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112-477: 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 kilometers 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

224-549: A fluorescent lamp or other electrical discharge lamps. It is also used in radiation detectors such as the Geiger-Müller counter or the ionization chamber . The ionization process is widely used in a variety of equipment in fundamental science (e.g., mass spectrometry ) and in medical treatment (e.g., radiation therapy ). It is also widely used for air purification, though studies have shown harmful effects of this application. Negatively charged ions are produced when

336-521: A supernova remnant , a special diffuse nebula . Although much of the optical and X-ray emission from supernova remnants originates from ionized gas, a great amount of the radio emission is a form of non-thermal emission called synchrotron emission . This emission originates from high-velocity electrons oscillating within magnetic fields . Ionization Ionization (or ionisation specifically in Britain, Ireland, Australia and New Zealand)

448-433: A class of emission nebula associated with giant molecular clouds. These form as a molecular cloud collapses under its own weight, producing stars. Massive stars may form in the center, and their ultraviolet radiation ionizes the surrounding gas, making it visible at optical wavelengths . The region of ionized hydrogen surrounding the massive stars is known as an H II region while the shells of neutral hydrogen surrounding

560-727: A classical electron in the laboratory frame. In other words, in the Kramers–Henneberger frame the classical electron is at rest. Starting in the lab frame (velocity gauge), we may describe the electron with the Hamiltonian: In the dipole approximation, the quiver motion of a classical electron in the laboratory frame for an arbitrary field can be obtained from the vector potential of the electromagnetic field: where α 0 ≡ E 0 ω − 2 {\displaystyle \alpha _{0}\equiv E_{0}\omega ^{-2}} for

672-421: A coherent superposition of the two states. Under subsequent action of the same pulse, due to interference in the transition amplitudes of the lambda system, the field cannot ionize the population completely and a fraction of the population will be trapped in a coherent superposition of the quasi degenerate levels. According to this explanation the states with higher angular momentum – with more sublevels – would have

784-435: 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

896-568: A few thousand particles per cm 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

1008-418: A free electron collides with an atom and is subsequently trapped inside the electric potential barrier, releasing any excess energy. The process is known as electron capture ionization . Positively charged ions are produced by transferring an amount of energy to a bound electron in a collision with charged particles (e.g. ions, electrons or positrons) or with photons. The threshold amount of the required energy

1120-485: A higher probability of trapping the population. In general the strength of the trapping will be determined by the strength of the two photon coupling between the quasi-degenerate levels via the continuum. In 1996, using a very stable laser and by minimizing the masking effects of the focal region expansion with increasing intensity, Talebpour et al. observed structures on the curves of singly charged ions of Xe, Kr and Ar. These structures were attributed to electron trapping in

1232-949: 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

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1344-405: 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. 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

1456-556: A linearly polarized laser with frequency ω {\displaystyle \omega } is given by where The coefficients f l m {\displaystyle f_{lm}} , g ( γ ) {\displaystyle g(\gamma )} and C n ∗ l ∗ {\displaystyle C_{n^{*}l^{*}}} are given by The coefficient A m ( ω , γ ) {\displaystyle A_{m}(\omega ,\gamma )}

1568-413: A monochromatic plane wave. By applying a transformation to the laboratory frame equal to the quiver motion α ( t ) {\displaystyle \mathbf {\alpha } (t)} one moves to the ‘oscillating’ or ‘Kramers–Henneberger’ frame, in which the classical electron is at rest. By a phase factor transformation for convenience one obtains the ‘space-translated’ Hamiltonian, which

1680-568: A nebular cloud the size of the Earth would have a total mass of only a few kilograms . Earth's air has a density of approximately 10 molecules per cubic centimeter; by contrast, the densest nebulae can have densities of 10 molecules per cubic centimeter. Many nebulae are visible due to fluorescence caused by embedded hot stars, while others are so diffused that they can be detected only with long exposures and special filters. Some nebulae are variably illuminated by T Tauri variable stars. Originally,

1792-497: A region with a sufficiently high electric field in a gaseous medium that can be ionized, such as air . Following an original ionization event, due to such as ionizing radiation, the positive ion drifts towards the cathode , while the free electron drifts towards the anode of the device. If the electric field is strong enough, the free electron gains sufficient energy to liberate a further electron when it next collides with another molecule. The two free electrons then travel towards

