Hubble Space Telescope
The Hubble Space Telescope is a space telescope, launched into low Earth orbit in 1990 and remains in operation. Although not the first space telescope, Hubble is one of the largest and most versatile and is well known as both a vital research tool and a public relations boon for astronomy; the HST is named after the astronomer Edwin Hubble and is one of NASA's Great Observatories, along with the Compton Gamma Ray Observatory, the Chandra X-ray Observatory and the Spitzer Space Telescope. With a 2.4-meter mirror, Hubble's four main instruments observe in the ultraviolet and near infrared regions of the electromagnetic spectrum. Hubble's orbit outside the distortion of Earth's atmosphere allows it to take high-resolution images, with lower background light than ground-based telescopes. Hubble has recorded some of the most detailed visible light images allowing a deep view into space and time. Many Hubble observations have led to breakthroughs in astrophysics, such as determining the rate of expansion of the universe.
The HST was built by the United States space agency NASA, with contributions from the European Space Agency. The Space Telescope Science Institute selects Hubble's targets and processes the resulting data, while the Goddard Space Flight Center controls the spacecraft. Space telescopes were proposed as early as 1923. Hubble was funded in the 1970s, with a proposed launch in 1983, but the project was beset by technical delays, budget problems, the Challenger disaster; when launched in 1990, Hubble's main mirror was found to have been ground incorrectly, creating a spherical aberration, compromising the telescope's capabilities. The optics were corrected to their intended quality by a servicing mission in 1993. Hubble is the only telescope designed to be serviced in space by astronauts. After launch by Space Shuttle Discovery in 1990, five subsequent Space Shuttle missions repaired and replaced systems on the telescope, including all five of the main instruments; the fifth mission was canceled on safety grounds following the Columbia disaster.
However, after spirited public discussion, NASA administrator Mike Griffin approved the fifth servicing mission, completed in 2009. The telescope is operating as of 2019, could last until 2030–2040. After numerous delays, its successor, the James Webb Space Telescope, is scheduled to be launched in March 2021. In 1923, Hermann Oberth—considered a father of modern rocketry, along with Robert H. Goddard and Konstantin Tsiolkovsky—published Die Rakete zu den Planetenräumen, which mentioned how a telescope could be propelled into Earth orbit by a rocket; the history of the Hubble Space Telescope can be traced back as far as 1946, to the astronomer Lyman Spitzer's paper "Astronomical advantages of an extraterrestrial observatory". In it, he discussed the two main advantages that a space-based observatory would have over ground-based telescopes. First, the angular resolution would be limited only by diffraction, rather than by the turbulence in the atmosphere, which causes stars to twinkle, known to astronomers as seeing.
At that time ground-based telescopes were limited to resolutions of 0.5–1.0 arcseconds, compared to a theoretical diffraction-limited resolution of about 0.05 arcsec for a telescope with a mirror 2.5 m in diameter. Second, a space-based telescope could observe infrared and ultraviolet light, which are absorbed by the atmosphere. Spitzer devoted much of his career to pushing for the development of a space telescope. In 1962, a report by the US National Academy of Sciences recommended the development of a space telescope as part of the space program, in 1965 Spitzer was appointed as head of a committee given the task of defining scientific objectives for a large space telescope. Space-based astronomy had begun on a small scale following World War II, as scientists made use of developments that had taken place in rocket technology; the first ultraviolet spectrum of the Sun was obtained in 1946, the National Aeronautics and Space Administration launched the Orbiting Solar Observatory to obtain UV, X-ray, gamma-ray spectra in 1962.
An orbiting solar telescope was launched in 1962 by the United Kingdom as part of the Ariel space program, in 1966 NASA launched the first Orbiting Astronomical Observatory mission. OAO-1's battery failed after three days, it was followed by OAO-2, which carried out ultraviolet observations of stars and galaxies from its launch in 1968 until 1972, well beyond its original planned lifetime of one year. The OSO and OAO missions demonstrated the important role space-based observations could play in astronomy, in 1968, NASA developed firm plans for a space-based reflecting telescope with a mirror 3 m in diameter, known provisionally as the Large Orbiting Telescope or Large Space Telescope, with a launch slated for 1979; these plans emphasized the need for manned maintenance missions to the telescope to ensure such a costly program had a lengthy working life, the concurrent development of plans for the reusable Space Shuttle indicated that the technology to allow this was soon to become available.
