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Uva-DARE (Digital Academic Repository) UvA-DARE (Digital Academic Repository) Advanced evolution of helium stars and massive close binaries Habets, G.M.H.J. Publication date 1985 Link to publication Citation for published version (APA): Habets, G. M. H. J. (1985). Advanced evolution of helium stars and massive close binaries. General rights It is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulations If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: https://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. UvA-DARE is a service provided by the library of the University of Amsterdam (https://dare.uva.nl) Download date:28 Sep 2021 IIIA.. THE EVOLUTION OF A SINGLE AND A BINARY HELIUM STAR OF 2.5 M^ UP TO NEONN IGNITION; CASE BB MASS TRANSFER. Suanary. Thee evolution of a single helium star of 2.5 M0 is calculated from the heliumm Zero Age main sequence up to off-centre neon ignition. In the carbon- shelll burning phase the 2.5 M0 helium star becomes a red giant and possibly enterss the Cepheid pulsational instability strip. As a red giant the 2.5 M0 heliumm star may resemble a R Coronae Borealis (R CrB) star. The mass-exchange phasee and the subsequent evolution up to neon igntion of a 2.5 M0 helium star inn a binary is calculated, with the aim to explore the evolutionary history of thee B-emission X-ray (Be/X-ray) binaries. The orbital parameters and the mass off the companion star (a 17 M@ hydrogen star) were chosen such that Roche-lobe overfloww occurred during carbon-shell burning. [The progenitor of this system consistedd of 13.5 + 6 M0 hydrogen-rich stars which underwent case B mass transfer.. After the mass transfer the system is expected to have become a Be- starr binary]. The helium star loses about 0.3 M0 to its companion and (again) neonn is Ignited at "- 0.16 MQ in the 2.2 M0 (case BB) mass-exchange remnant. 122 16^ 20 2k i* Thee core region, mainly composed of C, 0, Ne, Mg, and some He at the boundaryy of the core (denoted in the following as the "core") of the single 2.55 M© helium star as well as that of the 2.2 M0 remnant, is larger than the Chandrasekharr limiting mass at neon ignition. Hence, these cores are expected too undergo core collapse and to produce neutron stars. NumericalNumerical instabilities are encountered when carbon burning is treated with a simplee two-point difference equation. Therefore, an implicit difference scheme basedd on a three-point difference equation is used to overcome most of these instabilities.. The characteristics of some other solutions for preventing the numericall instabilities are discussed. The effects of neutrino losses are investigatedd for the advanced evolutionary phases. The validity of the ideal gass law for the ionic equation of state is examined. Thee orbital dimensions after the supernova (SN) explosion of the 2.2 M0 remnantt in the binary are calculated under the assumption of symmetric SN mass ejectionn and neglecting the effects of impact of the SN shell on the orbit and onn the companion (these effects are proven to be negligible). The orbital eccentricityy after the SN explosion is found to be small (•*• 0.043). The orbitall dimensions before and after the SN explosion are compared with those off some observed Be-star binaries, Be/X-ray binaries, and other X-ray binaries -- 47 - withh known eccentricities. For the known Be/X-ray and other X-ray binaries the pre—SNN orbit and the neutron star progenitor masses are calculated (assuming circularr pre-SN orbits, a symmetric SN explosion, and neglecting the effects off impact of the SN shell). The assumption of a circular pre-SN orbit is found too be consistent with observations. Our calculcations thus confirm the model off the formation of Be/X-ray binaries by mass-transfer dominated evolution in ann intermediate-mass binary. 