Alpha Prescription Research Articles

The final orbital separation in common envelope evolution

In the majority of population synthesis calculations of close binary stars, the common envelope (CE) phase is modeled using a standard prescription based upon the conservation of energy, known as the alpha prescription. In this prescription, the orbital separation of the secondary and giant core at the end of the CE phase is taken to be the orbital separation when the envelope becomes unbound. However, recent observations of planetary nebulae with binary cores (BPNe), believed to be the immediate products of CE evolution, indicate orbital periods that are significantly shorter than predicted by population synthesis models using the alpha prescription. We argue that unbinding the envelope provides a necessary, but not sufficient, condition to escape a merger during CE evolution. The spiral-in of the secondary must also be halted. This requires the additional dynamical constraint that the frictional torque on the secondary be reduced to approximately zero. In this paper, we undertake a preliminary examination of the effect of adding this dynamical constraint in population synthesis calculations of BPNe. We assume that the frictional torque will be sufficiently reduced when the secondary enters a region within the giant where the mass-radius profile is flat. We crudely estimate the location of this region as a function of the core mass based upon existing stellar models of AGB stars between 1 and 7 M⊙. We calculate a theoretical orbital period distribution of BPNe using a population synthesis code that incorporates this dynamical constraint along with the alpha prescription.

Magnetic torques on T Tauri stars: Accreting versus non-accreting systems

Context. Classical T Tauri stars (CTTs) magnetically interact with their surrounding disks, a process that is thought to regulate their rotational evolution. Aims. We compute torques acting on the stellar surface of CTTs that arise from different accreting (accretion funnels) and ejecting (stellar winds and magnetospheric ejections) flow components. Furthermore, we compare the magnetic braking due to stellar winds in two different systems: isolated (i.e., weak-line T Tauri and main-sequence) and accreting (i.e., classical T Tauri) stars. Methods. We use 2.5D magnetohydrodynamic, time-dependent, axisymmetric simulations that were computed with the PLUTO code. For both systems, the stellar wind is thermally driven. In the star-disk-interaction (SDI) simulations, the accretion disk is Keplerian, viscous, and resistive, and is modeled with an alpha prescription. Two series of simulations are presented, one for each system (i.e., isolated and accreting stars). Results. In classical T Tauri systems, the presence of magnetospheric ejections confines the stellar-wind expansion, resulting in an hourglass-shaped geometry of the outflow, and the formation of the accretion columns modifies the amount of open magnetic flux exploited by the stellar wind. These effects have a strong impact on the stellar-wind properties, and we show that the stellar-wind braking is more efficient in the SDI systems than in the isolated ones. We further derive torque scalings over a wide range of magnetic field strengths for each flow component in an SDI system (i.e., magnetospheric accretion and ejections, and stellar winds), which directly applies a torque on the stellar surface. Conclusions. In all the performed SDI simulations, the stellar wind extracts less than 2% of the mass accretion rate and the disk is truncated by up to 66% of the corotation radius. All simulations show a net spin-up torque. We conclude that in order to achieve a stellar-spin equilibrium, we need either more massive stellar winds or disks that are truncated closer to the corotation radius, which increases the torque efficiency of the magnetospheric ejections.

Analytical model for the local vertical structure of thin accretion discs

ABSTRACT We derive several analytical relations and approximate solutions for the local vertical structure of viscous thin accretion discs. Under the alpha prescription, when the viscous heating is proportional to the gas pressure p, we derive the analytical relation between the radiative flux F and the radiation pressure P: (F/F0)2 = [1 − (P/Pc)5/4]/[1 − (P0/Pc)5/4], where the subscript 0 means the value at the surface and the subscript c is the value at the disc centre. Both F and P are approximately integrated to yield the well-known uniform heating model. In this case, furthermore, the height z and density ρ are approximately fitted as a function of the optical depth τ. When the viscous heating is proportional to the radiation pressure P and the disc is almost isothermal, the flux F is proportional to z as F = (3/2)αΩPz, where α and Ω are the alpha parameter and angular speed, respectively. In this case, moreover, the height and density are analytically solved and expressed as $z=(\sqrt{2}c_{\rm T}/\Omega) {\rm erf}^{-1}(1-\tau /\tau _{\rm c})$ and ρ = ρcexp { − [erf−1(1 − τ/τc)]2}, cT being the isothermal sound speed, and erf−1 the inverse of the error function.

