H-alpha (Hα) is a specific deep-red visible spectral line in the Balmer series with a wavelength of 656.28 nm in air; it occurs when a hydrogen electron falls from its third to second lowest energy level. H-alpha light is important to astronomers as it is emitted by many emission nebulae and can be used to observe features in the Sun's atmosphere, including solar prominences and the chromosphere.
According to the Bohr model of the atom, electrons exist in quantized energy levels surrounding the atom's nucleus. These energy levels are described by the principal quantum number n = 1, 2, 3, ... . Electrons may only exist in these states, and may only transit between these states.
The set of transitions from n ≥ 3 to n = 2 is called the Balmer series and its members are named sequentially by Greek letters:
For the Lyman series the naming convention is:
H-alpha has a wavelength of 656.281 nm, is visible in the red part of the electromagnetic spectrum, and is the easiest way for astronomers to trace the ionized hydrogen content of gas clouds. Since it takes nearly as much energy to excite the hydrogen atom's electron from n = 1 to n = 3 (12.1 eV, via the Rydberg formula) as it does to ionize the hydrogen atom (13.6 eV), ionization is far more probable than excitation to the n = 3 level. After ionization, the electron and proton recombine to form a new hydrogen atom. In the new atom, the electron may begin in any energy level, and subsequently cascades to the ground state (n = 1), emitting photons with each transition. Approximately half the time, this cascade will include the n = 3 to n = 2 transition and the atom will emit H-alpha light. Therefore, the H-alpha line occurs where hydrogen is being ionized.
The H-alpha line saturates (self-absorbs) relatively easily because hydrogen is the primary component of nebulae, so while it can indicate the shape and extent of the cloud, it cannot be used to accurately determine the cloud's mass. Instead, molecules such as carbon dioxide, carbon monoxide, formaldehyde, ammonia, or acetonitrile are typically used to determine the mass of a cloud.
An H-alpha filter is an optical filter designed to transmit a narrow bandwidth of light generally centred on the H-alpha wavelength. These filters can be dichroic filters manufactured by multiple (~50) vacuum-deposited layers. These layers are selected to produce interference effects that filter out any wavelengths except at the requisite band.
Taken in isolation, H-alpha dichroic filters are useful in astrophotography and for reducing the effects of light pollution. They do not have narrow enough bandwidth for observing the sun's atmosphere.
For observing the sun, a much narrower band filter can be made from three parts: an "energy rejection filter" which is usually a piece of red glass that absorbs most of the unwanted wavelengths, a Fabry–Pérot etalon which transmits several wavelengths including one centred on the H-alpha emission line, and a "blocking filter" -a dichroic filter which transmits the H-alpha line while stopping those other wavelengths that passed through the etalon. This combination will pass only a narrow (<0.1 nm) range of wavelengths of light centred on the H-alpha emission line.
The physics of the etalon and the dichroic interference filters are essentially the same (relying on constructive/destructive interference of light reflecting between surfaces), but the implementation is different (a dichroic interference filter relies on the interference of internal reflections while the etalon has a relatively large air gap). Due to the high velocities sometimes associated with features visible in H-alpha light (such as fast moving prominences and ejections), solar H-alpha etalons can often be tuned (by tilting or changing the temperature) to cope with the associated Doppler effect.
Commercially available H-alpha filters for amateur solar observing usually state bandwidths in Angstrom units and are typically 0.7Å (0.07 nm). By using a second etalon, this can be reduced to 0.5Å leading to improved contrast in details observed on the sun's disc.
An even more narrow band filter can be made using a Lyot filter.
139 Tauri is a single, blue-white hued star in the zodiac constellation of Taurus. It is faintly visible to the naked eye with an apparent visual magnitude of 4.81. The distance to this star, as determined from an annual parallax shift of 2.10±0.19 mas, is roughly 1,600 light years. Because this star is located near the ecliptic, it is subject to occultations by the Moon. One such event was observed April 28, 1990.This is a massive B-type lower-luminosity supergiant or bright giant star with a stellar classification of B1 Ib or B0.5 II, respectively. It is around 22.5 million years old with a high rate of spin, showing a projected rotational velocity of 140 km/s. J. D. Rosendhal (1973) identified weak emission features associated with an asymmetric H-alpha absorption line, providing evidence of mass loss. The star has about 10 times the mass of the Sun and around 20 times the Sun's radius. It is radiating over 80,000 times the Sun's luminosity from its photosphere at an effective temperature of around 24,660 K. Stars such as this with 10 or more solar masses are expected to end their life by exploding as a Type II supernova.Bessel function
Bessel functions, first defined by the mathematician Daniel Bernoulli and then generalized by Friedrich Bessel, are the canonical solutions y(x) of Bessel's differential equation
for an arbitrary complex number α, the order of the Bessel function. Although α and −α produce the same differential equation for real α, it is conventional to define different Bessel functions for these two values in such a way that the Bessel functions are mostly smooth functions of α.
