Near and far field

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Near_and_far_field

Differences between Fraunhofer diffraction and Fresnel diffraction

The near field and far field are regions of the electromagnetic (EM) field around an object, such as a transmitting antenna, or the result of radiation scattering off an object. Non-radiative near-field behaviors dominate close to the antenna or scattering object, while electromagnetic radiation far-field behaviors dominate at greater distances.

Far-field E (electric) and B (magnetic) field strength decreases as the distance from the source increases, resulting in an inverse-square law for the radiated power intensity of electromagnetic radiation. By contrast, near-field E and B strength decrease more rapidly with distance: the radiative field decreases by the inverse-distance squared, the reactive field by an inverse-cube law, resulting in a diminished power in the parts of the electric field by an inverse fourth-power and sixth-power, respectively. The rapid drop in power contained in the near-field ensures that effects due to the near-field essentially vanish a few wavelengths away from the radiating part of the antenna.

Summary of regions and their interactions

Near field: This dipole pattern shows a magnetic field ${\displaystyle \overrightarrow{\mathbf{B}}}$ in red. The potential energy momentarily stored in this magnetic field is indicative of the reactive near field.

Far field: The radiation pattern can extend into the far field, where the reactive stored energy has no significant presence.

In a normally-operating antenna, positive and negative charges have no way of leaving the metal surface, and are separated from each other by the excitation "signal" voltage (a transmitter or other EM exciting potential). This generates an oscillating (or reversing) electrical dipole, which affects both the near field and the far field.

The boundary between the near field and far field regions is only vaguely defined, and it depends on the dominant wavelength (λ) emitted by the source and the size of the radiating element.

Near field

The near field refers to places nearby the antenna conductors, or inside any polarizable media surrounding it, where the generation and emission of electromagnetic waves can be interfered with while the field lines remain electrically attached to the antenna, hence absorption of radiation in the near field by adjacent conducting objects detectably affects the loading on the signal generator (the transmitter). The electric and magnetic fields can exist independently of each other in the near field, and one type of field can be disproportionately larger than the other, in different subregions.

An easy-to-observe example of a near-field effect is the change of noise levels picked up by a set of rabbit ear TV antennas when a human body part is moved in close to the "ears". Likewise the change in sound quality of an FM radio tuned to a distant station when a person walks about in the area within an arm's length of its antenna.

The near field is governed by multipole type fields, which can be considered as collections of dipoles with a fixed phase relationship. The general purpose of conventional antennas is to communicate wirelessly over long distances, well into their far fields, and for calculations of radiation and reception for many simple antennas, most of the complicated effects in the near field can be conveniently ignored.

Reactive near field

The interaction with the medium (e.g. body capacitance) can cause energy to deflect back to the source feeding the antenna, as occurs in the reactive near field. This zone is roughly within 1/6 of a wavelength of the nearest antenna surface.

The near field has been of increasing interest, particularly in the development of capacitive sensing technologies such as those used in the touchscreens of smart phones and tablet computers. Although the far field is the usual region of antenna function, certain devices that are called antennas but are specialized for near-field communication do exist. Magnetic induction as seen in a transformer can be seen as a very simple example of this type of near-field electromagnetic interaction. For example send / receive coils for RFID, and emission coils for wireless charging and inductive heating; however their technical classification as "antennas" is contentious.

Radiative near field

The interaction with the medium can fail to return energy back to the source, but cause a distortion in the electromagnetic wave that deviates significantly from that found in free space, and this indicates the radiative near-field region, which is somewhat further away. Passive reflecting elements can be placed in this zone for the purpose of beam forming, such as the case with the Yagi–Uda antenna. Alternatively, multiple active elements can also be combined to form an antenna array, with lobe shape becoming a factor of element distances and excitation phasing.

Transition zone

Another intermediate region, called the transition zone, is defined on a somewhat different basis, namely antenna geometry and excitation wavelength. It is approximately one wavelength from the antenna, and is where the electric and magnetic parts of the radiated waves first balance out: The electric field of a linear antenna gains its corresponding magnetic field, and the magnetic field of a loop antenna gains its electric field. It can either be considered the furthest part of the near field, or the nearest part of the far field. It is from beyond this point that the electromagnetic wave becomes self-propagating. The electric and magnetic field portions of the wave are proportional to each other at a ratio defined by the characteristic impedance of the medium through which the wave is propagating.

Far field

In contrast, the far field is the region in which the field has settled into "normal" electromagnetic radiation. In this region, it is dominated by transverse electric or magnetic fields with electric dipole characteristics. In the far-field region of an antenna, radiated power decreases as the square of distance, and absorption of the radiation does not feed back to the transmitter.

In the far-field region, each of the electric and magnetic parts of the EM field is "produced by" (or associated with) a change in the other part, and the ratio of electric and magnetic field intensities is simply the wave impedance in the medium.

