Stellar adiabatic mass loss model and applications

Roche-lobe overflow and common envelope evolution are very important in binary evolution, which is believed to be the main evolutionary channel to hot subdwarf stars. The details of these processes are difficult to model, but adiabatic expansion provides an excellent approximation to the structure of a donor star undergoing dynamical time scale mass transfer. We can use this model to study the responses of stars of various masses and evolutionary stages as potential donor stars, with the urgent goal of obtaining more accurate stability criteria for dynamical mass transfer in binary population synthesis studies. As examples, we describe here several models with the initial masses equal to 1 Msun and 10 Msun, and identify potential limitations to the use of our results for giant-branch stars.Comment: 7 pages, 5 figures,Accepted for publication in AP&SS, Special issue Hot Sub-dwarf Stars, in Han Z., Jeffery S., Podsiadlowski Ph. ed

Discount Functions for Fitting Individual Data

The commonly used hyperbolic and quasi-hyperbolic discount functions imply decreasing impatience, which is the prevailing empirical phenomenon in intertemporal choice, in particular for aggregate behavior. At the individual level there is much variation, however, and there will always be some individuals who exhibit increasing impatience. Hence, to fit data at the individual level, new discount functions are needed. This paper introduces such functions, with constant absolute (CADI) or constant relative (CRDI) decreasing impatience. These functions can accommodate any degree of decreasing or increasing impatience, which makes them sufficiently flexible for analyses at the individual level. The CADI and CRDI discount functions are the analogs of the well known CARA and CRRA utility functions for decision under risk

Characterizing QALYs by Risk Neutrality

This paper shows that QALYs can be derived from more elementary conditions than thought hitherto in the literature: it suffices to impose risk neutrality for life years in every health state. This derivation of QALYs is appealing because it does not require knowledge of concepts from utility theory such as utility independence. Therefore our axiomatization greatly facilitates the assessment of the normative (non)validity of QALYs in medical decision making. Moreover, risk neutrality can easily be tested in experimental designs, which makes it straightforwar

Nash was a first to axiomatize expected utility

Nash is famous for many inventions, but it is less known that he, simultaneously with Marschak, also was the first to axiomatize expected utility for risk. In particular, these authors were the first to state the independence condition, a condition that should have been but was not stated by von Neumann and Morgenstern. Marschak’s paper resulted from interactions with several people at the Cowles Commission. We document unique letters and personal communications with Nash, Samuelson, Arrow, Dalkey, and others, making plausible that Nash made his discovery independently from the others

Utility Independence of Multiattribute Utility Theory is Equivalent to Standard Sequence Invariance of Conjoint Measurement

Utility independence is a central condition in multiattribute utility theory, where attributes of outcomes are aggregated in the context of risk. The aggregation of attributes in the absence of risk is studied in conjoint measurement. In conjoint measurement, standard sequences have been widely used to empirically measure and test utility functions, and to theoretically analyze them. This paper shows that utility independence and standard sequences are closely related: utility independence is equivalent to a standard sequence invariance condition when applied to risk. This simple relation between two widely used conditions in adjacent fields of research is surprising and useful. It facilitates the testing of utility independence because standard sequences are flexible and can avoid cancelation biases that affect direct tests of utility independence. Extensions of our results to nonexpected utility models can now be provided easily. We discuss applications to the measurement of quality-adjusted life-years (QALY) in the health domain

Time-Tradeoff Sequences For Analyzing Discounting And Time Inconsistency

ABSTRACT. This paper introduces time-tradeoff (TTO) sequences as a new tool to analyze time inconsistency and intertemporal choice. TTO sequences simplify the measurement of discount functions, requiring no assumption about utility. They also simplify the qualitative testing of time inconsistencies, and allow for quantitative measurements thereof. TTO sequences can easily be administered using only pencil and paper. They readily show which subjects are most prone to time inconsistencies. We further use them to axiomatically analyze and empirically test (quasi-)hyperbolic discount functions. An experiment demonstrates the feasibility of measuring TTO sequences. Our data falsify (quasi-)hyperbolic discount functions and call for the development of models that can accommodate increasing impatience

Habitable Zones and UV Habitable Zones around Host Stars

Ultraviolet radiation is a double-edged sword to life. If it is too strong, the terrestrial biological systems will be damaged. And if it is too weak, the synthesis of many biochemical compounds can not go along. We try to obtain the continuous ultraviolet habitable zones, and compare the ultraviolet habitable zones with the habitable zones of host stars. Using the boundary ultraviolet radiation of ultraviolet habitable zone, we calculate the ultraviolet habitable zones of host stars with masses from 0.08 to 4.00 \mo. For the host stars with effective temperatures lower than 4,600 K, the ultraviolet habitable zones are closer than the habitable zones. For the host stars with effective temperatures higher than 7,137 K, the ultraviolet habitable zones are farther than the habitable zones. For hot subdwarf as a host star, the distance of the ultraviolet habitable zone is about ten times more than that of the habitable zone, which is not suitable for life existence.Comment: 5 pages, 3 figure

Habitable Zones of Host Stars During the Post-MS Phase

A star will become brighter and brighter with stellar evolution, and the distance of its habitable zone will become farther and farther. Some planets outside the habitable zone of a host star during the main sequence phase may enter the habitable zone of the host star during other evolutionary phases. A terrestrial planet within the habitable zone of its host star is generally thought to be suited to life existence. Furthermore, a rocky moon around a giant planet may be also suited to life survive, provided that the planet-moon system is within the habitable zone of its host star. Using Eggleton's code and the boundary flux of habitable zone, we calculate the habitable zone of our Solar after the main sequence phase. It is found that Mars' orbit and Jupiter's orbit will enter the habitable zone of Solar during the subgiant branch phase and the red giant branch phase, respectively. And the orbit of Saturn will enter the habitable zone of Solar during the He-burning phase for about 137 million years. Life is unlikely at any time on Saturn, as it is a giant gaseous planet. However, Titan, the rocky moon of Saturn, may be suitable for biological evolution and become another Earth during that time. For low-mass stars, there are similar habitable zones during the He-burning phase as our Solar, because there are similar core masses and luminosities for these stars during that phase.Comment: 6 pages, 7 figures. Accepted by Ap & S

WD + MS systems as the progenitor of SNe Ia

We show the initial and final parameter space for SNe Ia in a ($\log P^{\rm i}, M_{\rm 2}^{\rm i}$) plane and find that the positions of some famous recurrent novae, as well as a supersoft X-ray source (SSS), RX J0513.9-6951, are well explained by our model. The model can also explain the space velocity and mass of Tycho G, which is now suggested to be the companion star of Tycho's supernova. Our study indicates that the SSS, V Sge, might be the potential progenitor of supernovae like SN 2002ic if the delayed dynamical-instability model due to Han & Podsiadlowski (2006) is appropriate. Following the work of Meng, Chen & Han (2009), we found that the SD model (WD + MS) with an optically thick wind can explain the birth rate of supernovae like SN 2006X and reproduce the distribution of the color excess of SNe Ia. The model also predicts that at least 75% of all SNe Ia may show a polarization signal in their spectra.Comment: 6 pages, 2 figures, accepted for publication in Astrophysics & Space Science (Proceeding of the 4th Meeting on Hot Subdwarf Stars and Related Objects, edited by Zhanwen Han, Simon Jeffery & Philipp Podsiadlowski