Coping with loss

2MASS J15274848+3536572 (J1527) is a semidetached binary system consisting of a main-sequence star and a white dwarf (WD) in an orbit of 0.2556686 day. The magnetic braking (MB) mechanism plays an important role in driving the mass transfer of binary systems with an orbital period longer than 3 hr. Based on the standard and saturated MB laws, in this work we perform a detailed stellar evolution model for the formation of J1527. The simulated results indicate that two MB laws can successfully reproduce the observed orbital period, WD mass, donor-star mass, donor-star radius, surface gravity ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="normal">log</mml:mi> <mml:mi>g</mml:mi> </mml:math> ) and effective temperature of the donor star. However, the standard and saturated MB laws predicted a current mass transfer rate of 10 −8 and 7.5 × 10 −10 M ⊙ yr −1 , respectively, which are much higher than the inferred value (≤3.9 × 10 −11 M ⊙ yr −1 ) according to the effective temperature detected in the WD. A sudden mass loss (4 × 10 −4 M ⊙ ) caused by the recent strong hydrogen shell flash on the surface of the WD could result in an instantaneous orbital expansion and a sharp decay of the mass-transfer rate. To produce inferred mean mass transfer rate, it requires a relatively low mass transfer rate prior to the hydrogen shell flash, which favors the saturated MB law.

Binaries that evolved from red giant (RG) binaries through stable Roche lobe overflow follow the mass–orbital period relation if the donor’s core is degenerate. This relation is important for the studies of long orbital period blue stragglers, subdwarf B stars, and millisecond pulsars. To examine the influence of mass transfer schemes on this relation, we model the evolution of RG binaries at metallicity Z = 0.02 and Z = 0.001 with two different mass transfer schemes. In one of the scheme, it is assumed that mass transfer only occurs when the donor star’s radius is just larger than its Roche lobe radius (‘classical’ scheme). In another mass transfer scheme, the mass transfer can also occur when the donor’s radius is smaller than its Roche lobe radius as proposed by Ritter (1988) and further studied by Kolb &amp; Ritter (1990; ‘Kolb’ scheme). We find that the mass transfer scheme has a significant influence on the evolution of RG binaries. In these RG binaries initiating mass transfer on the upper part of the RG branch, the final donor masses are smaller and orbital periods are larger in the models with the ‘Kolb’ scheme, compared with the models with the ‘classical’ scheme. The difference between orbital periods (donor masses) at the end of mass transfer under two different mass transfer schemes can be up to 500 d (0.04 M⊙) for the same donor mass (orbital period). The mass–orbital period relation from these models with the ‘Kolb’ scheme is above the relation from models with the ‘classical’ scheme. Additionally, similar to previous studies, we find that the final orbital period at metallicity Z = 0.02 is larger than that at metallicity Z = 0.001 for a given donor mass.

We study the physical and evolutionary properties of the "WD family" of AM CVn stars by computing realistic models of IDD systems. We evaluate self-consistently both the mass transfer rate from the donor, as determined by GW emission and interaction with the binary companion, and the thermal response of the accretor to mass deposition. We find that, after the onset of mass transfer, all the considered systems undergo a strong non-dynamical He-flash. However, due to the compactness of these systems, the expanding accretors fill their Roche lobe very soon, thus preventing the efficient heating of the external layers of the accreted CO WDs. Moreover, due to the loss of matter from the systems, the orbital separations enlarge and mass transfer comes to a halt. The further evolution depends on the value of $\dot{M}$, after the donors fill again their lobe. On one hand, if the accretion rate, as determined by the actual value of (M$_{don}$,M$_{acc}$), is high enough, the accretors experience several He-flashes of decreasing strength and then quiescent He-burning sets in. Later on, since the mass transfer rate in IDD is a permanently decreasing function of time, accretors experience several recurrent strong flashes. On the other hand, for intermediate and low values of $\dot{M}$, the accretors enter the strong flashes accretion regime. As expected, in all the considered systems the last He-flash is the strongest one, even if a dynamical event never occurs. When the mass accretion rate decreases below (2-3)$\times 10^{-8} M_\odot yr^{-1}$, the compressional heating of the He-shell becomes less efficient than the neutrino cooling, so that all the accretors in the considered systems evolve into massive degenerate objects. Our results suggest that SNe .Ia or type Ia Supernovae due to Edge-Lit Detonation in the WD family of AM CVn stars should be much more rare than previously expected.

