a ( i rj r ) GN i m i 1 j r 3 (1 (1 j r r ( r r i j r ) j i ) i e ) ravity -Body simulationG Gravity?) N dified MOffat MO Gravity? or on MOdified (MOG= S 1 G 1 16 R G 2 S g 4 1 d x, B 4 B 1 2 S 2 S 1 V 1 Cosmology g 4 G G gd x 2 G , and 2 G 2 V G G V G 2 鈴木隆之 2 V particle physics University gd 4 Yamaguchi x. Suzuki Laboratory of TheoreticalTakayuki 2nd grade PhD student ○ Basic theory and review of Moffat gravity Scalar Tensor Vector Gravity(STVG) ＡＣＴＩＯＮ developed by John Moffat 2005 1 1 S R 2 gd 4 x, G 16 G 1 1 2 4 S B B V gd x, 4 2 1 1 G G V G V S g G V gd 4 x. S 2 2 2 2 G 2 G G It have a massive vector field φμ(x)which couples with matter directly, and 3 scalar fields G(x), ω(x) and μ(x). Bμν = ∂μφν – ∂νφμ and Vφ(φ), VG(G), Vω(ω) and Vμ(μ) denote self-interaction potentials. G(x) is gravitational constant. Weak field approximation • The equation of motion of a test particle is given by du m u u m B u . ds • For weak fields the MOG acceleration law is d 2r G M N 1 1 re r , dt2 r 2 1/ 2 1 D 6250M kpc , M G D 1, , E 25000M 1/ 2 , 2 G M E N M G 20GN , d 2r G M eff , G G 1 1 re r . dt2 r 2 eff N key point : Vector field is couple with matter → Geodesic equation has external force term massive → It has effective range → Yukawa like force In fact, Newton gravity we recognize = (1+α)×Gravitation of the inverse square law － Yukawa like Repulsive force Why can MOG explain galaxy flat rotate curve without dark matter？ 11 if galaxy mass ～10 Ｍ☉ →linear plot 70 G G 1 1 rer G eff N 60 eff On disk scale 50 Ｇ∝ 15 r 40 10 30 20 5 10 200 400 600 800 1000 0.01 0.1 1 10 100 1000 104 kpc ←disk size→ ←satellite galaxy→ Equation of Kepler motion 2 GM GM v v r r 2 r if G∝r, v is constant! How are MOG different from MOND? As it is said from old days, MOND can explain galactic flat rotate curve without dark matter. MOND=MOdified Newton Dynamics：Mordehai Milgrom 1983 BUT, MOG is・・・ • It is not simple-minded phenomenalism. It is relativistic gravity theory. It can be derived from an action principle. • It can explain without dark matter from small scale(galaxy) to large scale(cosmology). • It can explain dark energy too. (arXiv:0710.0364) Moffat says － • A fitting routine has been applied to fit a large number of galaxy rotation curves (101 galaxies), using photometric data (58 galaxies) and a core model (43 galaxies) (J. R. Brownstein and JWM, 2005; J. R. Brownstein, 2009). •The fits to the data are remarkably good for STVG. For the photometric data, only one parameter, the mass-to-light ratio M/L, is used. But, above verification is the viewpoint from "statics". It is necessary to examine it about the real galactic "kinetic" evolution more. -body simulation. ○ the summary and motivation of my study a ( Method is very simple.-body simulation i rj r ) study is verification of MoffatGN gravityi m from the viewpoint of N My i 1 j r 3 (1performing(1 normal N j r r ( r r i j r ) j i ) after havingi e changed) equation of motion. ・・・ ball. cold collapse the isodensity seems to be "an gravitational collapse of The -body simulation. This Very simple N formation. exercise simulation" for beginners But,It's a bare process of the elliptical galaxy ). details poster(P31 If you want to knowplease the watch my -purpose PC farm at Center. for 。 ○ Acknowledgments , of National Astronomical Observatory of Japan Numerical computations wereCfCA carried out on the general Computational Astrophysics,天文シミュレーションプロジェクトの汎用計算機を使わせて頂きました には国立天文台 数値計算 Thanks to.