IAL 23: The Post-Main-Sequence Life of Stars

Don't Panic


  1. Introduction
  2. Star Lifetimes (Reading Only)
  3. Consequences of Varying Star Lifetimes
  4. Post-Main Sequence
  5. Low-Mass Stars
  6. High-Mass Stars
  7. Supernovae
  8. Core Collapse SNe
  9. History of Supernovae
  10. SNe Ia
  11. SNe Ia and Cosmology
  12. The Old Gang

  1. Introduction

  2. Stars are born, stars die---and sometimes leave things like the Crab Nebula.

    Neither is birth nor death is a simple process. Both are much more complex than life on the main sequence.

    In this lecture, we look at
    star death.

    The dominant parameter for the fate (and everything else) of a star is its initial mass.

    Since initial mass varies continuously from 0.075 M_☉ (i.e., about 0.075 solar masses) to about 265 M_☉ (Wikipedia: List of most massive stars) and probably higher, the fate of stars varies continuously over a large range.

    We can't discuss the whole range of behavior.

    We will just cover the death of a Sun-like star and a generic massive star of mass greater than 8 M_☉.

    About 8 M_☉ is the biggest dividing line in the fate of stars.

    Below that line, a star ends as white dwarf after ejecting considerable mass to the interstellar medium (ISM).

    Above that line, a star explodes as core-collapse supernovae ejecting most of its mass into the interstellar medium (ISM) and leaving a neutron star or black hole compact remnant.

    This divergent fate is illustrated in the cartoons below.

  3. Star Lifetimes (Reading Only)

  4. As we emphasized in the Introduction, the dominant parameter for stars is stellar mass---for which the natural unit (as far as humans are concerned) is the solar mass M_☉=1.98892(25)*10**30 kg.

    In the following subsections, we describe how the stellar mass sets the lifetime of stars.

    1. Stellar Mass and Nuclear Burning:

      Stellar mass is dominant because it sets the amount of gravitational potential energy available to a star to convert into heat energy and because holding star up against its own self-gravity sets the interior pressure of the star.

      Although the detailed relationships are NOT simple, essentially, more mass, the more heat energy from contraction (i.e., from gravitational potential energy converted to heat energy) and the higher pressure.

      For ordinary stars the pressure is a combination of ideal gas pressure and radiation pressure---the later becomes more important with increasing internal temperature.

      The higher the core pressure, the higher the core density and the higher the nuclear burning rates.

      So the more mass, the higher the nuclear burning rates.

      The nuclear burning supplies heat energy that maintains the temperature and thus the pressure to support the star against contraction.

      The heat energy has to be supplied since it is always leaking away into space: radiative transfer and convection transport the heat energy out of the star.

      There is a stellar self-regulation for main-sequence stars that we discussed in the particular case of the Sun in IAL 8: The Sun that keeps main-sequence stars in many rather unchanging for the their main-sequence lifetimes.

    2. Length of Main-Sequence Lifetimes:

      The length of the main-sequence lifetimes is determined by the amount of central hydrogen that can be burnt to helium and the rate of nuclear burning.

      Now more massisve stars have more hydrogen to burn than less massive stars, but they also have higher nuclear burning rates as we argued in the last subsection.

      The latter factor wins in the war of trends: the more massive the Sun-star, the shorter its main-sequence lifetime.

      We can be more quantitative.

      First recall the mass-luminosity relation which is illustrated and described in the figure below.

      Now consider the figure below (local link / general link: star_lifetimes.html) where there are tabulated main-sequence lifetimes and an aprpoximate main-sequence lifetime formula is derived.

  5. Consequences of Varying Star Lifetimes

  6. From the calculations and tables in the section Star Lifetimes, one can see that the main-sequence lifetimes decrease dramatically with increasing stellar mass.

    The vastly differing main-sequence lifetimes lead to consequences we should discuss:

    1. Stars of Mass ≤∼ 5 M_☉:

      The orbits of objects in galaxies are continually evolving in a somewhat chaotic manner and and over periods of order tens of megayears objects that started close together are likely to far apart???.