The most important cases are when α is an integer or half-integer. Bessel functions for integer α are also known as cylinder functions or the cylindrical harmonics because they appear in the solution to Laplace's equation in cylindrical coordinates. Spherical Bessel functions with half-integer α are obtained when the Helmholtz equation is solved in spherical coordinates.CHRNA2
Neuronal acetylcholine receptor subunit alpha-2, also known as nAChRα2, is a protein that in humans is encoded by the CHRNA2 gene. The protein encoded by this gene is a subunit of certain nicotinic acetylcholine receptors (nAchR).CHRNA7
Neuronal acetylcholine receptor subunit alpha-7, also known as nAChRα7, is a protein that in humans is encoded by the CHRNA7 gene. The protein encoded by this gene is a subunit of certain nicotinic acetylcholine receptors (nAchR).CHRNB4
Neuronal acetylcholine receptor subunit beta-4 is a protein that in humans is encoded by the CHRNB4 gene.California Nebula
The California Nebula (NGC 1499) is an emission nebula located in the constellation Perseus. It is so named because it appears to resemble the outline of the US State of California on long exposure photographs. It is almost 2.5° long on the sky and, because of its very low surface brightness, it is extremely difficult to observe visually. It can be observed with a Hβ filter (isolates the Hβ line at 486 nm) in a rich-field telescope under dark skies. It lies at a distance of about 1,000 light years from Earth. Its fluorescence is due to excitation of the Hβ line in the nebula by the nearby prodigiously energetic O7 star, xi Persei (also known as Menkib, seen at center below it in the inset at right).The California Nebula was discovered by E. E. Barnard in 1884.
By coincidence, the California Nebula transits in the zenith in central California as the latitude matches the declination of the object.Gibbons–Hawking–York boundary term
In general relativity, the Gibbons–Hawking–York boundary term is a term that needs to be added to the Einstein–Hilbert action when the underlying spacetime manifold has a boundary.
The Einstein–Hilbert action is the basis for the most elementary variational principle from which the field equations of general relativity can be defined. However, the use of the Einstein–Hilbert action is appropriate only when the underlying spacetime manifold is closed, i.e., a manifold which is both compact and without boundary. In the event that the manifold has a boundary , the action should be supplemented by a boundary term so that the variational principle is well-defined.
The necessity of such a boundary term was first realised by York and later refined in a minor way by Gibbons and Hawking.
For a manifold that is not closed, the appropriate action is
where is the Einstein–Hilbert action, is the Gibbons–Hawking–York boundary term, is the induced metric (see section below on definitions) on the boundary, its determinant, is the trace of the second fundamental form, is equal to where is timelike and where is spacelike, and are the coordinates on the boundary. Varying the action with respect to the metric , subject to the condition
gives the Einstein equations; the addition of the boundary term means that in performing the variation, the geometry of the boundary encoded in the transverse metric is fixed (see section below). There remains ambiguity in the action up to an arbitrary functional of the induced metric .
That a boundary term is needed in the gravitational case is because , the gravitational Lagrangian density, contains second derivatives of the metric tensor. This is a non-typical feature of field theories, which are usually formulated in terms of Lagrangians that involve first derivatives of fields to be varied over only.
The GHY term is desirable, as it possesses a number of other key features. When passing to the Hamiltonian formalism, it is necessary to include the GHY term in order to reproduce the correct Arnowitt–Deser–Misner energy (ADM energy). The term is required to ensure the path integral (a la Hawking) for quantum gravity has the correct composition properties. When calculating black hole entropy using the Euclidean semiclassical approach, the entire contribution comes from the GHY term. This term has had more recent applications in loop quantum gravity in calculating transition amplitudes and background-independent scattering amplitudes.
In order to determine a finite value for the action, one may have to subtract off a surface term for flat spacetime:
where is the extrinsic curvature of the boundary imbedded flat spacetime. As is invariant under variations of , this addition term does not affect the field equations; as such, this is referred to as the non-dynamical term.Gum catalog
The Gum catalog is an astronomical catalog of 84 emission nebulae in the southern sky. It was made by the Australian astronomer Colin Stanley Gum (1924-1960) at Mount Stromlo Observatory using wide field photography. Gum published his findings in 1955 in a study entitled A study of diffuse southern H-alpha nebulae which presented a catalog of 84 nebulae or nebular complexes. Similar catalogs include the Sharpless catalog and the RCW catalog, and many of the Gum objects are repeated in these other catalogs.
