Helium 3

The Helium-3 saga (Adapted from Charbonnel & Zahn 2007, Lagarde et al. 2012)

The classical theory of stellar evolution predicts a very simple Galactic destiny to 3He, dominated by a large production of this stable isotope in low-mass stars (Iben 1967; Rood 1972; Rood et al. 1976; Dearborn et al. 1996; Weiss et al. 1996). In stars with an initial mass ≤ 2-2.5 Msun, 3He is indeed produced first through D-processing on the pre-main sequence and then through the pp-chain on the main sequence. This fresh 3He is engulfed in the stellar enveloppe during the so-called first dredge-up (Iben 1967).
In classical stellar models it survives the following evolution phases and is released in the interstellar matter through stellar wind and planetary nebula ejection (Rood 1972; Vassiliadis & Wood 1993; Dearborn et al. 1996; Weiss et al. 1996; Forestini & Charbonnel 1997)

Two planetary nebulae, namely NGC 3242 and J320, have been found to behave classically (Rood et al. 1992, 1995; Balser et al. 1999b, 2006).
Slightly more massive than the Sun, they are indeed caught in the act of returning to the interstellar matter fresh elements synthesized in their womb among which 3He with the amount predicted by classical stellar models (Balser et al. 1997, 1999b, 2006; Galli et al. 1997).
As a consequence, one expects a large increase of 3 He with time in the Galaxy with respect to its primordial abundance, as well as a large abundance gradient with galactocentric radius.

But this stellar 3He has never showed up anywhere else!

3He is measured only in relatively young objects of the Milky Way : the Sun and the solar system (meteorites, lunar soil and rocks, solar wind, Jupiter’s atmosphere; Black 1971, 1972; Geiss & Reeves 1972; Geiss 1993; Mahaffy et al. 1998), the local interstellar cloud (Gloecker & Geiss 1996, 1998), a couple of planetary nebulae (see references above), and HII regions (Balser et al. 1994, 1999a; Bania et al. 1997, 2002).
According to classical theory, the latter objects should be highly enriched in 3He since they just formed out of matter that has undergone 12 billion years of chemical evolution. However, their 3He content is similar to that of the Sun, and thus no evidence for any enrichment of 3He during the last 4.5 Gyr was found. In addition, the “best” determination in a Galactic HII region (namely S209) by Bania et al. (2002) has yield a 3He abundance almost identical to the WMAP+BBN value, indicating that the stellar contribution to 3He is minute.
As a consequence no chemical evolution model computed with standard nucleosynthesis predictions is able to reproduce the observed 3He abundances (see Tosi 1996 and references therein).

This is the so-called “3He problem” that could be resolved if less than ~10% of the low-mass stars were releasing 3He as predicted by classical stellar theory (Galli et al. 1997; Charbonnel & do Nascimento 1998; Tosi 1998, 2000; Palla et al.~2000, 2002; Romano et al.~2003), among which NGC 3242 and J320.
In other words, the lack of increase in the Galactic 3He abundance can be accounted for if most (≥.90%) low-mass stars consume most of the 3He they produce during the main sequence before it can be emitted in the interstellar medium.
This requires physical processes which the classical theory of stellar evolution does not take into account, but which have been revealed by anomalous carbon isotopic ratios observed at the surface of relatively bright low-mass red giants. One observes indeed a sudden (and unexpected) drop of the 12C/13C ratio as low-mass stars get over the so-called luminosity bump on the red giant branch (RGB; see e.g. Charbonnel et al. 1998 and references in Charbonnel & Zahn 2007).

This reveals that some mixing occurs in their radiative interior, between the hydrogen-burning shell and the convective envelope. This non-canonical mixing (i.e. not due to convection) appears to be quite general since it operates in about 96% of all low-mass stars, whether they belong to the field, to open, or globular clusters (Charbonnel & Do Nascimento 1998).
This high number satisfies the Galactic requirements for the evolution of the 3He abundance since the mechanism responsible for the low values of 12C/13C is also expected to lead to the destruction of 3He by a large factor in the bulk of the envelope material, as initially suggested by Rood et al. (1984; see also Charbonnel 1995; Hogan 1995; Weiss et al. 1996; Charbonnel & Zahn 2007). It is important to note that NGC~3242 has a carbon isotopic ratio in agreement with the predictions of the classical stellar models (Palla et al. 2002), in contrast with the majority of PNe which present isotopic ratios below the classical predictions (Palla et al. 2000).

