[image: image.jpeg]


*Erysichthon:*  the sacred tree slayer

Were you to ever find yourself in the mythological Universe, be well
aware:  all that strides upon Earth, burrows through its depths or soars
through its unbounded skies lives fully and in earnest.    The life force
so pervades this realm that one will find spirits innervating everything
from the simplest grass blades and streambed pebbles to the mightiest oaks
and distant mountain summits.   The mythological Universe, being
perpetually youthful, reveled in its own invention and vitality.
Consequently, all gratuitously destructive acts were deeply tragic and
those who perpetuated them almost always suffered.    Today we'll encounter
a particularly destructive king who suffered in a unique and horrific way.
  Erysichthon, a King of Thessaly, thought his "grand home" so small as to
be unworthy of the description.      Whereas rulers of adjacent kingdoms
resided in palatial splendor, he thought his furnishings simple and his
abode hardly commodious.  So, one day he decided to construct a grand
banquet hall just outside his home. He chose for its location the beautiful
oak grove adjacent to his residence.  Erysichthon certainly knew, and
certainly didn't care, that those trees, in particular the grand oak at the
grove center, were sacred to Demeter, goddess of the harvest.  Determined
to have his own way, the king gathered many men from his court, equipped
them each with an axe, and led them into the cluster of trees.  "Cut them
all," he commanded.  "Every last  one."     His men were all initially
reluctant to comply.   They merely stared nervously at the trees that
seemed to be regarding them all sternly, like sentinels surrounding a
fortress.    A few of the men even thought they could hear faint murmurings
issuing from some of the oaks.    The king reiterated his command with such
vehemence that the men set aside their anxiety and proceeded to cut down
all the trees except for the grand central oak.   When all the oaks had
been felled except for the central one, none of the men moved to strike
it.    Erysichthon demanded that they work together to topple the massive
oak.  Despite the king's growing anger, none of the men dared cut it.  In
fact, they all appeared so frightened they were all moving slowly away from
the central tree.  Having realized that his men were ignoring his commands,
Erysichthon grabbed an axe and swung it violently into the oak's sturdy
trunk.   It bled profusely and, to the king's astonishment, whimpered.   He
paused for a moment while his men scattered away in all directions.
The king knew that if that final oak and the protruding roots radiating
away from it were not removed, his banquet hall could not be built.    He
steadied himself and then rapidly struck the tree repeatedly.  Even though
the whimpers sharpened into shrieks and the blood hemorrhaged into pools
gathering around the king's feet, he persisted until it finally fell with a
ground shaking thud.    As the tree collapsed onto the forest floor, a
hamadryad prayed to Demeter to avenge the tree's slaughter.   Hamadryads
were a special race of dryads known to only inhabit oak trees.    As was
true with many of the other dryads, a hamadryad resided within a single
tree and perished when her host tree died.    Having immediately heard the
desperate prayer,  the moderately tempered Demeter grew so
uncharacteristically furious at Erysichthon's wanton destruction, she vowed
to punish him as severely as possible.  She even went so far as to travel
to the distant land of Scythia to contact her arch nemesis, Limos, the
Greek goddess of starvation.  (The Romans called her "Famine.")   Demeter
implored Limos to help her avenge the loss of her sacred grove and the
hamadryad that dwelt within its largest oak.  Despite their mutual enmity,
Limos so loathed such brutality against trees that she agreed to help
Demeter.     While Erysichthon slept, Limos crept into his room and
embraced him tightly.    The king woke up screaming for he was nearly
crippled by excruciating hunger. He called for his servants to bring him as
much food as they could carry as quickly as possible.   For the rest of the
night, Erysichthon ate rapaciously, hardly seeming to breathe between
bites.    The more he ate, the hungrier he became.  Such was the dark
sorcery Limos practiced on him:  the consumption of food served only to
intensify the hunger, not satiate it.  The next morning he remained as
ravenously hungry as he had been when he had awakened.    He commanded all
his servants to continue bringing him food.   Not much time passed before
he had exhausted his food reserves.    He then opened the royal treasury
and over a remarkably short time period spent all the funds therein to
procure more provender.  The castle was a ceaseless buzz of activity, what
with some servants preparing food while others were rushing out with gold
in hand to buy provisions.  Even his only child, a daughter named  Mestra,
assisted the staff in feeding her father. She was horrified to watch him
consuming his meals so furiously.  He did not dine with relish, but instead
with miserable desperation as he strove in vain to quell the hunger that
was causing him unspeakable agony.    When the money was gone, he was
reduced to selling everything he possessed:  every piece of furniture,
every tapestry, eventually even the castle and the servants, themselves,
were sold as he tried to buy more food.  His dutiful daughter was then the
only one left to serve him, which she did tirelessly.   Once a proud king,
the wretched Erysichthon became a waif condemned to live in the very oak
grove he had decimated.   All he did was sit trembling in front of a tree
stump he used as a dining table which Mestra supplied to the best of her
ability. Yet, when he exhausted the last bit of money and food, he sold his
only daughter as a slave.     While Mestra was walking toward the dock to
meet her new master, she prayed to the sea god Poseidon, her former lover,
for help.     He transformed her into a fisherman so that when the man who
had purchased Mestra arrived, she was nowhere to be found.    As soon as
the man left, Mestra was transformed back into her original form.  Poseidon
told her that such was the love they once shared that he would always
transform her into a different person or animal whenever she needed him to
do so.  She ran to her father and explained what had happened.   Mestra
offered to let herself be sold again and again only to then be changed into
some different person or creature whenever she would venture down to the
shore to enter into the new master's service.  Apparently when the slave
owners approached Erysichthon for a refund, he had already spent the money
and was so tormented by pain and misery they didn't press him for
compensation.   This trick worked for a while.  However, one day she was
purchased by a sea captain who had secretly watched her while she traveled
down to the dock.  He saw her change into a sea urchin which he then
captured and brought aboard his ship.   He isn't said if she then reverted
back to her original form or was condemned to remain as a sea urchin for
the rest of her life.    In either case, she remained a captive aboard the
vessel and never returned to her father.    Deprived of every last
resource, the lonely and hunger ravaged Erysichthon started to devour his
own flesh.    Eventually a woodsman happened upon him and literally found a
half eaten corpse lying on the forest floor. Its dried blood coated the
very soil onto which the hamadryad's own blood had been spilled.
Erysichthon ate as much of himself as he could before he died.


