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Spin and Magnetism of White Dwarfs
Abstract
The magnetism and rotation of white dwarf (WD) stars are investigated in
relation to a hydromagnetic dynamo operating in the progenitor during shell
burning phases. We find that the downward pumping of angular momentum in the
convective envelope can, by itself, trigger dynamo action near the
core-envelope boundary in an isolated intermediate-mass star. A solar-mass star
must receive additional angular momentum following its rotational braking on
the main sequence, either by a merger with a planet, or by tidal interaction in
a stellar binary. Several arguments point to the outer core as the source for a
magnetic field in the WD remnant: i) the outer third of a ~0.55$M_\odot$ WD is
processed during the shell burning phases of the progenitor; ii) escape of
magnetic helicity through the envelope mediates the growth of (compensating)
helicity in the core, as is needed to maintain a stable magnetic field in the
remnant; and iii) intense radiation flux at the core boundary facilitates
magnetic buoyancy within a relatively thick tachocline layer. The helicity flux
into the core is dominated by a persistent magnetic twist, which maintains
solid rotation in the core against a latitude-dependent convective stress. The
magnetic field deposited in an isolated massive WD can reach ~10MG, and is
enhanced in strength if the star experiences an interaction with a brown dwarf
or low-mass star. A buried toroidal field experiences moderate ohmic decay
above an age ~1 Gyr, which may lead to growth or decay of the external magnetic
field. The final WD spin period is related to a critical Coriolis parameter
below which magnetic activity shuts off, and core and envelope decouple; it
generally sits in the range of hours to days. A wider range of spin periods is
possible when the star spins rapidly enough that core and envelope remain
magnetically coupled, ranging from less than a day up to a year. (abridged)
... again, assuming experimental precision of 1 part per 10 n , e.g. for n = 2, where we used B = B tacho ≈ 4.1 · 10 3 T ≈ 8 · 10 −12 GeV 2 , L = L tacho 10 2 km ≈ 10 21 GeV −1 , where L tacho is the thickness of the tachocline in the magnetic white dwarf (Kissin and Thompson, 2015). The total bound on l n (∆x) min = α 0 l P l (see Eq. (127)) reads: (144)). ...
... Accordingly, the repulsive magnetic field of the tachocline exactly "neutralizes" the magnetic field in white dwarfs (see Eq. (A.18) and the analog of (Kissin and Thompson, 2015)): ...
... Let us consider some properties of the anchored twisted MFTs depending on the toroidal field in the tachocline through the shear flows instability development (see analogous Fig. 6a,b). The complete cooling of the O-loop inside the twisted magnetic tube near the tachocline leads to production of the γ-quanta of axion origin with the probability P W D a→γ = 1 4 (g aγ B M S L M S ) 2 < 0.022, (A.19) where g aγ = 4.4 · 10 −11 GeV −1 is the hadron axion coupling constant to photons (see Eq. A.3), B M S B z ≈ B tacho is the horizontal magnetic field of the O-loop (see Fig. 6a), L M S < d is the height of the magnetic shear steps, d 100 km is the thickness of the tachocline in magnetic white dwarfs (Kissin and Thompson, 2015). ...
It is shown that the holographic principle of quantum gravity (in the hologram of the Universe, and therefore in our Galaxy, and of course on the Sun!), in which the conflict between the theory of gravitation and quantum mechanics disappears, gives rise to the Babcock-Leighton holographic mechanism. Unlike the solar dynamo models, it generates a strong toroidal magnetic field by means of the thermomagnetic Ettingshausen-Nernst (EN) effect in the tachocline. Hence, it can be shown that with the help of the thermomagnetic EN effect, a simple estimate of the magnetic pressure of an ideal gas in the tachocline of e.g. the Sun can indirectly prove that by using the holographic principle of quantum gravity, the repulsive toroidal magnetic field of the tachocline ($B_{tacho}^{Sun} = 4.1 \cdot 10^7 ~G = - B_{core}^{Sun}$) precisely "neutralizes" the magnetic field in the Sun core, since the projections of the magnetic fields in the tachocline and the core have equal values but opposite directions. The basic problem is a generalized problem of the antidynamo model of magnetic flux tubes (MFTs), where the nature of both holographic effects (the thermomagnetic EN~effect and Babcock-Leighton holographic mechanism), including magnetic cycles, manifests itself in the modulation of asymmetric dark matter (WIMP ADM) and, consequently, the solar axion in the Sun interior.
... One of the key developments was the recognition that magnetic white dwarfs are nearly exclusively found as isolated stars, or in cataclysmic variables (Liebert et al. 2005). This empirical finding led to the hypothesis that fields are generated during common envelope evolution (Tout et al. 2008;Nordhaus et al. 2011;Belloni & Schreiber 2020), a process that may function effectively for stars, brown dwarfs, and giant planets that are engulfed during the post-main sequence (Farihi et al. 2011;Kissin & Thompson Farihi et al. where the principal findings can be summarized as follows. ...
This paper reports the ULTRACAM discovery of dipolar surface spots in two cool magnetic white dwarfs with Balmer emission lines, while a third system exhibits a single spot, similar to the prototype GD 356. The light curves are modeled with simple, circular, isothermal dark spots, yielding relatively large regions with minimum angular radii of 20○. For those stars with two light curve minima, the dual spots are likely observed at high inclination (or colatitude), however, identical and antipodal spots cannot simultaneously reproduce both the distinct minima depths and the phases of the light curve maxima. The amplitudes of the multi-band photometric variability reported here are all several times larger than that observed in the prototype GD 356; nevertheless, all DAHe stars with available data appear to have light curve amplitudes that increase toward the blue in correlated ratios. This behavior is consistent with cool spots that produce higher contrasts at shorter wavelengths, with remarkably similar spectral properties given the diversity of magnetic field strengths and rotation rates. These findings support the interpretation that some magnetic white dwarfs generate intrinsic chromospheres as they cool, and that no external source is responsible for the observed temperature inversion. Spectroscopic time-series data for DAHe stars is paramount for further characterization, where it is important to obtain well-sampled data, and consider wavelength shifts, equivalent widths, and spectropolarimetry.
... One of the key developments was the recognition that magnetic white dwarfs are nearly exclusively found as isolated stars, or in cataclysmic variables (Liebert et al. 2005). This empirical finding led to the hypothesis that fields are generated during common envelope evolution (Tout et al. 2008;Nordhaus et al. 2011;Belloni & Schreiber 2020), a process that may function effectively for stars, brown dwarfs, and giant planets that are engulfed during the post-main sequence (Farihi et al. 2011;Kissin & Thompson 2015;Guidarelli et al. 2019). And while fast-spinning and massive magnetic white dwarfs are known, and thus consistent with a stellar merger origin (Ferrario et al. 1997b;García-Berro et al. 2012;Kilic et al. 2021;Williams et al. 2022), it is also clear that magnetism, high remnant mass, and rapid rotation are far from tightly correlated (Ferrario & Wickramasinghe 2005;Brinkworth et al. 2013). ...
This paper reports the ULTRACAM discovery of dipolar surface spots in two cool magnetic white dwarfs with Balmer emission lines, while a third system exhibits a single spot, similar to the prototype GD 356. The light curves are modeled with simple, circular, isothermal dark spots, yielding relatively large regions with minimum angular radii of 20 deg. For those stars with two light curve minima, the dual spots are likely observed at high inclination (or colatitude), however, identical and antipodal spots cannot simultaneously reproduce both the distinct minima depths and the phases of the light curve maxima. The amplitudes of the multi-band photometric variability reported here are all several times larger than that observed in the prototype GD 356; nevertheless, all DAHe stars with available data appear to have light curve amplitudes that increase toward the blue in correlated ratios. This behavior is consistent with cool spots that produce higher contrasts at shorter wavelengths, with remarkably similar spectral properties given the diversity of magnetic field strengths and rotation rates. These findings support the interpretation that some magnetic white dwarfs generate intrinsic chromospheres as they cool, and that no external source is responsible for the observed temperature inversion. Spectroscopic time-series data for DAHe stars is paramount for further characterization, where it is important to obtain well-sampled data, and consider wavelength shifts, equivalent widths, and spectropolarimetry.
... One possible field origin may be the magnetic fields apparently detected by using asteroseismology tools on Kepler photometry (Stello et al. 2016) in the cores of some red giants. Another possible source could be a dynamo operating in a shell undergoing fusion (Kissin & Thompson 2015). In contrast, the nearly total lack of fields in the youngest normal-mass WDs may pose a serious problem for one of the oldest theories of WD field origins, the retention (freezing) and amplification of the magnetic flux observed in the atmospheres of the Table 2. Empty circles represent WDs in which no magnetic field was detected. ...
The presence of a strong magnetic field is a feature common to a significant fraction of degenerate stars, yet little is understood about the field’s origin and evolution. New observational constraints from volume-limited surveys point to a more complex situation than a single mechanism valid for all stars. We show that in high-mass white dwarfs, which are probably the results of mergers, magnetic fields are extremely common and very strong and appear immediately in the cooling phase. These fields may have been generated by a dynamo active during the merging. Lower-mass white dwarfs, which are often the product of single-star evolution, are rarely detectably magnetic at birth, but fields appear very slowly, and very weakly, in about a quarter of them. What we may see is an internal field produced in an earlier evolutionary stage that gradually relaxes to the surface from the interior. The frequency and strength of magnetic fields continue to increase to eventually rival those of highly massive stars, particularly after the stars cool past the start of core crystallization, an effect that could be responsible for a dynamo mechanism similar to the one that is active in Earth’s interior.
