Tidal Excitation of Modes in Binary Systems with Applications to Binary Pulsars

We consider the tidal excitation of modes in a binary system of arbitrary eccentricity. For a circular orbit, the modes generally undergo forced oscillation with a period equal to the orbital period ($T$). For an eccentric orbit, the amplitude of each tidally excited mode can be written approximately as the sum of an oscillatory term that varies sinusoidally with the mode frequency and a `static' term that follows the time dependence of the tidal forcing function. The oscillatory term falls off exponentially with increasing \b (defined as the ratio of the periastron passage time to the mode period), whereas the `static' term is independent of \b. For small \b modes (\b \approx 1), the two terms are comparable, and the magnitude of the mode amplitude is nearly constant over the orbit. For large \b modes (\b \gta a few), the oscillatory term is very small compared to the `static' term, in which case the mode amplitude, like the tidal force, varies as the distance cubed. For main sequence stars, $p$, $f$, and low order $g$-modes generally have large \b and hence small amplitudes of oscillation. High overtone $g$-modes, however, have small overlap with the tidal forcing function. Thus, we expect an intermediate overtone $g$-mode with \b \sim 1 to have the largest oscillation amplitude. The dependence on mode damping and the stellar rotation rate is considered, as well as the effects of orbital evolution. We apply our work to the two binary pulsar system: PSR J0045-7319 and PSR B1259-63.Comment: 28 pages of uuencoded compressed postscript. 9 postscript figures available by anonymous ftp from ftp://brmha.mit.edu/ To be published in ApJ

GW170817 Most Likely Made a Black Hole

There are two outstanding issues regarding the neutron-star merger event GW170817: the nature of the compact remnant and the interstellar shock. The mass of the remnant of GW170817, $\sim$2.7 $M_\odot$, implies the remnant could be either a massive, rotating, neutron star, or a black hole. We report Chandra Director's Discretionary Time observations made in 2017 December and 2018 January, and we reanalyze earlier observations from 2017 August and 2017 September, in order to address these unresolved issues. We estimate the X-ray flux from a neutron star remnant and compare that to the measured X-ray flux. If we assume that the spin-down luminosity of any putative neutron star is converted to pulsar wind nebula X-ray emission in the 0.5-8 keV band with an efficiency of $10^{-3}$, for a dipole magnetic field with $3 \times 10^{11}$ G < $B$ < $10^{14}$ G, a rising X-ray signal would result and would be brighter than that observed by day 107, we therefore conclude that the remnant of GW170817 is most likely a black hole. Independent of any assumptions of X-ray efficiency, however, if the remnant is a rapidly-rotating, magnetized, neutron star, the total energy in the external shock should rise by a factor $\sim$$10^2$ (to $\sim$$10^{52}$ erg) after a few years, therefore, Chandra observations over the next year or two that do not show substantial brightening will rule out such a remnant. The same observations can distinguish between two different models for the relativistic outflow, either an angular or radially varying structure.Comment: 10 pages, 4 figures, accepted to ApJ

Differential rotation enhanced dissipation of tides in the PSR J0045-7319 Binary

Recent observations of PSR J0045-7319, a radio pulsar in a close eccentric orbit with a massive B-star companion, indicate that the system's orbital period is decreasing on a timescale of $\approx 5 \times10^{5}$ years, which is much shorter than the timescale of $\approx$ 10^9 years given by the standard theory of tidal dissipation in radiative stars. Observations also provide strong evidence that the B-star is rotating rapidly, perhaps at nearly its break up speed. We show that the dissipation of the dynamical tide in a star rotating in the same direction as the orbital motion of its companion (prograde rotation) with a speed greater than the orbital angular speed of the star at periastron results in an increase in the orbital period of the binary system with time. Thus, since the observed time derivative of the orbital period is large and negative, the B-star in the PSR J0045-7319 binary must have retrograde rotation if tidal effects are to account for the orbital decay. We also show that the time scale for the synchronization of the B-star's spin with the orbital angular speed of the star at periastron is comparable to the orbital evolution time. From the work of Goldreich and Nicholson (1989) we therefore expect that the B-star should be rotating differentially, with the outer layers rotating more slowly than the interior. We show that the dissipation of the dynamical tide in such a differentially rotating B-star is enhanced by almost three orders of magnitude leading to an orbital evolution time for the PSR J0045-7319 Binary that is consistent with the observations.Comment: 8 pages, tex. Submitted to Ap

The structure of the central disk of NGC 1068: a clumpy disk model

NGC 1068 is one of the best studied Seyfert II galaxies, for which the blackhole mass has been determined from the Doppler velocities of water maser. We show that the standard $\alpha$-disk model of NGC 1068 gives disk mass between the radii of 0.65 pc and 1.1 pc (the region from which water maser emission is detected) to be about 7x10$^7$ M$_\odot$ (for $\alpha=0.1$), more than four times the blackhole mass, and a Toomre Q-parameter for the disk is $\sim$0.001. This disk is therefore highly self-gravitating and is subject to large-amplitude density fluctuations. We conclude that the standard $\alpha$-viscosity description for the structure of the accretion disk is invalid for NGC 1068. In this paper we develop a new model for the accretion disk. The disk is considered to be composed of gravitationally bound clumps; accretion in this clumped disk model arises because of gravitational interaction of clumps with each other and the dynamical frictional drag exerted on clumps from the stars in the central region of the galaxy. The clumped disk model provides a self-consistent description of the observations of NGC 1068. The computed temperature and density are within the allowed parameter range for water maser emission, and the rotational velocity in the disk falls off as $r^{-0.35}$.Comment: To appear in Ap