1.. Introduction. PaczynskiPaczynski (1971a), Arnett (1972a, b), Savonije and Takens (1976), Woosley ett al. (1980, 1984), Nomoto (1980a, b, 1981, 1982a, b, 1984a, b, c, e), and Delgadoo and Thomas (1981) have calculated the advanced evolution of helium starss with masses of 2.0 MQ or larger. In the lower mass range (up to about 3 MQ)) the radii of these stars undergo considerable expansion, which in a binary cann cause the onset of a second phase of mass transfer (Delgado and Thomas, 1981).. An important question is: for which masses do these stars - even after aa second phase of mass transfer in a binary - still collapse to a neutron star.. In order to explore this problem we calculated in full detail the behaviourr with time of the radius, the core mass, and other parameters of a 2.55 MQ helium star during its advanced evolution. We investigate whether or nott the core of the 2.5 MQ helium star will collapse and form a neutron star [ass is suggested by the calculations of Woosley et al. (1980) and Hillebrandt (1982a),, cf. Habets (1984), but contradicted by the results of Delgado and Thomass (1981)]. Our results (paragraphs 2 to 4 below) confirm the evolution towardss core collapse. In paragraph 5 we compute the orbital dimensions after thee SN explosion of such a helium star and in paragraph 6 we compare these withh observed orbital dimensions of Be and other X-ray binaries, and Be-star binariess with known eccentricities in order to test the suggestion of Rappaportt and Van den Heuvel (1982) that Be/X-ray binaries are formed by a mass-transferr dominated evolution in an intermediate-mass binary. Thee evolution from the helium Zero Age main sequence to the onset of neon burningg of a 2.5 MQ helium star is described In paragraphs 2 to 4. The mass exchangee in a binary consisting of a 2.5 M0 helium star and a 17 M@ hydrogen starr is calculated for the case in which the 2.5 M0 star fills its Roche lobe duringg the carbon-shell burning phase (paragraph 3). The orbital parameters of thiss binary were chosen such that the progenitor system could have been a 13.5 -- 48 - ++ 6 Mg system which underwent case B mass transfer. After the second phase of masss transfer (case BB) the evolution of the remnant of the 2.5 M0 helium star iss calculated until neon ignites off-centre. Inn paragraph 4 we investigate the effects of possible numerical instabilitiess - as found by Sugimoto (1970a) and Paczynski (1974a) - on the resultss for the carbon-burning phase. By using an improved difference scheme thee effects of these instabilities on the final results are expected to be negligible. 2.. The evolution of a 2.5 M^ helium star - single and in a binary - up to neon ignition. Inn Figure 1 the evolutionary history of the central density, pc, and temperature,, T , (both in decimal logarithms) is shown. The evolutionary track off the 2.5 Mg helium star in the Hertzsprung-Russell (HR) diagram is depicted inn Figure 2. The fully drawn curves in Figures 1 and 2 are the tracks without masss exchange, the dotted curves are with mass transfer to the 17 M@ companion.. In Figure 3 the evolution of the radius versus core mass (both scaless are decimal logarithms) is given. The dotted track is with mass exchange,, the deviation from the solid curve is marked with an arrow. The obliquee lines in Figure 1 are the approximate lines of constant electron degeneracyy parameter £ as defined in Chapter II. The curve y - 1 is the approximatee demarcation line of the non-relativistic and relativistic regimes. Thee meaning of the letters in the Figures 1-3 is as follows: A-B, the helium main-sequencee phase and the exhaustion of helium in the core; B-C, the radiativee helium-shell burning phase and the gravitational contraction of the 122 16 C-- 0 core; C-D, the ignition of carbon, radiative and convective core- carbonn burning and radiative carbon-shell burning; D-E, the convective carbon- shelll burning phase and the gravitational contraction of the 0-Ne-Mg core; E 20 0 orr E' (in case of mass exchange), the radiative off-centre ignition of Ne, andd convective off-centre neon burning. Thee Figures 4 and 5 show the evolution of the inner regions with time. 10 0 Figuree 5 is for the case with mass exchange. Time is here defined as log r ((tf11 -. - t 0i)/y )> where t , is the evolutionary time in years elapsed sincee the arrival of the 2.5 M0 helium star on the helium main sequence and tf.. , is chosen to be (about) one year later than the t •, in the final XX 111 3. J. cvui model.. Thus, t ]_ is zero in the first model, which is derived with a -- 49 - Schwarzschildd fitting technique (see Chapter II). The dotted lines In Figures 44 and 5 indicate the boundary of the core which is defined by the region interiorr to the helium shell with maximum energy generation.
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