# Mu Cephei

Mu Cephei (Latinized from μ Cephei, abbreviated Mu Cep or μ Cep), also known as the Garnet Star, is a red supergiant star in the constellation Cepheus. It appears garnet red and is located at the edge of the IC 1396 nebula. It is a 4th magnitude star easily visible to the naked eye under good observing conditions. Since 1943, the spectrum of this star has served as a spectral standard by which other stars are classified.
Mu Cephei is more than 100,000 times brighter than the Sun, with an absolute visual magnitude of −7.6. It is also one of the largest known stars with a radius around or over 1,000 times that of the sun (R$_☉$), and were it placed in the Sun's position it would engulf the orbit of Mars and Jupiter.

## History

The deep red color of Mu Cephei was noted by William Herschel, who described it as "a very fine deep garnet colour, such as the periodical star ο Ceti". It is thus commonly known as Herschel's "Garnet Star". Mu Cephei was called Garnet sidus by Giuseppe Piazzi in his catalogue. An alternative name, Erakis, used in Antonín Bečvář's star catalogue, is probably due to confusion with Mu Draconis, which was previously called ‹See RfD› al-Rāqis in Arabic. The IAU Working Group on Star Names approved the name Garnet Star for Mu Cephei on 19 September 2024 and it is now so entered in the IAU Catalog of Star Names.
In 1848, English astronomer John Russell Hind discovered that Mu Cephei was variable. This variability was quickly confirmed by German astronomer Friedrich Wilhelm Argelander. Almost continual records of the star's variability have been maintained since 1881.
The angular diameter of μ Cephei has been measured interferometrically. One of the most recent measurements gives a diameter of 18.672±0.435 mas at 800 μm, modelled as a limb-darkened disk 20.584±0.480 mas across. However, this later turned out to be the surrounding molecular layer and not the actual star, as the star has an angular diameter of 14.11 ± 0.6 mas. μ Cephei was used as one of the original "dagger stars", those with well-defined spectra that could be used for the classification of other stars, for MK spectral classifications. In 1943 it was the standard star for M2 Ia, updated in 1980 to be the standard star for the new type M2- Ia.

## Distance

The distance to Mu Cephei is not very well known. The Hipparcos satellite was used to measure a parallax of 0.55±0.20 mas, which corresponds to an estimated distance of 1,800 parsecs. However, this value is close to the margin of error. A determination of the distance based upon a size comparison with Betelgeuse gives an estimate of 390±140 parsecs.
Calculation of the distance from the measured angular diameter, surface brightness, and calculated luminosity leads to 641 pc. Averaging the distances of nearby luminous stars with similar reddening and reliable Gaia Data Release 2 parallaxes gives a distance of 940 pc.

## Surroundings

Mu Cephei is surrounded by a shell extending out to a distance at least equal to 0.33 times the star's radius with a temperature of 2,055±25 K. This outer shell appears to contain molecular gases such as CO, H$_2$O, and SiO. Infrared observations suggest the presence of a wide ring of dust and water with an inner radius about twice that of the star itself, extending to about four times the radius of the star.
The star is surrounded by a spherical shell of ejected material that extends outward to an angular distance of 6″ with an expansion velocity of 10 km s$^{−1}$. This indicates an age of about 2,000–3,000 years for the shell. Closer to the star, this material shows a pronounced asymmetry, which may be shaped as a torus.

## Variability

Mu Cephei is a variable star and the prototype of the obsolete class of the Mu Cephei variables. It is now considered to be a semiregular variable of type SRc. Its apparent brightness varies erratically between magnitude 3.4 and 5.1. Many different periods have been reported, but they are consistently near 860 days or 4,400 days.

## Properties

A very luminous red supergiant, Mu Cephei is among the largest stars visible to the naked eye, and one of the largest known cool supergiants. It is a runaway star with a peculiar velocity of 80.7±17.7 km/s, and has been described as a hypergiant.
The bolometric luminosity, summed over all wavelengths, is calculated from integrating the spectral energy distribution (SED) to be 269,000 L$_☉$, making μ Cephei one of the most luminous red supergiants in the Milky Way. Its effective temperature of 3,750 K, determined from colour index relations, implies a radius of 1,259 R$_☉$. Other recent publications give similar effective temperatures. Calculation of the luminosity from a visual and infrared colour relation give 340,000 L$_☉$ and a corresponding radius of 1,420 R$_☉$. An estimate made based on its angular diameter and an assumed distance of 2,400 light years gives it a radius of 1,650 R$_☉$, however the angular diameter used later turned out to be the diameter of the molecular layer around the star.
The radius has been estimated to be 830 R$_☉$ in 2010 based on the star's effective temperature of 3660 K and the 111,200 L$_☉$ luminosity estimate.
A 2019 paper measurement based on the 641+148 −144 pc distance gives the star a lower luminosity below 140,000 L$_☉$ and a correspondingly lower radius of 972±228 R$_☉$, and as well as a lower temperature of 3,551±136 K. These parameters are all consistent with those estimated for Betelgeuse.
The initial mass of Mu Cephei has been estimated from its position relative to theoretical stellar evolutionary tracks to be between 15 M$_☉$ and 25 M$_☉$. The star currently has a mass loss rate of (4.9±1.0)×10$^{−7}$ M$_☉$ per year.

## Supernova

Mu Cephei is nearing death. It has begun to fuse helium into carbon, whereas a main sequence star fuses hydrogen into helium. When a supergiant star has converted elements in its core to iron, the core collapses to produce a supernova and the star is destroyed, leaving behind a vast gaseous cloud and a small, dense remnant. For a star as massive as Mu Cephei the remnant is likely to be a black hole. The most massive red supergiants will evolve back to blue supergiants, Luminous blue variables, or Wolf-Rayet stars before their cores collapse, and Mu Cephei appears to be massive enough for this to happen. A post-red supergiant will produce a type IIn or type II-b supernova, while a Wolf Rayet star will produce a type Ib or Ic supernova.

## Components

There are several faint stars within two arc-minutes of Mu Cephei, and listed in multiple star catalogues.
| NAME | Right ascension | Declination | Apparent magnitude (V) | Database references |
| μ Cep B (CCDM J21435+5847B) | 21$^h$ 43$^m$ 27.8$^s$ | +58° 46′ 45″ | 12.3 | |
| μ Cep C (CCDM J21435+5847C) | 21$^h$ 43$^m$ 25.6$^s$ | +58° 47′ 08″ | 12.7 | Simbad |