Alfirk (Beta Cephei)

Alfirk, Beta Cephei (β Cep), is a triple star system located approximately 690 light-years away in the northern constellation Cepheus. With an apparent magnitude of 3.23, it is the third brightest point of light in Cepheus, after Alderamin (Alpha Cephei) and Errai (Gamma Cephei). The primary component in the system serves as the prototype for a class of variable stars known as the Beta Cephei variables.

Star system

Beta Cephei is a triple star composed of a binary pair, Beta Cephei A, and a companion, Beta Cephei B. The two components of the binary star are designated Beta Cephei Aa and Beta Cephei Ab. Beta Cephei Aa, the primary component in the system, is officially known as Alfirk.

Alfirk is a hot blue subgiant star of the spectral type B1 IV. Older sources classify it as a B-type giant. The star has a mass of 7.4 solar masses and a radius 7.22 times that of the Sun. With an effective temperature of around 23,600 K, it is 20,000 times more luminous than the Sun. It spins with a projected rotational velocity of 28 km/s, taking around 51 days to complete a revolution.

Alfirk has an estimated age of only 8.7 million years. Even though it is still a very young star, it is approaching the end of its main sequence lifetime. It has evolved quickly because of its high mass.

The close companion, Beta Cephei Ab, is believed to be a B6-type star with a mass of 5 solar masses. It is classified as a Be star, a fast-spinning B-type main sequence star with a gaseous disk of material expelled as a result of the rapid rotation.

Beta Cephei Aa and Ab have an orbital period of 29616.54 ± 1.36 days (81 years). The system has a semi-major axis of 206.96 ± 0.53 milliarcseconds.

Beta Cephei Ab was first resolved using speckle interferometry with a 200-inch telescope in 1972. It was discovered by a team led by D. Y. Gezari of the Department of Earth and Space Sciences, State University of New York at Stony Brook. The astronomers reported the presence of a companion at a separation of 0.255 ± 0.010 arcseconds and proposed that tidal interaction may contribute to the variation mechanism of Beta Cephei.

The more distant companion, Beta Cephei B, is a white main sequence star with the stellar classification A2 V. With an apparent visual magnitude of 7.8, it is invisible to the unaided eye. The star is separated by 13.6 arcseconds from Alfirk, corresponding to a physical distance of 2,840 astronomical units (AU).

Alfirk serves as the prototype for a class of pulsating variable stars called the Beta Cephei variables. Its brightness varies from magnitude 3.16 to 3.27 with a period of 4.57 hours. The star appears the brightest when it is the smallest and hottest.

Alfirk (Beta Cephei), image credit: ESO/Digitized Sky Survey 2 (CC BY 4.0)

Beta Cephei variables

Beta Cephei variables are stars that show small rapid brightness variations due to pulsations of their surfaces. These pulsations are linked with unusual properties of iron in the stars’ interiors, where temperatures reach 200,000 K. The stars vary in brightness by 0.01 to 0.3 magnitudes with periods of 2.4 to 7.2 hours. The variations are greater – up to 1 magnitude – at ultraviolet wavelengths.

The pulsations of β Cephei variables are driven by the kappa mechanism and p-mode pulsations. The letter kappa (κ) indicates the radiative opacity at any depth of a star’s atmosphere. In β Cep stars, the opacity of iron increases at a depth where the temperatures reach 200,000 K. This results in a buildup of energy, which causes increased pressure that pushes the layer out in a cycle that repeats itself over several hours.

Beta Cephei stars are typically hot blue stars of the spectral type B. They are not to be mistaken for Cepheid variables, a class of pulsating supergiants named after the class prototype Delta Cephei. The pulsations in Beta Cephei variables are driven by iron opacity whereas in Cepheid variables they are caused by the opacity of doubly ionized helium.

Beta Cephei variables are sometimes called Beta Canis Majoris stars, after the brighter Mirzam (Beta Canis Majoris) in the constellation Canis Major.

Other than Mirzam and Alfirk, bright examples of this class include Hadar (Beta Centauri) and Epsilon Centauri in the constellation Centaurus, Spica (Alpha Virginis) in Virgo, Mimosa (Beta Crucis) and Imai (Delta Crucis) in Crux, Shaula (Lambda Scorpii), Alniyat (Sigma Scorpii) and Kappa Scorpii in Scorpius, Uridim (Alpha Lupi) and Delta Lupi in Lupus, Alpha Muscae in Musca, Algenib (Gamma Pegasi) in Pegasus, Epsilon Persei in Perseus, and Theta Ophiuchi in Ophiuchus.