The continuing success of the OAO program encouraged strong consensus within the astronomical community that the LST should be a major goal. In 1970, NASA established two committees, one to plan the engineering side of the space telescope project, the other to determine the scientific goals of the mission. Once these had been established, the next hurdle for NASA was to obtain funding for the instrument, which would be far more costly than any Earth-bas
A gamma ray or gamma radiation, is a penetrating electromagnetic radiation arising from the radioactive decay of atomic nuclei. It consists of the shortest wavelength electromagnetic waves and so imparts the highest photon energy. Paul Villard, a French chemist and physicist, discovered gamma radiation in 1900 while studying radiation emitted by radium. In 1903, Ernest Rutherford named this radiation gamma rays based on their strong penetration of matter. Gamma rays from radioactive decay are in the energy range from a few keV to ~8 MeV, corresponding to the typical energy levels in nuclei with reasonably long lifetimes; the energy spectrum of gamma rays can be used to identify the decaying radionuclides using gamma spectroscopy. Very-high-energy gamma rays in the 100–1000 TeV range have been observed from sources such as the Cygnus X-3 microquasar. Natural sources of gamma rays originating on Earth are as a result of radioactive decay and secondary radiation from atmospheric interactions with cosmic ray particles.
However there are other rare natural sources, such as terrestrial gamma-ray flashes, that produce gamma rays from electron action upon the nucleus. Notable artificial sources of gamma rays include fission, such as occurs in nuclear reactors, as well as high energy physics experiments, such as neutral pion decay and nuclear fusion. Gamma rays and X-rays are both electromagnetic radiation and they overlap in the electromagnetic spectrum, the terminology varies between scientific disciplines. In some fields of physics, they are distinguished by their origin: Gamma rays are created by nuclear decay, while in the case of X-rays, the origin is outside the nucleus. In astrophysics, gamma rays are conventionally defined as having photon energies above 100 keV and are the subject of gamma ray astronomy, while radiation below 100 keV is classified as X-rays and is the subject of X-ray astronomy; this convention stems from the early man-made X-rays, which had energies only up to 100 keV, whereas many gamma rays could go to higher energies.
A large fraction of astronomical gamma rays are screened by Earth's atmosphere. Gamma rays are thus biologically hazardous. Due to their high penetration power, they can damage internal organs. Unlike alpha and beta rays, they pass through the body and thus pose a formidable radiation protection challenge, requiring shielding made from dense materials such as lead or concrete; the first gamma ray source to be discovered was the radioactive decay process called gamma decay. In this type of decay, an excited nucleus emits a gamma ray immediately upon formation. Paul Villard, a French chemist and physicist, discovered gamma radiation in 1900, while studying radiation emitted from radium. Villard knew that his described radiation was more powerful than described types of rays from radium, which included beta rays, first noted as "radioactivity" by Henri Becquerel in 1896, alpha rays, discovered as a less penetrating form of radiation by Rutherford, in 1899. However, Villard did not consider naming them as a different fundamental type.
In 1903, Villard's radiation was recognized as being of a type fundamentally different from named rays by Ernest Rutherford, who named Villard's rays "gamma rays" by analogy with the beta and alpha rays that Rutherford had differentiated in 1899. The "rays" emitted by radioactive elements were named in order of their power to penetrate various materials, using the first three letters of the Greek alphabet: alpha rays as the least penetrating, followed by beta rays, followed by gamma rays as the most penetrating. Rutherford noted that gamma rays were not deflected by a magnetic field, another property making them unlike alpha and beta rays. Gamma rays were first thought to be particles like alpha and beta rays. Rutherford believed that they might be fast beta particles, but their failure to be deflected by a magnetic field indicated that they had no charge. In 1914, gamma rays were observed to be reflected from crystal surfaces, proving that they were electromagnetic radiation. Rutherford and his co-worker Edward Andrade measured the wavelengths of gamma rays from radium, found that they were similar to X-rays, but with shorter wavelengths and higher frequency.