The quest for a mechanism that could lead to that extra-mixing has first been unsuccessful. But recently Eggleton et al. (2006) suggested a possible cause of such mixing, namely the molecular weight inversion created by the 3He(3He,2p)4He reaction in the upper part of the hydrogen-burning shell. Based on 3D hydrodynamic simulations of a low-mass star at the RGB tip (Dearborn et al. 2006), they found that such a µ-profile is unstable and produces very efficient mixing. They claimed that this mixing was due to the well-known Rayleigh-Taylor instability, which occurs in incompressible fluids when there is a density inversion. In stellar interiors, which are stratified due to their compressibility, a similar dynamical instability occurs when the Ledoux criterion for convection is satisfied, but it acts to render the temperature gradient adiabatic rather than to suppress the density inversion. Presumably it is that instability Eggleton and colleagues have observed with their 3D code, as attested by the high velocities they quote.

In reality, the first instability to occur in a star, as the inverse µ-gradient gradually builds up, is the thermohaline instability, as was pointed out by Charbonnel & Zahn (2007). This double-diffusive instability is observed in salted water in the form of elongated fingers, when the temperature is stably stratified, but salt is not, with fresh water at the bottom and salted at the top, the overall stratification being dynamically stable (Stern 1960).

On Earth, this phenomenon leads to the well-known thermohaline circulation (THC) which is the global density-driven circulation of the oceans. The thermohaline circulation is sometimes called the ocean conveyor belt, the great ocean conveyer, the global conveyor belt, or, most commonly, the meridional overturning circulation. More [here] and [here]

It was Ulrich (1972) who first noticed that the 3He(3He,2p)4He reaction would cause a µ-inversion, and he was the first to derive a prescription for the turbulent diffusivity produced by the thermohaline instability in stellar radiation zones. This prescription is based on a linear analysis, and it is certainly very crude, but it has the merit to exist.

When it is applied to the µ-inversion layer in RGB stars, with the shape factor recommended by Ulrich, it yields a surface composition that is compatible with the observations of the carbon isotopic ratio as well as of the abundances of lithium, carbon and nitrogen in RGB stars (Fig.3 of Charbonnel & Zahn 2007).
Simultaneously thermohaline mixing leads to the destruction of most of the 3He produced during the star’s lifetime (Fig.4 of Charbonnel & Zahn 2007).

It seems thus that we have finally identified the physical mechanism responsible for abundance anomalies in RGB stars, which simultaneously accounts for the measurements if 3He in Galactic HII regions.

The inclusion of thermohaline mixing in stellar models provides a solution to the long-standing “3He problem” on a Galactic scale. Stellar models including rotation-induced mixing and thermohaline instability reproduce also the observations of D and 4He (Lagarde et al. 2012).

A problem remains however, namely that all RGB stars brighter than the bump should undergo thermohaline mixing since they develop the same µ-inversion. As underlined by Balser et al. (2007), this was obviously not the case at least in two stars, i.e., in the RGB progenitors of NGC3242 and J320.
On the other hand the carbon isotopic ratio data indicate that a few RGB stars escape that extra-mixing – about 4% according to Charbonnel & do Nascimento (1998). This is consistent with the predictions of the chemical evolution models, which suggest that fewer than 10% of all planetary nebulae enrich the ISM with 3He at the level of classical stellar models, thus supporting the self-consistency of the extra-mixing mechanism.

It is tempting to confront these numbers with the fraction of the Ap stars (suspected to all host magnetic fields) relative to all A stars, which is 5 – 10% as estimated Wolff (1968). Since A-type stars are the progenitors of the more massive RGB stars, we are led to conjecture that in those giants that show no sign of extra-mixing the thermohaline instability is inhibited by a deeply buried magnetic field.

The end of the story can be found in Charbonnel & Zahn (2007b), and in Lagarde et al. (2012).