A Hertzsprung–Russell diagram, showing the luminosities and surface temperatures at which many classes of pulsating stars are found. Additional lines indicate where stars are found when they first fuse hydrogen into helium (zero-age main sequence, ZAMS), evolutionary tracks for stars of masses between 1 and 10 times that of the Sun, and the track along which a typical white dwarf of about 60% the Sun’s mass cools. Image credit: Wikimedia Commons/Warrickball (CC BY-SA 4.0)

North Star

Beta Cephei is one of the stars in the far northern sky that take turns as the North Star over the course of Earth’s 25,770-year precession cycle. Beta and Iota Cephei will be twin pole stars around the year 5200 AD, when they take over from the brighter Errai (Gamma Cephei). Errai will replace Polaris (Alpha Ursae Minoris) after the year 3000 AD and appear the closest to the pole around 4200 AD.

Alfirk and Iota Cephei will be replaced as pole stars by Alderamin (Alpha Cephei) around the year 7500 AD. The two stars will not be very accurate markers of true north. Each will come within 5 degrees of the pole. In comparison, Polaris comes within 0.5 degrees and is considerably brighter and easier to spot.

Other stars that take turns as the North Star include Deneb and Fawaris in the constellation Cygnus, Vega in Lyra, Iota Herculis and Tau Herculis in Hercules, Edasich, Thuban and Kappa Draconis in Draco, and Kochab in Ursa Minor.

Facts

Shining at magnitude 3.23, Alfirk is, on average, the 216th brightest star in the night sky. It is usually slightly fainter than its Cepheus neighbour Errai (Gamma Cephei) and Delta Lupi in Lupus. It is about as bright as Yed Posterior (Epsilon Ophiuchi) in Ophiuchus and Eta Serpentis in Serpens, and it just outshines Alpha Pictoris in Pictor, Antinous (Theta Aquilae) in Aquila, Sigma Puppis in Puppis, Pi Hydrae in Hydra, and Brachium (Sigma Librae) in Libra.

In traditional Chinese astronomy, Beta Cephei formed an asterism called 上衛 (Shàng Wèi), Left Wall First Imperial Guard. The asterism was part of the Purple Forbidden Enclosure, which contained constellations near the north celestial pole.

The variation in the radial velocity of Beta Cephei was discovered by American astronomer Edwin Brant Frost in 1902. Frost initially assumed that the star was a spectroscopic binary and that the radial velocity radiations were caused by the star’s orbital motion. By 1906, he found a period of 0.19 days.

Alniyat and Mirzam were discovered to be variables of the same type several years later. The variable radial velocity of Alniyat was first reported by the American astronomer Vesto Slipher in 1904.

The brightness variations of Beta Cephei were first detected by the German astronomer Paul Guthnick in 1913. The light variability had the same period as that determined by Frost.

The variations of Beta Cephei stars were linked with pulsations by R. D. Levee and Otto Struve in 1952 and 1955. Based on spectroscopic studies of Alniyat, both astronomers concluded that the variability was intrinsic to the star and attributed the dominant period to stellar pulsations.

Polish astronomer Wojciech Dziembowski studied the pulsations of β Cephei stars with a focus on the excitation mechanism throughout his career. In the early 1990s, he concluded that these stars lay in the region of the Hertzsprung-Russell diagram where their oscillations could be driven by the kappa mechanism.

Name

The name Alfirk (pronunciation: /ˈælfərk/) is derived from the Arabic al-firqah or al-firq, meaning “the flock (of sheep).” It was historically also spelled Alphirk. It comes from the name Al Kawākib al Firḳ, “the stars of the flock,” which originally referred to Beta Cephei, Alderamin (Alpha Cephei), and Eta Cephei. Kaukaba al-firq was used for Alderamin and Alfirk and kawakib al-firq for Alpha, Beta and Eta Cephei. The name Al Kawākib al Firḳ appeared in Timurid astronomer Ulugh Beg’s star catalogue Zij-i Sultani of 1438-1439.

The International Astronomical Union’s (IAU) Working Group on Star Names (WGSN) approved the name Alfirk for Beta Cephei Aa on August 21, 2016. The name formally applies only to the primary component but has historically been used for the whole star system.