This was recognized as giving them more energy per photon, as soon as the latter term became accepted. A gamma decay was understood to emit a gamma photon. Natural sources of gamma rays on Earth include gamma decay from occurring radioisotopes such as potassium-40, as a secondary radiation from various atmospheric interactions with cosmic ray particles; some rare terrestrial natural sources that produce gamma rays that are not of a nuclear origin, are lightning strikes and terrestrial gamma-ray flashes, which produce high energy emissions from natural high-energy voltages. Gamma rays are produced by a number of astronomical processes in which high-energy electrons are produced; such electrons produce secondary gamma rays by the mechanisms of bremsstrahlung, inverse Compton scattering and synchrotron radiation. A large fraction of such astronomical gamma rays are screened by Earth's atmosphere. Notable artificial sources of gamma rays include fission, such as occurs in nuclear reactors, as well as high energy physics experiments, such as neutral pion decay and nuclear fusion.
A sample of gamma ray-emitting material, used for irradiating or imaging is known as a gamma source. It is called a radioactive sou
Chandra X-ray Observatory
The Chandra X-ray Observatory known as the Advanced X-ray Astrophysics Facility, is a Flagship-class space telescope launched on STS-93 by NASA on July 23, 1999. Chandra is sensitive to X-ray sources 100 times fainter than any previous X-ray telescope, enabled by the high angular resolution of its mirrors. Since the Earth's atmosphere absorbs the vast majority of X-rays, they are not detectable from Earth-based telescopes. Chandra is an Earth satellite in a 64-hour orbit, its mission is ongoing as of 2019. Chandra is one of the Great Observatories, along with the Hubble Space Telescope, Compton Gamma Ray Observatory, the Spitzer Space Telescope; the telescope is named after the Nobel Prize-winning Indian-American astrophysicist Subrahmanyan Chandrasekhar. Its mission is similar to that of ESA's XMM-Newton spacecraft launched in 1999. In 1976 the Chandra X-ray Observatory was proposed to NASA by Riccardo Giacconi and Harvey Tananbaum. Preliminary work began the following year at Marshall Space Flight Center and the Smithsonian Astrophysical Observatory.
In the meantime, in 1978, NASA launched the first imaging X-ray telescope, into orbit. Work continued on the AXAF project throughout the 1990s. In 1992, to reduce costs, the spacecraft was redesigned. Four of the twelve planned mirrors were eliminated. AXAF's planned orbit was changed to an elliptical one, reaching one third of the way to the Moon's at its farthest point; this eliminated the possibility of improvement or repair by the space shuttle but put the observatory above the Earth's radiation belts for most of its orbit. AXAF was tested by TRW in Redondo Beach, California. AXAF was renamed Chandra as part of a contest held by NASA in 1998, which drew more than 6,000 submissions worldwide; the contest winners, Jatila van der Veen and Tyrel Johnson, suggested the name in honor of Nobel Prize–winning Indian-American astrophysicist Subrahmanyan Chandrasekhar. He is known for his work in determining the maximum mass of white dwarf stars, leading to greater understanding of high energy astronomical phenomena such as neutron stars and black holes.
Fittingly, the name Chandra means "moon" in Sanskrit. Scheduled to be launched in December 1998, the spacecraft was delayed several months being launched in July 23, 1999, at 04:31 UTC by Space Shuttle Columbia during STS-93. Chandra was deployed from Columbia at 11:47 UTC; the Inertial Upper Stage's first stage motor ignited at 12:48 UTC, after burning for 125 seconds and separating, the second stage ignited at 12:51 UTC and burned for 117 seconds. At 22,753 kilograms, it was the heaviest payload launched by the shuttle, a consequence of the two-stage Inertial Upper Stage booster rocket system needed to transport the spacecraft to its high orbit. Chandra has been returning data since the month, it is operated by the SAO at the Chandra X-ray Center in Cambridge, with assistance from MIT and Northrop Grumman Space Technology. The ACIS CCDs suffered particle damage during early radiation belt passages. To prevent further damage, the instrument is now removed from the telescope's focal plane during passages.
Although Chandra was given an expected lifetime of 5 years, on September 4, 2001, NASA extended its lifetime to 10 years "based on the observatory's outstanding results." Physically Chandra could last much longer. A 2004 study performed at the Chandra X-ray Center indicated that the observatory could last at least 15 years. In July 2008, the International X-ray Observatory, a joint project between ESA, NASA and JAXA, was proposed as the next major X-ray observatory but was cancelled. ESA resurrected the project as the Advanced Telescope for High Energy Astrophysics with a proposed launch in 2028. On October 10, 2018, Chandra entered safe mode operations, due to a gyroscope glitch. NASA reported. Within days, the 3-second error in data from one gyro was understood, plans were made to return Chandra to full service; the gyroscope that experienced the glitch is otherwise healthy. The data gathered by Chandra has advanced the field of X-ray astronomy. Here are some examples of discoveries supported by observations from Chandra: The first light image, of supernova remnant Cassiopeia A, gave astronomers their first glimpse of the compact object at the center of the remnant a neutron star or black hole.
