Evolution of Mass Functions of Coeval Stars through Wind Mass Loss and Binary Interactions

Accurate determinations of stellar mass functions and ages of stellar populations are crucial to much of astrophysics. We analyse the evolution of stellar mass functions of coeval main sequence stars including all relevant aspects of single- and binary-star evolution. We show that the slope of the upper part of the mass function in a stellar cluster can be quite different to the slope of the initial mass function. Wind mass loss from massive stars leads to an accumulation of stars which is visible as a peak at the high mass end of mass functions, thereby flattening the mass function slope. Mass accretion and mergers in close binary systems create a tail of rejuvenated binary products. These blue straggler stars extend the single star mass function by up to a factor of two in mass and can appear up to ten times younger than their parent stellar cluster. Cluster ages derived from their most massive stars that are close to the turn-off may thus be significantly biased. To overcome such difficulties, we propose the use of the binary tail of stellar mass functions as an unambiguous clock to derive the cluster age because the location of the onset of the binary tail identifies the cluster turn-off mass. It is indicated by a pronounced jump in the mass function of old stellar populations and by the wind mass loss peak in young stellar populations. We further characterise the binary induced blue straggler population in star clusters in terms of their frequency, binary fraction and apparent age.Comment: 21 pages, 22 figures, accepted for publication in Ap

The spectroscopic Hertzsprung-Russell diagram of Galactic massive stars

The distribution of stars in the Hertzsprung-Russell diagram narrates their evolutionary history and directly assesses their properties. Placing stars in this diagram however requires the knowledge of their distances and interstellar extinctions, which are often poorly known for Galactic stars. The spectroscopic Hertzsprung-Russell diagram (sHRD) tells similar evolutionary tales, but is independent of distance and extinction measurements. Based on spectroscopically derived effective temperatures and gravities of almost 600 stars, we derive for the first time the observational distribution of Galactic massive stars in the sHRD. While biases and statistical limitations in the data prevent detailed quantitative conclusions at this time, we see several clear qualitative trends. By comparing the observational sHRD with different state-of-the-art stellar evolutionary predictions, we conclude that convective core overshooting may be mass-dependent and, at high mass ($\geq 15\,M_\odot$), stronger than previously thought. Furthermore, we find evidence for an empirical upper limit in the sHRD for stars with $T_{\rm{eff}}$ between 10000 and 32000 K and, a strikingly large number of objects below this line. This over-density may be due to inflation expanding envelopes in massive main-sequence stars near the Eddington limit.Comment: 5 pages, 2 figures, 1 table; accepted for publication in A&A Letter

A Note on Asymptotic Freedom at High Temperatures

This short note considers, within the external field approach outlined in hep-ph/0202026, the role of the lowest lying gluon Landau mode in QCD in the high temperature limit. Its influence on a temperature- and field-dependent running coupling constant is examined. The thermal imaginary part of the mode is temperature-independent in our approach and exactly cancels the well-known zero temperature imaginary part, thus rendering the Savvidy vacuum stable. Combining the real part of the mode with the contributions from the higher lying Landau modes and the vacuum contribution, a field-independent coupling alpha_s(T) is obtained. It can be interpreted as the ordinary zero temperature running coupling constant with average thermal momenta \approx 2pi T for gluons and \approx pi T for quarks.Comment: 4 pages; minor changes, version to appear in Phys. Rev.