      So lower-mass stars (i.e., those less than about 5 M_☉) and their natal star formation regions are likely to be far apart long before the end of the main-sequence lifetimes???.

      Star formation regions tend only to exist for of order tens of megayears???, and so the natal star formation regions will NOT only be likely to be far away, but actually gone long before the end of the main-sequence lifetimes???.

      So we will never find the
      Sun's natal star formation region. But clues about it are embedded in primitive Solar System material such as some meteorites that have undergone little chemical processing since the solar system formation.

    2. Stars of Mass ≥∼ 8 M_☉:

      More massive stars, particularly those over about 8 M_☉ initially will have strong feedback effects on their natal star formation regions the interstellar medium (ISM) in general.

      The more massive stars are OB stars (although the low end of the B star range drops to 2 M_☉)

      Groups of OB stars are called OB associations.

      The massive stars NOT only have have short main-sequence lifetimes, but short formation periods???.

      Their electromagnetic radiation (EMR) will evaporate interstellar dust, molecules, and heat the star formation region ISM.

      The heating increase the pressure in the in star formation region and stop collapse.???

      Moreover, the massive stars will have episodes early and late in their lifetimes of strong stellar winds that will blow bubbles of low density regions in the star formation region and tend to blow it apart.???

      Those stars above about 8 M_☉ will explode as core-collapse supernovae

      The fast moving supernova ejecta will also push away the star formation region.

      The upshot is that the massive stars will tend to turn off star formation right where they form.

      This turning off is illustrated in the figure below.

      So massive
      stars bite the hand that fed them.

      But on the other hand, the force of their stellar winds and supernova ejecta can increase ISM density in adjacent regions, and thus trigger more star formation there.

      Additionally, the massive stars post-main-sequence phase stellar winds and and supernova ejecta will enrich the ISM in metals formed during their lifetimes and/or in the supernova explosion itself.

      As we said above, the feedback effects of massive stars are complex.

    3. Stars of Mass ≤∼ 0.9 M_☉:

      Main-sequence stars less than about 0.9 M_☉ are K stars and M stars are very common.

      In the solar neighborhood (which is approximately the Orion Arm of the Milky Way), these stars are about 88 % of all Main-sequence stars (Wikipedia: Stellar classification: Class K).

      The frequency of main-sequence K stars and M stars probably varies wildly throughout the observable universe, but nevertheless, they probably make up the majority of all main-sequence stars in all locations.

      Yours truly finds it mind blowing that no stars initially of mass less than about 0.9 M_☉ has ever left the main sequence in the history of observable universe.

      Since the Big Bang the age of the observable universe = 13.797(23) Gyr (Planck 2018) (see also Wikipedia: Age of the universe; Wikipedia: Λ-CDM odel: Parameters), and so none of these stars has had the time to evolve off the main sequence since there minimum age is about 14 Gyr (see Table: Approximate Main-Sequence Lifetimes).

      Theoretically, we know that they must lose some mass in their late phases and evolve into white dwarfs.

      We will never see that happen on the foreseeable time scale of humankind.

  7. Post-Main Sequence

  8. What happens to stars when they exhaust the hydrogen in their nuclear burning cores?

    At that point they cease to be main-sequence stars and they leave the main sequence on the Hertzsprung-Russell (HR) diagram.

    They become post-main-sequence stars.

    The following HR diagram illustrates the post-main-sequence evolutionary tracks for stars of several stellar masses and introduces some of the terminology for post-main-sequence evolution.

    The diagram suggests what is true---late stellar evolution is immensely complex.

    We CANNOT cover everything or discuss all objects.

    So we will only follow a few stories.

    For these stories, we will adopt the mass divisions of Bennett et al. (2008, p. 565ff).

    1. Low-mass stars: less than about 2 M_☉.
    2. Mid-mass stars: about 2--8 M_☉.
    3. High-mass stars: greater than about M_☉.

    Absolutely, note that this division is a particular choice suitable to our discussion. Many other choices can be made particularly for more detailed or advanced discusions.

    One has to say, in fact, that stellar behavior varies continuously with stellar mass.

