Constraining self-interacting dark matter with scaling laws of observed halo surface densities

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1 Constraining self-interacting dark matter with scaling laws of observed halo surface densities Anastasia Sokolenko, T.Bringmann (University of Oslo) K.Bondarenko and A.Boyarsky (Leiden University) Rencontres de Moriond, 0th March 018

2 Beyond ΛCDM Lambda Cold Dark Matter (ΛCDM) is known to describe observational data very well at large scales The properties of DM particles relevant for the structure formation at small scales are much less constrained DM that is slightly warm or self-interacting shares all the success of CDM at large scales and predicts interesting physics at small. We will discuss one potentially efficient method to constrain the strength of DM self-interaction using astronomical data Anastasia Sokolenko UNIVERSITY OF OSLO 1

3 What do we expect from a SIDM halo? The probability of scattering is proportional to DM density ρ Far from the centre the density is low, no scattering and the halo behaves as in CDM In the inner part the density is high enough, an equilibrium can be established Anastasia Sokolenko UNIVERSITY OF OSLO

4 What do we expect from a SIDM halo? We can expect that the DM density profile can be approximated by NFW outside certain characteristic radius r SIDM and by a solution of the Jeans equation with constant velocity dispersion σ tot inside r SIDM σtot ( ) d r dρ = 4πGr ρ, (1) 3 dr ρ dr where σ tot is a constant 3D velocity dispersion of DM particles For small enough crosssections σ/m we expect to have a cored solution of Jeans equation with finite density in the center ρ(r) ρ(r)[m /pc 3 ] CDM SIDM1 r SIDM r[kpc] Anastasia Sokolenko UNIVERSITY OF OSLO 3

5 What do we expect from a SIDM halo? r SIDM should grow with the cross-section σ/m. If we could find r SIDM from observation, this could give also a constraint on σ/m ρ(r)[m /pc 3 ] CDM SIDM1 r c r SIDM r[kpc] In doing so, two problems arise: Theoretical. The core radius r c is observed, but r SIDM is related to σ/m! Observational. Many uncertainties in the determination of core radius for each halo Anastasia Sokolenko UNIVERSITY OF OSLO 4

6 Surface density 4 To marginalize over uncertainties and find a universal DM property use a quantity obeying a scaling law Log 10 SD[M /pc ] Log 10 v c [km/s] Dwarf LSB GHASP THINGS_DS THINGS_Kroupa THINGS_free LITTLETHINGS LITTLETHINGSfixedc SPARC Cluster Surface density: SD(r) = M(r) 4 3 πr = ρ r. () a simple scaling law that ranges from dwarfs to galaxy clusters! In CDM this law is related to concentration-mass relation [ ] ( ) M 00 c = h 1 (3) M Anastasia Sokolenko UNIVERSITY OF OSLO 5

7 Idea of the method 100 The larger is σ/m, larger is the core and the smaller is core density ρ(r) r The inner surface density will decrease for larger cross-sections Log 10 SD[M /pc ] Data Prediction σ/m=0.1 cm /g Log 10 SD[M /pc ] Data Prediction σ/m=1 cm /g Log 10 M 00 [M ] Log 10 M 00 [M ] Anastasia Sokolenko UNIVERSITY OF OSLO 6

8 Model To derive quantitative bound on σ/m we have to take into account the theoretical uncertainties: Relate r SIDM to σ/m Common lore: r SIDM is defined by the requirement of one collision per particle for life time [ ] σ m ρ SIDMv SIDM t age = ξ (4) Introduce parameter κ = ρ c ρ SIDM With this arrangements, we can derive the relation between the surface density and σ/m and fit the surface density data SD(σ/m) = κr c ( σ 4πG m 3 ξ ) t age rsidm (σ/m) 1/3 (5) Anastasia Sokolenko UNIVERSITY OF OSLO 7

9 Comparison with simulations We reconstruct unknown parameters ξ and κ by comparison with 8 [ ], [ ] simulated halos from M and 8 cluster-sized halos [ ] We find the average ξ = 1.86 and κ = 3.5 (σ/m) sim ξ/(σ/m) ξ= v c [km/s] κ 0 10 Sim, SIDM c Anastasia Sokolenko UNIVERSITY OF OSLO 8

10 Result We use the likelihood method for Gaussian distribution to estimate the statistical bound on the effective cross-section value. Using 95% confidence level we find [ ] σ/m < 0.3 cm /g (6) 4 -Log[L/L min ] 3 1 All objects No clusters No baryon-dominated Dwarf only σ /m[cm /g] Anastasia Sokolenko UNIVERSITY OF OSLO 9

11 Predicting κ κ = ρ c ρ looks like a redundant parameter. If we know NFW SIDM parameters R 00 and M 00 at large scales for each σ/m we should be able to predict ρ SIDM (r) and, therefore, κ Using available simulations we found a simple model that does this Reminder: we assume an equilibrium inside r SIDM, it is described by isotropic Jeans equation σ tot 3 d dr ( r ρ ) dρ dr = 4πGr ρ (7) Second order equation requires boundary conditions + we have to define σ tot. Assuming a cored solution (ρ (0) = 0) we need two other conditions to fix SIDM profile for r < r SIDM We choose these conditions to be equal mass and equal kinetic energy at r SIDM Anastasia Sokolenko UNIVERSITY OF OSLO 10

12 Energy conservation at r SIDM We test these assumptions with simulations and they work within 5% E SIDM /E CDM SIDM0.1 SIDM0.5 SIDM1 SIDM5 SIDM c Anastasia Sokolenko UNIVERSITY OF OSLO 11

13 Prediction of the density profile Solving the Jeans equation with such boundary conditions we find the density profile ρ[m /pc 3 ] Data Prediction r SIDM κ Sim Pred, isotropic r[kpc] c One can see that the predicted density is lower than the simulation data and average κ is also too small κ sim / κ pred = 1.6 Anastasia Sokolenko UNIVERSITY OF OSLO 1

14 Anisotropy The reason for this is anisotropic velocity dispersion β(r) = 1 σ θ + σ φ σ r We find that simulated SIDM halos have significant anisotropy inside r SIDM! β 0.0 β SIDM1 CDM -0. SIDM1 CDM r[kpc] r[kpc] Surprising - expect no anisotropy in the equilibrium inside r SIDM! Anastasia Sokolenko UNIVERSITY OF OSLO 13

15 Prediction of the density profile with anisotropy Taking this into account we get much better result. We find a simple ansatz for the anisotropy, β(r), for a given cross-section and solve anisotropic Jeans equations with the same β(r) for all halos ρ[m /pc 3 ] Data Pred., isotropic Pred., anisotropic r SIDM r[kpc] κ 0 Sim, SIDM1 10 Pred.(<β>), anisotropic c Predicted profile with anisotropy describes the data well Anastasia Sokolenko UNIVERSITY OF OSLO 14

16 Conclusions We demonstrated that inner surface density of DM halos provides an efficient way to constrain DM self-interaction. The universal power law that surface density obeys allows to get a meaningful constraint despite large observational uncertainties for each of the objects All existing constraints on σ/m suffer from a theoretical uncertainty as the literature does not the provide direct prediction of the observationally relevant scale the core radius We have proposed a simple model that predicts the inner properties of SIDM halos using M 00, R 00 and σ/m as input and tested the validity of our approach using 8 halos simulated for various values of the cross-sections Anastasia Sokolenko UNIVERSITY OF OSLO 15