Two magnetic braking models are implemented in MESA for use in the MIST stellar model grids. Stars less than about 1.3 $M_{\odot}$ are observed to spin down over time through interaction with their magnetized stellar winds (i.e., magnetic braking). This is the basis for gyrochronology, and fundamental to the evolution of lower mass stars. The detailed physics behind magnetic braking are uncertain, as are 1D stellar evolution models. Thus, we calibrate our models and compare to data from open clusters. Each braking model tested here is capable of reproducing the data, albeit with some important distinctions. The Matt et al. (2015) prescription matches the slowly rotating stars observed in open clusters, but tends to overestimate the presence of rapidly rotating stars. The Garraffo et al. (2018) prescription often produces too much angular momentum loss to accurately match the observed slow sequence for lower mass stars, but reproduces the bimodal nature of slow and rapidly rotating stars observed in open clusters fairly well. We find additional evidence that some level of mass dependency may be missing in these braking models to match the rotation periods observed in clusters older than 1 Gyr better.
The time evolution of angular momentum and surface rotation of massive stars is strongly influenced by fossil magnetic fields via magnetic braking. We present a new module containing a simple, comprehensive implementation of such a field at the surface of a massive star within the Modules for Experiments in Stellar Astrophysics (MESA) software instrument. We test two limiting scenarios for magnetic braking: distributing the angular momentum loss throughout the star in the first case, and restricting the angular momentum loss to a surface reservoir in the second case. We perform a systematic in…
Sco X-1 is a low-mass X-ray binary (LMXB) that has one of the most precisely determined set of binary parameters such as the mass accretion rate, companions mass ratio and the orbital period. For this system, as well as for a large fraction of other well-studied LMXBs, the observationally-inferred mass accretion rate is known to strongly exceed the theoretically expected mass transfer rate. We suggest that this discrepancy can be solved by applying a modified magnetic braking prescription, which accounts for increased wind mass loss in evolved stars compared to main sequence stars. Using our m…
Extremely low-mass white dwarfs (ELM WDs) are the result of binary evolution in which a low-mass donor star is stripped by its companion leaving behind a helium-core white dwarf. We explore the formation of ELM WDs in binary systems considering the Convection And Rotation Boosted magnetic braking treatment. Our evolutionary sequences were calculated using the MESA code, with initial masses of 1.0 and 1.2 Msun (donor), and 1.4 (accretor), compatible with low mass X-ray binaries (LMXB) systems. We obtain ELM models in the range 0.15 to 0.27 Msun from a broad range of initial orbital periods, 1 t…
A modest change in magnetic braking at the fully convective boundary explains cataclysmic variable evolution
Universidad Técnica Federico Santa María (UTFSM)（费德里科·圣玛丽亚技术大学）；Pontificia Universidad Católica de Valparaíso (PUCV)（瓦尔帕莱索天主教 Pontificia 大学）；University of Sheffield（谢菲尔德大学）；Yunnan Observatories, CAS（中国科学院云南天文台）；Leibniz-Institut für Astrophysik Potsdam (AIP)（波茨坦阿基米德天体物理研究所）
在一些早期类型的恒星表面的磁场已被直接检测到。这些场的量值在几百G到几kG之间。我们研究了磁制动对自转（$\upsilon_{\rm ini}$ =200 km s $^{-1}$）10 M $_\odot$恒星模型在主序相太阳金属丰度演化的影响.根据ud-Doula等人对磁风约束的二维MHD模拟推导出的形式，磁制动过程被包含在我们的恒星模型中。关于恒星内部的磁场大小和角动量输运机制的效率，我们做了各种各样的假设。当磁制动发生在模型与差动旋转，强烈和快速的混合是在表面获得伴随着在表面速度的快速降低。这样的过程可以解释一些MS星表现出强烈的混合和低表面速度。当固体旋转被施加在内部时，恒星被如此迅速地减速，以至于表面富集比没有磁制动的类似模型要小。在这两种模型（差分或均匀旋转），磁制动由于几个100 G的字段显着降低了角动量的核心在MS阶段。这种减少在固体旋转模型中要大得多。
Our binary evolutionary code predicted until now the position of both stars in the HRD, the characteristics of the accretion disk around the gainer in the case that there is enough space between both stars for this disk. Our code includes a complete description of the tidal interaction. The code was now extended with the action of magnetic braking. Without this phenomenon the rotational velocity of the gainer can not be predicted.Magnetic braking and tides act together and the evolution of the equatorial velocity can now be followed up from birth to death of the binary. From Figure (1) in the …
Evolution of cataclysmic variables under different magnetic braking prescriptions
School of Physical Science and Technology, Xinjiang University（新疆大学物理科学与技术学院）；Department of Nuclear Physics and Astronomy, Institute of Engineering Physics, Samarkand State University（撒马尔罕国立大学工程物理学院核物理与天文学系）
