Axial instability of rotating relativistic stars

Perturbations of rotating relativistic stars can be classified by their behavior under parity. For axial perturbations (r-modes), initial data with negative canonical energy is found with angular dependence $e^{im\phi}$ for all values of $m\geq 2$ and for arbitrarily slow rotation. This implies instability (or marginal stability) of such perturbations for rotating perfect fluids. This low $m$-instability is strikingly different from the instability to polar perturbations, which sets in first for large values of $m$. The timescale for the axial instability appears, for small angular velocity $\Omega$, to be proportional to a high power of $\Omega$. As in the case of polar modes, viscosity will again presumably enforce stability except for hot, rapidly rotating neutron stars. This work complements Andersson's numerical investigation of axial modes in slowly rotating stars.Comment: Latex, 18 pages. Equations 84 and 85 are corrected. Discussion of timescales is corrected and update

Relativistic precession around rotating neutron stars: Effects due to frame-dragging and stellar oblateness

General relativity predicts that a rotating body produces a frame-dragging (or Lense-Thirring) effect: the orbital plane of a test particle in a non-equatorial orbit precesses about the body's symmetry axis. In this paper we compute the precession frequencies of circular orbits around rapidly rotating neutron stars for a variety of masses and equations of state. The precession frequencies computed are expressed as numerical functions of the orbital frequency observed at infinity. The post-Newtonian expansion of the exact precession formula is examined to identify the relative magnitudes of the precession caused by the Lense-Thirring effect, the usual Newtonian quadrupole effect and relativistic corrections. The first post-Newtonian correction to the Newtonian quadrupole precession is derived in the limit of slow rotation. We show that the post-Newtonian precession formula is a good approximation to the exact precession close to the neutron star in the slow rotation limit (up to \sim 400 Hz in the present context). The results are applied to recent RXTE observations of neutron star low-mass X-ray binaries, which display kHz quasi-periodic oscillations and, within the framework of beat frequency models, allow the measurement of both the neutron star spin frequency and the Keplerian frequency of the innermost ring of matter in the accretion disk around it. For a wide range of realistic equations of state, we find that the predicted precession frequency of this ring is close to one half of the low-frequency (\sim 20 - 35 Hz) quasi-periodic oscillations seen in several Atoll sources.Comment: 35 pages including 10 figures and 6 tables. To appear in the Astrophysical Journa

Gravitational Radiation Instability in Hot Young Neutron Stars

We show that gravitational radiation drives an instability in hot young rapidly rotating neutron stars. This instability occurs primarily in the l=2 r-mode and will carry away most of the angular momentum of a rapidly rotating star by gravitational radiation. On the timescale needed to cool a young neutron star to about T=10^9 K (about one year) this instability can reduce the rotation rate of a rapidly rotating star to about 0.076\Omega_K, where \Omega_K is the Keplerian angular velocity where mass shedding occurs. In older colder neutron stars this instability is suppressed by viscous effects, allowing older stars to be spun up by accretion to larger angular velocities.Comment: 4 Pages, 2 Figure

Hydrostatic Expansion and Spin Changes During Type I X-Ray Bursts

We present calculations of the spin-down of a neutron star atmosphere due to hydrostatic expansion during a Type I X-ray burst. We show that (i) Cumming and Bildsten overestimated the spin-down of rigidly-rotating atmospheres by a factor of two, and (ii) general relativity has a small (5-10%) effect on the angular momentum conservation law. We rescale our results to different neutron star masses, rotation rates and equations of state, and present some detailed rotational profiles. Comparing with recent observations of large frequency shifts in MXB 1658-298 and 4U 1916-053, we find that the spin-down expected if the atmosphere rotates rigidly is a factor of two to three less than the observed values. If differential rotation is allowed to persist, we find that the upper layers of the atmosphere spin down by an amount comparable to the observed values; however, there is no compelling reason to expect the observed spin frequency to be that of only the outermost layers. We conclude that hydrostatic expansion and angular momentum conservation alone cannot account for the largest frequency shifts observed during Type I bursts.Comment: Submitted to the Astrophysical Journal (13 pages, including 4 figures

Low frequency of HER2 amplification and overexpression in early onset gastric cancer

