INTRODUCTION
CARACTERISCTICS
MYTHOLOGY
HOW TO FIND THE DISTANCE TO A CEPHEID?
WHAT IS A PULSATIVE VARIABLE STAR?
THE PERIOD-LUMINOSITY RELATIONSHIP (1912)
THE BAADE-WESSELINK METHOD
BIBLIOGRAPHY

INTRODUCTION

Cepheus and his variable star Delta

Delta Cepheus is in the small circumpolar constellation of Cepheus, constellation looking like a roofed house or a pointing hat. With Andromeda, Perseus, Cassiopeia , Pegasus they are in the same area in the sky, near the pole star. Cepheus' stars are less brighter than those of Cassiopeia or Perseus.
Delta Cepheus is a variable yellow supergiant star. It is a binary star but its companion (of seventh magnitude ) is separated by a good 41 seconds of arc. Delta Cepheus belongs to Cepheids of population I (one of the 2 types of Cepheids), variable stars, with a very steady period exceding one day and rich in metals.Its variations in brightness were first discovered, in 1784, by John Goodricke, an english amateur astronomer.
These stars are now called Cepheids after the first star of this type (delta Cepheus) to be discovered.
Most of the Cepheids variables are used as primary distance markers.



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DELTA CEPHEUS' CARACTERISTICS

Delta Cepheus is in the classical cepheids group

Apparent magnitude from 3,6 to 4,3
Average apparent magnitude 4
Distance from Earth About 1000 light years
Period 5,3663days or 5d 8h 47min 31s
Luminosity from 1400 to 3100 solar lum
Radius 30 solar rad
Surface temperature 6150K
Mass 9 solar mass
Spectral type F8 Ib




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MYTHOLOGY

Cepheus comes from the greek word :Kefeus. Cepheus looked by the ancient greeks


Andromeda was the daughter of Cassiopeia and Cepheus, king of Ethiopia. Cassiopeia boasted that she and her daughter were more beautiful than any of Poseidon's many nymphs, including the Nereid sea-maidens. The God of the Seas punished the vain mother by sending a monster, the Cetus, to ravage the entire coast of Cassiopeia's homeland. Andromeda was chained , naked, to a rock by the seashore, to be sacrificed to the dreadful sea monster. Whilst awaiting her death, she was rescued by Perseus.
Perseus was passing by, on his winged horse, Pegasus, after slaying the Gorgon Medusa which was so ugly that it turned everything that looked at it to stone. Perseus attracted by Andromeda's beauty decided to release Andromeda , but only if he could marry her afterwards. Cassiopeia and Cepheus had no other choicebut to give their consent..
Perseus showed the head of Medusa to the monster , bewildering and turning it to stone.
He married the princess and the two went on to live a long and happy life together, on the island of Seriphos.
When Cepheus and Cassiopeia died, Poseidon placed them both in the heavens. Now , all five of them, along with Andromeda , Perseus and Pegasus, are immortilized in the sky for ever.

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HOW TO FIND THE DISTANCE TO A CEPHEID?

Henrietta Leavitt
· Henrietta Leavitt (1868-1921) was the daughter of a americanCongregational Minister. After graduating from Radcliffe College, (former Society for Collegiate Instruction for Women), in 1892, she discovered astronomy.In 1895, after several years of illness, she settled for a volunteer Research Assistant position at the Harvard College Observatory. Being a woman, she had no chance to do theorical work. Director Charles Pickering (then the world's expert in photographic photometry) assigned Leavitt the tedious task of cataloguing variable stars.
She became head of this department and found ,from photographs of the Magellanic Clouds, 1 777 new variable stars including 20 Cepheids. These stars change from bright to dim to bright again fairly regularly. Leavitt discovered that brighter Cepheids stars have longer periods of variability.Leavitt supposed all the stars in the Magellanic Clouds were at the distance from Earth.
She realized that the Cepheids' periods must depend on their "absolute" luminosity not on their "apparent" luminosity. Then she wrote the Cepheid period-luminosity relationship, which allows astronomers to measure the distance between Earth and any Cepheid star , inside and outside the Milky Way. Pickering did not allow her to follow up her topics of study.
Called "the most brilliant woman at Harvard", she died of cancer in her 50s, without having been nominated for the Nobel Prize she deserved.