Stars form in dense cores of molecular clouds that are observed to be significantly magnetized. In the simplest case of a laminar (non-turbulent) core with the magnetic field aligned with the rotation axis, both analytic considerations and numerical simulations have shown that the formation of a large, $10^2\au$-scale, rotationally supported protostellar disk is suppressed by magnetic braking in the ideal MHD limit for a realistic level of core magnetization. This theoretical difficulty in forming protostellar disks is termed "magnetic braking catastrophe". A possible resolution to this proble…
It is difficult for the intermediate-mass X-ray binaries (IMXBs) evolutionary channel to form intermediate-mass binary pulsars (IMBPs) with a short orbital period (less than 3 d) via stable mass transfer. The main reason is that the magnetic braking mechanisms are generally thought not to work for donor stars with a mass of greater than 1.5 $\rm M_{\odot}$ in the canonical model. However, some intermediate-mass stars have anomalously strong magnetic fields (about 100 -- 10000 G), i. e. so-called Ap or Bp stars. With the coupling between the magnetic field and the irradiation-driven wind from t…
Testing an Ap-like Magnetic Braking Origin for the Extended Main Sequence in Young Open Clusters
School of Physics and Astronomy, Sun Yat-sen University（中山大学物理学院）；CSST Science Center for the Guangdong-Hong Kong-Macau Greater Bay Area（粤港澳大湾区空间望远镜科学中心）
The present work attempts to analytically explain the effects on the moment of inertia, $I$, caused by the evolution of stellar velocity in main-sequence stars. We have found that the effects linked to stellar oblateness can be estimated from the variation of the magnetic braking index denoted by $Δq$. We have also found that the effect of $\dot{I}$ is here a determining factor for understanding the delicate mechanisms that control the spin-down of stars in this evolutionary phase. We note that our models predict that the behaviour of the variations of the braking index is distinct when the st…
Surface magnetic fields have a strong impact on stellar mass loss and rotation and, as a consequence, on the evolution of massive stars. In this work we study the influence of an evolving dipolar surface fossil magnetic field with an initial field strength of 4 kG on the characteristics of 15 M$_{\odot}$ solar metallicity models using the Geneva stellar evolution code. Non-rotating and rotating models considering two different scenarios for internal angular momentum transport are computed, including magnetic field evolution, mass-loss quenching, and magnetic braking. Magnetic field evolution r…
We develop new angular momentum evolution models for stars with masses of $0.5$ to $1.6~\rm M_\odot$ and from the pre-main-sequence (\rm PMS) through the end of their main-sequence (\rm MS) lifetime. The parametric models include magnetic braking based on numerical simulations of magnetised stellar winds, mass loss rate prescription, core-envelope decoupling as well as disk locking phenomena. We have also accounted for recent developments in modelling dramatically weakened magnetic braking in stars more evolved than the Sun. We fit the free parameters in our model by comparing model prediction…
We use two-dimensional axisymmetric magnetohydrodynamic simulations to compute steady-state solutions for solar-like stellar winds from rotating stars with dipolar magnetic fields. Our parameter study includes 50 simulations covering a wide range of relative magnetic field strengths and rotation rates, extending from the slow- and approaching the fast-magnetic-rotator regimes. Using the simulations to compute the angular momentum loss, we derive a semi-analytic formulation for the external torque on the star that fits all of the simulations to a precision of a few percents. This formula provid…
We present a new method for constraining the mass transfer evolution of low mass X-ray binaries (LMXBs) - a reverse population synthesis technique. This is done using the detailed 1D stellar evolution code MESA (Modules for Experiments in Stellar Astrophysics) to evolve a high-resolution grid of binary systems spanning a comprehensive range of initial donor masses and orbital periods. We use the recently developed Convection And Rotation Boosted (CARB) magnetic braking scheme. The CARB magnetic braking scheme is the only magnetic braking prescription capable of reproducing an entire sample of …
The majority of stars reside in multiple systems, especially binaries. The formation and early evolution of binaries is a longstanding problem in star formation that is not fully understood. In particular, how the magnetic field observed in star-forming cores shapes the binary characteristics remains relatively unexplored. We demonstrate numerically, using the ENZO-MHD code, that a magnetic field of the observed strength can drastically change two of the basic quantities of a binary system: the orbital separation and mass ratio of the two components. Our calculations focus on the protostellar …
