The Upper Luminosity Limit of Massive Stars
Cool hypergiants (Ia+ or Ia0) are a class of rare supergiant stars with Teff below ~10,000 K. They are physically different from supergiants of luminosity class Ia. The usual Ia+ designation does not mean that they are always more luminous than the former, but they differ in their spectral properties. These stars show one or more broad emission components in the Balmer H alpha line profile, which is a signature of an extended atmosphere or of a relatively large rate of mass loss. Another important spectroscopic aspect of hypergiants is that their absorption lines are significantly broader than those of the Ia stars of similar spectral type and luminosity. Rho Cas and HR 8752 are the prototype objects of the yellow hypergiants (F-G Ia+). They are among the most massive (20-40 M_sun) cool stars presently known. These stars exist near the Eddington luminosity limit, and exhibit a wide range of uncommon stellar properties. Their atmospheres are unstable, which causes quasi-periodic pulsation variability, strongly developed large-scale velocity fields, excessive mass-loss, and extended circumstellar envelopes.
We summarize three fundamental questions for the study of hypergiants:
- Why do hypergiants of similar bolometric luminosity and spectral type as normal supergiants display the signatures of strong large-scale photospheric motions and enhanced mass loss? Why do these properties appear to be absent for normal supergiants?
- What is the evolutionary status of the yellow hypergiants, and how do they fit into the broader scheme of massive star evolution? Are they the likely progenitors of (Type II) supernovae in the not too distant future?
- Can an understanding of their atmospheric dynamics and circumstellar environments provide clues about the origin of the luminosity boundary for evolved stars? Do these dynamics characterize the hypergiants uniquely, or do they occur modified in other classes of luminous stars as well?
In 1995 Nieuwenhuijzen & de Jager published a classic paper on the atmospheric accelerations and stability of supergiant atmospheres. It provided a well-founded theoretical explanation for the conspicuously sparse amount of white (late A to early F-type) supergiants in the H-R-diagram. Most of the known yellow hypergiants appear to cluster around 6500 K <= Teff <= 7500 K with different luminosities, while the area around 10,000 K and log(L*/L_sun) >= 5.7 is nearly devoid of stars. Due to a natural deficiency of cool supergiants it is possibly hard to judge the reality of their absence in the upper portion of the H-R diagram, but stellar population studies support only a minimal number of very luminous white supergiants. This area was tentatively baptized the `Evolutionary Void' after detailed calculations revealed that hydrostatically stable solutions cannot be computed for the atmospheres of -blueward- evolving yellow hypergiants at a lower temperature boundary of Teff~=8300 K. These calculations involve a time-independent solution of the momentum equation, which considers the Newtonian gravity acceleration derived from the evolutionary mass, the gas, radiation and turbulent pressure gradients, and the momentum of the stellar wind. The latter requires the observed mass-loss rate. An `effective acceleration' for the atmosphere is obtained iteratively, but which becomes negative at the cool border of the Void. The outwards directed net force causes an unstable atmosphere above 8300 K. A remarkable byproduct of this study is that as stars move along their evolutoinary track, for time scales longer than the dynamic time scale of the atmosphere, the atmosphere continuously adapts to the new (L*, Teff)-values, and remains stable without reaching the Eddington limit. Common practice of determining the stability limit of massive stars by extrapolating hydrostatic models to a `modified' Eddington limit (i.e. utilizing a flux-mean opacity for the atmosphere which includes line opacity) is therefore not justified. When a real star slowly changes its effective gravity acceleration to zero during evolution the atmosphere puffs up, thereby decreasing the opacity to the classic electron scattering value.
It has also been proposed that recurrent eruptions in yellow hypergiants occur when these stars approach the cool boundary of the Void, and `bounce off' redward (Fig. 1). This bouncing against the void may explain why most of the cool luminous hypergiants cluster near its low-temperature boundary, while the identification of hypergiants of later spectral type, possibly like VY CMa (of M-type), is seldom. An increase of the photospheric temperature of HR 8752 by 3000 K-4000 K has been observed based on high-resolution spectra collected over the past thirty years. The effective temperature of IRC+10420 has been as low as 5270 K and increased to ~7000~K in 1992. The natural question arises whether (apparent) evolutionary changes on human time-scales result from an actual active reconstruction of the stellar interior, or by some hitherto unknown envelope mechanism? Is there a global instability mechanism in these stars other than stellar pulsation, which changes their spectral types, perhaps triggered by some internal or external cause? Is the void an eternal obstacle for their evolution and will the yellow hypergiants eventually fade as supernovae, or will they rapidly evolve across the hypergiant void into early A-type supergiants (e.g. the least luminous S Dor stars), after having lost large amounts of mass?
Two regions in the upper H-R diagram can be outlined where in the atmospheres of luminous blueward evolving stars (hence very evolved objects) five conditions are obeyed. These are:
- the effective gravity acceleration in the atmosphere g_eff < 0.3 cm/s^2.
- d rho / dz < 0 (z is the vertical height; rho is gas mass-density) in the relatively deep parts of the photosphere.
- the sonic point ( i.e. the level where the wind velocity equals the speed of sound) lies inside the photosphere.
- the sum of g_eff + g_puls < 0 during part of the pulsation cycle, where g_puls are variable pulsation acceleration forces.
- the first adiabatic index Gamma_1 < 4/3 in part of the line forming portion of the photosphere.
The two regions were baptized the 'Yellow Void' and the 'Blue Instability Region' (r.h.s. of Fig. 1). The yellow-red area contains all red and yellow hypergiants. The blue area contains many S Dor stars (LBVs) in their stable states. This is one of the bases for the assumption that yellow hypergiants are dynamically unstable stars that are evolving blueward and that, having entered the blue instability region, show up as S Dor stars (LBVs).
Figure 1: Left-hand panel: Position of a number of super- and hypergiant stars according to their surface temperatures and total intrinsic brightnesses (or luminosities). The surface temperatures of stars marked in the right-hand half of the figure are below 10,000 K, and called cool luminous stars. The stars marked in the left-hand half of the diagram are hot (blue) luminous stars, such as the Luminous Blue Variables. The surface temperature of the yellow hypergiants Rho Cas, HR 8752, and IRC+10420 changes over time, marked with horizontal lines between the observed minimum and maximum temperatures. The blue horizontal line for Rho Cas shows the temperature change from about 7500 K to below 4000 K observed over about 200 days during the eruption of 2000. Right-hand panel: Areas in the upper part of the HR diagram where stars are dynamically unstable according to the criterion < Gamma_1 > < 4/3. The diagram shows the 'yellow-red' and the 'blue' dynamic instability regions. No model calculations are so far available above and below the upper and lower dashed horizontal lines, respectively.
Read more: Stellar Atmospheric Stability Theory
- de Jager, C., Lobel, A., Nieuwenhuijzen, H., & Stothers, R. 2001, Monthly Notices of the Royal Astronomical Society, 327, 452, Instability Regions in the Upper HR Diagram. PDF ADS