1904-779: A relatively recently identified astronomical phenomenon. In contrast to the typical and well known gaseous nebulae within the plane of the Milky Way galaxy , IFNs lie beyond the main body of the galaxy. Most nebulae can be described as diffuse nebulae, which means that they are extended and contain no well-defined boundaries. Diffuse nebulae can be divided into emission nebulae , reflection nebulae and dark nebulae . Visible light nebulae may be divided into emission nebulae, which emit spectral line radiation from excited or ionized gas (mostly ionized hydrogen ); they are often called H II regions , H II referring to ionized hydrogen), and reflection nebulae which are visible primarily due to

2016-544: A result, the electron re-scattering can be taken as the main mechanism for the occurrence of the NSI process. The ionization of inner valence electrons are responsible for the fragmentation of polyatomic molecules in strong laser fields. According to a qualitative model the dissociation of the molecules occurs through a three-step mechanism: The short pulse induced molecular fragmentation may be used as an ion source for high performance mass spectroscopy. The selectivity provided by

2128-482: 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

2240-416: A short pulse based source is superior to that expected when using the conventional electron ionization based sources, in particular when the identification of optical isomers is required. The Kramers–Henneberger frame is the non-inertial frame moving with the free electron under the influence of the harmonic laser pulse, obtained by applying a translation to the laboratory frame equal to the quiver motion of

2352-457: 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

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2464-410: A state such as 6f of Xe which consists of 7 quasi-degnerate levels in the range of the laser bandwidth. These levels along with the continuum constitute a lambda system. The mechanism of the lambda type trapping is schematically presented in figure. At the rising part of the pulse (a) the excited state (with two degenerate levels 1 and 2) are not in multiphoton resonance with the ground state. The electron

2576-460: Is adopted from the field of ionization of atoms by X rays and electron projectiles where the SO process is one of the major mechanisms responsible for the multiple ionization of atoms. The SO model describes the NSI process as a mechanism where one electron is ionized by the laser field and the departure of this electron is so rapid that the remaining electrons do not have enough time to adjust themselves to

2688-401: Is another channel A + L − > A + + {\displaystyle A+L->A^{++}} which is the main contribution to the production of doubly charged ions at lower intensities. The first observation of triple NSI in argon interacting with a 1  μm laser was reported by Augst et al. Later, systematically studying the NSI of all rare gas atoms,

2800-502: 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

2912-412: Is expected to spawn a planetary nebula about 12 billion years after its formation. A supernova occurs when a high-mass star reaches the end of its life. When nuclear fusion in the core of the star stops, the star collapses. The gas falling inward either rebounds or gets so strongly heated that it expands outwards from the core, thus causing the star to explode. The expanding shell of gas forms

3024-568: Is given by where The quasi-static tunneling (QST) is the ionization whose rate can be satisfactorily predicted by the ADK model, i.e. the limit of the PPT model when γ {\displaystyle \gamma } approaches zero. The rate of QST is given by As compared to W P P T {\displaystyle W_{PPT}} the absence of summation over n, which represent different above threshold ionization (ATI) peaks,

3136-455: Is ionized through multiphoton coupling with the continuum. As the intensity of the pulse is increased the excited state and the continuum are shifted in energy due to the Stark shift. At the peak of the pulse (b) the excited states go into multiphoton resonance with the ground state. As the intensity starts to decrease (c), the two state are coupled through continuum and the population is trapped in

3248-442: Is known as ionization potential . The study of such collisions is of fundamental importance with regard to the few-body problem , which is one of the major unsolved problems in physics. Kinematically complete experiments , i.e. experiments in which the complete momentum vector of all collision fragments (the scattered projectile, the recoiling target-ion, and the ejected electron) are determined, have contributed to major advances in

3360-452: 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

3472-435: 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

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3584-470: Is proportional to intensity) where ionization due to re-scattering can occur. The re-scattering model in Kuchiev's version (Kuchiev's model) is quantum mechanical. The basic idea of the model is illustrated by Feynman diagrams in figure a. First both electrons are in the ground state of an atom. The lines marked a and b describe the corresponding atomic states. Then the electron a is ionized. The beginning of