... One possible field origin may be the magnetic fields apparently detected by using asteroseismology tools on Kepler photometry (Stello et al. 2016) in the cores of some red giants. Another possible source could be a dynamo operating in a shell undergoing fusion (Kissin & Thompson 2015). In contrast, the nearly total lack of fields in the youngest normal-mass WDs may pose a serious problem for one of the oldest theories of WD field origins, the retention (freezing) and amplification of the magnetic flux observed in the atmospheres of the (chemically peculiar) Ap and Bp main sequence stars (Woltjer 1964;Landstreet 1967;Angel et al. 1981). ...
The presence of a strong magnetic field is a feature common to a significant fraction of degenerate stars, yet little is understood about field origin and evolution. New observational constraints from volume-limited surveys point to a more complex situation than a single mechanism valid for all stars. We show that in high-mass white dwarfs, which are probably the results of mergers, magnetic fields are extremely common and very strong, and appear immediately in the cooling phase. These fields may have been generated by a dynamo active during the merging. Lower mass white dwarfs, which are often the product of single star evolution, are rarely detectably magnetic at birth, but fields appear very slowly, and very weakly, in about a quarter of them. What we may see is an internal field produced in an earlier evolutionary stage that gradually relaxes to the surface from the interior. The frequency and strength of magnetic fields continue to increase to eventually rival those of highly-massive stars, particularly after the stars cool past the start of core crystallisation, an effect that could be responsible for a dynamo mechanism similar to the one that is active in Earth's interior.
... The results for the macroscale generated hot outflow coincide for different ambient temperatures are displayed for two limiting ambient system cases: a = 2.5 (cyan, orange -magnetically dominant entire system) and a = 10 (blue, green -magnetically dominant degenerate fluid) for a degenerate fluid (left column) and for a hot relativistic fluid (right column) -the larger the H 0 the smaller is the maximal value for all scales in both fluids netic fields in the envelope phase of star accretion, for instance cases of intermediate-field WDs found in CVs and some HFMWDs are argued to be formed through interface dynamo/disk dynamo processes (Tout et al. 2008;Nordhaus et al. 2010). We remind the reader that such a combined scenario is absent in the pure degenerate e-i case for the primarily magnetic ambient system, hence, such a possibility is entirely due to the hot contamination found in accreting stars/binary systems; the unified Dynamo/RD scenario was found for a degenerate e-i system only for a kinetic ambient system argued to explain the core-dynamo (Ruderman and Sutherland 1973;Kissin and Thompson 2015) formation of magnetic fields of HFMWDs (Kotorashvili et al. 2020). Interestingly, the existence of super-Alfvénic large-scale hot flows for our composite system (with different solutions of dispersion relations coexisting in both fluids) may explain the formation of transient jets fed by short-scale fluctuations of both fluids that follow Dynamo -a well-established path of Unified Dynamo/Reverse Dynamo. ...
We have shown the simultaneous generation of macroscale fast flows and strong magnetic fields in the two-temperature relativistic electron–ion plasmas of astrophysical objects due to the Unified Reverse Dynamo/Dynamo mechanism. The resulting dynamical magnetic-field amplification and/or flow acceleration is directly proportional to the initial turbulent kinetic/magnetic (magnetic) energy; the process is very sensitive to the relativistically hot electron–ion fraction temperature and the magnetofluid coupling. It is shown that for realistic physical parameters of White Dwarfs accreting hot astrophysical flow /Binary systems there always exists such a real solution of the dispersion relation for which the formation of dispersive strong super-Alfvénic macroscale flow/outflow with Alfvén–Mach number \(> 10^{6}\) and/or generation of superstrong magnetic fields is guaranteed.
... Field generation based on a dynamo operating in the region outside the core in a star powered by nuclear fusion in shells, possibly stimulated by the angular momentum added by ingestion of a planet, is discussed by Kissin & Thompson (2015). The resulting field can reach 10 MG. ...
Many stars evolve into magnetic white dwarfs, and observations may help to understand when the magnetic field appears at the stellar surface, if and how it evolves during the cooling phase, and, above all, what are the mechanisms that generate it. After obtaining new spectropolarimetric observations and combining them with previous literature data, we have checked almost the entire population of about 152 white dwarfs within 20 pc from the Sun for the presence of magnetic fields, with a sensitivity that ranges from better than 1 kG for most of the stars of spectral class DA, to 1 MG for some of the featureless white dwarfs. We find that 33 white dwarfs of the local 20 pc volume are magnetic. Statistically, the data are consistent with the possibility that the frequency of the magnetic field occurrence is similar in stars of all spectral classes, except that in the local 20 pc volume, either DQ stars are more frequently magnetic, or host much stronger fields than average. The distribution of the observed field strength ranges from 40 kG to 300 MG and is uniform per decade, in striking contrast to the field frequency distribution resulting from spectroscopic surveys. Remarkably, no fields weaker than 40 kG are found. We confirm that magnetic fields are more frequent in white dwarfs with higher than average mass, especially in younger stars. We find a marked deficiency of magnetic white dwarfs younger than 0.5 Gyr, and we find that the frequency of the occurrence of the magnetic field is significantly higher in white dwarfs that have undergone the process of core crystallisation than in white dwarfs with fully liquid core. There is no obvious evidence of field strength decay with time. We discuss the implications of our findings in relation to some of the proposals that have been put forward to explain the origin and evolution of magnetic fields in degenerate stars, in particular those that predict the presence of a dynamo acting during the crystallisation phase.
... The residue perhaps also is manifest in the resulting change of magnetic field strength (Farihi et al. 2011;Kissin & Thompson 2015). The Gaia-SDSS spectroscopic white dwarf catalogue in Gentile Fusillo et al. (2019) reveals that up to 50 per cent of white dwarfs whose progenitors had masses of 6-8 M have magnetic fields above the typical 1 MG detection limit (Kepler et al. 2013). ...
Identifying planets around O-type and B-type stars is inherently difficult; the most massive known planet host has a mass of only about $3\, \mathrm{M}_{\odot }$. However, planetary systems which survive the transformation of their host stars into white dwarfs can be detected via photospheric trace metals, circumstellar dusty and gaseous discs, and transits of planetary debris crossing our line of sight. These signatures offer the potential to explore the efficiency of planet formation for host stars with masses up to the core-collapse boundary at $\approx 8\, \mathrm{M}_{\odot }$, a mass regime rarely investigated in planet formation theory. Here, we establish limits on where both major and minor planets must reside around $\approx 6\rm {-}8\, \mathrm{M}_{\odot }$ stars in order to survive into the white dwarf phase. For this mass range, we find that intact terrestrial or giant planets need to leave the main sequence beyond approximate minimum star–planet separations of, respectively, about 3 and 6 au. In these systems, rubble pile minor planets of radii 10, 1.0, and 0.1 km would have been shorn apart by giant branch radiative YORP spin-up if they formed and remained within, respectively, tens, hundreds, and thousands of au. These boundary values would help distinguish the nature of the progenitor of metal pollution in white dwarf atmospheres. We find that planet formation around the highest mass white dwarf progenitors may be feasible, and hence encourage both dedicated planet formation investigations for these systems and spectroscopic analyses of the highest mass white dwarfs.
... Asteroseismic observations appear to disfavor envelope differential rotation (Di Mauro et al. 2016;Klion & Quataert 2017;Di Mauro et al. 2018), though currently their ability to distinguish between the models is limited. Both models may have some tension with observations, as Kissin & Thompson (2015a) predict rotation rates that are too slow for low-mass (M 1.2M ) RGB stars, and Kissin & Thompson (2015b) appear to predict anomalously slow rotation rates for some WDs. ...
The angular momentum (AM) evolution of stellar interiors, along with the resulting rotation rates of stellar remnants, remains poorly understood. Asteroseismic measurements of red giant stars reveal that their cores rotate much faster than their surfaces, but much slower than theoretically predicted, indicating an unidentified source of AM transport operates in their radiative cores. Motivated by this, we investigate the magnetic Tayler instability and argue that it saturates when turbulent dissipation of the perturbed magnetic field energy is equal to magnetic energy generation via winding. This leads to larger magnetic field amplitudes, more efficient AM transport, and smaller shears than predicted by the classic Tayler–Spruit dynamo. We provide prescriptions for the effective AM diffusivity and incorporate them into numerical stellar models, finding they largely reproduce (1) the nearly rigid rotation of the Sun and main sequence stars, (2) the core rotation rates of low-mass red giants during hydrogen shell and helium burning, and (3) the rotation rates of white dwarfs. We discuss implications for stellar rotational evolution, internal rotation profiles, rotational mixing, and the spins of compact objects.
... Asteroseismic observations appear to disfavor envelope differential rotation (Di Mauro et al. 2016;Klion & Quataert 2017;Di Mauro et al. 2018), though currently their ability to distinguish between the models is limited. Both models may have some tension with observations, as Kissin & Thompson (2015a) predicts rotation rates that are too slow for low-mass (M 1.2M ) RGB stars, and Kissin & Thompson (2015b) appear to predict anomalously slow rotation rates for some white dwarfs. ...
