Stellar Structure and evolution Lecture 11: Evolution of massive stars

Learning Outcomes The student will learn the following concepts Evolution of a high mass star - burning stages and lifetimes The detailed model predictions and a schematic overview The effect of mass-loss and stellar winds The Eddington luminosity The initial mass function and the upper mass limit

Example set of models - “the Geneva Group” See handout of paper of Schaller et al. (1992): the “standard” set of stellar evolutionary models form the Geneva group. 1st line in table NB = model number (51) AGE = age in yrs MASS = current mass LOGL = log L/L LOGTE = log Teff X,Y,C12…NE22 = surface abundance of H,He, 12C … 22Ne (these are mass fractions) 2nd line QCC = fraction of stellar mass within convective core MDOT = mass loss rate: RHOC=central density LOGTC = log Tc X,Y,C12…NE22 = central abundances 

Massive stars Lets consider the upper mass region, in particular the 15M - 25M star. What is the main-sequence lifetime of a 25M star ? What are the timescales of its lifetime after it leaves the main-sequence ? What is the status the star at the last point in the Geneva tracks ?

Schematic description The evolution of massive stars have the following general characteristics and differences to lower mass evolution The electrons in their cores do not become degenerate until the final burning stages, when iron core is reached Mass-loss plays an important role in the entire evolution (we will come back to this) The luminosity remains approximately constant in spite of internal changes. The track on the HRD is therefore horizontal. For a 15-25M stars we have seen a gradual redwards movement. But for higher mass (or stars with different initial compositions) the star back and forth between low and high effective temperatures

From the main-sequence to He burning The cores of massive stars are convective, hence newly formed He is evenly mixed in the core. As the hydrogen is consumed, the core contracts and also shrinks in mass (see QCC values). The convective core becomes exhausted homogeneously, while it contracts to a smaller volume and becomes hotter. The star also develops a H-burning shell around the He dominated core. The temperature at the bottom of the hydrogen envelope is too high to sustain hydrostatic equilibrium. The envelope expands and the star becomes cooler, moving to the red region of the HRD. It becomes a red supergiant star. Due to the rapid drop in temperature throughout the outer atmosphere, the criterion for convection is reached in this region and a convection zone develops, reaching deep into the star. It dredges up some of the material from the original convective core. This core material can appear at the stellar surface in the atmosphere of the red supergiants.

Schemactic picture of convective regions “Cloudy” areas indicate convective regions Solid lines show mass values for which radius is 0.25 and 0.5 of total radius Dashed lines show masses within which 0.5 and 0.9 of the luminosity is produced

From He burning to core-collapse The He burning core is surrounded by a H-burning shell The triple- process liberates less energy per unit mass than for H-burning (~10%). Hence the lifetime is shorter, again around 10% There is no He-flash as densities in the He-core are not high enough for electron degeneracy. Schematic figure below shows the structure of a star after a large fraction of He is converted to C. We have core of 12C and 16O, surrounded by He and H burning shells. The core will again contract and the temperature will rise, allowing C and O burning to Mg and Si (see Lecture 6). 7. This process continues, with increasing Z, building up heavier and heavier elements until the iron group elements of Ni, Fe and Co are formed. The core is surrounded by a series of shells at lower T, and lower 

Typical Timescales for later burning phases Massive stars of course spend most of their lives on the main-sequence, and illustrative timescales for 15M - stars given below. The Geneva tracks only go up to the end of carbon burning, but other authors have followed the burning through to the production of an iron core (e.g. Heger & Langer 2000, ApJ 528, 368) Central burning phase time (yrs) Hydrogen 10 x 106 Helium 1 x 106 Carbon 400 Oxygen 1 Silicon 10-2

Mass-loss from high mass stars Large amount of evidence now that high mass stars loose mass through a strong stellar wind. The winds are driven by radiation pressure - UV photons from a hot, very luminous star absorbed by the optically thick outer atmosphere layers. atmosphere is optically thick at the wavelength of many strong UV transitions (resonance transitions) of lines of Fe, O, Si, C (and others). photons absorbed, imparting momentum to the gas and driving an outward wind. measured in O and B-stars, and leads to (terminal) wind velocities of up to 4000 km/s and mass-loss rates of up to 5 x 10-5 M yr-1 Huge effect on massive stellar evolution - the outer layers are effectively stripped off the star.

