Widdekind

Would it be possible, to observe "exo-comets" -- are not comets much bigger, and more luminous, than planets (when they're 'active' & off-gassing) ? The presence of comets, i.e., "Kuiper Belt like objects", might indicate the presence of exo-planets.

If, by applying the Correspondence Principle, to the Classical Relativistic 4-vector equation [math]\vec{p} \circ \vec{p} = m^2[/math] yields the Klein-Gordon equation [math]\left( \partial_t^2 - \partial_x^2 \right) \Psi = m^2 \Psi[/math]; then, why not simply extend the 4-dot product, from Minkowskian flat space [math]\vec{p} \circ \vec{p} \equiv p^{\mu} p^{\nu} \eta_{\mu \nu}[/math], to curved space, via the GR metric [math]\eta_{\mu \nu} \rightarrow g_{\mu \nu}[/math], i.e., [math]\vec{p} \circ \vec{p} \equiv p^{\mu} p^{\nu} g_{\mu \nu}[/math] ? Likewise, for purposes of computing the metric tensor, from the wave-functions, via the Stress-Energy Tensor, one could simply treat the quantum wave-functions as "smeared out particles" (could one quote "the big names, in the big chairs", and simply say, "shut up & calculate" ?), and calculate the SET with terms vaguely like [math]T_{\mu \nu} = \Psi^{*} p_{\mu} p_{\nu} \Psi[/math] ??

Thanks for the clarifications. If I might impose -- if interferometry allows multiple radio dishes, to be "thralled" together, to mimic a (patchy) radar of much larger dimensions... can something similar be done, at optical wavelengths ? To wit, could a "farm" of "solar panels", as it were, be thralled together, to mimic large >1000m, multi-acre, mirrors ??

[math]T^4® = \frac{3 G M \dot{M}}{8 \pi \sigma r^3} \left[1 - \sqrt{\frac{R}{r}} \right][/math] [math]C_S^2 \approx \frac{k_B T}{\bar{m}}[/math] [math]v_K^2 \equiv \frac{G M}{r}[/math] [math]\dot{M}_{Edd} \equiv \frac{4 \pi c}{\sigma_T} \bar{m} R[/math] Defining [math]\dot{M} \equiv \mu \dot{M}_{Edd}[/math], then w.h.t.: [math]\therefore \left(\frac{C_S}{v_K}\right)^8 \approx \mu \left( \frac{k_B}{G M \bar{m}} \right)^3 \left( \frac{3 k_B c R}{2 \sigma \sigma_T} \right) r \left[1 - \sqrt{\frac{R}{r}} \right][/math] [math] \approx 2 \times 10^{-10} \left( \frac{\bar{m}}{m_H} \right)^{-3} \left( \frac{M}{M_{\odot}} \right)^{-3} \left( \frac{R}{R_{\odot}} \right)^2 \mu \left[ x - \sqrt{x} \right][/math] where we have defined [math]x \equiv r / R[/math]. Taking the eighth-root, w.h.t.: [math]\frac{C_S}{v_K} \approx 0.06 \left( \frac{\bar{m}}{m_H} \right)^{-3/8} \left( \frac{M}{M_{\odot}} \right)^{-3/8} \left( \frac{R}{R_{\odot}} \right)^{1/4} \mu^{1/8} \left[ x - \sqrt{x} \right]^{1/8}[/math] If we further assume a relativistic accretor, s.t. [math]R = \rho R_S[/math], where [math]R_S \approx 3 \; km[/math] per [math]M_{\odot}[/math], then w.h.t.: [math]\frac{C_S}{v_K} \approx 0.003 \left( \frac{\bar{m}}{m_H} \right)^{-3/8} \left( \frac{M}{M_{\odot}} \right)^{-3/8} \rho^{2/8} \mu^{1/8} \left[ x - \sqrt{x} \right]^{1/8}[/math] For NS & BH, [math]\rho \approx 3[/math], s.t.: [math]\frac{C_S}{v_K} \approx 0.004 \left( \frac{M}{M_{\odot}} \right)^{-3/8} \left[ x - \sqrt{x} \right]^{1/8}[/math] even assuming Eddington-rate accretion, of pure H plasma. For a typical NS ([math]M \approx 1.4 M_{\odot}[/math]), w.h.t.: [math]\frac{C_S}{v_K} \approx 0.003 \left[ x - \sqrt{x} \right]^{1/8}[/math] The fore-going formula only approaches parity, as [math]x \rightarrow 300[/math], at [math]\approx 1000 R_S[/math], or [math]\approx R_{\oplus} \approx R_{WD}[/math]. Inside of that radius, even as [math]v_K \rightarrow c[/math], Accretion Disk temperatures peak around 1-2 KeV << mc2. Does this imply, that inner-disk flows are "cold", Relativistically (and relatively) speaking ? Is this why Accretion Disks are "radiatively inefficient" s.t. "advective cooling (carrying the energy with the flow) dominates" ? As [math]v_K \rightarrow c[/math], even as [math]v_K >> C_S[/math], wouldn't most thermal emission be "headlighted" forward, with the flow ? How, then, would such inner-disk regions radiate ?? References: Kolb. Extreme Environment Astrophysics. Chris Done & Marek Gierlinski. Observing the effects of the event horizon in black holes, Mon. Not. R. Astron. Soc. 000, 1–15 (2002).

