Third Dredge-Up in Evolved Stars

• Third dredge-up (TDU) is a mixing event during TP-AGB evolution that transports carbon and heavy elements from the helium intershell to the stellar surface.
• It is quantified by the dredge-up efficiency parameter (lambda), which regulates core mass growth and is calibrated using the white-dwarf initial-final mass relation.
• Observational tracers like technetium lines and carbon enhancements provide evidence for TDU, offering insights into nucleosynthesis and stellar evolution.

Searching arXiv for recent and relevant papers on Third Dredge-Up to support the article. Third dredge-up (TDU, also 3DU) is the recurrent envelope-mixing episode of thermally pulsing asymptotic giant branch (TP-AGB) evolution in which the convective envelope penetrates inward after a thermal pulse and transports material from the He-intershell to the stellar surface. In standard TP-AGB structure, the relevant layers are an electron-degenerate core, a He-burning shell, a H-burning shell, the He-rich intershell between them, and the deep convective envelope. TDU is the mechanism that mixes freshly synthesized carbon and heavy elements to the surface, drives the M-to-S-to-C chemical sequence, modifies dust formation and mass loss, affects chemical yields, and helps set the final white-dwarf mass (Karakas et al., 2014, Marigo, 2022).

1. Pulse-cycle context and transported material

TDU is embedded in the thermal-pulse cycle. A thermal pulse is triggered by instability of the geometrically thin He-burning shell; the pulse produces a pulse-driven convective zone in the intershell; the star then enters a power-down phase in which the pulse energy goes mainly into expansion; the H-burning shell is temporarily quenched; and the cooling of the inner envelope increases opacity enough for the base of the convective envelope to move inward in mass. TDU occurs when that envelope penetration reaches layers previously homogenized by the pulse-driven convection, so that carbon and other He-burning products are mixed into the envelope (Karakas et al., 2014).

In TP-AGB models used to calibrate TDU with the white-dwarf initial-final mass relation (IFMR), the intershell composition adopted for the dredged-up material is typically

$$\mathrm{He/C/O}=0.70\text{--}0.78/0.20\text{--}0.25/0.005\text{--}0.02$$

in mass fraction. The physical consequence is twofold. First, TDU reduces the growth of the H-exhausted core because core material accumulated during the interpulse is partly mixed back outward. Second, it raises the surface carbon abundance, changes the atmospheric C/O ratio and carbon excess, and thereby alters opacity, pulsation, dust formation, and wind driving. In this sense TDU is not merely a surface-abundance phenomenon but a structural regulator of TP-AGB evolution (Marigo, 2022).

2. Quantitative characterization and onset criteria

The standard quantitative descriptor of TDU is the dredge-up efficiency parameter

$$\lambda=\frac{\Delta M_{\rm 3DU}}{\Delta M_{\rm c}}$$

or, in equivalent notation,

$$\lambda=\frac{\Delta M_{\rm dup}}{\Delta M_{\rm core}},$$

where the numerator is the mass dredged up after a pulse and the denominator is the core growth during the preceding interpulse. Larger $\lambda$ means more efficient cancellation of interpulse core growth. The onset of dredge-up is often parameterized by a minimum core mass $M_{\rm c}^{\rm min}$, while detailed calculations also track the core mass at first TDU and the maximum $\lambda$ reached over the TP-AGB (Marigo, 2022, Addari et al., 2024).

In super-AGB calculations, the timing of TDU relative to the pulse-driven convective zone is made explicit with

$\Delta t=t_2-t_1,$

where $t_1$ is the time of pulse-driven convection-zone extinction and $t_2$ is the beginning of TDU; the latter is defined as the time when the base of the convective envelope has deepened in mass by $1\%$ of $$\lambda=\frac{\Delta M_{\rm 3DU}}{\Delta M_{\rm c}}$$0 for a given dredge-up event. When $$\lambda=\frac{\Delta M_{\rm 3DU}}{\Delta M_{\rm c}}$$1, TDU begins while the pulse-driven convection zone is still active, allowing H-rich envelope material to interact with He-burning convection and potentially trigger proton-ingestion events (Jones et al., 2015).

