Gravitational instability of finite isothermal spheres in general relativity. Analogy with neutron stars

We investigate the effects of relativity on the gravitational instability of finite isothermal gaseous spheres. In the first part of the paper, we treat the gravitational field within the framework of Newtonian mechanics but we use a relativistic equation of state in the condition of hydrostatic equilibrium. In the second part of the paper, we study the full general relativistic problem for a gas described by an equation of state $p=q\epsilon$ such that the pressure is proportional to the energy density (``isothermal'' distribution). For $q=1/3$, this equation of state describes the core of neutron stars. The mass-density diagram displays some damped oscillations and there exists a critical value of mass-energy above which no equilibrium state is possible. We show analytically that the mass peaks are associated with new modes of instability. These results are strikingly similar to those obtained by Antonov [Vest. Leningr. Gos. Univ. 7, 135 (1962)] and Lynden-Bell & Wood (1968) for a classical isothermal gas. Our study completes the analogy between isothermal spheres and neutron stars investigated by Yabushita [MNRAS 167, 95 (1974)].Comment: Submitted to Astron. Astrophy

Spectroscopy by frequency entangled photon pairs

Quantum spectroscopy was performed using the frequency-entangled broadband photon pairs generated by spontaneous parametric down-conversion. An absorptive sample was placed in front of the idler photon detector, and the frequency of signal photons was resolved by a diffraction grating. The absorption spectrum of the sample was measured by counting the coincidences, and the result is in agreement with the one measured by a conventional spectrophotometer with a classical light source.Comment: 11 pages, 5 figures, to be published in Phys. Lett.

Multi--Pressure Polytropes as Models for the Structure and Stability of Molecular Clouds. I. Theory

Molecular clouds are supported by thermal pressure, magnetic pressure, and turbulent pressure. Each of these can be modeled with a polytropic equation of state, so that overall the total pressure is the sum of the individual components. We model the turbulent pressure as being due to a superposition of Alfven waves. The theory of polytropes is generalized to allow for the flow of entropy in response to a perturbation, as expected for the entropy associated with wave pressure. The equation of state of molecular clouds is "soft", so that the properties of the clouds are generally governed by the conditions at the surface. In general, the polytropes are not isentropic, and this permits large density and pressure drops to occur between the center and the edge of the polytropes, as is observed.Comment: Submitted to ApJ with 10 figure

Dynamical stability of infinite homogeneous self-gravitating systems: application of the Nyquist method

We complete classical investigations concerning the dynamical stability of an infinite homogeneous gaseous medium described by the Euler-Poisson system or an infinite homogeneous stellar system described by the Vlasov-Poisson system (Jeans problem). To determine the stability of an infinite homogeneous stellar system with respect to a perturbation of wavenumber k, we apply the Nyquist method. We first consider the case of single-humped distributions and show that, for infinite homogeneous systems, the onset of instability is the same in a stellar system and in the corresponding barotropic gas, contrary to the case of inhomogeneous systems. We show that this result is true for any symmetric single-humped velocity distribution, not only for the Maxwellian. If we specialize on isothermal and polytropic distributions, analytical expressions for the growth rate, damping rate and pulsation period of the perturbation can be given. Then, we consider the Vlasov stability of symmetric and asymmetric double-humped distributions (two-stream stellar systems) and determine the stability diagrams depending on the degree of asymmetry. We compare these results with the Euler stability of two self-gravitating gaseous streams. Finally, we determine the corresponding stability diagrams in the case of plasmas and compare the results with self-gravitating systems

Habitable Zones in the Universe

Habitability varies dramatically with location and time in the universe. This was recognized centuries ago, but it was only in the last few decades that astronomers began to systematize the study of habitability. The introduction of the concept of the habitable zone was key to progress in this area. The habitable zone concept was first applied to the space around a star, now called the Circumstellar Habitable Zone. Recently, other, vastly broader, habitable zones have been proposed. We review the historical development of the concept of habitable zones and the present state of the research. We also suggest ways to make progress on each of the habitable zones and to unify them into a single concept encompassing the entire universe.Comment: 71 pages, 3 figures, 1 table; to be published in Origins of Life and Evolution of Biospheres; table slightly revise