3696-433: Is remarkable. The calculations of PPT are done in the E -gauge, meaning that the laser field is taken as electromagnetic waves. The ionization rate can also be calculated in A -gauge, which emphasizes the particle nature of light (absorbing multiple photons during ionization). This approach was adopted by Krainov model based on the earlier works of Faisal and Reiss. The resulting rate is given by where: In calculating

3808-461: Is the process by which an atom or a molecule acquires a negative or positive charge by gaining or losing electrons , often in conjunction with other chemical changes. The resulting electrically charged atom or molecule is called an ion . Ionization can result from the loss of an electron after collisions with subatomic particles , collisions with other atoms, molecules, electrons, positrons , protons , antiprotons and ions, or through

3920-448: 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 George Herbig and Guillermo Haro made independent observations of several of these objects in

4032-457: Is the rate of quasi-static tunneling to i'th charge state and α n ( λ ) {\displaystyle \alpha _{n}(\lambda )} are some constants depending on the wavelength of the laser (but not on the pulse duration). Two models have been proposed to explain the non-sequential ionization; the shake-off model and electron re-scattering model. The shake-off (SO) model, first proposed by Fittinghoff et al.,

4144-499: Is the time-dependent energy difference between the two dressed states. In interaction with a short pulse, if the dynamic resonance is reached in the rising or the falling part of the pulse, the population practically remains in the ground state and the effect of multiphoton resonances may be neglected. However, if the states go onto resonance at the peak of the pulse, where d W / d t = 0 {\displaystyle \mathrm {d} W/\mathrm {d} t=0} , then

4256-441: 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. 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

4368-477: Is unitarily equivalent to the lab-frame Hamiltonian, which contains the original potential centered on the oscillating point − α ( t ) {\displaystyle -\mathbf {\alpha } (t)} : The utility of the KH frame lies in the fact that in this frame the laser-atom interaction can be reduced to the form of an oscillating potential energy, where the natural parameters describing

4480-450: Is visible to the human eye from Earth would appear larger, but no brighter, from close by. The Orion Nebula , the brightest nebula in the sky and occupying an area twice the angular diameter of the full Moon , can be viewed with the naked eye but was missed by early astronomers. Although denser than the space surrounding them, most nebulae are far less dense than any vacuum created on Earth (10 to 10 molecules per cubic centimeter) –

4592-704: The Andromeda Galaxy is located. He also cataloged the Omicron Velorum star cluster as a "nebulous star" and other nebulous objects, such as Brocchi's Cluster . The supernovas that created the Crab Nebula , SN 1054 , was observed by Arabic and Chinese astronomers in 1054. In 1610, Nicolas-Claude Fabri de Peiresc discovered the Orion Nebula using a telescope. This nebula was also observed by Johann Baptist Cysat in 1618. However,

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4704-548: The Cape of Good Hope , most of which were previously unknown. Charles Messier then compiled a catalog of 103 "nebulae" (now called Messier objects , which included what are now known to be galaxies) by 1781; his interest was detecting comets , and these were objects that might be mistaken for them. The number of nebulae was then greatly increased by the efforts of William Herschel and his sister, Caroline Herschel . Their Catalogue of One Thousand New Nebulae and Clusters of Stars

4816-553: The Great Debate , it became clear that many "nebulae" were in fact galaxies far from the Milky Way . Slipher and Edwin Hubble continued to collect the spectra from many different nebulae, finding 29 that showed emission spectra and 33 that had the continuous spectra of star light. In 1922, Hubble announced that nearly all nebulae are associated with stars and that their illumination comes from star light. He also discovered that

4928-571: 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

5040-462: The ionization energy of atoms is often used to demonstrate the periodic behavior of atoms with respect to the atomic number, as summarized by ordering atoms in Mendeleev's table . This is a valuable tool for establishing and understanding the ordering of electrons in atomic orbitals without going into the details of wave functions or the ionization process. An example is presented in the figure to

5152-548: The ultraviolet radiation it emits can ionize the surrounding nebula that it has thrown off. The Sun will produce a planetary nebula and its core will remain behind in the form of a white dwarf . Objects named nebulae belong to four major groups. Before their nature was understood, galaxies ("spiral nebulae") and star clusters too distant to be resolved as stars were also classified as nebulae, but no longer are. Not all cloud-like structures are nebulae; Herbig–Haro objects are an example. Integrated flux nebulae are