    One also has to say that stellar mass is the dominant parameter for stellar evolution, but not the only one: other key ones are angular momentum, metallicity, and companion status (i.e., is the star a single star or part of a multiple star system).

    We will allude as needed to these other parameters, but to keep things simple we will largely skirt them.

    You may well ask how do we know the stories of late-star evolution?

    We only have a snapshot of astronomical time and CANNOT follow any star's evolution: we only see it at one instant.

    Well a cycle of observation and modeling---the good old scientific method.

    The observations include
    stars of the same type in different stages of their evolution---but it takes modeling to know that---and stars of different types of the same approximate age in star clusters---all almost the same age since they formed at approximately the same time.

    The modeling includes enormous computer calculations.

    Many of the results of these calculations defy any simple explanation.

    We just have to say the computer model says such-and-such in many cases. Sometimes we handwave---i.e., present plausible explanations that makes results intelligible, but do NOT prove them or fully prove them.

    Caveat: the post-main-sequence evolution of stars is fairly well understood in qualitatively from a combination of observations and theory.

    But quantitative predictions are difficult. The three-dimensional hydrodynamic computations required test the limits of our modern computer codes.

    We can only tell the best story we can given present understanding.

  9. Low-Mass Stars

  10. Recall that for our discussion, we set low-mass stars to be those of mass less than about 8 M_☉.

    But this group is really diverse itself.

    So we will just Sun-like star: i.e., a star of about 1 M_☉ initially.

    The figure below illustrates the life of a such a star.

    When the hydrogen in the core of the
    Sun becomes exhausted, the main-sequence lifetime ends in about 6 Gyr (FK-493). Then there is a rather complex evolution---to say the least.

    1. A hydrogen burning shell will still exist around the core.

    2. The Sun's core continue contracting because of thermal energy loss, but it will get hotter because of the contraction.

    3. The energy generation rate will actually increase because of the hotter core.

    4. The Sun will then expand into a RED GIANT with a radius of order 1 AU because of the extra heating (Se-249; FK-470).

        [Red giantism is something we understand in a computer modeling sense. We put the right ingredients into a computer model and they show that after the core hydrogen burning is over stars should expand into red giants. But there is no short explanation of the process.]

    5. The Sun will then be much brighter than it is now, but its photosphere temperature will be lower eventually reaching about 3000 K (Ze2002-341).

    6. By Wien's law, the peak wavelength of it's emission will then be

            wavelength_max = about 3000 micron-K / 3000 K  = 1 micron
            and thus in the infrared.  

    7. The Sun in the visible will be red: hence the name RED GIANT.

    8. When the helium core's temperature reaches about 100*10**6 K, the HELIUM will suddenly start burning to CARBON and OXYGEN pretty much everywhere in the core within perhaps a few minutes (Ze2002-343).

    9. This is the HELIUM FLASH. We never see this event because it is always buried in the core and lasts only seconds---but theoretically it must happens it seems (FK-473).

      HELIUM FLASHES happen only to stars in the 0.4--2 or 3 solar mass range (Se-251; FK-472).

    10. Post-helium flash, the Sun will then contract and become a bit less bright oddly enough. Essentially this is because there is again nuclear burning in the core, but now its helium burning.

    11. At this stage the Sun is called a HORIZONTAL BRANCH STAR (Shu-152;. Se-252).

    12. But the helium burns much more quickly than hydrogen.

      So the helium exhausts in the core and then there is an non-burning carbon-oxygen core, surrounded by a helium-burning shell surrounded by a hydrogen-burning shell.

    13. The Sun then puffs up to be a RED GIANT again---but only for awhile.

    14. The helium burning is unstable and of order every 100,000 years has a runaway burst of burning called a THERMAL PULSE (FK-493).

      Each THERMAL PULSE causes a superwind that blows off much of the Sun's envelope.

    15. The escaping material forms a complex expanding nebula called a planetary nebula---the name is a total misnomer since these nebulae have nothing to do with planets.