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WHAT IS A PULSATIVE VARIABLE STAR? Properties of a variable star

In a pulsative variable, the variations in luminosity are due to expansion and contraction of the outer layers. These star have used up their main supply of hydrogen and begin to pulsate.By Doppler effect, the outer layer velocity can be measured (usually in the range of 40~200~km/s). These pulsations produce variations in luminosity (and magnitude), radius, temperature and density.



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THE PERIOD-LUMINOSITY RELATIONSHIP (1912)

The first relation found by Leavitt was (from Small Magellanic clouds' cepheids):
L(apparent) = 3.E-8. P where L is the average apparent luminosity in Sirius.
P is the period of variability in days.
Then, she proposed L(absolute ) = C P , supposing all the Cepheids were at the same distance.
The problem was to "calibrate" this relationship, in other words, to find the C constant.
In 1913, Ejnar Hertzsprung succeeded in the determination of the distance of some Cepheids in our galaxy. Then he found C= 400, with L in solar luminosity and P in days. These calculations were refined in 1918 by the American Shapley and in the 50's by the German Baade.


If we know P (by observing the cycles of variability), we can know L (absolute luminosity).
L' (apparent luminosity) was obtained by photographs , now by CCD cameras.
L (abs Lum) is defined for a distance d = 10pc.Using the Pogson relationship, it is easy to convert L (luminosity) into M (magnitude), hence 2 new relationships:

M= a log P + b
and
m-M = 5logD -5

m: apparent magnitude
M: absolute magnitude
D : distance Cépheid-Earth in pc ( 1 parsec= 3,26ly)
a and b are constants.

The Hertzprung's relationship (used for classical Cepheids) must be modified in the case of other type's Cepheids (RR Lyrae and W Virgo).

The magnitude variations as a function of time is called the light curve of a star. See under, the light curve of delta Cepheus, allowing the determination of magnitudes and periods.


Hubble himself, in 1924, used this method to give an estimation of the dimensions of our galaxy.
In 1997, Hipparcos satellite could measure the distances of close Cepheids or these distances had already been measured by Herzsprung (1913) Shapley (1918) and Baade (1950).Hipparcos used the trigonometric parallax method and found from 10% to 15% longer distances.
Now , astronomers think that even for the nearest Cepheids, a precision of 10% from trigonometric parallax is probably optimistic.

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THE BAADE-WESSELINK METHOD

This method is based on the variations (in function of time) of the radius R and of the effective temperature T. The source luminosity is a function of R and T (Stefan law) and absolute bolometric magnitude Mbol (including all the wavelengths) also is function of R and T.
By Doppler effect, one can determine the velocity of the stellar surface during its pulsations, hence compute the variation of the star's radius DR.
Mbol and T are estimated from the 2 types of spectrum.
Finally, one can determine L and the distance D but this method is rather complicated. Nevertheless it was applied for the expansion of the circumstellar ring around SN 1987 A.

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WEBOGRAPHY

http://www.astrosurf.com/sar/apex/const/const_cep.html
http://www3.sympatico.ca/edugas/constellations/cephee.htm
http://fr.encyclopedia.yahoo.com/articles/c/c0002783_p0.html
http://www.mgroleau.ca/~manuel/constellations/cep.html
http://mesetoiles.free.fr/cephee.htm
http://perso.wanadoo.fr/noirmain/var.htm
http://savar.astronomie.ch/volume5/page6/const20.html
http://perso.club-internet.fr/gibouin/constellation/cephee.htm
http://home.tiscali.be/jeanmarie.heirebrant/c.htm
http://webast.ast.obs-mip.fr/users/koechlin/Francais.html
http://www.obspm.fr/actual/nouvelle/dec01/kervella.fr.shtml

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