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Wednesday, September 16, 2020

Steradian

From Wikipedia, the free encyclopedia
 
Steradian
Solid Angle, 1 Steradian.svg
A graphical representation of 1 steradian.The sphere has radius r, and in this case the area A of the highlighted surface patch is r2. The solid angle Ω equals [A/r2] sr which is 1 sr in this example. The entire sphere has a solid angle of 4πsr.
General information
Unit systemSI derived unit
Unit ofSolid angle
Symbolsr 
Conversions
1 sr in ...... is equal to ...
   SI base units   1 m2/m2

The steradian (symbol: sr) or square radian is the SI unit of solid angle. It is used in three-dimensional geometry, and is analogous to the radian, which quantifies planar angles. Whereas an angle in radians, projected onto a circle, gives a length on the circumference, a solid angle in steradians, projected onto a sphere, gives an area on the surface. The name is derived from the Greek στερεός stereos 'solid' + radian.

The steradian, like the radian, is a dimensionless unit, the quotient of the area subtended and the square of its distance from the center. Both the numerator and denominator of this ratio have dimension length squared (i.e. L2/L2 = 1, dimensionless). It is useful, however, to distinguish between dimensionless quantities of a different nature, so the symbol "sr" is used to indicate a solid angle. For example, radiant intensity can be measured in watts per steradian (W⋅sr−1). The steradian was formerly an SI supplementary unit, but this category was abolished in 1995 and the steradian is now considered an SI derived unit.

Definition

A steradian can be defined as the solid angle subtended at the center of a unit sphere by a unit area on its surface. For a general sphere of radius r, any portion of its surface with area A = r2 subtends one steradian at its center.

The solid angle is related to the area it cuts out of a sphere:

where
A is the surface area of the spherical cap, ,
r is the radius of the sphere, and
sr is the unit, steradian.

Because the surface area A of a sphere is 4πr2, the definition implies that a sphere subtends 4π steradians (≈ 12.56637 sr) at its center. By the same argument, the maximum solid angle that can be subtended at any point is 4π sr.

Other properties

Section of cone (1) and spherical cap (2) that subtend a solid angle of one steradian inside a sphere

If A = r2, it corresponds to the area of a spherical cap (A = 2πrh) (where h stands for the "height" of the cap) and the relationship h/r = 1/2π holds. Therefore, in this case, one steradian corresponds to the plane (i.e. radian) angle of the cross-section of a simple cone subtending the plane angle 2θ, with θ given by:

This angle corresponds to the plane aperture angle of 2θ ≈ 1.144 rad or 65.54°.

A steradian is also equal to the spherical area of a polygon having an angle excess of 1 radian, to 1/4π of a complete sphere, or to (180°/π)2
≈ 3282.80635 square degrees.

The solid angle of a cone whose cross-section subtends the angle 2θ is:

.

SI multiples

Millisteradians (msr) and microsteradians (μsr) are occasionally used to describe light and particle beams. Other multiples are rarely used.

Protoplanetary disk

From Wikipedia, the free encyclopedia
 

A protoplanetary disk is a rotating circumstellar disc of dense gas and dust surrounding a young newly formed star, a T Tauri star, or Herbig Ae/Be star. The protoplanetary disk may also be considered an accretion disk for the star itself, because gases or other material may be falling from the inner edge of the disk onto the surface of the star. This process should not be confused with the accretion process thought to build up the planets themselves. Externally illuminated photo-evaporating protoplanetary disks are called proplyds.

In July 2018, the first confirmed image of such a disk, containing a nascent exoplanet, named PDS 70b, was reported.

Formation

Fraction of stars that show some evidence of having a protoplanetary disk as a function of stellar age (in millions of years). The samples are nearby young clusters and associations. Figure taken from review of Mamajek (2009).

Protostars form from molecular clouds consisting primarily of molecular hydrogen. When a portion of a molecular cloud reaches a critical size, mass, or density, it begins to collapse under its own gravity. As this collapsing cloud, called a solar nebula, becomes denser, random gas motions originally present in the cloud average out in favor of the direction of the nebula's net angular momentum. Conservation of angular momentum causes the rotation to increase as the nebula radius decreases. This rotation causes the cloud to flatten out—much like forming a flat pizza out of dough—and take the form of a disk. This occurs because centripetal acceleration from the orbital motion resists the gravitational pull of the star only in the radial direction, but the cloud remains free to collapse in the vertical direction. The outcome is the formation of a thin disc supported by gas pressure in the vertical direction. The initial collapse takes about 100,000 years. After that time the star reaches a surface temperature similar to that of a main sequence star of the same mass and becomes visible.