The angular momentum (AM) evolution of stellar interiors, along with the resulting rotation rates of stellar remnants, remains poorly understood. Asteroseismic measurements of red giant stars reveal that their cores rotate much faster than their surfaces, but much slower than theoretically predicted, indicating an unidentified source of AM transport operates in their radiative cores. Motivated by this, we investigate the magnetic Tayler instability and argue that it saturates when turbulent dissipation of the perturbed magnetic field energy is equal to magnetic energy generation via winding. This leads to larger magnetic field amplitudes, more efficient AM transport, and smaller shears than predicted by the classic Tayler-Spruit dynamo. We provide prescriptions for the effective AM diffusivity and incorporate them into numerical stellar models, finding they largely reproduce (1) the nearly rigid rotation of the Sun and main sequence stars, (2) the core rotation rates of low-mass red giants during hydrogen shell and helium burning, and (3) the rotation rates of white dwarfs. We discuss implications for stellar rotational evolution, internal rotation profiles, rotational mixing, and the spins of compact objects.
Context. Theoretical works have looked into the various topologies and amplitudes, as well as the stability of the magnetic field that is expected to be present in the radiative interior of stars evolving after the main sequence. From these studies, we know that strong stable “fossil” fields might be trapped inside evolved stars. These could trigger the strong transport of angular momentum from the core to the envelope, a process that is not generally included in state-of-the-art stellar models. This may therefore have a substantial impact on the mixing and the inferred stellar parameters. Such internal magnetic fields have never been observed in evolved stars. As a result, there is a major piece missing from our global picture of stars as dynamical bodies.
Aims. Asteroseismology has opened a window onto stellar internal dynamics, as oscillation frequencies, amplitudes, and lifetimes are affected by processes that are taking place inside the star. The detection of buried magnetic fields could therefore be possible through the measurement of their impact on the oscillations of stars. This advancement would be groundbreaking for our knowledge of stellar dynamics. In this scope, magnetic signatures on mixed-mode frequencies have recently been characterized, but the task of detection remains challenging as the mixed-mode frequency pattern is highly complex and affected by rotational effects, while modes of different radial orders are often intertwined. In this work, we aim to build a bridge between theoretical prescriptions and complex asteroseismic data analysis to facilitate a future search and characterization of internal magnetism with asteroseismology.
Methods. We investigated the effect of magnetic fields inside evolved stars with solar-like oscillations on the estimation of the period spacing of gravity-mode (g-mode) components of simulated mixed gravito-acoustic modes. We derived a new corrected stretching function of the power spectrum density to account for the presence of magnetic signatures on their frequencies.
Results. We demonstrate that the strong dependency of the amplitude of the magnetic signature with mixed-mode frequencies leads to biased estimates of period spacings towards lower values. We also show that a careful analysis of the oscillation frequency pattern through various period spacing estimates and across a broad frequency range might lead to the first detection of magnetic fields inside red giants and at the same time, we adjust the measured value of g-mode period spacing.
We investigate the effects of mass transfer and gravitational wave (GW) radiation on the orbital evolution of contact neutron-star-white-dwarf (NS-WD) binaries, and the detectability of these binaries by space GW detectors (e.g., Laser Interferometer Space Antenna, LISA; Taiji; Tianqin). A NS-WD binary becomes contact when the WD component fills its Roche lobe, at which the GW frequency ranges from ∼0.0023 to 0.72 Hz for WD with masses ∼0.05 − 1.4M⊙. We find that some high-mass NS-WD binaries may undergo direct coalescence after unstable mass transfer. However, the majority of NS-WD binaries can avoid direct coalescence because mass transfer after contact can lead to a reversal of the orbital evolution. Our model can well interpret the orbital evolution of the ultra-compact X-ray source 4U 1820–30. For a 4-year observation of 4U 1820–30, the expected signal-to-noise-ratio (SNR) in GW characteristic strain is ∼11.0/10.4/2.2 (LISA/Taiji/Tianqin). The evolution of GW frequencies of NS-WD binaries depends on the WD masses. NS-WD binaries with masses larger than 4U 1820–30 are expected to be detected with significantly larger SNRs. For a (1.4 + 0.5)M⊙ NS-WD binary close to contact, the expected SNR for a one week observation is ∼27/40/28 (LISA/Taiji/Tianqin). For NS-WD binaries with masses of (1.4 + ≳1.1)M⊙, the significant change of GW frequencies and amplitudes can be measured, and thus it is possible to determine the binary evolution stage. At distances up to the edge of the Galaxy (∼100 kpc), high-mass NS-WD binaries will be still detectable with SNR≳1.
A significant fraction of white dwarfs possess a magnetic field with strengths ranging from a few kG up to about 1000 MG. However, the incidence of magnetism varies when the white dwarf population is broken down into different spectral types providing clues on the formation of magnetic fields in white dwarfs. Several scenarios for the origin of magnetic fields have been proposed from a fossil field origin to dynamo generation at various stages of evolution. Offset dipoles are often assumed sufficient to model the field structure, however time-resolved spectropolarimetric observations have revealed more complex structures such as magnetic spots or multipoles. Surface mapping of these field structures combined with measured rotation rates help distinguish scenarios involving single star evolution from other scenarios involving binary interactions. I describe key observational properties of magnetic white dwarfs such as age, mass, and field strength, and confront proposed formation scenarios with these properties.
We present an analysis of photometric, spectroscopic and spectropolarimetric data of the nearby, cool, magnetic DZ white dwarf PM J08186−3110. High dispersion spectra show the presence of Zeeman splitted spectral lines due to the presence of a surface average magnetic field of 92 kG. The strong magnesium and calcium lines show extended wings shaped by interactions with neutral helium in a dense, cool helium-rich atmosphere. We found that the abundance of heavy elements varied between spectra taken ten years apart but we could not establish a time-scale for these variations; such variations may be linked to surface abundance variations in the magnetized atmosphere. Finally, we show that volume limited samples reveal that about 40% of DZ white dwarfs with effective temperatures below 7000 K are magnetic.
We have shown the generation/amplification of fast macro-scale plasma flows in the degenerate two-fluid astrophysical systems with initial turbulent (micro-scale) magnetic/velocity fields due to the Unified Reverse Dynamo/Dynamo mechanism. This process is simultaneous with and complementary to the micro-scale unified dynamo. It is found that the generation of macro-scale flows is an essential consequence of the magneto-fluid coupling; the generation of macro-scale fast flows and magnetic fields are simultaneous, they grow proportionately. The resulting dynamical flow acceleration is directly proportional to the initial turbulent magnetic (kinetic/magnetic) energy in degenerate e-i (degenerate e-p) astrophysical plasma; the process is very sensitive to both the degeneracy level of the system and the magneto-fluid coupling. In case of degenerate e-p plasma, for realistic physical parameters, there always exists such a real solution of dispersion relation for which the formation of strong macro-scale flow/outflow is guaranteed; the generated/accelerated locally super-Alfvénic flows are extremely fast with Alfvén Mach number >103\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$> 10^{3}$\end{document} as observed in a variety of astrophysical outflows.
We report the discovery of a nearby massive white dwarf with He–H atmosphere. The white dwarf is located at a distance of 74.5 ± 0.9 pc. Its radius, mass, effective temperature, H/He ratio, and age are R = 2500 ± 100 km, M = 1.33 ± 0.01 M⊙, Teff = 31 200 ± 1200 K, H/He ∼ 0.1, and 330 ± 40 Myr, respectively. The observed spectrum is redshifted by Vr = +240 ± 15 km s−1, which is mostly attributed to the gravitational redshift. The white dwarf shows a regular stable photometric variability with amplitude Δg ≈ 0.06m and period P = 353.456 s suggesting rapid rotation. This massive, hot, and rapidly rotating white dwarf is likely to originate from the merging of close binary white dwarf system that avoided explosion in a thermonuclear Type Ia supernova.
This paper reports circular spectropolarimetry and X-ray observations of several polluted white dwarfs including WD 1145+017, with the aim to constrain the behavior of disk material and instantaneous accretion rates in these evolved planetary systems. Two stars with previously observed Zeeman splitting, WD 0322-019 and WD 2105-820, are detected above 5 sigma and > 1 kG, while WD 1145+017, WD 1929+011, and WD 2326+049 yield (null) detections below this minimum level of confidence. For these latter three stars, high-resolution spectra and atmospheric modeling are used to obtain limits on magnetic field strengths via the absence of Zeeman splitting, finding B* < 20 kG based on data with resolving power R near 40 000. An analytical framework is presented for bulk Earth composition material falling onto the magnetic polar regions of white dwarfs, where X-rays and cyclotron radiation may contribute to accretion luminosity. This analysis is applied to X-ray data for WD 1145+017, WD 1729+371, and WD 2326+049, and the upper bound count rates are modeled with spectra for a range of plasma kT = 1 - 10 keV in both the magnetic and non-magnetic accretion regimes. The results for all three stars are consistent with a typical dusty white dwarf in a steady-state at 1e8 - 1e9 g/s. In particular, the non-magnetic limits for WD 1145+017 are found to be well below previous estimates of up to 1e12 g/s, and likely below 1e10 g/s, thus suggesting the star-disk system may be average in its evolutionary state, and only special in viewing geometry.