Black widows are millisecond pulsars with low-mass companions, a few per cent the mass of the sun, on orbits of several hours. These companions are presumably the remnants of main sequence stars that lost their mass through a combination of Roche-lobe overflow and ablation by the host pulsar's high-energy radiation. While ablation itself is too weak to significantly reduce the mass of the companion star, the ablated wind couples to its magnetic field, removes orbital angular momentum, and thus maintains stable Roche-lobe overflow. We use the MESA stellar evolution code, complemented by analyti…
We investigate whether or not the low ionisation fractions in molecular cloud cores can solve the `magnetic braking catastrophe', where magnetic fields prevent the formation of circumstellar discs around young stars. We perform three-dimensional smoothed particle non-ideal magnetohydrodynamics (MHD) simulations of the gravitational collapse of one solar mass molecular cloud cores, incorporating the effects of ambipolar diffusion, Ohmic resistivity and the Hall effect alongside a self-consistent calculation of the ionisation chemistry assuming 0.1 micron grains. When including only ambipolar di…
Using a generalized function of the stellar spin-down law, we investigate the age dependence of the magnetic braking index ($q$). Our survey includes 9 open clusters aged lower than 1 Gyr and ranged in mass from 0.7 to 1.1$M_{\odot}$. Our aim is to verify the time behavior of the nonextensive braking index $q$ which brings the cumulative distribution of the rotational velocities of the stars of the youngest cluster ($α{\rm Per}$) taken at the future age of an older cluster. As a result, the $q$-index is calculated over time $t-t_{α{\rm Per}}$, where $t$ is the age of older open cluster used to…
Anti-Solar Differential Rotation May Have Revived Magnetic Braking in the Subgiant 31 Aquilae
Center for Solar-Stellar Connections, WDRC（太阳-恒星联系中心，WDRC）；Institute for Astronomy, University of Hawai‘i（夏威夷大学天体物理研究所）；Department of Astronomy & Astrophysics, University of Chicago（芝加哥大学天文与天体物理系）；Lockheed Martin Solar and Astrophysics Laboratory（洛克希德·马丁太阳与天体物理实验室）；Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM（巴黎萨克雷大学、巴黎西岱大学、CEA、CNRS、AIM）；Department of Physics and Astronomy, Uppsala University（乌普萨拉大学物理与天文系）；Harvard-Smithsonian Center for Astrophysics（哈佛-史密森尼天体物理中心）；Vanderbilt University, Department of Physics & Astronomy（范德堡大学物理与天文系）；Department of Astronomy, Yale University（耶鲁大学天文系）；Sydney Institute for Astronomy (SIfA), School of Physics, University of Sydney（悉尼大学物理学院悉尼天体物理研究所(SIfA)）
Sun-like and low-mass stars possess high temperature coronae and lose mass in the form of stellar winds, driven by thermal pressure and complex magnetohydrodynamic processes. These magnetized outflows probably do not significantly affect the star's structural evolution on the Main Sequence, but they brake the stellar rotation by removing angular momentum, a mechanism known as magnetic braking. Previous studies have shown how the braking torque depends on magnetic field strength and geometry, stellar mass and radius, mass-loss rate, and the rotation rate of the star, assuming a fixed coronal te…
Supermassive stars (SMSs) are candidates for being progenitors of supermassive quasars at high redshifts. However, their formation process requires strong mechanisms that would be able to extract the angular momentum of the gas that the SMSs accrete. We investigate under which conditions the magnetic coupling between an accreting SMS and its winds can remove enough angular momentum for accretion to proceed from a Keplerian disc. We numerically computed the rotational properties of accreting SMSs that rotate at the $ΩΓ$-limit and estimated the magnetic field that is required to maintain the rot…
Sigma Ori E, a massive helium B-type star, shows a high surface rotation and a strong surface magnetic field potentially challenging the process of wind magnetic braking. The Gaia satellite provides an accurate distance to that star and confirms its membership to the sigma Ori cluster. We account for these two key pieces of information to investigate whether single star models can reproduce the observed properties of sigma Ori E and provide new estimates for its metallicity, mass, and age. We compute rotating stellar models accounting for wind magnetic braking and magnetic quenching of the mas…
