Lyman-alpha Forest: 3D - UC Berkeley Cosmology Group · 2011. 4. 9. · k e ik⊥ ·x0 F˜ k e...
Transcript of Lyman-alpha Forest: 3D - UC Berkeley Cosmology Group · 2011. 4. 9. · k e ik⊥ ·x0 F˜ k e...
![Page 1: Lyman-alpha Forest: 3D - UC Berkeley Cosmology Group · 2011. 4. 9. · k e ik⊥ ·x0 F˜ k e ik⊥ ·x1 F˜ k e ik⊥ ·x2 F˜ k e ik⊥ ·x3 This is the traditional way of thinking](https://reader036.fdocument.pub/reader036/viewer/2022071501/61204ce710066d46160385e9/html5/thumbnails/1.jpg)
Lyman-alpha Forest: 3D
Matt McQuinn
arxiv:1102.1752 w/ Martin Whitearxiv: 1010.5250 w/ Lars Hernquist, Adam Lidz, Matias
Zaldarriaga
Friday, April 8, 2011
![Page 2: Lyman-alpha Forest: 3D - UC Berkeley Cosmology Group · 2011. 4. 9. · k e ik⊥ ·x0 F˜ k e ik⊥ ·x1 F˜ k e ik⊥ ·x2 F˜ k e ik⊥ ·x3 This is the traditional way of thinking](https://reader036.fdocument.pub/reader036/viewer/2022071501/61204ce710066d46160385e9/html5/thumbnails/2.jpg)
The Lyman-α Forest1 Gpc
BOSS will take 160,000 of these!(although, the above is R=70,000, S/N>100 whereas think R=2000, S/N>2)
Friday, April 8, 2011
![Page 3: Lyman-alpha Forest: 3D - UC Berkeley Cosmology Group · 2011. 4. 9. · k e ik⊥ ·x0 F˜ k e ik⊥ ·x1 F˜ k e ik⊥ ·x2 F˜ k e ik⊥ ·x3 This is the traditional way of thinking](https://reader036.fdocument.pub/reader036/viewer/2022071501/61204ce710066d46160385e9/html5/thumbnails/3.jpg)
3D Lyman-α Forest is being measured with BOSS
Previous theoretical work: McDonald 2003, White 2003, McDonald and Eisenstein 2007Slosar et al (2010), White et al (2010)
Nic Ross/Andreu Font
Friday, April 8, 2011
![Page 4: Lyman-alpha Forest: 3D - UC Berkeley Cosmology Group · 2011. 4. 9. · k e ik⊥ ·x0 F˜ k e ik⊥ ·x1 F˜ k e ik⊥ ·x2 F˜ k e ik⊥ ·x3 This is the traditional way of thinking](https://reader036.fdocument.pub/reader036/viewer/2022071501/61204ce710066d46160385e9/html5/thumbnails/4.jpg)
Topics to tackle:• What is sensitivity of a survey to 3D
correlations in the flux? (a bit technical)
• What is the optimal design for a 3D Lyman-alpha survey?
• What are the interesting things to measure?
(talk will run on short side so please ask ?s)Friday, April 8, 2011
![Page 5: Lyman-alpha Forest: 3D - UC Berkeley Cosmology Group · 2011. 4. 9. · k e ik⊥ ·x0 F˜ k e ik⊥ ·x1 F˜ k e ik⊥ ·x2 F˜ k e ik⊥ ·x3 This is the traditional way of thinking](https://reader036.fdocument.pub/reader036/viewer/2022071501/61204ce710066d46160385e9/html5/thumbnails/5.jpg)
How to best measure 2 pt correlations in the 3D Lyman-α Forest:
We want to estimate the power spectrum:
Goal: A nice expression for the S/N of estimator.Friday, April 8, 2011
![Page 6: Lyman-alpha Forest: 3D - UC Berkeley Cosmology Group · 2011. 4. 9. · k e ik⊥ ·x0 F˜ k e ik⊥ ·x1 F˜ k e ik⊥ ·x2 F˜ k e ik⊥ ·x3 This is the traditional way of thinking](https://reader036.fdocument.pub/reader036/viewer/2022071501/61204ce710066d46160385e9/html5/thumbnails/6.jpg)
But quasar’s transverse separation is large (>~10 Mpc) so C is diagonally dominated
where if we approximate off-diagonal in C as zero
where A is just a normalization factor &
is the line of sight power.