In the Crab Nebula, another supernova remnant, Chandra showed a never-before-seen ring around the central pulsar and jets that had only been seen by earlier telescopes. The first X-ray emission was seen from the supermassive black hole, Sagittarius A*, at the center of the Milky Way. Chandra found much more cool gas than expected spiraling into the center of the Andromeda Galaxy. Pressure fronts were observed in detail for the first time in Abell 2142, where clusters of galaxies are merging; the earliest images in X-rays of the shock wave of a supernova were taken of SN 1987A. Chandra showed for the first time the shadow of a small galaxy as it is being cannibalized by a larger one, in an image of Perseus A. A new type of black hole was discovered in galaxy M82, mid-mass objects purported to be the missing link between stellar-sized black holes and super massive black holes. X-ray emission lines were associated for the first time with a gamma-ray burst
A magnetar is a type of neutron star believed to have an powerful magnetic field. The magnetic field decay powers the emission of high-energy electromagnetic radiation X-rays and gamma rays; the theory regarding these objects was proposed by Robert Duncan and Christopher Thompson in 1992, but the first recorded burst of gamma rays thought to have been from a magnetar had been detected on March 5, 1979. During the following decade, the magnetar hypothesis became accepted as a explanation for soft gamma repeaters and anomalous X-ray pulsars. Like other neutron stars, magnetars are around 20 kilometres in diameter and have a mass 2–3 times that of the Sun; the density of the interior of a magnetar is such that a tablespoon of its substance would have a mass of over 100 million tons. Magnetars are differentiated from other neutron stars by having stronger magnetic fields, by rotating comparatively quicker. Most neutron stars rotate once every one to ten seconds, whereas magnetars rotate once in less than one second.
A magnetar's magnetic field gives rise to strong and characteristic bursts of X-rays and gamma rays. The active life of a magnetar is short, their strong magnetic fields decay after about 10,000 years, after which activity and strong X-ray emission cease. Given the number of magnetars observable today, one estimate puts the number of inactive magnetars in the Milky Way at 30 million or more. Starquakes triggered on the surface of the magnetar disturb the magnetic field which encompasses it leading to powerful gamma ray flare emissions which have been recorded on Earth in 1979, 1998, 2004. Magnetars are characterized by their powerful magnetic fields of 108 to 1011 tesla; these magnetic fields are hundreds of millions of times stronger than any man-made magnet, quadrillions of times more powerful than the field surrounding Earth. Earth has a geomagnetic field of 30–60 microteslas, a neodymium-based, rare-earth magnet has a field of about 1.25 tesla, with a magnetic energy density of 4.0×105 J/m3.
A magnetar's 1010 tesla field, by contrast, has an energy density of 4.0×1025 J/m3, with an E/c2 mass density more than 10,000 times that of lead. The magnetic field of a magnetar would be lethal at a distance of 1000 km due to the strong magnetic field distorting the electron clouds of the subject's constituent atoms, rendering the chemistry of life impossible. At a distance of halfway from Earth to the moon, a magnetar could strip information from the magnetic stripes of all credit cards on Earth; as of 2010, they are the most powerful magnetic objects detected throughout the universe. As described in the February 2003 Scientific American cover story, remarkable things happen within a magnetic field of magnetar strength. "X-ray photons split in two or merge. The vacuum itself is polarized, becoming birefringent, like a calcite crystal. Atoms are deformed into long cylinders thinner than the quantum-relativistic de Broglie wavelength of an electron." In a field of about 105 teslas atomic orbitals deform into rod shapes.
