A dwarf galaxy is a small galaxy composed of about 1000 up to several billion stars, as compared to the Milky Way's 200–400 billion stars. The Large Magellanic Cloud, which closely orbits the Milky Way and contains over 30 billion stars,
is sometimes classified as a dwarf galaxy; others consider it a
full-fledged galaxy. Dwarf galaxies' formation and activity are thought
to be heavily influenced by interactions with larger galaxies.
Astronomers identify numerous types of dwarf galaxies, based on their
shape and composition.
Formation
Dwarf galaxies like NGC 5264 typically possess around a billion stars.
The Phoenix Dwarf Galaxy is a dwarf irregular galaxy, featuring younger stars in its inner regions and older ones at its outskirts.
There are many dwarf galaxies in the Local Group; these small galaxies frequently orbit larger galaxies, such as the Milky Way, the Andromeda Galaxy and the Triangulum Galaxy. A 2007 paper has suggested that many dwarf galaxies were created by galactic tides
during the early evolutions of the Milky Way and Andromeda. Tidal dwarf
galaxies are produced when galaxies collide and their gravitational masses interact. Streams of galactic material are pulled away from the parent galaxies and the halos of dark matter that surround them. A 2018 study suggests that some local dwarf galaxies formed extremely early, during the Dark Ages within the first billion years after the Big Bang.
More than 20 known dwarf galaxies orbit the Milky Way, and recent observations have also led astronomers to believe the largest globular cluster in the Milky Way, Omega Centauri, is in fact the core of a dwarf galaxy with a black hole at its centre, which was at some time absorbed by the Milky Way.
Common types
UGC 11411 is a galaxy known as an irregular blue compact dwarf (BCD) galaxy.
In astronomy, a blue compact dwarf galaxy (BCD galaxy) is a small galaxy which contains large clusters of young, hot, massive stars. These stars, the brightest of which are blue, cause the galaxy itself to appear blue in colour. Most BCD galaxies are also classified as dwarf irregular galaxies or as dwarf lenticular galaxies.
Because they are composed of star clusters, BCD galaxies lack a uniform
shape. They consume gas intensely, which causes their stars to become
very violent when forming.
BCD galaxies cool in the process of forming new stars.
The galaxies' stars are all formed at different time periods, so the
galaxies have time to cool and to build up matter to form new stars. As
time passes, this star formation changes the shape of the galaxies.
Ultra-faint dwarf galaxies (UFDs) are a class of galaxies that contain from a few hundred to one hundred thousand stars, making them the faintest galaxies in the Universe. UFDs resemble globular clusters (GCs) in appearance but have very different properties. Unlike GCs, UFDs contain a significant amount of dark matter and are more extended. UFDs were first discovered with the advent of digital sky surveys in 2005, in particular with the Sloan Digital Sky Survey (SDSS).
UFDs are the most dark matter-dominated systems known. Astronomers believe that UFDs encode valuable information about the early Universe, as all UFDs discovered so far are ancient systems that have likely formed very early on, only a few million years after the Big Bang and before the epoch of reionization.
Recent theoretical work has hypothesised the existence of a population
of young UFDs that form at a much later time than the ancient UFDs. These galaxies have not been observed in our Universe so far.
Ultra-compact dwarfs
Ultra-compact dwarf galaxies (UCD) are a class of very compact galaxies with very high stellar densities,
discovered in the 2000s.
They are thought to be on the order of 200 light years across, containing about 100 million stars.
It is theorised that these are the cores of nucleated dwarf elliptical
galaxies that have been stripped of gas and outlying stars by tidal interactions, travelling through the hearts of rich clusters. UCDs have been found in the Virgo Cluster, Fornax Cluster, Abell 1689, and the Coma Cluster, amongst others.
In particular, an unprecedentedly large sample of ~ 100 UCDs has been
found in the core region of the Virgo cluster by the Next Generation
Virgo Cluster Survey team. The first ever relatively robust studies of the global properties of Virgo UCDs suggest that
UCDs have distinct dynamical
and structural properties from normal globular clusters. An extreme example of UCD is M60-UCD1,
about 54 million light years away, which contains approximately 200
million solar masses within a 160 light year radius; the stars in its
central region are packed 25 times more densely than stars in Earth's
region in the Milky Way.