This diagonal approximation for the estimator is suboptimal at the percent-level for BOSS and 10% level for any conceivable quasar survey compared to the minimum variance estimator.
(δF is the Fourier transform of the flux along sightline n)
Friday, April 8, 2011
![Page 7: Lyman-alpha Forest: 3D - UC Berkeley Cosmology Group · 2011. 4. 9. · k e ik⊥ ·x0 F˜ k e ik⊥ ·x1 F˜ k e ik⊥ ·x2 F˜ k e ik⊥ ·x3 This is the traditional way of thinking](https://reader036.fdocument.pub/reader036/viewer/2022071501/61204ce710066d46160385e9/html5/thumbnails/7.jpg)
Minimum Variance Quadratic Estimator (cont)
-- Can write a matrix expansion (only involving matrix multiplications) that converges to minimum variance quadratic estimator.
--Next order term in the expansion suppresses the weight of spectra that have an overdensity of sources within r⊥⋅k⊥ < 1.
McQuinn & White (2010)Friday, April 8, 2011
![Page 8: Lyman-alpha Forest: 3D - UC Berkeley Cosmology Group · 2011. 4. 9. · k e ik⊥ ·x0 F˜ k e ik⊥ ·x1 F˜ k e ik⊥ ·x2 F˜ k e ik⊥ ·x3 This is the traditional way of thinking](https://reader036.fdocument.pub/reader036/viewer/2022071501/61204ce710066d46160385e9/html5/thumbnails/8.jpg)
Alternatively, think Monte Carlo Integration
F̃k�eik⊥·x0 F̃k�e
ik⊥·x1 F̃k�eik⊥·x2 F̃k�e
ik⊥·x3
This is the traditional way of thinking about problem (McDonald and Eisenstein 2007, White et al 2010). It turns out to be identical to diagonal covariance approximation for quadratic estimator if you weight sight-lines by (total power)-1.
Estimator also easily generalizable to correlation function: Equivalent to weighting each real space flux pixel by variance in flux over total variance (flux + noise), where variance is measured over a scale of > 10Mpc.
3D Flux(k) = N−1�
∀iF̃k�,ie
ik⊥·xi �PF = |3D Flux(k)|2
Friday, April 8, 2011
![Page 9: Lyman-alpha Forest: 3D - UC Berkeley Cosmology Group · 2011. 4. 9. · k e ik⊥ ·x0 F˜ k e ik⊥ ·x1 F˜ k e ik⊥ ·x2 F˜ k e ik⊥ ·x3 This is the traditional way of thinking](https://reader036.fdocument.pub/reader036/viewer/2022071501/61204ce710066d46160385e9/html5/thumbnails/9.jpg)
On a single mode, this estimator has variance:
Sensitivity to PF only depends on one #, neff! where
BOSS
neff depends extremely weakly on kll in practice over kll of most interest. One
number determines the sensitivity of a
survey!
and
limiting quasar magnitude
where
Friday, April 8, 2011
![Page 10: Lyman-alpha Forest: 3D - UC Berkeley Cosmology Group · 2011. 4. 9. · k e ik⊥ ·x0 F˜ k e ik⊥ ·x1 F˜ k e ik⊥ ·x2 F˜ k e ik⊥ ·x3 This is the traditional way of thinking](https://reader036.fdocument.pub/reader036/viewer/2022071501/61204ce710066d46160385e9/html5/thumbnails/10.jpg)
It is simple to see how much weight is given each quasar.
need S/N > 2 on continuum in 1A pixels for quasar to be useful
calculated at kll = 0.0014 s km -1 but depends weakly on this
Friday, April 8, 2011
![Page 11: Lyman-alpha Forest: 3D - UC Berkeley Cosmology Group · 2011. 4. 9. · k e ik⊥ ·x0 F˜ k e ik⊥ ·x1 F˜ k e ik⊥ ·x2 F˜ k e ik⊥ ·x3 This is the traditional way of thinking](https://reader036.fdocument.pub/reader036/viewer/2022071501/61204ce710066d46160385e9/html5/thumbnails/11.jpg)
Effective Volume
neff = 10 -4 Mpc -2
neff = 10 -3 Mpc -2
neff = 10 -2 Mpc -2
S/N
on
mod
e
BOSS can almost image large-scale modes at z~2!
