Figure 13 - uploaded by Yevgeni Kissin
Content may be subject to copyright.
Red line: orbital semimajor axis of a Jupiter-mass planet interacting with a RGB star and starting from a circular orbit with ai = 1 AU. Black line: stellar radius. Spiral-in of planet just below the tip of the RGB deposits angular momentum and triggers a dynamo process near the core–envelope boundary (Paper II).
Source publication
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 gian...
Citations
... MNRAS 521, 4122-4130 (2023) made on angular momentum transport mechanisms through more precise measures of the core-to-surface rotation ratios of post-MS stars (Deheuvels et al. 2014 ), and of the position and strength of a rotation rate gradient (Di Mauro et al. 2018 ). For example, a rotation profile with a constant rotation rate internal to the base of the conv ectiv e zone (BCZ), and a decreased rotation rate that is inversely dependent on radius in the BCZ, could be indicative of angular momentum transport from deep fossil magnetic fields (Gough & Thompson 1990 ;Kissin & Thompson 2015 ;Takahashi & Langer 2021 ). This results from differential rotation being damped along poloidal field lines (Garaud 2002 ;Strugarek, Brun & Zahn 2011 ). ...
... The mock rotation profiles are moti v ated by, but not representati ve of, v arious angular momentum transport MNRAS 521, 4122-4130 (2023) processes. The BCZ step rotation profile (red) is a signature of angular momentum transport by fossil magnetic fields, which results in solid body rotation in the radiative region and inverse rotation rate on radius in the conv ectiv e re gion (Kissin & Thompson 2015 ;Takahashi & Langer 2021 ). The H-burning step rotation profile (purple) is indicative of turbulent angular momentum transport through internal gra vity wa ves (Pin c ¸on et al. 2017 ) or magnetorotational instabilities (Balbus & Ha wle y 1994 ;Arlt et al. 2003 ;Menou & Mer 2006 ;Spada et al. 2016 ) which result in a strong gradient in rotation rate close to the core. ...
Rotationally-induced mode splitting frequencies of low-luminosity subgiants suggest that angular momentum transport mechanisms are 1-2 orders of magnitude more efficient in these stars than predicted by theory. Constraints on the rotation profile of low-luminosity subgiants could be used to identify the dominant mechanism for angular momentum transport. We develop a forward model for the rotation profile given observed rotational splittings, assuming a step-like rotation profile. We identify a consistent degeneracy between the position of the profile discontinuity and the surface rotation rate. We perform mock experiments that show the discontinuity position can be better constrained with a prior on the surface rotation rate, which is informed by star spot modulations. We finally apply this approach to KIC 12508433, a well-studied low-luminosity subgiant, as an example case. With the observed surface rotation prior, we obtain a factor of two increase in precision of the position of strong rotation gradient. We recover the literature values of the core and surface rotation rates and find the highest support for a discontinuity in the radiative zone. Auxiliary measurements of surface rotation could substantially improve inferences on the rotation profile of low-luminosity subgiants with already available data.
... One possible configuration for red giants is to have a solid-body rotation profile in radiative zones, combined to a profile in the power law of the radius in convective zones, 59, 60 of the form Ω(r) ∝ r −α , with α ∈ [1.0, 1.5]. These studies 59,60 showed that such a rotation profile could explain the core rotation rate of red giant branch stars inferred from seismic data. 49,50 However, these results are in contradiction with recent studies 61-63 who seem to indicate that the transition from the slow rotating envelope to the fast rotating core in red giant stars seems to be located in the radiative zone, close to the hydrogen burning shell. ...
... Their results show that such a rotation profile cannot be used to explain the individual rotational splittings unless α is allowed to reach higher values of the order of 3.5, in contradiction with theoretical values. 59 This suggests that fossil magnetic fields are not the explanation for the efficient angular momentum transport process acting in evolved stars, and other processes must also be invoked. ...
... The existence of large databases of rotation rates, including spot modulations (e.g McQuillan et al. 2014;Ceillier et al. 2017;Santos et al. 2019;Gaulme et al. 2020;Santos et al. 2021) and spectroscopic v i sin measurements (e.g., Massarotti et al. 2008;Zorec & Royer 2012;Tayar et al. 2015) have significantly improved our theoretical predictions for the surface rotation rate evolution (Matt et al. 2015;van Saders et al. 2016;). In addition, the ability to use asteroseismology, the study of stellar oscillations, to constrain the internal rotation rates (Beck et al. 2012;Deheuvels et al. 2012;Mosser et al. 2012;Deheuvels et al. 2014;García & Ballot 2019;Aerts et al. 2019;Li et al. 2020b;Pedersen et al. 2021) of these stars have greatly constrained the rates and timescales of angular momentum transport (Tayar & Pinsonneault 2013;Cantiello et al. 2014) and led to significant theoretical work on the location of differential rotation and the mechanisms determining the rotation profile (Kissin & Thompson 2015;Fuller et al. 2019;Takahashi & Langer 2021). ...