5264-409: 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

5376-555: The H II region are known as photodissociation region . Examples of star-forming regions are the Orion Nebula , the Rosette Nebula and the Omega Nebula . Feedback from star-formation, in the form of supernova explosions of massive stars, stellar winds or ultraviolet radiation from massive stars, or outflows from low-mass stars may disrupt the cloud, destroying the nebula after several million years. Other nebulae form as

5488-529: The TDSE. In high frequency Floquet theory, to lowest order in ω − 1 {\displaystyle \omega ^{-1}} the system reduces to the so-called ‘structure equation’, which has the form of a typical energy-eigenvalue Schrödinger equation containing the ‘dressed potential’ V 0 ( α 0 , r ) {\displaystyle V_{0}(\alpha _{0},\mathbf {r} )} (the cycle-average of

5600-691: 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. As of 2010, almost 1000 objects are contained in the MHO catalog. HH objects have been observed in the ultraviolet spectrum. Nebula Most nebulae are of vast size; some are hundreds of light-years in diameter. A nebula that

5712-502: 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. 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

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5824-429: The anode and gain sufficient energy from the electric field to cause impact ionization when the next collisions occur; and so on. This is effectively a chain reaction of electron generation, and is dependent on the free electrons gaining sufficient energy between collisions to sustain the avalanche. Ionization efficiency is the ratio of the number of ions formed to the number of electrons or photons used. The trend in

5936-441: The approach of Becker and Faisal (which is equivalent to Kuchiev's model in spirit), this drawback does not exist. In fact, their model is more exact and does not suffer from the large number of approximations made by Kuchiev. Their calculation results perfectly fit with the experimental results of Walker et al. Becker and Faisal have been able to fit the experimental results on the multiple NSI of rare gas atoms using their model. As

6048-534: The atom or molecule is interacting with near-infrared strong laser pulses. This process can be understood as a process by which a bounded electron, through the absorption of more than one photon from the laser field, is ionized. This picture is generally known as multiphoton ionization (MPI). Keldysh modeled the MPI process as a transition of the electron from the ground state of the atom to the Volkov states. In this model

6160-450: 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

6272-471: The different types of nebulae. Some nebulae form from gas that is already in the interstellar medium while others are produced by stars. Examples of the former case are giant molecular clouds , the coldest, densest phase of interstellar gas, which can form by the cooling and condensation of more diffuse gas. Examples of the latter case are planetary nebulae formed from material shed by a star in late stages of its stellar evolution . Star-forming regions are

6384-404: The electron dynamics are ω {\displaystyle \omega } and α 0 {\displaystyle \alpha _{0}} (sometimes called the “excursion amplitude’, obtained from α ( t ) {\displaystyle \mathbf {\alpha } (t)} ). From here one can apply Floquet theory to calculate quasi-stationary solutions of

6496-405: The emission spectrum nebulae are nearly always associated with stars having spectral classifications of B or hotter (including all O-type main sequence stars ), while nebulae with continuous spectra appear with cooler stars. Both Hubble and Henry Norris Russell concluded that the nebulae surrounding the hotter stars are transformed in some manner. There are a variety of formation mechanisms for

6608-517: The end of the jet can re-ionise some material, giving rise to bright "caps". 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

6720-441: The excited state is populated. After being populated, since the ionization potential of the excited state is small, it is expected that the electron will be instantly ionized. In 1992, de Boer and Muller showed that Xe atoms subjected to short laser pulses could survive in the highly excited states 4f, 5f, and 6f. These states were believed to have been excited by the dynamic Stark shift of the levels into multiphoton resonance with

6832-510: The expelled gases, producing emission nebulae with spectra similar to those of emission nebulae found in star formation regions. They are H II regions , because mostly hydrogen is ionized, but planetary are denser and more compact than nebulae found in star formation regions. Planetary nebulae were given their name by the first astronomical observers who were initially unable to distinguish them from planets, and who tended to confuse them with planets, which were of more interest to them. The Sun

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6944-646: The experimental point of view, the NS double ionization refers to processes which somehow enhance the rate of production of doubly charged ions by a huge factor at intensities below the saturation intensity of the singly charged ion. Many, on the other hand, prefer to define the NSI as a process by which two electrons are ionized nearly simultaneously. This definition implies that apart from the sequential channel A + L − > A + + L − > A + + {\displaystyle A+L->A^{+}+L->A^{++}} there

