Angular momentum transport throughout stellar evolution

Speaker: Moyano, Facundo David Affiliation: Yunnan Observatories Kunming, China In collaboration with: Patrick Eggenberger, Beatriz Bordadágua, Zhanwen Han, Hongwei Ge, Zhengwei Liu Angular momentum transport throughout stellar evolution Credit: MPI for Solar System Research Moyano, Facundo D. -- Yunnan Observatories Angular momentum transport throughout stellar evolution Slide 2 4.2 4.4 4.6 4.8 5 4.35 4.4 4.45 4.5 4.55 No rotation Only rotation Rotation + magnetic fields log(L/L⊙) log(Teff) HR diagram of a 15 M⊙ star during the main sequence Why should we care about angular momentum transport? See Maeder & Meynet(2003,2004,2005); Brott+2011; Yoon+2012 No rotation Differential rotation Solid body rotation Moyano, Facundo D. -- Yunnan Observatories Angular momentum transport throughout stellar evolution Slide 3 Shear induced rotational mixing Transport efficiency scales with the amplitude of differential rotation Transport efficiency scales with the angular velocity, i.e. when the stellar regions rotate faster See Heger+2000; Maeder & Meynet 2000; Brott+2011 Meridional circulation X [Rsun] Z [Rsun] Figure from Decressin+2009 Moyano, Facundo D. -- Yunnan Observatories Angular momentum transport throughout stellar evolution Slide 4 Adapted from Bouabid+2013 Period spacing pattern at different rotational velocities No rotation Moderate rotation Fast rotation Slow rotation: rotational splittings Fast rotation: non-uniform period spacings ➔Pulsation frequencies are split due to rotation ➔Rotational splittings can be used to determine core and envelope rotation rates ➔Rotation decreases the spacing between pulsation periods ➔Slope of period spacing pattern can be used to measure the core rotation rate of fast rotators See Bouabid+13; Ouazzani+19; Aerts+10,19 Figure from Charpinet+2018 Moyano, Facundo D. -- Yunnan Observatories Angular momentum transport throughout stellar evolution Slide 5 0.5 1 1.5 2 2.5 3 3.5 3.5 3.6 3.7 3.8 3.9 log(L/L⊙) log(Teff) How is the angular momentum redistributed during the life of a star? Data: Mosser+12,24; Deheuvels+14,15,20; Hermes+17; Gehan+18; García+22; Ouazzani+19; Tayar+19,25(in prep); GangLi+20,24; Charpinet+18; Pedersen+22; Aerts+2025, and others Moyano, Facundo D. -- Yunnan Observatories Angular momentum transport throughout stellar evolution Slide 6 0.5 1 1.5 2 2.5 3 3.5 3.5 3.6 3.7 3.8 3.9 log(L/L⊙) log(Teff) How is the angular momentum redistributed during the life of a star? Data: Mosser+12,24; Deheuvels+14,15,20; Hermes+17; Gehan+18; García+22; Ouazzani+19; Tayar+19,25(in prep); GangLi+20,24; Charpinet+18; Pedersen+22; Aerts+2025, and others Moyano, Facundo D. -- Yunnan Observatories Angular momentum transport throughout stellar evolution Slide 7 0.5 1 1.5 2 2.5 3 3.5 3.5 3.6 3.7 3.8 3.9 log(L/L⊙) log(Teff) How is the angular momentum redistributed during the life of a star? Data: Mosser+12,24; Deheuvels+14,15,20; Hermes+17; Gehan+18; García+22; Ouazzani+19; Tayar+19,25(in prep); GangLi+20,24; Charpinet+18; Pedersen+22; Aerts+2025, and others Moyano, Facundo D. -- Yunnan Observatories Angular momentum transport throughout stellar evolution Slide 8 0.5 1 1.5 2 2.5 3 3.5 3.5 3.6 3.7 3.8 3.9 log(L/L⊙) log(Teff) How is the angular momentum redistributed during the life of a star? Data: Mosser+12,24; Deheuvels+14,15,20; Hermes+17; Gehan+18; García+22; Ouazzani+19; Tayar+19,25(in prep); GangLi+20,24; Charpinet+18; Pedersen+22; Aerts+2025, and