Galaxies: Quasars:
Friday, April 8, 2011
![Page 12: Lyman-alpha Forest: 3D - UC Berkeley Cosmology Group · 2011. 4. 9. · k e ik⊥ ·x0 F˜ k e ik⊥ ·x1 F˜ k e ik⊥ ·x2 F˜ k e ik⊥ ·x3 This is the traditional way of thinking](https://reader036.fdocument.pub/reader036/viewer/2022071501/61204ce710066d46160385e9/html5/thumbnails/12.jpg)
Using Forest from Galaxies
z=2z=3
z=4
limiting quasar magnitude
Friday, April 8, 2011
![Page 13: Lyman-alpha Forest: 3D - UC Berkeley Cosmology Group · 2011. 4. 9. · k e ik⊥ ·x0 F˜ k e ik⊥ ·x1 F˜ k e ik⊥ ·x2 F˜ k e ik⊥ ·x3 This is the traditional way of thinking](https://reader036.fdocument.pub/reader036/viewer/2022071501/61204ce710066d46160385e9/html5/thumbnails/13.jpg)
Survey Design
k = 0.1 Mpc-1 k = 0.5 Mpc-1
Red dashed: contours of constant (survey area)/(limiting flux)2
solid black: contours of constant sensitivity (S/N on P in dk/k=0.2)
limiti
ng m
agni
tude
Friday, April 8, 2011
![Page 14: Lyman-alpha Forest: 3D - UC Berkeley Cosmology Group · 2011. 4. 9. · k e ik⊥ ·x0 F˜ k e ik⊥ ·x1 F˜ k e ik⊥ ·x2 F˜ k e ik⊥ ·x3 This is the traditional way of thinking](https://reader036.fdocument.pub/reader036/viewer/2022071501/61204ce710066d46160385e9/html5/thumbnails/14.jpg)
Cosmological Constraints from BAO
Assumes area A=104 deg2 and depth L=1 Gpc, but scales as [AL]^{-1/2}
BOSS
BigBOSS
Friday, April 8, 2011
![Page 15: Lyman-alpha Forest: 3D - UC Berkeley Cosmology Group · 2011. 4. 9. · k e ik⊥ ·x0 F˜ k e ik⊥ ·x1 F˜ k e ik⊥ ·x2 F˜ k e ik⊥ ·x3 This is the traditional way of thinking](https://reader036.fdocument.pub/reader036/viewer/2022071501/61204ce710066d46160385e9/html5/thumbnails/15.jpg)
Now that I’ve got you trapped.....some
Astrophysics
Friday, April 8, 2011
![Page 16: Lyman-alpha Forest: 3D - UC Berkeley Cosmology Group · 2011. 4. 9. · k e ik⊥ ·x0 F˜ k e ik⊥ ·x1 F˜ k e ik⊥ ·x2 F˜ k e ik⊥ ·x3 This is the traditional way of thinking](https://reader036.fdocument.pub/reader036/viewer/2022071501/61204ce710066d46160385e9/html5/thumbnails/16.jpg)
Contributions to Lyα forest Fluctuations
Intensity fluctuations in
Croft ’03
430 Mpc
[k3P(k)/2π
2]1/2
Friday, April 8, 2011
![Page 17: Lyman-alpha Forest: 3D - UC Berkeley Cosmology Group · 2011. 4. 9. · k e ik⊥ ·x0 F˜ k e ik⊥ ·x1 F˜ k e ik⊥ ·x2 F˜ k e ik⊥ ·x3 This is the traditional way of thinking](https://reader036.fdocument.pub/reader036/viewer/2022071501/61204ce710066d46160385e9/html5/thumbnails/17.jpg)
Effect of temperature fluctuations on line-of-sight power spectrum is small (also see Lai et al (2005)
Similar conclusions hold for intensity (Croft ’03, McDonald et al 05)
Friday, April 8, 2011
![Page 18: Lyman-alpha Forest: 3D - UC Berkeley Cosmology Group · 2011. 4. 9. · k e ik⊥ ·x0 F˜ k e ik⊥ ·x1 F˜ k e ik⊥ ·x2 F˜ k e ik⊥ ·x3 This is the traditional way of thinking](https://reader036.fdocument.pub/reader036/viewer/2022071501/61204ce710066d46160385e9/html5/thumbnails/18.jpg)
Have very small effect in 1D
10!2 10!1 100 1010
0.5
1
k !Mpc!1"
F!log!k"#k l
l"
10!2 10!1 10010!4
10!3
10!2
10!1
k !Mpc!1"
DimensionlessPower
The contribution of different 3D modes to