Gravitational instability of finite isothermal spheres

We investigate the stability of bounded self-gravitating systems in the canonical ensemble by using a thermodynamical approach. Our study extends the earlier work of Padmanabhan [Astrophys. J. Supp. 71, 651 (1989)] in the microcanonical ensemble. By studying the second variations of the free energy, we find that instability sets in precisely at the point of minimum temperature in agreement with the theorem of Katz [ Mon. Not. R. astr. Soc. 183, 765 (1978)]. The perturbation that induces instability at this point is calculated explicitly; it has not a ``core-halo'' structure contrary to what happens in the microcanonical ensemble. We also study Jeans type gravitational instability of isothermal gaseous spheres described by Navier-Stokes equations. We show analytically the equivalence between dynamical stability and thermodynamical stability and the fact that the stability of isothermal gas spheres does not depend on the viscosity. This confirms the findings of Semelin et al. [astro-ph/9908073] who used numerical methods. We also give a simpler derivation of the geometric hierarchy of scales inducing instability discovered by these authors. The density profiles that trigger these instabilities are calculated analytically; they present more and more oscillations that also follow a geometric progression. This suggests that the system will fragmentate in a series of `clumps' and that these `clumps' will themselves fragmentate in substructures. The fact that both the domain sizes leading to instability and the `clumps' sizes within a box follow a geometric progression with the same ratio suggests a fractal-like behaviour. This gives further support to the interpretation of de Vega et al. [Nature, 383, 56 (1996)].Comment: Submitted to Astron. Astrophy

Does the use of the 2009 FIGO classification of endometrial cancer impact on indications of the sentinel node biopsy?

<p>Abstract</p> <p>Background</p> <p>Lymphadenectomy is debated in early stages endometrial cancer. Moreover, a new FIGO classification of endometrial cancer, merging stages IA and IB has been recently published. Therefore, the aims of the present study was to evaluate the relevance of the sentinel node (SN) procedure in women with endometrial cancer and to discuss whether the use of the 2009 FIGO classification could modify the indications for SN procedure.</p> <p>Methods</p> <p>Eighty-five patients with endometrial cancer underwent the SN procedure followed by pelvic lymphadenectomy. SNs were detected with a dual or single labelling method in 74 and 11 cases, respectively. All SNs were analysed by both H&E staining and immunohistochemistry. Presumed stage before surgery was assessed for all patients based on MR imaging features using the 1988 FIGO classification and the 2009 FIGO classification.</p> <p>Results</p> <p>An SN was detected in 88.2% of cases (75/85 women). Among the fourteen patients with lymph node metastases one-half were detected by serial sectioning and immunohistochemical analysis. There were no false negative case. Using the 1988 FIGO classification and the 2009 FIGO classification, the correlation between preoperative MRI staging and final histology was moderate with Kappa = 0.24 and Kappa = 0.45, respectively. None of the patients with grade 1 endometrioid carcinoma on biopsy and IA 2009 FIGO stage on MR imaging exhibited positive SN. In patients with grade 2-3 endometrioid carcinoma and stage IA on MR imaging, the rate of positive SN reached 16.6% with an incidence of micrometastases of 50%.</p> <p>Conclusions</p> <p>The present study suggests that sentinel node biopsy is an adequate technique to evaluate lymph node status. The use of the 2009 FIGO classification increases the accuracy of MR imaging to stage patients with early stages of endometrial cancer and contributes to clarify the indication of SN biopsy according to tumour grade and histological type.</p

Is lymphadenectomy a prognostic marker in endometrioid adenocarcinoma of the human endometrium?

<p>Abstract</p> <p>Background</p> <p>During surgery for endometrial cancer, a pelvic lymphadenectomy with or without para-aortic lymphadenectomy is performed at least in patients with risk factors (stage I, grading 2 and/or histological subtypes with higher risk of lymphatic spread), and is hence recommended by the International Federation of Obstetrics and Gynecology (FIGO). Although lymph node metastases are important prognostic parameters, it has been contentious whether a pelvic lymph node dissection itself has a prognostic impact in the treatment of endometrial cancer, especially in endometrioid adenocarcinoma. Therefore, this study evaluated whether lymphadenectomy has a prognostic impact in patients with endometrioid adenocarcinoma.</p> <p>Methods</p> <p>The benefits of lymphadenectomy were examined in 214 patients with a histological diagnosis of endometrial adenocarcinoma. Tumour characteristics were analysed with respect to the surgical and pathological stage.</p> <p>Results</p> <p>Of the 214 patients with endometrial adenocarcinoma, 171 (79.9%) were classified as FIGO stage I, 15 (7.0%) FIGO stage II, 21 (9.8%) FIGO stage III and 7 (3.3%) FIGO stage IV. One hundred and thirty four (62.6%) of the patients had a histological grade 1 tumour, while 56 (26.2%) and 24 (11.2%) had a histological grade 2 or grade 3 tumour, respectively. Lymphadenectomy was performed in 151 (70.6%) patients. Only 11 (5.1%) patients showed metastatic disease in the lymph nodes. The performance of a lymphadenectomy resulted in significantly increased cause-specific and overall survival, while progression-free survival was not affected by this operative procedure.</p> <p>Conclusions</p> <p>The performance of an operative lymphadenectomy resulted in better survival of patients with endometrioid adenocarcinoma. This increase was significant for cause-specific and overall survival, while there was a tendency only towards increased progression-free survival. Therefore, even in endometrioid adenocarcinoma, a pelvic and/or para-aortic lymphadenectomy should be performed.</p