Self consistent kinetic simulations of SPT and HEMP thrusters including the near-field plume region

The Particle-in-Cell (PIC) method was used to study two different ion thruster concepts - Stationary Plasma Thrusters (SPT) and High Efficiency Multistage Plasma Thrusters (HEMP-T), in particular the plasma properties in the discharge chamber due to the different magnetic field configurations. Special attention was paid to the simulation of plasma particle fluxes on the thrusters channel surfaces. In both cases, PIC proved itself as a powerful tool, delivering important insight into the basic physics of the different thruster concepts. The simulations demonstrated that the new HEMP thruster concept allows for a high thermal efficiency due to both minimal energy dissipation and high acceleration efficiency. In the HEMP thruster the plasma contact to the wall is limited only to very small areas of the magnetic field cusps, which results in much smaller ion energy flux to the thruster channel surface as compared to SPT. The erosion yields for dielectric discharge channel walls of SPT and HEMP thrusters were calculated with the binary collision code SDTrimSP. For SPT, an erosion rate on the level of 1 mm of sputtered material per hour was observed. For HEMP, thruster simulations have shown that there is no erosion inside the dielectric discharge channel.Comment: 14 pages, 11 figures This work was presented at 21st International Conference on Numerical Simulation of Plasmas (ICNSP'09

A census of massive stars in NGC 346. Stellar parameters and rotational velocities

Spectroscopy for 247 stars towards the young cluster NGC 346 in the Small Magellanic Cloud has been combined with that for 116 targets from the VLT-FLAMES Survey of Massive Stars. Spectral classification yields a sample of 47 O-type and 287 B-type spectra, while radial-velocity variations and/or spectral multiplicity have been used to identify 45 candidate single-lined systems, 17 double-lined systems, and one triple-lined system. Atmospheric parameters (T$_eff$ and log$g$) and projected rotational velocities ($v_e$sin$i$) have been estimated using TLUSTY model atmospheres; independent estimates of $v_e$sin$i$ were also obtained using a Fourier Transform method. Luminosities have been inferred from stellar apparent magnitudes and used in conjunction with the T$_eff$ and $v_e$sin$i$ estimates to constrain stellar masses and ages using the BONNSAI package. We find that targets towards the inner region of NGC 346 have higher median masses and projected rotational velocities, together with smaller median ages than the rest of the sample. There appears to be a population of very young targets with ages of less than 2 Myr, which have presumably all formed within the cluster. The more massive targets are found to have lower $v_e$sin$i$ consistent with previous studies. No significant evidence is found for differences with metallicity in the stellar rotational velocities of early-type stars, although the targets in the SMC may rotate faster than those in young Galactic clusters. The rotational velocity distribution for single non-supergiant B-type stars is inferred and implies that a significant number have low rotational velocity ($\simeq$10\% with $v_e$<40 km/s), together with a peak in the probability distribution at $v_e \simeq$300 km/s. Larger projected rotational velocity estimates have been found for our Be-type sample and imply that most have rotational velocities between 200-450 km/s.Comment: Accepted by A&

Computing in Additive Networks with Bounded-Information Codes

This paper studies the theory of the additive wireless network model, in which the received signal is abstracted as an addition of the transmitted signals. Our central observation is that the crucial challenge for computing in this model is not high contention, as assumed previously, but rather guaranteeing a bounded amount of \emph{information} in each neighborhood per round, a property that we show is achievable using a new random coding technique. Technically, we provide efficient algorithms for fundamental distributed tasks in additive networks, such as solving various symmetry breaking problems, approximating network parameters, and solving an \emph{asymmetry revealing} problem such as computing a maximal input. The key method used is a novel random coding technique that allows a node to successfully decode the received information, as long as it does not contain too many distinct values. We then design our algorithms to produce a limited amount of information in each neighborhood in order to leverage our enriched toolbox for computing in additive networks

Pre-supernova evolution, compact object masses and explosion properties of stripped binary stars