M59-UCD3 is approximately the same size as M60-UCD1 with a half-light radius, rh, of approximately 20 parsecs but is 40% more luminous with an absolute visual magnitude of approximately −14.6. This makes M59-UCD3 the densest known galaxy.
Based on stellar orbital velocities, two UCD in the Virgo Cluster are claimed to have supermassive black holes weighing 13% and 18% of the galaxies' masses.
Omega Centauri (ω Cen, NGC 5139, or Caldwell 80) is a globular cluster in the constellation of Centaurus that was first identified as a non-stellar object by Edmond Halley in 1677. Located at a distance of 17,090 light-years (5,240 parsecs), it is the largest-known globular cluster in the Milky Way at a diameter of roughly 150 light-years. It is estimated to contain approximately 10 million stars, with a total mass of 4 million solar masses, making it the most massive known globular cluster in the Milky Way.
Omega Centauri is very different from most other galactic
globular clusters to the extent that it is thought to have originated as
the core remnant of a disrupted dwarf galaxy.
Observation history
Around 150 AD, Greco-Roman writer and astronomer Ptolemy catalogued this object in his Almagest as a star on the centaur's back, "Quae est in principio scapulae". German cartographer Johann Bayer used Ptolemy's data to designate this object "Omega Centauri" with his 1603 publication of Uranometria. Using a telescope from the South Atlantic island of Saint Helena, English astronomer Edmond Halley
rediscovered this object in 1677, listing it as a non-stellar object.
In 1716, it was published by Halley among his list of six "luminous
spots or patches" in the Philosophical Transactions of the Royal Society.
Swiss astronomer Jean-Philippe de Cheseaux included Omega Centauri in his 1746 list of 21 nebulae, as did French astronomer Lacaille in 1755, whence the catalogue number is designated L I.5. It was first recognized as a globular cluster by Scottish astronomer James Dunlop in 1826, who described it as a "beautiful globe of stars very gradually and moderately compressed to the centre".
Properties
At a distance of about 15,800 light-years (4,800 parsecs) from Earth, Omega Centauri is one of the few globular clusters visible to the naked eye—and appears almost as large as the full Moon when seen from a dark, rural area. It is the brightest, largest and, at 4 million solar masses, the most massive-known globular cluster associated with the Milky Way. Of all the globular clusters in the Local Group of galaxies, only Mayall II in the Andromeda Galaxy is brighter and more massive. Orbiting through the Milky Way, Omega Centauri contains several million Population II stars and is about 12 billion years old.
The stars in the core of Omega Centauri are so crowded that they
are estimated to average only 0.1 light-year away from each other. The internal dynamics have been analyzed using measurements of the radial velocities of 469 stars. The members of this cluster are orbiting the center of mass with a peak velocity dispersion of 7.9 km s−1.
The mass distribution inferred from the kinematics is slightly more
extended than, though not strongly inconsistent with, the luminosity
distribution.
Evidence of a central black hole
The
central region of Omega Centauri. The lower illustration charts the
future positions of the stars highlighted by the white box in the top
image. Each streak represents the star's predicted motion over the next
600 years. The period between dots corresponds to 30 years. October 2010
A 2008 study presented evidence for an intermediate-mass black hole at the center of Omega Centauri, based on observations made by the Hubble Space Telescope and Gemini Observatory on Cerro Pachón in Chile. Hubble's Advanced Camera for Surveys
showed that stars are bunching up near the center of Omega Centauri, as
evidenced by the gradual increase in starlight near the center. Using
instruments at the Gemini Observatory to measure the speed of stars
swirling in the cluster's core, E. Noyola and colleagues found that
stars closer to the core are moving faster than stars farther away. This
measurement was interpreted to mean that unseen matter at the core is
interacting gravitationally with nearby stars. By comparing these
results with standard models, the astronomers concluded that the most
likely cause was the gravitational pull of a dense, massive object such
as a black hole. They calculated the object's mass at 40,000 solar masses.