The internal rotation and magnetism of evolved massive stars are considered in response to i) the inward pumping of angular momentum through deep and slowly rotating convective layers; and ii) the winding up of a helical magnetic field in radiative layers. Field winding can transport angular momentum effectively even when the toroidal field is limited by kinking. Magnetic helicity is pumped into a growing radiative layer from an adjacent convective envelope (or core). The receding convective envelope that forms during the early accretion phase of a massive star is the dominant source of helicity in its core, yielding a $\sim 10^{13}$ G polar magnetic field in a collapsed neutron star (NS) remnant. Using MESA models of various masses, we find that the NS rotation varies significantly, from $P_{\rm NS} \sim 0.1-1$ s in a 13$\,M_\odot$ model to $P_{\rm NS} \sim 2$ ms in a $25\,M_\odot$ model with an extended core. Stronger inward pumping of angular momentum is found in more massive stars, due to the growing thickness of the convective shells that form during the later stages of thermonuclear burning. On the other hand, stars that lose enough mass to form blue supergiants in isolation end up as very slow rotators. The tidal spin-up of a 40$\,M_\odot$ star by a massive binary companion is found to dramatically increase the spin of the remnant black hole, allowing a rotationally supported torus to form during the collapse. The implications for post-collapse decay or amplification of the magnetic field are also considered.
We present the first radiation magnetohydrodynamics simulations of the
atmosphere of white dwarf stars. We demonstrate that convective energy transfer
is seriously impeded by magnetic fields when the plasma-beta parameter, the
thermal to magnetic pressure ratio, becomes smaller than unity. The critical
field strength that inhibits convection in the photosphere of white dwarfs is
in the range B = 1-50 kG, which is much smaller than the typical 1-1000 MG
field strengths observed in magnetic white dwarfs, implying that these objects
have radiative atmospheres. We have then employed evolutionary models to study
the cooling process of high-field magnetic white dwarfs, where convection is
entirely suppressed during the full evolution (B > 10 MG). We find that the
inhibition of convection has no effect on cooling rates until the effective
temperature (Teff) reaches a value of around 5500 K. In this regime, the
standard convective sequences start to deviate from the ones without convection
owing to the convective coupling between the outer layers and the degenerate
reservoir of thermal energy. Since no magnetic white dwarfs are currently known
at the low temperatures where this coupling significantly changes the
evolution, effects of magnetism on cooling rates are not expected to be
observed. This result contrasts with a recent suggestion that magnetic white
dwarfs with Teff < 10,000 K cool significantly slower than non-magnetic
degenerates.
The internal rotation of post-main sequence stars is investigated, in
response to the convective pumping of angular momentum toward the stellar core,
combined with a tight magnetic coupling between core and envelope. The spin
evolution is calculated using model stars of initial mass 1, 1.5 and
$5\,M_\odot$, taking into account mass loss on the giant branches and the
partitioning of angular momentum between the outer and inner envelope. We also
include the deposition of orbital angular momentum from a sub-stellar
companion, as influenced by tidal drag as well as the excitation of orbital
eccentricity by a fluctuating gravitational quadrupole moment. A range of
angular velocity profiles $\Omega(r)$ is considered in the deep convective
envelope, ranging from solid rotation to constant specific angular momentum. We
focus on the backreaction of the Coriolis force on the inward pumping of
angular momentum, and the threshold for dynamo action in the inner envelope.
Quantitative agreement with measurements of core rotation in subgiants and
post-He core flash stars by Kepler is obtained with a two-layer angular
velocity profile: uniform specific angular momentum where the Coriolis
parameter ${\rm Co} \equiv \Omega \tau_{\rm con} \lesssim 1$ (here $\tau_{\rm
con}$ is the convective time); and $\Omega(r) \propto r^{-1}$ where ${\rm Co}
\gtrsim 1$. The inner profile is interpreted in terms of a balance between the
Coriolis force and angular pressure gradients driven by the convective cell
structure. Including the effect of angular momentum pumping on the surface
rotation of subgiants also reduces the need for an additional magnetic wind
torque. The co-evolution of internal magnetic fields and rotation is considered
in Paper II, where we explain when and how a strong core-envelope coupling is
established, and how it may break down as the result of stellar mass loss.
We investigate the magnetic field at the surface of 48 red giants selected as
promising for detection of Stokes V Zeeman signatures in their spectral lines.
We use the spectropolarimeters Narval and ESPaDOnS to detect circular
polarization within the photospheric absorption lines of our targets and use
the least-squares deconvolution (LSD) method. We also measure the classical
S-index activity indicator, and the stellar radial velocity. To infer the
evolutionary status of our giants and to interpret our results, we use
state-of-the-art stellar evolutionary models with predictions of convective
turnover times. We unambiguously detect magnetic fields via Zeeman signatures
in 29 of the 48 red giants in our sample. Zeeman signatures are found in all
but one of the 24 red giants exhibiting signs of activity, as well as 6 out of
17 bright giant stars.The majority of the magnetically detected giants are
either in the first dredge up phase or at the beginning of core He burning,
i.e. phases when the convective turnover time is at a maximum: this corresponds
to a 'magnetic strip' for red giants in the Hertzsprung-Russell diagram. A
close study of the 16 giants with known rotational periods shows that the
measured magnetic field strength is tightly correlated with the rotational
properties, namely to the rotational period and to the Rossby number Ro. Our
results show that the magnetic fields of these giants are produced by a dynamo.
Four stars for which the magnetic field is measured to be outstandingly strong
with respect to that expected from the rotational period/magnetic field
relation or their evolutionary status are interpreted as being probable
descendants of magnetic Ap stars. In addition to the weak-field giant Pollux, 4
bright giants (Aldebaran, Alphard, Arcturus, eta Psc) are detected with
magnetic field strength at the sub-gauss level.
Observations of late-type main-sequence stars have revealed empirical scalings of coronal activity versus rotation period
or Rossby number Ro (a ratio of rotation period to convective turnover time) which has hitherto lacked explanation. For Ro ≫ 1,
the activity observed as X-ray to bolometric flux varies as Ro−q with 2 ≤ q ≤ 3, whilst |q| < 0.13 for Ro ≪ 1. Here, we explain the transition between these two regimes and the power law in the Ro ≫ 1 regime by constructing
an expression for the coronal luminosity based on dynamo magnetic field generation and magnetic buoyancy. We explain the Ro ≪ 1
behaviour from the inference that observed rotation is correlated with internal differential rotation and argue that once
the shear time-scale is shorter than the convective turnover time, eddies will be shredded on the shear time-scale and so
the eddy correlation time actually becomes the shear time and the convection time drops out of the equations. We explain the
Ro ≫ 1 behaviour using a dynamo saturation theory based on magnetic helicity buildup and buoyant loss.
Asteroseismology of 1.0-2.0 M ☉ red giants by the Kepler satellite has enabled the first definitive measurements of interior rotation in both first ascent red giant branch (RGB) stars and those on the helium burning clump. The inferred rotation rates are 10-30 days for the 0.2 M ☉ He degenerate cores on the RGB and 30-100 days for the He burning core in a clump star. Using the Modules for Experiments in Stellar Evolution code, we calculate state-of-the-art stellar evolution models of low mass rotating stars from the zero-age main sequence to the cooling white dwarf (WD) stage. We include transport of angular momentum due to rotationally induced instabilities and circulations, as well as magnetic fields in radiative zones (generated by the Tayler-Spruit dynamo). We find that all models fail to predict core rotation as slow as observed on the RGB and during core He burning, implying that an unmodeled angular momentum transport process must be operating on the early RGB of low mass stars. Later evolution of the star from the He burning clump to the cooling WD phase appears to be at nearly constant core angular momentum. We also incorporate the adiabatic pulsation code, ADIPLS, to explicitly highlight this shortfall when applied to a specific Kepler asteroseismic target, KIC8366239.
Observations of magnetic A, B and O stars show that the poloidal magnetic
flux per unit mass has an upper bound of 10^-6.5 G cm^2/g. A similar upper
bound is found for magnetic white dwarfs even though the highest magnetic field
strengths at their surfaces are much larger. For magnetic A and B stars there
also appears to be a well defined lower bound below which the incidence of
magnetism declines rapidly. According to recent hypotheses, both groups of
stars may result from merging stars and owe their strong magnetism to fields
generated by a dynamo mechanism as they merge. We postulate a simple dynamo
that generates magnetic field from differential rotation. The growth of
magnetic fields is limited by the requirement that the poloidal field
stabilizes the toroidal and vice versa. While magnetic torques dissipate the
differential rotation, toroidal field is generated from poloidal by an Omega
dynamo. We further suppose that mechanisms that lead to the decay of toroidal
field lead to the generation of poloidal. Both poloidal and toroidal fields
reach a stable configuration which is independent of the size of small initial
seed fields but proportional to the initial differential rotation. We pose the
hypothesis that strongly magnetic stars form from the merging of two stellar
objects. The highest fields are generated when the merge introduces
differential rotation that amounts to critical break up velocity within the
condensed object. Calibration of a simplistic dynamo model with the observed
maximum flux per unit mass for main-sequence stars and white dwarfs indicates
that about 1.5x10^-4 of the decaying toroidal flux must appear as poloidal. The
highest fields in single white dwarfs are generated when two degenerate cores
merge inside a common envelope or when two white dwarfs merge by
gravitational-radiation angular momentum loss.
