# VV Cephei

VV Cephei, also known as HD 208816, is an eclipsing binary star system located in the constellation Cepheus. It is both a B[e] star and shell star. As a 5th magnitude star, it is visible to the naked eye under good observing conditions.
VV Cephei is an eclipsing binary with the third longest known period. A red supergiant fills its Roche lobe when closest to a companion blue star, the latter appearing to be on the main sequence. Matter flows from the red supergiant onto the blue companion for at least part of the orbit and the hot star is obscured by a large disk of material. The supergiant primary, known as VV Cephei A, is currently recognised as one of the largest stars in the galaxy although its size is not certain. Estimates range from 660 R$_☉$ to over 1,000 R$_☉$.

## Variability

The fact that VV Cephei is an eclipsing binary system was discovered by American astronomer Dean McLaughlin in 1936. VV Cephei experiences both primary and secondary eclipses during a 20.3 year orbit. The primary eclipses totally obscure the hot secondary star and last for nearly 18 months. Secondary eclipses are so shallow that they have not been detected photometrically since the secondary obscures such a small proportion of the large cool primary star. The timing and duration of the eclipses is variable, although the exact onset is difficult to measure because it is gradual. Only ε Aurigae (period = 27.08 years), and AS Leonis Minoris (period = 69.1 years) have longer periods.
VV Cephei also shows semiregular variations of a few tenths of a magnitude. Visual and infrared variations appear unrelated to variations at ultraviolet wavelengths. A period of 58 days has been reported in UV, while the dominant period for longer wavelengths is 118.5 days. The short wavelength variations are thought to be caused by the disc around the hot secondary, while pulsation of the red supergiant primary caused the other variations. It has been predicted that the disc surrounding the secondary would produce such brightness variability.

## Spectrum

The spectrum of VV Cep can be resolved into two main components, originating from a cool supergiant and a hot small star surrounded by a disk. The material surrounding the hot secondary produces emission lines, including [Fe$_{II}$] forbidden lines, the B[e] phenomenon known from other stars surrounded by circumstellar disks. The hydrogen emission lines are double-peaked, caused by a narrow central absorption component. This is caused by seeing the disk almost edge on where it intercepts continuum radiation from the star. This is characteristic of shell stars.
Forbidden lines, mainly of Fe$_{II}$ but also of Cu$_{II}$ and Ni$_{II}$, are mostly constant in radial velocity and during eclipses, so they are thought to originate in distant circumbinary material.
The spectrum varies dramatically during the primary eclipses, particularly at the ultraviolet wavelengths produced most strongly by the hot companion and its disc. The typical B spectrum with some emission is replaced by a spectrum dominated by thousands of emission lines as portions of the disc are seen with the continuum from the star blocked. During ingress and egress, the emission line profiles change as one side or the other of the disc close to the star becomes visible while the other is still eclipsed. The colour of the system as a whole is also changed during eclipse, with much of the blue light from the companion blocked.
Out of eclipses, certain spectral lines vary strongly and erratically in both strength and shape, as well as the continuum. Rapid random variations in the short wavelength (i.e. hot) continuum appear to arise from the disc around the B component. Shell absorption lines show variable radial velocities, possibly due to variations in accretion from the disk. Emission from Fe$_{II}$ and Mg$_{II}$ strengthens around periastron or secondary eclipses, which occur at about the same time, but the emission lines also vary randomly throughout the orbit.
In the optical spectrum, the H$_α$ is the only clear emission feature. Its strength varies randomly and rapidly out of eclipse, but it becomes much weaker and relatively constant during the primary eclipses.

## Distance

The distance to VV Cephei is uncertain. The Hipparcos and Gaia Data Release 2 parallax measurements imply distances of 0.752 and 0.6 kiloparsecs respectively, while an analysis by Bailer-Jones et al. using the Gaia Data Release 3 parallax provide a photogeometric distance of 1.02 kpc. These parallaxes are subject to inaccuracies, as changness in VV Cephei A's brightness can cause a measurable astrometric shift and therefore affect the parallax measurement. Another study give a higher distance of 1.5±0.4 kpc based on comparisons of linear and angular orbits. An older analysis from 1977 applied the Barnes-Evans relation to give a distance of 1.28 kpc.

## Properties
### Mass

It should be possible to calculate the masses of eclipsing binary stars with some accuracy, but in this case mass loss, changes in the orbital parameters, a disk obscuring the hot secondary, and doubt about the distance of the system have led to wildly varying estimates. The traditional model, from the spectroscopically derived orbit, has the masses of both stars around 20 M$_☉$, which is typical for a luminous red supergiant and an early B main sequence star. However, another model has been proposed based on the unexpected timing of the 1997 eclipse. Assuming that the change is due to mass transfer altering the orbit, dramatically lower mass values are required. In this model, the primary is a 2.5 M$_☉$ AGB star and the secondary is an 8 M$_☉$ B star. The spectroscopic radial velocities showing the secondary with equal mass to the primary is explained as being of a portion of the disc rather than the star itself.

### Radius

Radius estimates of VV Cephei vary widely. Early estimates of the radius of the primary range from 1,200 to 1,600 solar radii, with an upper limit of 1,900 R$_☉$. The roche lobe is calculated to be about 1,800 R$_☉$, thus the radius cannot be larger than this. Infrared and near-infrared photometry, together with the spectral energy distribution of an M2 supergiant give an angular diameter of 6.38 milliarcseconds. This give a physical radius of either 694 R$_☉$ or 1,050 R$_☉$, adopting distances of 1,018 and 1,500 parsecs respectively. The angular diameter has later been measured in 2021 at 7.251 mas, giving a radius of 779 R$_☉$ at the adopted Gaia DR3 distance of 1 kpc. However, this measurement might have been affected by the binarity of VV Cephei. A 2024 study give a radius of 660 R$_☉$ adopting the Gaia DR3 distance.
The size of the secondary is even more uncertain, since it is physically and photometrically obscured by a much larger disc several hundred R$_☉$ across. The secondary is certainly much smaller than either the primary or the disc, and has been calculated at 13 R$_☉$ to 25 R$_☉$ from the orbital solution.

### Effective temperature

The temperature of the VV Cephei stars is again uncertain, partly because there simply isn't a single temperature that can be assigned to a significantly non-spherical diffuse star orbiting a hot companion. The effective temperature generally quoted for stars is the temperature of a spherical blackbody that approximates the electromagnetic radiation output of the actual star, accounting for emission and absorption in the spectrum. VV Cephei A is fairly clearly identified as an M2 supergiant, and as such, it is given a temperature around 3,800 K. The secondary star is heavily obscured by a disk of material from the primary, and its spectrum is almost undetectable against the disc emission. Detection of some ultraviolet absorption lines narrow down the spectral type to early B and it is apparently a main-sequence star, but likely to be abnormal in several respects due to mass transfer from the supergiant.
VV Cephei A has some emission lines, but these are produced from the accretion disc around the hot secondary.