line-of-sight mode
3D and 1D power spectrafor same input spectrum
kll = 0.1
kll = 0.01
kll = 1
Friday, April 8, 2011
![Page 19: Lyman-alpha Forest: 3D - UC Berkeley Cosmology Group · 2011. 4. 9. · k e ik⊥ ·x0 F˜ k e ik⊥ ·x1 F˜ k e ik⊥ ·x2 F˜ k e ik⊥ ·x3 This is the traditional way of thinking](https://reader036.fdocument.pub/reader036/viewer/2022071501/61204ce710066d46160385e9/html5/thumbnails/19.jpg)
Effect of Temperature Fluctuations using temperature fluctuations in simulation of HeII reionization
Here, “BOSS” is a survey with
limiting magnitude of 22 in 8000 deg2 and
BigBOSS is a magnitude fainter
We have nice formula for relative impact of T fluctuations; McQuinn et al (2011)Friday, April 8, 2011
![Page 20: Lyman-alpha Forest: 3D - UC Berkeley Cosmology Group · 2011. 4. 9. · k e ik⊥ ·x0 F˜ k e ik⊥ ·x1 F˜ k e ik⊥ ·x2 F˜ k e ik⊥ ·x3 This is the traditional way of thinking](https://reader036.fdocument.pub/reader036/viewer/2022071501/61204ce710066d46160385e9/html5/thumbnails/20.jpg)
Intensity Fluctuations
For infinite quasar lifetimes and fixed attenuation length:
<L^2>/<L>2 very sensitive to bright end
of quasar LF
Friday, April 8, 2011
![Page 21: Lyman-alpha Forest: 3D - UC Berkeley Cosmology Group · 2011. 4. 9. · k e ik⊥ ·x0 F˜ k e ik⊥ ·x1 F˜ k e ik⊥ ·x2 F˜ k e ik⊥ ·x3 This is the traditional way of thinking](https://reader036.fdocument.pub/reader036/viewer/2022071501/61204ce710066d46160385e9/html5/thumbnails/21.jpg)
Effect of Intensity Fluctuations
Also see Slosar, Ho, White & Louis ’10 Friday, April 8, 2011
![Page 22: Lyman-alpha Forest: 3D - UC Berkeley Cosmology Group · 2011. 4. 9. · k e ik⊥ ·x0 F˜ k e ik⊥ ·x1 F˜ k e ik⊥ ·x2 F˜ k e ik⊥ ·x3 This is the traditional way of thinking](https://reader036.fdocument.pub/reader036/viewer/2022071501/61204ce710066d46160385e9/html5/thumbnails/22.jpg)
Conclusions• If you want to estimate the sensitivity of any 3D
Lyα survey, only need one number, neff, and you can easily calculate it’s sensitivity
• In general, want equivalent of S/N> 2 in 1A pixels for a quasar to carry much weight.
• The rule of thumb is to go deep enough to capture all quasars with L> L*
• May be able to measure H(z), DA, temperature power, intensity power, quasar bias, DLA bias etc
• 3D Lyα surveys are awesome!
Friday, April 8, 2011
![Page 23: Lyman-alpha Forest: 3D - UC Berkeley Cosmology Group · 2011. 4. 9. · k e ik⊥ ·x0 F˜ k e ik⊥ ·x1 F˜ k e ik⊥ ·x2 F˜ k e ik⊥ ·x3 This is the traditional way of thinking](https://reader036.fdocument.pub/reader036/viewer/2022071501/61204ce710066d46160385e9/html5/thumbnails/23.jpg)
DLAs
Friday, April 8, 2011
![Page 24: Lyman-alpha Forest: 3D - UC Berkeley Cosmology Group · 2011. 4. 9. · k e ik⊥ ·x0 F˜ k e ik⊥ ·x1 F˜ k e ik⊥ ·x2 F˜ k e ik⊥ ·x3 This is the traditional way of thinking](https://reader036.fdocument.pub/reader036/viewer/2022071501/61204ce710066d46160385e9/html5/thumbnails/24.jpg)
contours of constant neff
limiting quasar magnitudequas
ar m
agni
tude
at
whi
ch s
pect
ra
have
S/N
=1
in 1
A p
ixel
s
BOSS
neff in unitsof 10-3 Mpc-2
Friday, April 8, 2011