arXiv subjects

K. Young

Publications and source records attributed to K. Young.

At least 37 records · Page 2Linked to original sources

arXiv1999

SUSY Transformations for Quasinormal and Total-Transmission Modes of Open Systems

Quasinormal modes are the counterparts in open systems of normal modes in conservative systems; defined by outgoing-wave boundary conditions, they have complex eigenvalues. The conditions are studied for a system to have a supersymmetric(SUSY) partner with the same complex quasinormal-mode spectrum (or the same except for one eigenvalue). The discussion naturally includes total-transmission modes as well(incoming at one extreme and outgoing at the other). Several types of SUSY transformations emerge, and each is illustrated with examples, including the transformation among different Poschl-Teller potentials and the well-known identity in spectrum between the two parity sectors of linearized gravitational waves propagating on a Schwarzschild background. In contrast to the case of normal modes, there may be multiple essentially isospectral partners, each missing a different state. The SUSY transformation preserves orthonormality under a bilinear map which is the analog of the usual inner product for conservative systems. SUSY transformations can lead to doubled quasinormal and total-transmission modes; this phenomenon is analysed and illustrated. The existence or otherwise of SUSY partners is also relevant to the question of inversion: are open wave systems uniquely determined by their complex spectra?

math-ph↗

arXiv1999

The Light Curve and Evolutionary Status of the Carbon Star V Hya

V Hya, an evolved carbon star with a complex circumstellar envelope, has two variability periods, 530d and 6000d (17 years). We analyze recent light curve data and show that both variations have benn present for at least 100 years and have been regular over this time. The 530d period and its 1.5 - 2 magnitude amplitude show that V Hya is a Mira variable. We suggest that the star is in a binary system (as also suspected from the structure of the circumstellar envelope) and that the 17-year variation is due to extinction by circumstellar dust orbiting with the companion. The properties of the envelope found from molecular line observations: the fast molecular wind, the relatively small size of the dense circumstellar envelope, and the high mass loss rate, all suggest that V Hya has entered its `superwind' phase. However, its spectral type, period, colors, and lack of ionizing radiation show that the star is still on the AGB. These properties add to the evidence that the complex structures of many planetary planetary nebulae, including fast stellar winds, originate during the final phases of mass loss on the AGB.

astro-ph↗

arXiv1999

Jordan blocks and generalized bi-orthogonal bases: realizations in open wave systems

Dissipative systems can be described in terms of non-hermitian hamiltonians H, whose left eigenvectors f^j and right eigenvectors f_j form a bi-orthogonal system. Bi-orthogonal systems could suffer from two difficulties. (a) If the eigenvectors do not span the whole space, then H can only be diagonalized to blocks (the Jordan-block problem). (b) Normalization would not be possible and many familiar-looking formulas would fail if (f^j,f_j) = 0 for some j (the orthonormalization problem). Waves in open systems provide a well-founded realization of a bi-orthogonal system, and it is shown that these two problems can indeed occur and are both related to higher-order poles in the frequency-domain Green's function. The resolution is then given by introducing a generalized duality transformation involving extra basis vectors, whose time evolution is modified by polynomials in the time t. One thus obtains a nontrivial extension of the bi-orthogonal formalism for dissipative systems.

math-ph↗

arXiv1999

Waves in Open Systems: Eigenfunction Expansions

An open system is not conservative because energy can escape to the outside. An open system by itself is thus not conservative. As a result, the time-evolution operator is not hermitian in the usual sense and the eigenfunctions (factorized solutions in space and time) are no longer normal modes but quasinormal modes (QNMs) whose frequencies $ω$ are complex. QNM analysis has been a powerful tool for investigating open systems. Previous studies have been mostly system specific, and use a few QNMs to provide approximate descriptions. Here we review recent developments which aim at a unifying treatment. The formulation leads to a mathematical structure in close analogy to that in conservative, hermitian systems. Many of the mathematical tools for the latter can hence be transcribed. Emphasis is placed on those cases in which the QNMs form a complete set for outgoing wavefunctions, so that in principle all the QNMs together give an exact description of the dynamics. Applications to optics in microspheres and to gravitational waves from black holes are reviewed, and directions for further development are outlined.

gr-qc↗

arXiv1999

The Circumstellar Envelope of pi Gru

CO(J = 2-1) and SiO(J = 5-4) emission has been observed from the molecular envelope around the nearby S star pi Gru. The CO line profile differs from the usual parabolic shape seen in uniformly expanding envelopes; it has a Voigt-like profile and two horns. A model for line formation in the envelope shows that a tilted, expanding disk reproduces the observations well. The star also has a fast molecular wind, with a projected outflow speed of at least 70 and perhaps as high as 90 km/s. The fast wind is presumably ejected from the poles of the disk. These observations show that the complex structure seen in many planetary nebulae, including quadrupolar structure and fast winds, may largely evolve from structure formed while the progenitor star is in the last stages of evolution on the AGB.

