the large scale structure of warm dark matter - ntuausm_lmu_de_01.pdf · the large scale structure...

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

OUTLINE

• free-streaming

• the halo model

• simulations - dark matter only

• degeneracies: WDM+b & WDM+ν


ΛCDM, PRESENT TIME

73% Dark Energy or Λ 23% Cold Dark Matter 4.5% Baryonic matter negligible radiation and other standard model matter


73% Dark Energy or Λ 23% Cold Dark Matter 4.5% Baryonic matter negligible radiation and other standard model matter

ΛCDM, PRESENT TIME


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")


CONSTRAINTS

• 1 measurement: Dark Matter abundance from CMB experiments (WMAP7, assuming standard ΛCDM):

!dm = 0.227± 0.014


CONSTRAINTS


• 1 constraint: Choose a heavy DM particle á la WIMP → constraints from DM high-density regions

!dm = 0.227± 0.014


CONSTRAINTS


• 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


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?


THE HALO MODEL

less abstract

almost analytical

can modify individual

components


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)


SPLITTING THE FIELD

• in CDM, assume: all of density field ← haloes

• in WDM, split: clumped + smooth


!(x) =N!

i=1

Mi uh(|x! x0,i|,Mi) + !s(x)


SPLITTING THE FIELD

• volume average

• get background values

• define a “clumped fraction”

!!(x)" = !!s(x)"+ !!c(x)"



SPLITTING THE FIELD

• volume average



!̄ = !̄s + !̄c



SPLITTING THE FIELD

• volume average



!̄ = !̄s + !̄c


f = !̄c/!̄ =1

!̄

!!

Mcut

dMMdn

dM


SPLITTING THE FIELD

• volume average



!̄ = !̄s + !̄c mass function(no. density of haloes per dM)


f = !̄c/!̄ =1

!̄

!!

Mcut

dMMdn

dM


!!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))



SPLITTING THE FIELD


+ 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)#



SPLITTING THE FIELD


+ 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)

⇓



SPLITTING THE FIELD


!!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)"



SPLITTING THE FIELD


!!i(x)!j(x+ r)" = !̄i!̄j (1 + "ij(r))

= !̄2s (1 + "ss(r)) + !̄2c (1 + "cc(r)) + 2!̄c!̄s (1 + "cs(r))



SPLITTING THE FIELD


!!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)

⇓



SPLITTING THE FIELD


!!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)



Zavala et al. (2009)

CALIBRATING THE HALO MODEL

f = !̄c/!̄ =1

!̄

!!

Mcut

dMMdn

dM


CALIBRATING THE HALO MODELDunstan, Abazajian, Polisensky & Ricotti (2011)

dn

dM

!

!

!

WDM

=

"

1 +M1/2

M

#

!!dn

dM

!

!

!

CDM

! = 1.2


CALIBRATING THE HALO MODELSchneider, Smith, Maccio & Moore (2012)

dn

dM

!

!

!

WDM

=

"

1 +M1/2

M

#

!!dn

dM

!

!

!

CDM

! = 1.16


• arXiv, Monday

•merger trees

• no top-down

• smooth accretion!

CALIBRATING THE HALO MODELBenson et al. (2012)


WDM SIMULATIONSViel, Markovic, Baldi & Weller (MNRAS; 2012)

z = 0


Viel, Markovic, Baldi & Weller (MNRAS; 2012)

WDM SIMULATIONS

T 2nlin(k) ! PWDM(k)/P!CDM(k) = (1 + (! k)!l)!s/!

Depends on particle massThursday, 20 September, 2012

WDM+b

• blue: SF, winds

• cooling erases WDM effect

Viel, Markovic, Baldi & Weller (MNRAS; 2012)


WORK IN PROGRESS...


WDM+ν

• neutrinos = HDM

• CLASS code (Lesgourgues, 2011)

• halofit (CDM-based)

• ... new, calibrated halo model

Markovic, Abdalla, Lahav & Weller (in prep)


WDM+ν

Linear

free-streaming

scale


WDM+ν

halofit


WDM+ν

halofit+correction


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!


•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


the large scale structure of warm dark matter - ntuausm_lmu_de_01.pdf · the large scale structure...

Documents