Angular momentum transport by gravity waves and its effect on the rotation of the solar interior

We calculate the excitation of low frequency gravity waves by turbulent convection in the sun and the effect of the angular momentum carried by these waves on the rotation profile of the sun's radiative interior. We find that the gravity waves generated by convection in the sun provide a very efficient means of coupling the rotation in the radiative interior to that of the convection zone. In a differentially rotating star, waves of different azimuthal number have their frequencies in the local rest frame of the star Doppler shifted by different amounts. This leads to a difference in their local dissipation rate and hence a redistribution of angular momentum in the star. We find that the time scale for establishing uniform rotation throughout much of the radiative interior of the sun is $\sim 10^7$ years, which provides a possible explanation for the helioseismic observations that the solar interior is rotating as a solid body.Comment: 10 pages, tex, 3 figures. To appear in ApJ lette

Antibacterial responses of retinal Müller glia: production of antimicrobial peptides, oxidative burst and phagocytosis

BACKGROUND: We have previously shown that, in response to microbial infection, activated Müller glia secrete inflammatory cytokines/chemokines and exhibit antimicrobial properties. The aim of this study is to understand the mechanisms and the key components involved in this response. METHODS: Immortalized human retinal Müller glia (MIO-M1 cells) were challenged with Staphylococcus (S) aureus, the leading cause of severe intraocular infection followed by RT(2) profile PCR array analysis. The expression of human β-defensin 1 (HBD1), 2 (HBD2), 3 (HBD3), hepcidine and cathelicidin LL37 was checked by RT-PCR and quantified by Taqman® qPCR. The expression of AMPs was confirmed at protein level by dot-blot analysis. The production of ROS was measured by dicholoro-dihydro-fluorescein diacetate (DCFH-DA) staining by flow cytometry as well as fluorescence microscopy. The level of nitric oxide (NO) was measured by measuring a stable metabolite, nitrite using the Griess reagent. In vitro killing assay was performed by Live/Dead® BacLight™ staining as well as by dilution plating in suspension and adherent conditions following S. aureus infection. Phagocytosis was measured by CFU enumeration following infection. RESULTS: PCR array data showed that, in comparison to uninfected control cells, bacterial challenge significantly (> two-fold) induced the expression of 26 genes involved in cytokine/chemokine, antimicrobials, Toll-like receptor, apoptotic, and NF-κB signaling. RT-PCR analysis showed time-dependent increased expression of HBD1, HBD2, HBD3, LL-37, and hepcidin mRNA in bacteria-challenged Müller glia. The expression of these antimicrobial molecules was also increased at the protein level in the culture supernatant, as detected by dot-blot analysis. Additionally, the bacteria-stimulated Müller glia were found to produce reactive oxygen (ROS) and reactive nitrogen (RNS) species. In vitro, killing assays revealed that Müller glia exhibited bactericidal activity against S. aureus in both adherent and suspension cultures. Furthermore, our data demonstrated that Müller glia can phagocytize and kill the bacteria in a time-dependent manner. CONCLUSIONS: These data suggest that retinal Müller glia behave like classical innate immune cells by producing a variety of antimicrobial molecules in response to bacterial challenge, suggesting their pivotal role in retinal innate defense

Tidal spin-up of stars in dense stellar cusps around massive black holes

We show that main-sequence stars in dense stellar cusps around massive black holes are likely to rotate at a significant fraction of the centrifugal breakup velocity due to spin-up by hyperbolic tidal encounters. We use realistic stellar structure models to calculate analytically the tidal spin-up in soft encounters, and extrapolate these results to close and penetrating collisions using smoothed particle hydrodynamics simulations. We find that the spin-up falls off only slowly with distance from the black hole because the increased tidal coupling in slower collisions at larger distances compensates for the decrease in the stellar density. We apply our results to the stars near the massive black hole in the Galactic Center. Over their lifetime, ~1 Msol main sequence stars in the inner 0.3 pc of the Galactic Center are spun-up on average to ~10%--30% of the centrifugal breakup limit. Such rotation is ~20--60 times higher than is usual for such stars and may affect their subsequent evolution and their observed properties.Comment: 25 pages, 7 figures. Submitted to Ap

X-ray Lines From Gamma-ray Bursts

X-ray lines have been recently detected in the afterglows of a few gamma-ray bursts. We derive constraints on the physical conditions in the line-emitting gas, using as an example the multiple K$_\alpha$ lines detected by Reeves et al. (2002) in GRB 011211. We argue that models previously discussed in the literature require either a very extreme geometry or too much mass in the line-emitting region. We propose a new model in which gamma-rays and radiation from the early x-ray afterglow are back-scattered by an electron-positron pair screen at a distance of about $10^{14}-10^{15}$ cm from the source and irradiate the expanding outer layers of the supernova ejecta, thereby producing x-ray lines. The model suffers from fewer problems compared to previous models. It also has the advantage of requiring only a single explosion to produce both the GRB and the supernova ejecta, in contrast to most other models for the lines which require the supernova to go off days or weeks prior to the GRB. The model, however, has difficulty explaining the $>10^{48}$ ergs of energy emitted in the x-ray lines, which requires somewhat extreme choices of model parameters. The difficulties associated with the various models are not particular to GRB 011211. They are likely to pose a problem for any GRB with x-ray lines.Comment: 19 pages, 1 figure, submitted to Ap.