Alpha Cassiopeiae

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Schedar, α Cas
Cassiopeia constellation map.svg
Shedar is the α star found at the bottom right of the "W"
Observation data
Epoch J2000      Equinox J2000
Constellation Cassiopeia
Right ascension 00h 40m 30.4405s[1]
Declination +56° 32′ 14.392″[1]
Apparent magnitude (V) 2.240[2]
Characteristics
Spectral type K0IIIa[1]
U−B color index 1.14[3]
B−V color index 1.16[3]
Variable type Suspected
Astrometry
Radial velocity (Rv) −4.31 km/s
Proper motion (μ) RA: 50.36[1] mas/yr
Dec.: −32.17[1] mas/yr
Parallax (π) 14.29 ± 0.15[4] mas
Distance 228 ± 2 ly
(70.0 ± 0.7 pc)
Absolute magnitude (MV) −1.985[2]
Details
Mass 4–5[5] M
Radius 42.1 ± 1.7[6] R
Luminosity 676[7] L
Temperature 4,530[5] K
Metallicity [Fe/H] –0.1[8] dex
Rotational velocity (v sin i) 21[9] km/s
Age 1–2×108[5] years
Other designations
α Cas, 18 Cas, HR 168, BD+55°139, HD 3712, SAO 21609, FK5 21, HIP 3179, GC 792, ADS 561, CCDM J00405+5632
Database references
SIMBAD data

Coordinates: Sky map 00h 40m 30.5s, +56° 32′ 14.5″

Alpha Cassiopeiae (α Cas, α Cassiopeiae ) is a second magnitude star in the constellation Cassiopeia, with the traditional name Schedar, sometimes spelt Shedir. Though listed as the alpha star by Johann Bayer, Schedar's visual brightness closely rivals the beta star in the constellation, Caph. Depending on which passband is used, α Cas may be marginally brighter or dimmer than β Cas. However, recent calculations from the All-Sky catalog indicate that Schedar is the brightest in Cassiopeia, with a visual magnitude of 2.240. With Schedar located farther away from Earth than Caph, at 228 light years versus 54, Schedar is almost 18 times brighter than its rival insofar as intrinsic brightness is concerned.

Visibility[edit]

Cassiopeia in the context of the Milky Way.

With a declination of 56° 32' North, Schedar is principally visible in the northern hemisphere. The star is yet discernible to most observers across the globe reaching as far south as Perth, Australia, Santiago, Chile and other settlements north ± 33° South latitude, albeit just above the horizon. Schedar is located in line-of-sight of the Milky Way galaxy, so there are other notable celestial objects one can view close to this star—the Pacman Nebula, NGC 436 and NGC 457 being a few.

Alpha Cas reaches its zenith above cities like Edinburgh, Copenhagen and Moscow. It is circumpolar throughout Europe, Russia, and as far south as Los Angeles, California on the North American continent as well as other locations around the globe having a latitude greater than ± 33° North. Since Schedar is listed as a second magnitude star (equal to Beta Cas), it is easily observable to the naked eye as long as one's stargazing is not hindered by the light pollution common to most cities.

The best time for your observation is during the late autumn months of the northern hemisphere, when Cassiopeia passes the meridian at midnight, but given its circumpolar nature in many northern localities, it is visible to many of the world's inhabitants throughout the year.

Photometric variations[edit]

Depending on the photometric system used, Schedar's apparent magnitude is marginally brighter or dimmer than Caph, the beta star in the constellation. The Johnson UBV system throughout the latter half of the twentieth century indicated a visual magnitude that ranged from about 2.20 to 2.23, thus making it slightly brighter than Caph with its variable magnitude ranging from 2.25 to 2.31.[1] However recent calculations in the optical V band between 500—600 nanometers (nm) by Floor Van Leeuwen in 2007 produced a new measurement for both stars, 2.4107 for Schedar and 2.3579 for Caph, suggesting that Caph ranks as the brightest in the constellation.[4] The confusion arises because of the use of different passbands.

