Amos Harpaz

Rotation, planets, and the ‘second parameter’ of the horizontal branch

ABSTRA C T We analyse the angular momentum evolution from the red giant branch (RGB) to the horizontal branch (HB) and along the HB. Using rotation velocities for stars in the globular cluster M13, we find that the required angular momentum for the fast rotators is up to 1‐3 orders of magnitude (depending on some assumptions) larger than that of the Sun. Planets of masses up to 5 times Jupiter’s mass and up to an initial orbital separation of ,2 au are sufficient to spin-up the RGB progenitors of most of these fast rotators. Other stars have been spun-up by brown dwarfs or low-mass main-sequence stars. Our results show that the fast rotating HB stars have been probably spun-up by planets, brown dwarfs or low-mass main-sequence stars while they evolved on the RGB. We argue that the angular momentum considerations presented in this paper further support the ‘planet second parameter’ model. In this model, the ‘second parameter’ process, which determines the distribution of stars on the HB, is interaction with low-mass companions, in most cases with gas-giant planets, and in a minority of cases with brown dwarfs or low-mass main-sequence stars. The masses and initial orbital separations of the planets (or brown dwarfs or low-mass main-sequence stars) form a rich spectrum of different physical parameters, which manifests itself in the rich varieties of HB morphologies observed in the different globular clusters.

Can a single AGB star form an axially symmetric planetary nebula

We apply a method, which is traditionally used for the solar magnetic field, to estimate the magnetic activity of AGB stars. We find that any magnetic field model which tries to explain axisymmetrical mass loss from single AGB stars encounters severe difficulties. This order of magnitude calculation suggests that megnetic activity in AGB stars could be significant only if the envelope is spun up by a binary companion. But then other effects due to the companion are likely to be more dominant than the magnetic activity. We then conduct a preliminary study of a possible mechanism by which a single star might lose mass axisymmetrically. The results suggest that as the envelope mass of an AGB star decreases to < 0.1 solar mass, the nature of the fundamental mode excitation could change. It is possible that, due to the same mechanism, higher order radial modes and nonradial p-modes could become significant to the mass loss process when the envelope mass becomes very low. We argue, however, that even this mechanism, if it works, requires a binary companion to spin up the AGB envelope.

Eccentric Binary Model for Off-Center Planetary Nebula Nuclei

We examine the influence of eccentric binary progenitors on the morphologies of their descendant planetary nebulae. In particular, we consider how mass loss via a stellar wind by an asymptotic giant branch (AGB) star in an eccentric binary can lead to the displacement of the central star in the equatorial plane. We postulate that the mass-loss rate from the AGB star varies systematically with orbital phase. Such variations may be due to several effects, including a tidal enhancement of the stellar wind near periastron and a cessation of the stellar wind when the Roche lobe of the AGB star encroaches on its extended atmosphere. Our results may pertain to binary systems with semimajor axes in the range of a 7-80 AU, which corresponds to orbital periods in the range P 15-500 yr. We apply the results to planetary nebulae in general, and MyCn 18 (the Hourglass Nebula) in particular, where the central star was recently found by the Hubble Space Telescope to be displaced from the center of the nebula. The results of this paper may be applied to circumstellar matter around more massive stars, such as progenitors of supernovae, by rescaling the physical properties of the binary stars and the wind velocities.

The Rings around the Egg Nebula

We present an eccentric binary model for the formation of the proto-planetary nebula CRL 2688 (the Egg Nebula) that exhibits multiple concentric shells. Given the apparent regularity of the structure in the Egg Nebula, we postulate that the shells are caused by the periodic passages of a companion star. Such an orbital period would have to lie in the range of 100-500 yr, the apparent time that corresponds to the spacing between the rings. We assume, in this model, that an asymptotic giant branch (AGB) star, which is the origin of the matter within the planetary nebula, loses mass in a spherically symmetric wind. We further suppose that the AGB star has an extended atmosphere (out to ~10 stellar radii) in which the outflow speed is less than the escape speed; still farther out, grains form and radiation pressure accelerates the grains along with the trapped gas to the escape speed. Once escape speed has been attained, the presence of a companion star will not significantly affect the trajectories of the matter leaving in the wind and the mass loss will be approximately spherically symmetric. On the other hand, if the companion star is sufficiently close that the Roche lobe of the AGB star moves inside the extended atmosphere, then the slowly moving material will be forced to flow approximately along the critical potential surface (i.e., the Roche lobe) until it flows into the potential lobe of the companion star. Therefore, in our model, the shells are caused by periodic cessations of the isotropic wind rather than by any periodic enhancement in the mass-loss process. We carry out detailed binary evolution calculations within the context of this scenario, taking into account the nuclear evolution and stellar wind losses of the giant as well as the effects of mass loss and mass transfer on the evolution of the eccentric binary orbit. From the initial binary parameters that we find are required to produce a multiple concentric shell nebula and the known properties of primordial binaries, we conclude that ~0.3% of all planetaries should go through a phase with multiple concentric shells.

