User:Tohline/Appendix/Ramblings/OriginOfPlanetaryNebulae - Revision history

Tohline: /* See Also */

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Tohline: /* Hansen & Kawaler (1994) */

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Hansen & Kawaler (1994)

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	<font color="red">'''Mass Loss & Formation of Planetary Nebula:'''</font>		<font color="red">'''Mass Loss & Formation of Planetary Nebula:'''</font> (§2.4.1, pp. 60-61) "<font color="darkgreen">The ignition of helium under electron degenerate conditions …</font>" occurs via "<font color="darkgreen">… an explosive runaway or ''helium flash''. … The major evidence that leads us to believe that the helium flash is not explosive enough to disrupt the star in a serious fashion is that stars in the post-helium flash stage are observed and they constitute the horizontal branch of globular clusters, for example.</font>"

			(§2.4.1, p. 62) "<font color="darkgreen">The critical point about the</font> [observationally determined] <font color="darkgreen">masses … for RR Lyrae stars, and therefore HB stars, is that they are less than the masses of their progenitor main sequence stars. If these results are correct, then mass must have been lost during the time elapsed between the main sequence and the HB stages. Such mass loss from red giants is observed, but the physical mechanism is not well understood.</font>"

	==Rose (1998)==		==Rose (1998)==

Tohline: /* Hansen & Kawaler (1994) */

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Hansen & Kawaler (1994)

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	Here, we consider the descriptions presented by [<b>[[User:Tohline/Appendix/References#HK94\|<font color="red">HK94</font>]]</b>].		Here, we consider the descriptions presented by [<b>[[User:Tohline/Appendix/References#HK94\|<font color="red">HK94</font>]]</b>].

	<font color="red">'''Evolution to the Red-Giant Branch & the SC Limit:'''</font> (§2.3, p. 53) "<font color="darkgreen">Following exhaustion of hydrogen in the core, the growing helium remnant is surrounded by an active shell of burning hydrogen, which supplies the power for the star.</font>"		<font color="red">'''Evolution to the Red-Giant Branch & the SC Limit:'''</font> (§2.3, pp. 53-55) "<font color="darkgreen">Following exhaustion of hydrogen in the core, the growing helium remnant is surrounded by an active shell of burning hydrogen, which supplies the power for the star. The core itself, however, has no energy source of its own (except some input from contraction) and hence it tends to be isothermal since no temperature gradients are required. It is at this point … that the structure of the star begins to change radically and the main sequence phase ends. … evolution to … the red giant branch (RGB) is characterized by a continual expansion and reddening of the star to lower [surface] temperatures. </font>"

			"<font color="darkgreen">In an early 1942 study Schönberg and Chandrasekhar demonstrated that when an isothermal helium core is built up to a mass corresponding to about 10% of the initial hydrogen mass of the star, it is no longer possible to maintain quasi-hydrostatic equilibrium for the core of the model star if pressure support is due to an ideal gas. Other studies, including evolutionary calculations, support this by showing that the core contracts and heats rapidly … The envelope … however, responds by expanding rapidly … This signals the end of the main sequence phase of evolution for the star …</font>"

	<font color="red">'''Stellar Pulsation:'''</font>		<font color="red">'''Stellar Pulsation:'''</font>

Tohline: /* Textbook Explanations */

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Textbook Explanations

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	<font color="red">'''Mass Loss:'''</font> (§6-9, p. 501) "<font color="darkgreen">Mass loss is a self-descriptive term that is used to describe any process by which the main body of the star, defined as the gravitationally bound mass, reduces its mass by ejecting surface layers … Mass loss can occur in a variety of forms and can be initiated by a variety of physical mechanisms. Any catastrophic event in which a massive outer layer is lifted off into space by some internal instability must result in a drastically new structure for the remaining core. So special are these circumstances that they will not be discussed here..</font>"		<font color="red">'''Mass Loss:'''</font> (§6-9, p. 501) "<font color="darkgreen">Mass loss is a self-descriptive term that is used to describe any process by which the main body of the star, defined as the gravitationally bound mass, reduces its mass by ejecting surface layers … Mass loss can occur in a variety of forms and can be initiated by a variety of physical mechanisms. Any catastrophic event in which a massive outer layer is lifted off into space by some internal instability must result in a drastically new structure for the remaining core. So special are these circumstances that they will not be discussed here..</font>"

			==Hansen & Kawaler (1994)==

			Here, we consider the descriptions presented by [<b>[[User:Tohline/Appendix/References#HK94\|<font color="red">HK94</font>]]</b>].

