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
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.
A more complete list can be found for example in Maddalena et al. (1986) Table 1
Individual components
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 105M☉. 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 parsecs)
away from the Sun. The "tail" however is up to 1530 light-years (470
parsecs) away from the Sun. The Orion A cloud is therefore longer than
the projected length of 130 light-years (40 parsecs) and has a true
length of 290 light-years (90 parsecs).
Orion Molecular Clouds
The Orion Molecular Clouds
(OMC 1 to OMC 4) are molecular clouds located behind the Orion Nebula.
Most of the light from the OMCs are blocked by material from the Orion
Nebula, but some features like the Kleinmann-Low Nebula and the Becklin-Neugebauer object can be seen in the infrared. The clouds can be seen in the far-infrared and in radio wavelengths. The Trapezium Cluster
has a small angular separation from the Kleinmann-Low Nebula, but the
Trapezium Cluster is located inside the Orion Nebula, which is closer
towards Earth.
Orion B
Orion B is about 1370 light-years (420 parsecs) from Earth. It has a size of about 1.5 kpc² and a mass in the order of 105M☉. It contains several star forming regions with the star cluster inside the Flame Nebula being the largest cluster.
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.
The Lambda Orionis ring is a large molecular ring, centered around Lambda Orioinis (Meissa). It was suggested that this ring formed after a supernova occurred 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.
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
parsecs) to the Sun.
Hydrodynamic
escape occurs if there is a strong thermally driven atmospheric escape
of light atoms which, through drag effects (collisions), also drive off
heavier atoms. The heaviest species of atom that can be removed in this manner is called the cross-over mass.
In order to maintain a significant hydrodynamic escape, a large source of energy at a certain altitude is required. Soft X-ray or extreme ultraviolet radiation, momentum transfer from impacting meteoroids or asteroids, or the heat input from planetary accretion processes may provide the requisite energy for hydrodynamic escape.
Calculations
Estimating
the rate of hydrodynamic escape is important in analyzing both the
history and current state of a planet's atmosphere. In 1981, Watson et
al. published
calculations that describe energy-limited escape, where all incoming
energy is balanced by escape to space. Recent numerical simulations on
exoplanets have suggested that this calculation overestimates the
hydrodynamic flux by 20 - 100 times. However, as a special case and upper limit approximation on the atmospheric escape, it is worth noting here.
Hydrodynamic escape flux (Φ, [m-2s-1]) in an energy-limited escape can be calculated, assuming (1) an atmosphere composed of non-viscous, (2) constant-molecular-weight gas, with (3) isotropic pressure, (4) fixed temperature, (5) perfect extreme ultraviolet (XUV) absorption, and that (6) pressure decreases to zero as distance from the planet increases.
RXUV is the effective radius where the XUV absorption occurs [m].
Corrections to this model have been proposed over the years to account for the Roche lobe of a planet and efficiency in absorbing photon flux.
However, as computational power has improved, increasingly sophisticated models have emerged, incorporating radiative transfer, photochemistry, and hydrodynamics that provide better estimates of hydrodynamic escape.
Isotope fractionation as evidence
The root mean square thermal velocity (vth) of an atomic species is
where k is the Boltzmann constant, T is the temperature, and m
is the mass of the species.
Lighter molecules or atoms will therefore be moving faster than heavier
molecules or atoms at the same temperature. This is why atomic hydrogen
escapes preferentially from an atmosphere and also explains why the
ratio of lighter to heavier isotopes of atmospheric particles can indicate hydrodynamic escape.
Specifically, the ratio of different noble gas isotopes (20Ne/22Ne, 36Ar/38Ar, 78,80,82,83,86Kr/84Kr, 124,126,128,129,131,132,134,136Xe/130Xe) or hydrogen isotopes (D/H)
can be compared to solar levels to indicate likelihood of hydrodynamic
escape in the atmospheric evolution. Ratios larger or smaller than
compared with that in the sun or CI chondrites,
which are used as proxy for the sun, indicate that significant
hydrodynamic escape has occurred since the formation of the planet.
Since lighter atoms preferentially escape, we expect smaller ratios for
the noble gas isotopes (or a larger D/H) correspond to a greater
likelihood of hydrodynamic escape, as indicated in the table.