      Note the name
      planetary nebula originated in the 18th century because the closest, most obvious planetary nebulae are large enough to have a finite disk in a telescope and there greenish color made them look sort of like Uranus (FK-494; CK-329).

      Planetary nebula atoms are excited by UV radiation from the remnant star---which is very hot on the surface---and emit copious LINE SPECTRA.

      Green lines from doubly ionized oxygen are often particularly noticeable (Se-268).

      Planetary nebulae have huge range of behavior---which we won't go into here, but we will show some pictures.

      planetary nebulae disperse in the interstellar medium after a few thousands to tens of thousands of years.

      After some thermal pulses, the remnant Sun will have lost most of its hydrogen and helium and perhaps about half its mass and shrunk to a size of order the size of the EARTH.

    16. The Sun is then a white dwarf.

      The time from becoming a 2nd red giant (AGB star) to being a white dwarf is about 0.7 Myr (FK-493).

    The SOLAR white dwarf will be mostly CARBON and OXYGEN from helium burning. The Sun CANNOT burn carbon and oxygen: it's core never gets hot and dense enough.

    Stars that start out more massive than about 4 solar masses can burn carbon and oxygen (FK-497), but if they too end as white dwarfs if they arn't massive enough to become supernovae: i.e., have masses greater than about 8 solar masses.

    But although the SOLAR white dwarfs will be mostly carbon and oxygen, the lighter helium and hydrogen atoms float on the top and form a skin.

    The figure below shows how white dwarfs are held up in hydrostatic equilibrium against gravitational collapse under their own self-gravity.

    White dwarfs are initially very hot with photospheric temperatures of order 30,000 ??? to 150,000 K (see Wikipedia: White dwarf: Radiation and cooling).

    Initially, a white dwarf's EMR peaks in the UV and in the visible they appear white: hence the "white" in white dwarf.

    But they arn't very bright because of their small size.

    But white dwarfs have no nuclear burning energy sources.

    They can only lose heat energy and cool off forever. See the figure below of white dwarf cooling off to become a black dwarf.

  11. High-Mass Stars

  12. Supernovae

  13. Supernovae (SNe) is that are the powerful explosions of stars and are of considerable astrophysical importance.

    They are among the brightest astrophysical objects and, unlike most observable astrophysical objects, they evolve rapidly in time.

    The brightest type of SNe (at least on average), Type Ia SNe are currently of great importance in cosmology and, in particular, in the determination of the cosmological parameters.

    All types of SNe eject into the interstellar medium (ISM) heavy elements (carbon and above) synthesized in the explosion or from pre-explosion evolution.

    This element yield from supernovae drives most of the heavy element evolution of the observable universe.

    Rocky planets, like the Earth, and life as we know it would probably NOT be possible without the heavy elements from SNe.

    The cosmic composition is approximately illustrated in the figure below (local link / general link: solar_composition.html).

    The physics of the explosions of all
    supernova types is of intrinsic interest and is also of interest in understanding material properties under extreme conditions.

    So SNe are important in evolution of the universe.

    But they are a bit complicated too.

    A first reason is that the two main classes of SNe---Type Ia SNe and core-collapse supernovae---are distinct phenomena.

    Yes they have many similar aspects and yes the same researchers study both, but their essential explosion mechanisms are different. So any general talk on SNe must be a talk on two things.

    A second reason is the growth of knowledge---the more we know about some field, the more complex it becomes.

    Climbing the hill of any specialized field is hard these days---especially if you are rolling downhill like me.

  14. Core Collapse SNe

    The impact of supernova ejecta, especially core-collapse SNe ejecta, on the ISM is also important in the creation and dispersal of star-forming regions.

    A supernova remnant is the expanding ejecta of a supernova explosion. It carries the heavy elements synthesized in the supernova or pre-supernova stellar evolution out into interstellar space. Supernova remnants are often roundish shells, but they can also be messy and have filaments like the Crab nebula. They exist for thousands of years before being broken up and dispersed in the ISM out of which new stars form.

    The compact remains of core-collapse SNe are neutron stars. See figure below.