At extremely low metallicity, TDU is not ubiquitous. In one grid of $$\lambda=\frac{\Delta M_{\rm 3DU}}{\Delta M_{\rm c}}$$2–$$\lambda=\frac{\Delta M_{\rm 3DU}}{\Delta M_{\rm c}}$$3 models, TDU occurs only over a restricted mass range at finite extremely metal-poor composition, roughly $$\lambda=\frac{\Delta M_{\rm 3DU}}{\Delta M_{\rm c}}$$4 to $$\lambda=\frac{\Delta M_{\rm 3DU}}{\Delta M_{\rm c}}$$5 at $$\lambda=\frac{\Delta M_{\rm 3DU}}{\Delta M_{\rm c}}$$6, with the upper limit shrinking to $$\lambda=\frac{\Delta M_{\rm 3DU}}{\Delta M_{\rm c}}$$7 at $$\lambda=\frac{\Delta M_{\rm 3DU}}{\Delta M_{\rm c}}$$8 and $$\lambda=\frac{\Delta M_{\rm 3DU}}{\Delta M_{\rm c}}$$9 at $$\lambda=\frac{\Delta M_{\rm dup}}{\Delta M_{\rm core}},$$0; no TDU events are found for $$\lambda=\frac{\Delta M_{\rm dup}}{\Delta M_{\rm core}},$$1. That work identifies a critical core mass of about $$\lambda=\frac{\Delta M_{\rm dup}}{\Delta M_{\rm core}},$$2, together with a pulse-strength condition based on the pressure width of the He-flash convective zone, as necessary for TDU onset (Suda et al., 2010).

3. Observational diagnostics and empirical evidence

The decisive empirical tracer of recent TDU is technetium. Because $$\lambda=\frac{\Delta M_{\rm dup}}{\Delta M_{\rm core}},$$3 has no stable isotope and a half-life of about $$\lambda=\frac{\Delta M_{\rm dup}}{\Delta M_{\rm core}},$$4 to $$\lambda=\frac{\Delta M_{\rm dup}}{\Delta M_{\rm core}},$$5 yr, its presence in a cool giant atmosphere implies recent internal $$\lambda=\frac{\Delta M_{\rm dup}}{\Delta M_{\rm core}},$$6-process nucleosynthesis followed by dredge-up. The key optical Tc I resonance lines are at $$\lambda=\frac{\Delta M_{\rm dup}}{\Delta M_{\rm core}},$$7, $$\lambda=\frac{\Delta M_{\rm dup}}{\Delta M_{\rm core}},$$8, and $$\lambda=\frac{\Delta M_{\rm dup}}{\Delta M_{\rm core}},$$9 Å. Tc-rich S stars are therefore interpreted as intrinsic TP-AGB stars currently undergoing or having recently undergone TDU, whereas Tc-poor S stars are generally extrinsic systems enriched by binary mass transfer from a former AGB companion (Shetye et al., 2018, Shetye et al., 2019).

Gaia-based analyses of intrinsic S stars have turned TDU onset into a direct observational problem. One study of six Tc-rich S stars found them at low TP-AGB luminosities, as low as $\lambda$0, with initial masses around $\lambda$1 and metallicities roughly $\lambda$2 to $\lambda$3. The sample showed Tc-rich, Nb-poor, mildly carbon-enriched, moderately $\lambda$4-process-enhanced atmospheres, consistent with stars at the beginning of the TP-AGB shortly after TDU onset. This provides direct evidence that TDU can occur in stars with initial masses as low as about $\lambda$5–$\lambda$6 at mildly subsolar metallicity, provided sufficiently efficient envelope-boundary mixing is present in the models (Shetye et al., 2019).

A larger S-star analysis reinforced the Tc-based intrinsic/extrinsic dichotomy with the Zr-Nb clock. In intrinsic stars, freshly synthesized Zr is present while $\lambda$7Zr has not yet fully decayed to Nb, so they are Zr-rich and comparatively Nb-poor; extrinsic stars are Nb-rich. That study also identified V915 Aql as a particularly challenging case: it is Tc-rich and lies near a $\lambda$8, $\lambda$9 location in the HR diagram, although the authors’ standard models did not predict TDU below $M_{\rm c}^{\rm min}$0 (Shetye et al., 2018).

Tc-rich M stars extend the observational sequence toward even earlier dredge-up. Nucleosynthesis models show that during the first TDU episodes the surface Tc abundance can increase strongly while the Zr enhancement remains observationally subtle. In that framework, detectable Tc in an M star can precede the spectroscopic transition to an S star. The proposed Tc-rich M regime is approximately

$M_{\rm c}^{\rm min}$1

with the M-to-S transition near $M_{\rm c}^{\rm min}$2 dex. This supports the interpretation of Tc as a more immediate TDU diagnostic than ZrO-band morphology in oxygen-rich stars (Shetye et al., 28 Jul 2025).