We continue our study of a powerful weak-field MHD instability. Consequences of the instability for pressure-supported systems
are discussed, with emphasis upon stellar radiative zones. It is suggested that the instability, rather than hydromagnetic
waves, is responsible for establishing uniform rotation in weakly magnetized stellar radiative zones. When the Brunt–Väisälä
frequency much exceeds the rotation frequency, only displacements in spherical shells are unstable. Thus the transport induced
by the instability is tangential and leads to little radial mixing. If angular velocity is initially constant on cylinders,
the effect of the instability is to transport angular momentum from the poles to the equator. If angular momentum is locally
deposited by thermalization of the instability, this will probably have the effect of establishing solid-body rotation in
radiative zones. If angular momentum is not deposited locally, it will tend to accumulate in the mid-plane of the star, with
uncertain consequences. It may contribute to an anisotropic wind.
A review of the instability in discs is also presented.
A full list of white dwarfs which have been observed for evidence of
magnetic field is presented. The observations of continuous circular
polarization are discussed along with the derivation of the mean field
projected on the line of sight. New field upper limits are presented for
several white dwarfs with strong spectral lines observed for the Zeeman
effect. The obtained material is used to determine quantitatively the
distribution of magnetic fields over the population of white dwarfs. The
temperature, composition, and rotation of magnetic white dwarfs are
examined, and the possible effect of white dwarf magnetic fields on
accretion of material from the interstellar medium is considered. The
space density and possible origin of magnetic white dwarfs is also
discussed.
To obtain a better statistics on the occurrence of magnetism among white
dwarfs, we searched the spectra of the hydrogen atmosphere white dwarf stars
(DAs) in the Data Release 7 of the Sloan Digital Sky Survey (SDSS) for Zeeman
splittings and estimated the magnetic fields. We found 521 DAs with detectable
Zeeman splittings, with fields in the range from around 1 MG to 733 MG, which
amounts to 4% of all DAs observed. As the SDSS spectra have low signal-to-noise
ratios, we carefully investigated by simulations with theoretical spectra how
reliable our detection of magnetic field was.
Stellar physics and evolution calculations enable a broad range of research in astrophysics. Modules for Experiments in Stellar Astrophysics (MESA) is a suite of open source, robust, efficient, thread-safe libraries for a wide range of applications in computational stellar astrophysics. A one-dimensional stellar evolution module, MESAstar, combines many of the numerical and physics modules for simulations of a wide range of stellar evolution scenarios ranging from very low mass to massive stars, including advanced evolutionary phases. MESAstar solves the fully coupled structure and composition equations simultaneously. It uses adaptive mesh refinement and sophisticated timestep controls, and supports shared memory parallelism based on OpenMP. State-of-the-art modules provide equation of state, opacity, nuclear reaction rates, element diffusion data, and atmosphere boundary conditions. Each module is constructed as a separate Fortran 95 library with its own explicitly defined public interface to facilitate independent development. Several detailed examples indicate the extensive verification and testing that is continuously performed and demonstrate the wide range of capabilities that MESA possesses. These examples include evolutionary tracks of very low mass stars, brown dwarfs, and gas giant planets to very old ages; the complete evolutionary track of a 1 M ☉ star from the pre-main sequence (PMS) to a cooling white dwarf; the solar sound speed profile; the evolution of intermediate-mass stars through the He-core burning phase and thermal pulses on the He-shell burning asymptotic giant branch phase; the interior structure of slowly pulsating B Stars and Beta Cepheids; the complete evolutionary tracks of massive stars from the PMS to the onset of core collapse; mass transfer from stars undergoing Roche lobe overflow; and the evolution of helium accretion onto a neutron star. MESA can be downloaded from the project Web site (http://mesa.sourceforge.net/).
We present direct numerical simulations based on the full MHD equations of dynamo action in a nonrotating, convectively stable layer containing a forced, localized velocity shear. The dynamo operates by the interaction of two MHD processes: the production of toroidal magnetic field from poloidal field by the shear, and the regeneration of poloidal loops from toroidal field due to the combined action of magnetic buoyancy and Kelvin-Helmholtz instabilities. The nature of the dynamo process is such that it can occur only if the initial magnetic fields exceed a critical value that typically depends on the magnetic Reynolds number. As such, this dynamo does not operate in the kinematic limit. Several different behaviors are observed, including steady dynamo production and cyclic as well as chaotic activity. In the cyclic regimes, the dynamo process exhibits polarity reversals and periods of reduced activity.
The Sloan Digital Sky Survey has already more than doubled the sample of white dwarfs with spectral classifications, the subset with detached M dwarf companions, and the subset of magnetic white dwarfs. In the course of assessing these new discoveries, we have noticed a curious, unexpected property of the total lists of magnetic white dwarfs and of white dwarf plus main-sequence binaries: there appears to be virtually zero overlap between the two samples! No confirmed magnetic white dwarf has yet been found in such a pairing with a main-sequence star. The same statement can be made for the samples of white dwarf–M dwarf pairs in wide, common proper motion systems. This contrasts with the situation for interacting binaries, in which an estimated 25% of the accreting systems have a magnetic white dwarf primary. Alternative explanations are discussed for the observed absence of magnetic white dwarf–main-sequence pairs, but the recent discoveries of very low accretion rate magnetic binaries pose difficulties for each. A plausible explanation may be that the presence of the companion and the likely large mass and small radius of the magnetic white dwarf (relative to nonmagnetic degenerate dwarfs) may provide a selection effect against the discovery of the latter in such binary systems. More careful analysis of the existing samples may yet uncover members of this class of binary, and the sample sizes will continue to grow. The question of whether the mass and field distributions of the magnetic primaries in interacting binaries are similar to those of the isolated magnetic white dwarfs (including those in wider binaries) must also be answered.
The space mission Kepler provides us with long and uninterrupted photometric
time series of red giants. We are now able to probe the rotational behaviour in
their deep interiors using the observations of mixed modes. We aim to measure
the rotational splittings in red giants and to derive scaling relations for
rotation related to seismic and fundamental stellar parameters. We have
developed a dedicated method for automated measurements of the rotational
splittings in a large number of red giants. Ensemble asteroseismology, namely
the examination of a large number of red giants at different stages of their
evolution, allows us to derive global information on stellar evolution. We have
measured rotational splittings in a sample of about 300 red giants. We have
also shown that these splittings are dominated by the core rotation. Under the
assumption that a linear analysis can provide the rotational splitting, we
observe a small increase of the core rotation of stars ascending the red giant
branch. Alternatively, an important slow down is observed for red-clump stars
compared to the red giant branch. We also show that, at fixed stellar radius,
the specific angular momentum increases with increasing stellar mass. Ensemble
asteroseismology indicates what has been indirectly suspected for a while: our
interpretation of the observed rotational splittings leads to the conclusion
that the mean core rotation significantly slows down during the red giant
phase. The slow-down occurs in the last stages of the red giant branch. This
spinning down explains, for instance, the long rotation periods measured in
white dwarfs
We show that a steady mean-field dynamo in astrophysical rotators leads to an outflow of relative magnetic helicity and thus magnetic energy available for particle and wind acceleration in a corona. The connection between energy and magnetic helicity arises because mean-field generation is linked to an inverse cascade of magnetic helicity. To maintain a steady state in large magnetic Reynolds number rotators, there must then be an escape of relative magnetic helicity associated with the mean field, accompanied by an equal and opposite contribution from the fluctuating field. From the helicity flow, a lower limit on the magnetic energy deposited in the corona can be estimated. Steady coronal activity including the dissipation of magnetic energy, and formation of multi-scale helical structures therefore necessarily accompanies an internal dynamo. This highlights the importance of boundary conditions which allow this to occur for non-linear astrophysical dynamo simulations. Our theoretical estimate of the power delivered by a mean-field dynamo is consistent with that inferred from observations to be delivered to the solar corona, the Galactic corona, and Seyfert 1 AGN coronae.
In this third paper in a series on stable magnetic equilibria in stars, I look at the stability of axisymmetric field configurations
and, in particular, the relative strengths of the toroidal and poloidal components. Both toroidal and poloidal fields are
unstable on their own, and stability is achieved by adding the two together in some ratio. I use Tayler's stability conditions
for toroidal fields and other analytic tools to predict the range of stable ratios and then check these predictions by running
numerical simulations. If the energy in the poloidal component as a fraction of the total magnetic energy is written as Ep/E, it is found that the stability condition is a(E/U) < Ep/E≲ 0.8 where E/U is the ratio of magnetic to gravitational energy in the star and a is some dimensionless factor whose value is of order 10 in a main-sequence star and of order 103 in a neutron star. In other words, whilst the poloidal component cannot be significantly stronger than the toroidal, the
toroidal field can be very much stronger than the poloidal–given that in realistic stars we expect E/U < 10−6. The implications of this result are discussed in various contexts such as the emission of gravitational waves by neutron
stars, free precession and a ‘hidden’ energy source for magnetars.
High-field magnetic white dwarfs have been long suspected to be the result of
stellar mergers. However, the nature of the coalescing stars and the precise
mechanism that produces the magnetic field are still unknown. Here we show that
the hot, convective, differentially rotating corona present in the outer layers
of the remnant of the merger of two degenerate cores is able to produce
magnetic fields of the required strength that do not decay for long timescales.
We also show, using an state-of-the-art Monte Carlo simulator, that the
expected number of high-field magnetic white dwarfs produced in this way is
consistent with that found in the Solar neighborhood.