astro-ph↗

arXiv1999

Waves in Open Systems via Bi-orthogonal Basis

Dissipative quantum systems are sometimes phenomenologically described in terms of a non-hermitian hamiltonian $H$, with different left and right eigenvectors forming a bi-orthogonal basis. It is shown that the dynamics of waves in open systems can be cast exactly into this form, thus providing a well-founded realization of the phenomenological description and at the same time placing these open systems into a well-known framework. The formalism leads to a generalization of norms and inner products for open systems, which in contrast to earlier works is finite without the need for regularization. The inner product allows transcription of much of the formalism for conservative systems, including perturbation theory and second-quantization.

math-ph↗

arXiv1999

Perturbative Approach to the Quasinormal Modes of Dirty Black Holes

Using a recently developed perturbation theory for uasinormal modes (QNM's), we evaluate the shifts in the real and imaginary parts of the QNM frequencies due to a quasi-static perturbation of the black hole spacetime. We show the perturbed QNM spectrum of a black hole can have interesting features using a simple model based on the scalar wave equation.

gr-qc↗

arXiv1999

Quasinormal Modes of Dirty Black Holes

Quasinormal mode (QNM) gravitational radiation from black holes is expected to be observed in a few years. A perturbative formula is derived for the shifts in both the real and the imaginary part of the QNM frequencies away from those of an idealized isolated black hole. The formulation provides a tool for understanding how the astrophysical environment surrounding a black hole, e.g., a massive accretion disk, affects the QNM spectrum of gravitational waves. We show, in a simple model, that the perturbed QNM spectrum can have interesting features.

gr-qc↗

arXiv1998

Second-quantization of open systems using quasinormal modes

The second-quantization of a scalar field in an open cavity is formulated, from first principles, in terms of the quasinormal modes (QNMs), which are the eigensolutions of the evolution equation that decay exponentially in time as energy leaks to the outside. This formulation provides a description involving the cavity degrees of freedom only, with the outside acting as a (thermal or driven) source. Thermal correlation functions and cavity Feynman propagators are thus expressed in terms of the QNMs, labeled by a discrete index rather than a continuous momentum. Single-resonance domination of the density of states and the spontaneous decay rate is then given a proper foundation. This is a first essential step towards the application of QNMs to cavity QED phenomena, to be reported elsewhere.

quant-ph↗

arXiv1997

Logarithmic perturbation theory for quasinormal modes

Logarithmic perturbation theory (LPT) is developed and applied to quasinormal modes (QNMs) in open systems. QNMs often do not form a complete set, so LPT is especially convenient because summation over a complete set of unperturbed states is not required. Attention is paid to potentials with exponential tails, and the example of a Poschl-Teller potential is briefly discussed. A numerical method is developed that handles the exponentially large wavefunctions which appear in dealing with QNMs.

math-ph↗

arXiv1997

Multiple Molecular Winds in Evolved Stars I. A Survey of CO(2-1) and CO(3-2) Emission from 45 Nearby AGB Stars

This paper describes observations of a new phenomenon in evolved mass-losing AGB stars: the presence of two winds with different expansion velocities. CO(2-1) and CO(3-2) line emission was observed for 45 AGB stars at high velocity resolution and double winds found in 20% of the sample. Highly asymmetric lines were found in six other stars. The data tentatively suggest that double winds occur when the star undergoes a change (pulsational mode, chemical composition) and that the very narrow components represent the onset of a new phase of mass loss.

astro-ph↗

arXiv1997

Neutral carbon in the protoplanetary nebulae CRL 618 and CRL 2688

The 609u 3P1 -> 3P0 line of neutral atomic carbon has been detected in the protoplanetary nebulae CRL 618 and CRL 2688. CI appears to be about 7% as abundant as CO in CRL 2688, and 70% as abundant as CO in CRL 618. CI emission arises primarily from the slow component of the wind from these objects. The data presented here indicate that CI gradually becomes more abundant as the star leaves the AGB, and CI is significantly enhanced relative to CO before the star develops a large HII region.

astro-ph↗

arXiv1997

Neutral atomic carbon in the globules of the Helix

We report detection of the 609u line of neutral atomic carbon in globules of the Helix nebula. The measurements were made towards the position of peak CO emission. At the same position, we obtained high-quality CO(2-1) and 13CO(2-1) spectra and a 135" x 135" map in CO(2-1). The velocity distribution of CI shows six narrow (1 -> 2 km/sec) components which are associated with individual globules traced in CO. The CI column densities are 0.5 -> 1.2 x 10^16/cm^2. CI is found to be a factor of ~6 more abundant than CO. Our estimate for the mass of the neutral envelope is an order of magnitude larger than previous estimates. The large abundance of CI in the Helix can be understood as a result of the gradual photoionisation of the molecular envelope by the central star's radiation field.