Post-AGB abundances provide a complementary endpoint probe. In Galactic globular clusters, a compilation of 17 post-AGB stars found that 11 have CNO abundances and 4 of those show enhanced $M_{\rm c}^{\rm min}$3 relative to the RGB stars from which they descended; among 6 stars with only heavy-element abundances, 1 more shows $M_{\rm c}^{\rm min}$4-process evidence for TDU. The enhancement is mainly in the form of carbon, and all TDU-positive stars in that sample have $M_{\rm c}^{\rm min}$5 (Dixon, 2023).

4. Carbon-star formation, dust, mass loss, and the IFMR

Repeated TDU episodes raise the surface C/O ratio and the carbon excess, eventually converting an O-rich AGB star into a carbon star. The transition is chemically and dynamically consequential, but the change in mass loss is not instantaneous at $M_{\rm c}^{\rm min}$6. Solar-metallicity TP-AGB models calibrated to the IFMR emphasize that carbon-dust-driven winds become highly effective only once the carbon excess is large enough; before that, there can be a prolonged phase of only moderate mass loss even in a carbon star. That phase is central to the observed IFMR kink near $M_{\rm c}^{\rm min}$7 (Marigo, 2022).

Using the semi-empirical IFMR as a TDU calibrator, one study found that solar-metallicity TP-AGB models reproduce the white-dwarf final masses only if the dredge-up efficiency varies with initial mass: in low-mass stars with $M_{\rm c}^{\rm min}$8, $M_{\rm c}^{\rm min}$9; in intermediate-mass stars with $\lambda$0, $\lambda$1; and in more massive TP-AGB stars with $\lambda$2, the efficiency drops again. The same study suggested that a second kink may appear at the transition between the most massive carbon stars and stars dominated by hot-bottom burning (Marigo, 2022).

A closely related PARSEC+COLIBRI analysis of the IFMR reached a similar conclusion from a convective-boundary-mixing perspective. There the observed non-monotonic behavior around $\lambda$3–$\lambda$4 was attributed to recurrent but shallow TDU, carbon-star formation with mild carbon enrichment, and modest mass-loss rates. The preferred interpretation was that white dwarfs populating the kink had progenitor carbon stars with $\lambda$5. In that framework, a constant envelope-overshooting prescription cannot reproduce the IFMR; $\lambda$6 must vary with initial mass, while $\lambda$7 and $\lambda$8 remain mildly degenerate if the IFMR is used alone (Addari et al., 2024).

The observational relation between TDU and mass loss in Mira variables is more subtle than a monotonic post-dredge-up increase in wind strength. Studies using Tc as a 3DUP indicator found that, at a given pulsation period, Tc-poor Miras are redder in $\lambda$9 and $\Delta t=t_2-t_1,$0 than Tc-rich ones, implying stronger mid-IR excess and higher dust emission, while no clear systematic difference in gas mass-loss rates was detected. A later study with expanded Tc classifications similarly found no systematic difference in gas mass-loss rates, but Tc-poor Miras appear to have higher expansion velocities and, in the $\Delta t=t_2-t_1,$1–$\Delta t=t_2-t_1,$2 d interval, higher mid-IR fluxes by more than a factor of two in $\Delta t=t_2-t_1,$3 and Akari 18. The favored explanation is that 3DUP changes the dust reservoir—through reduced free oxygen after carbon enrichment and/or altered dust composition—more strongly than it changes the gross gas-loss rate (Uttenthaler et al., 2018, Uttenthaler et al., 2024).

5. Metallicity, mass regime, and extreme outcomes

Metallicity systematically modulates TDU. At lower metallicity, less dredged-up carbon is needed to raise C/O above unity, and some model grids find larger $\Delta t=t_2-t_1,$4 at fixed mass. In extremely metal-poor calculations, however, the TDU mass window narrows rather than simply shifting downward, and zero-metallicity models in one study showed no TDU at all (Suda et al., 2010). By contrast, for mildly subsolar metallicities around $\Delta t=t_2-t_1,$5 to $\Delta t=t_2-t_1,$6, direct observations of Tc-rich S stars indicate that TDU can begin in stars near $\Delta t=t_2-t_1,$7 (Shetye et al., 2019).

In super-AGB models, TDU acquires an additional role as a trigger of convective-reactive events. With decreasing metallicity and increasing pulse number, the time separation between pulse-driven convection and TDU shrinks. In a metallicity survey from $\Delta t=t_2-t_1,$8 down to $\Delta t=t_2-t_1,$9, $t_1$0 decreases with pulse number at all metallicities, and after about 10–15 pulses TDU can begin while the pulse-driven convection zone is still active; lower-metallicity models reach this state earlier. For $t_1$1, efficient TDU with $t_1$2 is reached by the fifteenth pulse at the latest, and the resulting proton-ingestion events can drive H-burning luminosities above $t_1$3, in some cases $t_1$4 (Jones et al., 2015).