Also known as the radiation-zone, the far field carries a relatively uniform wave pattern. The radiation zone is important because far fields in general fall off in amplitude by ${\displaystyle \frac{1}{r}.}$ This means that the total energy per unit area at a distance r is proportional to ${\displaystyle \frac{1}{r^2}.}$ The area of the sphere is proportional to ${\displaystyle r^2}$, so the total energy passing through the sphere is constant. This means that the far-field energy actually escapes to infinite distance (it radiates).

Definitions

The separation of the electric and magnetic fields into components is mathematical, rather than clearly physical, and is based on the relative rates at which the amplitude of different terms of the electric and magnetic field equations diminish as distance from the radiating element increases. The amplitudes of the far-field components fall off as ${\displaystyle 1/r}$, the radiative near-field amplitudes fall off as ${\displaystyle 1/r^2}$, and the reactive near-field amplitudes fall off as ${\displaystyle 1/r^3}$. Definitions of the regions attempt to characterize locations where the activity of the associated field components are the strongest. Mathematically, the distinction between field components is very clear, but the demarcation of the spatial field regions is subjective. All of the field components overlap everywhere, so for example, there are always substantial far-field and radiative near-field components in the closest-in near-field reactive region.

The regions defined below categorize field behaviors that are variable, even within the region of interest. Thus, the boundaries for these regions are approximate rules of thumb, as there are no precise cutoffs between them: All behavioral changes with distance are smooth changes. Even when precise boundaries can be defined in some cases, based primarily on antenna type and antenna size, experts may differ in their use of nomenclature to describe the regions. Because of these nuances, special care must be taken when interpreting technical literature that discusses far-field and near-field regions.

The term near-field region (also known as the near field or near zone) has the following meanings with respect to different telecommunications technologies:

• The close-in region of an antenna where the angular field distribution is dependent upon the distance from the antenna.
• In the study of diffraction and antenna design, the near field is that part of the radiated field that is below distances shorter than the Fraunhofer distance, which is given by ${\displaystyle d_{\text{F}}=\frac{2D^2}{\lambda }}$ from the source of the diffracting edge or antenna of longitude or diameter D.
• In optical fiber communications, the region near a source or aperture that is closer than the Rayleigh length. (Presuming a Gaussian beam, which is appropriate for fiber optics.)

Regions according to electromagnetic length

The most convenient practice is to define the size of the regions or zones in terms of fixed numbers (fractions) of wavelengths distant from the center of the radiating part of the antenna, with the clear understanding that the values chosen are only approximate and will be somewhat inappropriate for different antennas in different surroundings. The choice of the cut-off numbers is based on the relative strengths of the field component amplitudes typically seen in ordinary practice.

Electromagnetically short antennas

Field regions for antennas equal to, or shorter than, one-half wavelength of the radiation they emit, such as the whip antenna of a citizen's band radio, or an AM radio broadcast tower.

For antennas shorter than half of the wavelength of the radiation they emit (i.e., electromagnetically "short" antennas), the far and near regional boundaries are measured in terms of a simple ratio of the distance r from the radiating source to the wavelength λ of the radiation. For such an antenna, the near field is the region within a radius r ≪ λ, while the far-field is the region for which r ≫ 2 λ. The transition zone is the region between r = λ and r = 2 λ .

The length of the antenna, D, is not important, and the approximation is the same for all shorter antennas (sometimes idealized as so-called point antennas). In all such antennas, the short length means that charges and currents in each sub-section of the antenna are the same at any given time, since the antenna is too short for the RF transmitter voltage to reverse before its effects on charges and currents are felt over the entire antenna length.

Electromagnetically long antennas

For antennas physically larger than a half-wavelength of the radiation they emit, the near and far fields are defined in terms of the Fraunhofer distance. Named after Joseph von Fraunhofer, the following formula gives the Fraunhofer distance:

$${\displaystyle d_{\text{F}}=\frac{2D^2}{\lambda },}$$

where D is the largest dimension of the radiator (or the diameter of the antenna) and λ is the wavelength of the radio wave. Either of the following two relations are equivalent, emphasizing the size of the region in terms of wavelengths λ or diameters D:

$${\displaystyle d_{\text{F}}=2{\left(\frac{D}{\lambda }\right)}^2\lambda =2\left(\frac{D}{\lambda }\right)D}$$

This distance provides the limit between the near and far field. The parameter D corresponds to the physical length of an antenna, or the diameter of a reflector ("dish") antenna.

Having an antenna electromagnetically longer than one-half the dominated wavelength emitted considerably extends the near-field effects, especially that of focused antennas. Conversely, when a given antenna emits high frequency radiation, it will have a near-field region larger than what would be implied by a lower frequency (i.e. longer wavelength).