THE SOUTHWORTH PLANETARIUM
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Julian Date: 2459002.16
2019-2020:  CLIX


THE DAILY ASTRONOMER
Tuesday, June 2, 2020
Remote Planetarium 46:  H-R Diagram Part III

One aim of this Remote Planetarium course is to explain how astronomers
know what they know about the Universe.     We take it for granted that
information about objects as remote as stars and galaxies is readily
available online or in books.    That Earthbound humans have managed to
determine so much about worlds separated from us by such unfathomable
distances is astronomy's true miracle.   Today we continue our sequence
about the H-R (Hertzsprung-Russell) diagram.  This 1910 invention by Henry
Norris Russell and Enjar Hertzsprung has enabled astronomers to understand
stars in such great detail that it has often been called "The Astronomer's
Stone."

Yesterday we learned how the H-R Diagram can help us determine a
star's  *luminosity
class*.   These classes range from the hypergiants (O-Ia+) to  white dwarfs
(VII).     Today, we'll add more details to the HR Diagram so as to learn
other stellar properties.      The first of the new details involves*
stellar radii.  *
Before we proceed, let's quickly review two important geometric terms:
spherical radius and spherical volume.

[image: image.png]


A *radius* is the straight line distance from a sphere's center to any
point along the sphere's surface.    Most stars can be considered spherical
to a fair degree of accuracy.

[image: image.png]

One can calculate a sphere's volume if the radius is known.   For instance,
the volume of a sphere with a ten foot radius is 4/3(pi)(1000) = 4,188
cubic feet.   Even though the radius is small, the volume is quite large.
    Numbers  become impressively big when you cube them.       It is for
this reason that stars which have radii only a few times greater than the
Sun's will actually be much larger in terms of volume.  For instance, a
star with a radius ten times greater than the Sun's will be 1000 times
larger by volume.