Angular analysis[edit]

With the advances in optical interferometry in the 1990s, Schedar's angular diameter was measured in 1998 at various wavelengths ranging from 500—850 nm. The result was a limb darkened angular measurement of 5.62 ± 0.06 milliarcseconds (mas),[6] a diameter which equates to roughly 0.393 AU or 42.3R, assuming a parallax of 14.29 mas.[note 1] With the planet Mercury orbiting the Sun at approximately 0.4 AU, Schedar's photosphere extends to roughly half the mercurial orbit.

Properties[edit]

Cassiopeia starfield showing α Cas, the orange giant, in relation to the other stars in the constellation.

Schedar is an orange giant star whose spectral classification in the SIMBAD astronomical database is listed as K0IIIa, a stellar class that is notably cooler than the Sun.[1] However, because the orange giant is nearing the final stages of its evolution, the photosphere has expanded substantially, yielding a bolometric luminosity that is approximately 676L[note 2]

According to Hipparcos, the New Reduction (van Leeuwen, 2007), the estimated distance to the star is about 70 parsecs or 228 light years.[4] Like all giant stars, Schedar rotates slowly with an approximate velocity of 21 km/s—a speed which takes the star approximately 102 days to make one complete revolution on its axis.[9]

Schedar has been sometimes classified as a variable star, but no variability has been detected since the 19th century. Also, three companions to the star have been listed in the Washington Double Star Catalog, but it seems that all of them are just line-of-sight optical components.

Ethnological influences[edit]

Illustration from Gerardus Mercator showing Schedar near the heart of the celestial Queen.[10]

Etymology[edit]

The traditional name, Schedar, was first encountered in the Alfonsine tables of the thirteenth century. The term comes from the Arabic word صدر şadr, meaning "breast", a word which is derived from its relative position in the heart of the mythological queen Cassiopeia.[11] Johannes Hevelius used the name "Schedir" in his writings, although there are additional spellings of this Arabic transliteration such as Shedar, Shadar, Sheder, Seder, Shedis, and Shedir. Ulug Beg named the star "Al Dhāt al Kursiyy" (Arabic ألضة ألكرسي, meaning "the lady in the chair"), which Giovanni Battista Riccioli changed to "Dath Elkarti".[11]

In Chinese, 王良 (Wáng Liáng) refers to the Chinese asterism Wang Liang, a famous charioteer during the Spring and Autumn Period. The stellar pattern consists of α Cassiopeiae, β Cassiopeiae, κ Cassiopeiae, η Cassiopeiae and λ Cassiopeiae.[12] Consequently, α Cassiopeiae itself is known as 王良四 (Wáng Liáng sì, English: the Fourth Star of Wang Liang.)[13]

Legacy[edit]

In 1551, Gerardus Mercator, a Flemish cartographer, produced a celestial globe portraying the 48 traditional Ptolemaic constellations in addition to two others, Coma Berenices and Antinous.[10] On this globe, he represents Cassiopeia as the Queen of Ethiopia, punished for her boasting by being chained to a chair hanging upside-down. Schedar is found near her left breast, reflecting its Arabic etymological origin.

See also[edit]

Notes[edit]

  1. ^ To determine Schedar's average radius in terms of solar units, the calculations begin with the formula for angular diameter as follows:
    \begin{smallmatrix} {\delta} = \frac{d_S}{D_S}\end{smallmatrix}
    where {\delta} equals the angular diameter of Schedar in arcseconds, {d_S} the star's diameter in AU, and {D_S} the Distance from Earth in parsecs. If we know the angular diameter and the Distance, then we can solve for {d_S} as follows:
    \begin{smallmatrix}d_S = \delta \cdot D_S = {0.00562} \cdot 70.0 = 0.393 AU\end{smallmatrix}
    To obtain Schedar's radius:
    \begin{smallmatrix}R_S = {\left ( {\frac {d_S}{2}} \right )} = {\left ( {\frac {0.393}{2}} \right )} = 0.197 AU\end{smallmatrix}
    To convert 0.197 AU into Solar units, the math is straightforward. Since 1 AU = 149,597,871 km and the mean diameter of the Sun = 1,392,000 km (hence a mean radius of 696,000 km), the calculation is as follows:
    \begin{smallmatrix}d_S = {\left ( 0.197 AU \right )} {\left ( {\frac {149,597,871 km}{696,000 km}} \right )} = 42.31 R_{\odot} (rounded)\end{smallmatrix}.
  2. ^ The formula for Schedar's bolometric luminosity is as follows:
    \begin{smallmatrix}\frac{L_{\rm S}}{L_{\odot}} = {\left ( \frac{R_{\rm S}}{R_{\odot}} \right )}^2 {\left ( \frac{T_{\rm S}}{T_{\odot}} \right )}^4\end{smallmatrix} where... S = Schedar, L = Luminosity, R = Radius and T = Temperature.
    Therefore:
    \begin{smallmatrix}\frac{L_{\rm S}}{L_{\odot}} = {\left ( {\frac{42.3}{1}} \right )}^2 {\left ( {\frac{4,530}{5,778}} \right )}^4 = 676 L_{\odot}\end{smallmatrix}
    Note: Luminosity calculations are highly dependent on angular diameter and distance variables.