All evolved stars with masses M 2 M
☉ undergo an initiating off-center helium core flash in their Mc ≈ 0.48 M
☉ He core as they ascend the red giant branch (RGB). This off-center flash is the first of a few successive helium shell subflashes that remove the core electron degeneracy over 2 Myr, converting the object into a He-burning star. Though characterized by Thomas over 40 years ago, this core flash phase has yet to be observationally probed. Using the Modules for Experiments in Stellar Astrophysics () code, we show that red giant asteroseismology enabled by space-based photometry (i.e., Kepler and CoRoT) can probe these stars during the flash. The rapid ( 105 yr) contraction of the red giant envelope after the initiating flash dramatically improves the coupling of the p-modes to the core g-modes, making the detection of ℓ = 1 mixed modes possible for these 2 Myr. This duration implies that 1 in 35 stars near the red clump in the H-R diagram will be in their core flash phase. During this time, the star has a g-mode period spacing of ΔP
g ≈ 70-100 s, lower than the ΔP
g ≈ 250 s of He-burning stars in the red clump, but higher than the RGB stars at the same luminosity. This places them in an underpopulated part of the large frequency spacing (Δν) versus ΔP
g diagram that should ease their identification among the thousands of observed red giants.
When the core hydrogen is exhausted during stellar evolution, the central region of a star contracts and the outer envelope expands and cools, giving rise to a red giant. Convection takes place over much of the star's radius. Conservation of angular momentum requires that the cores of these stars rotate faster than their envelopes; indirect evidence supports this. Information about the angular-momentum distribution is inaccessible to direct observations, but it can be extracted from the effect of rotation on oscillation modes that probe the stellar interior. Here we report an increasing rotation rate from the surface of the star to the stellar core in the interiors of red giants, obtained using the rotational frequency splitting of recently detected 'mixed modes'. By comparison with theoretical stellar models, we conclude that the core must rotate at least ten times faster than the surface. This observational result confirms the theoretical prediction of a steep gradient in the rotation profile towards the deep stellar interior.
The origin of highly magnetized white dwarfs has remained a mystery since their initial discovery. Recent observations indicate that the formation of high-field magnetic white dwarfs is intimately related to strong binary interactions during post-main-sequence phases of stellar evolution. If a low-mass companion, such as a planet, brown dwarf, or low-mass star, is engulfed by a post-main-sequence giant, gravitational torques in the envelope of the giant lead to a reduction of the companion's orbit. Sufficiently low-mass companions in-spiral until they are shredded by the strong gravitational tides near the white dwarf core. Subsequent formation of a super-Eddington accretion disk from the disrupted companion inside a common envelope can dramatically amplify magnetic fields via a dynamo. Here, we show that these disk-generated fields are sufficiently strong to explain the observed range of magnetic field strengths for isolated, high-field magnetic white dwarfs. A higher-mass binary analogue may also contribute to the origin of magnetar fields.
We present magnetic flux measurements in seven rapidly rotating M dwarfs. Our
sample stars have X-ray and H-alpha emission indicative of saturated emission,
i.e., emission at a high level independent of rotation rate. Our measurements
are made using near-infrared FeH molecular spectra observed with HIRES at Keck.
Because of their large convective overturn times, the rotation velocity of M
stars with small Rossby numbers is relatively slow and does not hamper the
measurement of Zeeman splitting. The Rossby numbers of our sample stars are as
small as 0.01. All our sample stars exhibit magnetic flux of kilo-Gauss
strength. We find that the magnetic flux saturates in the same regime as
saturation of coronal and chromospheric emission, at a critical Rossby number
of around 0.1. The filling factors of both field and emission are near unity by
then. We conclude that the strength of surface magnetic fields remains
independent of rotation rate below that; making the Rossby number yet smaller
by a factor of ten has little effect. These saturated M-star dynamos generate
an integrated magnetic flux of roughly 3 kG, with a scatter of about 1 kG. The
relation between emission and flux also has substantial scatter.
Context. Betelgeuse is an M supergiant with a complex and extended
atmosphere, which also harbors spots and giant granules at its surface.
A possible magnetic field could contribute to the mass loss and to the
heating of the outer atmosphere. Aims: We observed Betelgeuse, to
directly study and infer the nature of its magnetic field.
Methods: We used the new-generation spectropolarimeter NARVAL and the
least square deconvolution (LSD) method to detect circular polarization
within the photospheric absorption lines of Betelgeuse. Results:
We have unambiguously detected a weak Stokes V signal in the spectral
lines of Betelgeuse, and measured the related surface-averaged
longitudinal magnetic field B_ℓ at 6 different epochs over one
month. The detected longitudinal field is about one Gauss and is
apparently increasing on the time scale of our observations.
Conclusions: This work presents the first direct detection of the
magnetic field of Betelgeuse. This magnetic field may be associated to
the giant convection cells that could enable a “local
dynamo”.
Based on observations obtained at the Télescope Bernard Lyot
(TBL) at Observatoire du Pic du Midi, CNRS/INSU and Université de
Toulouse, France.
The gas in the convective outer layers of the Sun rotates faster at the
equator than in the polar regions, yet deeper inside (in the radiative
zone) the gas rotates almost uniformly. There is a thin transition layer
between these zones, called the tachocline. This structure has been
measured seismologically, but no purely fluid-dynamical mechanism can
explain its existence. Here we argue that a self-consistent model
requires a large-scale magnetic field in the Sun's interior, as well as
consideration of the Coriolis effects in the convection zone and in the
tachocline. Turbulent stresses in the convection zone induce (through
Coriolis effects) a meridional circulation, causing the gas from the
convection zone to burrow downwards, thereby generating the horizontal
and vertical shear that characterizes the tachocline. The interior
magnetic field stops the burrowing, and confines the shear, as demanded
by the observed structure of the tachocline. We outline a dynamical
theory of the flow, from which we estimate a field strength of about
10-4 tesla just beneath the tachocline. An important test of
this picture, after numerical refinement, will be quantitative
consistency between the predicted and observed interior angular
velocities.
Planetary nebulae are thought to be formed when a slow wind from the progenitor giant star is overtaken by a subsequent fast wind generated as the star enters its white dwarf stage. A shock forms near the boundary between the winds, creating the relatively dense shell characteristic of a planetary nebula. A spherically symmetric wind will produce a spherically symmetric shell, yet over half of known planetary nebulae are not spherical; rather, they are elliptical or bipolar in shape. A magnetic field could launch and collimate a bipolar outflow, but the origin of such a field has hitherto been unclear, and some previous work has even suggested that a field could not be generated. Here we show that an asymptotic-giant-branch (AGB) star can indeed generate a strong magnetic field, having as its origin a dynamo at the interface between the rapidly rotating core and the more slowly rotating envelope of the star. The fields are strong enough to shape the bipolar outflows that produce the observed bipolar planetary nebulae. Magnetic braking of the stellar core during this process may also explain the puzzlingly slow rotation of most white dwarf stars.
Some main-sequence stars of spectral type A are observed to have a strong (0.03-3 tesla), static, large-scale magnetic field, of a chiefly dipolar shape: they are known as 'Ap stars', such as Alioth, the fifth star in the Big Dipper. Following the discovery of these fields, it was proposed that they are remnants of the star's formation, a 'fossil' field. An alternative suggestion is that they could be generated by a dynamo process in the star's convective core. The dynamo hypothesis, however, has difficulty explaining high field strengths and the observed lack of a correlation with rotation. The weakness of the fossil-field theory has been the absence of field configurations stable enough to survive in a star over its lifetime. Here we report numerical simulations that show that stable magnetic field configurations, with properties agreeing with those observed, can develop through evolution from arbitrary, unstable initial fields. The results are applicable equally to Ap stars, magnetic white dwarfs and some highly magnetized neutron stars known as magnetars. This establishes fossil fields as the natural, unifying explanation for the magnetism of all these stars.
The aim of this work is to use full evolutionary models to derive observational constraints on the mass loss rate of the upper Asymptotic Giant Branch (AGB) stars. The observations used to constrain the models are the relative number of luminous Lithium rich AGBs in the Magellanic Clouds and the s-process enhancement of the same sample. We find that we can put lower and upper limits to the mass loss rate during the AGB phase. The mass loss calibation obtained in this work implies that massive AGBs do not contribute significantly to the lithium enrichment of the interstellar medium.
