the large scale structure of warm dark matter - ntuausm_lmu_de_01.pdf · the large scale structure...
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THE LARGE SCALE STRUCTURE OF WARM DARK MATTER
Katarina MarkovicUniversity Observatory Munich (USM)
with Jochen Weller (USM), Robert Smith (Zurich), Marco Baldi (USM), Matteo Viel (Trieste) and Martin Kilbinger (Paris)
Kan!nsk
y
Particles and the Universe, Corfu, 20.09.2012
Thursday, 20 September, 2012
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OUTLINE
• free-streaming
• the halo model
• simulations - dark matter only
• degeneracies: WDM+b & WDM+ν
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ΛCDM, PRESENT TIME
73% Dark Energy or Λ 23% Cold Dark Matter 4.5% Baryonic matter negligible radiation and other standard model matter
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73% Dark Energy or Λ 23% Cold Dark Matter 4.5% Baryonic matter negligible radiation and other standard model matter
ΛCDM, PRESENT TIME
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WARM DARK MATTER PARTICLE
• DM: elementary particles
• DM: here assume thermal or sterile ν
•We have:
• choose a DM model → get rid of one variable
!dm(mdm, g!(Td), !!v")
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CONSTRAINTS
• 1 measurement: Dark Matter abundance from CMB experiments (WMAP7, assuming standard ΛCDM):
!dm = 0.227± 0.014
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CONSTRAINTS
• 1 measurement: Dark Matter abundance from CMB experiments (WMAP7, assuming standard ΛCDM):
• 1 constraint: Choose a heavy DM particle á la WIMP → constraints from DM high-density regions
!dm = 0.227± 0.014
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CONSTRAINTS
• 1 measurement: Dark Matter abundance from CMB experiments (WMAP7, assuming standard ΛCDM):
• 1 constraint: Choose a heavy DM particle á la WIMP → constraints from DM high-density regions
• 1 constraint: Choose a light particle (m ~ 1 keV) → Warm Dark Matter → constraints from Large Scale Structure
!dm = 0.227± 0.014
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FREE-STREAMING
• early relativistic particles ⇒ free-streaming
• density field fluctuations ← smoothened
• ∴ the linear matter power spectrum ← small scale suppression
• How does this translate to non-linearities?
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THE HALO MODEL
less abstract
almost analytical
can modify individual
components
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SPLITTING THE FIELD
• in CDM, assume: all of density field ← haloes
Smith & Markovic (PRD; 2011)
!(x) =N!
i=1
Mi uh(|x! x0,i|,Mi)
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SPLITTING THE FIELD
• in CDM, assume: all of density field ← haloes
• in WDM, split: clumped + smooth
Smith & Markovic (PRD; 2011)
!(x) =N!
i=1
Mi uh(|x! x0,i|,Mi) + !s(x)
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SPLITTING THE FIELD
• volume average
• get background values
• define a “clumped fraction”
!!(x)" = !!s(x)"+ !!c(x)"
Smith & Markovic (PRD; 2011)
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SPLITTING THE FIELD
• volume average
• get background values
• define a “clumped fraction”
!̄ = !̄s + !̄c
Smith & Markovic (PRD; 2011)
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SPLITTING THE FIELD
• volume average
• get background values
• define a “clumped fraction”
!̄ = !̄s + !̄c
Smith & Markovic (PRD; 2011)
f = !̄c/!̄ =1
!̄
!!
Mcut
dMMdn
dM
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SPLITTING THE FIELD
• volume average
• get background values
• define a “clumped fraction”
!̄ = !̄s + !̄c mass function(no. density of haloes per dM)
Smith & Markovic (PRD; 2011)
f = !̄c/!̄ =1
!̄
!!