According to A.Loeb's How Did the First Stars & Galaxies Form ?, the CMB Temperature fluctuations are of order O(10-5), indicating that density fluctuations were of a similar scale, back at z~1100. Now, our sun; and, our galaxy, both have density fluctuations RS/R ~ 10-5. So, theoretically, fully-formed stars, or galaxies, as seen today, could account for the ancient anisotropies, billions of years ago, at the CMB LSS. What, then, is the 'problem' with finding sufficient 'seeds' for structure formation ?

In SN, which generate NS, one witnesses "matter fall-back", where some baryons fail to escape the compact core's gravity. At higher & higher progenitor masses, wouldn't one witness increasing gravity, s.t. there would be a regime, of "neutrino fall-back"... and then "photon fall-back" ? Such "failed SN", which would generate BHs, might, then, eject no matter; emit no neutrinos; emit no photons. Could you create stellar-mass BHs, in "cloaked covert-ness", by such a "failed SN" scenario ??? Refs: Kolb. Extreme Environment Astrophysics. Schilling. Flash!

Degeneracy is common in stars, sub-stars ('Brown Dwarfs'), and super-planets ('Gas Giants'). And, even at standard terrestrial temperatures & pressures, the outer 'conduction' electrons, in solid metals, are considered to be Degenerate. What, then, happens, in the molten iron cores, of 'super-earth' sized rocky planets, [math]m \leq 10 M_{\oplus}[/math] ? As you squeeze iron atoms together, first the outer 'valence' electrons will "blur" into "bands"; but, as you squeeze them further, progressively more & more, deeper & deeper level'ed, electrons will also become "band blurred". Is the iron in the core of the earth, in an "ultra-conductive" Degenerate state, e.g., hypothetical hydrogen super-conductor in the core of Jupiter ? Naively, according to the H.U.P., if electrons normally confined, in atomic isolation, to orbitals of isolated size-scale [math]\Delta x[/math], are compressed due to pressure, down to a size-scale of [math]\Delta x' < \Delta x[/math], then would not the "Degeneracy partial pressure", of that "blurring band" of electrons, be related to that band's Fermi Energy, [math]E_F \approx \frac{\hbar^2}{2 m_e \Delta x'^2} - \frac{\hbar^2}{2 m_e \Delta x^2} = E_0 \left( \left[ \frac{\Delta x}{\Delta x'}\right]^2 -1 \right) [/math] ? If so, then, as P increases, more & more orbitals-cum-bands provide more & more Degeneracy-P support.