Additionally, a far-field region distance d_F must satisfy these two conditions.

$${\displaystyle d_{\text{F}}\gg D}$$

$${\displaystyle d_{\text{F}}\gg \lambda }$$

where D is the largest physical linear dimension of the antenna and d_F is the far-field distance. The far-field distance is the distance from the transmitting antenna to the beginning of the Fraunhofer region, or far field.

Transition zone

The transition zone between these near and far field regions, extending over the distance from one to two wavelengths from the antenna, is the intermediate region in which both near-field and far-field effects are important. In this region, near-field behavior dies out and ceases to be important, leaving far-field effects as dominant interactions. (See the "Far Field" image above.)

Regions according to diffraction behavior

Near- and far-field regions for an antenna larger (diameter or length D) than the wavelength of the radiation it emits, so that D⁄λ ≫ 1. Examples are radar dishes, satellite dish antennas, radio telescopes, and other highly directional antennas.

Far-field diffraction

Main article: Fraunhofer diffraction

As far as acoustic wave sources are concerned, if the source has a maximum overall dimension or aperture width (D) that is large compared to the wavelength λ, the far-field region is commonly taken to exist at distances, when the Fresnel parameter ${\displaystyle S}$ is larger than 1:

$${\displaystyle S=\frac{4\lambda }{D^2}r>1,\text{ for }r>r_{\text{F}}=\frac{D^2}{4\lambda }.}$$

For a beam focused at infinity, the far-field region is sometimes referred to as the Fraunhofer region. Other synonyms are far field, far zone, and radiation field. Any electromagnetic radiation consists of an electric field component E and a magnetic field component H. In the far field, the relationship between the electric field component E and the magnetic component H is that characteristic of any freely propagating wave, where E and H have equal magnitudes at any point in space (where measured in units where c = 1).

Near-field diffraction

Main article: Fresnel diffraction

In contrast to the far field, the diffraction pattern in the near field typically differs significantly from that observed at infinity and varies with distance from the source. In the near field, the relationship between E and H becomes very complex. Also, unlike the far field where electromagnetic waves are usually characterized by a single polarization type (horizontal, vertical, circular, or elliptical), all four polarization types can be present in the near field.

The near field is a region in which there are strong inductive and capacitive effects from the currents and charges in the antenna that cause electromagnetic components that do not behave like far-field radiation. These effects decrease in power far more quickly with distance than do the far-field radiation effects. Non-propagating (or evanescent) fields extinguish very rapidly with distance, which makes their effects almost exclusively felt in the near-field region.

Also, in the part of the near field closest to the antenna (called the reactive near field, see below), absorption of electromagnetic power in the region by a second device has effects that feed back to the transmitter, increasing the load on the transmitter that feeds the antenna by decreasing the antenna impedance that the transmitter "sees". Thus, the transmitter can sense when power is being absorbed in the closest near-field zone (by a second antenna or some other object) and is forced to supply extra power to its antenna, and to draw extra power from its own power supply, whereas if no power is being absorbed there, the transmitter does not have to supply extra power.

Near-field characteristics

Differences between Fraunhofer diffraction and Fresnel diffraction.

The near field itself is further divided into the reactive near field and the radiative near field. The reactive and radiative near-field designations are also a function of wavelength (or distance). However, these boundary regions are a fraction of one wavelength within the near field. The outer boundary of the reactive near-field region is commonly considered to be a distance of $\frac{1}{2\pi }$ times the wavelength (i.e., $\frac{\lambda }{2\pi }$ or approximately 0.159λ) from the antenna surface. The reactive near-field is also called the inductive near-field. The radiative near field (also called the Fresnel region) covers the remainder of the near-field region, from $\frac{\lambda }{2\pi }$ out to the Fraunhofer distance.

Reactive near field, or the nearest part of the near field

In the reactive near field (very close to the antenna), the relationship between the strengths of the E and H fields is often too complicated to easily predict, and difficult to measure. Either field component (E or H) may dominate at one point, and the opposite relationship dominate at a point only a short distance away. This makes finding the true power density in this region problematic. This is because to calculate power, not only E and H both have to be measured but the phase relationship between E and H as well as the angle between the two vectors must also be known in every point of space.

In this reactive region, not only is an electromagnetic wave being radiated outward into far space but there is a reactive component to the electromagnetic field, meaning that the strength, direction, and phase of the electric and magnetic fields around the antenna are sensitive to EM absorption and re-emission in this region, and respond to it. In contrast, absorption far from the antenna has negligible effect on the fields near the antenna, and causes no back-reaction in the transmitter.

