µ ² _k ² P (k) (22)

F = b ^F _⌘ f

b ^F _⇢ (23)

✓ S N

◆ 2 F

= N _k P _F ² (k)

F 2 (k) (24)

✓ _1D ◆ ²

2 Galaxy Power spectrum

h ^g (k) _g (k 0)i = (2⇡) ^{3 D} (k + k 0) P ^g (k) (12) Kaiser formula

P _g (k) = b ² _g 1 + _g µ ² _k ² P (k) (13)

g = f

b _g (14)

✓ S N

◆ 2 g

= N _k P _g ² (k)

g 2 (k) (15)

g 2 (k) = 2 P _g (k) + n _g ¹ ² (16)

II. LY↵ CLUSTERING

First done by [1], we will use terminology from [2].

Ly↵ forest trace total density

F (x) = F [⇢(x)] (17)

Definition of galaxy overdensity

F (x) = ¯ F (1 + _F (x)) (18)

Redshift space distortions

F [⇢, ⌘] = F [⇢ = 0, ⌘ = 0] + @F

@⇢ ^⇢ + @F

@⌘ ⌘ + ... (19)

Fourier space bias

F (k) = b ^F _⇢ + b ^F _⌘ f µ ² _k _⇢ (k) = b _F 1 + _F µ ² _k _⇢ (k) (20) Ly↵ forest Power spectrum

h ^F (k) _F (k 0)i = (2⇡) ^{3 D} (k + k 0) P ^F (k) (21) Kaiser formula

P _F (k) = b ² _F 1 + _F µ ² _k ² P (k) (22)

F = b ^F _⌘ f

b ^F _⇢ (23)

✓ S N

◆ 2 F

= N _k P _F ² (k)

F 2 (k) (24)

F 2 (k) = 2

✓

P _F (k) + P ^1D (kµ) + P _N n ^2D _q

◆ ²

(25)

Galaxy clustering

2 Galaxy Power spectrum

h ^g (k) _g (k 0)i = (2⇡) ^{3 D} (k + k 0) P ^g (k) (12) Kaiser formula

P _g (k) = b ² _g 1 + _g µ ² _k ² P (k) (13)

g = f

b _g (14)

✓ S N

◆ 2 g

= N _k P _g ² (k)

g 2 (k) (15)

g 2 (k) = 2 P _g (k) + n _g ¹ ² (16)

II. LY↵ CLUSTERING

First done by [1], we will use terminology from [2].

Ly↵ forest trace total density

F (x) = F [⇢(x)] (17)

Definition of galaxy overdensity

F (x) = ¯ F (1 + _F (x)) (18)

Redshift space distortions

F [⇢, ⌘] = F [⇢ = 0, ⌘ = 0] + @F

@⇢ ^⇢ + @F

@⌘ ⌘ + ... (19)

Fourier space bias

F (k) = b ^F _⇢ + b ^F _⌘ f µ ² _k _⇢ (k) = b _F 1 + _F µ ² _k _⇢ (k) (20) Ly↵ forest Power spectrum

h ^F (k) _F (k 0)i = (2⇡) ^{3 D} (k + k 0) P ^F (k) (21) Kaiser formula

P _F (k) = b ² _F 1 + _F µ ² _k ² P (k) (22)

F = b ^F _⌘ f

b ^F _⇢ (23)

✓ S N

◆ 2 F

= N _k P _F ² (k)

F 2 (k) (24)

F 2 (k) = 2

✓

P _F (k) + P ^1D (kµ) + P _N n ^2D _q

◆ ²

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2 Galaxy Power spectrum

h

^g

(k)

_g

(k 0)i = (2⇡)

^{3 D}

(k + k 0) P

^g

(k) (12) Kaiser formula

P

_g

(k) = b

²_g

1 +

_g

µ

²_k ²

P (k) (13)

g

= f

b

_g

(14)

✓ S N

◆

2 g

= N

_k

P

_g²

(k)

g2

(k) (15)

g2

(k) = 2 P

_g

(k) + n

_g ¹ ²

(16)

II. LY↵ CLUSTERING

First done by [1], we will use terminology from [2].