At 1010 teslas, a hydrogen atom becomes a spindle 200 times narrower than its normal diameter. The strong fields of magnetars are understood as resulting from a magnetohydrodynamic dynamo process in the turbulent dense conducting fluid that exists before the neutron star settles into its equilibrium configuration; these fields persist due to persistent currents in a proton-superconductor phase of matter that exists at an intermediate depth within the neutron star. A similar magnetohydrodynamic dynamo process produces more intense transient fields during coalescence of pairs of neutron stars; when in a supernova, a star collapses to a neutron star, its magnetic field increases in strength. Halving a linear dimension increases the magnetic field fourfold. Duncan and Thompson calculated that when the spin and magnetic field of a newly formed neutron star falls into the right ranges, a dynamo mechanism could act, converting heat and rotational energy into magnetic energy and increasing the magnetic field an enormous 108 teslas, to more than 1011 teslas.
The result is a magnetar. It is estimated that about one in ten supernova explosions results in a magnetar rather than a more standard neutron star or pulsar. On March 5, 1979, a few months after the successful dropping of satellites into the atmosphere of Venus, the two unmanned Soviet spaceprobes, Venera 11 and 12, that were drifting through the Solar System were hit by a blast of gamma radiation at 10:51 EST; this contact raised the radiation readings on both the probes from a normal 100 counts per second to over 200,000 counts a second, in only a fraction of a millisecond. This burst of gamma rays continued to spread. Eleven seconds Helios 2, a NASA probe, in orbit around the Sun, was saturated by the blast of radiation, it soon hit Venus, the Pioneer Venus Orbiter's detectors were overcome by the wave. Seconds Earth received the wave of radiation, where the powerful output of gamma rays inundated the detectors of three U. S. Department of Defense Vela satellites, the Soviet Prognoz 7 satellite, the Einstein Observatory.
Just before the wave exited the Solar System, the blast hit the International Sun–Earth Explorer. This powerful blast of gamma radiation constituted the strongest wave of extra-solar gamma rays detected; because gamma rays travel at the speed of light and the time of the pulse
A millisecond pulsar is a pulsar with a rotational period in the range of about 1–10 milliseconds. Millisecond pulsars have been detected in the radio, X-ray, gamma ray portions of the electromagnetic spectrum; the leading theory for the origin of millisecond pulsars is that they are old rotating neutron stars which have been spun up or "recycled" through accretion of matter from a companion star in a close binary system. For this reason, millisecond pulsars are sometimes called recycled pulsars. Millisecond pulsars are thought to be related to low-mass X-ray binary systems, it is thought that the X-rays in these systems are emitted by the accretion disk of a neutron star produced by the outer layers of a companion star that has overflowed its Roche lobe. The transfer of angular momentum from this accretion event can theoretically increase the rotation rate of the pulsar to hundreds of times a second, as is observed in millisecond pulsars. However, there has been recent evidence that the standard evolutionary model fails to explain the evolution of all millisecond pulsars young millisecond pulsars with high magnetic fields, e.g. PSR B1937+21.
Bülent Kiziltan and S. E. Thorsett showed that different millisecond pulsars must form by at least two distinct processes, but the nature of the other process remains a mystery. Many millisecond pulsars are found in globular clusters; this is consistent with the spin-up theory of their formation, as the high stellar density of these clusters implies a much higher likelihood of a pulsar having a giant companion star. There are 130 millisecond pulsars known in globular clusters; the globular cluster Terzan 5 alone contains 37 of these, followed by 47 Tucanae with 22 and M28 and M15 with 8 pulsars each. Millisecond pulsars, which can be timed with high precision, are better clocks than the best atomic clocks of 1997; this makes them sensitive probes of their environments. For example, anything placed in orbit around them causes periodic Doppler shifts in their pulses' arrival times on Earth, which can be analyzed to reveal the presence of the companion and, with enough data, provide precise measurements of the orbit and the object's mass.
The technique is so sensitive that objects as small as asteroids can be detected if they happen to orbit a millisecond pulsar. The first confirmed exoplanets, discovered several years before the first detections of exoplanets around "normal" solar-like stars, were found in orbit around a millisecond pulsar, PSR B1257+12; these planets remained for many years the only Earth-mass objects known outside the Solar System. One of them, PSR B1257+12 D, has an smaller mass, comparable to that of our Moon, is still today the smallest-mass object known beyond the Solar System; the first millisecond pulsar, PSR B1937 +21, was discovered in 1982 by al.. Spinning 641 times a second, it remains the second fastest-spinning millisecond pulsar of the 200 that have been discovered. Pulsar PSR J1748-2446ad, discovered in 2005, is, as of 2012, the fastest-spinning pulsar known, spinning 716 times a second. Current theories of neutron star structure and evolution predict that pulsars would break apart if they spun at a rate of c. 1500 rotations per second or more, that at a rate of above about 1000 rotations per second they would lose energy by gravitational radiation faster than the accretion process would speed them up.