Very close to the antenna, in the reactive region, energy of a certain amount, if not absorbed by a receiver, is held back and is stored very near the antenna surface. This energy is carried back and forth from the antenna to the reactive near field by electromagnetic radiation of the type that slowly changes electrostatic and magnetostatic effects. For example, current flowing in the antenna creates a purely magnetic component in the near field, which then collapses as the antenna current begins to reverse, causing transfer of the field's magnetic energy back to electrons in the antenna as the changing magnetic field causes a self-inductive effect on the antenna that generated it. This returns energy to the antenna in a regenerative way, so that it is not lost. A similar process happens as electric charge builds up in one section of the antenna under the pressure of the signal voltage, and causes a local electric field around that section of antenna, due to the antenna's self-capacitance. When the signal reverses so that charge is allowed to flow away from this region again, the built-up electric field assists in pushing electrons back in the new direction of their flow, as with the discharge of any unipolar capacitor. This again transfers energy back to the antenna current.

Because of this energy storage and return effect, if either of the inductive or electrostatic effects in the reactive near field transfer any field energy to electrons in a different (nearby) conductor, then this energy is lost to the primary antenna. When this happens, an extra drain is seen on the transmitter, resulting from the reactive near-field energy that is not returned. This effect shows up as a different impedance in the antenna, as seen by the transmitter.

The reactive component of the near field can give ambiguous or undetermined results when attempting measurements in this region. In other regions, the power density is inversely proportional to the square of the distance from the antenna. In the vicinity very close to the antenna, however, the energy level can rise dramatically with only a small decrease in distance toward the antenna. This energy can adversely affect both humans and measurement equipment because of the high powers involved.

Radiative near field (Fresnel region), or farthest part of the near field

The radiative near field (sometimes called the Fresnel region) does not contain reactive field components from the source antenna, since it is far enough from the antenna that back-coupling of the fields becomes out of phase with the antenna signal, and thus cannot efficiently return inductive or capacitive energy from antenna currents or charges. The energy in the radiative near field is thus all radiant energy, although its mixture of magnetic and electric components are still different from the far field. Further out into the radiative near field (one half wavelength to 1 wavelength from the source), the E and H field relationship is more predictable, but the E to H relationship is still complex. However, since the radiative near field is still part of the near field, there is potential for unanticipated (or adverse) conditions.

For example, metal objects such as steel beams can act as antennas by inductively receiving and then "re-radiating" some of the energy in the radiative near field, forming a new radiating surface to consider. Depending on antenna characteristics and frequencies, such coupling may be far more efficient than simple antenna reception in the yet-more-distant far field, so far more power may be transferred to the secondary "antenna" in this region than would be the case with a more distant antenna. When a secondary radiating antenna surface is thus activated, it then creates its own near-field regions, but the same conditions apply to them.

Compared to the far field

The near field is remarkable for reproducing classical electromagnetic induction and electric charge effects on the EM field, which effects "die-out" with increasing distance from the antenna: The magnetic field component that’s in phase quadrature to electric fields is proportional to the inverse-cube of the distance (${\displaystyle 1/r^3}$) and electric field strength proportional to inverse-square of distance (${\displaystyle 1/r^2}$). This fall-off is far more rapid than the classical radiated far-field (E and B fields, which are proportional to the simple inverse-distance (${\displaystyle 1/r}$). Typically near-field effects are not important farther away than a few wavelengths of the antenna.

More-distant near-field effects also involve energy transfer effects that couple directly to receivers near the antenna, affecting the power output of the transmitter if they do couple, but not otherwise. In a sense, the near field offers energy that is available to a receiver only if the energy is tapped, and this is sensed by the transmitter by means of responding to electromagnetic near fields emanating from the receiver. Again, this is the same principle that applies in induction coupled devices, such as a transformer, which draws more power at the primary circuit, if power is drawn from the secondary circuit. This is different with the far field, which constantly draws the same energy from the transmitter, whether it is immediately received, or not.

The amplitude of other components (non-radiative/non-dipole) of the electromagnetic field close to the antenna may be quite powerful, but, because of more rapid fall-off with distance than ${\displaystyle 1/r}$ behavior, they do not radiate energy to infinite distances. Instead, their energies remain trapped in the region near the antenna, not drawing power from the transmitter unless they excite a receiver in the area close to the antenna. Thus, the near fields only transfer energy to very nearby receivers, and, when they do, the result is felt as an extra power draw in the transmitter. As an example of such an effect, power is transferred across space in a common transformer or metal detector by means of near-field phenomena (in this case inductive coupling), in a strictly short-range effect (i.e., the range within one wavelength of the signal).

Classical EM modelling

A "radiation pattern" for an antenna, by definition showing only the far field.

Solving Maxwell's equations for the electric and magnetic fields for a localized oscillating source, such as an antenna, surrounded by a homogeneous material (typically vacuum or air), yields fields that, far away, decay in proportion to ${\displaystyle 1/r}$ where r is the distance from the source. These are the radiating fields, and the region where r is large enough for these fields to dominate is the far field.