			<font color="red">'''Evolution to the Red-Giant Branch & the SC Limit:'''</font> (§2.3, p. 53) "<font color="darkgreen">Following exhaustion of hydrogen in the core, the growing helium remnant is surrounded by an active shell of burning hydrogen, which supplies the power for the star.</font>"


			<font color="red">'''Stellar Pulsation:'''</font>


			<font color="red">'''Mass Loss & Formation of Planetary Nebula:'''</font>

	==Rose (1998)==		==Rose (1998)==

Tohline: /* Padmanabhan (2000) */

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Padmanabhan (2000)

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	<font color="red">'''Stellar Pulsation:'''</font> (Vol. II, §3.7.2, p. 178) "<font color="darkgreen">~~The~~ net amount of work done by each layer of the star during one cycle of oscillation ~~is the difference between the heat flowing into the gas and the heat leaving the gas.~~ To drive the oscillations, heat must enter the layer during the high-temperature part of the cycle and exit during the low-temperature part. Different layers of the star may have different phase relations as regards such a process, and whether the oscillations will be sustained or not will depend on the net effect. Favourable circumstances for sustained oscillations occur if</font>," for example, the opacity in a layer of the envelope increases when the layer is compressed. "<font color="darkgreen">(Under normal circumstances, opacity actually decreases with compression.) … [~~this~~] exception ~~[can] occur~~ in the layers of the star that are partially ionized.</font>"		<font color="red">'''Stellar Pulsation:'''</font> (Vol. II, §3.7.2, p. 178) Finite-amplitude, ''sustained'' oscillations in stars can only be explained in terms of ''non-adiabatic'' effects. Such explanations are usually couched in terms of a measure of the "<font color="darkgreen">net amount of work done by each layer of the star during one cycle of oscillation … To drive the oscillations, heat must enter the layer during the high-temperature part of the cycle and exit during the low-temperature part. Different layers of the star may have different phase relations as regards such a process, and whether the oscillations will be sustained or not will depend on the net effect. Favourable circumstances for sustained oscillations occur if</font>," for example, the opacity in a layer of the envelope increases when the layer is compressed. "<font color="darkgreen">(Under normal circumstances, opacity actually decreases with compression.) … [This] exception occurs in the layers of the star that are partially ionized … This mechanism is called the <b>κ mechanism</b>.</font>"

Tohline: /* Padmanabhan (2000) */

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Padmanabhan (2000)

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	<font color="red">'''Stellar Pulsation:'''</font>		<font color="red">'''Stellar Pulsation:'''</font> (Vol. II, §3.7.2, p. 178) "<font color="darkgreen">The net amount of work done by each layer of the star during one cycle of oscillation is the difference between the heat flowing into the gas and the heat leaving the gas. To drive the oscillations, heat must enter the layer during the high-temperature part of the cycle and exit during the low-temperature part. Different layers of the star may have different phase relations as regards such a process, and whether the oscillations will be sustained or not will depend on the net effect. Favourable circumstances for sustained oscillations occur if</font>," for example, the opacity in a layer of the envelope increases when the layer is compressed. "<font color="darkgreen">(Under normal circumstances, opacity actually decreases with compression.) … [this] exception [can] occur in the layers of the star that are partially ionized.</font>"

Tohline: /* Padmanabhan (2000) */

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Padmanabhan (2000)

