Exploring Extended MOND in Galaxy Clusters. Alistair Hodson Supervisor Hongsheng Zhao

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1 Exploring Extended MOND in Galaxy Clusters Alistair Hodson Supervisor Hongsheng Zhao

2 Overview What is Extended MOND (EMOND)? What is the motivation for EMOND? What are the implications of EMOND? How successful is EMOND?

3 Some Background on Clusters in MOND Galaxy clusters cannot be explained by the current MOND formulation alone. MOND alleviates the mass discrepancy, but is not consistent with dynamical mass Central regions of clusters exhibit even larger mass discrepancies

4 3 Possible Conclusions

5 3 Possible Conclusions MOND is Falsified

6 3 Possible Conclusions MOND is Falsified Missing Mass?

7 3 Possible Conclusions MOND is Falsified Missing Mass? Missing Gravity?

8 3 Possible Conclusions MOND is Falsified Missing Mass? Missing Gravity?

9 Door 2 - Are We Just Missing Mass? Is MOND making a yet unknown mass prediction in clusters? Neutrino Mass? (Sanders 2003, Angus et al 2008, Angus 2008) Non-luminous Baryonic matter clumping on the cluster scale?

10 Door 3 Are We Just Missing Gravity? Newtonian breaks down at low accelerations. Does MOND break down in some limit? Can a generalized MOND explain Clusters and Galaxies simultaneously? Essence of Extended MOND (EMOND)

11 What is Extended MOND? Generalization of MOND EMOND assumes that acceleration scale of MOND is not constant. a0 increases in deep potential wells (Zhao, H & Famaey,B 2011)

12 What is the Motivation for EMOND? MOND works well in galaxies, but not in galaxy clusters. The effective mass of a galaxy cluster in MOND would increase if a0 were higher (Newtonian breaks down at higher accelerations). It was noted that Clusters are in much deeper potential wells than galaxies.

13 The EMOND formulation L MOND = ρφ a π G F(x M 2 ) 2 Φ N = [μ Φ M ] L EMOND = ρφ A 0 Φ 2 2 ) 8 π G F(x EM 2 Φ N = μ Φ E + T 2 x M = Φ x EM = a 0 Φ A 0 (Φ) F y α y for y 1 F y α 2 3 y3/2 for y 1 T 2 = A 0 Φ A 0 Φ F x 2 x 2 F x 2 Bekenstein, J, Milgrom, M 1984 Zhao, H & Famaey,B 2011

14 Some Immediate Implications of EMOND A 0 must be larger in galaxy clusters A 0 must be a 0 in galaxies A 0 must not tend to infinity in very deep potentials Term 2 is more complicated to calculate Even a constant gravitational potential will affect dynamics

15 Possible A 0 Interpolation Functions Exponential function A 0 exp Φ = min(a 0max, a 0 e Φ Φs ) μ function A 0 μ Φ = A 0 max μ Φ Φ s Φ s is defined such that: A 0 a 0 as Φ Φ ext

16 Solving the EMOND Equation For a single isolated and spherical body and assuming T 2 0 and simple μ function dφ N dr = μ Φ E A 0 Φ dφ E dr dφ E dr = 1 2 dφ N dr + dφ N dr 4 A 0 Φ E + dφ N dr Solved iteratively as a boundary value problem Boundary potential Constant External Potential 10-6 c 2 (m s -1 ) 2 Famaey, B et al 2007

17 Sanity Check Galaxy Model 10 7 Solar Mass Galaxy Solar Mass Galaxy ROTATION SPEED (km/s) Radius (kpc)

18 Modelling the Galaxy Clusters in EMOND

19 Initial Assumptions Spherical Symmetry EMOND s extra term T 2 is negligible Constant External Potential from nearest neighbour No neutrino mass

20 X-ray Gas Density ρ r < r out = m p n p n e 1 2 n p n e = n 0 2 ρ r > r out = 0 r r c 1 + r2 r c 2 α 3β α/ rγ r s γ 2 ε/γ + n r2 r c2 2 3β 2 X-ray Gas Temperature T/T mg r/r Vikhlinen, A 2005

21 Modelling the BCG Herniquist Profile Assume M/L= 1 Assume Scale length is 20 kpc for every BCG Φ H r = M H r = G M r + a h M r2 r + a h 2 Cluster Angus et al 2008 BCG Mass (10 11 Solar Mass) A133 8 A A A A A A RXJ MKW4 7.1

22 Calculating the Dynamical Mass Hydrostatic Equilibrium Isotropic System Solve Collisionless Boltzmann Equation M D (r) k T r r w m p G d ln ρ X d ln r + d ln T d ln r

23 Mass Results

24 A133

25 A262

26 A478

27 A1413

28 A1795

29 A1991

30 A2029

31 RXJ1159

32 MKW4

33 An Alternative Formulation?

34 EQUMOND L Q = 1 8 π G 2 Φ Φ N a 0 2 Q x Q 2 ρφ 2 Φ EQ = [ν Φ N ] L EQ = 1 8 π G 2 Φ Φ N A 0 Φ 2 2 N Q x EQ ρφ 2 Φ EQ = ν Φ + T 2 x Q = Φ N x EQ = a 0 Φ N A 0 (Φ N ) Q y α y for y 1 Q y α 4 3 y3/4 for y 1 T 2 = A 0 Φ N A 0 Φ N Q x 2 x 2 Q x 2 Milgrom, M 2010

35 EQUMOND Approach Same method and interpolation functions as in EMOND Constant External Field now Newtonian Equivalent Scale Potentials need renormalized accordingly

36 Calculating the Required Mass of the Cluster dφ N dr = G M N(r) r 2 A 0 Φ N = A 0 max μ Φ N + Φ ext Φ s M EQ r = Φ E r 2 G Φ EQ Φ N ν Φ N A 0 Φ N

37 EQUMOND Galaxy Test 10 7 Solar Mass Galaxy Solar Mass Galaxy

38 EQUMOND Masses - 1

39 EQUMOND Masses - 2

40 EQUMOND Masses - 3

41 EQUMOND Masses - 4

42 EQUMOND Masses - 5

43 The difficulty of EMOND Defining r out Calculating the External field Determining a good A 0 function Black holes experiencing deep-mond if A 0 becomes too large

44 Conclusion and Future Work EMOND can reconcile mass discrepancy in clusters But required a very large A 0 EQUMOND alternative can be constructed Need to Understand Term 2 in more detail Investigate, Develop and Test different A 0 functions Try and find a natural A 0 cut off point