Ly↵ forest trace total density

F (x) = F [⇢(x)] (17)

Definition of galaxy overdensity

F (x) = ¯ F (1 +

_F

(x)) (18)

Redshift space distortions

F [⇢, ⌘] = F [⇢ = 0, ⌘ = 0] + @F

@⇢

^⇢

+ @F

@⌘ ⌘ + ... (19)

Fourier space bias

F

(k) = b

^F_⇢

+ b

^F_⌘

f µ

²_k _⇢

(k) = b

_F

1 +

_F

µ

²_k _⇢

(k) (20) Ly↵ forest Power spectrum

h

^F

(k)

_F

(k 0)i = (2⇡)

^{3 D}

(k + k 0) P

^F

(k) (21) Kaiser formula

P

_F

(k) = b

²_F

1 +

_F

µ

²_k ²

P (k) (22)

F

= b

^F_⌘

f

b

^F_⇢

(23)

✓ S N

◆

2 F

= N

_k

P

_F²

(k)

F2

(k) (24)

F2

(k) = 2

✓

P

_F

(k) + P

^1D

(kµ) + P

_N

n

^2D_q

◆

²

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Forest clustering

3 III. CROSS-CORRELATION

We will use terminology from [2].

Ly↵ forest Power spectrum

h

^F

(k)

_Q

(k 0)i = (2⇡)

^{3 D}

(k + k 0) P

^{F Q}

(k) (26) Kaiser formula

P

_{F Q}

(k) = b

_F

b

_Q

1 +

_F

µ

²_k

1 +

_Q

µ

²_k

P (k) (27)

✓ S N

◆

2

F Q

= N

_k

P

_{F Q}²

(k)

F Q2

(k) (28)

F Q2

(k) = P

_{F Q}²

(k) +

✓

P

_F

(k) + P

^1D

(kµ) + P

_N

n

^2D_q

◆ ✓

P

_Q

(k) + 1 n

^3D_q

◆ (29)

IV. EBOSS SRD

F2

(k) = 2

✓

P

_F

(k) + P

^1D

(kµ) + P

_N

n

^2D_q

◆

²

= 2 P

_F

(k) + P

^1D

(kµ) n

^2D_{ef f}

!

2

⇠ 2 P

^1D

(kµ) n

^2D_{ef f}

!

2

(30)

n

_{ef f}

= n

^2D_q

h⌫i = n

^2Dq

⌧ P

^1D

(kµ)

P

^1D

(kµ) + P

_N

(31)

BAO2

/ 1

A n

²_{ef f}

(32)

BOSS2

BOSS+eBOSS2

= A

^BOSS

A

^eBOSS

(n

^BOSS_{ef f}

)

²

+ A

^eBOSS

(n

^BOSS+eBOSS_{ef f}

)

²

A

^BOSS

(n

^BOSS_{ef f}

)

²

= (1 Y ) + Y (1 + X)

²

(33)

BOSS2

BOSS+eBOSS2

= (1 Y ) + Y (1 + X)

²

(34)

1 + X = n

^BOSS+eBOSS_{ef f}

n

^BOSS_{ef f}

(35)

Y = A

^eBOSS

A

^BOSS

(36)

dX = f

n

^2D_{q BOSS}

⇠ 0.067 f (37)

dX = ⌫

_new

⌫

_old

h⌫

^BOSS

i ⇠ 0.025 (38)

3 III. CROSS-CORRELATION

We will use terminology from [2].

Ly↵ forest Power spectrum

h

^F

(k)

_Q

(k 0)i = (2⇡)

^{3 D}

(k + k 0) P

^{F Q}

(k) (26) Kaiser formula

P

_{F Q}

(k) = b

_F

b

_Q

1 +

_F

µ

²_k

1 +

_Q

µ

²_k

P (k) (27)

✓ S N

◆

2

F Q

= N

_k

P

_{F Q}²

(k)

F Q2

(k) (28)

F Q2

(k) = P

_{F Q}²

(k) +

✓

P

_F

(k) + P

^1D

(kµ) + P

_N

n

^2D_q

◆ ✓

P

_Q

(k) + 1 n

^3D_q

◆ (29)

IV. EBOSS SRD

F2

(k) = 2

✓

P

_F

(k) + P

^1D

(kµ) + P

_N

n

^2D_q

◆

²

= 2 P

_F

(k) + P

^1D

(kµ) n

^2D_{ef f}

!

2

⇠ 2 P

^1D

(kµ) n

^2D_{ef f}

!

