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TODO: identify the actual plotted branches from an intact source figure. The descriptions below explain how to do so.

In an old globular cluster's colour-magnitude diagram, the expected principal sequences are the main sequence below the main-sequence turnoff, the subgiant branch leading to the red giant branch, the horizontal branch above the main-sequence turnoff and extending across colour, and an Asymptotic giant branch above the horizontal branch, generally near and somewhat blueward of the red giant branch. A sufficiently deep diagram can also show a faint blue white dwarf cooling sequence; blue stragglers may lie above and blueward of the old main-sequence turnoff.

The two panels use the colour index $B-V$, increasing toward cooler, redder stars. On a conventional apparent-astronomical magnitude vertical axis, brighter stars are higher. These coordinate conventions locate the branches just described.

The supplied PDF does not permit a complete identification of the plotted branches. Its upper image data are corrupt and render as a grey rectangle, covering the main-sequence turnoffs and evolved populations; only lower fragments and $B-V$ axes survive. Thus the list above identifies the relevant stellar evolution phases and how to recognize them on an intact plot, rather than claiming that every listed sequence is visibly present in this damaged source. In particular, neither a plotted white dwarf sequence nor individual blue stragglers can be confirmed from it.

TODO: assign the physical differences to the actual two panels once the missing evolved-star sequences are recovered.

The main intrinsic parameters for old globular clusters are age, metallicity, helium abundance and the distribution of envelope masses after red giant branch mass loss. Distance and foreground interstellar extinction alter the appearance and must first be removed before assigning intrinsic differences.

Age controls the main-sequence turnoff: a more massive star has a shorter main-sequence lifetime, approximately fuel divided by luminosity. An older coeval population therefore has a smaller turnoff mass and a fainter, generally redder main-sequence turnoff. The separation in astronomical magnitude between the main-sequence turnoff and horizontal branch is useful because a common distance modulus cancels.

At comparable age, larger metallicity increases stellar-envelope opacity and atmospheric line blanketing. This generally makes the red giant branch and main sequence redder; metal-poor populations tend to have hotter, bluer red giant branches. Metallicity also affects hydrogen burning through the CNO cycle, so a quantitative age inference needs composition-dependent stellar models.

The horizontal branch is especially sensitive to envelope mass: at similar helium-core mass, a thinner hydrogen envelope gives a higher effective temperature and hence a bluer location. Red giant branch mass loss, age and helium abundance all influence that envelope and produce the familiar “second parameter” complexity. Enhanced helium also changes mean molecular weight, luminosity and evolutionary lifetime, and can shift main sequences and horizontal branches.

Interstellar extinction dims the diagram, while wavelength-dependent interstellar extinction reddens $B-V$; distance primarily supplies a vertical distance modulus shift. A systematic bend or different horizontal branch colour distribution cannot be explained by distance alone. Because the source hides the evolved branches, it is not possible to assign “older”, “more metal rich”, or “bluer horizontal branch” to a particular panel reliably. The preceding mechanisms give the warranted physical interpretation without inventing the lost observational differences.

On the main sequence, central hydrogen burning converts four protons into helium, positrons, neutrinos and released energy. The net reaction is $4p\to {}^4\mathrm{He}+2e^{+}+2{\nu }_e$, with positron annihilation contributing to the total roughly $26.7\mathrm{MeV}$ release before subtracting escaping neutrino energy. In the low-mass main-sequence stars of an old globular cluster, the proton–proton chain generally dominates. The CNO cycle makes the same net conversion and becomes important in hotter burning regions.

After central hydrogen exhaustion, a subgiant contracts its helium core and establishes a hydrogen-burning shell. On the red giant branch, that shell supplies most of the luminosity, commonly through the temperature-sensitive CNO cycle, while the inert helium core grows and becomes supported mainly by electron degeneracy pressure. The envelope expands and its surface cools. The helium core is not yet powered by helium nuclear fusion.

Helium ignition in a sufficiently low-mass degenerate core produces the helium flash, removing the strong electron degeneracy pressure dominance. A horizontal-branch star subsequently burns helium in its core through the Triple-alpha process, $3{}^4\mathrm{He}\to {}^{12}\mathrm{C}+\gamma$, and through ${}^{12}\mathrm{C}(\alpha ,\gamma ){}^{16}\mathrm{O}$. A surrounding hydrogen-burning shell can continue simultaneously.

After central helium exhaustion, the Asymptotic giant branch has an inert carbon-oxygen core with a helium-burning shell and an outer hydrogen-burning shell. Alternation between quiescent burning and helium-shell thermal pulses drives mixing and substantial mass loss. Subsequent post-asymptotic giant branch evolution exposes a hot core that may ionize its expelled envelope as a planetary nebula. Finally a white dwarf cools mainly by loss of stored thermal energy, rather than sustained central nuclear fusion.

For ordinary single stars in these old globular clusters, no current core-collapse supernovae are expected, and no new black holes are expected from the normal plotted population. Their main-sequence turnoff masses are typically around $0.8M_{\odot }$, far below the roughly $8M_{\odot }$ initial-mass scale for advanced burning and core collapse. More massive original stars exhausted their much shorter main-sequence lifetimes long ago. The precise transition mass depends on composition and mass loss, but this large separation makes the conclusion robust.

The low-mass stars now leaving the main sequence evolve through the red giant branch, helium ignition, horizontal branch and Asymptotic giant branch. They lose their envelopes and leave mainly carbon-oxygen white dwarfs, typically around $0.5$–$0.6M_{\odot }$ for current old-cluster progenitors, supported by electron degeneracy pressure. A visible planetary nebula is possible if the exposed core heats before the ejecta disperse; it is not guaranteed for every low-mass remnant. Lower-mass main-sequence stars repeat this evolution only much later, and the very lowest-mass isolated stars can ultimately leave helium-rich degenerate remnants without igniting helium.