Context. The binary system SDSS J1257+5428 consists of an extremely low-mass white dwarf (WD) with a mass ranging from ∼0.1 to ∼0.24 M⊙, along with a more massive WD companion of approximately 1 M⊙ that is significantly hotter. Recently, a tertiary WD orbiting this binary was discovered, setting a lower limit for the total age (∼4 Gyr) of the triple and providing further constraints on SDSS J1257+5428 that could be used to constrain its formation pathways. Up to now, the existence of this system has been described as paradoxical since tested models for its formation cannot account for its properties. Aims. Here we investigate under which conditions SDSS J1257+5428 could be understood as a descendant of a cataclysmic variable with an evolved donor star, which is a scenario that has never been explored in detail. Methods. We used the rapid BSE code for pre-common-envelope (CE) evolution and the detailed MESA code for post-CE evolution to carry out binary evolution simulations and searched for potential formation pathways for SDSS J1257+5428 that lead to its observed characteristics. For the post-CE evolution, we adopted a boosted version of the CARB model, which has been successfully used to explain the properties of close binary stars hosting evolved solar-type stars. Results. We find that SDSS J1257+5428 can be explained as a post-cataclysmic-variable system if (i) the progenitor of the extremely low-mass WD was initially a solar-type star that evolved into a subgiant before the onset of mass transfer and underwent hydrogen shell flashes after the mass transfer stopped, (ii) the massive WD was highly or entirely rejuvenated during the cataclysmic variable evolution, and (iii) magnetic braking was strong enough to make the evolution convergent. In this case, the torques due to magnetic braking need to be stronger than those provided by the CARB model by a factor of ∼100. Conclusions. We conclude that SDSS J1257+5428 can be reasonably well explained as having originated from a cataclysmic variable that hosted an evolved donor star and should no longer be regarded as paradoxical. If our formation channel is correct, our findings provide further support that stronger magnetic braking acts on progenitors of (i) close detached WD binaries, (ii) close detached millisecond pulsar with extremely low-mass WDs, (iii) AM CVn binaries, and (iv) ultra-compact X-ray binaries, in comparison to the magnetic braking strength required to explain binaries hosting main-sequence stars and single main-sequence stars.

Doubly-degenerate binary systems consisting of two white dwarfs both composed of carbon and oxygen and close enough that mass is transferred from the less massive to the more massive are possible progenitors of type Ia supernovae. If the mass transfer rate is slow enough that the accreting white dwarf can reach 1.38 solar masses then it can ignite carbon degenerately at its centre. This can lead to a thermonuclear runaway and thence a supernova explosion. However if the accretion rate is too high the outer layers of the white dwarf heat up too much and carbon ignites there non-degenerately. A series of mild carbon flashes can then propagate inwards and convert the carbon to neon relatively gently. There is no thermonuclear runaway and no supernova. We have determined the critical rate for accretion and find it to be generally about two-fifths of the Eddington rate. In the case of actual bianry stars the mass transfer rate falls off as mass is transferred so we find that this rate can be very much exceeded at the onset of mass transfer. We determine combinations of white dwarf masses that can lead to central degenerate carbon ignition.

Many previous works studied the dynamical time-scale mass transfer stability criteria based on the donor response with neglecting the stellar structure of the accretor. In this letter, we investigate the radial response of accretors with mass accumulation and its effect on the binary mass transfer stability. We perform a series of detailed stellar evolution simulations with different types of accretors and obtain the radial variations of stars accreting at different rates. Since the time within which the donor loses half of the original mass has a correlation with the donor mass, we approximately obtain the mean mass transfer rate as a function of mass ratio. Assuming that the common envelope (CE) phase occurs if the accretor radius exceeds the outer Roche lobe radius, we obtain the critical mass ratio of dynamically unstable mass transfer. We find the critical mass ratios for donors filling their Roche lobes at the Main Sequence (MS) and Hertzsprung Gap (HG) stages are smaller than that derived from the radial response of the donor in the traditional way. Our results may suggest that the binary is easier to enter into the CE phase for a donor star at the MS or HG stage than previously believed.