7056-480: The explosion lies in the center of the Crab Nebula and its core is now a neutron star . Still other nebulae form as planetary nebulae . This is the final stage of a low-mass star's life, like Earth's Sun. Stars with a mass up to 8–10 solar masses evolve into red giants and slowly lose their outer layers during pulsations in their atmospheres. When a star has lost enough material, its temperature increases and

7168-411: The field during the rising part of the laser pulse. Subsequent evolution of the laser pulse did not completely ionize these states, leaving behind some highly excited atoms. We shall refer to this phenomenon as "population trapping". We mention the theoretical calculation that incomplete ionization occurs whenever there is parallel resonant excitation into a common level with ionization loss. We consider

7280-522: The first detailed study of the Orion Nebula was not performed until 1659 by Christiaan Huygens , who also believed he was the first person to discover this nebulosity. In 1715, Edmond Halley published a list of six nebulae. This number steadily increased during the century, with Jean-Philippe de Cheseaux compiling a list of 20 (including eight not previously known) in 1746. From 1751 to 1753, Nicolas-Louis de Lacaille cataloged 42 nebulae from

7392-596: The first order correction in the quasi-classical action. Larochelle et al. have compared the theoretically predicted ion versus intensity curves of rare gas atoms interacting with a Ti:Sapphire laser with experimental measurement. They have shown that the total ionization rate predicted by the PPT model fit very well the experimental ion yields for all rare gases in the intermediate regime of the Keldysh parameter. The rate of MPI on atom with an ionization potential E i {\displaystyle E_{i}} in

7504-467: 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

7616-434: The generalized Rabi frequency, Γ ( t ) = Γ m I ( t ) m / 2 {\displaystyle \Gamma (t)=\Gamma _{m}I(t)^{m/2}} coupling the two states. According to Story et al., the probability of remaining in the ground state, P g {\displaystyle P_{g}} , is given by where W {\displaystyle W}

7728-403: The ground state. Within the dressed atom picture, the ground state dressed by m {\displaystyle m} photons and the resonant state undergo an avoided crossing at the resonance intensity I r {\displaystyle I_{r}} . The minimum distance, V m {\displaystyle V_{m}} , at the avoided crossing is proportional to

7840-409: The interaction with electromagnetic radiation . Heterolytic bond cleavage and heterolytic substitution reactions can result in the formation of ion pairs. Ionization can occur through radioactive decay by the internal conversion process, in which an excited nucleus transfers its energy to one of the inner-shell electrons causing it to be ejected. Everyday examples of gas ionization occur within

7952-457: The ion excitation to a discrete or continuum state. Figure b describes the exchange process. Kuchiev's model, contrary to Corkum's model, does not predict any threshold intensity for the occurrence of NS ionization. Kuchiev did not include the Coulomb effects on the dynamics of the ionized electron. This resulted in the underestimation of the double ionization rate by a huge factor. Obviously, in

8064-425: The ionization process is shown by the intersection with a sloped dashed line. where the MPI occurs. The propagation of the ionized electron in the laser field, during which it absorbs other photons (ATI), is shown by the full thick line. The collision of this electron with the parent atomic ion is shown by a vertical dotted line representing the Coulomb interaction between the electrons. The state marked with c describes

8176-421: The ionization process, the energy of the electron exceeds the energy difference of the potential barrier it is trying to pass. The classical description, however, cannot describe tunnel ionization since the process involves the passage of electron through a classically forbidden potential barrier. The interaction of atoms and molecules with sufficiently strong laser pulses or with other charged particles leads to

8288-614: The ionization to singly or multiply charged ions. The ionization rate, i.e. the ionization probability in unit time, can be calculated using quantum mechanics . (There are classical methods available also, like the Classical Trajectory Monte Carlo Method (CTMC) ,but it is not overall accepted and often criticized by the community.) There are two quantum mechanical methods exist, perturbative and non-perturbative methods like time-dependent coupled-channel or time independent close coupling methods where

8400-476: 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. The stars from which HH jets are emitted are all very young stars,

8512-467: 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

8624-399: The laser at larger distances from the nucleus. This is in contrast to the approximation made by neglecting the potential of the laser at regions near the nucleus. Perelomov et al. included the Coulomb interaction at larger internuclear distances. Their model (which we call the PPT model) was derived for short range potential and includes the effect of the long range Coulomb interaction through