... The identity of this mechanism has remained unclear, as no current theories perfectly match all the observations (e.g., Eggenberger et al. 2019;den Hartogh et al. 2020). In addition, the radial location of the differential rotation is unclear, and various authors have argued that it could be in the surface convection zone (Kissin & Thompson 2015;Takahashi & Langer 2021) although others expect it to be concentrated in radiative regions (Fuller et al. 2019;Fellay et al. 2021). For most stars, getting measurements of the rotation rate at more than two locations-usually a "core" and a "surface"-has been challenging because of the limitations of the measurable oscillation modes, and thus this conflict has remained unresolved. ...
In this paper, we report the potential detection of a nonmonotonic radial rotation profile in a low-mass lower-luminosity giant star. For most low- and intermediate-mass stars, the rotation on the main sequence seems to be close to rigid. As these stars evolve into giants, the core contracts and the envelope expands, which should suggest a radial rotation profile with a fast core and a slower envelope and surface. KIC 9267654, however, seems to show a surface rotation rate that is faster than its bulk envelope rotation rate, in conflict with this simple angular momentum conservation argument. We improve the spectroscopic surface constraint, show that the pulsation frequencies are consistent with the previously published core and envelope rotation rates, and demonstrate that the star does not show strong chemical peculiarities. We discuss the evidence against any tidally interacting stellar companion. Finally, we discuss the possible origin of this unusual rotation profile, including the potential ingestion of a giant planet or unusual angular momentum transport by tidal inertial waves triggered by a close substellar companion, and encourage further observational and theoretical efforts.
... One uncertainty in our analysis is that it is not clear whether convection efficiently enforces solid-body rotation. This is not the case, e.g., in simulations of slowly rotating red-giant convection (e.g., Brun & Palacios 2009; see also Kissin & Thompson 2015 for a theoretical analysis of this problem). The numerical evidence does suggest, however, that an approach to solid-body rotation is more likely in the rapidly rotating limit considered here (e.g., Gastine & Wicht 2012;Yadav et al. 2013;Mabuchi et al. 2015). ...
Both the core collapse of rotating massive stars, and the coalescence of neutron star (NS) binaries result in the formation of a hot, differentially rotating NS remnant. The timescales over which differential rotation is removed by internal angular-momentum transport processes ( viscosity ) have key implications for the remnant’s long-term stability and the NS equation of state (EOS). Guided by a nonrotating model of a cooling proto-NS, we estimate the dominant sources of viscosity using an externally imposed angular-velocity profile Ω( r ). Although the magneto-rotational instability provides the dominant source of effective viscosity at large radii, convection and/or the Tayler–Spruit dynamo dominate in the core of merger remnants where d Ω/ dr ≥ 0. Furthermore, the viscous timescale in the remnant core is sufficiently short that solid-body rotation will be enforced faster than matter is accreted from rotationally supported outer layers. Guided by these results, we develop a toy model for how the merger remnant core grows in mass and angular momentum due to accretion. We find that merger remnants with sufficiently massive and slowly rotating initial cores may collapse to black holes via envelope accretion, even when the total remnant mass is less than the usually considered threshold ≈1.2 M TOV for forming a stable solid-body rotating NS remnant (where M TOV is the maximum nonrotating NS mass supported by the EOS). This qualitatively new picture of the post-merger remnant evolution and stability criterion has important implications for the expected electromagnetic counterparts from binary NS mergers and for multimessenger constraints on the NS EOS.
... The existence of large databases of rotation rates, including spot modulations (e.g McQuillan et al. 2014;Ceillier et al. 2017;Santos et al. 2019;Gaulme et al. 2020;Santos et al. 2021) and spectroscopic v sin i measurements (e.g Zorec & Royer 2012;Massarotti et al. 2008;Tayar et al. 2015) have significantly improved our theoretical predictions for the surface rotation rate evolution (Matt et al. 2015;van Saders et al. 2016;). In addition, the ability to use asteroseismology, the study of stellar oscillations, to constrain the internal rotation rates (Beck et al. 2012;Mosser et al. 2012;Deheuvels et al. 2012Deheuvels et al. , 2014Van Reeth et al. 2016;Aerts et al. 2019;García & Ballot 2019;Li et al. 2020b;Pedersen et al. 2021) of these stars have greatly constrained the rates and timescales of angular momentum transport (Tayar & Pinsonneault 2013;Cantiello et al. 2014) and led to significant theoretical work on the location of differential rotation and the mechanisms determining the rotation profile (Kissin & Thompson 2015;Fuller et al. 2019;Takahashi & Langer 2021). ...