We examine the proposal that the subset of neutron-star and black-hole X-ray binaries that form with Ap or Bp star companions will experience systemic angular-momentum losses due to magnetic braking, not otherwise operative with intermediate-mass companion stars. We suggest that for donor stars possessing the anomalously high magnetic fields associated with Ap and Bp stars, a magnetically coupled, irradiation-driven stellar wind can lead to substantial systemic loss of angular momentum. Hence, these systems, which would otherwise not be expected to experience ‘magnetic braking’, evolve to shorter orbital periods during mass transfer. In this paper, we detail how such a magnetic braking scenario operates. We apply it to a specific astrophysics problem involving the formation of compact black-hole binaries with low-mass donor stars. At present, it is not understood how these systems form, given that lowmass companion stars are not likely to provide sufficient gravitational potential to unbind the envelope of the massive progenitor of the black hole during a prior ‘common-envelope’ phase. On the other hand, intermediate-mass companions, such as Ap and Bp stars, could more readily eject the common envelope. However, in the absence of magnetic braking, such systems tend to evolve to long orbital periods. We show that, with the proposed magnetic braking properties afforded by Ap and Bp companions, such a scenario can lead to the formation of compact black-hole binaries with orbital periods, donor masses, lifetimes and production rates that are in accord with the observations. In spite of these successes, our models reveal a significant discrepancy between the calculated effective temperatures and the observed spectral types of the donor stars. Finally, we show that this temperature discrepancy would still exist for other scenarios invoking initially intermediate-mass donor stars, and this presents a substantial unresolved mystery.

We performed numerical simulations of the common envelope (CE) interaction between thermally pulsing asymptotic giant branch (AGB) stars of 1.7 and 3.7 M$_{\odot }$, respectively, and a 0.6 M$_{\odot }$ compact companion. We use tabulated equations of state to take into account recombination energy. For the first time, formation and growth of dust is calculated explicitly, using a carbon dust nucleation network with a C/O abundance ratio of 2.5 (by number). The first dust grains appear within $\sim$1–3 yr after the onset of the CE, forming an optically thick shell at $\sim$10–20 au, growing in thickness and radius to values of $\sim$400–500 au over $\sim$40 yr, with temperatures around 400 K. Most dust is formed in unbound material, having little effect on mass ejection or orbital evolution. By the end of the simulations, the total dust yield is $\sim 8.4\times 10^{-3}$ and $\sim 2.2\times 10^{-2}$ M$_{\odot }$ for the CE with a 1.7 and a 3.7 M$_{\odot }$ AGB star, respectively, corresponding to a nucleation efficiency close to 100 per cent, if no dust destruction mechanism is considered. Despite comparable dust yields to single AGB stars, in CE ejections the dust forms a thousand times faster, over tens of years as opposed to tens of thousands of years. This rapid dust formation may account for the shift in the infrared of the spectral energy distribution of some optical transients known as luminous red novae. Simulated dusty CEs support the idea that extreme carbon stars and ‘water fountains’ may be objects observed after a CE event.

Cataclysmic variables are interacting binary systems in which the evolution of the system is driven by the loss of orbital angular momentum. In this thesis I investigate possible angular momentum loss mechanisms and try to reconcile the differences between the observed and theoretically predicted minimum period and the orbital period distribution for systems with orbital periods below the period gap. Specifically I use a general consequential angular momentum loss mechanism (CAML) which depends linearly upon the mass transfer rate in the system, and a deformation mechanism which bloats the donor star. Numerical models to include the effects of circumbinary discs and irradiation driven winds from the donor star on the evolution of CVs were developed, the circumbinary disc model is able to raise the minimum period to the observed value. Systems subject to irradiation driven winds and high CAML efficiencies exhibit mass transfer cycles; these could explain the range of mass transfer rates observed in CVs with similar orbital periods. I also consider the possibility that the observed minimum period is purely an age effect. <br> I model possible parent distributions by using an additional intrinsic angular momentum loss to set the minimum period to the observed value, with different spectra of donor star masses, white dwarf masses, efficiencies for the CAML and bloating mechanisms. A statistical test was developed and used to calculate a probability that the observed distribution is drawn from the modelled parent distribution. None of the calculated distributions gives a better fit than that for a flat distribution. This is suggestive of some additional evolutionary mechanism or selection effect. <br> I also investigate the apparent difference between the distributions of magnetic and non-magnetic CVs over the period range (1.3 ≤ <i>P/hr</i> ≤ 15), concluding that it is likely that these systems evolve via different mechanisms for orbital periods above the lower edge of the period gap.