Mcut
dMMdn
dM
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!!i(x)!j(x+ r)" = !̄i!̄j (1 + !"i(x)"j(x+ r)")
SPLITTING THE FIELD
• we want statistic of clustering, so as always:
!i(x) ! !̄i (1 + "i(x))
Smith & Markovic (PRD; 2011)
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SPLITTING THE FIELD
• we want statistic of clustering, so as always:
+ statistical isotropy &
homogeneity
!!i(x)!j(x+ r)" = !̄i!̄j (1 + "ij(r))
!i(x) ! !̄i (1 + "i(x))
!ij(|r|) ! !ij(r) ! ""i(x)"j(x+ r)#
Smith & Markovic (PRD; 2011)
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SPLITTING THE FIELD
• we want statistic of clustering, so as always:
+ statistical isotropy &
homogeneity
!!i(x)!j(x+ r)" = !̄i!̄j (1 + "ij(r))
!i(x) ! !̄i (1 + "i(x))
!ij(|r|) ! !ij(r) ! ""i(x)"j(x+ r)#
!(x) = (1! f)!s(x) + f!c(x)
⇓
Smith & Markovic (PRD; 2011)
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SPLITTING THE FIELD
• we want statistic of clustering, so as always:
!!i(x)!j(x+ r)" = !̄i!̄j (1 + "ij(r))
= !!s(x)!s(x+ r)"+ !!c(x)!c(x+ r)"+ 2 !!c(x)!s(x+ r)"
Smith & Markovic (PRD; 2011)
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SPLITTING THE FIELD
• we want statistic of clustering, so as always:
!!i(x)!j(x+ r)" = !̄i!̄j (1 + "ij(r))
= !̄2s (1 + "ss(r)) + !̄2c (1 + "cc(r)) + 2!̄c!̄s (1 + "cs(r))
Smith & Markovic (PRD; 2011)
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SPLITTING THE FIELD
• we want statistic of clustering, so as always:
!!i(x)!j(x+ r)" = !̄i!̄j (1 + "ij(r))
= !̄2s (1 + "ss(r)) + !̄2c (1 + "cc(r)) + 2!̄c!̄s (1 + "cs(r))
!(r) = (1! f)2!ss(r) + 2f(1! f)!sc(r) + f2!cc(r)
⇓
Smith & Markovic (PRD; 2011)
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SPLITTING THE FIELD
• we want statistic of clustering, so as always:
!!i(x)!j(x+ r)" = !̄i!̄j (1 + "ij(r))
= !̄2s (1 + "ss(r)) + !̄2c (1 + "cc(r)) + 2!̄c!̄s (1 + "cs(r))
⇓P (k) = (1! f)2Pss(k) + 2(1! f)fPsc(k) + f2Pcc(k)
P2hcc (k) + P
1hcc (k)
Smith & Markovic (PRD; 2011)
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Zavala et al. (2009)
CALIBRATING THE HALO MODEL
f = !̄c/!̄ =1
!̄
!!
Mcut
dMMdn
dM
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CALIBRATING THE HALO MODELDunstan, Abazajian, Polisensky & Ricotti (2011)
dn
dM
!
!
!
WDM
=
"
1 +M1/2
M
#
!!dn
dM
!
!
!
CDM
! = 1.2
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CALIBRATING THE HALO MODELSchneider, Smith, Maccio & Moore (2012)
dn
dM
!
!
!
WDM
=
"
1 +M1/2
M
#
!!dn
dM
!
!
!
CDM
! = 1.16
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• arXiv, Monday
•merger trees
• no top-down
• smooth accretion!
CALIBRATING THE HALO MODELBenson et al. (2012)
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WDM SIMULATIONSViel, Markovic, Baldi & Weller (MNRAS; 2012)
z = 0
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Viel, Markovic, Baldi & Weller (MNRAS; 2012)
WDM SIMULATIONS
T 2nlin(k) ! PWDM(k)/P!CDM(k) = (1 + (! k)!l)!s/!
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WDM+b
• blue: SF, winds
• cooling erases WDM effect
Viel, Markovic, Baldi & Weller (MNRAS; 2012)
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WORK IN PROGRESS...
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WDM+ν
• neutrinos = HDM
• CLASS code (Lesgourgues, 2011)
• halofit (CDM-based)
• ... new, calibrated halo model
Markovic, Abdalla, Lahav & Weller (in prep)
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WDM+ν
Linear
free-streaming
scale
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WDM+ν
halofit
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WDM+ν
halofit+correction
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TL;DR
•WDM is a generalisation of CDM.
•We know good prescriptions to calculate non-linear corrections in ΛWDM.
• BUT we need to know baryonic effects!
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•WDM is a generalisation of CDM.
•We know good prescriptions to calculate non-linear corrections in ΛWDM.
• BUT we need to know baryonic effects!
TL;DL
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