More recent work has challenged conclusions that there is a black
hole in the cluster's core, in particular disputing the proposed
location of the cluster center.Calculations using a revised location for the center found that the
velocity of core stars does not vary with distance, as would be expected
if an intermediate-mass black hole were present. The same studies also
found that starlight does not increase toward the center but instead
remains relatively constant. The authors noted that their results do not
entirely rule out the black hole proposed by Noyola and colleagues, but
they do not confirm it, and they limit its maximum mass to 12,000 solar
masses.
Disrupted dwarf galaxy
It has been speculated that Omega Centauri is the core of a dwarf galaxy that was disrupted and absorbed by the Milky Way. Indeed, Kapteyn's Star, which is currently only 13 light-years away from Earth, is thought to originate from Omega Centauri. Omega Centauri's chemistry and motion in the Milky Way are also consistent with this picture. Like Mayall II, Omega Centauri has a range of metallicities
and stellar ages that suggests that it did not all form at once (as
globular clusters are thought to form) and may in fact be the remainder
of the core of a smaller galaxy long since incorporated into the Milky
Way.
In fiction
The novel Singularity (2012), by Ian Douglas, presents as fact that Omega Centauri and Kapteyn's Star
originate from a disrupted dwarf galaxy, and this origin is central to
the novel's plot. A number of scientific aspects of Omega Centauri are
discussed as the story progresses, including the likely radiation
environment inside the cluster and what the sky might look like from
inside the cluster.
Newly observed active regions on the solar disk are assigned 4-digit region numbers by the Space Weather Prediction Center
(SWPC) on the day following the initial observation. The region number
assigned to a particular active region is one added to the previously
assigned number. For example, the first observation of active region
8090, or AR8090, was followed by AR8091.
According to the SWPC, a number is assigned to a region if it meets at least one of the following criteria:
It contains a sunspot group of class C or larger based on the Modified Zurich Class sunspot classification system.
It contains a sunspot group of class A or B confirmed by at least
two observers, preferably with observations more than one hour apart.
It has produced a solar flare with an X-ray burst.
It contains plage with a white-light brightness of at least 2.5 (on a linear scale 1-5, 5=flare) and has an extent of at least five heliographic degrees.
It contains plage that is bright near the west limb and is suspected of growing.
The region numbers reached 10,000 in July 2002. However, the SWPC continued using 4-digits, with the inclusion of leading zeros.
Magnetic field
A highly simplified diagram of the magnetic field of an active region illustrating its bipolar nature.
Mount Wilson magnetic classification
The
Mount Wilson magnetic classification system, also known as the Hale
magnetic classification system, is a method of classifying the magnetic
field of active regions. It was first introduced in 1919 by George Ellery Hale and coworkers working at the Mount Wilson Observatory.
It originally included only the α, β, and γ magnetic classifications,
but it was later modified by H. Künzel in 1965 to include the δ
qualifier.
An active region containing a single sunspot or group of sunspots
all having the same magnetic polarity. An opposite polarity counterpart
is still present, but is weak or not concentrated enough to form
sunspots.
An active region with at least two sunspots or sunspot groups that
have opposite magnetic polarity. A simple neutral line between the two
polarities is also present.
An active region with sunspots having completely intermixed magnetic polarity.
β-γ
An active region with at least two sunspots or sunspot groups that
have opposite magnetic polarity (hence β) but no well-defined neutral
line dividing the opposite polarities (hence γ).
A qualifier to the other classes indicating the presence of opposite
polarity umbrae within a single penumbra separated by at most 2° in
heliographic distance.
β-δ
An active region with a β magnetic field and at least one pair of opposite polarity umbrae within a single penumbra (hence δ).
β-γ-δ
An active region with a β-γ magnetic field and at least one pair of opposite polarity umbrae within a single penumbra (hence δ).
γ-δ
An active region with a γ magnetic field and at least one pair of opposite polarity umbrae within a single penumbra (hence δ).
An active region seen in visible light showing a group of sunspots.
The strong magnetic flux found in active regions is often strong enough to inhibit convection.
Without convection transporting energy from the Sun's interior to the
photosphere, surface temperature decreases along with the intensity of
emitted black body radiation. These areas of cooler plasma are known as sunspots, and often appear in groups. However, not all active regions possess sunspots.
Magnetic flux emergence
Active regions form through the process of magnetic flux emergence, during which magnetic fields generated by the solar dynamo emerge from the solar interior.
