1,008 research outputs found
A unified description of anti-dynamo conditions for incompressible flows
A general type of mathematical argument is described, which applies to all
the cases in which dynamo maintenance of a steady magnetic field by motion in a
uniform density is known to be impossible. Previous work has demonstrated that
magnetic field decay is unavoidable under conditions of axisymmetry and in
spherical or planar incompressible flows. These known results are encompassed
by a calculation for flows described in terms of a generalized
poloidal-toroidal representation of the magnetic field with respect to an
arbitrary two dimensional surface. We show that when the velocity field is two
dimensional, the dynamo growth, if any, that results, is linear in one of the
projections of the field while the other projections remain constant. We also
obtain criteria for the existence of and classification into two and three
dimensional velocity results which are satisfied by a restricted set of
geometries. In addition, we discuss the forms of spatial variation of the
density and the resistivity that are allowed so that field decay still occurs
for this set of geometries.Comment: 8 pages, Asian Journal of Physics, in pres
Stellar and gas dynamical model for tidal disruption events in a quiescent galaxy
A detailed model of the tidal disruption events (TDEs) has been constructed
using stellar dynamical and gas dynamical inputs that include black hole (BH)
mass , specific orbital energy and angular momentum , star
mass and radius , and the pericenter of the star orbit
. We solved the steady state
Fokker--Planck equation using the standard loss cone theory for the galactic
density profile and stellar mass function
where and obtained the feeding rate of stars
to the BH integrated over the phase space as , where for and Yr for
. We use this to model the in-fall rate of the disrupted debris,
, and discuss the
conditions for the disk formation, finding that the accretion disk is almost
always formed for the fiduciary range of the physical parameters. We also find
the conditions under which the disk formed from the tidal debris of a given
star with a super Eddington accretion phase. We have simulated the light curve
profiles in the relevant optical g band and soft X-rays for both super and
sub-Eddington accretion disks as a function of
. Using this, standard cosmological
parameters, and mission instrument details, we predict the detectable TDE rates
for various forthcoming surveys finally as a function of .Comment: 56 pages; 22 Figures, Accepted in the Astrophysical Journal, updated
paper includes proof correction
Cosmic spin and mass evolution of black holes and its impact
We build an evolution model of the central black hole that depends on the
processes of gas accretion, the capture of stars, mergers as well as
electromagnetic torque. In case of gas accretion in the presence of cooling
sources, the flow is momentum-driven, after which the black hole reaches a
saturated mass; subsequently, it grows only by stellar capture and mergers. We
model the evolution of the mass and spin with the initial seed mass and spin in
CDM cosmology. For stellar capture, we have assumed a power-law
density profile for the stellar cusp in a framework of relativistic loss cone
theory that include the effects of black hole spin, Carter's constant, loss
cone angular momentum, and capture radius. Based on this, the predicted capture
rates of -- yr are closer to the observed range. We
have considered the merger activity to be effective for , and we
self-consistently include the Blandford-Znajek torque. We calculate these
effects on the black hole growth individually and in combination, for deriving
the evolution. Before saturation, accretion dominates the black hole growth
( of the final mass), and subsequently, stellar capture and mergers
take over with roughly equal contribution. The simulations of the evolution of
the relation using these effects are consistent with
available observations. We run our model backward in time and retrodict the
parameters at formation. Our model will provide useful inputs for building
demographics of the black holes and in formation scenarios involving stellar
capture.Comment: 56 pages, 27 figures; accepted for publication in the Astrophysical
Journal; v2: updated references, typos fixed, editorial changes; v3:
corrections during proof
Models of force-free spheres and applications to solar active regions
Here we present a systematic study of force-free field equation for simple
axisymmetric configurations in spherical geometry. The condition of
separability of solutions in radial and angular variables leads to two classes
of solutions: linear and non-linear force-free fields. We have studied these
linear solutions Chandrasekhar (1956) and extended the non-linear solutions
given in Low \& Lou (1990) to the irreducible rational form , which is
allowed for all cases of odd and to cases of for even . We have
further calculated their energies and relative helicities for magnetic field
configurations in finite and infinite shell geometries. We demonstrate here a
method here to be used to fit observed magnetograms as well as to provide good
exact input fields for testing other numerical codes used in reconstruction on
the non-linear force-free fields.Comment: 7 pages, 2 figure
Magnetohydrostatic flux tube model in the solar atmosphere
We construct two classes of the magnetohydrostatic equilibria of the
axisymmetric flux tubes with twisted magnetic fields in the stratified solar
atmosphere that span from the photosphere to the transition region. We built
the models by incorporating specific forms of the gas pressure and poloidal
current in the Grad-Shafranov equation. This model gives both closed and open
field structure of the flux tube. The other open field model we construct is
based on the self-similar formulation, where we have incorporated specific
forms of the gas pressure, poloidal current and two different shape functions.
We study the homology of the parameter space that is consistent with the solar
atmosphere and find that the estimation of the magnetic structure inside the
flux tubes is consistent with the observation and simulation results of the
magnetic bright points.Comment: 2 pages, 1 figure; to appear in the proceedings of IAU Symposium 340:
Long-term datasets for the understanding of solar and stellar magnetic cycle
On Compressing U-net Using Knowledge Distillation
We study the use of knowledge distillation to compress the U-net
architecture. We show that, while standard distillation is not sufficient to
reliably train a compressed U-net, introducing other regularization methods,
such as batch normalization and class re-weighting, in knowledge distillation
significantly improves the training process. This allows us to compress a U-net
by over 1000x, i.e., to 0.1% of its original number of parameters, at a
negligible decrease in performance.Comment: 4 pages, 1 figur
Kinematics of and emission from helically orbiting blobs in a relativistic magnetized jet
We present a general relativistic (GR) model of jet variability in active
galactic nuclei due to orbiting blobs in helical motion along a funnel or cone
shaped magnetic surface anchored to the accretion disk near the black hole.