In general, the fields of a source in a homogeneous isotropic medium can be written as a multipole expansion. The terms in this expansion are spherical harmonics (which give the angular dependence) multiplied by spherical Bessel functions (which give the radial dependence). For large r, the spherical Bessel functions decay as ${\displaystyle 1/r}$, giving the radiated field above. As one gets closer and closer to the source (smaller r), approaching the near field, other powers of r become significant.

The next term that becomes significant is proportional to ${\displaystyle 1/r^2}$ and is sometimes called the induction term. It can be thought of as the primarily magnetic energy stored in the field, and returned to the antenna in every half-cycle, through self-induction. For even smaller r, terms proportional to ${\displaystyle 1/r^3}$ become significant; this is sometimes called the electrostatic field term and can be thought of as stemming from the electrical charge in the antenna element.

Very close to the source, the multipole expansion is less useful (too many terms are required for an accurate description of the fields). Rather, in the near field, it is sometimes useful to express the contributions as a sum of radiating fields combined with evanescent fields, where the latter are exponentially decaying with r. And in the source itself, or as soon as one enters a region of inhomogeneous materials, the multipole expansion is no longer valid and the full solution of Maxwell's equations is generally required.

Antennas

If an oscillating electrical current is applied to a conductive structure of some type, electric and magnetic fields will appear in space about that structure. If those fields are lost to a propagating space wave the structure is often termed an antenna. Such an antenna can be an assemblage of conductors in space typical of radio devices or it can be an aperture with a given current distribution radiating into space as is typical of microwave or optical devices. The actual values of the fields in space about the antenna are usually quite complex and can vary with distance from the antenna in various ways.

However, in many practical applications, one is interested only in effects where the distance from the antenna to the observer is very much greater than the largest dimension of the transmitting antenna. The equations describing the fields created about the antenna can be simplified by assuming a large separation and dropping all terms that provide only minor contributions to the final field. These simplified distributions have been termed the "far field" and usually have the property that the angular distribution of energy does not change with distance, although the energy levels still vary with distance and time. Such an angular energy distribution is usually termed an antenna pattern.

Note that, by the principle of reciprocity, the pattern observed when a particular antenna is transmitting is identical to the pattern measured when the same antenna is used for reception. Typically one finds simple relations describing the antenna far-field patterns, often involving trigonometric functions or at worst Fourier or Hankel transform relationships between the antenna current distributions and the observed far-field patterns. While far-field simplifications are very useful in engineering calculations, this does not mean the near-field functions cannot be calculated, especially using modern computer techniques. An examination of how the near fields form about an antenna structure can give great insight into the operations of such devices.

Impedance

The electromagnetic field in the far-field region of an antenna is independent of the details of the near field and the nature of the antenna. The wave impedance is the ratio of the strength of the electric and magnetic fields, which in the far field are in phase with each other. Thus, the far field "impedance of free space" is resistive and is given by:

$${\displaystyle Z_0\stackrel{\underset{\mathrm{d}\mathrm{e}\mathrm{f}}{}}{=}\sqrt{\frac{{\mu }_0}{{\epsilon }_0}}={\mu }_0{c}_0=\frac{1}{{\epsilon }_0{c}_0}.}$$

With the usual approximation for the speed of light in free space c₀ ≈ 2.9979 × 10⁸ m/s, this gives the frequently used expression:

$${\displaystyle Z_0\approx \pi 119.92\mathsf{\Omega }\approx \pi 120\mathsf{\Omega }\approx 377\mathsf{\Omega }}$$

The electromagnetic field in the near-field region of an electrically small coil antenna is predominantly magnetic. For small values of r/ λ  the impedance of a magnetic loop is low and inductive, at short range being asymptotic to:

$${\displaystyle |Z_{\mathsf{W}}|\approx {\pi }^{2}240\mathsf{\Omega }\frac{r}{\lambda }\approx 2370\mathsf{\Omega }\frac{r}{\lambda }.}$$

The electromagnetic field in the near-field region of an electrically short rod antenna is predominantly electric. For small values of r/ λ  the impedance is high and capacitive, at short range being asymptotic to:

$${\displaystyle |Z_{\mathsf{W}}|\approx 60\mathsf{\Omega }\frac{\lambda }{r}.}$$

In both cases, the wave impedance converges on that of free space as the range approaches the far field.

Luminous blue variable

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Luminous_blue_variable

Luminous blue variable AG Carinae as seen by the Hubble Space Telescope

Luminous blue variables (LBVs) are massive evolved stars that show unpredictable and sometimes dramatic variations in their spectra and brightness. They are also known as S Doradus variables after S Doradus, one of the brightest stars of the Large Magellanic Cloud. They are extraordinarily rare, with just 20 objects listed in the General Catalogue of Variable Stars as SDor, and a number of these are no longer considered LBVs.

