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*Melampus:*  The first mortal soothsayer
It must be said that many of the mythological characters we've
encountered so far haven't been particularly pleasant.   The gods tended to
behave rashly and mete out punishments unjustly merely to avenge slights or
minor assaults on their dignity.    Philandering men showed callous
indifference to the anguish their infidelities engendered in the scorned
women who would sometimes avenge themselves on the children of those men.
   Such was the way of the disturbed world in the grand mythological soap
opera.
Melampus, on the other hand, was kindly and compassionate from birth and
reaped great reward as a consequence.       Melampus was the child of
Idomene and Amythaon, the latter of whom was the grandson of Salmoneus, the
fun-loving, Zeus-impersonating fellow we encountered yesterday.      One
day when Melampus was playing outside while under the care of his servants,
he saw a serpent's nest around an oak tree.  It contains a large adult
serpent and two of its children.  The nervous servants noticed the child
close to the serpent's nest and immediately crushed the adult serpent under
a rock.    When the servants moved to kill the two young serpents, Melampus
gathered them up by his chest.  "Please don't hurt them," he begged.  "They
are young and I shall take care of them."    The servants relented and
Melampus took them home and raised the serpents to maturity.   One night he
awoke in a panic as he felt the two then-older serpents licking his ears.
 "Accept this gift from us whom you saved from slaughter," one of the
serpents hissed. Melampus looked at them with astonishment.  "I know what
you're saying," he whispered.  "From this point on shall you know the
languages of all creatures that fly in the air and slither on the ground.
So, too, shall you, through the murmuring of our kindred, know the future
that other men cannot foresee."          Melampus was determined to employ
this newly acquired skill to benefit others.  He was given an opportunity
to do so soon thereafter.  Anaxagoras, king of the region where Melampus
was living, had a son who had inexplicably gone crazy. The desperate king
offered a great reward to anyone who managed to cure his son's madness.
Melampus devised a clever plan.  He sacrificed an ox and then slit it
open.    He waited nearby until a venue of vultures arrived to feed on the
carcass.  As the vultures dined, Melampus approached them and asked for any
information about the prince's sickness. The oldest vulture, Makamenides,
explained that the king had offered a sacrifice many months before.
Anaxagoras' son was so frightened by the knife his father used during the
ritual that he tossed the bloody instrument aside.   The knife became
lodged in a nearby oak tree, injuring the tree's resident hamadryad.
This tree spirit then afflicted the king son' with madness to punish the
king for the injury.  Makamenides knew what had transpired because he was
flying close to the ground while waiting to eat part of the sacrificial
animal.   The vulture instructed Melampus to travel to the oak tree and
speak with the hamadryad herself.  "You'll know the oak tree because the
knife still protrudes out of it."   Melampus found the oak tree and spoke
to its attendant dryad.   She told him that to cure the prince's madness,
he would have to remove the knife, which was still causing her immense
pain.    He would then have to boil the knife in water.  ""If the prince
drinks the rusty water in which the knife was boiled, his madness will be
cured."     Melampus brought the knife to Anaxagoras' palace and explained
how he could heal his son.   The king abided by these instructions and told
his son to drink the water.   Soon after he had done so, he recovered his
senses.      The King was so grateful he offered Melampus two thirds of his
kingdom. The other third was given to Melampus' brother Blas.
Anaxagoras' relinquished control of his domain to Melampus, who, as we
would expect, became a wise and beloved ruler.   Nevertheless, a few
miscreants who didn't love Melampus kidnapped him in the hope that his
people would pay a ransom for his release.    While Melampus languished in
an old cell his kidnappers had constructed, he heard termites talking
within the cell's ceiling.   "One more day and we shall burrow through this
wooden beam," one of them said to all the others.  "Eat quickly and let's
be done with it."  Melampus begged his captors to move him to a different
cell.  "I know this cell will collapse soon!" he told them. "Move
elsewhere, I beg you."       The captors were initially reluctant to do so.
However Melampus became so insistent they finally moved him to a different
cell just before the first one caved in.   Realizing that their prisoner
was prophetic, they released him at once, fearing reprisal from the gods
whom they assumed had bestowed such powers onto him.   Melampus became
highly regarded for being a fine king and a gifted soothsayer, the first
mortal who developed such powers.  Having been so kind and congenial,
Melampus' life was largely devoid of strife.   Perhaps for this reason, he
became one of the more obscure figures in a mythological world that tended
to bestow fame on its least agreeable denizens.

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2019-2020:  CLXI

THE DAILY ASTRONOMER
Thursday, June 4, 2020
Remote Planetarium 48:  Stellar Evolution II

The core of every active star is a thermonuclear fusion furnace.   Within
the core lighter elements are fused to form heavier elements.  This process
generates radiant energy that migrates out of the core through the star's
outer layers and then into space.  Whenever you see sunlight, you're
observing energy that originated in the solar core about 300,000 years
before.  Although stars seem immortal relative to our brief mortal lives,
they all have finite life spans as their fuel reserves are also finite.
They only have so much fuel to fuse before they perish.    Of course, even
the most short lived stars will persist for a few million years.    Counter
intuitively, the more massive the star the shorter its lifespan.
The more massive stars expend their fuel reserves far more quickly than the
low mass stars.

The following list shows a sample of main sequence lifetimes (the amount of
time a star of a given mass remains on the main sequence before evolving
away from it.)

*[Note:* a solar mass equals the mass of the Sun.  For instance, a 3 solar
mass star is three times as massive as the Sun.]

