Miami Modified dark matter in galaxy clusters. Douglas Edmonds Emory & Henry College

Transcription

1 Miami 2015 Modified dark matter in galaxy clusters Douglas Edmonds Emory & Henry College

2 Collaboration D. Edmonds Emory & Henry College D. Farrah Virginia Tech C.M. Ho Michigan State University D. Minic Virginia Tech Y.J. Ng University of North Carolina T. Takeuchi Virginia Tech

3 Outline Modified Dark Matter (MDM) What is MDM? MDM from entropic gravity What is the mass profile of an MDM halo? Does MDM resolve mass discrepancies? Observed galactic rotation curves Observed vs. dynamical mass in Galaxy clusters

4 MDM MoNDian Modified dark matter (MDM) is dark matter i.e., it is an EXTRA source (beyond the baryonic source) MDM is NOT a modification of gravity

5 MDM Theory via entropic gravity FΔx = TΔS entropic force from 1 st and 2 nd laws of thermodynamics ΔS = 2πk mc! Δx kt =!a 2πc! F entropic = m! a Bekenstein-Hawking formula for black hole entropy (at event horizon) Unruh temperature Newton s 2 nd law (Vector from gradient of entropy) Verlinde, 2010 [arxiv: ]

6 Consider a quasi-local (spherical) holographic screen with area and temperature A = 4πr 2 E = NkT / 2 MDM Theory via entropic gravity Equipartition of energy:, N = A / l 2 P = Ac 3 / (G ) being the total number of degrees of freedom (bits) on the screen T Unruh temperature for a uniformly accelerating (Rindler) observer kt = a 2πc Along with E = Mc 2 Mc 2 = Ac2 a 4πG = r2 c 2 a G a = GM r 2 Newton s law of gravity Verlinde, 2010 [arxiv: ]

7 Generalization to de Sitter space: MDM Theory via entropic gravity Unruh temperature measured by an inertial observer, where T ds = a 0 2πkc a 0 = c Λ / 3 T ds+a = a2 + a 0 2 2πkc Unruh temperature measured by a non-inertial observer with accleration a Net temperature measured by a non-inertial observer T T ds+a T ds = # 2πkc a2 +a 2 0 a & $% 0'( Verlinde s approach F entropic = T " = m a 2 +a 2 $ # 0 a 0 % Deser & Levin [arxiv:gr-qc/ ]; Jacobson [arxiv:gr-qc/ ]; Ho, Minic & Ng [arxiv: ]

8 Consider a quasi-local (spherical) holographic screen with area and effective temperature A = 4πr 2 MDM Theory via entropic gravity T a 2 + a 0 2 a 0 = 2πck T = 2πck " $ # 2 E Nk % " ' = 4π $ & # Unruh equipartition Einstein MG % ' = G M A & r 2 where M represents the total mass enclosed within the volume. M = M + M ' M ', where is the dark matter mass. What is the MDM mass profile? Ho, Minic & Ng [arxiv: ]; [arxiv: ]; [arxiv: ]

9 What is the mass profile? MDM Theory observational constraints F entropic = T " = m a 2 +a 2 $ # 0 a 0 % a >> a 0, F entropic ma; a << a 0, F entropic ma 2 / (2a 0 ) a << a 0 For, consistency with flat rotation curves (v independent of r) and the observed Tully-Fisher relation ( ) requires that v 4 M a (2a N a 3 0 / π )1/4 The entropic force for the low acceleration regime is then where a c F entropic ma2 2a 0 m a N a c F MoND is the critical acceleration in MOND, and we have used the fact that a 0 2πa c Ho, Minic & Ng [arxiv: ]; [arxiv: ]; [arxiv: ]

10 What is the mass profile? MDM Theory observational constraints Galactic rotation curves suggest: ' M ' = M 1! ) # () π " a 0 a $ & % 2 *, +, Note: This form is also suggested by introducing a fundamental acceleration which is related to the cosmological constant into Jacobson s rewriting of GR as a form of thermodynamics Ho, Minic & Ng [arxiv: ]; Jacobson [1995; Phys. Rev. Lett. 75]