We construct a magnetic helicity conserving dynamo theory which incorporates a calculated magnetic helicity current. In this model the fluid helicity plays a small role in large scale magnetic field generation. Instead, the dynamo process is dominated by a new quantity, derived from asymmetries in the second derivative of the velocity correlation function, closely related to the `twist and fold' dynamo model. The turbulent damping term is, as expected, almost unchanged. Numerical simulations with a spatially constant fluid helicity and vanishing resistivity are not expected to generate large scale fields in equipartition with the turbulent energy density. The prospects for driving a fast dynamo under these circumstances are uncertain, but if it is possible, then the field must be largely force-free. On the other hand, there is an efficient analog to the $\alpha-\Omega$ dynamo. Systems whose turbulence is driven by some anisotropic local instability in a shearing flow, like real stars and accretion disks, and some computer simulations, may successfully drive the generation of strong large scale magnetic fields, provided that $\partial_r\Omega< \partial_\theta v_z\omega_\theta>>0$. We show that this criterion is usually satisfied. Such dynamos will include a persistent, spatially coherent vertical magnetic helicity current with the same sign as $-\partial_r\Omega$, that is, positive for an accretion disk and negative for the Sun. We comment on the role of random magnetic helicity currents in storing turbulent energy in a disordered magnetic field, which will generate an equipartition, disordered field in a turbulent medium, and also a declining long wavelength tail to the power spectrum. As a result, calculations of the galactic `seed' field are largely irrelevant. Comment: 28 pages, accepted by The Astrophysical Journal
We consider the backreaction of the magnetic field on the magnetic dynamo coefficients and the role of boundary conditions in interpreting whether numerical evidence for suppression is dynamical. If a uniform field in a periodic box serves as the initial condition for modeling the backreaction on the turbulent EMF, then the magnitude of the turbulent EMF and thus the dynamo coefficient $\a$, have a stringent upper limit that depends on the magnetic Reynolds number $R_M$ to a power of order -1. This is not a dynamic suppression but results just because of the imposed boundary conditions. In contrast, when mean field gradients are allowed within the simulation region, or non-periodic boundary are used, the upper limit is independent of $R_M$ and takes its kinematic value. Thus only for simulations of the latter types could a measured suppression be the result of a dynamic backreaction. This is fundamental for understanding a long-standing controversy surrounding $\alpha$ suppression. Numerical simulations which do not allow any field gradients and invoke periodic boundary conditions appear to show a strong $\alpha$ suppression (e.g. Cattaneo & Hughes 1996). Simulations of accretion discs which allow field gradients and allow free boundary conditions (Brandenburg & Donner 1997) suggest a dynamo $\alpha$ which is not suppressed by a power of $R_M$. Our results are consistent with both types of simulations. Comment: LaTex, version in press, ApJ
Evidence is presented from numerical magneto-hydrodynamical simulations for the existence of magnetic activity in late-type giant stars. A red supergiant with stellar parameters similar to that of Betelgeuse (alpha Orionis) is modeled as a "star-in-a-box" with the high-order "Pencil Code". Both linear kinematic and non-linear saturated dynamo action are found: the non-linear magnetic field saturates at a super-equipartition value (a factor two above equipartition yielding surface fields with strengths on the order of 500 Gauss), while in the linear regime two different modes of dynamo action are found. It is speculated that magnetic activity of late-type giants may influence dust and wind formation and possibly lead to the heating of the outer atmospheres of these stars. Comment: 7 pages, 9 figures (2 in color), submitted to A&A
The available information on isotopic abundances in the atmospheres of low-mass Red Giant Branch (RGB) and Asymptotic Giant Branch (AGB) stars requires that episodes of extensive mixing occur below the convective envelope, reaching down to layers close to the hydrogen burning shell (Cool Bottom Processing). Recently \cite{Busso:2007jw} suggested that dynamo-produced buoyant magnetic flux tubes could provide the necessary physical mechanisms and also supply sufficient transport rates. Here, we present an $\alpha-\Omega$ dynamo in the envelope of an RGB/AGB star in which shear and rotation drain via turbulent dissipation and Poynting flux. In this context, if the dynamo is to sustain throughout either phase, convection must resupply shear. Under this condition, volume-averaged, peak toroidal field strengths of $<B_\phi>\simeq3\times10^3$ G (RGB) and $<B_\phi>\simeq5\times10^3$ G (AGB) are possible at the base of the convection zone. If the magnetic fields are concentrated in flux tubes, the corresponding field strengths are comparable to those required by Cool Bottom Processing. Comment: Replaced to correct small error in published version: In \S 2.1, paragraphs 2 and 3 incorrectly refer to the poloidal field when qualitatively discussing magnetic diffusion in the shear zone. The correct physical interpretation is that the toroidal field diffuses through the shear zone consistent with the value of $\beta_\phi$
The Sun's magnetic field is the engine and energy source driving all phenomena collectively defining solar activity, which in turn structures the whole heliosphere and significantly impacts Earth's atmosphere down at least to the stratosphere. The solar magnetic field is believed to originate through the action of a hydromagnetic dynamo process operating in the Sun's interior, where the strongly turbulent environment of the convection zone leads to flow-field interactions taking place on an extremely wide range of spatial and temporal scales. Following a necessarily brief observational overview of the solar magnetic field and its cycle, this review on solar dynamo theory is structured around three areas in which significant advances have been made in recent years: (a) global magnetohydrodynamical simulations of convection and magnetic cycles, (b) the turbulent electromotive force and the dynamo saturation problem, and (c) flux transport dynamos, and their application to model cycle fluctuations and grand minima and to carry out cycle prediction.
We study the flux of small-scale magnetic helicity in simulations of
driven statistically homogeneous magnetohydrodynamic turbulence in a
periodic box with an imposed large-scale shear. The simulations show
that in the regime of strong dynamo action the eddy-scale magnetic
helicity flux has only two significant terms: advective motion driven by
the large-scale velocity field and the Vishniac-Cho (VC) flux which
moves helicity across the magnetic field lines. The contribution of all
the other terms is negligible. The VC flux is highly correlated with the
large-scale electromotive force and is responsible for large-scale
dynamo action, while the advective term is not. The VC flux is driven by
the anisotropy of the turbulence. We derive analytical expressions for
it in terms of the small-scale velocity or magnetic field. These
expressions are used to predict the existence and strength of dynamo
action for different turbulent anisotropies and tested against the
results of the simulations.
Conference was held in Göttingen, Germany, on 2001 August 5-10. Proceedings will be edited by Boris T. Gänsicke, Klaus Beuermann, & Klaus Reinsch and published in the ASP Conference Series.
Electrical and thermal conductivities are calculated for the dense
matter in the liquid metal phase for various elemental compositions of
astrophysical importance. The calculation takes account of the best
knowledge available on the structure factor of the ions in the
high-temperature, classical limit and the dielectric screening due to
degenerate electrons. The numerical results are parameterized in
analytic formulae that would facilitate practical uses of the results.
An overall accuracy of about 1 percent has been retained for most of the
analytic formulae. Compared with the results of the present calculation,
it is found that Yakovlev and Urpin's (1980) results overestimate the
resistivity (underestimate the conductivity) by 30-60 percent at
relatively low densities.
The evolutionary path from main sequence stars to neutron stars has not yet been definitively determined. The following seems, however, common to published models1,3 : (a) The pre-neutron star stage has a very dense carbon-oxygen core of mass Mc˜1.4 M, surrounded by a more massive hydrogen and helium shell-burning envelope; the total stellar mass is ˜ 4 to 8 M. The core is initially kept below the carbon ignition temperature by conventional neutrino emission processes.
Radio pulsars are thought to born with spin periods of 0.02-0.5 s and space velocities of 100-1,000 km s(-1), and they are inferred to have initial dipole magnetic fields of 10(11)-10(13) G (refs 1-5). The average space velocity of their progenitor stars is less than 15 km s(-1), which means that pulsars must receive a substantial 'kick' at birth. Here we propose that the birth characteristics of pulsars have a simple physical connection with each other. Magnetic fields maintained by differential rotation between the core and envelope of the progenitor would keep the whole star in a state of approximately uniform rotation until 10 years before the explosion. Such a slowly rotating core has 1,000 times less angular momentum than required to explain the rotation of pulsars. The specific physical process that 'kicks' the neutron star at birth has not been identified, but unless its force is exerted exactly head-on(6) it will also cause the neutron star to rotate. We identify this process as the origin of the spin of pulsars. Such kicks may cause a correlation between the velocity and spin vectors of pulsars. We predict that many neutron stars are born with periods longer than 2 s, and never become radio pulsars.
Recent spectropolarimetric observations of Ap and Bp stars with improved sensitivity have suggested that most Ap and Bp stars are magnetic with dipolar fields of at least a few hundred gauss. These new estimates suggest that the range of magnetic fluxes found for the majority of magnetic white dwarfs is similar to that of main-sequence Ap–Bp stars, thus strengthening the empirical evidence for an evolutionary link between magnetism on the main sequence and magnetism in white dwarfs. We draw parallels between the magnetic white dwarfs and the magnetic neutron stars and argue that the observed range of magnetic fields in isolated neutron stars (Bp∼ 1011–1015 G) could also be explained if their mainly O-type progenitors have effective dipolar fields in the range of a few gauss to a few kilogauss, assuming approximate magnetic flux conservation with the upper limit being consistent with the recent measurement of a field of Bp∼ 1100 G for θ Orion C.
In the magnetic field–rotation diagram, the magnetic white dwarfs can be divided into three groups of different origin: a significant group of strongly magnetized slow rotators (Prot∼ 50 –100 yr) that have originated from single-star evolution, a group of strongly magnetized fast rotators (Prot∼ 700 s), typified by EUVE J0317–853, that have originated from a merger, and a group of modest rotators (Prot∼ hours–days) of mixed origin (single-star and CV-type binary evolution). We propose that the neutron stars may similarly divide into distinct classes at birth, and suggest that the magnetars may be the counterparts of the slowly rotating high-field magnetic white dwarfs.
The origin, evolution and role of magnetic fields in the production and shaping of proto-planetary nebulae (PPNe) and planetary nebulae (PNe) are a subject of active research. Most PNe and PPNe are axisymmetric with many exhibiting highly collimated outflows; however, it is important to understand whether such structures can be generated by isolated stars or require the presence of a binary companion. Towards this end, we study a dynamical, large-scale −Ω interface dynamo operating in a 3.0 M⊙ Asymptotic Giant Branch (AGB) star in both an isolated setting and a setting in which a low-mass companion is embedded inside the envelope. The back reaction of the fields on the shear is included and differential rotation and rotation deplete via turbulent dissipation and Poynting flux. For the isolated star, the shear must be resupplied in order to sufficiently sustain the dynamo. Furthermore, we investigate the energy requirements that convection must satisfy to accomplish this by analogy to the Sun. For the common envelope case, a robust dynamo results, unbinding the envelope under a range of conditions. Two qualitatively different types of explosion may arise: (i) magnetically induced, possibly resulting in collimated bipolar outflows and (ii) thermally induced from turbulent dissipation, possibly resulting in quasi-spherical outflows. A range of models is presented for a variety of companion masses.