Isotopic fractionation in Venus, Earth, and Mars
Source
36Ar/38Ar
20Ne/22Ne
82Kr/84Kr
128Xe/130Xe
Sun
5.8
13.7
20.501
50.873
CI chondrites
5.3±0.05
8.9±1.3
20.149±0.080
50.73±0.38
Venus
5.56±0.62
11.8±0.7
--
--
Earth
5.320±0.002
9.800±0.08
20.217±0.021
47.146±0.047
Mars
4.1±0.2
10.1±0.7
20.54±0.20
47.67±1.03
Matching these ratios can also be used to validate or verify
computational models seeking to describe atmospheric evolution. This
method has also been used to determine the escape of oxygen relative to
hydrogen in early atmospheres.
Examples
Exoplanets that are extremely close to their parent star, such as hot Jupiters can experience significant hydrodynamic escape to the point where the star "burns off" their atmosphere upon which they cease to be gas giants and are left with just the core, at which point they would be called Chthonian planets. Hydrodynamic escape has been observed for exoplanets close to their host star, including the hot JupitersHD 209458b.
Within a stellar lifetime, the solar flux may change. Younger stars produce more EUV, and the early protoatmospheres of Earth, Mars, and Venus likely underwent hydrodynamic escape, which accounts for the noble gas isotope fractionation present in their atmospheres.
Illustration of the dynamo mechanism that generates the Earth's magnetic field: convection currents of fluid metal in the Earth's outer core, driven by heat flow from the inner core, organized into rolls by the Coriolis force, generate circulating electric currents, which supports the magnetic field.[1]
In physics, the dynamo theory proposes a mechanism by which a celestial body such as Earth or a star generates a magnetic field. The dynamo theory describes the process through which a rotating, convecting, and electrically conducting fluid can maintain a magnetic field over astronomical time scales. A dynamo is thought to be the source of the Earth's magnetic field and the magnetic fields of Mercury and the Jovian planets.
History of theory
When William Gilbert published de Magnete
in 1600, he concluded that the Earth is magnetic and proposed the first
hypothesis for the origin of this magnetism: permanent magnetism such
as that found in lodestone. In 1822, André-Marie Ampère proposed that internal currents are responsible of Earth Magnetism. In 1919, Joseph Larmor proposed that a dynamo might be generating the field.However, even after he advanced his hypothesis, some prominent scientists advanced alternative explanations. The Nobel Prize winner Patrick Blackett did a series of experiments looking for a fundamental relation between angular momentum and magnetic moment, but found none.
Walter M. Elsasser,
considered a "father" of the presently accepted dynamo theory as an
explanation of the Earth's magnetism, proposed that this magnetic field
resulted from electric currents induced in the fluid outer core of the
Earth. He revealed the history of the Earth's magnetic field through
pioneering the study of the magnetic orientation of minerals in rocks.
In order to maintain the magnetic field against ohmic decay (which would occur for the dipole field in 20,000 years), the outer core must be convecting. The convection
is likely some combination of thermal and compositional convection.
The mantle controls the rate at which heat is extracted from the core.
Heat sources include gravitational energy released by the compression of
the core, gravitational energy released by the rejection of light
elements (probably sulfur, oxygen, or silicon) at the inner core boundary as it grows, latent heat of crystallization at the inner core boundary, and radioactivity of potassium, uranium and thorium.
At the dawn of the 21st century, numerical modeling of the
Earth's magnetic field has not been successfully demonstrated. Initial
models are focused on field generation by convection in the planet's
fluid outer core. It was possible to show the generation of a strong,
Earth-like field when the model assumed a uniform core-surface
temperature and exceptionally high viscosities for the core fluid.
Computations which incorporated more realistic parameter values yielded
magnetic fields that were less Earth-like, but indicated that model
refinements
may ultimately lead to an accurate analytic model. Slight variations
in the core-surface temperature, in the range of a few millikelvins,
result in significant increases in convective flow and produce more
realistic magnetic fields.