Considering a radiation pressure driven flow in the inner region, we find that
it stabilizes the flow, yielding Lorentz factors ranging between 1.1 and 7 at
small radii for reasonable initial conditions. Assuming these as inputs,
simulated light curves (LCs) for the funnel model include Doppler and
gravitational shifts, aberration, light bending, and time delay. These LCs are
studied for quasi-periodic oscillations (QPOs) and the power spectral density
(PSD) shape and yield an increased amplitude ( 12 %); a beamed portion
and a systematic phase shift with respect to that from a previous special
relativistic model. The results strongly justify implementing a realistic
magnetic surface geometry in Schwarzschild geometry to describe effects on
emission from orbital features in the jet close to the horizon radius. A power
law shaped PSD with a typical slope of and QPOs with timescales in the
range of days consistent with optical variability in Blazars,
emerges from the simulations for black hole masses and initial Lorentz factors .
The models presented here can be applied to explain radio, optical, and X-ray
variability from a range of jetted sources including active galactic nuclei,
X-ray binaries and neutron stars.Comment: 41 pages, 13 Figures (19 sub-figures), 2 Tables, 1 Appendix; minor
corrections made; Accepted for publication in the Astrophysical Journa
A global galactic dynamo with a corona constrained by relative helicity
We present a model for a global axisymmetric turbulent dynamo operating in a
galaxy with a corona which treats the supernovae (SNe) and magneto-rotational
instability (MRI) driven turbulence parameters under a common formalism. The
nonlinear quenching of the dynamo is alleviated by inclusion of small-scale
advective and diffusive magnetic helicity fluxes, which allow the gauge
invariant magnetic helicity to be transferred outside the disk and consequently
build up a corona during the course of dynamo action. The time-dependent dynamo
equations are expressed in a separable form and solved through an eigenvector
expansion constructed using the steady-state solutions of the dynamo equation.
The parametric evolution of the dynamo solution allows us to estimate the final
structure of the global magnetic field and the saturated value of the
turbulence parameter , even before solving the dynamical equations
for evolution of magnetic fields in the disk and the corona, along with
-quenching. We then solve these equations simultaneously to study the
saturation of large-scale magnetic field, its dependence on the small-scale
magnetic helicity fluxes and corresponding evolution of the force-free field in
the corona. The quadrupolar large-scale magnetic field in the disk is found to
reach equipartition strength within a timescale of 1 Gyr. The large-scale
magnetic field in the corona obtained is much weaker in strength compared to
the field inside the disk and has only a weak impact on the dynamo operation.Comment: 59 pages, 14 figures, 37 sub-figures, 2 tables and 7 appendices.
Accepted for publication in Ap
Topological and statistical properties of nonlinear force-free fields
We use our semi-analytic solution of the nonlinear force-free field equation
to construct three-dimensional magnetic fields that are applicable to the solar
corona and study their statistical properties for estimating the degree of
braiding exhibited by these fields. We present a new formula for calculating
the winding number and compare it with the formula for the crossing number. The
comparison is shown for a toy model of two helices and for realistic cases of
nonlinear force-free fields; conceptually the formulae are nearly the same but
the resulting distributions calculated for a given topology can be different.
We also calculate linkages, which are useful topological quantities that are
independent measures of the contribution of magnetic braiding to the total free
energy and relative helicity of the field. Finally, we derive new analytical
bounds for the free energy and relative helicity for the field configurations
in terms of the linking number. These bounds will be of utility in estimating
the braided energy available for nano-flares or for eruptions.Comment: 22 pages, 8 figures, 1 table, to appear in a special issue of
Advances in Space Research on the "Dynamic Sun
Open and closed magnetic configurations of twisted flux tubes
We construct two classes of magnetohydrostatic (MHS) equilibria for an
axisymmetric vertical flux tube spanning from the photosphere to the lower part
of the transition region within a realistic stratified solar atmosphere subject
to solar gravity. We assume a general quadratic expression of the magnetic flux
function for the gas pressure and poloidal current and solve the Grad-Shafranov
equation analytically. The solution is a combination of a homogeneous and a
particular part where the former is separable by a Coulomb function in and
exponential in , while the particular part is an open configuration that has
no dependence. We also present another open field solution by using a
self-similar formulation with two different profile functions and incorporating
stratified solar gravity to maintain the magnetohydrostatic equilibria, which
is a modification of earlier self-similar models with a twist. We study the
admitted parameter space that is consistent with the conditions in the solar
atmosphere and derive magnetic and the thermodynamic structures inside the flux
tube that are reasonably consistent with the photospheric magnetic bright
points (MBPs) for both open and closed field Coulomb function and self-similar
models as estimated from observations and simulations. The obtained open and
closed field flux tube solutions can be used as the background conditions for
the numerical simulations for the study of the wave propagation through the
flux tubes. The solutions can also be used to construct realistic magnetic
canopies.Comment: 34 pages; 21 figures with 29 sub-figures; 6 tables, Accepted in the
Astrophysical Journa
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