... Eggenberger et al. 2019;den Hartogh et al. 2020). In addition, the radial location of the differential rotation is unclear, and various authors have argued that it could be in the surface convection zone (Kissin & Thompson 2015;Takahashi & Langer 2021) although others expect it to be concentrated in radiative regions (Fuller et al. 2019;Fellay et al. 2021). For most stars, getting measurements of the rotation rate at more than two locations-usually a 'core' and a 'surface'-has been challenging because of the limitations of the measurable oscillation modes, and thus this conflict has remained unresolved. ...
In this paper, we report the potential detection of a nonmonotonic radial rotation profile in a low-mass lower-luminosity giant star. For most low- and intermediate-mass stars, the rotation on the main sequence seems to be close to rigid. As these stars evolve into giants, the core contracts and the envelope expands, which should suggest a radial rotation profile with a fast core and a slower envelope and surface. KIC 9267654, however, seems to show a surface rotation rate that is faster than its bulk envelope rotation rate, in conflict with this simple angular momentum conservation argument. We improve the spectroscopic surface constraint, show that the pulsation frequencies are consistent with the previously published core and envelope rotation rates, and demonstrate that the star does not show strong chemical peculiarities. We discuss the evidence against any tidally interacting stellar companion. Finally, we discuss the possible origin of this unusual rotation profile, including the potential ingestion of a giant planet or unusual angular momentum transport by tidal inertial waves triggered by a close substellar companion, and encourage further observational and theoretical efforts.
... One uncertainty in our analysis is that it is not clear whether convection efficiently enforces solid body rotation. This is not the case, e.g., in simulations of slowly rotating red-giant convection (e.g., Brun & Palacios 2009; see also Kissin & Thompson 2015 for a theoretical analysis of this problem). The numerical evidence does suggest, however, that an approach to solid body rotation is more likely in the rapidly rotating limit considered here (e.g., Gastine & Wicht 2012;Yadav et al. 2013;Mabuchi et al. 2015). ...
Both the core collapse of rotating massive stars, and the coalescence of neutron star (NS) binaries, result in the formation of a hot, differentially rotating NS remnant. The timescales over which differential rotation is removed by internal angular-momentum transport processes ("viscosity") has key implications for the remnant's long-term stability and the NS equation-of-state (EOS). Guided by a non-rotating model of a cooling proto-NS, we estimate the dominant sources of viscosity using an externally imposed angular velocity profile $\Omega(r)$. Although the magnetorotational instability provides the dominant source of effective viscosity at large radii, convection and/or the Spruit-Tayler dynamo dominate in the core of merger remnants where $d\Omega/dr \geq 0$. Furthermore, the viscous timescale in the remnant core is sufficiently short that solid body rotation will be enforced faster than matter is accreted from rotationally-supported outer layers. Guided by these results, we develop a toy model for how the merger remnant core grows in mass and angular momentum due to accretion. We find that merger remnants with sufficiently massive and slowly rotating initial cores may collapse to black holes via envelope accretion, even when the total remnant mass is less than the usually considered threshold $\approx 1.2 M_{\rm TOV}$ for forming a stable solid-body rotating NS remnant (where $M_{\rm TOV}$ is the maximum non-rotating NS mass supported by the EOS). This qualitatively new picture of the post-merger remnant evolution and stability criterion has important implications for the expected electromagnetic counterparts from binary NS mergers and for multi-messenger constraints on the NS EOS.
... One possible configuration for red giants is to have a solid-body rotation profile in radiative zones, combined to a profile in the power law of the radius in convective zones 59,60 , of the form Ω(r) ∝ r −α , with α ∈ [1.0, 1.5]. These studies 59,60 showed that such a rotation profile could explain the core rotation rate of red giant branch stars inferred from seismic data 49,50 . ...
... A detailed analysis of the case of Kepler 56 was recently performed 64 , including a full dedicated modelling of the internal structure of the star and an MCMC analysis of the rotational splittings using simple parametric profiles, including the power law solution provided by large scale fossil fields. Their results show that such a rotation profile cannot be used to explain the individual rotational splittings unless α is allowed to reach higher values of the order of 3.5, in contradiction with theoretical values 59 . This suggests that fossil magnetic fields are not the explanation for the efficient angular momentum transport process acting in evolved stars, and other processes must also be invoked. ...
The possibility of measuring the internal rotation of the Sun and stars thanks to helio- and asteroseismology offers tremendous constraints on hydro- and magnetohydrodynamical processes acting in stellar interiors. Understanding the processes responsible for the transport of angular momentum in stellar interiors is crucial as they will also influence the transport of chemicals and thus the evolution of stars. Here we present some of the key results obtained in both fields and how detailed seismic analyses can provide stringent constraints on the physics of angular momentum transport in the interior of low mass stars and potentially rule out some candidates.
