EUROPA: beware of the bull

Europa, the daughter of the Phoenician king Agenor and Telephassa, was playing with the Tyrian girls by the sea when she spied a beautiful white bull walking across an adjacent pasture.    Though this bull was large and seemed imposing, Europa felt a strange attraction to it.    The bull approached and commanded the affection of all the girls around it.   Europa, at first reluctant to approach the creature, eventually gathered up a collection of spring flowers which she gently hung as a garland around the bull's horns.  The bull repaid this kindness by kissing Europa's hands and face and soon interacted only with her.   Beguiled by this attention, Europa mounted the bull's back and was promptly swept out to sea.   At once, Europa's joy sharpened into horror as she watched the shore recede in the distance.   The bull delivered the terrified young maiden to the island of Crete, where she saw a Satyr dancing to the sea's wind tones.     Deposited upon the beach, Europa resolved to avoid the Satyr, for they were known to be lustful and wrathful beings.    Yet, as soon as Europa stood, the Satyr approached her.  Before Europa could protest, the Satyr vanished, replaced by the form of Zeus.  He told Europa that he had seen her and summoned a bull to convey her to this remote island.     Unlike Callisto, who wisely fled from Zeus at first contact, Europa was said to have yielded to Zeus at once.    They made love under a plane tree: a tree that thereafter became an evergreen, the love of Europa and Zeus having endowed it with the ability to remain fertile even in the coldest seasons.         Zeus showed his love to Europa by giving her three presents:  a spear that always struck its target, a tireless hound Laelaps, and a bronze-man named Talos who patrolled Crete and repelled strangers.  Europa bore Zeus three children:  Minos, Rhadamanthys, and Sarpedon.     The last two children were minor characters.  However, the first, Minos, became the Cretan King whose wife gave birth to the dreaded Minotaur.   

             Anxious to know what happened to his daughter after she was spirited away by the bull, Agenor sent his sons and wife out to search for Europa. Cadmus, the eldest son, sought his sisters through many lands. Finally, he consulted the Delphic Oracle.   He was told to abandon his quest for Europa at once. Instead, Cadmus was instructed to construct a settlement destined to become a city of great prominence.   Through the Sibyl, Apollo told Cadmus to wander through the land until he saw a cow with a half moon on its hindquarters.  He was told to follow the cow until it laid down.  On the spot of its repose Cadmus was to build his settlement.   Cadmus abided by these instructions and in so doing founded the great city of Thebes.

           None of the other siblings ever found Europa.   She eventually married Asterius, king of Crete, who adopted and helped to raise the children she conceived with Zeus.     The bull Zeus used to lure Europa became the constellation Taurus the Bull.   (According to other authorities, Taurus was the Bull who sired the Minotaur onto King Minos' wife, Pasiphae.) 

 

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THE DAILY ASTRONOMER
Wednesday, July 1, 2020

Remote Planetarium 56:   Extrinsic Variable Stars

What precisely is a " variable star?"  This question, like so many others, has both a simple and far more complicated answer.      Simply, a variable star is one that exhibits changes in brightness that are either predictable or occur randomly.  We can further ascribe stellar  variability to either external or internal causes.   Stars whose variability is caused by external factors are described as "extrinsic variables," whereas those whose brightness varies due to internal processes are known as "intrinsic variables."    Today's RP focuses on the first variety.

We recognize two types of extrinsic variables:

• Eclipsing binaries
• Rotating variables

-ECLIPSING BINARIES-

A binary star is one in which two stars are gravitationally bound and in orbit around each other.  More precisely, these stars are in orbit around a common center of gravity, called the barycenter.     Such stars are hardly rare.  More than half of the stars we can see are systems of two or more stars.   Because these stars are so distant, we cannot see the individual components.   Binary stars appear as single stars from our perspective.  The apparent brightness of that star is actually the combined brightness of both components.    

Albireo: a binary star at the southern end of Cygnus the Swan.     Although Albireo appears as a single star when observed with the naked eye, its two stars are resolvable when seen through even smaller telescopes.   Astronomers who separate these stars in their telescopes refer to the practice as "splitting Albireo."