The white-dwarf descendants of low-metallicity TP-AGB stars retain a strong memory of whether TDU occurred. Full progenitor-to-white-dwarf calculations for $t_1$5 show that, in the absence of TDU, low-mass white dwarfs are born with thick H envelopes and stable H burning can become the dominant luminosity source over $t_1$6, delaying cooling by more than a factor of 2 at intermediate luminosities. When TDU is induced through TP-AGB overshooting with $t_1$7, the envelope carbon enrichment exceeds three orders of magnitude, post-AGB $t_1$8 reaches roughly $t_1$9–$t_2$0, the final H layer is reduced by more than a factor of two, and residual H burning largely ceases to matter (Althaus et al., 2015).

Not all stars in the nominal TDU mass-metallicity regime actually dredge up. A particularly striking counterexample is the Small Magellanic Cloud post-AGB star J005252.87-722842.9, with $t_2$1 K, $t_2$2, $t_2$3, and an inferred initial mass of roughly $t_2$4–$t_2$5. Standard models for that regime predict repeated TDU and carbon enrichment, yet the star shows no confirmed carbon enhancement, with $t_2$6, and no convincing $t_2$7-process enhancement, with $t_2$8. This has been interpreted as the first observational evidence for a star that failed the third dredge-up, implying a possible evolutionary channel in which a low-mass, metal-poor star leaves the AGB without effective TDU (Kamath et al., 2017).

6. Uncertainties, calibration strategies, and emerging probes

TDU remains one of the least secure ingredients of TP-AGB theory because it depends sensitively on convective-boundary mixing, pulse strength, envelope mass, mass loss, opacity changes after C/O evolution, and numerical treatment. Review work has emphasized that after decades of modeling there is still no consensus on the initial mass at which dredge-up begins, and that $t_2$9, $1\%$0, and the number of dredge-up episodes are strongly code-dependent (Karakas et al., 2014).

Current observational calibration strategies reflect that uncertainty. The IFMR provides an integral constraint on core growth and TP-AGB wind truncation (Marigo, 2022, Addari et al., 2024). Intrinsic S stars provide a near-onset chemical constraint because their C/O ratios between about 0.5 and 1 imply only a limited number of TDU episodes. A pulsation-based study of intrinsic S-type AGB stars found that their initial-mass distribution peaks at $1\%$1–$1\%$2, but also appears to include stars with initial masses down to about $1\%$3; the authors concluded that the minimum mass for TDU must be recalibrated downward relative to many current detailed models (Mori et al., 13 Aug 2025). This suggests that the low-mass onset problem seen in Gaia-based S-star analyses is not confined to a few anomalous objects.

The strongest current tensions concern the relation between carbon enrichment and $1\%$4-process enrichment, and the minimum mass for TDU. In the S-star literature, some stars require more dredge-up episodes to explain their heavy-element enhancements than are compatible with their observed low C/O ratios, while other stars, such as V915 Aql, appear to show Tc at masses lower than many models predict (Shetye et al., 2018, Shetye et al., 2019). A plausible implication is that the physics controlling partial mixing, carbon enrichment, and $1\%$5C-pocket formation is not yet captured consistently across the first few pulses.

New circumstellar diagnostics are being explored but are conditional rather than definitive. In SiO maser surveys, isotopologue-dominated $1\%$6 and $1\%$7 spectra are proposed to require a modest TDU-induced isotopic enhancement together with very low turbulence velocity, $1\%$8, so they are best interpreted as joint evolutionary-plus-excitation signatures rather than direct abundance meters (Lewis et al., 20 May 2026). Similarly, Tc-rich M stars appear to trace the earliest observable TDU episodes, but their narrow occupancy of the $1\%$9–$$\lambda=\frac{\Delta M_{\rm 3DU}}{\Delta M_{\rm c}}$$00 plane and their possible low masses underscore how incomplete current onset models remain (Shetye et al., 28 Jul 2025).

In present usage, TDU is therefore both a well-established process and a calibration frontier. Its occurrence is secure from Tc, carbon stars, $$\lambda=\frac{\Delta M_{\rm 3DU}}{\Delta M_{\rm c}}$$01-process enrichments, globular-cluster post-AGB abundances, white-dwarf remnant properties, and TP-AGB population constraints. Its detailed onset, pulse-by-pulse efficiency, metallicity dependence, and coupling to mass loss and convective-boundary mixing remain active problems whose solution now depends on combining stellar-population diagnostics, detailed abundance work, pulsation constraints, and white-dwarf endpoints across a wide metallicity range (Karakas et al., 2014, Mori et al., 13 Aug 2025).