It is now a T Tauri star. Accretion of gas onto the star continues for another 10 million years, before the disk disappears, perhaps being blown away by the young star's stellar wind, or perhaps simply ceasing to emit radiation after accretion has ended. The oldest protoplanetary disk yet discovered is 25 million years old.

Protoplanetary disk. Simulated spiral arm vs observational data.

Protoplanetary disks around T Tauri stars differ from the disks surrounding the primary components of close binary systems with respect to their size and temperature. Protoplanetary disks have radii up to 1000 AU, and only their innermost parts reach temperatures above 1000 K. They are very often accompanied by jets.

Protoplanetary disks have been observed around several young stars in our galaxy. Observations by the Hubble Space Telescope have shown proplyds and planetary disks to be forming within the Orion Nebula.

Protoplanetary disks are thought to be thin structures, with a typical vertical height much smaller than the radius, and a typical mass much smaller than the central young star.

The mass of a typical proto-planetary disk is dominated by its gas, however, the presence of dust grains has a major role in its evolution. Dust grains shield the mid-plane of the disk from energetic radiation from outer space that creates a dead zone in which the magnetorotational instability (MRI) no longer operates.

It is believed that these disks consist of a turbulent envelope of plasma, also called the active zone, that encases an extensive region of quiescent gas called the dead zone. The dead zone located at the mid-plane can slow down the flow of matter through the disk which prohibits achieving a steady state.

Planetary system

Protoplanetary disk surrounding the young star Elias 2-27, located some 450 light years away.

The nebular hypothesis of solar system formation describes how protoplanetary disks are thought to evolve into planetary systems. Electrostatic and gravitational interactions may cause the dust and ice grains in the disk to accrete into planetesimals. This process competes against the stellar wind, which drives the gas out of the system, and gravity (accretion) and internal stresses (viscosity), which pulls material into the central T Tauri star. Planetesimals constitute the building blocks of both terrestrial and giant planets.

Some of the moons of Jupiter, Saturn, and Uranus are believed to have formed from smaller, circumplanetary analogs of the protoplanetary disks. The formation of planets and moons in geometrically thin, gas- and dust-rich disks is the reason why the planets are arranged in an ecliptic plane. Tens of millions of years after the formation of the Solar System, the inner few AU of the Solar System likely contained dozens of moon- to Mars-sized bodies that were accreting and consolidating into the terrestrial planets that we now see. The Earth's moon likely formed after a Mars-sized protoplanet obliquely impacted the proto-Earth ~30 million years after the formation of the Solar System.

Debris disks

Artist's impression of the water snowline around the star V883 Orionis.

Gas-poor disks of circumstellar dust have been found around many nearby stars—most of which have ages in the range of ~10 million years (e.g. Beta Pictoris, 51 Ophiuchi) to billions of years (e.g. Tau Ceti). These systems are usually referred to as "debris disks". Given the older ages of these stars, and the short lifetimes of micrometer-sized dust grains around stars due to Poynting Robertson drag, collisions, and radiation pressure (typically hundreds to thousands of years), it is thought that this dust is from the collisions of planetesimals (e.g. asteroids, comets). Hence the debris disks around these examples (e.g. Vega, Alphecca, Fomalhaut, etc.) are probably not truly "protoplanetary", but represent a later stage of disk evolution where extrasolar analogs of the asteroid belt and Kuiper belt are home to dust-generating collisions between planetesimals.

Relation to abiogenesis

Based on recent computer model studies, the complex organic molecules necessary for life may have formed in the protoplanetary disk of dust grains surrounding the Sun before the formation of the Earth. According to the computer studies, this same process may also occur around other stars that acquire planets.