The aim of this work is to determine the deviation of the value of magnetic braking index $q$ from Skumanich $q=3$ canonical value for giant and main-sequence stars. In this context, the present work attempts to analytically calculate the braking index based on the balance of gravitational and centrifugal forces, a determining factor for understanding the delicate mechanisms that control the spin-down of stars in these evolutionary phases. In the present study, we used a wide sample of stellar targets from the \textit{Kepler} mission with well-defined mass, radius, and rotation period. As a re…
Massive stars with solar metallicity lose important amounts of rotational angular momentum through their winds. When a magnetic field is present at the surface of a star, efficient angular momentum losses can still be achieved even when the mass-loss rate is very modest, at lower metallicities, or for lower-initial-mass stars. In a close binary system, the effect of wind magnetic braking also interacts with the influence of tides, resulting in a complex evolution of rotation. We study the interactions between the process of wind magnetic braking and tides in close binary systems. We discuss th…
We investigate the role of latitudinal differential rotation (DR) in the spin evolution of solar-type stars. Recent asteroseismic observation detected the strong equator-fast DR in some solar-type stars. Numerical simulations show that the strong equator-fast DR is a typical feature of young fast-rotating stars and that this tendency is gradually reduced with stellar age. Incorporating these properties, we develop a model for the long-term evolution of stellar rotation. The magnetic braking is assumed to be regulated dominantly by the rotation rate in the low-latitude region. Therefore, in our…
The study of lithium (Li) surface abundance in the Sun and young stellar globular clusters which are seemingly anomalous in present-day scenarios, as well as the influence of rotation and magnetic braking (MB) on its depletion during pre-main sequence (PMS) and main sequence (MS). In this work, the effects of rotational mixing and of the rotational hydrostatic effects on Li abundances are studied by simulating several grids of PMS and MS rotating and non-rotating models. Those effects are combined with the additional impact of the MB (with magnetic field intensities ranging between 3.0 and 5.0…
Spectropolarimetric Constraints on the Maunder Minimum Analog HD 166620: Evidence for Weakened Magnetic Braking
Institute for Astronomy, University of Hawai‘i at Mānoa（夏威夷大学马诺阿分校天文研究所）；Department of Physics and Astronomy, Uppsala University（乌普萨拉大学物理与天文学系）；Center for Solar-Stellar Connections, WDRC（日恒联系中心，WDRC）
Post-merger rotational evolution of magnetised single hot subdwarfs results in slow rotation due to magnetic braking
Instituto de Astrofísica de La Plata, Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET)（拉普拉塔天文物理研究所）；Facultad de Ciencias Astronómicas y Geofísicas, Universidad Nacional de La Plata (UNLP)（拉普拉塔国立大学天文与地球物理学院）；Heidelberger Institut für Theoretische Studien (HITS)（海德堡理论研究所）；London Centre for Stellar Astrophysics（伦敦恒星天体物理学中心）
Stellar winds are thought to be the main process responsible for the spin down of main-sequence stars. The extraction of angular momentum by a magnetized wind has been studied for decades, leading to several formulations for the resulting torque. However, previous studies generally consider simple dipole or split monopole stellar magnetic topologies. Here we consider in addition to a dipolar stellar magnetic field, both quadrupolar and octupolar configurations, while also varying the rotation rate and the magnetic field strength. 60 simulations made with a 2.5D, cylindrical and axisymmetric se…
A knowledge of stellar ages is crucial for our understanding of many astrophysical phenomena, and yet ages can be difficult to determine. As they become older, stars lose mass and angular momentum, resulting in an observed slowdown in surface rotation. The technique of 'gyrochronology' uses the rotation period of a star to calculate its age. However, stars of known age must be used for calibration, and, until recently, the approach was untested for old stars (older than 1 gigayear, Gyr). Rotation periods are now known for stars in an open cluster of intermediate age (NGC 6819; 2.5 Gyr old), an…
It is generally believed that Ultracompact X-ray binaries (UCXBs) evolved from binaries consisting of a neutron star accreting from a low-mass white dwarf or helium star where mass transfer is driven by gravitational radiation. However, the standard white-dwarf evolutionary channel cannot produce the relatively long-period ($40 - 60$\,min) UCXBs with high time-averaged mass-transfer rate. In this work, we explore an alternative evolutionary route toward UCXBs where the companions evolve from intermediate-mass Ap/Bp stars with an anomalously strong magnetic field ($100 - 10000$\,G). Including t…
