1,674 research outputs found
Modular Solutions to Equations of Generalized Halphen Type
Solutions to a class of differential systems that generalize the Halphen
system are determined in terms of automorphic functions whose groups are
commensurable with the modular group. These functions all uniformize Riemann
surfaces of genus zero and have --series with integral coefficients.
Rational maps relating these functions are derived, implying subgroup relations
between their automorphism groups, as well as symmetrization maps relating the
associated differential systems.Comment: PlainTeX 36gs. (Formula for Hecke operator corrected.
Superwind-driven Intense H Emission in NGC 6240 II: Detailed Comparison of Kinematical and Morphological Structures of the Warm and Cold Molecular Gas
We report on our new analysis of the spatial and kinematical distribution of
warm and cold molecular gas in NGC 6240, which was undertaken to explore the
origin of its unusually luminous H emission. By comparing three-dimensional
emission-line data (in space and velocity) of CO (J=2-1) in the radio and H
in the near infrared, we are able to study the H emitting efficiency,
defined in terms of the intensity ratio of H to CO [(H)/(CO)], as
a function of velocity. The integrated H emitting efficiency is calculated
by integrating the velocity profile of H emitting efficiency in blue, red,
and total (blue + red) velocity regions of the profile. We find that (1) both
the total H emitting efficiency and the blue-to-red ratio of the efficiency
are larger in regions surrounding the CO and H intensity peaks, and (2) the
H emitting efficiency and the kinematical conditions in the warm molecular
gas are closely related to each other. A collision between the molecular gas
concentration and the external superwind outflow from the southern nucleus
seems plausible to explain these characteristics, since it can reproduce the
enhanced emitting efficiency of blueshifted H around the molecular gas
concentration, if we assume that the superwind blows from the southern nucleus
toward us, hitting the entire gas concentration from behind. In this model,
internal cloud-cloud collisions within the molecular gas concentration are
enhanced by the interaction with the superwind outflow, and efficient and
intense shock-excited H emission is expected as a result of the
cloud-crushing mechanism.Comment: 12 pages, 6 figures, accepted for publication in A
Sub-parsec-scale Accleration of the Radio Jet in the Powerful Radio Galaxy NGC 6251
In order to investigate the genesis of powerful radio jet, we have mapped the
central 10 pc region of the nearby radio galaxy NGC 6251 with a 0.2 pc
resolution using Very Long Baseline Interferometer (VLBI) at two radio
frequencies, 5 GHz and 15 GHz, we have found the sub-parsec-scale counterjet
for the first time in this radio galaxy. This discovery allows us to
investigate the jet acceleration based on the relativistic beaming model.Comment: 7 pages with 7 figures. To appear in PASJ, 52, No. 5, Oct. 25, 200
Irregular conformal blocks, with an application to the fifth and fourth Painlev\'e equations
We develop the theory of irregular conformal blocks of the Virasoro algebra.
In previous studies, expansions of irregular conformal blocks at regular
singular points were obtained as degeneration limits of regular conformal
blocks; however, such expansions at irregular singular points were not clearly
understood. This is because precise definitions of irregular vertex operators
had not been provided previously. In this paper, we present precise definitions
of irregular vertex operators of two types and we prove that one of our vertex
operators exists uniquely. Then, we define irregular conformal blocks with at
most two irregular singular points as expectation values of given irregular
vertex operators. Our definitions provide an understanding of expansions of
irregular conformal blocks and enable us to obtain expansions at irregular
singular points.
As an application, we propose conjectural formulas of series expansions of
the tau functions of the fifth and fourth Painlev\'e equations, using
expansions of irregular conformal blocks at an irregular singular point.Comment: 26 page
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