Gallery

Herbig–Haro object

From Wikipedia, the free encyclopedia
 
HH 24 is located in the Orion B molecular cloud
HH 32 looks like a star due to its intense brightness. The surrounding gas appears like clouds around a full moon.
Hubble Space Telescope images of HH 24 (left) and HH 32 (right; top) – colourful nebulae are typical of Herbig–Haro objects

Herbig–Haro (HH) objects are bright patches of nebulosity associated with newborn stars. They are formed when narrow jets of partially ionised gas ejected by stars collide with nearby clouds of gas and dust at several hundred kilometres per second. Herbig–Haro objects are commonly found in star-forming regions, and several are often seen around a single star, aligned with its rotational axis. Most of them lie within about one parsec (3.26 light-years) of the source, although some have been observed several parsecs away. HH objects are transient phenomena that last around a few tens of thousands of years. They can change visibly over timescales of a few years as they move rapidly away from their parent star into the gas clouds of interstellar space (the interstellar medium or ISM). Hubble Space Telescope observations have revealed the complex evolution of HH objects over the period of a few years, as parts of the nebula fade while others brighten as they collide with the clumpy material of the interstellar medium.

First observed in the late 19th century by Sherburne Wesley Burnham, Herbig–Haro objects were recognised as a distinct type of emission nebula in the 1940s. The first astronomers to study them in detail were George Herbig and Guillermo Haro, after whom they have been named. Herbig and Haro were working independently on studies of star formation when they first analysed the objects, and recognised that they were a by-product of the star formation process. Although HH objects are a visible wavelength phenomena, many remain invisible at these wavelengths due to dust and gas, and can only be detected at infrared wavelengths. Such objects, when observed in near infrared, are called molecular hydrogen emission-line objects (MHOs).

Discovery and history of observations

The first HH object was observed in the late 19th century by Sherburne Wesley Burnham, when he observed the star T Tauri with the 36-inch (910 mm) refracting telescope at Lick Observatory and noted a small patch of nebulosity nearby. It was thought to be an emission nebula, later becoming known as Burnham's Nebula, and was not recognized as a distinct class of object. T Tauri was found to be a very young and variable star, and is the prototype of the class of similar objects known as T Tauri stars which have yet to reach a state of hydrostatic equilibrium between gravitational collapse and energy generation through nuclear fusion at their centres. Fifty years after Burnham's discovery, several similar nebulae were discovered with almost star-like appearance. Both Haro and Herbig made independent observations of several of these objects in the Orion Nebula during the 1940s. Herbig also looked at Burnham's Nebula and found it displayed an unusual electromagnetic spectrum, with prominent emission lines of hydrogen, sulfur and oxygen. Haro found that all the objects of this type were invisible in infrared light.

Following their independent discoveries, Herbig and Haro met at an astronomy conference in Tucson, Arizona in December 1949. Herbig had initially paid little attention to the objects he had discovered, being primarily concerned with the nearby stars, but on hearing Haro's findings he carried out more detailed studies of them. The Soviet astronomer Viktor Ambartsumian gave the objects their name (Herbig–Haro objects, normally shortened to HH objects), and based on their occurrence near young stars (a few hundred thousand years old), suggested they might represent an early stage in the formation of T Tauri stars. Studies of the HH objects showed they were highly ionised, and early theorists speculated that they were reflection nebulae containing low-luminosity hot stars deep inside. But the absence of infrared radiation from the nebulae meant there could not be stars within them, as these would have emitted abundant infrared light. In 1975 American astronomer R. D. Schwartz theorized that winds from T Tauri stars produce shocks in the ambient medium on encounter, resulting in generation of visible light. With the discovery of the first proto-stellar jet in HH 46/47, it became clear that HH objects are indeed shock-induced phenomena with shocks being driven by a collimated jet from protostars.

Formation

Illustration depicting two arrows of matter moving outwards in opposite directions from a star-disk system, and creating bright emission caps at the ends, where they collide with the surrounding medium
Yellow-green emission cap produced by red jet from a star in a deep green nebula
HH objects are formed when accreted material is ejected by a protostar as ionized gas along the star's axis of rotation, as exemplified by HH 34 (right).

Stars form by gravitational collapse of interstellar gas clouds. As the collapse increases the density, radiative energy loss decreases due to increased opacity. This raises the temperature of the cloud which prevents further collapse, and a hydrostatic equilibrium is established. Gas continues to fall towards the core in a rotating disk. The core of this system is called a protostar. Some of the accreting material is ejected out along the star's axis of rotation in two jets of partially ionised gas (plasma). The mechanism for producing these collimated bipolar jets is not entirely understood, but it is believed that interaction between the accretion disk and the stellar magnetic field accelerates some of the accreting material from within a few astronomical units of the star away from the disk plane. At these distances the outflow is divergent, fanning out at an angle in the range of 10−30°, but it becomes increasingly collimated at distances of tens to hundreds of astronomical units from the source, as its expansion is constrained. The jets also carry away the excess angular momentum resulting from accretion of material onto the star, which would otherwise cause the star to rotate too rapidly and disintegrate. When these jets collide with the interstellar medium, they give rise to the small patches of bright emission which comprise HH objects.

