Evolution of Star Clusters near the Galactic Center: Fully Self-consistent N-body Simulations

We have performed fully self-consistent $N$-body simulations of star clusters near the Galactic center (GC). Such simulations have not been performed because it is difficult to perform fast and accurate simulations of such systems using conventional methods. We used the Bridge code, which integrates the parent galaxy using the tree algorithm and the star cluster using the fourth-order Hermite scheme with individual timestep. The interaction between the parent galaxy and the star cluster is calculate with the tree algorithm. Therefore, the Bridge code can handle both the orbital and internal evolutions of star clusters correctly at the same time. We investigated the evolution of star clusters using the Bridge code and compared the results with previous studies. We found that 1) the inspiral timescale of the star clusters is shorter than that obtained with "traditional" simulations, in which the orbital evolution of star clusters is calculated analytically using the dynamical friction formula and 2) the core collapse of the star cluster increases the core density and help the cluster survive. The initial conditions of star clusters is not so severe as previously suggested.Comment: 19 pages, 19 figures, accepted for publication in Ap

BRIDGE: A Direct-tree Hybrid N-body Algorithm for Fully Self-consistent Simulations of Star Clusters and their Parent Galaxies

We developed a new direct-tree hybrid N-body algorithm for fully self-consistent N-body simulations of star clusters in their parent galaxies. In such simulations, star clusters need high accuracy, while galaxies need a fast scheme because of the large number of the particles required to model it. In our new algorithm, the internal motion of the star cluster is calculated accurately using the direct Hermite scheme with individual timesteps and all other motions are calculated using the tree code with second-order leapfrog integrator. The direct and tree schemes are combined using an extension of the mixed variable symplectic (MVS) scheme. Thus, the Hamiltonian corresponding to everything other than the internal motion of the star cluster is integrated with the leapfrog, which is symplectic. Using this algorithm, we performed fully self-consistent N-body simulations of star clusters in their parent galaxy. The internal and orbital evolutions of the star cluster agreed well with those obtained using the direct scheme. We also performed fully self-consistent N-body simulation for large-N models ($N=2\times 10^6$). In this case, the calculation speed was seven times faster than what would be if the direct scheme was used.Comment: 12 pages, 13 figures, Accepted for PAS

Quintessence, scalar-tensor theories and non-Newtonian gravity

We discuss some of the issues which we encounter when we try to invoke the scalar-tensor theories of gravitation as a theoretical basis of quintessence. One of the advantages of appealing to these theories is that they allow us to implement the scenario of a ``decaying cosmological constant,'' which offers a reasonable understanding of why the observed upper bound of the cosmological constant is smaller than the theoretically natural value by as much as 120 orders of magnitude. In this context, the scalar field can be a candidate of quintessence in a broader sense. We find, however, a serious drawback in the prototype Brans-Dicke model with $\Lambda$ added; a static universe in the physical conformal frame which is chosen to have constant particle masses. We propose a remedy by modifying the matter coupling of the scalar field taking advantage of scale invariance and its breakdown through quantum anomaly. By combining this with a conjecture on another cosmological constant problem coming from the vacuum energy of matter fields, we expect a possible link between quintessence and non-Newtonian gravity featuring violation of Weak Equivalence Principle and intermediate force range, likely within the experimental constraints. A new prediction is also offered on the time-variability of the gravitational constant.Comment: 12 pages LaTex including 1 eps figur

Exact solution of Riemann--Hilbert problem for a correlation function of the XY spin chain

A correlation function of the XY spin chain is studied at zero temperature. This is called the Emptiness Formation Probability (EFP) and is expressed by the Fredholm determinant in the thermodynamic limit. We formulate the associated Riemann--Hilbert problem and solve it exactly. The EFP is shown to decay in Gaussian.Comment: 7 pages, to be published in J. Phys. Soc. Jp

Negative energy and stability in scalar-tensor gravity

Linearized gravitational waves in Brans-Dicke and scalar-tensor theories carry negative energy. A gauge-invariant analysis shows that the background Minkowski space is stable at the classical level with respect to linear scalar and tensor inhomogeneous perturbations.Comment: 9 pages, latex, to appear in Phys. Rev.

