Matteo Cantiello added Segue_to_RGs_maybe_something__.tex  almost 9 years ago

Commit id: c7c3a877305bacb489859ffae3968e16d03f5500

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%[Segue to RGs: maybe something about the unknown evolution of fields as  %stars evolve]  Both low-mass solar-like and intermediate-mass stars evolve to become  red giants when their hydrogen-core burning is exhausted. Red giants, like  the Sun, show a broad comb-like frequency spectrum of radial and non-radial  acoustic oscillation modes excited by turbulent surface convection [ref  deRidder].   The observed mode power across the spectrum has an overall bell-like  shape whose central frequency, \numax, decreases as a star expands during the  red giant evolution phase[REF Brown1991,KeplerObsPaper]. %[This 'frequency  %of maximum power' shows tight correlation with stellar surface gravity[REF  %Brown]].   The comb structure of the spectrum arises from a series of   overtone modes separated by the so-called large frequency separation for  each spherical degree, $l$. For observations of unresolved distant stars,  geometric cancellation prevents detection of modes with $l>3$.   Their spectra are therefore dominated by a pattern of radial ($l=0$) and  quadrupole ($l=2$) modes that form close pairs for each overtone with dipole  ($l=1$) modes located roughly halfway between successive radial-quadrupole pairs,  with only a weak signal of octupole modes ($l=3$).  %Due to geometric cancellation for higher degree modes, only a weak signal  %of octapole modes are seen and no significant signal for $l>3$.   %[SHORT VERISON: The spectral comb structure arise from a series of   %overtone modes, and due to geometric cancellation of high spherical degree  %the frequency pattern is dominated by radial (l=0) and quadrupole (l=2) modes  %that form close pairs for each overtone with dipole (l=1) modes   %located roughly halfway in between. Generally, only a weak signal of  %octapole (l=3) modes are seen.]   The dipole modes have turned out to be particularly useful probes of  internal structure [REF Dupret2009/Montalban20??].   They have been used to  distinguish hydrogen-shell and helium-core burning stars [REF  Bedding2011/Stello2013/Mosser2014] and to measure radial differential rotation [REF  Beck12/Mosser2012]. This fortune arise because %[through resonance coupling where]  each acoustic non-radial envelope mode couple to multiple gravity  modes in the core forming several mixed modes %observable at the surface,  with frequencies observable in the vicinity of the acoustic mode.  This coupling is strongest for dipole modes making them the most useful  probes of the core [REF Unno/Dupret?].