Discovery and history

P Cygni profile of a spectral line

The LBV stars P Cygni and η Carinae have been known as unusual variables since the 17th century, but their true nature was not fully understood until late in the 20th century.

In 1922 John Charles Duncan published the first three variable stars ever detected in an external galaxy, variables 1, 2, and 3, in the Triangulum Galaxy (M33). These were followed up by Edwin Hubble with three more in 1926: A, B, and C in M33. Then in 1929 Hubble added a list of variables detected in M31. Of these, Var A, Var B, Var C, and Var 2 in M33 and Var 19 in M31 were followed up with a detailed study by Hubble and Allan Sandage in 1953. Var 1 in M33 was excluded as being too faint and Var 3 had already been classified as a Cepheid variable. At the time they were simply described as irregular variables, although remarkable for being the brightest stars in those galaxies. The original Hubble Sandage paper contains a footnote that S Doradus might be the same type of star, but expressed strong reservations, so the link would have to wait several decades to be confirmed.

Later papers referred to these five stars as Hubble–Sandage variables. In the 1970s, Var 83 in M33 and AE Andromedae, AF Andromedae (=Var 19), Var 15, and Var A-1 in M31 were added to the list and described by several authors as "luminous blue variables", although it was not considered a formal name at the time. The spectra were found to contain lines with P Cygni profiles and were compared to η Carinae. In 1978, Roberta M. Humphreys published a study of eight variables in M31 and M33 (excluding Var A) and referred to them as luminous blue variables, as well as making the link to the S Doradus class of variable stars. In 1984 in a presentation at the IAU symposium, Peter Conti formally grouped the S Doradus variables, Hubble–Sandage variables, η Carinae, P Cygni, and other similar stars together under the term "luminous blue variables" and shortened it to LBV. He also clearly separated them from those other luminous blue stars, the Wolf–Rayet stars.

Variable star types are usually named after the first member discovered to be variable, for example δ Sct variables named after the star δ Sct. The first luminous blue variable to be identified as a variable star was P Cygni, and these stars have been referred to as P Cygni type variables. The General Catalogue of Variable Stars decided there was a possibility of confusion with P Cygni profiles, which also occur in other types of stars, and chose the acronym SDOR for "variables of the S Doradus type". The term "S Doradus variable" was used to describe P Cygni, S Doradus, η Carinae, and the Hubble-Sandage variables as a group in 1974.

Physical properties

Upper portion of H-R Diagram showing the location of the S Doradus instability strip and the location of LBV outbursts. Main sequence is the thin sloping line on the lower left.

LBVs are massive unstable supergiant (or hypergiant) stars that show a variety of spectroscopic and photometric variation, most obviously periodic outbursts and occasional much larger eruptions.

In their "quiescent" state they are typically B-type stars, occasionally slightly hotter, with unusual emission lines. They are found in a region of the Hertzsprung–Russell diagram known as the S Doradus instability strip, where the least luminous have a temperature around 10,000 K and a luminosity about 250,000 times that of the Sun, whereas the most luminous have a temperature around 25,000 K and a luminosity over a million times that of the Sun, making them some of the most luminous of all stars.

During a normal outburst the temperature decreases to around 8,500 K for all stars, slightly hotter than the yellow hypergiants. The bolometric luminosity usually remains constant, which means that visual brightness increases somewhat by a magnitude or two. S Doradus typifies this behaviour. A few examples have been found where luminosity appears to change during an outburst, but the properties of these unusual stars are difficult to determine accurately. For example, AG Carinae may decrease in luminosity by around 30% during outbursts; and AFGL 2298 has been observed to dramatically increase its luminosity during an outburst although it is not clear if that should be classified as a modest giant eruption. S Doradus typifies this behaviour, which has been referred to as strong-active cycle, and it is regarded as a key criterion for identifying luminous blue variables. Two distinct periodicities are seen, either variations taking longer than 20 years, or less than 10 years. In some cases, the variations are much smaller, less than half a magnitude, with only small temperature reductions. These are referred to as weak-active cycles and always occur on timescales of less than 10 years.

Some LBVs have been observed to undergo giant eruptions with dramatically increased mass loss and luminosity, so violent that several were initially catalogued as supernovae. The outbursts mean there are usually nebulae around such stars; η Carinae is the best-studied and most luminous known example, but may not be typical. It is generally assumed that all luminous blue variables undergo one or more of these large eruptions, but they have only been observed in two or three well-studied stars and possibly a handful of supernova imposters. The two clear examples in the Milky Way galaxy, P Cygni and η Carinae, and the possible example in the Small Magellanic Cloud, HD 5980A, have not shown strong-cycle variations. It is still possible that the two types of variability occur in different groups of stars. 3-D simulations have shown that these outbursts may be caused by variations in helium opacity.