Properties

Plot of light intensity vs wavelength featuring several dips, caused by absorption of light emitted from the star by the molecules in surrounding medium
Infrared spectrum of HH 46/47 obtained by the Spitzer Space Telescope, showing the medium in immediate vicinity of the star being silicate-rich

Electromagnetic emission from HH objects is caused when their associated shock waves collide with the interstellar medium, creating what is called the "terminal working surfaces". The spectrum is continuous, but also has intense emission lines of neutral and ionized species. Spectroscopic observations of HH objects' doppler shifts indicate velocities of several hundred kilometers per second, but the emission lines in those spectra are weaker than what would be expected from such high-speed collisions. This suggests that some of the material they are colliding with is also moving along the beam, although at a lower speed. Spectroscopic observations of HH objects show they are moving away from the source stars at speeds of several hundred kilometres per second. In recent years, the high optical resolution of the Hubble Space Telescope has revealed the proper motion (movement along the sky plane) of many HH objects in observations spaced several years apart. As they move away from the parent star, HH objects evolve significantly, varying in brightness on timescales of a few years. Individual compact knots or clumps within an object may brighten and fade or disappear entirely, while new knots have been seen to appear. These arise likely because of the precession of their jets, along with the pulsating and intermittent eruptions from their parent stars. Faster jets catch up with earlier slower jets, creating the so-called "internal working surfaces", where streams of gas collide and generate shock waves and consequent emissions.

The total mass being ejected by stars to form typical HH objects is estimated to be of the order of 10−8 to 10−6 M per year, a very small amount of material compared to the mass of the stars themselves but amounting to about 1–10% of the total mass accreted by the source stars in a year. Mass loss tends to decrease with increasing age of the source. The temperatures observed in HH objects are typically about 9,000–12,000 K, similar to those found in other ionized nebulae such as H II regions and planetary nebulae. Densities, on the other hand, are higher than in other nebulae, ranging from a few thousand to a few tens of thousands of particles per cm3, compared to a few thousand particles per cm3 in most H II regions and planetary nebulae.

Densities also decrease as the source evolves over time. HH objects consist mostly of hydrogen and helium, which account for about 75% and 24% of their mass respectively. Around 1% of the mass of HH objects is made up of heavier chemical elements, including oxygen, sulfur, nitrogen, iron, calcium and magnesium. Abundances of these elements, determined from emission lines of respective ions, are generally similar to their cosmic abundances. Many chemical compounds found in the surrounding interstellar medium, but not present in the source material, such as metal hydrides, are believed to have been produced by shock-induced chemical reactions. Around 20–30% of the gas in HH objects is ionized near the source star, but this proportion decreases at increasing distances. This implies the material is ionized in the polar jet, and recombines as it moves away from the star, rather than being ionized by later collisions. Shocking at the end of the jet can re-ionise some material, giving rise to bright "caps".

Numbers and distribution

Blue- and orange-appearing turbulent caps of emission
HH 2 (lower right), HH 34 (lower left), and HH 47 (top) were numbered in order of their discovery; it is estimated that there are up to 150,000 such objects in the Milky Way.

HH objects are named approximately in order of their identification; HH 1/2 being the earliest such objects to be identified. More than a thousand individual objects are now known. They are always present in star-forming H II regions, and are often found in large groups. They are typically observed near Bok globules (dark nebulae which contain very young stars) and often emanate from them. Several HH objects have been seen near a single energy source, forming a string of objects along the line of the polar axis of the parent star. The number of known HH objects has increased rapidly over the last few years, but that is a very small proportion of the estimated up to 150,000 in the Milky Way, the vast majority of which are too far away to be resolved. Most HH objects lie within about one parsec of their parent star. Many, however, are seen several parsecs away.

