Evolution Off the Main Sequence Todays Lecture: Homework 4: Due Today Homework 5: Due Classtime, Tuesday, March 11 Help Session: Wed., March 12, 5:00-6:30, LGRT 1033 Midterm Exam, in class Thursday, March 13 Reading for Today: Chapter Reading for Next Lecture: Chapter Red Giant Stars Helium Burning/Horizontal Branch AGB Stars Evolution of Massive Stars

Properties of stars on the main sequence are determined by mass. Stars range in mass from 0.08 to larger than 100 M ⊙. The lifetimes depend on M/L, high mass stars have very short lifetimes. The Main Sequence - Stars are in hydrostatic equilibrium, fusing hydrogen into helium in their cores.

As stars age on the main sequence the fraction of hydrogen in the core decreases, while the fraction of helium increases. Stars must adjust their structure slowly to maintain hydrostatic equilibrium. The central temperature of the stars rise, to maintain the rate of fusion with diminishing hydrogen supply in the core. Evolution while on the Main Sequence

As the central temperature rises, the star must adjust to maintain hydrostatic equilibrium. Both the luminosity and radius of stars like the Sun increases slowly over their main sequence lifetime. Evolution while on the Main Sequence

Evolution Off the Main Sequence At the end of its main sequence life, stars build up an inert helium core. The fusion of hydrogen is now primarily in a shell surrounding the helium core. The inert helium core contracts, releasing gravitational potential energy that heats the surrounding regions promoting more vigorous fusion in the hydrogen shell above the core. At first the changes in structure are slow, and the luminosity of the star increases slightly, and the star expands and cools. Subgiant Star

The star is no longer in a stable equilibrium. The helium core is contracting and heating. The increasing core temperature invigorates hydrogen shell fusion and the stars converts hydrogen into helium at an ever increasing rate and the luminosity of the star begins to increase more dramatically.

Energy transport within the star cannot keep pace with the rising luminosity of the hydrogen shell fusion, therefore much of this new thermal energy is trapped in the star. The trapped thermal energy causes the outer envelope of the star to expand greatly. As it expands, the surface of the stars cools. Thus the star has become much more luminous and cooler. The star is becoming a red giant star.

Red Giant Stars The outer envelop of the star expands enormously and cools, while the inner core contracts and the central core temperature rises. The star is red giant star – expands to hundreds of times larger than its main sequence size.

In the H-R diagram, the star becomes more luminous and cooler. Therefore, it moves up and to the right in the diagram. On the red giant branch (RGB). A star like the sun spends years on the main sequence, ending as a subgiant star. In about 10 9 more years it will evolve to the tip of the red giant branch.

The inert helium core grows as hydrogen shell fusion increases the mass of the core. The core contracts and gets hotter and denser. For stars M > 0.4 solar masses, e ventually the core reaches temperatures of over 120 million K, at which point helium fusion can occur via the triple-alpha process:

Triple-Alpha: Details of the triple-α process are given below: 4 He + 4 He → 8 Be E = -92 keV 4 He + 8 Be → 12 C + γ E = 7.37 MeV net result is 3 He → 12 C E = 7.28 MeV The 8 Be nuclei is unstable and will decay back into two He nuclei. During the brief time its 8 Be, if another He nuclei tunnels in, then can form a stable C nuclei. Because the Couloumb barriers for these reactions are even larger than for the hydrogen fusion reactions, helium fusion requires temperatures in excess of 10 8 K.

Helium ignition occurs, and now the star has a central source of energy. The core ceases to contract and the star rapidly reestablishes hydrostatic equilibrium. The new equilibrium for a star like the Sun is now a yellow giant more luminous by about a factor of 100 than when on the main sequence. The star is now a horizontal branch star. Horizontal Branch Stars

Horizontal Branch stars are fusing He into C in the core and H into He in a shell. The central temperature is greater than 120 million K. Since, stars are more luminous now than they were on the main sequence and because He fusion produces about 4 times less energy than H fusion, the Horizontal Branch phase is much shorter than the main sequence. For a star like the Sun, this phase may only last about 100 million years.

Asymptotic Giant Branch (AGB) Stars When the core He is exhausted, the star undergoes a similar evolution as it did at the end of the main sequence phase. The core contracts and invigorates the shell burning. As before, the outer envelope expands, and the star undergoes a second red giant phase called an asymptotic giant branch or AGB star.

