Physical origin of population-dependent red-giant-branch mass loss in globular clusters and its role in the second-parameter problem of horizontal-branch morphology

Globular clusters (GCs) host two or more stellar generations, and helium-enriched second-generation (2G) stars must lose more mass along the red giant branch (RGB) than first-generation (1G) stars to reproduce the observed horizontal-branch (HB) morphologies. Tailo et al. (2020) measured this mass-loss difference in 46 GCs and showed it correlates with the populations' helium enhancement and with cluster mass, consistent with a scenario in which early destruction of pre-main-sequence accretion discs leaves 2G stars rapidly rotating, delaying the helium flash and extending RGB mass loss. However, the quantitative physical theory behind this empirical correlation remains unbuilt: no stellar-evolution computation connects the disc-early-loss scenario to the measured mass-loss differences, asteroseismology has not yet tested the required high core rotation of 2G red giants, alternative helium-driven mass-loss channels (pulsation plus magneto-acoustic driving) are unmodeled in 1D codes, and the classic second-parameter problem of HB morphology is only partially decomposed into mass loss, helium, age, and environment. All of these strands remain open, with substantial recent progress on the observational side (asteroseismic masses in M4, M80, M9, M19, 47 Tuc; extension of the mass-loss–helium correlation to intermediate populations in NGC 6752 and NGC 2808) but no resolution.

Background

Globular clusters (GCs) are ancient, massive, gravitationally bound stellar systems. Nearly all Galactic GCs host multiple stellar populations (MPs): a first generation (1G) with the primordial chemical composition, and one or more second generations (2G) showing the imprint of high-temperature hydrogen burning — enhanced helium (mass fraction $Y$), N, Na, Al, and depleted C, O, Mg. MPs are traced with multi-band Hubble Space Telescope photometry (e.g., 'chromosome maps', pseudo-two-color diagrams of ultraviolet filters that separate populations by their CNO-sensitive colors), and population-specific helium spreads $\delta Y_{\max}$ have been inferred independently for dozens of clusters (Milone et al. 2018, MNRAS 481, 5098).

After central hydrogen exhaustion, low-mass stars ascend the red giant branch (RGB), powered by a hydrogen-burning shell around an inert, growing helium core, until degenerate helium ignition (the helium flash) settles them on the horizontal branch (HB), burning helium in core and hydrogen in shell. The color (effective temperature) spread along the HB of coeval, mono-metallic cluster stars is a classic puzzle: metallicity is the 'first parameter' setting HB type, but clusters of nearly identical metallicity and age — most famously M3 versus M13 — show dramatically different HB morphology, requiring a 'second parameter' (van den Bergh 1967; Sandage & Wildey 1967). Because HB position is set by the stellar mass at the flash, the integrated RGB mass loss $\mu$ is a prime second-parameter candidate; it is usually parameterized by the Reimers (1975) law with efficiency $\eta_{\rm R}$, which is calibrated rather than derived from first principles.

Helium complicates this: for fixed mass loss, higher $Y$ yields bluer HB stars, so helium and mass loss are degenerate when both are fit to HB photometry alone. Tailo et al. (2020, MNRAS 498, 5745) broke this degeneracy for 46 GCs by fixing 1G, 2G, and extreme-2G (2Ge) helium abundances from independent RGB-star measurements and fitting population-synthesis models to the HBs. They found: (i) 1G mass loss correlates tightly with cluster metallicity; (ii) 2Ge stars of essentially all clusters lose more mass than 1G stars, and the mass-loss difference $\Delta\mu_{\rm e}$ correlates with the maximum internal helium variation $\delta Y_{\max}$ and with cluster (initial) mass; (iii) age is not the dominant second parameter. As a physical interpretation they invoked the pre-main-sequence disc early-loss scenario (Tailo et al. 2015, Nature 523, 318; D'Antona et al. 2016, MNRAS 458, 2122): 2Ge stars form in the dense cluster center, where dynamical encounters destroy their pre-main-sequence accretion discs early. Disc locking then spins up the contracting protostar's core; the resulting fast rotation delays the helium flash (and slightly raises its luminosity), extending RGB lifetime and hence integrated mass loss — the same mechanism earlier invoked for the 'blue hook' stars of $\omega$ Cen (an ultrahot subpopulation at the far-blue end of the horizontal branch), where it required extreme core-mass increases.

The scenario faces three unresolved difficulties that define the open problem. First, the quantitative link is missing: the computation promised by Tailo et al. (2020) — stellar-evolution models of 2G stars with disc-locking initial rotation, followed through the RGB with a mass-loss prescription, reproducing the observed $\Delta\mu_{\rm e}$–$\delta Y_{\max}$ and $\Delta\mu_{\rm e}$–cluster-mass correlations — has not been published. Second, rotation rates of order 100 times the currently measured values would be needed in 2G red-giant cores; asteroseismology (the study of global oscillation modes, whose frequency splittings reveal internal rotation) has measured the core rotation of only one low-mass field red giant in this context (KIC 7341231, $\omega\simeq0.7\,\mu$Hz, Deheuvels et al. 2012), far below model requirements, but no asteroseismic rotation data exist for 2G GC giants. Third, an alternative channel — enhanced helium itself raising surface activity, pulsation, and chromospheric magneto-acoustic (i.e., wave-driven, magnetically modulated) mass loss (McDonald & van Loon 2007) — remains unmodeled in one-dimensional stellar-evolution codes, leaving the interpretation untested against alternatives.

Problem Statement

Establish the physical origin of the population-dependent mass loss along the red giant branch that Tailo et al. (2020) measured in 46 Galactic globular clusters — the excess integrated RGB mass loss $\Delta\mu_{\rm e}$ of the extreme, helium-enriched second-generation (2Ge) stars relative to first-generation (1G) stars, correlating with the populations' helium enhancement $\delta Y_{\max}$ and with cluster mass — and thereby complete the physical account of the second parameter of horizontal-branch morphology. The open problem has three unresolved strands, each still to be tested quantitatively against the observed $\Delta\mu_{\rm e}$–$\delta Y_{\max}$ and $\Delta\mu_{\rm e}$–cluster-mass relations: the quantitative link between the populations' early pre-main-sequence disc loss and rotation history (rotation locked to an early-destroyed disc, delayed helium flash, extended RGB lifetime) and those relations, including the core-rotation rates the scenario requires in present-day 2G red giants; whether 2G red-giant cores rotate at the rates the scenario needs; and whether the alternative mechanism of helium-enhanced surface activity driving pulsation and magneto-acoustic mass loss reproduces the same correlations without early disc loss.

References

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