Constraining Dark Matter Equation of State with CLASH Clusters

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1 Constraining Dark Matter Equation of State with CLASH Clusters Barbara Sartoris, Andrea Biviano, Piero Rosati and the CLASH team University of Trieste

2 The Equation of state No direct observations of the EoS have been carried out to confirm the assumption of DM to be pressureless. Bharadwaj & Kar (2003) first proposed that combined measurements of rotation curves and gravitational lensing could be used to determine the equation of state of a galactic fluid. Equation of State = 8πG p c 4 r (r) = 2 [ ( m(r)g [ r (r) ( 1 2 m(r)g )] r 2 c 2 r c 2 r )] = [ 8 ( ) ( 8πG p c 4 t (r) = G [ m (r) r m(r) ] ) ] [ ] [ 1 + r (r) ] + c 2 r [ m(r)g ][ ] (r) + (r) 2 + (r) c 2 r r where p (r) and p (r) refer to the radial and tangential pre Density w = p r +2p t c 2 3ρ Radial Pressure profile Tangential Pressure profile 4πρ(r)r 2 = m(r)

3 Potentials and Mass profiles Kinematic approach ndition (i) the tt c In the weak field approximation 2 R tt y, the function m K (r) = r2 G Φ K 4πG (c 2 ρ + p c 2 r +2p t ) r 2 dr Using the Jeans equation r m K (<r)= r σ2 r G [ d ln ρn d ln r + d ln σ2 r d ln r +2β ] Lensing approach [ Apply Fermat s principle to the time-like geodesics δ q2 Consider an effective refractive index n(r) =1 Φ(r) n(r) [ ] dr 2 + r 2 dω 2 =0. q 1 2 m(r) r 2 [ (2m ) 2 dr+o, 2m ] r r Φ, Φ2. Φ(r) = Gm k r 2 ; r m(r) =2m lens (r) m k. 2 Φ lens (r) =Φ(r)+ m(r) r 2 dr, Faber & Visser 2006, Lake 2004

4 Constraining Dark Matter Equation of State: Serra & Romero 2011 Lensing Masses CL 0024 low quality lensing data low member number kinematical evidence of merging X-ray Masses Kinematic Masses

5 Galaxy cluster MACS J (z = 0.44) Properties of MACS 1206: Relaxed (X-ray, kinematics) No strong elongation bias ( X-ray and lensing predictions on mass profiles agree) Concentric distribution of different mass components High quality lensing and dynamical data (~600 spect members) MACS 1206 is ideally suitable for testing the Equation of State of cluster fluid

6 MACS J : Mass profile from kinematic Projected mass profiles : X- ray Lensing (Weak + Strong) (NFW ) Kinematic (NFW) Biviano at al 2013 Umetsu at al 2012

7 Constraining Dark Matter Equation of State w(r) = p r(r)+2p t (r) 3ρ(r) 2 3 m K (r) m lens (r) 2 m lens (r) m K (r)( Results obtained using different profiles for M K : NFW!=O (blue curve) NFW!=T (magenta curve) NFW!=C (green curve) w(r) Averaging over all radii NFW, =O NFW, =C NFW, =T r [Mpc] w = ± 0.03 (stat) ± 0.1 (syst) for the NFW!=O model.

8 Constraining Dark Matter Equation of State w(r) = p r(r)+2p t (r) 3ρ(r) 2 3 m K (r) m lens (r) 2 m lens (r) m K (r)( clusters Results obtained using different profiles for M K : NFW!=O (blue curve) NFW!=T (magenta curve) NFW!=C (green curve) w(r) Averaging over all radii w = ± 0.03 (stat) ± 0.1 (syst) -0.4 NFW, =O r [Mpc] for the NFW!=O model.

9 Conclusions By using high quality kinematic and lensing mass analysis of MACS 1206 cluster we have obtained the most stringent constraint on DM EoS to date. w = ± 0.03 (stat) ± 0.1 (syst) CLASH - VLT final sample will provide the mass estimates for 12 clusters allowing us to further reduce the uncertainties on the DM Equation of state and control the systematics The possibility of non-negligible pressure fluid introduces a new free parameter into the analysis of combined kinematic and lensing observations.