2

(30)

n

_{ef f}

= n

^2D_q

h⌫i = n

^2Dq

⌧ P

^1D

(kµ)

P

^1D

(kµ) + P

_N

(31)

BAO2

/ 1

A n

²_{ef f}

(32)

BOSS2

BOSS+eBOSS2

= A

^BOSS

A

^eBOSS

(n

^BOSS_{ef f}

)

²

+ A

^eBOSS

(n

^BOSS+eBOSS_{ef f}

)

²

A

^BOSS

(n

^BOSS_{ef f}

)

²

= (1 Y ) + Y (1 + X)

²

(33)

BOSS2

BOSS+eBOSS2

= (1 Y ) + Y (1 + X)

²

(34)

1 + X = n

^BOSS+eBOSS_{ef f}

n

^BOSS_{ef f}

(35)

Y = A

^eBOSS

A

^BOSS

(36)

dX = f

n

^2D_{q BOSS}

⇠ 0.067 f (37)

dX = ⌫

_new

⌫

_old

h⌫

^BOSS

i ⇠ 0.025 (38)

Cross-correlation

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Outline

• ^Motivation

• Introducing the Lyman-α forest

• Physics of the Lyman-α forest

• Lyman-α forest as a biased tracer

• Analysing the Lyman-α forest

• Recent results from BOSS

(24)

Fuerteventura - Sep 21th 2017 Andreu Font-Ribera - Large Scale Structure with the Lyman-α Forest

Analysing the Lyman-α forest

24

f _q ( ) = C _q ( )F _q ( )

= _↵ (1 + z)

Observed flux Transmitted fraction

Quasar continuum

Absorption redshift Observed wavelength

LyaF wavelength (121.6 nm)

F (x) = F (x) F ¯ F ¯

Flux fluctuations in pixels trace the density along the line of sight to the quasar

N.G. Busca et al.: BAO in the Lyα forest of BOSS quasars

(section 4). This early freezing of procedures resulted in some that are suboptimal but which will be improved in future analy- ses. We note, however, that the procedures used to extract cosmological information (section 5) were decided on only after de-masking the data.

440 460 480 500 520 540

! (nm)

!5 0 5 10 15 20

flux [10!17 erg s!1 cm!2 A!1 ]

Method 1 Method 2

Fig. 3. An example of a BOSS quasar spectrum of redshift 3.239. The red and blue lines cover the forest region used here, 104.5 < λ_rf < 118.0. This region is sandwiched between the quasar’s Lyβ and Lyα emission lines respectively at 435 and 515 nm. The blue line is an estimate of the continuum (unab- sorbed flux) by method 2 and the red line is the estimate of the product of the continuum and the mean absorption by method 1.

3.1. Continuum fits, method 1

Both methods for estimating the product C_qF assume that C_q is, to first approximation, proportional to a universal quasar spectrum that is a function of rest-frame wavelength, λ_rf = λ/(1 + z_q) (for quasar redshift z_q), multiplied by a mean transmission fraction that slowly varies with absorber redshift. Following this as- sumption, the universal spectrum is found by stacking the ap- propriately normalized spectra of quasars in our sample, thus averaging out the fluctuating Lyα absorption. The product C_qF for individual quasars is then derived from the universal spectrum by normalizing it to account for the quasar’s mean forest flux and then modifying its slope to account for spectral-index diversity and/or photo-spectroscopic miscalibration.

Method 1 estimates directly the product C_qF in equation 2.

An example is given by the red line in figure 3. The estimate is made by modeling each spectrum as

C_qF = a_q

! λ

⟨λ⟩

"^bq

f (λ_rf,z) (6)

where a_q is a normalization, b_q a “deformation parameter”, and

⟨λ⟩ is the mean wavelength in the forest for the quasar q and f (λ_rf,z) is the mean normalized flux obtained by stacking spectra in bins of width ∆z = 0.1:

f (λ_rf,z) = #

q

w_qf_q(λ)/ f_q¹²⁸/ #

q

w_q . (7)

Here z is the redshift of the absorption line at observed wave-

at wavelength λ and f_q¹²⁸ is the average of the flux of quasar q for 127.5 < λ_rf < 128.5 nm. The weight w_q(λ) is given by w⁻¹_q = 1/[ivar(λ) · ( fq¹²⁸)²] + σ²_{f lux, LSS}. The quantity ivar is the pipeline estimate of the inverse flux variance in the pixel corre- sponding to wavelength λ. The quantity σ²_{f lux, LSS} is the contri- bution to the variance in the flux due to the LSS. We approxi- mate it by its value at the typical redshift of the survey, z ∼ 2.3:

σ²_{f lux, LSS} ∼ 0.035 (section 3.3).

Figure 4 shows the resulting mean δ_i as a function of observed wavelength. The mean fluctuates about zero with up to 2% deviations with correlated features that include the H and K lines of singly ionised calcium (presumably originataing from some combination of solar neighborhood, interstellar medium and the Milky Way halo absorption) and features related to Balmer lines. These Balmer features are a by-product of imper- fect masking of Balmer absorption lines in F-star spectroscopic standards, which are used to produce calibration vectors (in the conversion of CCD counts to flux) for DR9 quasars. Therefore such Balmer artifacts are constant for all fibers in a plate fed to one of the two spectrographs and so they are approximately constant for every ’half-plate’.