... In contrast to our models, Kissin & Thompson (2015) proposed that magnetic torques enforce nearly rigid rotation in radiative regions, while convective AM pumping causes differential rotation in thick convective layers (see also Takahashi & Langer 2021). Kissin & Thompson (2018) examined the core AM of massive stars in this scenario, predicting slowly rotating NSs in single stars, but finding that tidal spin-up of a red supergiant progenitor can lead to a rapidly rotating NS or BH. ...
The angular momentum (AM) content of massive stellar cores helps to determine the natal spin rates of neutron stars and black holes. Asteroseismic measurements of low-mass stars have proven that stellar cores rotate slower than predicted by most prior work, so revised models are necessary. In this work, we apply an updated AM transport model based on the Tayler instability to massive helium stars in close binaries, in which tidal spin-up can greatly increase the star's AM. Consistent with prior work, these stars can produce highly spinning black holes upon core-collapse if the orbital period is less than $P_{\rm orb} \lesssim \! 1 \, {\rm day}$. For neutron stars, we predict a strong correlation between the pre-explosion mass and the neutron star rotation rate, with millisecond periods ($P_{\rm NS} \lesssim 5 \, {\rm ms}$) only achievable for massive ($M \gtrsim 10 \, M_\odot$) helium stars in tight ($P_{\rm orb} \lesssim 1 \, {\rm day}$) binaries. Finally, we discuss our models in relation to type Ib/c supernovae, superluminous supernove, gamma-ray bursts, and LIGO measurements of black hole spins. Our models are roughly consistent with the rates and energetics of these phenomena, with the exception of broad-lined Ic supernovae, whose high rates and ejecta energies are difficult to explain.
... For the red giants studied by Deheuvels et al. (2015) ∆Ω max ≈ 4×10 −6 s −1 . This is on the order of what Cantiello et al. (2014) and Kissin & Thompson (2015b) suggest is needed to match asteroseismic inferences of core-envelope shear in red giants, so an order unity pre-factor in equation (15) would suffice to bring our bound into agreement with their calculations, and it seems possible that most or all of the differential rotation in such stars is in their convective envelopes. However, because equation (15) is an upper bound, it remains possible that a substantial component lies in the radiative zone (Fuller et al. 2019) and some astereoseismic evidence indicates that there is more shear in the radiative zones of red giants than in their convection zones (Mauro et al. 2018). ...
Differential rotation is central to a great many mysteries in stars and planets. In part I, we predicted the order of magnitude and scaling of the differential rotation in both hydrodynamic and magnetohydrodynamic convection zones. Our results apply to both slowly and rapidly rotating systems, and provide a general picture of differential rotation in stars and fluid planets. We further calculated the scalings of the meridional circulation, entropy gradient, and baroclinicity. In this companion paper, we compare these predictions with a variety of observations and numerical simulations. With a few exceptions, we find that these are consistent in both the slowly rotating and rapidly rotating limits. Our results help to localize core–envelope shear in red giant stars, suggest a rotation-dependent frequency shift in the internal gravity waves of massive stars, and potentially explain observed deviations from von Zeipel’s gravity darkening in late-type stars.
... Observations suggest that the thermal wind term is substantial, though there remain uncertainties as to its precise contribution (Caccin et al. 1976;Rast et al. 2008;Teplitskaya et al. 2015). Other models suggest that turbulent anisotropy is the most relevant factor in setting the differential rotation (Ruediger 1989;Kueker et al. 1993;Kitchatinov 2013), and more complex models with various parameterizations have also been proposed (Tuominen & Ruediger 1989;Kissin & Thompson 2015;Brun & Rempel 2009). One of our goals in this work is to understand which of the proposed effects matter the most and under what circumstances. ...
... This bound is particularly important in red giants, for which the Brünt-Väisälä frequency corresponds to periods of order 100 d or more. If the observed core-envelope shear in these systems is primarily in the convective envelope and not the interior radiative layer then the relative shear needs to be of order unity (Kissin & Thompson 2015), and this requires that the absolute shear be less than of order |N |. Because the time-scale |N | −1 is so long and the observed shear is so large, this favors scenarios which place significant shear in the radiative zones of red giants . ...
We derive the scaling of differential rotation in both slowly and rapidly rotating convection zones using order of magnitude methods. Our calculations apply across stars and fluid planets and all rotation rates, as well as to both magnetized and purely hydrodynamic systems. We find shear |R∇Ω| of order the angular frequency Ω for slowly rotating systems with Ω ≪ |N|, where N is the Brünt–Väisälä frequency, and find that it declines as a power law in Ω for rapidly rotating systems with Ω ≫ |N|. We further calculate the meridional circulation rate and baroclinicity and examine the magnetic field strength in the rapidly rotating limit. Our results are in general agreement with simulations and observations and we perform a detailed comparison with those in a companion paper.