The Gum Nebula is named for Gum, who discovered it as Gum 12; it is an emission nebula that can be found in the southern constellations Vela and Puppis.HD 107914
HD 107914 is a binary star in the constellation Centaurus, with an estimated distance of 255.5 light-years (78.3 pc) from the Solar System. The primary has a stellar classification of A7-8 III, making it a giant star.
Measurement of the proper motion of this system show that it has a low transverse velocity relative to the Sun. For this reason, it has been compared to the hypothetical "Nemesis" star since it may pass through the Oort cloud in the future. The star is too far away to be a companion to the Sun. However, preliminary measurements of the H-alpha line in the star's spectrum show a radial velocity in the range from –13 to +3 km/s. (This result was obtained by M. Muterspaugh and M. Williamson at a robotic spectroscopic telescope in Arizona.) Such values for the radial velocity are too small to produce a likely collision course with the Solar System. For example, if Vr = –10 km/s, then the distance from the Sun to HD 107914 at closest approach will be about 5.2 ly (1.6 pc).NGC 691
NGC 691 is an unbarred spiral galaxy located in the constellation Aries. It is located at a distance of circa 120 million light years from Earth, which, given its apparent dimensions, means that NGC 691 is about 130,000 light years across. It was discovered by William Herschel on November 13, 1786.NGC 691 features a multiple ring structure, with three rings recognised in the infrared, with diameters of 1.03, 1.67, and 2.79 arcminutes. When imaged in H-alpha, the galaxy appears patchy. The total star formation rate of the galaxy is estimated to be about 0.6 M☉ per year. One supernova has been observed in NGC 691, SN 2005W. It was discovered by Yoji Hirose in unfiltered CCD frames taken on Feb. 1.442 UT with a 0.35-m f/6.8 Schmidt-Cassegrain reflector. The supernova was located 56" east and 1" south of the center of NGC 691 and at the time of the discovery had an apparent magnitude of 15.2. Spectrographic observations indicated it was a type Ia supernova about a week before maximum. The peak magnitude of the supernova was 14.3, on February 10.759.NGC 691 is the foremost member of a galaxy group known as the NGC 691 group. Other members of the group include IC 163, NGC 678, NGC 680, NGC 694, IC 167, and NGC 697.NGC 877
NGC 877 is an intermediate spiral galaxy located in the constellation Aries. It is located at a distance of circa 160 million light years from Earth, which, given its apparent dimensions, means that NGC 877 is about 115,000 light years across. It was discovered by William Herschel on October 14, 1784. It interacts with NGC 876.
NGC 877 features two spiral arms with a grand design pattern and slightly disturbed morphology. When pictured in H-alpha, the arms have numerous knots and appear brighter than the nucleus. The northwest part of the galaxy has higher polarised emission than the rest of the galaxy. A bar appears in radio waves.
The nucleus has activity that resembles that of a HII region. The galaxy has been categorised as a luminous infrared galaxy, a category of galaxies associated with high star formation rate. The total infrared luminosity of the galaxy is estimated to be between 1011.04 L☉ and 1011.1 L☉, lying near the threshold to classify a galaxy as luminous infrared. The total star formation rate in NGC 877 is estimated to be between 20 and 53 M☉ per year.One possible supernova has been observed in NGC 877, SN 2019rn. It was discovered by the robotic sky survey ATLAS on January 12.30, 2019, using a twin 0.5m telescope system. It had apparent magnitude 18.9 on discovery. The supernova was initially classified as a type II supernova with spectroscopic observations by Keck-II, and further spectographic observations categorised it as type IIb, although it could also be a cataclysmic variable or another type of variable star.NGC 877 forms a pair with the edge-on spiral galaxy NGC 876, which lies 2.1 arcminutes to the southwest. At the distance of NGC 877, this corresponds to a projected distance of 30 kpc. A low surface brightness bridge connects the two galaxies. NGC 870 and NGC 871 are two other nearby galaxies. NGC 877 is the brightest and most massive member of a galaxy group known as the NGC 877 group or LGG 35. Other members of the group include NGC 876 and NGC 871, as well as UGC 1693, IC 1791, UGC 1773, and UGC 1817. The group contains large amounts of HI gas.NGC 89
NGC 89 is a barred spiral or lenticular galaxy, part of Robert's Quartet, a group of four interacting galaxies. This member has a Seyfert 2 nucleus with extra-planar features emitting H-alpha radiation. There are filamentary features on each side of the disk, including a jet-like structure extending about 4 kpc in the NE direction. It may have lost its neutral hydrogen (H1) gas due to interactions with the other members of the clusters—most likely NGC 92.Post-Newtonian expansion
Post-Newtonian expansions in general relativity are used for finding an approximate solution of the Einstein field equations for the metric tensor. The approximations are expanded in small parameters which express orders of deviations from Newton's law of universal gravitation. This allows approximations to Einstein's equations to be made in the case of weak fields. Higher order terms can be added to increase accuracy, but for strong fields sometimes it is preferable to solve the complete equations numerically. This method is a common mark of effective field theories. In the limit, when the small parameters are equal to 0, the post-Newtonian expansion reduces to Newton's law of gravity.Rényi entropy
In information theory, the Rényi entropy generalizes the Hartley entropy, the Shannon entropy, the collision entropy and the min-entropy. Entropies quantify the diversity, uncertainty, or randomness of a system. The Rényi entropy is named after Alfréd Rényi. In the context of fractal dimension estimation, the Rényi entropy forms the basis of the concept of generalized dimensions.