However, in early 2007 data from the Rossi X-ray Timing Explorer and INTEGRAL spacecraft discovered a neutron star XTE J1739-285 rotating at 1122 Hz. The result is not statistically significant, with a significance level of only 3 sigma. Therefore, while it is an interesting candidate for further observations, current results are inconclusive. Still, it is believed. Furthermore, one X-ray pulsar that spins at 599 revolutions per second, IGR J00291+5934, is a prime candidate for helping detect such waves in the future. "Pinning Down a Pulsar's Age". Science News. "How Millisecond Pulsars Spin So Fast". Universe Today. "Fast-Spinning Star Could Test Gravitational Waves". New Scientist. "Astronomical whirling dervishes hide their age well". Astronomy Now. Audio: Cain/Gay - Pulsars Astronomy Cast - Nov 2009
Polarization is a property applying to transverse waves that specifies the geometrical orientation of the oscillations. In a transverse wave, the direction of the oscillation is perpendicular to the direction of motion of the wave. A simple example of a polarized transverse wave is vibrations traveling along a taut string. Depending on how the string is plucked, the vibrations can be in a vertical direction, horizontal direction, or at any angle perpendicular to the string. In contrast, in longitudinal waves, such as sound waves in a liquid or gas, the displacement of the particles in the oscillation is always in the direction of propagation, so these waves do not exhibit polarization. Transverse waves that exhibit polarization include electromagnetic waves such as light and radio waves, gravitational waves, transverse sound waves in solids. In some types of transverse waves, the wave displacement is limited to a single direction, so these do not exhibit polarization. An electromagnetic wave such as light consists of a coupled oscillating electric field and magnetic field which are always perpendicular.
In linear polarization, the fields oscillate in a single direction. In circular or elliptical polarization, the fields rotate at a constant rate in a plane as the wave travels; the rotation can have two possible directions. Light or other electromagnetic radiation from many sources, such as the sun and incandescent lamps, consists of short wave trains with an equal mixture of polarizations. Polarized light can be produced by passing unpolarized light through a polarizer, which allows waves of only one polarization to pass through; the most common optical materials are isotropic and do not affect the polarization of light passing through them. Some of these are used to make polarizing filters. Light is partially polarized when it reflects from a surface. According to quantum mechanics, electromagnetic waves can be viewed as streams of particles called photons; when viewed in this way, the polarization of an electromagnetic wave is determined by a quantum mechanical property of photons called their spin.
A photon has one of two possible spins: it can either spin in a right hand sense or a left hand sense about its direction of travel. Circularly polarized electromagnetic waves are composed of photons with only one type of spin, either right- or left-hand. Linearly polarized waves consist of photons that are in a superposition of right and left circularly polarized states, with equal amplitude and phases synchronized to give oscillation in a plane. Polarization is an important parameter in areas of science dealing with transverse waves, such as optics, seismology and microwaves. Impacted are technologies such as lasers and optical fiber telecommunications, radar. Most sources of light are classified as incoherent and unpolarized because they consist of a random mixture of waves having different spatial characteristics, frequencies and polarization states. However, for understanding electromagnetic waves and polarization in particular, it is easiest to just consider coherent plane waves. Characterizing an optical system in relation to a plane wave with those given parameters can be used to predict its response to a more general case, since a wave with any specified spatial structure can be decomposed into a combination of plane waves.
And incoherent states can be modeled stochastically as a weighted combination of such uncorrelated waves with some distribution of frequencies and polarizations. Electromagnetic waves, traveling in free space or another homogeneous isotropic non-attenuating medium, are properly described as transverse waves, meaning that a plane wave's electric field vector E and magnetic field H are in directions perpendicular to the direction of wave propagation. By convention, the "polarization" direction of an electromagnetic wave is given by its electric field vector. Considering a monochromatic plane wave of optical frequency f, let us take the direction of propagation as the z axis. Being a transverse wave the E and H fields must contain components only in the x and y directions whereas Ez = Hz = 0. Using complex notation, the instantaneous physical electric and magnetic fields are given by the real parts of the complex quantities occurring in the following equations; as a function of time t and spatial position z these complex fields can be written as: E → =