   - 60 solar masses     3 million years
   - 30 solar masses     11 million years
   - 10 solar masses      32 million years
   - 3 solar masses       370 million years
   - 1  solar masses      10 billion years
   - 0.1 solar masses    1-2 trillion years

Yesterday, we learned the Sun's fate after it exhausts its hydrogen
reserves.  It will expand to become a *red giant* and its core will start
fusing helium to produce carbon.     As the Sun is not massive enough to
produce the core pressures and temperatures necessary to ignite carbon
fusion, it will expel its outer layers to form a *planetary nebula*.  The
core will then form a *white dwarf,* a stellar remnant that will slowly
cool to become a black dwarf.

Not all stars follow the same life cycle, however.   Stars that are at
least eight times as massive as the Sun undergo more complex changes before
they end their lives.        First of all, more massive stars are able to
produce the core temperatures necessary to fuse carbon and other heavier
elements.    [Next week we will be devoting an entire class to these
element-creating fusion reactions, a process known as *stellar
nucleosynthesis*.  Today we're focusing solely on the stellar evolutionary
track.]

[image: 6592_fig20_13.jpg]

The most massive stars will experience multiple phases of fusion
reactions.    Hydrogen into helium; helium into carbon; carbon into oxygen
or nitrogen or another product.  Various other fusion reactions will then
occur in multiple stages until the star's core collects iron heated to
three billion degrees!      Iron is the end point of these reactions
because iron fusion is endothermic.   The energy invested into this
reaction is greater than the energy the reactions impart back into the
star.     All lighter element reactions produce more energy than is
required to produce them. (The hydrogen to helium reaction is the most
energy efficient.)  Consequently, when a star collects iron in its core,
the balance between the star's gravitational contraction and outward energy
pressure is violently disrupted.   The outer layers collapse down onto the
star's inner region so quickly that the gravitational potential energy is
converted into kinetic energy resulting in an explosion called a* Type II
supernova.*

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A *type II supernova* explodes from the inside out.    The supernova energy
produces all the elements heavier than iron.  It also disperses this heavy
element material throughout its local region, chemically enriching the
interstellar medium within its vicinity.

What happens next depends on two factors:  the star's mass and
*metallicity.*

*Metallicity *refers to the star's "metal content."   The astronomical
definition of "metal" is profoundly different from the chemical
definition.     Astronomically, a metal is any element heavier than
helium.        During the earliest epochs of star formation, the Universe
consisted primarily of hydrogen and helium with scant traces of slightly
heavier elements.      The first stars would have formed only out of clouds
consisting of hydrogen and helium.     They and other stars that also form
from hydrogen and helium are considered *metal free.*        The metal
content of any star depends on its 'population.'      Astronomers recognize
three distinct stellar population types:


   - *POPULATION I:  * "metal rich" stars.  They are comparatively young,
   They formed out of interactions between heavy-element laden supernova
   debris and gas/dust clouds.  They tend to revolve around the spiral arms of
   the Milky Way Galaxy.  The Sun is a perfect example of a Population I
   star.
   - *POPULATION II:  *"metal poor" stars.   These stars formed much
   earlier when the nebulae were not as chemically enriched as they were when
   the later Population I stars formed.       Population II stars are
   typically located around the galactic nucleus and in *globular clusters* in
   particular.  Globular clusters are large, old,  globe-shaped star clusters
   located in the galactic halo.
   - *POPULATION III:* the very first stars. This population is
   hypothetical, meaning none have yet been observed.   They would have been
   highly massive and therefore lived briefly.    These stars consisted of
   hardly any metals, except for any metals ejected by Population III star
   supernovae.


-Stars that are up to* nine times more massive* than the Sun will end their
lives as white dwarf stars.   More massive stars will form one of two
objects: *neutron stars* or *black holes*.    [We'll be discussing these
objects in greater detail in a later class.]

-Stars between *9 - 25 times more massive* than the Sun will end their
lives as *neutron stars*.    Neutron stars are the densest objects in the
known Universe.  When the stellar remnant is more than 1.4 times as massive
as the Sun, the gravitational compression overpowers the electron
degeneracy that sustains the shapes of white dwarf stars.     The object is
then compressed down to a much smaller volume.  If the progenitor star is
between 9 - 25 times as massive as the Sun, *neutron degeneracy* will halt
further collapse to produce a neutron star.   While a white dwarf is about
the size of a planet, a neutron star's size is that of a city.   Even the
largest cities are minuscule compared to the size of Earth.

-Stars *25-40 times more massive *than the Sun can either become a neutron
star or a black hole "by fallback," depending on their metallicity.
Stars toward the lower end of this mass range will become black holes by
fallback unless they have comparatively mid to high metallicities.   Stars
at the mid to upper range will only become neutron stars if they have high
metallicities.  A *black hole* is a region where the gravitational
attraction is powerful that nothing can escape from it, not even light.
[We will be devoting an entire class soon just to black holes.]   A *black
hole by fallback *occurs when the material within a star starts to push
outward after the supernova explosion, only to collapse back onto the core
to form the black hole.

-*Stars more than 40 times more massive* than the Sun will either become a
black hole directly (immediate without any fall back), a black hole by fall
back or a neutron star depending on the star's metallicity.   Refer to the
chart below.    For instance, a metal free star of 60 solar masses will
become a black hole directly, whereas a 60 solar mass star with a high
metallicity will form a neutron star.      * Note:  Some stars are now
believed to be able to form black holes without an associated Type II
supernova.  *

[The blank space between 140-260 solar masses refers to a region of pair
instability, a topic we haven't even mentioned yet and so won't discuss, at
least for now.]


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Next week we will discuss nucleosynthesis, neutron stars and black holes in
much greater detail.    Today, our aim was merely to explain how a star's
mass determines its fate and what that fate will be.


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