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	<font color="red">'''Mass Loss & Formation of Planetary Nebula:'''</font>		<font color="red">'''Mass Loss & Formation of Planetary Nebula:'''</font> (Vol. II, §3.6, p. 163) "<font color="darkgreen">The rapid expansion of the star … implies that the outer regions of the star are very loosely bound. Hence it is possible for matter to escape from the star in the form of a steady outflow, usually called a ''stellar wind''. … Modelling the resulting stellar wind from fundamental considerations is extremely difficult and no reliable theory exists at present.''</font>"

			(Vol. II, §3.6, p. 165) For sufficiently low mass stars, "<font color="darkgreen">… carbon ignition does not take place … and a more gradual ejection of material from the star in the form of shell flashes, winds, and envelope pulsations will lead to an expanding shell of gas around the core. This expanding shell of gas is called a ''planetary nebula''.</font>"

	==Maoz (2016)==		==Maoz (2016)==

Tohline: /* Padmanabhan (2000) */

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Padmanabhan (2000)

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	<font color="red">'''Mass Loss & ~~the~~ Formation of Planetary ~~Nebulae~~:'''</font>		<font color="red">'''Mass Loss & Formation of Planetary Nebula:'''</font>

	==Maoz (2016)==		==Maoz (2016)==

Tohline: /* Padmanabhan (2000) */

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Padmanabhan (2000)

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	He also emphasizes the following. (Vol. II, §3.4.3, p. 148) "<font color="darkgreen">During</font>" evolution from the main sequence to the red-giant branch, "<font color="darkgreen">the core and the envelope regions behave in a very different way. The study of the trajectories of different mass shells inside the star as functions of time based on numerical integration of equations of stellar evolution shows that the core collapses while the envelope expands.</font>"		He also emphasizes the following. (Vol. II, §3.4.3, p. 148) "<font color="darkgreen">During</font>" evolution from the main sequence to the red-giant branch, "<font color="darkgreen">the core and the envelope regions behave in a very different way. The study of the trajectories of different mass shells inside the star as functions of time based on numerical integration of equations of stellar evolution shows that the core collapses while the envelope expands.</font>"


			<font color="red">'''Stellar Pulsation:'''</font>


			<font color="red">'''Mass Loss & the Formation of Planetary Nebulae:'''</font>

	==Maoz (2016)==		==Maoz (2016)==

Tohline: /* Padmanabhan (2000) */

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Padmanabhan (2000)

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	==Padmanabhan (2000)==		==Padmanabhan (2000)==

	Here, we consider the descriptions presented by [<b>[[User:Tohline/Appendix/References#P00\|<font color="red">P00</font>]]</b>] .		Here, we consider the descriptions presented by [<b>[[User:Tohline/Appendix/References#P00\|<font color="red">P00</font>]]</b>]; note that in Chapter 3 of Volume II, subsection 3.4 is titled, ''<b>Evolution of High-Mass Stars</b>'' while subsection 3.5 is titled, ''<b>Evolution of Low-Mass Stars</b>''.

	<font color="red">'''Evolution to the Red-Giant Branch:'''</font> (Vol. II, §3.4.3, p. 142) Once the hydrogen fuel in the core is nearly exhausted and hydrogen burning occurs primarily in a shell immediately surrounding the core, "<font color="darkgreen">Further evolution depends on the structural changes that take place in the [inert] helium core … the helium core is fairly homogeneous [in, for example, a <math>~5 M_\odot</math> star] because of the mixing that is due to the original convective transport … Further, it will be nearly isothermal because the vanishing of luminosity implies the vanishing of the temperature gradient. The equilibrium of such a star depends on the ability of an isothermal core (with mass <math>~M_\mathrm{ic} \equiv qM</math>) to support the envelope of mass <math>~(1-q)M</math>. It turns out that this is possible only if the fraction of the mass in the core is below a critical value called the</font>" Schönberg-Chandrasekhar limit.		<font color="red">'''Evolution to the Red-Giant Branch & the SC Limit:'''</font> (Vol. II, §3.4.3, p. 142) Once the hydrogen fuel in the core is nearly exhausted and hydrogen burning occurs primarily in a shell immediately surrounding the core, "<font color="darkgreen">Further evolution depends on the structural changes that take place in the [inert] helium core … the helium core is fairly homogeneous [in, for example, a <math>~5 M_\odot</math> star] because of the mixing that is due to the original convective transport … Further, it will be nearly isothermal because the vanishing of luminosity implies the vanishing of the temperature gradient. The equilibrium of such a star depends on the ability of an isothermal core (with mass <math>~M_\mathrm{ic} \equiv qM</math>) to support the envelope of mass <math>~(1-q)M</math>. It turns out that this is possible only if the fraction of the mass in the core is below a critical value called the</font>" Schönberg-Chandrasekhar (SC) limit.

