Lightcurve of Algol
The Flammarion Book of Astronomy - G.C. Flammarion (194/1968). P. 48 in: Shrapnel 4 (1989/1991).
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Phenomenological Modeling of the Light Curves of Algol-Type Eclipsing Binary Stars - Ivan L. Andronov
(Submitted on 17 Aug 2012 (v1), last revised 27 Aug 2012 (this version, v2))
We introduce a special class of functions for mathematical modeling of periodic signals of special shape with irregularly spaced arguments. This method was developed for determination of phenomenological characteristics of the light curves, which are necessary for registration in the "General Catalogue of Variable Stars" and other databases. For eclipsing binary stars with smooth light curves - of types EB and EW - it is recommended a trigonometric polynomial of optimal degree in a complete or symmetric form. For eclipsing binary systems with narrow minima (EA-type), statistically optimal is an approximation in a class of non-polynomial spline functions. It is used a combination of the second-order trigonometric polynomial (TP2, what describes effects of "reflection", "ellipsoidality" and "spotness") and localized contributions of minima (parametrized in depth and profile separately for primary and secondary minima). Such an approach is characterized by a statistical accuracy of the smoothing curve, which is up to ~1.5-2 times better than the trigonometric polynomial of statistically optimal degree, and the absence of false "waves" in the light curve associated with the effect of Gibbs. In addition to the minimum width, which can not be determined by a trigonometric polynomial approximation, the method allows to determine with better accuracy its depth, as well as to separate the effects of the eclipse and out-of-eclipse parts. For multi-color observations, improving the accuracy of the smoothing of the curve in each filter will allow to obtain with better accuracy the curves of the color index variations. Effectivity of the proposed method increases with decreasing eclipse depth. The method called NAV ("New Algol Variable"), was applied to eclipsing binary systems VSX J022427.8-104034=USNO-B1.0 0793-0023471 and BM UMa. For VSX0224, an alternative model of "double period" is discussed.
Comments: Astrophysics (accepted), 20 pages, 5 figures
Subjects: Solar and Stellar Astrophysics (astro-ph.SR)
DOI: 10.1007/s10511-012-9259-0
Cite as: arXiv:1208.3655 [astro-ph.SR]
(or arXiv:1208.3655v2 [astro-ph.SR] for this version)
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Beta Persei (Algol) - "...the Gorgon's head, a ghastly sight, deformed and dreadful, and a sight of woe".
- Homer, writing of Algol in the Iliad.
Algol is one of the most popular and well known variable stars in the sky. One of the reasons for this is that it is a star which can be observed with the unaided eye. Another reason is because it has a relatively short period of less than three days. This means a new observer can go outside every night and see a complete cycle of Algol in their first week of observing if the star is visible at night in their location.
Algol is an eclipsing binary star system 93 light-years away as determined by the Hipparcos satellite. The main star is a B8 main-sequence star 3 times as large as our sun and the secondary star is a K2-type subgiant. Together they rotate around each other. As seen from Earth, when one star blocks our view of the other star its overall brightness changes. There is a very faint third star in the system. It is an F1 main-sequence star orbiting the inner pair every 1.86 years.
Algol's variability was discovered in 1667 by the Italian astronomer Geminiano Montanari making it one of the first ever non-nova variable stars discovered. John Goodricke of England is credited with the discovery of Algol's periodicity in 1782-83. It was apparently also independently discovered by a German farmer named Palitzch. At first it was believed that a planet was causing the eclipses. In 1881 astronomers theorized it was actually an eclipsing binary system based on evidence presented by Edward Pickering, the Director of the Harvard College Observatory (HCO). In 1889 this theory was proven through spectrographic analysis by H.C. Vogel at Potsdam.
"The Demon Star"
Human history has not been kind to this star. Homer wrote of Algol in the Iliad: "...the Gorgon's head, a ghastly sight, deformed and dreadful, and a sight of woe". Some common names for Algol are The Demon, the Demon Star, the Blinking Demon, the Ghoul, and the Spectre's Head. Sounds rather more like members of a hard rock goth band than a beautiful astronomical object. The earliest known maligning of this star is from the Arabian name Ri'B al Ohill, the Demon's Head. We also have Al Ghul meaning Mischief-maker. In Hebrew it is called Rosh ha Sitan, Satan's Head, and also Lilith, Adam's legendary demonic first wife (predecessor to Eve) according to Babylonian myth. 17th century maps referred to it as Caput Larvae, a translation of "The Spectre's Head". The Chinese referred to it as Tseih She, the Piled-up Corpses. Even astrologers refer to it as the worst star in the heavens to be involved with. More recently, the name Algol has been given to a violent video game. What does a star have to do to get respect?
"The Algol Paradox"
One way is to excite scientists. Despite its popularity and the attention focused on Algol, it still is not fully understood and has a few surprises for researchers. Recently, "The Algol Paradox" is a term that has been used to describe a discrepancy in our theories of stellar evolution. The primary star should expand first due to its greater mass, yet we find that the secondary is the older star in the Algol system. Many theories abound about how this can be. The most popular is that the secondary star is indeed older than the primary. It is only smaller because it dumped a lot of its mass onto the younger star, making it more massive and subsequently to look beyond it's years.
