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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
207-780-4249   www.usm.maine.edu/planet
70 Falmouth Street   Portland, Maine 04103
43.6667° N                   70.2667° W 
Altitude:  10 feet below sea level
Founded January 1970
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.

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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.        

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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:


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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:

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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.  

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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:

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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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