References[edit]

  1. ^ a b c d e f g "SIMBAD query result: SCHEDAR -- Star". Centre de Données astronomiques de Strasbourg. Retrieved 2010-02-22. 
  2. ^ a b Kharchenko, N. V.; Roeser, S. (September 2009). "All-sky Compiled Catalogue of 2.5 million stars". VizieR (Centre de Données astronomiques de Strasbourg). Bibcode:2009yCat.1280....0K. Retrieved 2011-01-06. "The absolute magnitude is computed using the Kharcheko apparent magnitude of 2.240 and the Van Leeuwen parallax of 14.29" 
  3. ^ a b Mermilliod, J.-C. (1986). "Compilation of Eggen's UBV data, transformed to UBV (unpublished)". Catalogue of Eggen's UBV data. Bibcode:1986EgUBV........0M. 
  4. ^ a b c van Leeuwen, F (November 2007). "Hipparcos, the New Reduction". Astronomy and Astrophysics (Centre de Données astronomiques de Strasbourg) 474 (2): 653–664. arXiv:0708.1752. Bibcode:2007A&A...474..653V. doi:10.1051/0004-6361:20078357. Retrieved 2010-12-31. 
  5. ^ a b c Professor James B. (Jim) Kaler. "SHEDAR (Alpha Cassiopeiae)". University of Illinois. Archived from the original on 27 March 2010. Retrieved 2010-02-22. 
  6. ^ a b Hajian, Arsen R.; Armstrong, J. T.; Hummel, C. A.; Benson, J. A.;, et al (March 1998). "Direct Confirmation of Stellar Limb Darkening with the Navy Prototype Optical Interferometer" (PDF). The Astrophysical Journal 496 (1): 484. Bibcode:1998ApJ...496..484H. doi:10.1086/305388. Retrieved 2010-02-22. 
  7. ^ See Notes section for calculations
  8. ^ Soubiran, C.; Bienaymé, O.; Mishenina, T. V.; Kovtyukh, V. V. (2008). "Vertical distribution of Galactic disk stars. IV. AMR and AVR from clump giants" (PDF). Astronomy and Astrophysics 480 (1): 91–101. arXiv:0712.1370. Bibcode:2008A&A...480...91S. doi:10.1051/0004-6361:20078788. Retrieved 2010-12-31. 
  9. ^ a b "Bright Star Catalogue, 5th Revised Ed. (Hoffleit+, 1991)". VizieR. Centre de Données astronomiques de Strasbourg. Retrieved 2010-12-31. 
  10. ^ a b Gerard Mercator (1512-1594). "Cassiopeia — The Queen". The Mercator Globes at Harvard Map Collection. Retrieved 2011-01-02. 
  11. ^ a b Richard Hinckley Allen (1963). "Star Names: Their Lore and Meaning". Dover Publications. p. 142. Retrieved 2010-12-31. 
  12. ^ (Chinese) 中國星座神話, written by 陳久金. Published by 台灣書房出版有限公司, 2005, ISBN 978-986-7332-25-7.
  13. ^ (Chinese) 香港太空館 - 研究資源 - 亮星中英對照表, Hong Kong Space Museum. Accessed on line November 23, 2010.

External links[edit]