12 research outputs found
New Finite Rogers-Ramanujan Identities
We present two general finite extensions for each of the two Rogers-Ramanujan
identities. Of these one can be derived directly from Watson's transformation
formula by specialization or through Bailey's method, the second similar
formula can be proved either by using the first formula and the q-Gosper
algorithm, or through the so-called Bailey lattice.Comment: 19 pages. to appear in Ramanujan
Logarithmic and complex constant term identities
In recent work on the representation theory of vertex algebras related to the
Virasoro minimal models M(2,p), Adamovic and Milas discovered logarithmic
analogues of (special cases of) the famous Dyson and Morris constant term
identities. In this paper we show how the identities of Adamovic and Milas
arise naturally by differentiating as-yet-conjectural complex analogues of the
constant term identities of Dyson and Morris. We also discuss the existence of
complex and logarithmic constant term identities for arbitrary root systems,
and in particular prove complex and logarithmic constant term identities for
the root system G_2.Comment: 26 page
N-body simulations of gravitational dynamics
We describe the astrophysical and numerical basis of N-body simulations, both
of collisional stellar systems (dense star clusters and galactic centres) and
collisionless stellar dynamics (galaxies and large-scale structure). We explain
and discuss the state-of-the-art algorithms used for these quite different
regimes, attempt to give a fair critique, and point out possible directions of
future improvement and development. We briefly touch upon the history of N-body
simulations and their most important results.Comment: invited review (28 pages), to appear in European Physics Journal Plu
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
A MODEST review
We present an account of the state of the art in the fields explored by the
research community invested in 'Modeling and Observing DEnse STellar systems'.
For this purpose, we take as a basis the activities of the MODEST-17
conference, which was held at Charles University, Prague, in September 2017.
Reviewed topics include recent advances in fundamental stellar dynamics,
numerical methods for the solution of the gravitational N-body problem,
formation and evolution of young and old star clusters and galactic nuclei,
their elusive stellar populations, planetary systems, and exotic compact
objects, with timely attention to black holes of different classes of mass and
their role as sources of gravitational waves.
Such a breadth of topics reflects the growing role played by collisional
stellar dynamics in numerous areas of modern astrophysics. Indeed, in the next
decade, many revolutionary instruments will enable the derivation of positions
and velocities of individual stars in the Milky Way and its satellites and will
detect signals from a range of astrophysical sources in different portions of
the electromagnetic and gravitational spectrum, with an unprecedented
sensitivity. On the one hand, this wealth of data will allow us to address a
number of long-standing open questions in star cluster studies; on the other
hand, many unexpected properties of these systems will come to light,
stimulating further progress of our understanding of their formation and
evolution.Comment: 42 pages; accepted for publication in 'Computational Astrophysics and
Cosmology'. We are much grateful to the organisers of the MODEST-17
conference (Charles University, Prague, September 2017). We acknowledge the
input provided by all MODEST-17 participants, and, more generally, by the
members of the MODEST communit