We analyse the evolution of close binary systems containing a neutron star that lead to the formation of redback pulsars. Recently, there has been some debate on the origin of such systems and the formation mechanism of redbacks may still be considered as an open problem. We show that the operation of a strong evaporation mechanism, starting from the moment when the donor star becomes fully convective (or alternatively since the formation of the neutron star by accretion-induced collapse), produces systems with donor masses and orbital periods in the range corresponding to redbacks with donors appreciably smaller than their Roche lobes, i.e. they have low filling factors (lower than 0.75). Models of redback pulsars can be constructed assuming the occurrence of irradiation feedback. They have been shown to undergo cyclic mass transfer during the epoch at which they attain donor masses and orbital periods corresponding to redbacks, and stay in quasi-Roche lobe overflow conditions with high filling factors. We show that, if irradiation feedback occurs and radio ejection inhibits further accretion on to the neutron star after the first mass transfer cycle, the redback systems feature high filling factors. We suggest that the filling factor should be considered as a useful tool for discriminating among those redback formation mechanisms. We compare theoretical results with available observations and conclude that observations tend to favour models with high filling factors.

Wind mass transfer in binary systems with asymptotic giant branch (AGB) donor stars plays a fundamental role in the formation of a variety of objects, including barium stars and carbon-enhanced metal-poor (CEMP) stars. In an attempt to better understand the properties of these systems, we carry out a comprehensive set of smoothed-particle hydrodynamics (SPH) simulations of wind-losing AGB stars in binaries for a variety of binary mass ratios, orbital separations, initial wind velocities, and rotation rates of the donor star. The initial parameters of the simulated systems are chosen to match the expected progenitors of CEMP stars. We find that the strength of interaction between the wind and the stars depends on the ratio of wind velocity to orbital velocity (v∞/vorb) and on the binary mass ratio. Strong interaction occurs for close systems and comparable mass ratios, and gives rise to a complex morphology of the outflow and substantial angular-momentum loss, which leads to a shrinking of the orbit. As the orbital separation increases and the mass of the companion star decreases, the morphology of the outflow and the angular-momentum loss become more similar to the spherically symmetric wind case. We also explore the effects of tidal interaction and find that for orbital separations up to 7−10 AU, depending on mass ratio, spin-orbit coupling of the donor star occurs at some point during the AGB phase. If the initial wind velocity is relatively low, we find that corotation of the donor star results in a modified outflow morphology that resembles wind Roche-lobe overflow. In this case the mass-accretion efficiency and angular-momentum loss differ from those found for a non-rotating donor. Finally, we provide relations for the mass-accretion efficiency and angular-momentum loss as a function of v∞/vorb and the binary mass ratio that can be easily implemented in a population synthesis code to study populations of barium stars, CEMP stars, and other products of interaction in AGB binaries, such as cataclysmic binaries and type Ia supernovae.

The evolution of binaries containing low-mass donors (≤2 M☉) and degenerate accretors (i.e., white dwarfs [0.7 M☉] or neutron stars [1.4 M☉]) is systematically investigated over a wide expanse of parameter space. The donors are assumed to have metallicities in the range of 0.0001 ≤ Z ≤ 0.02 and could be either unevolved (zero-age main sequence) or ascending the red giant branch at the onset of mass transfer [corresponding to 5 ≲ Porb(hr) ≲ 2 × 103]. The evolutionary tracks form part of a very detailed grid of nearly 200 sequences, each corresponding to a different set of initial conditions. During the initial phases of their evolution, the systems resemble either low-mass X-ray binaries or cataclysmic variables. However, as has been pointed out by several authors (e.g., Podsiadlowski et al.), the evolutionary tracks can exhibit a wide variety of behaviors and outcomes. We focus on systems that evolve to produce helium-rich degenerate dwarfs (HeDDs) that are either detached or still losing mass after a Hubble time. Of the systems that avoid dynamical instability, some evolve to ultrashort values of Porb (<60 minutes), while others that lie above the bifurcation limit (which we show to be quite sensitive to the assumed metallicity) produce wide binary millisecond pulsars (BMSPs) containing HeDD companions that have Porb values of ≲2 × 104 hr. We also show that the mass and composition of the envelopes of HeDDs that are about to descend the cooling branch are particularly sensitive to the input physics and this in turn dictates whether they experience extremely vigorous hydrogen shell flashes. Our computed values of the envelope mass, menv (corresponding to the mass of those layers below the surface containing some hydrogen), typically have a dependence on the final donor mass (mf) and metallicity (Z) that can be expressed as menv ∝ mZ-0.2. Furthermore, for systems that do not evolve too close to the bifurcation limit, we find that the final orbital period is given by Porb,f(hr) ≅ 2.5 Z0.3 × 10. Finally, we use our results to comment on the properties of the optical companions to binary millisecond pulsars and compare their inferred ages with the spin-down times of the pulsars. The structure of young HeDDs should be particularly useful as starting models for more sophisticated cooling calculations that take into account important long-term physical processes and thus we are making our models available for retrieval.