A two-scalar model for a small but nonzero cosmological constant

We revisit a model of the two-scalar system proposed previously for understanding a small but nonzero cosmological constant. The model provides solutions of the scalar-fields energy $\rho_s$ which behaves truly constant for a limited time interval rather than in the way of tracker- or scaling-type variations. This causes a mini-inflation, as indicated by recent observations. As another novel feature, $\rho_s$ and the ordinary matter density $\rho_m$ fall off always side by side, but interlacing, also like (time)$^{-2}$ as an overall behavior in conformity with the scenario of a decaying cosmological constant. A mini-inflation occurs whenever $\rho_s$ overtakes $\rho_m$, which may happen more than once, shedding a new light on the coincidence problem. We present a new example of the solution, and offer an intuitive interpretation of the mechanism of the nonlinear dynamics. We also discuss a chaos-like nature of the solution.Comment: 9 pages plus 7 figure

Regulatory T cells in melanoma revisited by a computational clustering of FOXP3+ T cell subpopulations

CD4+ T cells that express the transcription factor FOXP3 (FOXP3+ T cells) are commonly regarded as immunosuppressive regulatory T cells (Treg). FOXP3+ T cells are reported to be increased in tumour-bearing patients or animals, and considered to suppress anti-tumour immunity, but the evidence is often contradictory. In addition, accumulating evidence indicates that FOXP3 is induced by antigenic stimulation, and that some non-Treg FOXP3+ T cells, especially memory-phenotype FOXP3low cells, produce proinflammatory cytokines. Accordingly, the subclassification of FOXP3+ T cells is fundamental for revealing the significance of FOXP3+ T cells in tumour immunity, but the arbitrariness and complexity of manual gating have complicated the issue. Here we report a computational method to automatically identify and classify FOXP3+ T cells into subsets using clustering algorithms. By analysing flow cytometric data of melanoma patients, the proposed method showed that the FOXP3+ subpopulation that had relatively high FOXP3, CD45RO, and CD25 expressions was increased in melanoma patients, whereas manual gating did not produce significant results on the FOXP3+ subpopulations. Interestingly, the computationally-identified FOXP3+ subpopulation included not only classical FOXP3high Treg but also memory-phenotype FOXP3low cells by manual gating. Furthermore, the proposed method successfully analysed an independent dataset, showing that the same FOXP3+ subpopulation was increased in melanoma patients, validating the method. Collectively, the proposed method successfully captured an important feature of melanoma without relying on the existing criteria of FOXP3+ T cells, revealing a hidden association between the T cell profile and melanoma, and providing new insights into FOXP3+ T cells and Treg

Boson stars in massive dilatonic gravity

We study equilibrium configurations of boson stars in the framework of a class scalar-tensor theories of gravity with massive gravitational scalar (dilaton). In particular we investigate the influence of the mass of the dilaton on the boson star structure. We find that the masses of the boson stars in presence of dilaton are close to those in general relativity and they are sensitive to the ratio of the boson mass to the dilaton mass within a typical few percent. It turns out also that the boson star structure is mainly sensitive to the mass term of the dilaton potential rather to the exact form of the potential.Comment: 9 pages, latex, 9 figures, one figure dropped, new comments added, new references added, typos correcte

Gaudin Hypothesis for the XYZ Spin Chain

The XYZ spin chain is considered in the framework of the generalized algebraic Bethe ansatz developed by Takhtajan and Faddeev. The sum of norms of the Bethe vectors is computed and expressed in the form of a Jacobian. This result corresponds to the Gaudin hypothesis for the XYZ spin chain.Comment: 12 pages, LaTeX2e (+ amssymb, amsthm); to appear in J. Phys.