If unsubtracted, the artifacts in figure 4 would lead to spurious correlations, especially between pairs of pixels with separations that are purely transverse to the line of sight. We have made a global correction by subtracting the quantity ⟨δ⟩(λ) in figure 4 (un-smoothed) from individual measurements of δ. This is justi- fied if the variance of the artifacts from half-plate-to-half-plate is suﬃciently small, as half-plate-wide deviations from our global correction could, in principle add spurious correlations.

We have investigated this variance both by measuring the Balmer artifacts in the calibration vectors themselves and by studying continuum regions of all available quasars in the DR9 sample. Both studies yield no detection of excess variance aris- ing from these artifacts, but do provide upper limits. The study of the calibration vectors indicate that the square-root of the variance is less than 20% of the mean Balmer artifact deviations and the study of quasar spectra indicate that the square-root of the variance is less than 100% of the mean Balmer artifacts (and less than 50% of the mean calcium line deviations).

We then performed Monte Carlo simulations by adding a random sampling of our measured artifacts to our data to con- firm that our global correction is adequate. We found that there is no significant eﬀect on the determination of the BAO peak position, even if the variations are as large as that allowed in our tests.

3.2. Continuum fits, method 2

Method 1 would be especially appropriate if the fluxes had a Gaussian distribution about the mean absorbed flux, C_qF. Since this is not the case, we have developed method 2 which explicitly uses the probability distribution function for the transmitted flux fraction F, P(F, z), where 0 < F < 1. We use the P(F, z) that results from the log-normal model used to generate mock data (see appendix A).

Using P(F, z), we can construct for each BOSS quasar the PDF of the flux in pixel i, f_i, by assuming a continuum C_q(λ_i) and convolving with the pixel noise, σ_i:

P ( f C (λ ), z ) ∝

$ 1

dFP(F, z ) exp

⎡

⎢−(C^qF − fⁱ)²⎤

⎥ (8)

Quasar Continuum x Mean Flux

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Fuerteventura - Sep 21th 2017 Andreu Font-Ribera - Large Scale Structure with the Lyman-α Forest

Analysing the Lyman-α forest

25

∆v

c = ∆z

1 + z = ∆λ

λ (5.1)

∆χ = c∆z

H(z) = ∆v

H(z)(1 + z) (5.2)

1˚ A ∼ 70 km s

⁻¹

∼ 0.7 h

⁻¹

Mpc (5.3)

∆χ = d

A

(z)(1 + z)∆θ (5.4)

1 deg ∼ 70 h

⁻¹

Mpc (5.5)

6 Conclusions

We detect cross-correlations on very large separations, well described by linear theory. Re- sults consistent with quasar clustering ([12]) and Lyα clustering ([13]), we get even better constraints on bias parameters.

Future studies will focus on radiation and small scales cross-correlations (proximity eﬀect).

Comment the strength of LyaF-QSO cross-correlations for cosmological studies.

Acknowledgments

This research used resources of the National Energy Research Scientific Computing Center (NERSC), which is supported by the Oﬃce of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231.

Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the Partic- ipating Institutions, the National Science Foundation, and the U.S. Department of Energy Oﬃce of Science. The SDSS-III web site is http://www.sdss3.org/.

SDSS-III is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS-III Collaboration including the University of Arizona, the Brazilian Participation Group, Brookhaven National Laboratory, University of Cambridge, Carnegie Mellon University, University of Florida, the French Participation Group, the German Par- ticipation Group, Harvard University, the Instituto de Astrofisica de Canarias, the Michigan State/Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence Berke- ley National Laboratory, Max Planck Institute for Astrophysics, Max Planck Institute for Extraterrestrial Physics, New Mexico State University, New York University, Ohio State Uni-

∆v

c = ∆z

1 + z = ∆λ

λ (5.1)

∆χ = c∆z

H(z) = ∆v

H(z)(1 + z) (5.2)

1˚ A ∼ 70 km s

⁻¹

∼ 0.7 h

⁻¹

Mpc (5.3)

∆χ = d

A

(z)(1 + z)∆θ (5.4)

1 deg ∼ 70 h

⁻¹

Mpc (5.5)

6 Conclusions

We detect cross-correlations on very large separations, well described by linear theory. Re- sults consistent with quasar clustering ([12]) and Lyα clustering ([13]), we get even better constraints on bias parameters.

Future studies will focus on radiation and small scales cross-correlations (proximity eﬀect).