Formal definition
Dynamo
theory describes the process through which a rotating, convecting, and
electrically conducting fluid acts to maintain a magnetic field. This
theory is used to explain the presence of anomalously long-lived
magnetic fields in astrophysical bodies. The conductive fluid in the
geodynamo is liquid iron in the outer core, and in the solar dynamo is ionized gas at the tachocline. Dynamo theory of astrophysical bodies uses magnetohydrodynamic equations to investigate how the fluid can continuously regenerate the magnetic field.
It was once believed that the dipole, which comprises much of the Earth's magnetic field
and is misaligned along the rotation axis by 11.3 degrees, was caused
by permanent magnetization of the materials in the earth. This means
that dynamo theory was originally used to explain the Sun's magnetic
field in its relationship with that of the Earth. However, this
hypothesis, which was initially proposed by Joseph Larmor in 1919, has been modified due to extensive studies of magnetic secular variation, paleomagnetism (including polarity reversals), seismology, and the solar system's abundance of elements. Also, the application of the theories of Carl Friedrich Gauss to magnetic observations showed that Earth's magnetic field had an internal, rather than external, origin.
There are three requisites for a dynamo to operate:
An electrically conductive fluid medium
Kinetic energy provided by planetary rotation
An internal energy source to drive convective motions within the fluid.
In the case of the Earth, the magnetic field is induced and
constantly maintained by the convection of liquid iron in the outer
core. A requirement for the induction of field is a rotating fluid.
Rotation in the outer core is supplied by the Coriolis effect
caused by the rotation of the Earth. The Coriolis force tends to
organize fluid motions and electric currents into columns (also see Taylor columns) aligned with the rotation axis. Induction or generation of magnetic field is described by the induction equation:
where u is velocity, B is magnetic field, t is time, and is the magnetic diffusivity with electrical conductivity and permeability. The ratio of the second term on the right hand side to the first term gives the magnetic Reynolds number, a dimensionless ratio of advection of magnetic field to diffusion.
Tidal heating supporting a dynamo
Tidal
forces between celestial orbiting bodies cause friction that heats up
their interiors. This is known as tidal heating, and it helps keep the
interior in a liquid state. A liquid interior that can conduct
electricity is required to produce a dynamo. Saturn's Enceladus and
Jupiter's Io have enough tidal heating to liquify their inner cores, but
they may not create a dynamo because they cannot conduct electricity.
Mercury, despite its small size, has a magnetic field, because it has a
conductive liquid core created by its iron composition and friction
resulting from its highly elliptical orbit.
It is theorized that the Moon once had a magnetic field, based on
evidence from magnetized lunar rocks, due to its short-lived closer
distance to Earth creating tidal heating. An orbit and rotation of a planet helps provide a liquid core, and supplements kinetic energy that supports a dynamo action.
Kinematic dynamo theory
In kinematic dynamo theory the velocity field is prescribed,
instead of being a dynamic variable: The model makes no provision for
the flow distorting in response to the magnetic field. This method
cannot provide the time variable behaviour of a fully nonlinear chaotic
dynamo, but can be used to study how magnetic field strength varies with
the flow structure and speed.
Using Maxwell's equations simultaneously with the curl of Ohm's law, one can derive what is basically a linear eigenvalue equation for magnetic fields (B), which can be done when assuming that the magnetic field is independent from the velocity field. One arrives at a critical magnetic Reynolds number,
above which the flow strength is sufficient to amplify the imposed
magnetic field, and below which the magnetic field dissipates.
Practical measure of possible dynamos
The
most functional feature of kinematic dynamo theory is that it can be
used to test whether a velocity field is or is not capable of dynamo
action. By experimentally applying a certain velocity field to a small
magnetic field, one can observe whether the magnetic field tends to grow
(or not) in response to the applied flow. If the magnetic field does
grow, then the system is either capable of dynamo action or is a dynamo,
but if the magnetic field does not grow, then it is simply referred to
as “not a dynamo”.
An analogous method called the membrane paradigm is a way of looking at black holes that allows for the material near their surfaces to be expressed in the language of dynamo theory.