Evidence for stellar winds: “P-Cygni” lines in hot stars - resonance transitions in optical or UV

Wolf-Rayet Stars H-deficient massive stars. Spectra show either strong abundances of He+N or C+O. These are products of H-burning and then He burning. Likely there is an evolutionary line, or a relation between initial mass and final WR star produced. Possible evolution scenario: O main-sequence star  blue supergiant  red supergiant  WR star

The Eddington luminosity Eddington derived the theoretical limit at which the radiation pressure of a light-emitting body would exceed the body's gravitational attraction. That is, a body emitting radiation at greater than the Eddington limit would break up from its own photon pressure (see class derivation). Violation of this implies violation of hydrostatic equilibrium. RHS of inequality represents the Eddington luminosity that cannot be surpassed If ≈es, then LEdd becomes determined uniquely by M. For massive main-sequence stars Main sequence should have an upper end (M≈180M, for s=es=0.04 m2 kg-1)

The initial mass function How many stars are formed at each mass in a star cluster, or star forming region ? Is it always the same distribution ? Is it constant across environments and galaxies ? (m) This intial mass function is also sometimes defined slightly differently as the amount of mass locked up in stars with masses in the interval (M, M+dM) formed within a given time within a given volume: Define the number of stars formed at a given time within a given volume, with masses in the range (M, M+dM) as a function solely of M

Total number of stars between the masses m1 and m2: Total mass locked up in stars between masses m1 and m2: Class question: A star cluster is born from a giant molecular cloud of 10,000 M . Assuming that all of the mass is converted into stars, estimate the mass of the gas that goes into forming massive stars (I.e stars with M≥10 M) How big do stars get ? Is there an upper mass cut-off ? What are the masses of the most massive stars ? The most luminous stars in the galaxy have inferred masses of ~150-300M but this value depends on estimate of logL/L and Teff. The former requires distance, reddening, bolometric correction and the later requires reliable model atmosphere. Probably uncertain within a factor 2.

Upper mass limit for stars (Assignment 2) Recent study in Nature (Figer 2005, Nat, 434, 152). The IMF was determined for a very massive cluster, which is massive enough that there is a reasonable probability that stars of masses >500M could exist in cluster, if they form. Assuming a standard Salpeter IMF holds in the Arches, how many stars would you expect to find above 140M if there was no imposed upper mass cut off ? [Note: number of stars with masses 10 < M < 140M is 296] What is the statistical probability that you find no stars in this region if there is no upper mass limit ?

The Arches cluster observed by HST

IMF constant at different Z Solar neighbourhood composition: H=70%, He=28% Metals=2% LMC Z=0.5Z, and SMC Z=0.2Z Starformation of massive stars proceeds independent of metallicity Local Group galaxies SMC and LMC are excellent laboratories to study massive star populations

No evidence for environment influence Whatever the star-formation rate, the IMF seems constant Starburst regions, “normal” young clusters, low mass clusters in Milky Way, LMC, SMC all similar IMF not measured well beyond the Magellanic Clouds

Summary We have covered qualitative description of the evolution of star from modern calculations The theoretical HRD in general, and 1M and 25M stars in detail Time-scales for evolutionary stages: 90% of massive star’s life is on main-sequence. Final stages of C-burning and beyond last few hundred years Massive stars loose mass - most massive become WR stars, with final masses significantly less than birth mass Derived the Eddington luminosity - the main-sequence should have upper mass limit The initial mass function implies significantly less massive stars than low mass stars born - implications for galactic evolution.