Asymptotic Giant Branch (AGB) Stars AGB stars have a collapsing inert Carbon/Oxygen rich core, surrounded by a shell of He fusing to C, and that is surrounded by a shell of hydrogen fusing into He.

Stars with mass < 4 solar masses, outer envelop expands, inert C/O core contracts, however, as we will discuss in the next lecture, electron degeneracy pressure halts core collapse, and no further fusion reactions occur. The outer envelope expands away (planetary nebulae) leaving a white dwarf remnant. Will discuss this evolution in the next lecture. Last Gasps of Stars Like the Sun

For stars with masses between about 4 and 8 solar masses the core can contract and heat to permit the fusion by alpha- capture into Ne and Mg (very short lived phase). These stars end their lives similar to the lower mass stars, producing a planetary nebulae and leaving behind a O/Ne/Mg rich white dwarf star. Evolution of More Massive Stars

Cepheid and RR Lyrae Variable Stars Stars typically in the Horizontal Branch phase of evolution can be unstable to pulsation. The instability strip covers low mass HB stars with masses of 1-2 solar masses (called RR Lyrae variables) and higher mass HB stars with masses of 2-15 solar masses (called Cepheid variables).

Cepheid and RR Lyrae Variable Stars Stars in the instability strip have outer envelopes that periodically expands and contracts, changing the total light output. Periods range from about 1 to 50 days. Variations in luminosity can be a factor of two or more.

Cepheid and RR Lyrae Variable Stars These variable stars have pulsation periods related to their mean luminosities. The more luminous Cepheids have longer pulsation periods. Since these stars are very luminous, they are good for distance indicators. Classical Cepheids, the relation between period and mean absolute visual magnitude is: M v = log P(days) – 1.43 Distances: m v - M v = 5 log (d/10pc)

Red Supergiant Stars As the most massive stars evolve, their outer envelopes expand to greater and greater dimensions. Massive stars become red supergiant stars. The outer envelope of the stars could easily have a radius 10 times the Earth’s orbit. Image of Betelgeuse, red supergiant star – 1000 times larger than the Sun.

In stars more massive than about 8 solar masses, the fusion of oxygen and silicon can result in the build up heavier and heavier nuclei in the core. Fusion Reactions in the Most Massive Stars

The fusion of heavier and heavier nuclei require higher and higher temperatures. To have a reasonable probability of tunneling, the energy of the particles must increase as the charge and mass of the particles involved in fusion increase. Much higher energies or temperatures are needed to fuse these heavy elements.

For energy generation, the end of the road is iron. Once iron is produced there are no further fusion reactions that can produce energy. Note that the amount of binding energy per nucleon released in the fusion of heavy elements is also decreasing as products approach iron.

Near the end of massive star’s lifetime, they begin to build up an inert iron core.

Evolutionary stages of a 25 solar mass star. Each successive fusion stage lasts for less and less time. Note that the last of these fusion stages last only days !!! The final fusion product is iron, although the subsequent collapse heats the core, no further energy can be produced. The core undergoes catastrophic collapse, resulting in a Type II Supernova explosion leaving behind either a neutron star or black hole remnant. We will discuss this evolution in more detail in a later lecture.

Synthesis of the Elements Big Bang (first few minutes of the Universe): formed mostly Hydrogen (H) and Helium (He), with small traces of Lithium and Beryllium. Primordial elements – made in Big Bang

Low and Intermediate Mass Stars: fusion in the cores of these stars produce He, Carbon (C) and some Oxygen (O) Elements made in low mass stars

High Mass Stars: C, O, Nitrogen (N), Neon (Ne), Magnesium (Mg), Silicon (Si), Sulfur (S), Argon (Ar), Calcium (Ca), Nickel (Ni), and Iron (Fe) Elements made in massive stars

Supernova explosions: The enormous amount energy released allows the fusion of elements to very high mass (requires energy – but plenty present). Elements beyond Iron and all the way to Uranium. Elements made in supernovae explosions

Measured abundance of the elements in Solar System: Pattern follows the fusion sequence in massive stars (even nuclei elements favored due to helium capture). Elements beyond iron and nickel are very rare.

We owe our existence to previous generations of stars. Composition of Earth: Iron, Oxygen, Silicon, and Magnesium and lesser amounts of Sulfur, Nickel, Calcium, Aluminum, Sodium ….. Human Body: Oxygen and Carbon, and lesser amounts of Hydrogen, Nitrogen, Calcium, ….. With the exception of H, the atoms in our body were made by fusion reactions in the cores of stars in the distant past, and expelled when the stars die.