Spontaneous breakdown of a topological supersymmetry
Kinematic
dynamo can be also viewed as the phenomenon of the spontaneous
breakdown of the topological supersymmetry of the associated stochastic
differential equation related to the flow of the background matter. Within stochastic supersymmetric theory, this supersymmetry is an intrinsic property of allstochastic differential equations,
its interpretation is that the model’s phase space preserves continuity
via continuous time flows. When the continuity of that flow
spontaneously breaks down, the system is in the stochastic state of deterministic chaos. In other words, kinematic dynamo arises because of chaotic flow in the underlying background matter.
Nonlinear dynamo theory
The
kinematic approximation becomes invalid when the magnetic field becomes
strong enough to affect the fluid motions. In that case the velocity
field becomes affected by the Lorentz force,
and so the induction equation is no longer linear in the magnetic
field. In most cases this leads to a quenching of the amplitude of the
dynamo. Such dynamos are sometimes also referred to as hydromagnetic dynamos.
Virtually all dynamos in astrophysics and geophysics are hydromagnetic dynamos.
The main idea of the theory is that any small magnetic field
existing in the outer core creates currents in the moving fluid there
due to Lorentz force. These currents create further magnetic field due
to Ampere's law. With the fluid motion, the currents are carried in a way that the magnetic field gets stronger (as long as is negative).
Thus a "seed" magnetic field can get stronger and stronger until it
reaches some value that is related to existing non-magnetic forces.
Numerical models are used to simulate fully nonlinear dynamos. The following equations are used:
The induction equation, presented above.
Maxwell's equations for negligible electric field:
The Navier-Stokes equation for conservation of momentum, again in the same approximation, with the magnetic force and gravitation force as the external forces:
A transport equation, usually of heat (sometimes of light element concentration):
where T is temperature, is the thermal diffusivity with k thermal conductivity, heat capacity, and density, and
is an optional heat source. Often the pressure is the dynamic pressure,
with the hydrostatic pressure and centripetal potential removed.
These equations are then non-dimensionalized, introducing the non-dimensional parameters,
Energy conversion between magnetic and kinematic energy
The scalar product of the above form of Navier-Stokes equation with gives the rate of increase of kinetic energy density, , on the left-hand side. The last term on the right-hand side is then , the local contribution to the kinetic energy due to Lorentz force.
The scalar product of the induction equation with gives the rate of increase of the magnetic energy density, , on the left-hand side. The last term on the right-hand side is then Since the equation is volume-integrated, this term is equivalent up to a boundary term (and with the double use of the scalar triple product identity) to (where one of Maxwell's equations was used). This is the local contribution to the magnetic energy due to fluid motion.
Thus the term
is the rate of transformation of kinetic energy to magnetic energy.
This has to be non-negative at least in part of the volume, for the
dynamo to produce magnetic field.[19]
From the diagram above, it is not clear why this term should be
positive. A simple argument can be based on consideration of net
effects. To create the magnetic field, the net electric current must
wrap around the axis of rotation of the planet. In that case, for the
term to be positive, the net flow of conducting matter must be towards
the axis of rotation. The diagram only shows a net flow from the poles
to the equator. However mass conservation requires an additional flow
from the equator toward the poles. If that flow was along the axis of
rotation, that implies the circulation would be completed by a flow from
the ones shown towards the axis of rotation, producing the desired
effect.
Order of magnitude of the magnetic field created by Earth's dynamo
The
above formula for the rate of conversion of kinetic energy to magnetic
energy, is equivalent to a rate of work done by a force of on the outer core matter, whose velocity is . This work is the result of non-magnetic forces acting on the fluid.
Of those, the gravitational force and the centrifugal force are conservative
and therefore have no overall contribution to fluid moving in closed
loops. Ekman number (defined above), which is the ratio between the two
remaining forces, namely the viscosity and Coriolis force, is very low
inside Earth's outer core, because its viscosity is low (1.2–1.5 ×10−2pascal-second) due to its liquidity.
Thus the main time-averaged contribution to the work is from Coriolis force, whose size is though this quantity and
are related only indirectly and are not in general equal locally (thus
they affect each other but not in the same place and time).
The current density J is itself the result of the magnetic field according to Ohm's law.
Again, due to matter motion and current flow, this is not necessarily
the field at the same place and time. However these relations can still
be used to deduce orders of magnitude of the quantities in question.