Star rotation rates, and (dynamo-driven) magnetic field strengths -- which are themselves mutually co-related -- decline with star age (Landstreet 2007). Mass-loss, from outflows correlated with the initially rapid rotation & strong fields, can account for such "braking" (Nariai 1969). Qualitatively, similar is seen, in the "spin down" of Pulsars, due to the emission of EM energy, causing "magnetic braking". Thus, could there be a connection, if crude, between (1) stellar coronae, which generate stellar winds & "astro-sphere nebulae"; (2) Pulsar Wind Nebulae; (3) magnetic braking & star spin-down ? To wit, could stellar coronae be so anomalously hot, b/c they absorb the emitted EM energy, from the central star's spinning magnetic field ? Moreover, astrophysical jets, from NS & BH, in accreting "LMXB" binary systems, form only in the relativistic-stars' "low-hard" state, of (A) low mass accretion rate; and (B) hard X-ray spectra, associated with energized, "up-scattered" (inverse Compton) photons, arising from the ~1-10 keV accretion disk, propagating through, and emerging from, an ultra-hot ~100-300 keV "Accretion Disk Corona" (ADC). (For, at higher accretion rates, and higher disk luminosities, all the extra photons actually cool the ADC down, to a common, and much reduced, AD-ADC temperature.) Note, that such ultra-hot ADC temperatures, where-with-in electron thermal energies are comparable to their rest-mass-energies, are characterized by electrons having trans-luminal velocities. And, the ADC is ~100x larger, than the central NS, thus extending out to where NS-anchored field lines would be "whipping around" at the speed-of-light, i.e., the "light cylinder". Thus, could there be a connection, between star magnetic fields, perhaps powering hot coronae, which then drive star outflows (winds, jets), which inflate circum-stellar nebulae (astro-spheres, Pulsar Wind Nebulae), but which bring about the magnetic braking & spin-down of said central star ?? (Indeed, our own sun has, at rotational mid-plane, an ionized "current sheet", separating polar regions of open, poloidal field lines -- resembling, qualitatively, an "ultra-diffuse accretion disk".) REFERENCES: Fabrika. Jets & Super-Critical Accretion Disk in SS433. Kolb. [Open University] Extreme Environment Astrophysics.

If neutrinos really propagate faster-than-light, wouldn't the neutrino burst, from SN1987a, have arrived at earth, long long before the optical flare, from the visible SN ?

Perhaps the planet has, literally, been "scorched" & "burned black" ??