We present the results of a photometric and spectroscopic study of the white dwarf candidate members of the intermediate age open clusters NGC3532 and NGC2287. Of the nine objects investigated, it is determined that six are probable members of the clusters, four in NGC3532 and two in NGC2287. For these six white dwarfs we use our estimates of their cooling times together with the cluster ages to constrain the lifetimes and masses of their progenitor stars. We examine the location of these objects in initial mass-final mass space and find that they now provide no evidence for substantial scatter in initial mass-final mass relation as suggested by previous investigations. Instead, we demonstrate that, when combined with current data from other solar metalicity open clusters and the Sirius binary system, they hint at an IFMR that is steeper in the initial mass range 3M$_{\odot}$$\simless$M$_{\rm init}$$\simless$4M$_{\odot}$ than at progenitor masses immediately lower and higher than this. This form is generally consistent with the predictions of stellar evolutionary models and can aid population synthesis models in reproducing the relatively sharp drop observed at the high mass end of the main peak in the mass distribution of white dwarfs. Comment: accepted for publication in MNRAS
Mean-field electrodynamics, including both α and β effects while accounting for the effects of small-scale magnetic fields, is derived for incompressible magnetohydrodynamics. The principal result is α=(α0+β0R⋅∇×R)/(1+R2), β=β0; where α0,β0 are conventional kinematic dynamo parameters, the reduction factor is proportional to the mean magnetic field R=Rm1/2B/(ρV2)1/2, Rm is the magnetic Reynolds number, and V is the characteristic turbulent velocity. This result follows from a generalization of the Zeldovich theorem to three dimensions, exploiting magnetic helicity balance.
Mass and radius relations for zero temperature spheres of chemical elements, using equation of state and numerical integration
A simple dynamo surface wave is presented to illustrate the basic principles of a dynamo operating in the thin layer of shear and suppressed eddy diffusion beneath the cyclonic convection in the convection zone of the sun. It is shown that the restriction of the shear delta(Omega)/delta(r) to a region below the convective zone provides the basic mode with a greatly reduced turbulent diffusion coefficient in the region of strong azimuthal field. The dynamo takes on the character of a surface wave tied to the lower surface z = 0 of the convective zone. There is a substantial body of evidence suggesting a fibril state for the principal flux bundles beneath the surface of the sun, with fundamental implications for the solar dynamo.
Magnetic fields can be created in stably stratified (non-convective) layers in a differentially rotating star. A magnetic instability in the toroidal field (wound up by differential rotation) replaces the role of convection in closing the field amplification loop. Tayler instability is likely to be the most relevant magnetic instability. A dynamo model is developed from these ingredients, and applied to the problem of angular momentum transport in stellar interiors. It produces a prodominantly horizontal field. This dynamo process might account for the observed pattern of rotation in the solar core. Comment: Expanded version as accepted by Astron. Astrophys
We study the incidence of magnetism in white dwarfs from three large and well-observed samples of hot, cool, and nearby white dwarfs in order to test whether the fraction of magnetic degenerates is biased, and whether it varies with effective temperature, cooling age, or distance. The magnetic fraction is considerably higher for the cool sample of Bergeron, Ruiz, and Leggett, and the Holberg, Oswalt, and Sion sample of local white dwarfs that it is for the generally-hotter white dwarfs of the Palomar Green Survey. We show that the mean mass of magnetic white dwarfs in this survey is 0.93 solar masses or more, so there may be a strong bias against their selection in the magnitude-limited Palomar Green Survey. We argue that this bias is not as important in the samples of cool and nearby white dwarfs. However, this bias may not account for all of the difference in the magnetic fractions of these samples. It is not clear that the magnetic white dwarfs in the cool and local samples are drawn from the same population as the hotter PG stars. In particular, two or threee of the cool sample are low-mass white dwarfs in unresolved binary systems. Moreover, there is a suggestion from the local sample that the fractional incidence may increase with decreasing temperature, luminosity, and/or cooling age. Overall, the true incidence of magnetism at the level of 2 megagauss or greater is at least 10%, and could be higher. Limited studies capable of detecting lower field strengths down to 10 kilogauss suggest by implication that the total fraction may be substantially higher than 10%. Comment: 16 pages, 2 figures, Astronomical Journal in press -- Jan 2003 issue
White dwarfs with surface magnetic fields in excess of $1 $MG are found as isolated single stars and relatively more often in magnetic cataclysmic variables. Some 1,253 white dwarfs with a detached low-mass main-sequence companion are identified in the Sloan Digital Sky Survey but none of these is observed to show evidence for Zeeman splitting of hydrogen lines associated with a magnetic field in excess of 1MG. If such high magnetic fields on white dwarfs result from the isolated evolution of a single star then there should be the same fraction of high field white dwarfs among this SDSS binary sample as among single stars. Thus we deduce that the origin of such high magnetic fields must be intimately tied to the formation of cataclysmic variables. CVs emerge from common envelope evolution as very close but detached binary stars that are then brought together by magnetic braking or gravitational radiation. We propose that the smaller the orbital separation at the end of the common envelope phase, the stronger the magnetic field. The magnetic cataclysmic variables originate from those common envelope systems that almost merge. We propose further that those common envelope systems that do merge are the progenitors of the single high field white dwarfs. Thus all highly magnetic white dwarfs, be they single stars or the components of MCVs, have a binary origin. This hypothesis also accounts for the relative dearth of single white dwarfs with fields of 10,000 - 1,000,000G. Such intermediate-field white dwarfs are found preferentially in cataclysmic variables. In addition the bias towards higher masses for highly magnetic white dwarfs is expected if a fraction of these form when two degenerate cores merge in a common envelope. Similar scenarios may account for very high field neutron stars. Comment: 6 pages, 1 figure, accepted by MNRAS
Gas supplied conservatively to a black hole at rates well below the Eddington rate may not be able to radiate effectively
and the net energy flux, including the energy transported by the viscous torque, is likely to be close to zero at all radii.
This has the consequence that the gas accretes with positive energy so that it may escape. Accordingly, we propose that only
a small fraction of the gas supplied actually falls on to the black hole, and that the binding energy it releases is transported
radially outward by the torque so as to drive away the remainder in the form of a wind. This is a generalization of and an
alternative to an ‘ADAF’ solution. Some observational implications and possible ways to distinguish these two types of flow
are briefly discussed.
I argue that the rotation of white dwarfs is not a remnant of the angular momentum of their main sequence progenitors but a result of the mass loss process on the AGB. Weak magnetic fields, if present in stellar interiors, are likely to maintain approximately uniform rotation in stars, both on the main sequence and on the giant branches. The nearly uniform rotation of the core of the Sun is evidence for the existence of such fields. Exactly axisymmetric mass loss on the AGB from uniformly rotating stars would lead lead to white dwarfs with very long rotation periods ($>$ 10 yr). Small random non-axisymmetries ($\sim 10^{-3}$) in the mass loss process, on the other hand, add sufficient angular momentum to explain the observed rotation periods around one day. The process illustrated with a computation of the probability distribution of the rotation periods under the combined influence of random forcing by weak nonaxisymmetries and angular momentum loss in the AGB superwind. Such asymmetries can in principle be observed by proper motion studies of the clumps in interferometric images of SiO maser emission.
We study the local stability of stratified, differentially-rotating fluids to axisymmetric perturbations in the presence of a weak magnetic field and of finite resistivity, viscosity and heat conductivity. This is a generalization of the Goldreich-Schubert-Fricke (GSF) double-diffusive analysis to the magnetized and resistive, triple-diffusive case. Our fifth-order dispersion relation admits a novel branch which describes a magnetized version of multi-diffusive modes. We derive necessary conditions for axisymmetric stability in the inviscid and perfect-conductor (double-diffusive) limits. In each case, rotation must be constant on cylinders and angular velocity must not decrease with distance from the rotation axis for stability, irrespective of the relative strength of viscous, resistive and heat diffusion. Therefore, in both double-diffusive limits, solid body rotation marginally satisfies our stability criteria. The role of weak magnetic fields is essential to reach these conclusions. The triple-diffusive situation is more complex, and its stability criteria are not easily stated. Numerical analysis of our general dispersion relation confirms our analytic double-diffusive criteria, but also shows that an unstable double-diffusive situation can be significantly stabilized by the addition of a third, ostensibly weaker, diffusion process. We describe a numerical application to the Sun's upper radiative zone and establish that it would be subject to unstable multi-diffusive modes if moderate or strong radial gradients of angular velocity were present. Comment: 29 pages, 1 table, accepted for publication in ApJ
We examine the effects of the engulfment of planets by giant stars on the evolution of late-type stars. We show that the rate at which dynamo-generated magnetic energy is being released exceeds 10% of the wind kinetic energy when the orbital angular momentum of the engulfed planet is more than ten times the angular momentum of the star as it leaves the main sequence. A significant enhancement in the mass-loss rate may be expected in this case, due to the formation of cool magnetic spots. We use the existing sample of extrasolar planets to estimate that at least 3.5% of the evolved solar-type stars will be significantly affected by the presence of planetary companions. Comment: 10 pages, 1 figure
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