In terms of order of magnitude, and , giving or:
The exact ratio between both sides is the square root of Elsasser number.
Note that the magnetic field direction cannot be inferred from
this approximation (at least not its sign) as it appears squared, and
is, indeed, sometimes reversed, though in general it lies on a similar axis to that of .
For earth outer core, ρ is approximately 104 kg/m3, Ω = 2π/day = 7.3×10−5/second and σ is approximately 107Ω−1m−1 .
This gives 2.7×10−4Tesla.
The magnetic field of a magnetic dipole
has an inverse cubic dependence in distance, so its order of magnitude
at the earth surface can be approximated by multiplying the above result
with (Router core⁄REarth)3 = (2890⁄6370)3 = 0.093 , giving 2.5×10−5 Tesla, not far from the measured value of 3×10−5 Tesla at the equator.
Numerical models
Broadly, models of the geodynamo attempt to produce magnetic fields
consistent with observed data given certain conditions and equations as
mentioned in the sections above. Implementing the magnetohydrodynamic
equations successfully was of particular significance because they
pushed dynamo models to self-consistency. Though geodynamo models are
especially prevalent, dynamo models are not necessarily restricted to
the geodynamo; solar and general dynamo models are also of interest.
Studying dynamo models has utility in the field of geophysics as doing
so can identify how various mechanisms form magnetic fields like those
produced by astrophysical bodies like Earth and how they cause magnetic
fields to exhibit certain features, such as pole reversals.
The equations used in numerical models of dynamo are highly complex. For decades, theorists were confined to two dimensional kinematic dynamo
models described above, in which the fluid motion is chosen in advance
and the effect on the magnetic field calculated. The progression from
linear to nonlinear, three dimensional models of dynamo was largely
hindered by the search for solutions to magnetohydrodynamic equations,
which eliminate the need for many of the assumptions made in kinematic
models and allow self-consistency.
The first self-consistent dynamo models, ones that determine
both the fluid motions and the magnetic field, were developed by two
groups in 1995, one in Japan and one in the United States. The latter was made as a model with regards to the geodynamo and
received significant attention because it successfully reproduced some
of the characteristics of the Earth's field. Following this breakthrough, there was a large swell in development of reasonable, three dimensional dynamo models.
Though many self-consistent models now exist, there are
significant differences among the models, both in the results they
produce and the way they were developed.
Given the complexity of developing a geodynamo model, there are many
places where discrepancies can occur such as when making assumptions
involving the mechanisms that provide energy for the dynamo, when
choosing values for parameters used in equations, or when normalizing
equations. In spite of the many differences that may occur, most models
have shared features like clear axial dipoles. In many of these models,
phenomena like secular variation and geomagnetic polarity reversals have also been successfully recreated.
Observations
Many observations can be made from dynamo models. Models can be used
to estimate how magnetic fields vary with time and can be compared to
observed paleomagnetic
data to find similarities between the model and the Earth. Due to the
uncertainty of paleomagnetic observations, however, comparisons may not
be entirely valid or useful. Simplified geodynamo models have shown relationships between the dynamo number (determined by variance in rotational rates
in the outer core and mirror-asymmetric convection (e.g. when
convection favors one direction in the north and the other in the
south)) and magnetic pole reversals as well as found similarities
between the geodynamo and the Sun's dynamo.
In many models, it appears that magnetic fields have somewhat random
magnitudes that follow a normal trend that average to zero.
In addition to these observations, general observations about the
mechanisms powering the geodynamo can be made based on how accurately
the model reflects actual data collected from Earth.
Modern modelling
The complexity of dynamo modelling is so great that models of the geodynamo are limited by the current power of supercomputers, particularly because calculating the Ekman and Rayleigh number of the outer core is extremely difficult and requires a vast number of computations.
Many improvements have been proposed in dynamo modelling since
the self-consistent breakthrough in 1995. One suggestion in studying
the complex magnetic field changes is applying spectral methods to simplify computations.
Ultimately, until considerable improvements in computer power are made,
the methods for computing realistic dynamo models will have to be made
more efficient, so making improvements in methods for computing the
model is of high importance for the advancement of numerical dynamo
modelling.