A galactic halo is an extended, roughly spherical component of a galaxy which extends beyond the main, visible component. Several distinct components of a galaxy comprise its halo:
The distinction between the halo and the main body of the galaxy is clearest in spiral galaxies, where the spherical shape of the halo contrasts with the flat disc. In an elliptical galaxy, there is no sharp transition between the other components of the galaxy and the halo.
A halo can be studied by observing its effect on the passage of light from distant bright objects like quasars that are in line of sight beyond the galaxy in question.
Components of the galactic halo
Stellar halo
The stellar halo is a nearly spherical population of field stars and globular clusters. It surrounds most disk galaxies as well as some elliptical galaxies of type cD.
A low amount (about one percent) of a galaxy's stellar mass resides in
the stellar halo, meaning its luminosity is much lower than other
components of the galaxy.
The Milky Way's stellar halo contains globular clusters, RR Lyrae stars with low metal content, and subdwarfs.
In our stellar halo, stars tend to be old (most are greater than 12
billion years old) and metal-poor, but there are also halo star clusters
with observed metal content similar to disk stars.
The halo stars of the Milky Way have an observed radial velocity
dispersion of about 200 km/s and a low average velocity of rotation of
about 50 km/s. Star formation in the stellar halo of the Milky Way ceased long ago.
Galactic corona
A
galactic corona is a distribution of gas extending far away from the
center of the galaxy. It can be detected by the distinct emission
spectrum it gives off, showing the presence of HI gas (H one, 21 cm microwave line) and other features detectable by X-ray spectroscopy.
Dark matter halo
The dark matter halo is a theorized distribution of dark matter
which extends throughout the galaxy extending far beyond its visible
components. The mass of the dark matter halo is far greater than the
mass of the other components of the galaxy. Its existence is
hypothesized in order to account for the gravitational potential that
determines the dynamics of bodies within galaxies. The nature of dark
matter halos is an important area in current research in cosmology, in particular its relation to galactic formation and evolution.
The Navarro–Frenk–White profile is a widely accepted density profile of the dark matter halo determined through numerical simulations. It represents the mass density of the dark matter halo as a function of , the distance from the galactic center:
where is a characteristic radius for the model, is the critical density (with being the Hubble constant), and
is a dimensionless constant. The invisible halo component cannot extend
with this density profile indefinitely, however; this would lead to a
diverging integral when calculating mass. It does, however, provide a
finite gravitational potential for all . Most measurements that can be made are relatively insensitive to the outer halo's mass distribution. This is a consequence of Newton's laws,
which state that if the shape of the halo is spheroidal or elliptical
there will be no net gravitational effect from halo mass a distance from the galactic center on an object that is closer to the galactic center than . The only dynamical variable related to the extent of the halo that can be constrained is the escape velocity:
the fastest-moving stellar objects still gravitationally bound to the
Galaxy can give a lower bound on the mass profile of the outer edges of
the dark halo.
Formation of galactic halos
The formation of stellar halos occurs naturally in a cold dark matter
model of the universe in which the evolution of systems such as halos
occurs from the bottom-up, meaning the large scale structure of galaxies
is formed starting with small objects. Halos, which are composed of
both baryonic
and dark matter, form by merging with each other. Evidence suggests
that the formation of galactic halos may also be due to the effects of
increased gravity and the presence of primordial black holes.
The gas from halo mergers goes toward the formation of the central
galactic components, while stars and dark matter remain in the galactic
halo.
On the other hand, the halo of the Milky Way Galaxy is thought to derive from the Gaia Sausage.
Meteorites are often studied as part of cosmochemistry.
Cosmochemistry (from Ancient Greekκόσμος (kósmos) 'universe', and χημεία (khēmeía) 'chemistry') or chemical cosmology is the study of the chemical composition of matter in the universe and the processes that led to those compositions. This is done primarily through the study of the chemical composition of meteorites and other physical samples. Given that the asteroid parent bodies of meteorites were some of the first solid material to condense from the early solar nebula, cosmochemists are generally, but not exclusively, concerned with the objects contained within the Solar System.