Many luminous blue variables also show small amplitude variability with periods less than a year, which appears typical of Alpha Cygni variables, and stochastic (i.e. totally random) variations.

Luminous blue variables are by definition more luminous than most stars and also more massive, but within a very wide range. The most luminous are more than a million L_☉ (Eta Carinae reaches 4.6 million) and have masses approaching, possibly exceeding, 100 M_☉. The least luminous have luminosities around a quarter of a million L_☉ and masses as low as 10 M_☉, although they would have been considerably more massive as main-sequence stars, due to their rapid mass loss. Their high mass loss rates could be due to outbursts and very high luminosity and show some enhancement of helium and nitrogen.

Evolution

The Homunculus Nebula, produced by the Great Outburst of η Carinae

Because of these stars' large mass and high luminosity, their lifetime is very short—only a few million years in total and much less than a million years in the LBV phase. They are rapidly evolving on observable timescales; examples have been detected where stars with Wolf–Rayet spectra (WNL/Ofpe) have developed to show LBV outbursts and a handful of supernovae have been traced to likely LBV progenitors. Recent theoretical research confirms the latter scenario, where luminous blue variable stars are the final evolutionary stage of some massive stars before they explode as supernovae, for at least stars with initial masses between 20 and 25 solar masses. For more-massive stars, computer simulations of their evolution suggest the luminous blue variable phase takes place during the latest phases of core hydrogen burning (LBV with high surface temperature), the hydrogen shell burning phase (LBV with lower surface temperature), and the earliest part of the core helium burning phase (LBV with high surface temperature again) before transitioning to the Wolf–Rayet phase, thus being analogous to the red giant and red supergiant phases of less massive stars.

There appear to be two groups of LBVs, one with luminosities above 630,000 times the Sun and the other with luminosities below 400,000 times the Sun, although this is disputed in more-recent research. Models have been constructed showing that the lower-luminosity group are post-red-supergiants with initial masses of 30–60 times the Sun, whereas the higher-luminosity group are population-II stars with initial masses 60–90 times the Sun that never develop to red supergiants, although they may become yellow hypergiants. Some models suggest that LBVs are a stage in the evolution of very massive stars required for them to shed excess mass, whereas others require that most of the mass is lost at an earlier cool-supergiant stage. Normal outbursts and the stellar winds in the quiescent state are not sufficient for the required mass loss, but LBVs occasionally produce abnormally large outbursts that can be mistaken for a faint supernova and these may shed the necessary mass. Recent models all agree that the LBV stage occurs after the main-sequence stage and before the hydrogen-depleted Wolf–Rayet stage, and that essentially all LBV stars will eventually explode as supernovae. LBVs apparently can explode directly as a supernova, but probably only a small fraction do. If the star does not lose enough mass before the end of the LBV stage, it may undergo a particularly powerful supernova created by pair-instability. The latest models of stellar evolution suggest that some single stars with initial masses around 20 times that of the Sun will explode as LBVs as type II-P, type IIb, or type Ib supernovae, whereas binary stars undergo much-more-complex evolution through envelope stripping leading to less predictable outcomes.

Supernova-like outbursts

Stars similar to η Carinae in nearby galaxies

Luminous blue variable stars can undergo "giant outbursts" with dramatically increased mass loss and luminosity. η Carinae is the prototypical example, with P Cygni showing one or more similar outbursts 300–400 years ago, but dozens have now been catalogued in external galaxies. Many of these were initially classified as supernovae but re-examined because of unusual features. The nature of the outbursts and of the progenitor stars seems to be highly variable, with the outbursts most likely having several different causes. The historical η Carinae and P Cygni outbursts, and several seen more recently in external galaxies, have lasted years or decades whereas some of the supernova imposter events have declined to normal brightness within months. Well-studied examples are:

• SN 1954J
• SN 1961V
• SN 1997bs

Early models of stellar evolution had predicted that although the high-mass stars that produce LBVs would often or always end their lives as supernovae, the supernova explosion would not occur at the LBV stage. Prompted by the progenitor of SN 1987A being a blue supergiant, and most likely an LBV, several subsequent supernovae have been associated with LBV progenitors. The progenitor of SN 2005gl has been shown to be an LBV apparently in outburst only a few years earlier. Progenitors of several other type IIn supernovae have been detected and were likely to have been LBVs:

• SN 2009ip
• SN 2010jl

Modelling suggests that at near-solar metallicity, stars with an initial mass around 20–25 M_☉ will explode as a supernova while in the LBV stage of their lives. They will be post-red-supergiants with luminosities a few hundred thousand times that of the Sun. The supernova is expected to be of type II, most likely type IIb, although possibly type IIn due to episodes of enhanced mass loss that occur as an LBV and in the yellow-hypergiant stage.