If the orbital plane of a binary star system is aligned with Earth, each component star will periodically move in front of the other from our perspective.  During one of these "transits," one component will be blocked from our view and so the brightness of the star, itself, will appear to diminish.  The diminishment will be greater when the secondary star (the dimmer) moves in front of the primary star.    

The archetype of eclipsing binaries is Algol, the second brightest star in the constellation Perseus.       In this system, the two component stars are separated by 0.05 AU (astronomical units), about 4.7 million miles.    The revolutionary period equals 2.86 days.      [We are ignoring Algol C, a third component of the Algol system that is not a part of the eclipsing binary system.]

The primary eclipse occurs when Algol B, the secondary star, passes in front of the brighter Algol A.    A secondary eclipse occurs when Algol A moves in front of Algol B.   The diagram below shows the light curve of the Algol system during an entire orbit.  

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Reminder:  apparent magnitude measures a celestial body's apparent brightness.   The dimmer the body, the higher the magnitude number.

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At the far left we see the green curve at magnitude 2.2: the apparent magnitude of Algol when we see its two main stars together.  We soon observe the curve "dip" as the secondary star transits the primary over a ten hour period.  During that passage, Algol's brightness first decreases.  It reaches a minimum when Algol B blocks Algol A to its fullest extent.  As Algol B begins to move away from Algol A, the star's brightness increases until the stars are once again both wholly visible.  A secondary eclipse -when A blocks B- decreases the brightness only slightly.

Our study of  variable stars requires examination of light curves

Astronomical almanacs will often include listings of "Algol at minimum" times.   At those times, Algol's brightness is at a minimum.  The following are the next few dates for these minima.  (We did notice include the July 1, 2020 at 7:04 a.m. minimum  as that time will precede today's posting.) 

• 4 July 2020     3:53 a.m.
• 7 July 2020     12:41 a.m.
• 9 July 2020     9:30 p.m.
• 12 July 2020    6:19 p.m. 

One can observe Algol in the pre-dawn eastern sky presently.     Algol, otherwise known as Beta Persei, is marked above.    Only the July 4th minimum will be observable.  We listed the others just for "fun."

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Remember:   the Bayer Nomenclature System assigns Greek letters to stars within a constellation in accordance to their relative brightness. The brightest is marked alpha, the second brightest beta, the third gamma, et cetera.   (Of course, this system has not proven to be the most accurate as its formulation (early 17th century) predated the development of photometers and other devices that can accurately measure stellar brightness.)  Beta Persei is the second brightest star in Perseus

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Astronomers have identified many Algol variables in our sky.    They are generally not as well known because (a) the magnitude range is small (b) the stars are not visible without telescopes or (c) the variability period is quite long.

For example:

Mintaka:   Orion's western belt star   (Delta Orionis)

Mintaka is an 'Algol variable.'  A 'minimum of Mintaka' occurs every 5.7 days.  However, the magnitude range is small:   2.14 at maximum ; 2.26 at minimum.    Hardly noticeable.  We won't bother listing Mintaka at minimum times for July because Orion isn't currently visible.   The constellation will return to the pre-dawn eastern sky by mid August.

-ROTATING VARIABLES-

The second type of extrinsic variable is the "rotating variable."  As the star rotates, its brightness changes.      Quite often, large darker regions along the star's photosphere pass in and out of our sight range.  When the dark spot is in view, the star's brightness is at a minimum.  When the star's brighter regions are aligned with our sightline, the star is at a maximum brightness.  

Ellipsoidal binaries provide another interesting example of rotating variables.  

These binary stars are close enough to induce tidal distortions in each other.  One can think of these shapes -roughly- like footballs.   As the stars revolve around each other while rotating on their axes, we will alternately see the shorter side of the "football" and then the longer side.    When the shorter side comes into view, the star is dimmer than it appears when we see the longer side.   

These variables are considered extrinsic because the brightness variation results from their rotations and not due to any internal process.    

Tomorrow, we'll begin our examination of intrinsic variables which constitute a much larger subset of  variable stars. 

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Skywatching Tip!

See the full moon on July 4

The last quarter moon on July 12

Moon is new on July 20th.

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