What would happen, if you considered cosmologically-distant light-sources, deep down in a rotating gravity well? If, as a first approximation, one were to assume a Kerr space-time, then would -- for calculating the 4-dot product at the emitter -- not the Schwarzschild Metric, for a polar-emitted photon ([math]\theta = d\theta = d\phi \equiv 0[/math]), e.g., long-type-GRBs, look vaguely like... [math] \left( \begin{array}{cccc} 1- r R_S/(r^2 + \alpha^2) & 0 & 0 & 0 \\ 0 & -(r^2 + \alpha^2) / (r^2 - \alpha^2 + r R_S) & 0 & 0 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & -1 \end{array} \right)[/math] ? At the emitter, the photon 4-vector is, in natural units (h = c = 1), [math]\lambda_e^{-1} \left( \begin{array}{c} 1 \\ -1 \\ 0 \\ 0 \end{array} \right)[/math]; and, the emitter 4-vector is [math]\gamma_e \left( \begin{array}{c} 1 \\ \beta_{e,r} \\ \beta_{e,\theta} \\ \beta_{e,\phi} \end{array} \right)[/math]. And then, the four-dot-product, at the emitter, becomes: [math]\left( \vec{k} \circ \vec{u} \right)_e = \left( \frac{\gamma_e}{\lambda_e} \right) \left( \left[ 1- \frac{r R_{S,e}}{r^2 + \alpha^2} \right] + \beta_{e,r} \left[ \frac{r^2 + \alpha^2}{r^2 - \alpha^2 + r R_{S,e}} \right] \right)[/math] And more, borrowing from the PP, the four-dot-product, at the observer, assumed-to-be in the observer's rest-frame, where [math]\gamma_o = \beta_o = 0[/math]; and, which rest-frame is further assumed-to-be non-rotating; thusly becomes: [math]\left( \vec{k} \circ \vec{u} \right)_o = \left( \frac{1}{\lambda_o} \right) \left( 1- \frac{R_{S,o}}{r} \right)[/math] And then: [math]1+z = \frac{\left( \vec{k} \circ \vec{u} \right)_e}{\left( \vec{k} \circ \vec{u} \right)_o}[/math] [math]\; \; \; \; = \left( \frac{\lambda_o}{\lambda_e} \right) \left( \frac{\gamma_e}{1- \frac{R_{S,o}}{r}} \right) \times \left( \left[ 1- \frac{r R_{S,e}}{r^2 + \alpha^2} \right] + \beta_{e,r} \left[ \frac{r^2 + \alpha^2}{r^2 - \alpha^2 + r R_{S,e}} \right] \right) [/math] For a maximally-rotating Kerr BH, the "Kerr radius" [math]\alpha = R_S / 2[/math]; and, emission can occur, from this "rotationally reduced" radius [math]r = \alpha[/math]. Assuming such, the above formula simplifies to: [math]1+z = \left( \frac{\lambda_o}{\lambda_e} \right) \left( \frac{\gamma_e}{1- \frac{R_{S,o}}{r}} \right) \times \beta_{e,r} [/math] Ignoring the O(10-5) effect, of our own assumed-to-be-the-observer gravity well, w.h.t.: [math]1+z = \left( \frac{\lambda_o}{\lambda_e} \right) \times \left( \gamma_e \, \beta_{e,r} \right) \rightarrow \infty [/math] What is the formula, for the "fall-back radius", for a given (rotating) BH, and a given "initial launch velocity", i.e., given [math]\beta_r[/math], how close can you get to a given (rotating) BH, and still escape ? Assuming that, per PP, [math]\lambda_o \approx 1/3 \lambda_e[/math]; and, assuming an average red-shift for long-GRBs of [math]<z> \approx 0.7[/math] (Mazure. Exploding Super-Stars); and, assuming essentially totally-radial (electron) emitter velocity; then, [math]\gamma_e \beta_e \approx 5[/math], i.e., ~0.98 c. Presumed-to-have-fallen-back electrons, acted, "long long ago, far far away", like "launch-vehicle rocket sleds for barely-escaping gamma-ray photons" ?? ADDENDA: This source seems partially poignant, and particularly interesting.

Our sun exhibits periodic field reversals (~10 years). Our earth exhibits periodic field reversals (~105 years). Our sun reverses field, at "solar maximum", when their are the maximum number of local field anomalies, called "sun spots". And, our earth, long-over-due for "scheduled" field reversal, is starting to show localized, anomalous, field-reversed regions, e.g., South Atlantic Anomaly (SAA). QUESTION: Could you call the SAA an "earth spot"? To wit, are "earth spots" and "sun spots" similar, if different-size-scaled, manifestations, of the same underlying Magnetic Dynamo field-reversal process ??

Could you use reflectors, anchored to the moon, for long-base-line Gravity Wave detectors? What about satellites, or systems thereof, in Geo-Synchronous Orbit? (Or, given the success of detecting earth's precession, with Relativistic accuracy, w/ gyro-scopes, could 3 mutually-perpendicular gyro-scopes detect GWs -- i.e., would GWs affect transverse vs. longitudinal rotations differently??)