List of LBVs

See also: List of most luminous stars

The identification of LBVs requires confirmation of the characteristic spectral and photometric variations, but these stars can be "quiescent" for decades or centuries at which time they are indistinguishable from many other hot luminous stars. A candidate luminous blue variable (cLBV) can be identified relatively quickly on the basis of its spectrum or luminosity, and dozens have been catalogued in the Milky Way during recent surveys.

Recent studies of dense clusters and mass spectrographic analysis of luminous stars have identified dozens of probable LBVs in the Milky Way out of a likely total population of just a few hundred, although few have been observed in enough detail to confirm the characteristic types of variability. In addition the majority of the LBVs in the Magellanic Clouds have been identified, several dozen in M31 and M33, plus a handful in other local group galaxies.

η Carinae, a luminous blue variable as seen from the Chandra X-ray Observatory

HD 168607 is the right star of the pair below the Omega Nebula. The other is the hypergiant HD 168625.

A selection of LBVs and suspected LBVs with nebula. Observed with Spizter.

Our galaxy

• η Carinae
• P Cygni
• AG Carinae
• HR Carinae
• V432 Carinae (Wray 15-751)
• V4029 Sagittarii (HD 168607)
• V905 Scorpii (HD 160529)
• V1672 Aquilae (AFGL 2298)
• W1-243 (in Westerlund 1)
• V481 Scuti (LBV G24.73+0.69)
• GCIRS 34W
• MWC 930 (= V446 Scuti)
• Wray 16-137
• WS1 (discovered as WISE Shell 1)
• MN44
• MN48

Suspected:

• G79.29+0.46
• Wray 17-96
• HD 316285
• MN 112
• GAL 026.47+00.02

Several more LBV’s have been found near or in the Galactic Center:

• V4650 Sagittarii (FMM 362 or qF362, in the Quintuplet cluster)
• V4998 Sagittarii (LBV3, G0.120 0.048, very close to the Quintuplet cluster)
• Pistol star, Peony star and LBV 1806-20 (candidate LBV’s, see below)

Large Magellanic Cloud

• S Doradus
• HD 269858 (= R127)
• HD 269006 (= R71)
• HD 269929 (= R143)
• HD 269662 (= R110)
• HD 269700 (= R116)
• HD 269582 (= MWC 112)
• HD 269216

Small Magellanic Cloud

• HD 5980 (= R14)
• HD 6884 (= R40)

Andromeda Galaxy

• AF Andromedae
• AE Andromedae
• Var 15
• Var A-1
• J004526.62+415006.3
• J004051.59+403303.0
• LAMOST J0037+4016

Triangulum Galaxy

• Var 2 (an extremely hot star showing no variability since 1935 and hardly studied)
• Var 83
• Var B
• Var C
• GR 290 (Romano's star, an unusually hot LBV)

NGC 2403:

• V12
• V37
• V38

NGC 1156

• J025941.21+251412.2
• J025941.54+251421.8

NGC 2366 (NGC 2363)

• NGC 2363-V1

NGC 4449

• J122809.72+440514.8
• J122817.83+440630.8

NGC 4736 (Messier 94)

• NGC 4736_1

PHL 293B

• Unnamed star that underwent an outburst from 1998 to 2008 in an unusual supernova-like event, and has now disappeared

Other

A number of cLBVs in the Milky Way (and in the case of Sanduleak -69° 202, in the LMC) are well known because of their extreme luminosity or unusual characteristics, including:

• GCIRS 16SW (S97, candidate LBV orbiting the black hole at the center of this galaxy)
• Wray 17-96 (unusual hypergiant in the gap between the two semi-stable LBV regions)
• Pistol Star (once thought to be the most luminous star in the galaxy)
• LBV 1806-20 (one of the most luminous stars known)
• Sanduleak -69° 202 (the star that exploded as SN 1987A)
• Cygnus OB2-12 (blue hypergiant and one of the most luminous stars known)
• HD 80077 (blue hypergiant)
• V1429 Aquilae (with a supergiant companion, very similar to a less luminous η Car)
• V4030 Sagittarii (hypergiant surrounded by a nebula identical to the one around Sanduleak -69° 202)
• WR 102ka (the Peony star, one of the most luminous stars known, and would be one of the hottest LBVs)
• Sher 25 (blue supergiant in NGC 3603 with a bipolar outflow and surrounded by a circumstellar ring)
• BD+40°4210 (blue supergiant in the stellar association Cygnus OB2)

Further well-known stars have been LBVs relatively recently, are LBVs in a stable phase or are not currently classified as LBVs but may be transitioning into LBVs:

• Zeta-1 Scorpii (naked-eye hypergiant)
• IRC+10420 (yellow hypergiant that has increased its temperature into the LBV range)
• V509 Cassiopeiae (= HR 8752, an unusual yellow hypergiant evolving bluewards)
• Rho Cassiopeiae (unstable yellow hypergiant suffering periodic outbursts)