Revisiting the escape speed impact on dark matter direct - - PowerPoint PPT Presentation

Revisiting the escape speed impact

• n

dark matter direct detection

Stefano Magni Ph.D. Student - LUPM (Montpellier) Based on collaborations with Julien Lavalle, paper in preparation

FFP14 Marseille July 15, 2014

Outline

• Introduction
• Astrophysical parameters and uncertainties
• Insights from the escape speed after the RAVE survey
• Consistent astrophysical modeling and impact on

exclusion curves

• Conclusions

LUX experiment

Direct detection rate and exclusion curves

vmin( Er)=√ Erm A 2mred

2

AstroPhysics

ρ0 η(Er)

dN dEr

( Er) = ΔM Δt

A2σ p,SI F2(Er) 2mred , p

2

mχ ρ0

∫

∣⃗ v '∣>v'min(Er )

d3⃗ v ' 1 v' f ⃗

v (⃗

v ') ¿

Particle + hadronic + nuclear physics Detector

ET =2.76 keV

90% C.L.

Reference speed function: the Standard Halo Model (SHM)

Maxwell-Boltzmann speed distribution Relies on isothermal assumption

f v( v)=4πv2 f ⃗

v(⃗

v )=4v2 π1/2 v0

3 e −( v2 v0 2)

¿

ρ0=0.3GeV /cm

3

v0=220 km/s

vesc=544km/s

(plus exponential cutoff at ) Important parameters and their standard values

vesc

σ∝v0

Impact of astrophysical parameters on exclusion curves

v esc

v 0

ρ0

mχ

ET =2.76 keV ET =2.76 keV ET =2.76 keV

vmin

small mχ large

dN dEr (Er )∝

∫

v>v min ∣⃗ v+⃗ v ⊕∣<v esc d v f v (v ) v

vmin

Astrophysical uncertainties

• Astrophysical parameters should be correlated:

gravitational dynamics

• Several studies based on kinametic data + mass models

Fairbairn et al. ('12), Catena & Ullio ('12), Bozorgna et al. ('13), Fornasa & Green ('13), etc.

• We focus on the latest estimate of the escape speed (RAVE

survey) which cannot be used blindly (relies on assumptions)

• We work out a consistent modeling, complementarity to

kinematical studies

• Escape speed important at low WIMP masses

Why focus on the escape speed?

vesc

Del Nobile et al, (2014)

v> vmin(Er) mχ

➢

Experimental treshold

➢

Energy resolution

➢

Escape speed! Several effects at work:

• Based on a selection of some stars from a catalog of 420000.

2) analysis with same likelihood but free

ΦMW ( R ,z )=Φ NFW

DM (r )+ ΦBAR( R, z)

Escape speed from RAVE (Piffl et al '13)

1) likelihood analysis at fixed

• Assumptions:

R0=8.28kpc n(v)∝(vesc−v)k

• Different analyses:

v esc=533−41

+ 54km/s

➢ ➢

➢

Mass model (NFW + fixed baryons) v 0=220 km/s v 0

2 free parameters

ρ NFW(r)= δ(c)ρc r r s(1+ r r s)

2 Piffl et al, (2013)

Old RAVE: (Smith et al. '07)

vesc=544−46

+ 64km/s

(90% C.L.)

(Leonard & Tremaine '90)

ρ(⃗ r )=ρDM(⃗ r )+ ρbaryons(⃗ r )

v c

2(R,0)=R ∂Φ(R,0)

∂ R

Φ(⃗ r )=ΦDM(⃗ r )+Φbaryons(⃗ r )

v esc(⃗ r)=√2∣Φ(⃗ r)−Φ(⃗ rmax)∣

ρ0=ρDM(⃗ r 0)

Reminder on mass models

Density of matter Gravitational Potential

• Circular speed
• Local dark

matter density

• Escape speed

So the correlation between , , and is clear

v 0 ρ0

v esc

R⊙

From RAVE's mass constraints to circular and escape speed

From RAVE's mass constraints to circular and escape speed

Impact on direct detection from uncorrelated astrophysical parameters

v esc

consistent with RAVE's second analysis

ET =2.76 keV

(Maxwell-Boltzmann assumed)

0.2GeV /cm

3≤ρ0≤0.5GeV /cm 3

(Bovy et al., 2012)

➢

29.9±1.7≤v c/R0≤31.6±1.7km s

−1kpc −1

(Mc Millan & Binney, 2009)

➢

Correlating the astrophysical parameters consistently with the RAVE's results

ET =2.76 keV

vesc( R0)∝f 2(Φ( R0)) vc( R0)∝f 1(Φ( R0))

functions of the mass model and

➔ Consistent way to use RAVE estimate of ➔ Uncertainties reduced: ➔ Exclusion more severe

vesc

0.374GeV /cm

3≤ρ0≤0.5GeV /cm 3

Now only

(6.2±3.4)10

−45cm 2

@ m χ=10GeV

(4.3±0.7)10

−46cm 2 @ m χ=100GeV

Beyond Maxwell-Boltzmann: ergodic speed distribution

f (v ,RSun)

f (ε)= 1

√8π ²[∫0

ε

d ψ d

2ρ

d ψ

2

1

√ε−ψ+ 1

ε

1/2(

d ρ d ψ)ψ=0]

ψ=−ΦMW(r)

ε=−E

ρ=ρ NFW (r)

References: Vergados '14, Bozorgna et al. '13, etc.

• MB (where ) relies on isothermal assumption
• Eddington equation

σ∝v0

f (ε )

ET =2.76 keV

➔ Less constraining at low masses w.r.t. MB,

with more uncertainties

@ m χ=10GeV @ m χ=100GeV

Beyond Maxwell-Boltzmann - Results

➔ Reference values and ncertainties:

(6.9±3.7)10

−45cm 2

(4.3±0.6)10

−46cm 2

Comparison with Germanium (used in SUPER CDMS)

v min(Er)=√ ErmA 2mred

2

¿

A=74

(most common isotope: )

Ge

mG e=72.63 a.m.u.

A=132

Xe

m Xe=131.29 a.m.u.

(most common isotope: )

➔ The exclusion curves are translated toward lower masses ➔ So for any given (low) uncertainties are reduced

mχ

ET =2.76 keV

Ge Ge

Conclusions and perspectives

• We have revisited RAVE's estimate of the escape speed
• It cannot be used blindly as it relies on assumptions
• We have converted the full information consistently into direct

detection limits

• RAVE's method is not free of systematic uncertainties (as the escape

speed definition)

• Test the method with cosmological simulations (P. Mollitor, E. Nezri)
• Go beyond isotropic case with generalized ergodic functions

➔ Astro parameters correlated + Maxwell-Boltzmann

+ ergodic distribution

➔ Stronger bounds ➔ Uncertainties: ➔ Complementary to kinematic methods

@ m χ=10GeV @ m χ=100GeV

(6.9±3.7)10

−45cm 2

(4.3±0.6)10

−46cm 2