others New subgiants & early red giants (Tayar+ in prep.) Moyano, Facundo D. -- Yunnan Observatories Angular momentum transport throughout stellar evolution Slide 9 0.5 1 1.5 2 2.5 3 3.5 3.5 3.6 3.7 3.8 3.9 log(L/L⊙) log(Teff) How is the angular momentum redistributed during the life of a star? Data: Mosser+12,24; Deheuvels+14,15,20; Hermes+17; Gehan+18; García+22; Ouazzani+19; Tayar+19,25(in prep); GangLi+20,24; Charpinet+18; Pedersen+22; Aerts+2025, and others Moyano, Facundo D. -- Yunnan Observatories Angular momentum transport throughout stellar evolution Slide 16 (e.g. Maeder & Meynet 2000, Heger+2000) (e.g. Pinçon+2017, Belkacem+2015; Talon & Charbonnel 2008; Varghese+2023; Rogers+2025 ) (e.g. Spruit+02, Kissin & Thompson, 2015; Spada+16 Fuller+19, Takahashi+21) Additional physical processes are needed Rotational instabilities Waves: internal gravity waves and mixed modes Magnetic fields Moyano, Facundo D. -- Yunnan Observatories Angular momentum transport throughout stellar evolution Slide 17 1 5 10 20 30 40 N: mixed modes density 0.8 1.0 2.0 3.0 4.0 Ωcore/2π[µHz] shear + circ modes w/damp modes wo/damp 2 3 4 5 6 7 8 9 10 15 R?[R] 0.2 0.5 1.0 2.0 3.0 4.0 5.0 Ωcore/2π[µHz] 2.0 M 1.3 M 1.0 M Ωobs RGB: Triana+17,Gehan+18 Ωobs SG: Deheuvels+14 Mixed modes (Bordadágua, Ahlborn, Coppée, et al. 2025) Mixed oscillation modes can transport angular momentum in the red giant branch (Belkacem+15a,b) Mixed oscillation modes were detected in subgiants and red giants Efficiency to extract angular momentum from the core is limited: ●With radiative damping→ lower efficiency ●No radiative damping → high efficiency Can extract angular momentum in localised regions, mainly the hydrogen-burning shell Core rotation rate [μHz] Radius [R☉] Adapted from Bordadágua+2025 Subgiants Red giant branch 1 5 10 20 30 40 N: mixed modes density 0.8 1.0 2.0 3.0 4.0 Ωcore/2π[µHz] shear + circ modes w/damp modes wo/damp 2 3 4 5 6 7 8 9 10 15 R?[R] 0.2 0.5 1.0 2.0 3.0 4.0 5.0 Ωcore/2π[µHz] 2.0 M 1.3 M 1.0 M Ωobs RGB: Triana+17,Gehan+18 Ωobs SG: Deheuvels+14 2, 1.3, 1 M☉ Moyano, Facundo D. -- Yunnan Observatories Angular momentum transport throughout stellar evolution Slide 18 10-2 10-1 100 101 102 103 104 105 0 0.5 1 1.5 2 Mosser+12; Gehan+18 (core) Deheuvels+14 (surface) Deheuvels+14 (core) Period [d] log R/R☉ Surface period j cons. TS dynamo Magnetic (ncv=0) Magnetic (ncv=2) 0 1 2 3 4 5 0 1 2 3 4 5 6 H burning shell convection base Ω ∝ r-1 Ω [10-6 rad s-1] radius [R☉] Large-scale magnetic fields (Takahashi & Langer, 2021) Large-scale magnetic fields in the whole star, magnetic fields and rotation treated altogether Nearly rigid rotation in radiative regions Differential rotation in convective zones Better agreement with core rotation rates of red giant branch stars and subgiants than previous models Angular velocity [10-6 rad/s] Adapted from Takahashi & Langer, 2021 Adapted from Takahashi & Langer, 2021 Subgiants and red giant branch stars Moyano, Facundo D. -- Yunnan Observatories Angular momentum transport throughout stellar evolution Slide 19 Convective pumping of angular momentum + radiative interior magnetically coupled (Kissin & Thompson, 2015) Rotation rate in the convective envelope is determined by the balance between the Coriolis force and inertial forces of convective plumes Rigid rotation in radiative regions coupled to the base of the convective envelope due to a large-scale magnetic dynamo Differential