STUDIES OF THERMALLY UNSTABLE ACCRETION DISKS AROUND BLACK HOLES WITH ADAPTIVE PSEUDOSPECTRAL DOMAIN DECOMPOSITION METHOD. II. LIMIT-CYCLE BEHAVIOR IN ACCRETION DISKS AROUND KERR BLACK HOLES

For the first time ever, we derive equations governing the time-evolution of fully relativistic slim accretion disks in the Kerr metric, and numerically construct their detailed non-stationary models. We discuss applications of these general results to a possible limit-cycle behavior of thermally unstable disks. Our equations and numerical method are applicable in a wide class of possible viscosity prescriptions, but in this paper we use a diffusive form of the "standard alpha prescription" that assumes the viscous torque is proportional to the total pressure. In this particular case, we find that the parameters which dominate the limit-cycle properties are the mass-supply rate and the value of the alpha-viscosity parameter. Although the duration of the cycle (or the outburst) does not exhibit any clear dependence on the black hole spin, the maximal outburst luminosity (in the Eddington units) is positively correlated with the spin value. We suggest a simple method for a rough estimate of the black hole spin based on the maximal luminosity and the ratio of outburst to cycle durations. We also discuss a temperature-luminosity relation for the Kerr black hole accretion discs limit-cycle. Based on these results we discuss the limit-cycle behavior observed in microquasar GRS 1915+105. We also extend this study to several non-standard viscosity prescriptions, including a "delayed heating" prescription recently stimulated by the recent MHD simulations of accretion disks.

ON THE DYNAMICS AND EVOLUTION OF GRAVITATIONAL INSTABILITY-DOMINATED DISKS

We derive the evolution equations describing a thin axisymmetric disk of gas and stars with an arbitrary rotation curve that is kept in a state of marginal gravitational instability and energy equilibrium due to the balance between energy released by accretion and energy lost due to decay of turbulence. Rather than adopt a parameterized alpha prescription, we instead use the condition of marginal gravitational instability to self-consistently determine the position- and time-dependent transport rates. We show that there is a steady-state configuration for disks dominated by gravitational instability, and that this steady state persists even when star formation is taken into account if the accretion rate is sufficiently large. For disks in this state we analytically determine the velocity dispersion, surface density, and rates of mass and angular momentum transport as a function of the gas mass fraction, the rotation curve, and the rate of external accretion onto the disk edge. We show that disks that are initially out of steady state will evolve into it on the viscous timescale of the disk, which is comparable to the orbital period if the accretion rate is high. Finally, we discuss the implications of these results for the structure of disks in a broad range of environments, including high redshift galaxies, the outer gaseous disks of local galaxies, and accretion disks around protostars.

Jet launching and field advection in quasi-Keplerian discs

AbstractThe fact that self-confined jets are observed around black holes, neutron stars and young forming stars points to a jet launching mechanism independent of the nature of the central object, namely the surrounding accretion disc. The properties of Jet Emitting Discs (JEDs) are briefly reviewed. It is argued that, within an alpha prescription for the turbulence (anomalous viscosity and diffusivity), the steady-state problem has been solved. Conditions for launching jets are very stringent and require a large scale magnetic field Bz close to equipartition with the total (gas and radiation) pressure. The total power feeding the jets decreases with the disc thickness: fat ADAF-like structures with h ~ r cannot drive super-Alfvénic jets. However, there exist also hot, optically thin JED solutions that would be observationally very similar to ADAFs.Finally, it is argued that variations in the large scale magnetic Bz field is the second parameter required to explain hysteresis cycles seen in LMXBs (the first one would be Ṁa).

Large scale magnetic fields in viscous resistive accretion disks

<i>Aims. <i/>Cold steady-state disk wind theory from near Keplerian accretion disks requires a large scale magnetic field at near equipartition strength. However the minimum magnetization has never been tested with time dependent simulations. We investigate the time evolution of a Shakura-Sunyaev accretion disk threaded by a weak vertical magnetic field. The strength of the field is such that the disk magnetization falls off rapidly with radius.<i>Methods. <i/>Four 2.5D numerical simulations of viscous resistive accretion disk are performed using the magnetohydrodynamic code PLUTO. In these simulations, a mean field approach is used and turbulence is assumed to give rise to anomalous transport coefficients (alpha prescription). <i>Results. <i/>The large scale magnetic field introduces only a small perturbation to the disk structure, with accretion driven by the dominant viscous torque. However, a super fast magnetosonic jet is observed to be launched from the innermost regions and remains stationary over more than 953 Keplerian orbits. This is the longest accretion-ejection simulation ever carried out. The self-confined jet is launched from a finite radial zone in the disk which remains constant over time. Ejection is made possible because the magnetization reaches unity at the disk surface, due to the steep density decrease. However, no ejection is reported when the midplane magnetization becomes too small. The asymptotic jet velocity remains nevertheless too low to explain observed jets. This is because of the negligible power carried away by the jet.<i>Conclusions. <i/>Astrophysical disks with superheated surface layers could drive analogous outflows even if their midplane magnetization is low. Sufficient angular momentum would be extracted by the turbulent viscosity to allow the accretion process to continue. The magnetized outflows would be no more than byproducts, rather than a fundamental driver of accretion. However, if the midplane magnetization increases towards the center, a natural transition to an inner jet dominated disk could be achieved.

