What are universal features of gravitating Q-balls? Takashi Tamaki(Nihon University) with Nobuyuki Sakai (Yamagata University) I.Introduction Q-balls:a kind of nontopological solitons consist of scalar fields Self-gravity may not be important? flat × with self-gravity ○ (mini-boson star) Kaup, PR172, 1331 (1968)

gravity-mediation type in the Affleck-Dine (AD) mechanism flat ○ × ○ ○ ``Q-balls” surrounded by Q-matter gravity TT, N. Sakai, PRD83, (2011) Here, gauge-mediation type  seek for universal features!! TT, N. Sakai, PRD84, (2011)

II. Model normalization

III. flat case Particle motion in trivial

Thick-wall solution Thin-wall solution

IV. gravitating case Particle motion in Signature of depends on r.  depends on ``time”.

Thick-wall Thin-wall

Thick-wallThin-wall changes ``quickly”. For various ?

strong gravity weak gravity WHY ???

V. thick-wall case weak gravity take up to first order in h,f. Let us evaluate Evaluate from We used Maclaurin expansion and neglected For We should compare with

and weak gravity We assumefor C =const. and approximating substitute into

as in the flat case

V. conclusion Gravitating Q-balls The thick-wall limit is completely different from the flat case. From the analytic estimation, our results hold for general potentials if a positive mass term is a leading order. exists !!

as in the flat case

Basic equations important quantities Total energy (Hamiltonian)

サイズの議論 mini-BS 1/m の半径  GM~1/m  BS の相互作用項の存在が本質的  e.g., GM~1/m_re Λ大Λ大 m(neutron) 程度  M=M( 太陽 )