According to the Open University text-book Extreme Environment Astrophysics, p.164, most x-ray flares, in active LMXB systems, are due to the sudden accretion, onto the central object, of "blobs" of material, from the surrounding accretion disk. Now, first, T-Tauri stars often flare up brightly; and, T-Tauri proto-stars, may be orbited, by "in-close" proto-Hot-Jupiters; and, many of those proto-Hot-Jupiters might "in-spiral", before their host star's core ignites, and their host star's "first light" sweeps out the circum-stellar, proto-planetary disk, thereby removing the material between the HJ and the central star, whose gravity & frictional forces were causing the "slow death spiral", of the planet, star-wards. QUESTION: Could the sudden, if "shrouded" accretion (amidst the thick circum-stellar, proto-planetary disk), of "proto-Hot-Jupiter blobs", account for the flares, in T-Tauri systems ?

Could Kepler detect proto-planets, orbiting proto-stars (e.g., T-Tauri phase proto-stars) ??

Couldn't there be qualitative correlations, between "young immature" astro-spheres; and "old mature" astro-spheres? In the extreme, young T-Tauri stars are still shrouded in their 'Bok Globules' & 'E.G.G.s', w/ no AS's to speak of; whereas, older MS and post-MS stars, having 'evaporated' from their initial birth clusters, have full-flowered AS's.

As pre-star 'cloud clumps' coalesce, collapse, and 'disk-down', they remain comparatively cool, e.g., ~3000K on descending Hayashi tracks. Before the central star reaches the MS, with 'first light' core H-burning ignition, wouldn't the circum-proto-stellar disk be colder, than when its central star is on the MS? Thus, the "snow line", beyond which giant planets can form, would have been much closer to the central proto-star. So, couldn't now-hot-Jupiters originally have been "fast forming cold sub-binary companions", which only became "blow torched", by the central star, millions of years later, when it ignited H-burning in its core? (Indeed, "disk fragmentation" seems to be a common occurrence -- pre-star cloud clumps often 'disk down' into binary/trinary star systems; circum-stellar disks fragment into planets; planets have moons...)

Before forming, pre-star 'cloud clumps' have generated no stellar winds -- instead of driving material away, through radiation pressures, they are still accreting material. But, once fully formed, after "first light", MS stars start shedding material, driving out stellar winds, that blow out 'astro-sphere' bubbles. Could, therefore, you not infer the age of a star, since it arrived on MS, by the size, of its ever-expanding astro-sphere ?

Neutronized 'neutronium' matter is, like regular rock, a 'structural material'. Neutronized matter has (1) an elastic regime (e.g., core bounce-and-rebound, during the SNe, out of whose ashes, NS's emerge); (2) a plastic regime (e.g., 'border-line' SN / HN, from 'border-line' super-massive / hyper-massive progenitor stars, ~30 Msol, which generate 'maximal NS' or 'minimal BH'); and (3) a failure regime (e.g., HNe, where gravity crushes the core, without bounce-back). The elasticity, of regular rock, which 'rolls' and flexes during terrestrial earth-quakes, is already difficult to recognize -- 'neutronium' would, in some sense, be 'ultra rock'. But, according to the Teaching Company lecture series Black Holes Explained, by Prof. Alex Filippenko, there is observational evidence, which can be construed, with some objects -- observed to be more massive, and denser, than typical NS -- not emitting radiation, from any visible surface; and, which emit radically red-shifted light, from the inner edges, of their accretion disks. If so, then there is observational evidence, for objects darker, denser, and more extreme, than even NS. Such "dark holes" might not be "infinitely" dense BH... but, never-the-less, some state of exotic-matter more extreme than 'neutronium'. Again, NS are produced in the SNe, of SM-progenitor stars, <30 Msol. Er go, yet-more-massive, HM-progenitor stars, >30 Msol, which generate HNe & GRBs, will leave behind "burning embers" commensurately more extreme still. In baryonic matter, 99% of the mass-energy... is 'glue'. The "bare naked" quarks, combined, account for ~10 MeV, out of ~1 GeV per nucleon. Now, according to the Bag-Model of Quark Confinement, a reasonably-accurate potential, for quarks inside nucleons, is V = k r, where k ~ 1 GeV / fm. In particular, the potential is zero at zero separation -- 'glue' is only 'engaged', when quarks start to stray ('when they tug on their tethers, the Color Force yanks their chains, and reels them in'). So, 'glue' is only 'energized' -- i.e., massive -- when quarks start to stray. Thus, as you compress neutronized 'neutronium' matter, why wouldn't you begin to press those quarks together, towards their r --> 0 regime of 'asymptotic freedom' (V ~ 0)? To wit, inside ultra-compact objects, why wouldn't gravitational compression "take over from", and "bear the burden of", the Color Force -- keeping the quarks confined, without the need for 'glue' ? If so, then, as you compressed an object, to densities > 1 / fm3, the quarks would interact less vigorously; produce less 'glue'; and, mass <99% less (to lowest order, [math]M® \propto R[/math]).