The clusters may already contain neutron stars and black holes made by their original massive stars; these remnants need not appear on an optical colour-magnitude diagram. Binary interactions can instead produce stripped helium white dwarfs, mergers or a possible Type Ia supernova; such exceptions are distinct from normal single-star core collapse. No such special progenitor can be established from the damaged plots. In particular, a luminous red giant is not by itself evidence for a massive core-collapse supernova progenitor.

The right panel of the figure in solution has luminosity increasing upwards and effective temperature decreasing to the right. An old globular cluster contains a low-mass main sequence, a main-sequence turnoff, subgiants, a red giant branch, a horizontal branch, an Asymptotic giant branch and a faint hot white dwarf sequence. Its high-mass main sequence is absent because those stars have evolved.

If a fraction $f_c=0.1$ of the star participates in hydrogen burning, with initial hydrogen mass fraction $X=0.7$, the available nuclear binding energy is $0.007f_{c}XM{c}^2$. Assuming a roughly constant luminosity and coeval stars,Taking the quoted core fraction as hydrogen fuel itself, $f_{c}X=0.1$, gives $1.98\times 10^{10}\mathrm{yr}$. Stating the fuel convention matters: burning the whole stellar mass overestimates the age by about an order of magnitude. Evolving luminosity and detailed stellar structure are needed for an accurate age.

The right panel of the figure in solution has luminosity increasing upwards and effective temperature decreasing to the right. An old globular cluster contains a low-mass main sequence, a main-sequence turnoff, subgiants, a red giant branch, a horizontal branch, an Asymptotic giant branch and a faint hot white dwarf sequence. Its high-mass main sequence is absent because those stars have evolved.

If a fraction $f_c=0.1$ of the star participates in hydrogen burning, with initial hydrogen mass fraction $X=0.7$, the available nuclear binding energy is $0.007f_{c}XM{c}^2$. Assuming a roughly constant luminosity and coeval stars,Taking the quoted core fraction as hydrogen fuel itself, $f_{c}X=0.1$, gives $1.98\times 10^{10}\mathrm{yr}$. Stating the fuel convention matters: burning the whole stellar mass overestimates the age by about an order of magnitude. Evolving luminosity and detailed stellar structure are needed for an accurate age.

As the star expands onto the red giant branch, a planet of fixed radius produces a shallower exoplanet transit, $\delta \propto R_{\star }^{-2}$. For a fixed circular orbit and an approximately central chord, duration grows approximately as $R_{\star }$, and transit probability also rises. At fixed orbital inclination the impact parameter in stellar-radius units decreases, further changing the chord. These statements neglect orbital evolution, stellar mass loss, tidal effects and eventual engulfment, all of which can matter for a very close planet.

Near a red giant's compact core, intense nuclear burning in a small region can produce a large $L_r/m_r$ and a steep required radiative gradient. Where this exceeds the adiabatic gradient, convection transports the released energy and mixes fuel. Core helium burning is a clear example: the strongly temperature-sensitive Triple-alpha process commonly produces a convective burning core; shell flashes can also make convective regions.^[ref]

The qualification matters: an inert degenerate helium core and a steady hydrogen-burning shell on the first-ascent red giant branch are not universally convective; conduction or radiation may dominate there. Red giants also commonly have deep convective envelopes. The physical condition is an excessive required radiative gradient, not proximity to the centre alone.

An old globular cluster has lost its original massive main-sequence members. Its main-sequence turnoff lies near a low stellar mass, typically around $0.8M_{\odot }$ for an age of order $10^{10}$ years. The diagram shows a lower main sequence, a subgiant branch, a prominent red giant branch, a horizontal branch of core-helium-burning stars, an Asymptotic giant branch and a faint white dwarf cooling sequence. The preceding schematic labels these features. A few blue stragglers may lie above the old turnoff because interaction or merger rejuvenated them; they do not imply a young age for the bulk population.

The numbered features in the original colour-magnitude diagram have the following interpretation.

Continuous star formation explains the coexistence of newly formed massive main-sequence stars with evolved low-mass remnants; interpreting a single sharp turnoff as the age of a coeval cluster would be inappropriate here.

Core-helium-burning stars populate the horizontal branch and red clump; hot subdwarf B stars provide examples with a helium-burning core of roughly half a solar mass and a very small remaining hydrogen envelope. Their high luminosity relative to mass, hot spectra and locations away from an ordinary hydrogen-burning main sequence are observational evidence for such evolved configurations.

A plausible history starts with a hydrogen-burning star. After central hydrogen exhaustion, hydrogen-shell burning builds a compact helium core and the envelope expands on the red giant branch. Sufficient core temperature ignites helium, often by a helium flash for a low-mass degenerate core. Strong mass loss or binary interaction can strip most of the hydrogen envelope, exposing a hot helium-burning remnant; retaining a substantial envelope instead gives an ordinary horizontal-branch or red-clump star.

The simple radiative Kramers scaling estimates a luminosity contrast but does not uniquely identify one evolutionary state or predict a real subdwarf luminosity precisely. A similarly low-mass helium white dwarf would be a cooling, degenerate object rather than the sustained high-temperature helium-burning configuration assumed here.

The concentration of core-helium-burning stars on the cool part of the horizontal branch. It must be distinguished from the ascending hydrogen-shell-burning red giant branch.

The population sequence connecting the main-sequence turnoff to the lower red giant branch in a coeval stellar population, tracing post-core-hydrogen-burning evolution before the large red-giant expansion. It is a feature of a population diagram associated with subgiant stars, rather than a separate universal line followed by every stellar mass.