History
In 1938, Swiss mineralogist Victor Goldschmidt
and his colleagues compiled a list of what they called "cosmic
abundances" based on their analysis of several terrestrial and meteorite
samples.
Goldschmidt justified the inclusion of meteorite composition data into
his table by claiming that terrestrial rocks were subjected to a
significant amount of chemical change due to the inherent processes of
the Earth and the atmosphere. This meant that studying terrestrial rocks
exclusively would not yield an accurate overall picture of the chemical
composition of the cosmos. Therefore, Goldschmidt concluded that
extraterrestrial material must also be included to produce more accurate
and robust data. This research is considered to be the foundation of
modern cosmochemistry.
During the 1950s and 1960s, cosmochemistry became more accepted as a science. Harold Urey, widely considered to be one of the fathers of cosmochemistry,
engaged in research that eventually led to an understanding of the
origin of the elements and the chemical abundance of stars. In 1956,
Urey and his colleague, German scientist Hans Suess, published the first table of cosmic abundances to include isotopes based on meteorite analysis.
The continued refinement of analytical instrumentation throughout the 1960s, especially that of mass spectrometry, allowed cosmochemists to perform detailed analyses of the isotopic abundances of elements within meteorites. in 1960, John Reynolds
determined, through the analysis of short-lived nuclides within
meteorites, that the elements of the Solar System were formed before the
Solar System itself which began to establish a timeline of the processes of the early Solar System.
Meteorites
Meteorites
are one of the most important tools that cosmochemists have for
studying the chemical nature of the Solar System. Many meteorites come
from material that is as old as the Solar System itself, and thus
provide scientists with a record from the early solar nebula. Carbonaceous chondrites
are especially primitive; that is they have retained many of their
chemical properties since their formation 4.56 billion years ago, and are therefore a major focus of cosmochemical investigations.
The most primitive meteorites also contain a small amount of material (< 0.1%) which is now recognized to be presolar grains
that are older than the Solar System itself, and which are derived
directly from the remnants of the individual supernovae that supplied
the dust from which the Solar System formed. These grains are
recognizable from their exotic chemistry which is alien to the Solar
System (such as matrixes of graphite, diamond, or silicon carbide). They
also often have isotope ratios which are not those of the rest of the
Solar System (in particular, the Sun), and which differ from each other,
indicating sources in a number of different explosive supernova events.
Meteorites also may contain interstellar dust grains, which have
collected from non-gaseous elements in the interstellar medium, as one
type of composite cosmic dust ("stardust").
On 30 July 2015, scientists reported that upon the first touchdown of the Philae lander on comet67/P's surface, measurements by the COSAC and Ptolemy instruments revealed sixteen organic compounds, four of which were seen for the first time on a comet, including acetamide, acetone, methyl isocyanate and propionaldehyde.
In 2004, scientists reported detecting the spectral signatures of anthracene and pyrene in the ultraviolet light emitted by the Red Rectangle nebula
(no other such complex molecules had ever been found before in outer
space). This discovery was considered a confirmation of a hypothesis
that as nebulae of the same type as the Red Rectangle approach the ends
of their lives, convection currents cause carbon and hydrogen in the
nebulae's core to get caught in stellar winds, and radiate outward.
As they cool, the atoms supposedly bond to each other in various ways
and eventually form particles of a million or more atoms. The scientists
inferred that since they discovered polycyclic aromatic hydrocarbons
(PAHs)—which may have been vital in the formation of early life on
Earth—in a nebula, by necessity they must originate in nebulae.
In August 2009, NASA scientists identified one of the fundamental chemical building-blocks of life (the amino acid glycine) in a comet for the first time.
In 2010, fullerenes (or "buckyballs") were detected in nebulae.
Fullerenes have been implicated in the origin of life; according to
astronomer Letizia Stanghellini, "It's possible that buckyballs from
outer space provided seeds for life on Earth."
In August 2011, findings by NASA, based on studies of meteorites found on Earth, suggests DNA and RNA components (adenine, guanine and related organic molecules), building blocks for life as we know it, may be formed extraterrestrially in outer space.
In October 2011, scientists reported that cosmic dust contains complex organic matter ("amorphous organic solids with a mixed aromatic-aliphatic structure") that could be created naturally, and rapidly, by stars.