The Rényi entropy is important in ecology and statistics as index of diversity. The Rényi entropy is also important in quantum information, where it can be used as a measure of entanglement. In the Heisenberg XY spin chain model, the Rényi entropy as a function of α can be calculated explicitly by virtue of the fact that it is an automorphic function with respect to a particular subgroup of the modular group. In theoretical computer science, the min-entropy is used in the context of randomness extractors.Solar flare
A solar flare is a sudden flash of increased brightness on the Sun, usually observed near its surface
and in close proximity to a sunspot group.
Powerful flares are often, but not always, accompanied by a coronal mass ejection. Even the most powerful flares are barely detectable in the total solar irradiance (the "solar constant").Solar flares occur in a power-law spectrum of magnitudes; an energy release of typically 1020 joules of energy suffices to produce a clearly observable event, while a major event can emit up to 1025 joules.Flares are closely associated with the ejection of plasmas and particles through the Sun's corona into outer space; flares also copiously emit radio waves.
If the ejection is in the direction of the Earth, particles associated with this disturbance can penetrate into the upper atmosphere (the ionosphere) and cause bright auroras, and may even disrupt long range radio communication.
It usually takes days for the solar plasma ejecta to reach Earth. Flares also occur on other stars, where the term stellar flare applies.
High-energy particles, which may be relativistic, can arrive almost simultaneously with the electromagnetic radiations.
On July 23, 2012, a massive, potentially damaging, solar storm (solar flare, coronal mass ejection and electromagnetic radiation) barely missed Earth. According to NASA, there may be as much as a 12% chance of a similar event occurring between 2012 and 2022.Struve function
In mathematics, the Struve functions Hα(x), are solutions y(x) of the non-homogeneous Bessel's differential equation:
introduced by Hermann Struve (1882). The complex number α is the order of the Struve function, and is often an integer. The modified Struve functions Lα(x) are equal to −ie−iαπ / 2Hα(ix).The INT Photometric H-Alpha Survey
The INT Photometric H-Alpha Survey (IPHAS) is an astronomical survey of the northern plane of our Galaxy, the Milky Way, as visible from the Isaac Newton Telescope (INT) in the Canary Islands, Spain. The survey uses two broad-band filters and a narrow H-alpha filter to obtain deep images of nebulae in our Galaxy and for identifying rare types of stars. Observations for the survey began in 2003 and are almost complete. The survey is being complemented by a sister survey of the southern Galactic Plane, VPHAS+. Once these two surveys are completed the data are expected to provide a significant leap in our knowledge of the extreme phases of stellar evolution.
The goals of the survey include:
Identification of rare objects that are often characterized by strong emission in H-Alpha compared to that in broad-band filters. This includes massive OB stars, supergiants, interacting binary stars and supernova progenitors.
Mapping Galactic extinction and nebulosity.
Identifying compact and extended planetary nebulae and symbiotic stars.
Cataloging of vast numbers of stars in our Galaxy.Because of the selection for young stars and nebulae, the survey will also increase the number of known OB associations, and other clusters.Wisconsin H-Alpha Mapper
The Wisconsin H-Alpha Mapper (WHAM) is a custom-built 0.6 metres (24 in) telescope operated by the University of Wisconsin–Madison, used to study the Hydrogen-alpha ions of the warm ionized medium. It is a tenant telescope at the Cerro Tololo Inter-American Observatory (CTIO), in the Coquimbo Region of northern Chile.Xi Cygni
ξ Cygni (Latinised as Xi Cygni) is a spectroscopic binary star in the constellation Cygnus. Its apparent magnitude is 3.73 and it is located around 360 parsecs (1,200 ly) away.
The system contains two stars which orbit every 18 years in a mildly eccentric orbit. The primary star is a supergiant with a spectral type of around K4, while the secondary is a A-type main-sequence star with a spectral type of A1.5. Stellar winds from the supergiant have been measured at around 50 km/s, but with variations in speed and individual line strengths.ξ Cygni is in the Kepler spacecraft's field of view but no planets have been detected.