rotation in convective zones determines the core rotation rate Moyano, Facundo D. -- Yunnan Observatories Angular momentum transport throughout stellar evolution Slide 20 Rotation rate in the convective envelope is determined by the balance between the Coriolis force and inertial forces of convective plumes Rigid rotation in radiative regions coupled to the base of the convective envelope due to a large-scale magnetic dynamo Differential rotation in convective zones determines the core rotation rate Convective pumping of angular momentum + radiative interior magnetically coupled (Kissin & Thompson, 2015) Moyano, Facundo D. -- Yunnan Observatories Angular momentum transport throughout stellar evolution Slide 21 Rotation rate in the convective envelope is determined by the balance between the Coriolis force and inertial forces of convective plumes Rigid rotation in radiative regions coupled to the base of the convective envelope due to a large-scale magnetic dynamo Differential rotation in convective zones determines the core rotation rate Core rotation rates are too slow compared to modern data Convective pumping of angular momentum + radiative interior magnetically coupled (Kissin & Thompson, 2015) Moyano, Facundo D. -- Yunnan Observatories Angular momentum transport throughout stellar evolution Slide 22 Normalised radial coordinate Adapted from Buldgen+2024 Rotation rate [nHz] (Buoyancy frequency)2 [10-5 s-2] There is differential rotation in radiative regions (Deheuvels+2014,Di Mauro+2018, Fellay+2021, Buldgen+2024) Rigid rotation in the radiative interior of subgiants and red giants are not favoured (e.g. Kissin & Thompson, 2015). Differential rotation seems to start developing close to the hydrogen-burning shell Internal distribution of angular velocities (rotation profiles) Inferred rotation profile of a subgiant Moyano, Facundo D. -- Yunnan Observatories Angular momentum transport throughout stellar evolution Slide 23 Best case study is the Sun (e.g. Couvidat+2003) Almost rigid rotation in radiative interior (except core) → early rejection of inefficient angular momentum transport in radiative regions (e.g. Pinsonneault+89, Eggenberger+05) Internal distribution of angular velocities (rotation profiles) Rotation rate [nHz] Radial coordinate [R☉] Adapted from Eggenberger+2022 only hydrodynamical processes (no magnetic fields) Internal rotation profile of the Sun versus models Moyano, Facundo D. -- Yunnan Observatories Angular momentum transport throughout stellar evolution Slide 24 Best case study is the Sun (e.g. Couvidat+2003) Almost rigid rotation in radiative interior (except core) → early rejection of inefficient angular momentum transport in radiative regions (e.g. Pinsonneault+89, Eggenberger+05) Internal magnetic fields driven by the Tayler-Spruit dynamo (Tayler+73, Spruit02) can reproduce the flat rotation profile of the Sun Internal distribution of angular velocities (rotation profiles) Initially weak radial magnetic fields Differential rotation converts radial fields into toroidal fields Tayler instability regenerates radial component Rotation rate [nHz] Radial coordinate [R☉] Adapted from Eggenberger+2022 only hydrodynamical processes (no magnetic fields) Drawings from Barrère+2022 Internal rotation profile of the Sun versus models Moyano, Facundo D. -- Yunnan Observatories Angular momentum transport throughout stellar evolution Slide 25 Tayler-Spruit dynamo cannot reproduce the core rotation