*RADIUS:*
We next present the H-R Diagram that includes stellar radii demarcations:


[image: image.jpeg]


Merely by placing a star on the diagram one can readily determine its
radius and therefore also its volume.    Let's look at two examples:  the
stars Arcturus and Deneb.

*Arcturus:*
Spectral type:  K0
Absolute magnitude: -0.30
With an absolute magnitude of -0.30, Arcturus' luminosity is 170 times
greater than the Sun's.     Arcturus is then placed on the upper right of
the diagram.    It is above the line marking 10 solar radii.  Its actual
radius is 25 times that of the Sun and is nearly 16,000 times larger in
terms of volume.
From yesterday:  Its luminosity class is III, making it a normal giant.

*Deneb:*
Spectral type:  A2
Absolute magnitude:  -8.38
Deneb is brilliant!   With a magnitude of -8.38, it is approximately
200,000 times more luminous than the Sun!      Its spectral type and
luminosity place it high toward the left of the H-R Diagram.       Its
radius is 203 times greater than the Sun's, making it 8.3 million times
larger in terms of volume.   Deneb's luminosity class is Ia (luminous
supergiant.)

*MASS*
The placement alone will yield direct information about any star's size.
 However, just placing a star on the H-R diagram will not enable an
astronomer to ascertain a star's mass, unless that star is on the main
sequence.      We now introduce the *Mass-Luminosity* relation. This
relation states that a star's mass determines its luminosity.        The
more massive the star, the more luminous it will be.     This relation
applies to main sequence stars.      The relationship between a star's mass
and luminosity depends on the star's mass.   If a star is up to 43% as
massive as the Sun, its luminosity equals its mass raised to the power of
2.3.   If the star's mass is between 0.43 solar masses and 2 solar masses,
the luminosity is equal to its mass raised to the fourth power.   [Note:  2
solar masses means twice as massive as the Sun.]   If a star is between 2
solar masses and 55 solar masses, its luminosity is equal to its mass
raised to the power 3.5.   Finally, if a star is more than 55 times as
massive as the Sun, its luminosity equals 32,000 times its mass.     These
different relations are summarized below:

[image: phpTS9ine.png]

The H-R Diagram below shows the masses along the main sequence.     It does
not show masses for the stars off the main sequence as those will vary
significantly.   We observe that even the most massive main sequence stars
can be more than 60 times as massive as the Sun,while the least massive red
dwarfs will be less than 10% as massive.    Let's look at two examples:
Altair and Procyon

*Altair:*
Spectral type:   A7
Absolute magnitude:  2.22
Altair is a main sequence star (luminosity class V) that is 1.79 times as
massive as the Sun and about 10 times more massive.

*Procyon:  *
Spectral type:  B1
Absolute magnitude: -3.55
Procyon is a main sequence star 11.5 times more massive and approximately
20,000 times more luminous than the Sun.

[image: image.png]


*STELLAR LIFETIMES:*
The final topic pertains to stellar lifetimes or, more specifically, the
amount of time a star will remain along the main sequence.     The H-R
Diagram above also contains this information.  The more massive the star,
the shorter the lifetime.   This relation seems counterintuitive because a
star generates energy by fusing lighter elements into heavier ones.     The
more massive stars do contain greater reserves of this material.  However,
the more massive stars also exhaust their fuel reserves far more quickly.
 Also, the least massive stars contain only convective interiors and so
more of their hydrogen reserves are available for the core fusion
reactions.

A star's lifetime can be approximated with the following formula:

[image: download (1).png]
A star's lifetime the sun's mass divided by the star's mass raised to the
power 2.5 and then multiplied by 10 billion.    Whereas a star as massive
as Spica will remain on the main sequence for slightly more than 10 million
years, a red dwarf such as Wolf 359 will be on the main sequence for more
than one trillion years.
By placing a main sequence star on the H-R Diagram, we can know its mass
and its main sequence lifetime.

  (We will find this inverse relation between mass and lifetime quite
useful when we determine a star cluster's age.)

Tomorrow, we return to the H-R Diagram to follow the evolutionary track of
the Sun and stars of comparable mass.


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