Stellar winds are thought to be the main process responsible for the spin down of main-sequence stars. The extraction of angular momentum by a magnetized wind has been studied for decades, leading to several formulations for the resulting torque. However, previous studies generally consider simple dipole or split monopole stellar magnetic topologies. Here we consider in addition to a dipolar stellar magnetic field, both quadrupolar and octupolar configurations, while also varying the rotation rate and the magnetic field strength. 60 simulations made with a 2.5D, cylindrical and axisymmetric se…
We present collapse simulations of strongly magnetised, 100 M_sun, turbulent cloud cores. Around the protostars formed during the collapse Keplerian discs with typical sizes of up to 100 AU build up in contrast to previous simulations neglecting turbulence. Analysing the condensations in which the discs form, we show that the magnetic flux loss is not sufficient to explain the build-up of Keplerian discs. The average magnetic field is strongly inclined to the disc which might reduce the magnetic braking efficiency. However, the main reason for the reduced magnetic braking efficiency is the hig…
Magnetic configurations, stable on the long term, appear to exist in various evolutionary phases, from Main-Sequence stars to white dwarfs and neutron stars. The large scale ordered nature of these fields, often approximately dipolar, and their scaling according to the flux conservation scenario favor the model of a fossil field (Duez et al. 2010). We make some first estimates of the magnetic coupling between the stellar cores and the outer layers in red giants and supergiants. Analytical expressions of the truncation radius of the field coupling are established for a convective envelope and f…
Sco X-1 is the brightest persistent X-ray in the sky. It is generally believed that Sco X-1 is a low-mass X-ray binary containing a neutron star accreting from a low-mass donor star where mass transfer is driven by the magnetic braking. However, the mass transfer rate predicted by the standard magnetic braking model is at least one order of magnitude lower than the one inferred by X-ray luminosity. In this work, we investigate whether this source could evolved from an intermediate-mass X-ray binary including Ap/Bp stars with a slightly strong magnetic field of 300 - 1000 G. The coupling betwee…
Collapsing magnetic traps (CMTs) are one proposed mechanism for generating non-thermal particle populations in solar flares. CMTs occur if an initially stretched magnetic field structure relaxes rapidly into a lower-energy configuration, which is believed to happen as a by-product of magnetic reconnection. A similar mechanism for energising particles has also been found to operate in the Earth's magnetotail. One particular feature proposed to be of importance for particle acceleration in the magnetotail is that of a braking plasma jet, i.e. a localised region of strong flow encountering strong…
We study the role of time dependent magnetic ellipticities ($ε_{B}$) on the calculation of the braking index of pulsars. Moreover, we study the consequences of such a $ε_{B}$ on the amplitude of gravitational waves (GWs) generated by pulsars with measured braking indices. We show that, since the ellipticity generated by the magnetic dipole is extremely small, the corresponding amplitude of GWs is much smaller than the amplitude obtained via the spindown limit.
I report on two new measures of the sudden change in the orbital period ($P$) across the nova eruption ($Δ$P) and the steady period change in quiescence ($\dot{P}$) for classical novae (CNe) RR Pic and HR Del, bringing a total of six such measures for CNe, all in a final report of my large and long observing program. The fractional changes ($Δ$P/P) in parts-per-million (ppm) are -290.71$\pm$0.28 (QZ Aur), -472.1$\pm$4.8 (HR Del), -4.46$\pm$0.03 (DQ Her), +39.6$\pm$0.5 (BT Mon), -2003.7$\pm$0.9 (RR Pic), and -273$\pm$61 (V1017 Sgr). These results are in stark opposition to the Hibernation Model…
The rotation rates of main-sequence stars slow over time as they gradually lose angular momentum to their magnetized stellar winds. The rate of angular momentum loss depends on the strength and morphology of the magnetic field, the mass-loss rate, and the stellar rotation period, mass, and radius. Previous observations suggested a shift in magnetic morphology between two F-type stars with similar rotation rates but very different ages (88 Leo and rho CrB). In this Letter, we identify a comparable transition in an evolutionary sequence of solar analogs with ages between 2-7 Gyr. We present new …