HH 46/47 is located about 450 parsecs (1,500 light-years) away from the Sun and is powered by a class I protostar binary. The bipolar jet is slamming into the surrounding medium at a velocity of 300 kilometers per second, producing two emission caps about 2.6 parsecs (8.5 light-years) apart. Jet outflow is accompanied by a 0.3 parsecs (0.98 light-years) long molecular gas outflow which is swept up by the jet itself. Infrared studies by Spitzer Space Telescope have revealed a variety of chemical compounds in the molecular outflow, including water (ice), methanol, methane, carbon dioxide (dry ice) and various silicates. Located around 460 parsecs (1,500 light-years) away in the Orion A molecular cloud, HH 34 is produced by a highly collimated bipolar jet powered by a class I protostar. Matter in the jet is moving at about 220 kilometers per second. Two bright bow shocks, separated by about 0.44 parsecs (1.4 light-years), are present on the opposite sides of the source, followed by series of fainter ones at larger distances, making the whole complex about 3 parsecs (9.8 light-years) long. The jet is surrounded by a 0.3 parsecs (0.98 light-years) long weak molecular outflow near the source.

Source stars

Thirteen-year timelapse of material ejecting from a class I protostar, forming the Herbig–Haro object HH 34

The stars from which HH jets are emitted are all very young stars, a few tens of thousands to about a million years old. The youngest of these are still protostars in the process of collecting from their surrounding gases. Astronomers divide these stars into classes 0, I, II and III, according to how much infrared radiation the stars emit. A greater amount of infrared radiation implies a larger amount of cooler material surrounding the star, which indicates it is still coalescing. The numbering of the classes arises because class 0 objects (the youngest) were not discovered until classes I, II and III had already been defined.

Class 0 objects are only a few thousand years old; so young that they are not yet undergoing nuclear fusion reactions at their centres. Instead, they are powered only by the gravitational potential energy released as material falls onto them. They mostly contain molecular outflows with low velocities (less than a hundred kilometres per second) and weak emissions in the outflows. Nuclear fusion has begun in the cores of Class I objects, but gas and dust are still falling onto their surfaces from the surrounding nebula, and most of their luminosity is accounted for by gravitational energy. They are generally still shrouded in dense clouds of dust and gas, which obscure all their visible light and as a result can only be observed at infrared and radio wavelengths. Outflows from this class are dominated by ionized species and velocities can range up to 400 kilometres per second. The in-fall of gas and dust has largely finished in Class II objects (Classical T Tauri stars), but they are still surrounded by disks of dust and gas, and produce weak outflows of low luminosity. Class III objects (Weak-line T Tauri stars) have only trace remnants of their original accretion disk.

About 80% of the stars giving rise to HH objects are binary or multiple systems (two or more stars orbiting each other), which is a much higher proportion than that found for low mass stars on the main sequence. This may indicate that binary systems are more likely to generate the jets which give rise to HH objects, and evidence suggests the largest HH outflows might be formed when multiple–star systems disintegrate. It is thought that most stars originate from multiple star systems, but that a sizable fraction of these systems are disrupted before their stars reach the main sequence due to gravitational interactions with nearby stars and dense clouds of gas.

Around proto-brown dwarfs

The first and currently only (as of May 2017) large-scale Herbig-Haro object around a proto-brown dwarf is HH 1165, which is connected to the proto-brown dwarf Mayrit 1701117. HH 1165 has a length of 0.8 light-years (0.26 parsec) and is located in the vicinity of the sigma Orionis cluster. Previously only small mini-jets (≤0.03 parsec) were found around proto-brown dwarfs.

Infrared counterparts

HH objects associated with very young stars or very massive protostars are often hidden from view at optical wavelengths by the cloud of gas and dust from which they form. The intervening material can diminish the visual magnitude by factors of tens or even hundreds at optical wavelengths. Such deeply embedded objects can only be observed at infrared or radio wavelengths, usually in the frequencies of hot molecular hydrogen or warm carbon monoxide emission. In recent years, infrared images have revealed dozens of examples of "infrared HH objects". Most look like bow waves (similar to the waves at the head of a ship), and so are usually referred to as molecular "bow shocks". The physics of infrared bow shocks can be understood in much the same way as that of HH objects, since these objects are essentially the same – supersonic shocks driven by collimated jets from the opposite poles of a protostar. It is only the conditions in the jet and surrounding cloud that are different, causing infrared emission from molecules rather than optical emission from atoms and ions. In 2009 the acronym "MHO", for Molecular Hydrogen emission-line Object, was approved for such objects, detected in near infrared, by the International Astronomical Union Working Group on Designations, and has been entered into their on-line Reference Dictionary of Nomenclature of Celestial Objects. The MHO catalog contains over 2000 objects.