This thesis investigates the synthesis and transfer of s-process elements in low-mass binary stars by combining stellar spectroscopy, stellar evolution modeling, and nuclear physics experiments. The first project follows a four-year high-resolution spectroscopic observation campaign. I observe intrinsic asymptotic giant branch and extrinsic binary companions across a broad range of metallicities, for which I derive orbits, stellar parameters, and chemical abundances. I determine abundances of carbon, ω-elements, and s-process elements, expanding the census of heavy element abundance patterns. Comparisons with AGB yield models confirm s-process enrichment in binary systems and reveal correlations between enrichment levels and progenitor AGB masses, establishing observational benchmarks for nucleosynthesis and mass transfer. For the second project, I compute a grid of 2691 binary stellar evolution models with the STARS code, spanning a range of metallicities, donor masses, and accreted masses. By comparing models with my observations of Ba, CH, and CEMP-s stars and the literature, I constrain accretion e!ciencies and progenitor properties. I find consistent AGB donor masses across metallicities. Results show CH and CEMP-s stars form through small accretion events (→0.1 M↑), weak Ba stars through moderate accretion (&lt;0.5 M↑), and that strong Ba stars require more substantial mass transfer (&gt;0.5 M↑). Metal-rich systems are found to accrete more material than metal-poor ones, linking abundance patterns and metallicity to accretion histories. In the third project, I perform a nuclear physics experiment to probe neutron-capture reactions that shape the end of the s-process. Using the activation method and beta spectroscopy, I measure the cross section of the double-magic nucleus 208Pb at 25 keV and establish an upper limit at 5 keV. These data provide useful inputs for stellar nucleosynthesis models, clarifying the role of Pb as an s-process termination point. Together, these studies bridge observations, modeling, and experiments to advance our understanding of the synthesis, transfer, and surface imprint of s-process elements in low-mass binary stars.

The evolution and the stability of mass transfer of CO+He white dwarf (WD) binaries are not well understood. Observationally they may emerge as AM CVn binaries and are important gravitational wave (GW) emitters. In this work, we have modeled the evolution of double WD binaries with accretor masses of 0.50–1.30 M ⊙ and donor masses of 0.17–0.45 M ⊙ using the detailed stellar evolution code mesa. We find that the evolution of binaries with same donor masses but different accretor masses is very similar and binaries with same accretor masses but larger He donor masses have larger maximum mass transfer rates and smaller minimum orbital periods. We also demonstrate that the GW signal from AM CVn binaries can be detected by spaceborne GW observatories, such as LISA and TianQin. There is a linear relation between the donor mass and gravitational wave frequency during the mass transfer phase. In our calculation, all binaries can have dynamically stable mass transfer, which is very different from previous studies. The threshold donor mass of Eddington-limited mass transfer for a given accretor WD mass is lower than previous studies. Assuming that a binary may enter a common envelope if the mass transfer rate exceeds the maximum stable burning rate of He, we provide a new criterion for double WDs surviving mass transfer, which is below the threshold of the Eddington limit. Finally, we find that some systems with oxygen–neon (ONe) WDs in our calculation may evolve into detached binaries consisting of neutron stars and extremely low-mass He WDs, and further ultracompact X-ray binaries.

In this talk, we will simply show the consequences of binary population synthesis for blue stragglers, such as the integrated spectral energy distribution (ISED), the color-magnitude diagram, the specific frequency, and the influences on colors. Blue stragglers have been found in all stellar populations and they are an important population component in both stellar evolution and star clusters. Much evidence shows that blue stragglers are relevant to primordial binaries. The binary population synthesis study shows that primordial binary evolution may produce blue stragglers at any given times. The specific frequency in this way decreases with time first, then increases when the age is larger than 10 Gyr, while that from angular momentum loss induced by magnetic braking in low-mass binaries increases with time and exceeds that of primordial binary evolution in a population older than 3 Gyr. Meanwhile, blue stragglers resulting from primordial binary evolution are dominant contributors to the ISEDs in ultraviolet and blue bands in a population between 0.3 and 2.0 Gyr. The mass fraction of the lost matter from the primary accreted by the secondary, beta, significantly affects on the final results, e.g. the specific frequency of blue stragglers decreasing with beta, blue stragglers produced from a high value of beta being more massive, then contributing more to the ISEDs of the host clusters. For old open clusters, it is appropriate to adopt a higher value of beta when the primary is in HG at the onset of mass transfer. Our study also shows that, for most Galactic open clusters, the specific frequency of blue stragglers obtained from our simulations is much lower than that of observations, which has been discussed in this talk.