On August 29, 2012, astronomers at Copenhagen University reported the detection of a specific sugar molecule, glycolaldehyde, in a distant star system. The molecule was found around the protostellar binary IRAS 16293-2422, which is located 400 light years from Earth. Glycolaldehyde is needed to form ribonucleic acid, or RNA, which is similar in function to DNA.
This finding suggests that complex organic molecules may form in
stellar systems prior to the formation of planets, eventually arriving
on young planets early in their formation.
In 2013, the Atacama Large Millimeter Array (ALMA Project) confirmed that researchers have discovered an important pair of prebiotic molecules in the icy particles in interstellar space
(ISM). The chemicals, found in a giant cloud of gas about 25,000
light-years from Earth in ISM, may be a precursor to a key component of
DNA and the other may have a role in the formation of an important amino acid. Researchers found a molecule called cyanomethanimine, which produces adenine, one of the four nucleobases that form the "rungs" in the ladder-like structure of DNA. The other molecule, called ethanamine, is thought to play a role in forming alanine,
one of the twenty amino acids in the genetic code. Previously,
scientists thought such processes took place in the very tenuous gas
between the stars. The new discoveries, however, suggest that the
chemical formation sequences for these molecules occurred not in gas,
but on the surfaces of ice grains in interstellar space.
NASA ALMA scientist Anthony Remijan stated that finding these molecules
in an interstellar gas cloud means that important building blocks for
DNA and amino acids can 'seed' newly formed planets with the chemical
precursors for life.
In physics, relativistic beaming (also known as Doppler beaming, Doppler boosting, or the headlight effect) is the process by which relativistic effects modify the apparent luminosity of emitting matter that is moving at speeds close to the speed of light. In an astronomical context, relativistic beaming commonly occurs in two oppositely-directed relativistic jets of plasma that originate from a central compact object that is accreting matter. Accreting compact objects and relativistic jets are invoked to explain x-ray binaries, gamma-ray bursts, and, on a much larger scale, active galactic nuclei (quasars
are also associated with an accreting compact object, but are thought
to be merely a particular variety of active galactic nuclei, or AGNs).
Beaming affects the apparent brightness of a moving object.
Consider a cloud of gas moving relative to the observer and emitting
electromagnetic radiation. If the gas is moving towards the observer, it
will be brighter than if it were at rest, but if the gas is moving
away, it will appear fainter. The magnitude of the effect is illustrated
by the AGN jets of the galaxies M87 and 3C 31
(see images at right). M87 has twin jets aimed almost directly towards
and away from Earth; the jet moving towards Earth is clearly visible
(the long, thin blueish feature in the top image), while the other jet
is so much fainter it is not visible.
In 3C 31, both jets (labeled in the lower figure) are at roughly right
angles to our line of sight, and thus, both are visible. The upper jet
actually points slightly more in Earth's direction and is therefore
brighter.
Relativistically moving objects are beamed due to a variety of physical effects. Light aberration causes most of the photons to be emitted along the object's direction of motion. The Doppler effect
changes the energy of the photons by red- or blue-shifting them.
Finally, time intervals as measured by clocks moving alongside the
emitting object are different from those measured by an observer on
Earth due to time dilation
and photon arrival time effects. How all of these effects modify the
brightness, or apparent luminosity, of a moving object is determined by
the equation describing the relativistic Doppler effect (which is why relativistic beaming is also known as Doppler beaming).
A simple jet model
The
simplest model for a jet is one where a single, homogeneous sphere is
travelling towards the Earth at nearly the speed of light. This simple
model is also an unrealistic one, but it does illustrate the physical
process of beaming quite well.
Synchrotron spectrum and the spectral index
Relativistic jets emit most of their energy via synchrotron emission.
In our simple model the sphere contains highly relativistic electrons
and a steady magnetic field. Electrons inside the blob travel at speeds
just a tiny fraction below the speed of light and are whipped around by
the magnetic field. Each change in direction by an electron is
accompanied by the release of energy in the form of a photon. With
enough electrons and a powerful enough magnetic field the relativistic
sphere can emit a huge number of photons, ranging from those at
relatively weak radio frequencies to powerful X-ray photons.