Most massive stars are born in binary or higher-order multiple systems and exchange mass with a companion during their lives. In particular, the progenitors of a large fraction of compact object mergers, and Galactic neutron stars (NSs) and black holes (BHs) have been stripped off their envelopes by a binary companion. Here, we study the evolution of single and stripped binary stars up to core collapse with the stellar evolution code MESA and their final fates with a parametric supernova (SN) model. We find that stripped binary stars can have systematically different pre-SN structures compared to genuine single stars and thus also different SN outcomes. The bases of these differences are already established by the end of core helium burning and are preserved up to core collapse. We find a non-monotonic pattern of NS and BH formation as a function of CO core mass that is different in single and stripped binary stars. In terms of initial masses, single stars of >35 Msun all form BHs, while this transition is only at 70 Msun in stripped stars. On average, stripped stars give rise to lower NS and BH masses, higher explosion energies, higher kick velocities and higher nickel yields. Within a simplified population synthesis model, we show that our results lead to a significant reduction of the rates of BH-NS and BH-BH mergers with respect to typical assumptions made on NS and BH formation. Therefore, we predict lower detection rates of such merger events by, e.g., advanced LIGO than is often considered. We further show how features in the NS-BH mass distribution of single and stripped stars relate to the chirp-mass distribution of compact object mergers. Further implications of our findings are discussed with respect to the missing red-supergiant problem, a possible mass gap between NSs and BHs, X-ray binaries and observationally inferred nickel masses from Type Ib/c and IIP Sne. [abridged]Comment: 25 pages (incl. appendix), 17 figures, 2 tables; final version accepted for publication in A&

Singularly perturbed boundary value problems in case of exchange of stablities

We consider a mixed boundary value problem for a system of two second order nonlinear differential equations where one equation is singularly perturbed. We assume that the associated equation has two intersecting families of equilibria. This property excludes the application of standard results. By means of the method of upper and lower solutions we prove the existence of a solution of the boundary value problem and determine its asymptotic behavior with respect to the small parameter. The results can be used to study differential systems modelling bimolecular reactions with fast reaction rates

Singularly perturbed reaction-diffusion systems in case of exchange of stabilities

We study singularly perturbed elliptic and parabolic differential equations under the assumption that the associated equation has intersecting families of equilibria (exchange of stabilities). We prove by means of the method of asymptotic lower and upper solutions that the asymptotic behavior with respect to the small parameter changes near the curve of exchange of stabilities. The application of that result to systems modelling fast bimolecular reactions in a heterogeneous environment implies a transition layer (jumping behavior) of the reaction rate. This behavior has to be taken into account for identification problems in reaction systems

Singularly perturbed elliptic problems in the case of exchange of stabilities

We consider the singularly perturbed boundary value problem (E_\ve) \, \ve^ 2 \Delta u = f(u,x,\ve) {for} x \in D, \, \frac{\partial u}{\partial n} - \lambda(x) u =0 \quad \mbox{for} \quad x \in \Gamma where $D \subset R^ 2$ is an open bounded simply connected region with smooth boundary $\Gamma$, \ve is a small positive parameter and $\partial/\partial n$ is the derivative along the inner normal of $\Gamma$. We assume that the degenerate problem $(E_0) \quad f(u,x,0) =0$ has two solutions $\varphi_1(x)$ and $\varphi_2(x)$ intersecting in an smooth Jordan curve ${ \cal C}$ located in $D$ such that $f_u(\varphi_i(x),x,0)$ changes its sign on ${\cal C}$ for $i=1,2$ (exchange of stabilities). By means of the method of asymptotic lower and upper solutions we prove that for sufficiently small \ve, problem (E_\ve) has at least one solution u(x,\ve) satisfying \alpha(x,\ve) \le u(x,\ve) \le \beta(x,\ve) where the upper and lower solutions \beta(x,\ve) and \alpha(x,\ve) respectively fulfil \beta(x,\ve) - \alpha(x,\ve) = O(\sqrt{\ve}) for $x$ in a $\delta$-neighborhood of ${\cal C}$ where $\delta$ is any fixed positive number sufficiently small, while \beta(x,\ve) - \alpha(x,\ve) = O(\ve) for $x \in \overline{D}\backslash D_\delta$. Applying this result to a special reaction system in a nonhomogeneous medium we prove that the reaction rate exhibits a spatial jumping behavior