Lightcurve of Algol
The Flammarion Book of Astronomy - G.C. Flammarion (194/1968). P. 48 in: Shrapnel 4 (1989/1991).
---
Phenomenological Modeling of the Light Curves of Algol-Type Eclipsing Binary Stars - Ivan L. Andronov
(Submitted on 17 Aug 2012 (v1), last revised 27 Aug 2012 (this version, v2))
We introduce a special class of functions for mathematical modeling of periodic signals of special shape with irregularly spaced arguments. This method was developed for determination of phenomenological characteristics of the light curves, which are necessary for registration in the "General Catalogue of Variable Stars" and other databases. For eclipsing binary stars with smooth light curves - of types EB and EW - it is recommended a trigonometric polynomial of optimal degree in a complete or symmetric form. For eclipsing binary systems with narrow minima (EA-type), statistically optimal is an approximation in a class of non-polynomial spline functions. It is used a combination of the second-order trigonometric polynomial (TP2, what describes effects of "reflection", "ellipsoidality" and "spotness") and localized contributions of minima (parametrized in depth and profile separately for primary and secondary minima). Such an approach is characterized by a statistical accuracy of the smoothing curve, which is up to ~1.5-2 times better than the trigonometric polynomial of statistically optimal degree, and the absence of false "waves" in the light curve associated with the effect of Gibbs. In addition to the minimum width, which can not be determined by a trigonometric polynomial approximation, the method allows to determine with better accuracy its depth, as well as to separate the effects of the eclipse and out-of-eclipse parts. For multi-color observations, improving the accuracy of the smoothing of the curve in each filter will allow to obtain with better accuracy the curves of the color index variations. Effectivity of the proposed method increases with decreasing eclipse depth. The method called NAV ("New Algol Variable"), was applied to eclipsing binary systems VSX J022427.8-104034=USNO-B1.0 0793-0023471 and BM UMa. For VSX0224, an alternative model of "double period" is discussed.
Comments: Astrophysics (accepted), 20 pages, 5 figures
Subjects: Solar and Stellar Astrophysics (astro-ph.SR)
DOI: 10.1007/s10511-012-9259-0
Cite as: arXiv:1208.3655 [astro-ph.SR]
(or arXiv:1208.3655v2 [astro-ph.SR] for this version)
---
Beta Persei (Algol) - "...the Gorgon's head, a ghastly sight, deformed and dreadful, and a sight of woe".
- Homer, writing of Algol in the Iliad.
Algol is one of the most popular and well known variable stars in the sky. One of the reasons for this is that it is a star which can be observed with the unaided eye. Another reason is because it has a relatively short period of less than three days. This means a new observer can go outside every night and see a complete cycle of Algol in their first week of observing if the star is visible at night in their location.
Algol is an eclipsing binary star system 93 light-years away as determined by the Hipparcos satellite. The main star is a B8 main-sequence star 3 times as large as our sun and the secondary star is a K2-type subgiant. Together they rotate around each other. As seen from Earth, when one star blocks our view of the other star its overall brightness changes. There is a very faint third star in the system. It is an F1 main-sequence star orbiting the inner pair every 1.86 years.
Algol's variability was discovered in 1667 by the Italian astronomer Geminiano Montanari making it one of the first ever non-nova variable stars discovered. John Goodricke of England is credited with the discovery of Algol's periodicity in 1782-83. It was apparently also independently discovered by a German farmer named Palitzch. At first it was believed that a planet was causing the eclipses. In 1881 astronomers theorized it was actually an eclipsing binary system based on evidence presented by Edward Pickering, the Director of the Harvard College Observatory (HCO). In 1889 this theory was proven through spectrographic analysis by H.C. Vogel at Potsdam.
"The Demon Star"
Human history has not been kind to this star. Homer wrote of Algol in the Iliad: "...the Gorgon's head, a ghastly sight, deformed and dreadful, and a sight of woe". Some common names for Algol are The Demon, the Demon Star, the Blinking Demon, the Ghoul, and the Spectre's Head. Sounds rather more like members of a hard rock goth band than a beautiful astronomical object. The earliest known maligning of this star is from the Arabian name Ri'B al Ohill, the Demon's Head. We also have Al Ghul meaning Mischief-maker. In Hebrew it is called Rosh ha Sitan, Satan's Head, and also Lilith, Adam's legendary demonic first wife (predecessor to Eve) according to Babylonian myth. 17th century maps referred to it as Caput Larvae, a translation of "The Spectre's Head". The Chinese referred to it as Tseih She, the Piled-up Corpses. Even astrologers refer to it as the worst star in the heavens to be involved with. More recently, the name Algol has been given to a violent video game. What does a star have to do to get respect?
"The Algol Paradox"
One way is to excite scientists. Despite its popularity and the attention focused on Algol, it still is not fully understood and has a few surprises for researchers. Recently, "The Algol Paradox" is a term that has been used to describe a discrepancy in our theories of stellar evolution. The primary star should expand first due to its greater mass, yet we find that the secondary is the older star in the Algol system. Many theories abound about how this can be. The most popular is that the secondary star is indeed older than the primary. It is only smaller because it dumped a lot of its mass onto the younger star, making it more massive and subsequently to look beyond it's years.