rate of red giants (Cantiello+2014) Lines: stellar evolution models computed from the zero age main sequence Evolution goes from left to right Initial mass: 1.5 M☉ Initial velocity: 120 km/s 1 order of magnitude Moyano, Facundo D. -- Yunnan Observatories Angular momentum transport throughout stellar evolution Slide 32 Extra slides Moyano, Facundo D. -- Yunnan Observatories Angular momentum transport throughout stellar evolution Slide 33 See Eggenberger, Moyano & den Hartogh(2022); Eggenberger+2019 It is still not possible to simultaneously account for subgiants and red giant branch stars simultaneously (Eggenberger+2019c) Core and surface rotation rates Moyano, Facundo D. -- Yunnan Observatories Angular momentum transport throughout stellar evolution Slide 34 Blue, red, and green lines: models computed with different initial velocities + original TS dynamo Light blue : model with prescription from Fuller+2019 Red and blue rectangles: core rotation rate as reported by Garcia+07, Fossat+2017 Core rotation rate of the Sun would further constrain the magnetic models (Eggenberger+2019b) Moyano, Facundo D. -- Yunnan Observatories Angular momentum transport throughout stellar evolution Slide 35 Core to surface rotation ratios of Gamma Doradus stars (GangLi+2020) versus models Moyano+2023 Moyano, Facundo D. -- Yunnan Observatories Angular momentum transport throughout stellar evolution Slide 36 GangLi+2024 Moyano, Facundo D. -- Yunnan Observatories Angular momentum transport throughout stellar evolution Slide 37 102 103 104 105 5.3 5.4 5.5 5.6 5.7 Filled : core Empty: envelope Core and envelope rotation rates [nHz] log(surface gravity) Core and envelope rotation rates of hot subdwarfs (only 5 with both measurements) Moyano, Facundo D. -- Yunnan Observatories Angular momentum transport throughout stellar evolution Slide 38 Hatt, Ong, Nielsen+2024 Measurements of internal magnetic fields in red giants Moyano, Facundo D. -- Yunnan Observatories Angular momentum transport throughout stellar evolution Slide 39 Hot subdwarfs’ core rotation rates might be affected by companions (see Ma & Fuller,2024) Moyano, Facundo D. -- Yunnan Observatories Angular momentum transport throughout stellar evolution Slide 40 -2 -1 0 1 2 3 3.6 3.8 4 4.2 4.4 4.6 4.8 5 5.2 log(L/L⊙) log(Teff) Core rotation rate vs surface gravity Evolutionary track in the HR diagram Core-helium burning Core-helium burning Envelope removal Envelope removal Angular momentum transport in hot subdwarfs Moyano+in prep. Moyano, Facundo D. -- Yunnan Observatories Angular momentum transport throughout stellar evolution Slide 41 50 100 150 200 250 300 350 400 4.4 4.6 4.8 5 5.2 5.4 5.6 5.8 6 Hot subdwarf - single Hot subdwarf - binary - Porb > 1d Core rotation rate [nHz] log(surface gravity) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Central 4He Moyano+in prep. Hints of angular momentum transfer to the stellar cores during common envelope ejection events Moyano, Facundo D. -- Yunnan Observatories Angular momentum transport throughout stellar evolution Slide 48 Magnetic fields Local conservation Figure adapted from Pedersen+2022 Main sequence stars with M ≈ 3 – 10 Msun Central hydrogen abundance Near-core rotation rate Moyano, Facundo D. -- Yunnan Observatories Angular momentum transport throughout stellar evolution Slide 49 Fuller+2019 Moyano, Facundo D. -- Yunnan Observatories Angular momentum transport throughout stellar evolution Slide 50 Fuller & Ma(2019)