According to the Discovery Channel documentary How the Universe Works -- Black Holes, our cosmos accords with the GR equations, of a Black Hole. If you "plug in the values of the mass of the universe, radius of the universe", it turns out, that our cosmos could exist inside the event horizon, of a BH. What if our cosmos is, in some way, the product, of a rotating BH ?

(1) I found a plot, of the (non-circular, eccentric) absolute space velocities (in the [math]\Pi, W, \Theta[/math] directions), of a sizeable sample, of Globular Clusters (GCs), orbiting our Milky Way Galaxy (MWG) (page 9) (2) I found a plot, of the (circular) space velocities, of a sizeable sample, of Molecular Clouds (MCs), rotating within the disk, of the MWG (figure 11) (1) + (2) I over-plotted all of the above, "like a stack of transparencies". Visually, the velocities of halo GCs, and disk MCs, match, quite closely (~200 km/s), beyond the galacto-centric orbital radius, of our star system (~8 kpc). However, the "inner disk" (r < Rsun) MCs, still revolving around our galaxy's core at ~200 km/s, are moving much faster (~2x), than "inner halo" GCs, at comparable galacto-centric radii. QUESTION: Why would disk material "behave differently", from halo material ? ADDENDUM: According to CalTech, Thus, halo-GCs may have formed z~5 (at the start of the cosmic Quasar-AGN era); then, (thick-)disk-GCs may have fored z~2 (at the end of the cosmic Quasar-AGN era). If so, then Quasars-AGNs were active (i.e., actively accreting material) during that "disking-down" period (5 > z > 2). And also, then, (1) the end of the Quasar-AGN era coincides with the (2) the end of the (thick-disk-)GC-formation era -- i.e., once our galactic disk fully formed (z~2), whatever had been conducive to GC formation, and galactic-core-BH accretion, in earlier eras (z>2), no longer existed. Today, surviving galactic GCs are ~100 ly across (Inglis. Observer's Guide to Stellar Evolution). However, GCs may "evaporate" from their peripheries, whilst contracting towards their cores (Wikipedia). So, if proto-GCs are ~0.1 kpc across, then perhaps a thick-disk environment >10x larger in extent (1-2 kpc) is required, for the formation, of such stellar systems ?? That is, the modern thin-disk, being only a few times thicker, than a proto-GC (0.4 kpc : 0.1 kpc), is not big enough, to support the assembly, of such stellar systems ?? In any event, there seems to be a close correlation, between (1) fully formed, stable, thin, disk; (2) end of core BH accretion & AGN action; (3) end of GC formation.

Are EM-force-carrying virtual photons red-shifted, by the distortions of the space-time fabric, near compact objects ?