astro-ph↗

arXiv1995

Wave Propagation in Gravitational Systems: Late Time Behavior

It is well-known that the dominant late time behavior of waves propagating on a Schwarzschild spacetime is a power-law tail; tails for other spacetimes have also been studied. This paper presents a systematic treatment of the tail phenomenon for a broad class of models via a Green's function formalism and establishes the following. (i) The tail is governed by a cut of the frequency Green's function $\tilde G(ω)$ along the $-$~Im~$ω$ axis, generalizing the Schwarzschild result. (ii) The $ω$ dependence of the cut is determined by the asymptotic but not the local structure of space. In particular it is independent of the presence of a horizon, and has the same form for the case of a star as well. (iii) Depending on the spatial asymptotics, the late time decay is not necessarily a power law in time. The Schwarzschild case with a power-law tail is exceptional among the class of the potentials having a logarithmic spatial dependence. (iv) Both the amplitude and the time dependence of the tail for a broad class of models are obtained analytically. (v) The analytical results are in perfect agreement with numerical calculations.

gr-qc↗

arXiv1995

Wave Propagation in Gravitational Systems: Completeness of Quasinormal Modes

The dynamics of relativistic stars and black holes are often studied in terms of the quasinormal modes (QNM's) of the Klein-Gordon (KG) equation with different effective potentials $V(x)$. In this paper we present a systematic study of the relation between the structure of the QNM's of the KG equation and the form of $V(x)$. In particular, we determine the requirements on $V(x)$ in order for the QNM's to form complete sets, and discuss in what sense they form complete sets. Among other implications, this study opens up the possibility of using QNM expansions to analyse the behavior of waves in relativistic systems, even for systems whose QNM's do {\it not} form a complete set. For such systems, we show that a complete set of QNM's can often be obtained by introducing an infinitesimal change in the effective potential.

gr-qc↗

arXiv1995

A CO(3-2) Survey of Nearby Mira Variables

A survey of CO(3-2) emission from optically visible oxygen-rich Mira variable stars within 500 pc of the sun was conducted. A molecular envelope was detected surrounding 36 of the 66 stars examined. Some of these stars have lower outflow velocities than any Miras previously detected in CO. The average terminal velocity of the ejected material was 7.0 km/sec, about half the value found in Miras selected by infrared criteria. None of the stars with spectral types earlier than M 5.5 were detected. The terminal velocity increases as the temperature of the stellar photosphere decreases, as would be expected for a radiation driven wind. Mass loss rates for the detected objects were calculated, and it was found that there is no correlation between the infrared color of a Mira variable, and its mass loss rate. The mass loss rate is correlated with the far infrared luminosity, although a few stars appear to have extensive dust envelopes without any detectable molecular wind. A power-law relationship is found to hold between the mass loss rate and the terminal velocity of the ejected material. This relationship indicates that the dust envelope should be optically thick in the near infrared and visible regions of the spectrum when the outflow velocity is > 17 km/sec. At the low end of the range of outflow velocities seen, the dust drift velocity may be high enough to lead to the destruction of the grains via sputtering. Half of the stars which were detected were re-observed in the CO(4-3) transition. A comparison of the outflow velocities obtained from these observations with those obtained by other investigators at lower frequencies shows no evidence for gradual acceleration of the outer molecular envelope.

astro-ph↗

arXiv1994

Maps of the Molecular Emission Around 18 Evolved Stars

We present maps at $20''$ resolution of the molecular emission around 18 evolved stars (14~asymptotic giant branch stars, one supergiant, two proto-planetary nebulae and one planetary nebula), mostly in the $^{12}$CO(3-2) line. Almost all molecular envelopes appear to be at least marginally resolved at this resolution. A substantial fraction of the molecular envelopes show clear deviations from spherical symmetry in the form of elliptical or bipolar envelopes. This indicates that there is a need to implement non-spherical mass loss in current scenarios of the late stages of stellar evolution, in particular on the asymptotic giant branch.

astro-ph↗

arXiv1994

Late Time Tail of Wave Propagation on Curved Spacetime

The late time behavior of waves propagating on a general curved spacetime is studied. The late time tail is not necessarily an inverse power of time. Our work extends, places in context, and provides understanding for the known results for the Schwarzschild spacetime. Analytic and numerical results are in excellent agreement.

gr-qc↗