11 Observations Galactic Rotation Curves Solve the force equation for circular orbits for a(r) and v(r) " F entropic = m a 2 +a 2 $ # 0 a 0 % = mgm ρ ' r! ( ) = a c # ρ '( r) = " r s r $ & % 2 ρ 0 d dr! # " r! 1+ r $ # & " r s % 2 M a 2 $ & % ln( 1+ cx) cx / ( 1+ cx) ( ) = v 200 x ln( 1+ c) c / ( 1+ c) v r " & r 2 1+ a 0 ), ( + # ' a * 2 $ - = mv2 % r Once we have a(r), we can find the MDM density profile We compare MDM fits to CDM (using NFW profile) DE, Farrah, Ho, Minic, Ng & Takeuchi, 2014 [arxiv: ] "# $ %

12 Observations Galactic Rotation Curves Data black squares MDM red line Stars blue line CDM (NFW) black line Gas green line [Sanders & Verheijen, 1998] Fitting parameters: MDM M/L CDM c, V 200, M/L DE, Farrah, Ho, Minic, Ng & Takeuchi, 2014 [arxiv: ]

13 Observations Galactic Rotation Curves MDM red line CDM (NFW) black line Fitting parameters: MDM M/L CDM c, V 200, M/L DE, Farrah, Ho, Minic, Ng & Takeuchi, 2014 [arxiv: ]

14 What is the mass profile? MDM Theory observational constraints Galactic rotation curves suggest: ' M ' = M 1! ) # () π " a 0 a $ & % 2 *, +, But, the mass profile above does not work for galaxy clusters. In principle, the mass profile may be modified in any number of ways search for mass profiles which are consistent with thermodynamics. A better profile for galaxy clusters:! α $ M ' = # & a2 0 " 1+ r / r s % a M 2 Note: This mass profile also works for galactic rotation curves.

15 Observations Galaxy Clusters M(r) = kt(r)r µm p G! d ln ρ g d lnr + d lnt(r) $ # & " d lnr % spherical symmetry and hydrostatic equilibrium (Sarazin 1988) Vikhlinin et al. (2006) ρ g =1.2m p n e n p modification of traditional β- model T(r) = T 0 t cool (r)t(r) Allen et al. (2001)

16 Observations Galaxy Clusters Dynamical (virial) mass: (implied by Newton) M N (r) = kt(r)r µm p G! d ln ρ g d lnr + d lnt(r) $ # & " d lnr % Total mass with MDM: '! α M MDM = M baryonic ) 1+ # ( " 1+ r / R s $ & a2 0 a 2 % *, + MOND effective mass (mass required in Newtonian dynamics to give the same observed acceleration as MOND): M MOND = M baryonic 1+ ( a c / a) 2

17 Observations Galaxy Clusters black solid: virial mass dashed: gas mass green solid: MDM dash-dotted: CDM dotted: MOND USGC S152 A133 A262 A1795 A1991 A383 A478 A2029 A2390 A907 A1413 RX J MKW 4

18 Conclusion Summary By generalizing entropic gravity to desitter space, we are led to a form of dark matter which naturally accounts for Milgrom s scaling. The mass profile is not uniquely determined we choose mass profiles that are consistent with thermodynamics. We have tested the MDM model at galactic and cluster scales, and it fares well. We can fit galactic rotation curves and galaxy cluster dynamics with the same dark matter mass profile up to a constant scale factor. We not only fit the average cluster mass, but the shape of the mass profile as well.

19 Conclusion Future Work Can we better constrain the mass profile? The Bullet Cluster; How strongly coupled is MDM to baryonic matter? How does MDM self-interact? Acoustic oscillations measured in the CMB Simulations of structure formation: Hard? Particle physics: MDM is (likely) non-local How does one detect such a thing?

20 Conclusion Thank you! Ho, Minic & Ng, 2010, Phys. Lett. B, 693, 567 Ho, Minic & Ng, 2011, Gen. Rel. and Grav., 43, 2567 Ho, Minic & Ng, 2012, Phys. Rev. D, 85, DE, Farrah, Ho, Minic, Ng & Takeuchi, 2014, ApJ 793, 41 DE, Farrah, Ho, Minic, Ng & Takeuchi, arxiv 2015?