GCs are, still, star clusters. So, if other types of star clusters 'evaporate' over time (e.g., open clusters), due to dynamical, dispersive, interactions with their environment; and if GCs are amongst the most ancient structures still surviving, into the present epoch, in our galactic environment, from the deep archaic past >12 Gya; and if all the ~150 GCs still orbiting our galaxy, have plunged through our galaxy's disk numerous times, over their >12 Gyr lifetimes; then, in real life, GCs are 'dispersively evaporated' over time in simulations, GCs are static-and-fixed DM particles, which are 'computationally immune' to interactions Thus, the discrepancy between (1) observations; and (2) simulations -- "the observed number of small satelite galaxies in galaxies disagrees with the expectations based on dark matter simmulations of galaxy formation" -- could be a numerical artifact, from the 'numerical immunity', of DM particles, once 'created' and inserted into the simulation's N-body 'particle list', to any-and-all further, and potentially disruptive-and-dispersive, interactions. Er go, there is no fundamental discrepancy, between observations & simulations on this point, save that, in real life, the number of GCs decreases over time, whereas they remain 'aloof and immune' in simulations. REFs: Inglis. Observer's Guide to Stellar Evolution. Nicolson. Dark Side of the Universe.

According to James Kaler's Astronomy!, pg.429, as middling-mass stars rise up the AGB, over the course of ~1 Gyr, their contracting He cores, non-fusing & degenerate, but surrounded by a H-burning shell, slowly heat up, from MS core temperatures of 15-20M K, to 100M K. At that point, the He-core re-ignites, in the 'Helium flash', eventually halting core collapse, and causing a 'bounce', wherein the core expands, and escapes degeneracy. Similarly, after core-He-burning stops, the now-CNO core, surrounded by a He-burning shell, re-contracts, evidently heating up from 100-140M K. Those temperatures can be inferred, from the ~T4 and ~T17 temperature dependences, of H-burning & He-burning, respectively. Evidently, the contracting cores "carry down in" their circum-core still-fusing shells, heating them up, and causing the observed ~1000x increases in Luminosity. At PNe phase, the He-shell-burning, CNO-core apparently 'blows its lid', expelling outlying envelope layers, and perhaps losing 'Grav. pressure confinement', quenching fusion? In any event, on the AGB, and GB -> WD tracks, the stellar-core is degenerate; whereas, from Helium-flash to HB/Red-Clump, the core is expanding & non-degenerate. The expansion, or 're-virialization', of the envelope, and its eventual expulsion, may arise from the increasing luminosity, and resulting radiation pressure, of the increasingly efficient core.

According to the Virial Theorem, for an idealized, isothermal, spherical inter-stellar cloud, 2 KT + UG = 0, s.t.: [math]\frac{3 k_B T}{\mu m_H} = \frac{3}{5} \frac{G M}{R}[/math] where the mean molecular weight is [math]\mu^{-1} = 13/16[/math] (primordial atomic gas) & [math]\mu^{-1} = 27/16[/math] (primordial ionized gas). Thus, [math]T_{vir} \approx 5 \times 10^6 K \times \left(\frac{M/M_{\odot}}{R/R_{\odot}} \right)[/math] for fully atomic gas (e.g. envelopes of low-mass stars). Thus, stars on the MS appear to be highly sub-virial, by roughly three orders-of-magnitude. But, such explains the "high-mass-loss-and-PNe-pocket", in the upper right-hand corner, of the HRD, (1) wherefrom stars descend, on their Hyashi tracks, towards the MS; (2) whereto stars ascend, off MS, on their various GBs. There, stars like Antares & Betelgeuse reside, having radii [math]\approx 10^3 R_{\odot}[/math], so that they have bloated up to become quasi-virial, with KT ~ UG. Thus, since those stellar envelopes have roughly as much thermal energy, as GBE, it is easy for them to be blown off, into circum-stellar mass-loss nebulae, or PNe. Thus, the pattern of tracking, across the HRD, by stars ascending on their GBs, when their cores are gravitationally collapsing, and their 'decoupled' envelopes expanding, represents a 'return' towards that initial state of quasi-virialization. Indeed, if-and-when core does not re-ignite (e.g., up AGB), such that the core keeps contracting, and dumping its GBE into its over-lying envelope, then even as the core "keeps on contracting", the envelope "keeps on expanding", eventually lifting up-and-off the star core completely, creating PNe.