Criticism of recent calculations of common envelope ejection

We re-examine a recent claim made by Han et al. that the ionization energy in the envelope has to be included in the ejection criterion of common envelopes. In particular, we argue that: (i) they include a mass-loss rate prior to the onset of the common envelope that is too low; (ii) they do not include the energy radiated by the accreting white dwarf companion, as well as that emitted by the core of the giant star; and (iii) as argued by one of us previously, the opacity in the envelope is too low for the efficient usage of the ionization energy.

Evolution of compact binary systems with X-ray heating

The evolution of low-mass X-ray binary systems is calculated with the inclusion of heating of the secondary star by the X-radiation from the primary. The secondary is assumed to be nonsynchronously rotating with the orbit, so that the X-ray heating may be taken to be approximately uniform over its surface. Due to the shadowing effect of a postulated accretion disk, only a portion of the X-ray flux reaches the secondary star. The evolution of binary systems with secondary stars of initial mass 0.4 and 1 M ⊙ is computed

The Role of Ionization Energy during Planetary Nebula Ejection

The conditions for release of the ionization energy in the envelope of an asymptotic giant branch star are studied. It is shown that the recombination that releases the ionization energy also causes a sharp drop of the opacity, thus enabling the released energy to flow outward freely. The possibility that the ionization energy, when released, drives the ejection of planetary nebula (PN) is discussed. Tests suggested to validate the hypothesis that the ionization energy drives PN ejection are examined, and it is found that these tests are not sensitive to details of the hypothesis they are supposed to validate.

Stellar structure and mass loss on the upper asymptotic giant branch

ABSTRA C T We examine the envelope properties of asymptotic giant branch (AGB) stars as they evolve on the upper AGB and during the early post-AGB phase. Because of the high mass-loss rate, the envelope mass decreases by more than an order of magnitude. This makes the density profile below the photosphere much shallower, and the entropy profile much steeper. We discuss the possible role of these changes in the profiles in the onset of the high mass-loss rate (superwind) and the large deviation from spherical mass loss at the termination of the AGB. We concentrate on the idea that the shallower density profile and steeper entropy profile allow the formation of cool magnetic spots, above which dust forms much more easily.

Radiation from a uniformly accelerated charge

The emission of radiation by a uniformly accelerated charge is analyzed. According to the standard approach, a radiation is observed whenever there is a relative acceleration between the charge and the observer. Analyzing difficulties that arose in the standard approach, we propose that a radiation is created whenever a relative acceleration between the charge and its own electric field exists. The electric field induced by a charge accelerated by an external (nongravitational) force is not accelerated with the charge. Hence the electric field is curved in the instantaneous rest frame of the accelerated charge. This curvature gives rise to a stress force, and the work done to overcome the stress force is the source of the energy carried by the radiation. In this way, the “energy balance paradox” finds its solution.

Overluminous Blue Horizontal-Branch Stars Formed by Low-Mass Companions

We construct a speculative scenario for rotation-induced extra helium mixing to the envelope of horizontal-branch (HB) stars. This scenario differs from previous ones in that the mixing occurs after the star has left the red giant branch (RGB). We follow the evolution of a low-metallicity star from the RGB to the HB, and examine the density profile and radius in the core-envelope boundary region. In the transition from the RGB to the HB the envelope shrinks by 2 orders of magnitude in size and the core swells, such that any nonnegligible rotation on the RGB will result in a strong rotational shear at the core-envelope boundary. For a nonnegligible rotation to exist on the RGB, the star has to be spun up by a companion spiraling inside its envelope (a common-envelope evolution). We speculate that shear instabilities on the HB might mix helium-rich core material to the envelope. The shallow density profile on the HB is less likely to prevent mixing. As previously shown, extra helium mixing can account for the overluminous blue HB stars found in some globular clusters. Although being speculative, this study supports the idea that the presence of low-mass companions, from planets to low-mass main-sequence stars, influence the evolution of stars, and can explain some properties of the color-magnitude (Hertzsprung-Russel) diagram of globular clusters. Namely, low-mass companions can be an ingredient in the so-called second parameter of globular clusters.