Cygnus X-2, super-Eddington mass transfer, and pulsar binaries

We consider the unusual evolutionary state of the secondary star in Cygnus X-2. Spectroscopic data give a low mass (M_2 \simeq 0.5 - 0.7\msun) and yet a large radius (R_2 \simeq 7\rsun) and high luminosity (L_2 \simeq 150\lsun). We show that this star closely resembles a remnant of early massive Case B evolution, during which the neutron star ejected most of the \sim 3\msun transferred from the donor (initial mass M_{\rm 2i}\sim 3.6\msun) on its thermal time-scale $\sim 10^6$ yr. As the system is far too wide to result from common-envelope evolution, this strongly supports the idea that a neutron star efficiently ejects the excess inflow during super--Eddington mass transfer. Cygnus X-2 is unusual in having had an initial mass ratio $q_{\rm i} = M_{\rm 2i}/M_1$ in a narrow critical range near $q_{\rm i}\simeq 2.6$. Smaller $q_{\rm i}$ lead to long-period systems with the former donor near the Hayashi line, and larger $q_{\rm i}$ to pulsar binaries with shorter periods and relatively massive white dwarf companions. The latter naturally explain the surprisingly large companion masses in several millisecond pulsar binaries. Systems like Cygnus X-2 may thus be an important channel for forming pulsar binaries.Comment: 9 pages, 4 encapsulated figures, LaTeX, revised version with a few typos corrected and an appendix added, accepted by MNRA

Period-doubling density waves in a chain

The authors consider a one-dimensional chain of N+2 identical particles with nearest-neighbour Lennard-Jones interaction and uniform friction. The chain is driven by a prescribed periodic motion of one end particle, with frequency v and 'strength' parameter alpha . The other end particle is held fixed. They demonstrate numerically that there is a region in the alpha -v plane where the chain has a stable state in which a density wave runs to and fro between the two ends of the chain, similarly to a ball bouncing between two walls. More importantly, they observe a period-doubling transition to chaos, for fixed v and increasing alpha , while the localised (solitary wave) character of the motion is preserve

Why we measure period fertility

Four reasons for measuring period fertility are distinguished: to explain fertility time trends, to anticipate future fertility, to construct theoretical models and to communicate with non-specialist audiences. The paper argues that not all measures are suitable for each purpose, and that tempo adjustment may be appropriate for some objectives but not others. In particular, it is argued that genuine timing effects do not bias or distort measures of period fertility as dependent variable. Several different concepts of bias or distortion are identified in relation to period fertility measures. Synthetic cohort indicators are a source of confusion since they conflate measurement and forecasting. Anticipating future fertility is more akin to forecasting than to measurement. Greater clarity about concepts and measures in the fertility arena could be achieved by a stronger emphasis on validation. Period incidence and occurrence-exposure rates have a straightforward interpretation. More complex period fertility measures are meaningful only if a direct or indirect criterion can be specified against which to evaluate them. Their performance against that criterion is what establishes them as valid or useful

A new interpretation of the period-luminosity sequences of long-period variables

Period-luminosity (PL) sequences of long period variables (LPVs) are commonly interpreted as different pulsation modes, but there is disagreement on the modal assignment. Here, we re-examine the observed PL sequences in the Large Magellanic Cloud, including the sequence of long secondary periods (LSPs), and their associated pulsation modes. Firstly, we theoretically model the sequences using linear, radial, non-adiabatic pulsation models and a population synthesis model of the LMC red giants. Then, we use a semi-empirical approach to assign modes to the pulsation sequences by exploiting observed multi-mode pulsators. As a result of the combined approaches, we consistently find that sequences B and C$^{\prime}$ both correspond to first overtone pulsation, although there are some fundamental mode pulsators at low luminosities on both sequences. The masses of these fundamental mode pulsators are larger at a given luminosity than the mass of the first overtone pulsators. These two sequences B and C$^{\prime}$ are separated by a small period interval in which large amplitude pulsation in a long secondary period (sequence D variability) occurs, meaning that the first overtone pulsation is not seen as the primary mode of pulsation. Observationally, this leads to the splitting of the first overtone pulsation sequence into the two observed sequences B and C$^{\prime}$. Our two independent examinations also show that sequences A$^{\prime}$, A and C correspond to third overtone, second overtone and fundamental mode pulsation, respectively.Comment: 10 pages, 7 figures, accepted for publication in Ap

Multiple period integrals and cohomology

This work gives a version of the Eichler-Shimura isomorphism with a non-abelian $H^1$ in group cohomology. Manin has given a map from vectors of cusp forms to a noncommutative cohomology set by means of iterated integrals. We show Manin's map is injective but far from surjective. By extending Manin's map we are able to construct a bijective map and remarkably this establishes the existence of a non-abelian version of the Eichler-Shimura map

Base Period, Qualifying Period and the Equilibrium Rate of Unemployment

Unemployment benefits, benefit duration, base period and qualifying period are constituent parameters of the unemployment insurance system in most OECD countries. From economic research we know that the amount and duration of unemployment benefits increase unemployment. To analyze the effects of the other two parameters we use a matching model with search frictions and show that there is a trade-off between the qualifying and the base period on the one hand and the amount and duration of the unemployment benefits on the other. A country that combines a high level of unemployment benefits with a long benefit duration can neutralize the effect on the equilibrium rate of unemployment with a long qualifying and/or a short base period. -- Lohnersatzleistungen, Anspruchsdauern, Rahmenfristen und Anwartschaftszeiten sind konstituierende Parameter der Arbeitslosenversicherungen in den meisten OECD Ländern. Ökonomische Untersuchungen zeigen, dass Höhe und Dauer der Lohnersatzleistungen die Arbeitslosigkeit erhöhen. Im Rahmen eines Matching-Modells untersuchen wir die Wirkung der anderen beiden Parameter und zeigen, dass ein trade-off zwischen der Anwartschaftszeit und der Rahmenfrist auf der einen und der Höhe und der Dauer der Lohnersatzleistungen auf der anderen Seite existiert. Ein Land mit einer hohen Arbeitslosenunterstützung und langer Anspruchsdauer kann die Wirkung auf die Arbeitslosenquote durch eine lange Anwartschaftszeit und eine kurze Rahmenfrist neutralisieren.Unemployment insurance,base period,qualifying period

Short period and long period in macroeconomics: an awkward distinction

Abstract: The aim of this paper is to show that the use and meaning of the well-known concepts of short period and long period is often unclear and may be seriously misleading when applied to macroeconomic analysis. Evidence of this confusion emerges through examination of four macroeconomics textbooks and reappraisal of the interpretative debate - which took place mainly in the 1980s and 1990s - aiming at establishing whether Keynes’s General Theory should be considered as a short- or long-period analysis of the aggregate level of production. Having explored some possible explanations for the difficulties in defining and applying these methodological tools at a ‘macro’ level, the conclusion is suggested that it would be preferable to abandon this terminology in classifying different aggregate models and simply to make explicit the given factors, independent and dependent variables in each model in use, exactly as Keynes did in Chapter 18 of his major work.