    Pulsars are radio-emitting young neutron stars. Neutron star are the compact remnants of core-collapse supernovae---they are the collapsed core. Neutron stars are super-dense objects with masses typically in the range 1.35--2 solar masses and radii of order 10 kilometers. As their name suggests, they are mainly made of neutrons

    Neutron stars are overwhelmingly most detectable when they are also pulsars. See the figure below (local link / general link: pulsar_magnetic_field_diagram.html).

  15. History of Supernovae

  16. Strange sights have been seen in the sky since forever---and we still have UFOs today---though, of course, they are NOT extraterrestrials---I've seen two myself---one turned out to be breaking-up Russian satellite and the other a flock of Canada geese---who seemed in a dark sky to be a flying wing executing a nifty U-turn.

    Among these are new stars or novae---using both terms in their historical sense, NOT in a modern sense. The term nova follows from the use by Tycho Brahe (1546--1601) in book supernova De Nova et Nullius Aevi Memoria Prius Visa Stella (1573)??? concerning SN 1572 (AKA Tycho) in Cassiopeia.

    Novae were star-like objects that appear where no star was before and then disappear within months or years. They showed no motion relative to the fixed stars and no stellar parallax---and so they could to be assumed to be in the realm of the fixed stars---but NOT eternal.

    Aristotelian cosmology---which became a philosophical dogma in Classical Antiquity and later in Medieval Islamic society, Medieval European Society, and Renaissance Europe---posited that there was no change in the heavens above the Moon.

    For Aristotle (384--322 BCE), the "supreme authority", see the figure below local link / general link: aristotle_supreme.html).

    Novae, in Aristotelian cosmology, were thus anomalies to be explained away as somehow sublunary or to be just ignored. Astronomers in the Aristotelian cosmology tradition do seem to have missed seeing a lot of novae.

    But the ancient Chinese astronomers---perhaps because they had no Aristotelian prejudices---or maybe they were just better observers---did observe a fair number of novae starting from the time of the Han dynasty (206 BCE--220 CE). They called these objects guest stars---just visitors in the celestial realm. What were the novae/guest stars?

    In some cases, it's hard to tell from ancient records. Many were probably cataclysmic variable stars or novae in the modern sense. These are both cases where accretion from a close binary companion onto a white dwarf star leads to a surface nuclear explosion---titanic events, but much less so than SNe.

    A few were SNe.

    The earliest nova (in a historical sense) that is likely to have been a supernova was SN 185---which occurred in 185 CE in constellation Circinus and was recorded by Chinese astronomers (i.e., it was a guest stars).

    Other retroactively recognized important SNe are SN 1006 (in Lupus), SN 1054 (in Taurus), SN 1572 (in Cassiopeia), SN 1604 (in Ophiuchus), and SN 1885A (in the Andromeda Galaxy (M31)).

    SN 1054 is famous for having given birth to the Crab nebula supernova remnant and the Crab pulsar.

    See Supernova videos below (local link / general link: supernova_videos.html):


    SN 1572 (AKA Tycho) was observed and reported on by Tycho Brahe (1546--1601)---that report made him famous and proved---although it took decades and a lot of other evidence for full acceptance---that Aristotelian cosmology was wrong and the heavens were NOT changeless.

    SN 1604 (AKA Kepler) is the last supernova observed in the Milky Way.

  17. SNe Ia

  18. SNe Ia and Cosmology

  19. The figure below (local link / general link: cosmos_history.html) is a preview of cosmology which we take up in IAL 30: Cosmology.

  20. The Old Gang

  21. Just a few images of the old gang of supernova research:

    1. David Branch image: My old boss.

    2. Stirling Colgate (1925--2013): images.

    3. For Stirling Colgate (1925--2013) and Craig Wheeler at the Aspen Center for Physics: see in ancient times.

    4. Bob Kirshner (1949--) images:

    5. Me et al.

    6. Me et al.

    7. And some of the new gang and me in Cefalu, 2006.

    8. The accelerating universe discoverers---and if it was disproven, would they have to take away the 2011 Nobel Prize in Physics for discovering it from my old pals. See the figure below (local link / general link: adam_riess.html).