Orion Molecular Cloud Complex

From Wikipedia, the free encyclopedia
 
Orion Molecular Cloud Complex
Molecular cloud
Molecular cloud complex
Orion Head to Toe.jpg
Part of the Orion Molecular Cloud Complex, with the Great Nebula in Orion near the center, along with the Belt of Orion, and Barnard's Loop curling around the image
Observation data: J2000.0 epoch
Right ascension 05h 35.3m
Declination−05° 23′
ConstellationOrion

DesignationsOrion Complex, Orion Cloud Complex, Orion Molecular Cloud Complex

The Orion Molecular Cloud Complex (or, simply, the Orion Complex) is a star forming region with stellar ages ranging up to 12 Myr. Two giant molecular clouds are a part of it, Orion A and Orion B. The stars currently forming within the Complex are located within these clouds. A number of other somewhat older stars no longer associated with the molecular gas are also part of the Complex, most notably the Orion's Belt (Orion OB1b), as well as the dispersed population north of it (Orion OB1a). Near the head of Orion there is also a population of young stars that is centered on Meissa. The Complex is between 1 000 and 1 400 light-years away, and hundreds of light-years across.

The Orion Complex is one of the most active regions of nearby stellar formation visible in the night sky, and is home to both protoplanetary discs and very young stars. Much of it is bright in infrared wavelengths due to the heat-intensive processes involved in stellar formation, though the complex contains dark nebulae, emission nebulae, reflection nebulae, and H II regions. The presence of ripples on the surface of Orion's Molecular Clouds was discovered in 2010. The ripples are a result of the expansion of the nebulae gas over pre-existing molecular gas.

The Orion Complex includes a large group of bright nebulae, dark clouds in the Orion constellation. Several nebulae can be observed through binoculars and small telescopes, and some parts (such as the Orion Nebula) are visible to the naked eye.

Nebulae within the complex

A labeled map of the Orion Molecular Cloud, with the images taken by IRAS and various telescopes that mapped CO in this part of the sky

The following is a list of notable regions within the larger Complex:

A more complete list can be found for example in Maddalena et al. (1986) Table 1

Individual components

Young stars in Orion A and Orion B molecular clouds. The clouds were imaged by Herschel and the newborn stars were imaged by ALMA and the VLA.

Orion A

The giant molecular cloud Orion A is the most active star-forming region in the local neighbourhood of the sun. In the last few million years about 3000 young stellar objects were formed in this region, including about 190 protostars and about 2600 pre-main sequence stars. The Orion A cloud has a mass in the order of 105 M. The stars in Orion A do not have the same distance to us. The "head" of the cloud, which also contains the Orion Nebula is about 1300 light-years (400 parsec) away from the sun. The "tail" however is up to 1530 light-years (470 parsec) away from the sun. The Orion A cloud is therefore longer than the projected length of 130 light-years (40 parsec) and has a true length of 290 light-years (90 parsec).

Orion B

Orion B is about 1370 light-years (420 parsec) distant to Earth. It has a size of about 1.5 kpc² and a mass in the order of 105 M. It contains several star forming regions with the star cluster inside the Flame Nebula being the largest cluster.

Orion OB1 association

The Orion OB1 association represents different stellar populations that are superimposed along our line of sight. The oldest group with 8-10 million years is Orion OB1a, northwest of Orion's Belt, and the youngest group with less than 2 million years is Orion OB1d, which contains the Orion Nebula cluster and NGC 2024.

Lambda Orionis molecular ring

The Lambda Orionis ring is a large molecular ring, centered around Lambda Orioinis (Meissa). It was suggested that this ring formed after a supernova happened inside the central star-forming region that once surrounded the Lambda Orionis Cluster, dispersing the material into the ring seen today. Star-formation is still continuing in regions of the ring.

Superbubble

Parts of the Orion-Eridanus superbubble were first seen as Barnard's Loop in Hydrogen-alpha images that warp around the eastern portion of Orion. The other part of the superbubble that is seen in H-alpha is the Eridanus Loop. The walls of the entire bubble are seen in far-infrared and HI. Some features of the Eridanus Loop might be as close as 590 light-years (180 parsec) to the sun.

Gallery

Lie point symmetry

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