Editing Appendix/Ramblings/OriginOfPlanetaryNebulae (section)

==Rose (1998)==

Here, we consider the descriptions presented by [http://adsabs.harvard.edu/abs/1998asa..book.....R W. K. Rose (1998)].

<font color="red">'''Evolution to the Red-Giant Branch &amp; the SC Limit:'''</font> (&sect;8.2, p. 267)  "<font color="darkgreen">&hellip; after hydrogen depletion has occurred in their cores main-sequence stars evolve onto the red-giant branch.  Low-mass stars <math>~(\mathrm{roughly}~M \leq 1.2 M_\odot)</math>, which burn hydrogen by means of the proton-proton chain on the main sequence evolve gradually from main sequence to red-giant evolutionary stages &hellip; The cores of stars that are sufficiently massive <math>~(\mathrm{roughly}~M \geq 1.2 M_\odot)</math> to burn hydrogen by means of the CNO cycle on the main sequence contract rapidly (i.e., in a Kelvin-Helmholtz timescale) after hydrogen core exhaustion, and then evolve more rapidly onto the red-giant branch &hellip;</font>"

(&sect;8.2, p. 268)  "<font color="darkgreen">Because the thermonuclear energy release that results from hydrogen burning is very large &hellip; the time-derivative term in Equation (2.131) can be neglected in calculating main-sequence stellar models.  If</font> [this same] <font color="darkgreen">term is neglected in calculating post-main-sequence evolution then the calculated stellar models have isothermal cores that are surrounded by hydrogen-burning shells.  Numerical calculations show that isothermal cores consisting of a nondegenerate gas surrounded by a hydrogen-burning shell source do not exist if the core mass exceeds <math>~\approx 0.1 - 0.15</math> times the mass of the star.  These limiting isothermal core masses are referred to collectively as the Sch&ouml;nberg-Chandrasekhar limit.   The existence of a limiting isothermal core for a particular initial mass main-sequence star shows that core contraction must occur in post-main-sequence evolution.</font>"

(&sect;8.2, p. 269)  "<font color="darkgreen">Numerical solutions of the equations of stellar interiors show that as the core mass of a red giant increases, the luminosity and radius increase by a large factor but the core radius changes by only a small amount.</font>"

<font color="red">'''Stellar Pulsation:'''</font> (&sect;8.1, p. 260)  "<font color="darkgreen">The instability that drives pulsations in RR Lyrae variables, Cepheids and long-period variables is associated with hydrogen and helium ionization zones.  The large heat capacity of these ionization zones causes the phase of maximum luminosity to be delayed by approximately 90&deg; as compared to the phase of minimum radius &hellip; Extensive hydrogen ionization zones cause</font> [long-period variables] <font color="darkgreen"> to become unstable to radial pulsations &hellip; The pulsations of &hellip; Cepheids result from both hydrogen and helium ionization zones.</font>"

(&sect;1.5, p. 24)  "<font color="darkgreen">&hellip; asymptotic-giant-branch stars become pulsationally unstable after their luminosities become</font> [greater or on the order of] <math>~2500 L_\odot</math>

<font color="red">'''Mass Loss &amp; Formation of Planetary Nebula:'''</font> (&sect;8.1, p. 260)  "<font color="darkgreen">The [pulsation] amplitudes</font>" of long-period variables "<font color="darkgreen">become sufficiently large that shock waves are generated in their atmospheres.  The standard scenario for producing mass loss from these stars is that shock waves eject mass.</font>"

(&sect;1.5, p. 24)  "<font color="darkgreen">Long-period variables experience significant mass loss.  The final phase of mass loss on the red-giant branch leads to the formation of a planetary nebula.  If a luminous red giant ejects a mass shell, and as a consequence the remnant star becomes nearly hydrogen deficient, then the remnant star evolves rapidly off the red-giant branch and into the region of the H-R diagram occupied by the central stars of planetary nebulae.</font>"