			For the remainder of §3.4.3, [<b>[[User:Tohline/Appendix/References#P00\|<font color="red">P00</font>]]</b>] discusses in considerable detail — relying heavily on virial-theorem-based arguments — how the SC limit should be viewed in high-mass stars, where the core remains non-degenerate, versus in low-mass stars where electron degeneracy sets in. Then in §3.5.1 (p. 152), he re-emphasizes that "<font color="darkgreen">The effect of shell burning is … very different in low-mass stars compared with what we have seen in high-mass stars. Because the cores are nearly degenerate, the [SC] limit is fairly irrelevant for low-mass stars. As the burning shell causes the core mass to exceed <math>~\sim 0.1 M_\odot</math>, the core contraction would have produced sufficient degeneracy to circumvent the [SC] constraint. At this stage, the core is made of degenerate, isothermal helium and no rapid core contraction occurs.</font>"

			He also emphasizes the following. (Vol. II, §3.4.3, p. 148) "<font color="darkgreen">During</font>" evolution from the main sequence to the red-giant branch, "<font color="darkgreen">the core and the envelope regions behave in a very different way. The study of the trajectories of different mass shells inside the star as functions of time based on numerical integration of equations of stellar evolution shows that the core collapses while the envelope expands.</font>"

	==Maoz (2016)==		==Maoz (2016)==

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	* [http://adsabs.harvard.edu/abs/1981ASSL...88..431R A. Renzini (1981, in Physical Processes in Red Giants; Proceedings of the Second Workshop, Erice, Italy, pp. 431 - 446)], ''Red Giants as Precursors of Planetary Nebulae.''		* [http://adsabs.harvard.edu/abs/1981ASSL...88..431R A. Renzini (1981, in Physical Processes in Red Giants; Proceedings of the Second Workshop, Erice, Italy, pp. 431 - 446)], ''Red Giants as Precursors of Planetary Nebulae.''
	* [http://adsabs.harvard.edu/abs/1984ApJ...277..333I I. Iben, Jr. (1984, ApJ, Vol. 277, pp. 333 - 354)], ''On the Frequency of Planetary Nebula Nuclei Powered by Helium Burning and on the Frequency of White Dwarfs with Hydrogen-Deficient Atmospheres.''		* [http://adsabs.harvard.edu/abs/1984ApJ...277..333I I. Iben, Jr. (1984, ApJ, Vol. 277, pp. 333 - 354)], ''On the Frequency of Planetary Nebula Nuclei Powered by Helium Burning and on the Frequency of White Dwarfs with Hydrogen-Deficient Atmospheres.''
			* [https://ui.adsabs.harvard.edu/abs/1989IAUS..131..541H/abstract I. Hachisu & M. Kato (1989)], in Planetary Nebulae. Proceedings of the 131st. Symposium of the International Astronomical Union, held in Mexico City, Mexico, October 5 - 9, 1987. Editor, Silvia Torres-Peimbert; Publisher, Kluwer Academic Publishers, Dordrecht, The Netherlands, Boston, MA, 1988: ''Common Envelope Evolutions of Binary System and Formation of Planetary Nebulae''


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