8736-432: The laser intensity is sufficiently high, the detailed structure of the atom or molecule can be ignored and analytic solution for the ionization rate is possible. Tunnel ionization is ionization due to quantum tunneling . In classical ionization, an electron must have enough energy to make it over the potential barrier, but quantum tunneling allows the electron simply to go through the potential barrier instead of going all

8848-409: 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

8960-503: The light they reflect. Reflection nebulae themselves do not emit significant amounts of visible light, but are near stars and reflect light from them. Similar nebulae not illuminated by stars do not exhibit visible radiation, but may be detected as opaque clouds blocking light from luminous objects behind them; they are called dark nebulae . Although these nebulae have different visibility at optical wavelengths, they are all bright sources of infrared emission, chiefly from dust within

9072-537: 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

9184-468: The model can be understood easily from Corkum's version. Corkum's model describes the NS ionization as a process whereby an electron is tunnel ionized. The electron then interacts with the laser field where it is accelerated away from the nuclear core. If the electron has been ionized at an appropriate phase of the field, it will pass by the position of the remaining ion half a cycle later, where it can free an additional electron by electron impact. Only half of

9296-445: The molecules of table sugar dissociate in water (sugar is dissolved) but exist as intact neutral entities. Another subtle event is the dissociation of sodium chloride (table salt) into sodium and chlorine ions. Although it may seem as a case of ionization, in reality the ions already exist within the crystal lattice. When salt is dissociated, its constituent ions are simply surrounded by water molecules and their effects are visible (e.g.

9408-401: The nebulae. Planetary nebulae are the remnants of the final stages of stellar evolution for mid-mass stars (varying in size between 0.5-~8 solar masses). Evolved asymptotic giant branch stars expel their outer layers outwards due to strong stellar winds, thus forming gaseous shells while leaving behind the star's core in the form of a white dwarf . Radiation from the hot white dwarf excites

9520-520: The new energy states. Therefore, there is a certain probability that, after the ionization of the first electron, a second electron is excited to states with higher energy (shake-up) or even ionized (shake-off). We should mention that, until now, there has been no quantitative calculation based on the SO model, and the model is still qualitative. The electron rescattering model was independently developed by Kuchiev, Schafer et al , Corkum, Becker and Faisal and Faisal and Becker. The principal features of

9632-419: 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

9744-404: The objects, and recognised that they were a by-product of the star formation process. Although HH objects are 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). The first HH object was observed in

9856-410: The oscillating potential). The interpretation of the presence of V 0 {\displaystyle V_{0}} is as follows: in the oscillating frame, the nucleus has an oscillatory motion of trajectory − α ( t ) {\displaystyle -\mathbf {\alpha } (t)} and V 0 {\displaystyle V_{0}} can be seen as

9968-435: 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

10080-529: 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

10192-415: The perturbation of the ground state by the laser field is neglected and the details of atomic structure in determining the ionization probability are not taken into account. The major difficulty with Keldysh's model was its neglect of the effects of Coulomb interaction on the final state of the electron. As it is observed from figure, the Coulomb field is not very small in magnitude compared to the potential of

10304-488: The potential of the smeared out nuclear charge along its trajectory. The KH frame is thus employed in theoretical studies of strong-field ionization and atomic stabilization (a predicted phenomenon in which the ionization probability of an atom in a high-intensity, high-frequency field actually decreases for intensities above a certain threshold) in conjunction with high-frequency Floquet theory. A substance may dissociate without necessarily producing ions. As an example,

10416-400: The quadruple NSI of Xe was observed. The most important conclusion of this study was the observation of the following relation between the rate of NSI to any charge state and the rate of tunnel ionization (predicted by the ADK formula) to the previous charge states; where W A D K ( A i + ) {\displaystyle W_{ADK}\left(A^{i+}\right)}

10528-459: The rate of MPI of atoms only transitions to the continuum states are considered. Such an approximation is acceptable as long as there is no multiphoton resonance between the ground state and some excited states. However, in real situation of interaction with pulsed lasers, during the evolution of laser intensity, due to different Stark shift of the ground and excited states there is a possibility that some excited state go into multiphoton resonance with

