Multiwavelength modelling the SED of supersoft X-ray sources. I. The method and examples

Radiation of supersoft X-ray sources (SSS) dominates both the supersof X-ray and the far-UV domain. A fraction of their radiation can be reprocessed into the thermal nebular emission, seen in the spectrum from the near-UV to longer wavelengths. In the case of symbiotic X-ray binaries (SyXBs) a strong contribution from their cool giants is indicated in the optical/near-IR. In this paper I introduce a method of multiwavelength modelling the spectral energy distribution (SED) of SSSs from the supersoft X-rays to the near-IR with the aim to determine the physical parameters of their composite spectra. The method is demonstrated on two extragalactic SSSs, the SyXB RX J0059.1-7505 (LIN 358) in the Small Magellanic Cloud (SMC), RX J0439.8-6809 in the Large Magellanic Cloud (LMC) and two Galactic SSSs, the classical nova RX J2030.5+5237 (V1974 Cyg) during its supersoft phase and the classical symbiotic star RX J1601.6+6648 (AG Dra) during its quiescent phase. The multiwavelength approach overcomes the problem of the mutual dependence between the temperature, luminosity and amount of absorption, which appears when only the X-ray data are fitted.Thus, the method provides an unambiguous solution. It was found that selection of the model (a blackbody or an atmospheric model) is not of crucial importance in fitting the global X-ray/IR SED. The multiwavelength modelling of the SED of SSSs is essential in determining their physical parameters.Comment: 15 pages, 11 figures, 2 tables, accepted for New Astronom

An exact corrected log-likelihood function for Cox's proportional hazards model under measurement error and some extensions

This paper studies Cox`s proportional hazards model under covariate measurement error. Nakamura`s (1990) methodology of corrected log-likelihood will be applied to the so called Breslow likelihood, which is, in the absence of measurement error, equivalent to partial likelihood. For a general error model with possibly heteroscedastic and non-normal additive measurement error, corrected estimators of the regression parameter as well as of the baseline hazard rate are obtained. The estimators proposed by Nakamura (1992), Kong, Huang and Li (1998) and Kong and Gu (1999) are reestablished in the special cases considered there. This sheds new light on these estimators and justifies them as exact corrected score estimators. Finally, the method will be extended to some variants of the Cox model