Comment the strength of LyaF-QSO cross-correlations for cosmological studies.

Acknowledgments

This research used resources of the National Energy Research Scientific Computing Center (NERSC), which is supported by the Oﬃce of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231.

Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the Partic- ipating Institutions, the National Science Foundation, and the U.S. Department of Energy Oﬃce of Science. The SDSS-III web site is http://www.sdss3.org/.

SDSS-III is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS-III Collaboration including the University of Arizona, the Brazilian Participation Group, Brookhaven National Laboratory, University of Cambridge, Carnegie Mellon University, University of Florida, the French Participation Group, the German Par- ticipation Group, Harvard University, the Instituto de Astrofisica de Canarias, the Michigan State/Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence Berke- ley National Laboratory, Max Planck Institute for Astrophysics, Max Planck Institute for Extraterrestrial Physics, New Mexico State University, New York University, Ohio State Uni- versity, Pennsylvania State University, University of Portsmouth, Princeton University, the Spanish Participation Group, University of Tokyo, University of Utah, Vanderbilt University,

1 Introduction

Introduction to Lyα , BAO, PT.

The relation between the observed quantities and the cosmological distances are:

1 + ¯z =

√λ₁ λ₂ λα

, (1.1)

r_⊥ = dA(¯z) (1 + ¯z) ∆θ , (1.2)

r_∥ =

!

dz c

H(z) ∼ c H(¯z)λα

∆λ (1.3)

∆θ

¯ ∆λ

1 + ¯z = √λ

z

1 λ₂ λ_α

r_⊥ = d_A(¯z) (1 + ¯z) ∆θ .

r_∥ = c (1 + ¯z) H(¯z) λ^α ∆λ



Figure 1. Diagram.

2 Notes from Uros

The question we want to answer is: how does the Lyα auto-correlation function vary as a function of rest-frame wavelength (i.e., separation from the quasar)?

2.1 Conditional probabilities

The 2-point Lyα correlation function ξ₁₂^{F F} = "δ₁^Fδ₂^F# can be related to the joint probability pF F(δ₁^F, δ₂^F) and to the conditional probability pF(δ^F₁ |δ2^F) :

pF F(δ₁^F, δ^F₂) = pF(δ₁^F) pF(δ₂^F|δ^F1 ) = pF(δ₁^F) pF(δ₂^F)$1 + ξ₁₂^{F F}%

(2.1) The 3-point function ζ₁₂₃^{F F Q} is equivalently defined

p_{F F Q}(δ^F₁ , δ₂^F, δ₃^Q) = p_Q(δ^Q₃ ) p_{F F}(δ₁^F, δ^F₂ |δ3^Q)

= p_Q(δ^Q₃ ) p_F(δ₂^F) p_F(δ₁^F)&

1 + ξ₁₂^{F F} + ξ₁₃^{F Q} + ξ₂₃^{F Q} + ζ₁₂₃^{F F Q}'

, (2.2)

1

BOSS : 160k quasar spectra over 10k sq.deg.

(x10 number of quasars at 2.15 < z < 3.5)

LyaF volume : 50 (Gpc/h)^3

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Analysing the Lyman-α forest

Gas Quasar

Quasar

r

Gas

Quasar Quasar

r

Two independent ways of measuring the BAO scale

Delubac et al. (2015) Font-Ribera et al. (2014) Bautista et al. (2017) —— DR11 —— du Mas des Bourboux (2017)

—— DR12 ——

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Outline

• ^Motivation

• Introducing the Lyman-α forest

• Physics of the Lyman-α forest

• Lyman-α forest as a biased tracer

• Analysing the Lyman-α forest

• Recent results from BOSS

(28)

Recent results from BOSS

Fo uri er tra ns fo rm

BOSS Galaxies z = 0.57 Planck Temperature

z = 1100

BOSS Galaxies z = 0.57

Oscillations clearly seen in CMB, but also in clustering of galaxies

BOSS Lyα

z = 2.35

(29)

Recent results from BOSS

Julian Bautista

(Moving from Utah to Portsmouth)

Bautista et al 2017

BAO from DR12

Lya auto-correlation

(30)

Recent results from BOSS

Helion du Mas des Bourboux (Moving from Saclay to Utah)

dMdB et al. 2017

BAO from DR12

Quasar-Lya cross

(31)

Recent results from BOSS

Expa ns io n ra te

Planck prediction

Acceleration

Deceleration

(32)

Recent results from BOSS

Dark Energy is now detected from

BAO data alone

In a flat LCDM model BAO

Planck

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Large Scale Structure with the Lyman-α Forest

Your Name and Collaborators