10640-456: The result of supernova explosions; the death throes of massive, short-lived stars. The materials thrown off from the supernova explosion are then ionized by the energy and the compact object that its core produces. One of the best examples of this is the Crab Nebula , in Taurus . The supernova event was recorded in the year 1054 and is labeled SN 1054 . The compact object that was created after

10752-509: The right. The periodic abrupt decrease in ionization potential after rare gas atoms, for instance, indicates the emergence of a new shell in alkali metals . In addition, the local maximums in the ionization energy plot, moving from left to right in a row, are indicative of s, p, d, and f sub-shells. Classical physics and the Bohr model of the atom can qualitatively explain photoionization and collision-mediated ionization. In these cases, during

10864-399: 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 to 10 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

10976-421: 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 cm, compared to

11088-427: 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

11200-409: 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. Electromagnetic emission from HH objects

11312-514: The spectra of about 70 nebulae. He found that roughly a third of them had the emission spectrum of a gas . The rest showed a continuous spectrum and were thus thought to consist of a mass of stars. A third category was added in 1912 when Vesto Slipher showed that the spectrum of the nebula that surrounded the star Merope matched the spectra of the Pleiades open cluster . Thus, the nebula radiates by reflected star light. In 1923, following

11424-412: 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

11536-489: The strong laser field. A more unambiguous demonstration of population trapping has been reported by T. Morishita and C. D. Lin . The phenomenon of non-sequential ionization (NSI) of atoms exposed to intense laser fields has been a subject of many theoretical and experimental studies since 1983. The pioneering work began with the observation of a "knee" structure on the Xe ion signal versus intensity curve by L’Huillier et al. From

11648-462: 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

11760-410: 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

11872-589: The term "nebula" was used to describe any diffused astronomical object , including galaxies beyond the Milky Way . The Andromeda Galaxy , for instance, was once referred to as the Andromeda Nebula (and spiral galaxies in general as "spiral nebulae") before the true nature of galaxies was confirmed in the early 20th century by Vesto Slipher , Edwin Hubble , and others. Edwin Hubble discovered that most nebulae are associated with stars and illuminated by starlight. He also helped categorize nebulae based on

11984-429: The theoretical understanding of the few-body problem in recent years. Adiabatic ionization is a form of ionization in which an electron is removed from or added to an atom or molecule in its lowest energy state to form an ion in its lowest energy state. The Townsend discharge is a good example of the creation of positive ions and free electrons due to ion impact. It is a cascade reaction involving electrons in

12096-420: The time the electron is released with the appropriate phase and the other half it never return to the nuclear core. The maximum kinetic energy that the returning electron can have is 3.17 times the ponderomotive potential ( U p {\displaystyle U_{p}} ) of the laser. Corkum's model places a cut-off limit on the minimum intensity ( U p {\displaystyle U_{p}}

12208-548: The type of light spectra they produced. Around 150 AD, Ptolemy recorded, in books VII–VIII of his Almagest , five stars that appeared nebulous. He also noted a region of nebulosity between the constellations Ursa Major and Leo that was not associated with any star . The first true nebula, as distinct from a star cluster , was mentioned by the Muslim Persian astronomer Abd al-Rahman al-Sufi in his Book of Fixed Stars (964). He noted "a little cloud" where

12320-431: The wave function is expanded in a finite basis set. There are numerous options available e.g. B-splines or Coulomb wave packets. Another non-perturbative method is to solve the corresponding Schrödinger equation fully numerically on a lattice. In general, the analytic solutions are not available, and the approximations required for manageable numerical calculations do not provide accurate enough results. However, when

12432-412: The way over it because of the wave nature of the electron. The probability of an electron's tunneling through the barrier drops off exponentially with the width of the potential barrier. Therefore, an electron with a higher energy can make it further up the potential barrier, leaving a much thinner barrier to tunnel through and thus a greater chance to do so. In practice, tunnel ionization is observable when

12544-442: Was published in 1786. A second catalog of a thousand was published in 1789, and the third and final catalog of 510 appeared in 1802. During much of their work, William Herschel believed that these nebulae were merely unresolved clusters of stars. In 1790, however, he discovered a star surrounded by nebulosity and concluded that this was a true nebulosity rather than a more distant cluster. Beginning in 1864, William Huggins examined

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