## Mass Loss Effects in the HR Diagram

Figure 27.4 illustrates the effects of mass loss for a 30 M0 star with a simple parametrization. The mass reduction makes the star less luminous, however it is overluminous for its actual mass, the MS band is more extended as the core mass fraction is larger (Fig. 24.3). In the expression of the MS lifetime tH ~ qcM/L, the quantities (qc x M) and L are reduced by mass loss so that on the whole tH does not change very much, increasing for current M rates, by about 5-10%.

Figure 27.4 illustrates the effects of mass loss for a 30 M0 star with a simple parametrization. The mass reduction makes the star less luminous, however it is overluminous for its actual mass, the MS band is more extended as the core mass fraction is larger (Fig. 24.3). In the expression of the MS lifetime tH ~ qcM/L, the quantities (qc x M) and L are reduced by mass loss so that on the whole tH does not change very much, increasing for current M rates, by about 5-10%.

log Tcfr

Fig. 27.4 MS tracks of a 30 M0 star with X = 0.70 and Z = 0.03 without mass loss and with M = NL/c2 (14.1) in CGS units for N = 70 (B) and N = 140 (C)

Fig. 27.5 Evolution of massive stars with mass loss and no overshooting for composition X = 0.70 and Z = 0.03 for two cases of mass loss rates with M = NL/c2 (14.1). Left: with N « 70. Right: with N « 140. From the author [339]

After the MS, the effects of mass loss on evolution are important. Figure 27.5 shows two cases (in case B: the final masses are 11.09, 12.49 and 24.80 M0 for the initial masses 15, 30 and 60 M0, respectively; in case C, the corresponding final masses are 3.50, 10.15 and 19.6 M0). Mass loss as in case B produces a shift of the "horn" of the He-burning phase to the red, particularly for the brightest stars. This results from the decrease or absence (Fig. 27.6) of an intermediate convective zone. The disappearance of this zone results from the reduction of the envelope. There is a shift from B supergiants to A and F supergiants and there are more red supergiants than without mass loss. The blue loops of the 9 and 15 M0 are smaller (Sect. 26.2.4). For the most massive stars (> 60 M0), the mass loss of the red supergiants removes the rest of the envelope. The star becomes a bare core, it evolves toward the He sequence (Fig. 24.2) and turns into a WR star.

For an extreme mass loss as in case C, the "horn" disappears. After the MS, the stars evolve quickly to the red supergiant stage, where they lose their envelope and become WR stars. Depending on M, stars with M > 60 M0 make only a limited excursion to the red in the HR diagram up to the region of the luminous blue variables (LBV). In the extreme case, the stars lose enough mass on the MS to keep an almost homogeneous composition. Such stars turn to WR stars after the MS phase.

The evolution toward or away from the red supergiant is determined by several effects. 1. The increasing mass fraction of the He core (for q > 0.5) favors a blue-ward evolution toward the He sequence. 2. As mentioned above, an intermediate convective zone maintains the star in the blue side of the HR diagram. 3. A helium enrichment of the envelope lowers the opacity, reduces the radius and favors a blue-ward evolution. 4. A large luminosity over mass ratio contributes to the envelope expansion, however this effect is small.

Fig. 27.6 Evolution of the internal structure of a 60 M0 star (X = 0.70, Z = 0.02) up to central C exhaustion with mass loss rates [271] and a core overshooting of 0.25 HP. Values of surface abundances in mass fractions are indicated with an index "s", while central abundances have an index "c". WN and WC indicate the Wolf-Rayet stages WN and WC. Same remarks as for Fig. 27.3. From the author [345]

Fig. 27.6 Evolution of the internal structure of a 60 M0 star (X = 0.70, Z = 0.02) up to central C exhaustion with mass loss rates [271] and a core overshooting of 0.25 HP. Values of surface abundances in mass fractions are indicated with an index "s", while central abundances have an index "c". WN and WC indicate the Wolf-Rayet stages WN and WC. Same remarks as for Fig. 27.3. From the author [345]

An increasing mass loss first favors evolution toward the red supergiant (effect nb. 2), then further mass loss (effect nb. 1) increases the core mass fraction q bringing the star to the He sequence, at the same time mass loss reveals the inner layers which are He rich (effect nb. 3). The fraction q necessary to initiate a blueward evolution of massive stars of Pop. I away from the red-supergiant stage are about 65, 77 and 97% at 60, 30 and 15 M0, respectively (cf. Fig. 24.3). Models with mass also better explain the upper limit of the distribution of massive stars in the HR diagram, an observed limit known as the Humphreys-Davidson limit [260, 261].

### 27.3.3 Internal Evolution with Mass Loss

Figure 27.6 illustrates the case of a 60 M0 star. During the MS phase, the main difference is the absence of semiconvection, this is due to the luminosity reduction and loss of a part of the envelope. The surface is going down to deeper Lagrangian coordinates progressively revealing the internal layers. Near the end of the MS stage, the surface reaches layers which were in the core. The effects of the CNO cycle become visible at the surface: He enhancement, C (and O) decrease, while the N abundance increases a lot (Fig. 27.11).

After central H exhaustion, a H-burning shell develops. The shell is rapidly narrowing and joined by the stellar surface, where H disappears. There the composition is nearly pure He. The mass of the He core increases until the H-burning shell disappears. Then, mass loss removes He layers, thus making the core mass to decrease (at the same rate as the total M [305]). Before the core decreases, the evolution of the central conditions in the log Tc vs. log gc is the same as for constant mass evolution, despite the loss of the half of the stellar mass. But, as soon as the mass of the He core is reduced, the evolution becomes different with a lower Tc at a given density.

The ongoing mass loss reveals the products of central He burning at the surface: huge relative enhancements of C and O, while He diminishes regularly. The star is now a WC star. At the end of the He-burning phase, the core contracts until central C-ignition. All phases after He exhaustion have a total duration equal to a fraction ~ 10-3 of the H-burning phase.

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