Association between practice patterns and body mass index percentile in infants and young children with cystic fibrosis

Background Few guidelines focus on the preventive and maintenance care of infants with cystic fibrosis (CF). We explored how practice variability at accredited CF centers affected nutritional outcomes. Methods A retrospective cohort study using Cystic Fibrosis Foundation registry data (1993–2004) from three CF centers compared the initial management with respiratory, antimicrobial, and nutritional agents in infants. Further, we examined the association between dornase alpha use prior to two years of age and BMI percentile over time accounting for several possible factors including gender, race, CF center, presentation, age at diagnosis, sweat value, F508del status, first Pseudomonas aeruginosa infection age, second-year weight percentile, supplemental feedings use, and pancreatic enzymes use. Results Patient characteristics and prescribed therapies were similar at all sites for 165 patients who met inclusion criteria. However, one CF center prescribed dornase alpha significantly more frequently, 82% vs. 10% ( p < 0.001), and supplemental feeds significantly less frequently, 56% vs. 78% ( p = 0.04). Dornase alpha prescription prior to age two was associated with a 10-percentile increase in BMI through age six compared to infants not prescribed dornase alpha. Conclusions Treating infants less than two years old with dornase alpha may improve nutritional outcome through age six.

Testing Accretion Disk Theory in Black Hole X‐Ray Binaries

We present results from spectral modeling of three black hole X-ray binaries: LMC X-3, GRO J1655-40, and XTE J1550-564. Using a sample of disk dominated observations, we fit the data with a range of spectral models that includes a simple multitemperature blackbody (DISKBB), a relativistic accretion disk model based on color-corrected blackbodies (KERRBB), and a relativistic model based on non-LTE atmosphere models within an alpha prescription (BHSPEC). BHSPEC provides the best fit for a BeppoSAX observation of LMC X-3, which has the broadest energy coverage of our sample. It also provides the best fit for multiple epochs of Rossi X-ray Timing Explorer (RXTE) data in this source, except at the very highest luminosity (L/L_{Edd} >~ 0.7), where additional physics must be coming into play. BHSPEC is also the best-fit model for multi-epoch RXTE observations of GRO J1655-40 and XTE J1550-564, although the best-fit inclination of the inner disk differs from the binary inclination. All our fits prefer alpha=0.01 to alpha=0.1, in apparent disagreement with the large stresses inferred from the rapid rise times observed in outbursts of these two sources. In all three sources our fits imply moderate black hole spins (a/M ~ 0.1 - 0.8), but this is sensitive to the reliability of independent measurements of these system parameters and to the physical assumptions which underly our spectral models.

Accretion Disks around Young Objects. I. The Detailed Vertical Structure

We discuss the properties of an accretion disk around a star with parameters typical of classical T Tauri stars (CTTS), and with the average accretion rate for these disks. The disk is assumed steady and geometrically thin. The turbulent viscosity coefficient is expressed using the alpha prescription and the main heating mechanisms considered are viscous dissipation and irradiation by the central star. The energy is transported by radiation, turbulent conduction and convection. We find that irradiation from the central star is the main heating agent of the disk, except in the innermost regions, R less than 2 AU. The irradiation increases the temperature of the outer disk relative to the purely viscous case. As a consequence, the outer disk (R larger than 5 AU) becomes less dense, optically thin and almost vertically isothermal, with a temperature distribution T proportional to R^{-1/2}. The decrease in surface density at the outer disk, decreases the disk mass by a factor of 4 respect to a purely viscous case. In addition, irradiation tends to make the outer disk regions stable against gravitational instabilities.

A Lagrangian ?prescription? for Landshoff's alpha prescription in the temporal gauge

I discuss the Landshoff alpha prescription for the propagator pole ambiguity in temporal gauge Yang-Mills theory. The prescription may be generated from a Lagrangian which includes an extra term that is explicitly gauge invariant. No explanation for this term is yet understood. Some of the positive and negative features of this extra term are highlighted. In particular it is consistent with a decoupling of Faddeev-Popov ghosts.