Alfirk was given the Bayer designation Beta Cephei by the German astronomer Johann Bayer in his star atlas Uranometria of 1603. Bayer described the star as being “under the belt at the edge of the side” (“sub cingulo ad finiftrum latus”). To the unaided eye, Beta Cephei appears just as bright as Errai (Gamma Cephei), the second brightest star in Cepheus. It periodically outshines Errai (mag. 3.21) during its pulsation cycle. Alderamin (Alpha Cephei), the constellation’s brightest star, is visibly brighter at magnitude 2.46.

Location

Beta Cephei appears in the far northern sky and is part of the stick house asterism that dominates the constellation Cepheus. Alderamin, the brightest star in Cepheus, lies on the imaginary line extended from Schedar through Caph in Cassiopeia’s W. It forms the base of the house asterism with the supergiant Zeta Cephei. Alfirk appears at the base of the roof, between Alderamin and Errai.

At declination 70° 34′, Alfirk is best seen from the northern hemisphere. It never rises above the horizon for observers south of the latitude 19° S. The star is circumpolar throughout Europe, northern Asia, and North America.

Location of Alfirk (Beta Cephei), image: Stellarium

Constellation

Alfirk is located in the constellation of Cepheus (the King). Cepheus is one of the northernmost constellations in the sky. From the northern hemisphere, it can be seen circling Polaris throughout the year. Like the nearby Cassiopeia, Draco, Ursa Minor and Camelopardalis, it was one of ancient Greek constellations catalogued by the Greco-Roman astronomer Claudius Ptolemy in his Almagest in the 2nd century CE. In Greek mythology, the constellation is associated with King Cepheus of Aethiopia, father of Andromeda and husband of Cassiopeia.

Cepheus is the 27th largest constellation in the sky, occupying an area of 588 square degrees of the sky in the region of the northern celestial pole. Its brightest star, the fast-spinning Alderamin (Alpha Cephei), shines at magnitude 2.46 from a distance of 49.05 light-years. It is the only star in the constellation brighter than magnitude 3.0.

Other relatively bright stars in Cepheus include the red giant Errai (Gamma Cephei), the K-type supergiant Zeta Cephei, the orange subgiant Eta Cephei, the orange giant Iota Cephei, the Cepheid variable prototype Delta Cephei, the white giant star Theta Cephei, the F-type star Epsilon Cephei, and the variable red supergiant Mu Cephei (Garnet Star).

Cepheus is also home to the blue-white supergiant Nu Cephei, the Mira variables T Cephei and S Cephei, the blue supergiant Lambda Cephei, the red supergiants VV Cephei A, MY Cephei, W Cephei, V419 Cephei, ST Cephei and V354 Cephei, the orange hypergiant RW Cephei, and the binary red dwarf system Kruger 60, one of the closest star systems to the Sun.

Many of the red supergiants in Cepheus are among the largest stars known. Mu Cephei and ST Cephei both have estimated radii over 1,200 times that of the Sun.

Cepheus constellation map by IAU and Sky&Telescope magazine (Roger Sinnott & Rick Fienberg) (CC BY 3.0)

Deep sky objects in Cepheus include the open cluster NGC 188 (the Polarissima Cluster), the Wizard Nebula (NGC 7380), the dark Seahorse Nebula (B150), the Shark Nebula (LDN 1235), the Ghost Nebula (Sh2-136), the Bow-Tie Nebula (NGC 40), the Question Mark Nebula (NGC 7822), the Rosebud Nebula (NGC 7129), the Cave Nebula (Sh2-155), the Flying Bat Nebula (Sh2-129), the Lion Nebula (Sh2-132), and the Fireworks Galaxy (NGC 6946).

The best time of the year to see the stars and deep sky objects in Cepheus is during the month of November, when the constellation appears higher above the horizon in the early evening. The entire constellation can be seen from locations north of the latitude 10° S.

The 10 brightest stars in Cepheus are Alderamin (Alpha Cep, mag. 2.5141), Errai (Gamma Cep, mag. 3.21), Alfirk (Beta Cep, mag. 3.23), Zeta Cephei (mag. 3.35), Eta Cephei (mag. 3.426), Iota Cephei (mag. 3.507), Delta Cephei A (mag. 4.07), Epsilon Cephei (mag. 4.18), Theta Cephei (mag. 4.22), and Garnet Star (Mu Cep, mag. 4.23).

Alfirk – Beta Cephei

Beta Cephei Aa

Beta Cephei Ab

Beta Cephei B