with age, stars brighten up & spin down

[Widdekind]

As stars age, their rotation rate declines, [math]\omega \propto t^{-1/2}[/math], cp. 'gyrochronology'. Meanwhile, their luminosity increases, comparably. Could there be a connection, between spin down, and brightening up ?

[insane_alien]

yep, the star expands.

 

conservation of angular momentum and increased surface area explain the effects.

[granpa]

but the core becomes denser

[insane_alien]

but the core becomes denser

 

but you cannot see the core, you see the photosphere which is what we measure rotation with.

[Widdekind]

yep, the star expands.

 

conservation of angular momentum and increased surface area explain the effects.

 

Crudely, [math]L = I \omega \approx M R^2 \omega[/math]. So, conservation of angular momentum, with [math]\omega \propto t^{-1/2}[/math], would require [math]R \propto t^{1/4} \propto \omega^{-1/2}[/math].

 

Our sun's luminosity is estimated to have increased ~30%, over the past 5 Gyr (UW). If attributed entirely to an increase in effective radius, then R² has increased by +30%, so [math]\omega[/math] has decreased by -30%. And, since, as our star expands, it actually cools; then, to account for a +30% increase in luminosity, with a decreasing temperature, would require >+30% 'extra' increase in R²; and, hence, a correspondingly greater decrease in rotation rate.

 

So, our sun has "spun down", by about -1/3^rd, since it formed, ~5 Gya ? The expansion, of the sun's envelope, can account, for the entire decrease in rotation rate, i.e. "ice skater pushing arms out" effect ?

 

What about the angular momentum, of the solar wind, and resulting heliosphere, i.e. a spinning ball of (admittedly diffuse) plasma ~100 AU across ?

[baric]

but you cannot see the core, you see the photosphere which is what we measure rotation with.

 

This is exactly correct.

[insane_alien]

So, our sun has "spun down", by about -1/3^rd, since it formed, ~5 Gya ? The expansion, of the sun's envelope, can account, for the entire decrease in rotation rate, i.e. "ice skater pushing arms out" effect ?

 

yep/ essentially. too tired for the maths, i'kk do it at the weekend if i remember.

What about the angular momentum, of the solar wind, and resulting heliosphere, i.e. a spinning ball of (admittedly diffuse) plasma ~100 AU across ?

 

well, its not so much a spinning ball as each ion of the solar wind is on its own hyperbolic escape trajectory.

 

but yes, what little rotational velocity it has gets less the further you go out. momentum is conserved.

[Widdekind]

At a mass-loss rate of [math]\dot{M}_{\odot} \approx 10^{-14} M_{\odot}/yr[/math], our sun has shed roughly a Neptune-mass of material, over its lifetime. All of that material, was shed, as plasma, i.e. "flux frozen" to solar magnetic field lines. So, is not our sun "dragging around" its heliosphere, as it spins, via those field lines ? And, a Neptune-mass of material, out at 100AU, might have more angular momentum, than even a whole solar mass of solar envelope, in at R_sun ~ 0.01 AU.

[Widdekind]

Both Jupiter and our Sun evidence differential rotation, with their poles spinning slower, than their equators. (For Jupiter, the difference is ~1%, for Sol, ~30%.) And, at least with Jupiter, the magnetic field rotates with the polar regions. Inexpertly, that implies, that the magnetic field rotates with the core, which is presumably about as big, as the (projection of the) slower-spinning polar regions; and that the core experiences a slowing torque, so progressively spinning down, whilst the equatorial regions swirl on ahead. Inexpertly, that resembles the spin down of pulsars, due to radio emission, from their spinning fields. Perhaps the equations for pulsar spin down apply to stars? If so, then their spinning down can be accounted for, by EM emissions. If not, then other physics are implied. "Skumanich" spindown of stars scales as P ~ t^-1/2.

 

http://en.wikipedia.org/wiki/Jupiter#Orbit_and_rotation

http://iopscience.iop.org/0004-637X/669/2/1167/fulltext/

[Enthalpy]

[The solar wind] is not so much a spinning ball as each ion of the solar wind is on its own hyperbolic escape trajectory.

Solar wind ions are not independent and their trajectory isn't hyperbolic. The density and speed of Solar wind follow a law that proves it.

 

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The original paper about gyrochronology is there:

http://arxiv.org/pdf/0704.3068v2.pdf

Edited October 7, 2012 by Enthalpy