73 research outputs found
Statistical Properties of the Linear Sigma Model
The statistical equilibrium properties of the linear sigma model are studied,
with a view towards characterizing the field configurations employed as initial
conditions for numerical simulations of the formation of disoriented chiral
condensates in high-energy nuclear collisions. The field is decomposed into its
spatial average (the order parameter) and the fluctuations (the quasi-
particles) and enclosed in a rectangular box with periodic boundary conditions.
The quantized quasi-particle modes are described approximately by Klein-Gordon
dispersion relations containing an effective mass that depends on both the
temperature and the magnitude of the order parameter. The thermal fluctuations
are instrumental in shaping the effective potential governing the order
parameter, and the evolution of its statistical distribution with temperature
is discussed, as is the behavior of the associated effective masses. As the
system is cooled the field fluctuations subside, causing a smooth change from
the high-temperature phase in which chiral symmetry is approximately restored
towards the normal phase. Of practical interest is the fact that the
equilibrium field configurations can be sampled in a simple manner, thus
providing a convenient means for specifying the initial conditions in dynamical
simulations of the non-equilibrium relaxation of the chiral field. The
corresponding correlation function is briefly considered and used to calculate
the spectral strength of radiated pions. Finally, by propagating samples of
initial configurations by the exact equation of motion, it has been ascertained
that the treatment is sufficiently accurate to be of practical utility.Comment: 42 pages total, incl 18 figs using pstricks ([email protected]
Horizontal Branch Stars: The Interplay between Observations and Theory, and Insights into the Formation of the Galaxy
We review HB stars in a broad astrophysical context, including both variable
and non-variable stars. A reassessment of the Oosterhoff dichotomy is
presented, which provides unprecedented detail regarding its origin and
systematics. We show that the Oosterhoff dichotomy and the distribution of
globular clusters (GCs) in the HB morphology-metallicity plane both exclude,
with high statistical significance, the possibility that the Galactic halo may
have formed from the accretion of dwarf galaxies resembling present-day Milky
Way satellites such as Fornax, Sagittarius, and the LMC. A rediscussion of the
second-parameter problem is presented. A technique is proposed to estimate the
HB types of extragalactic GCs on the basis of integrated far-UV photometry. The
relationship between the absolute V magnitude of the HB at the RR Lyrae level
and metallicity, as obtained on the basis of trigonometric parallax
measurements for the star RR Lyrae, is also revisited, giving a distance
modulus to the LMC of (m-M)_0 = 18.44+/-0.11. RR Lyrae period change rates are
studied. Finally, the conductive opacities used in evolutionary calculations of
low-mass stars are investigated. [ABRIDGED]Comment: 56 pages, 22 figures. Invited review, to appear in Astrophysics and
Space Scienc
- …