The figure of the sample spectrum shows basic features of a
simple synchrotron spectrum. At low frequencies the jet sphere is opaque
and its luminosity increases with frequency until it peaks and begins
to decline. In the sample image this peak frequency occurs at . At frequencies higher than this the jet sphere is transparent. The luminosity decreases with frequency until a break frequency is reached, after which it declines more rapidly. In the same image the break frequency occurs when .
The sharp break frequency occurs because at very high frequencies the
electrons which emit the photons lose most of their energy very rapidly.
A sharp decrease in the number of high energy electrons means a sharp
decrease in the spectrum.
The changes in slope in the synchrotron spectrum are parameterized with a spectral index. The spectral index, α, over a given frequency range is simply the slope on a diagram of vs. . (Of course for α to have real meaning the spectrum must be very nearly a straight line across the range in question.)
Beaming equation
In the simple jet model of a single homogeneous sphere the observed luminosity is related to the intrinsic luminosity as
where
The observed luminosity therefore depends on the speed of the jet and
the angle to the line of sight through the Doppler factor, , and also on the properties inside the jet, as shown by the exponent with the spectral index.
The beaming equation can be broken down into a series of three effects:
Relativistic aberration
Time dilation
Blue- or redshifting
Aberration
Aberration is the change in an object's apparent direction caused by the relative transverse motion of the observer. In inertial systems it is equal and opposite to the light time correction.
In everyday life aberration is a well-known phenomenon. Consider a
person standing in the rain on a day when there is no wind. If the
person is standing still, then the rain drops will follow a path that is
straight down to the ground. However, if the person is moving, for
example in a car, the rain will appear to be approaching at an angle.
This apparent change in the direction of the incoming raindrops is
aberration.
The amount of aberration depends on the speed of the emitted
object or wave relative to the observer. In the example above this would
be the speed of a car compared to the speed of the falling rain. This
does not change when the object is moving at a speed close to .
Like the classic and relativistic effects, aberration depends on: 1)
the speed of the emitter at the time of emission, and 2) the speed of
the observer at the time of absorption.
In the case of a relativistic jet, beaming (emission aberration)
will make it appear as if more energy is sent forward, along the
direction the jet is traveling. In the simple jet model a homogeneous
sphere will emit energy equally in all directions in the rest frame of
the sphere. In the rest frame of Earth the moving sphere will be
observed to be emitting most of its energy along its direction of
motion. The energy, therefore, is ‘beamed’ along that direction.
Quantitatively, aberration accounts for a change in luminosity of
Time dilation
Time dilation is a well-known consequence of special relativity and accounts for a change in observed luminosity of
Blue- or redshifting
Blue- or redshifting can change the observed luminosity at a particular frequency, but this is not a beaming effect.
Blueshifting accounts for a change in observed luminosity of
Lorentz invariants
A more-sophisticated method of deriving the beaming equations starts with the quantity . This quantity is a Lorentz invariant, so the value is the same in different reference frames.
Terminology
beamed, beaming
shorter terms for ‘relativistic beaming’
beta
the ratio of the jet speed to the speed of light, sometimes called ‘relativistic beta’
the jet on the far side of a source oriented close to the line of sight, can be very faint and difficult to observe
Doppler factor
a mathematical expression which measures the strength (or weakness) of relativistic effects in AGN, including beaming, based on the jet speed and its angle to the line of sight with Earth
flat spectrum
a term for a non-thermal spectrum that emits a great deal of energy at the higher frequencies when compared to the lower frequencies
intrinsic luminosity
the luminosity from the jet in the rest frame of the jet
a high velocity (close to c) stream of plasma emanating from the polar direction of an AGN
observed luminosity
the luminosity from the jet in the rest frame of Earth
spectral index
a measure of how a non-thermal spectrum changes with frequency. The smaller α is, the more significant the energy at higher frequencies is. Typically α is in the range of 0 to 2.
steep spectrum
a term for a non-thermal spectrum that emits little energy at the higher frequencies when compared to the lower frequencies
![{\displaystyle {\begin{smallmatrix}\left[{\ce {Fe}}/{\ce {H}}\right]\end{smallmatrix}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4c0821bd80891e071c08e7c7ee8e022baedf522c)
_meteorite.jpg)