BACKGROUND: The recent ToGA trial results indicated that trastuzumab is a new, effective, and well-tolerated treatment for HER2-positive gastric cancer (GC). Although GC mainly affects older patients, fewer than 10% of GC patients are considered early-onset (EOGC) (presenting at the age of 45 years or younger). These EOGC show different clinicopathological and molecular profiles compared to late onset GC suggesting that they represent a separate entity within gastric carcinogenesis. In light of potential trastuzumab benefit, subpopulations of GC such as EOGC (versus late onset) should be evaluated for their frequency of amplification and overexpression using currently available techniques. METHODS: Tissue microarray (TMA) blocks of 108 early onset GC and 91 late onset GC were stained by immunohistochemistry (IHC, Hercep test, DAKO) and chromogenic in situ hybridization (CISH, SPoT-Light, Invitrogen). RESULTS: Overall, we found only 5% HER2 high level amplification and 3% HER2 3+ overexpression (6/199). In addition, 8 patients (4%) showed a low level CISH amplification and 9 patients (4.5%) showed a 2+ IHC score. IHC and CISH showed 92% concordance and CISH showed less heterogeneity than IHC. In 2/199 cases (1%), IHC showed clinically relevant heterogeneity between TMA cores, but all cases with focal IHC 3+ expression were uniformly CISH high level amplified. Early onset GCs showed a significantly lower frequency of HER2 amplification (2%) and overexpression (0%) than late onset GCs (8% and 7% respectively) (p = 0.085 and p = 0.008 respectively). Proximal GC had more HER2 amplification (9% versus 3%) and overexpression (7% versus 2%) than distal tumours although this difference was not significant (p = 0.181 and p = 0.182 respectively). HER2 CISH showed more high level amplification in the intestinal type (7%, 16% if low-level included) compared to the mixed (5%, 5% if low-level included) and diffuse type (3%, 4% if low-level included) GCs (p = 0.029). A similar association was seen for HER2 IHC and histologic type (p = 0.008). Logistic regression indicated a significant association between HER2 expression and age, which remained significant when adjusted for both location and histological type. CONCLUSIONS: Even focal HER2 overexpression in GC points to uniform HER2 amplification by CISH. We show for the first time that early onset GC has a lower frequency of HER2 amplification and overexpression than late onset GC, and confirm that intestinal type GC shows the highest rate of HER2 amplification and overexpression

New Types of Thermodynamics from (1+1)(1+1)-Dimensional Black Holes

For normal thermodynamic systems superadditivity $\S$, homogeneity \H and concavity \C of the entropy hold, whereas for $(3+1)$-dimensional black holes the latter two properties are violated. We show that $(1+1)$-dimensional black holes exhibit qualitatively new types of thermodynamic behaviour, discussed here for the first time, in which \C always holds, \H is always violated and $\S$ may or may not be violated, depending of the magnitude of the black hole mass. Hence it is now seen that neither superadditivity nor concavity encapsulate the meaning of the second law in all situations.Comment: WATPHYS-TH93/05, Latex, 10 pgs. 1 figure (available on request), to appear in Class. Quant. Gra

Skin color influences transcutaneous bilirubin measurements:a systematic in vitro evaluation

Objective: Concerns have been raised about the effect of skin color on the accuracy of transcutaneous bilirubin (TcB) measurements, a widely used method for hyperbilirubinemia diagnosis in newborns. Literature is inconclusive, with both reported under- and overestimations of the TcB with increasing skin pigmentation. Therefore, the influence of skin color on TcB measurements was systematically evaluated in a controlled, in vitro setting. Methods: A bilirubin meter (JM-105) was evaluated on layered phantoms that mimic neonatal skin with varying dermal bilirubin concentrations (0–250 µmol/L) and varying epidermal melanosome volume fractions (0–40%; light-dark skin color). Results: TcB measurements were influenced by skin pigmentation. Larger mimicked melanosome volume fractions and higher bilirubin levels led to larger underestimations of the measured TcB, compared to an unpigmented epidermis. In the in vitro setting of this study, these underestimations amounted to 26–132 µmol/L at a TcB level of 250 µmol/L. Conclusion: This in vitro study provides insight into the effect of skin color on TcB measurements: the TcB is underestimated as skin pigmentation increases and this effect becomes more pronounced at higher bilirubin levels. Our results highlight the need for improved TcB meter design and cautious interpretation of TcB readings on newborns with dark skin. Impact: Key message: Skin color influences transcutaneous bilirubin measurements: the darker the skin, the larger the underestimation. What this study adds to existing literature: Existing literature is inconclusive regarding the influence of skin color on transcutaneous bilirubin measurements. This study systematically evaluates and clarifies the influence of skin color on transcutaneous bilirubin measurements in a controlled, in vitro setting. Impact: This study aids to better interpret the measured TcB level in patients with varying skin colors, and is particularly important when using TcB meters on patients with dark skin colors.</p

Exact Solution for the Metric and the Motion of Two Bodies in (1+1) Dimensional Gravity

We present the exact solution of two-body motion in (1+1) dimensional dilaton gravity by solving the constraint equations in the canonical formalism. The determining equation of the Hamiltonian is derived in a transcendental form and the Hamiltonian is expressed for the system of two identical particles in terms of the Lambert $W$ function. The $W$ function has two real branches which join smoothly onto each other and the Hamiltonian on the principal branch reduces to the Newtonian limit for small coupling constant. On the other branch the Hamiltonian yields a new set of motions which can not be understood as relativistically correcting the Newtonian motion. The explicit trajectory in the phase space $(r, p)$ is illustrated for various values of the energy. The analysis is extended to the case of unequal masses. The full expression of metric tensor is given and the consistency between the solution of the metric and the equations of motion is rigorously proved.Comment: 34 pages, LaTeX, 16 figure