Electromagnetic radiation: thermal emissions
Electromagnetic radiation in the context of thermal emissions refers to the process by which objects emit energy in the form of photons as they transition between quantized energy levels. When atoms or ions are excited, they can move to higher energy states and, upon returning to lower states, emit photons whose wavelengths correspond to the energy differences. This emission creates a thermal spectrum that can vary based on factors such as temperature, density, and the object's composition. At high densities, like those found in solids or liquids, energy levels overlap, allowing for a continuum of emitted wavelengths, referred to as thermal radiation or blackbody radiation.
Key principles governing thermal emissions include Wien's law, which relates peak wavelength to temperature, and the Stefan-Boltzmann law, which connects total energy emitted to temperature. These laws have been applied to various celestial bodies, including the Sun and planets, to derive their temperatures and gain insights into their characteristics. Thermal emissions play a critical role in astronomy, enabling scientists to study objects in our solar system and beyond, revealing information about their composition, mineral distribution, and formation processes. Overall, understanding thermal emissions provides valuable insights into both the physical properties of celestial bodies and the broader context of the universe.
Electromagnetic radiation: thermal emissions
Electromagnetic radiation emitted from the surface of an object provides valuable information regarding the object's physical state. Whenever the object's temperature is above absolute zero, the intensity of the radiation emitted and its distribution with wavelength—its thermal spectrum—largely depends only on the absolute temperature of the object. Thus, the temperature of an object can be determined from its thermal emissions.
Overview
An isolated atom or ion possesses a unique set of discrete, quantized energy levels. Transitions from a higher energy level to a lower one result in the emission of a photon of electromagnetic radiation whose wavelength depends on the difference in energy between the two levels. Specifically, Ephoton = Ehigher - Elower = hc/λ, where h is Planck’s constant, c is the speed of light in a vacuum, and λ is the wavelength of the photon emitted. The inverse process, involving the absorption of a photon of the same wavelength, will cause the atom or ion to transition from the lower energy state to the higher one. Thus, if an atom or ion is excited to one of its high energy states by a collision with some other atom or by absorbing radiation, cascading down to lower energy states produces emissions of photons of various specific wavelengths corresponding to the energy gaps between pair combinations of energy levels. This emission (or absorption) spectrum identifies the atom or ion involved in the process.
A discrete spectrum, however, can be quite complex because it depends not only on the temperature and chemical composition of the object but also on its density, the local gravity field, the object’s speed, and whether all parts are in thermal equilibrium. When atoms crowd together at high density, however—as in a solid, a liquid, or even a gas in the interior of a star—the energy levels of each atom or ion shift from their isolated configuration. The resulting smearing of energy levels relative to their isolated configuration permits a continuum of transitions where formerly only discrete transitions existed. If the material is dense enough, no restrictions exist as to which wavelengths can be emitted or absorbed. The electromagnetic radiation emitted, in this case, is called thermal radiation. In an idealized case where the composition and surface texture of the object can be neglected, the electromagnetic radiation emitted is also referred to as blackbody radiation. The shape and characteristics of the resulting spectrum depend only on the temperature of the object emitting the radiation.
Experimental investigations in the last quarter of the nineteenth century showed that relatively low-intensity emissions at short wavelengths characterize the thermal spectrum of a hot object, a rapid rise in intensity peaking at some intermediate wavelength, followed by a gradual diminishing in intensity at longer wavelengths. Furthermore, Wilhelm Wien, by applying the laws of thermodynamics to electromagnetic radiation, showed in 1893 that the wavelength at which the peak in the thermal spectrum appears depends on the temperature of the object according to the relation λpeak = b/T, where T is the absolute temperature of the object and b is a constant whose value is 2.898 10-3 meter kelvin. (Max Planck later showed that b is constituted from other fundamental constants of nature.)
In 1879, Jožef Stefan used the experimental measurements of thermal spectra to deduce an expression giving the irradiance, the total energy radiated per unit time interval by a blackbody per unit area of the emitting surface, as a function of the object’s temperature. In 1884, Ludwig Boltzmann provided the theoretical framework for the expression, which came to be known as the Stefan-Boltzmann law. This relation linking the irradiance with temperature, R = σT4, contains a new constant σ whose value is 5.67 10-8 joule/second/meter2/kelvin4 and indicates that the amount of energy radiated by a blackbody increases rapidly with temperature. Like the constant b, σ, too, was later shown to be composed of fundamental constants of nature.
By 1900, Max Planck had synthesized the prior experimental and theoretical information with his quantum hypothesis to deduce the precise relation that describes the blackbody spectrum of an object. The intensity I(λ,T) of light emitted at a wavelength λ by a blackbody at temperature T is given as
I(λ,T) = 2hc2/[λ5(ehc/λkT - 1)]
a relation known as Planck’s law. The constant k is Boltzmann’s constant. Though these relations strictly apply only to blackbodies, many objects, to varying degrees, approximate blackbodies, especially if their temperatures are very high or low.
Tracing an object’s thermal spectrum involves measuring light intensity through different filters that transmit electromagnetic radiation in relatively small bands of wavelengths. Modern technologies permit the fabrication of filters and detectors for any region of the electromagnetic spectrum. Typically, however, measuring the intensity of thermal emissions in only three or four wavelength bands suffices to determine the shape of an object’s thermal spectrum and, therefore, estimate its temperature. Because the Earth’s atmosphere filters incoming electromagnetic radiation, intensity measurements in parts of the infrared and radio regions and nearly all measurements at wavelengths shorter than the violet are best made from satellites outside the atmosphere. The solar system contains objects that produce phenomena at various temperatures.
The Sun, the hottest object in the solar system, generates enormous amounts of energy through nuclear reactions. Its hot, dense interior produces a spectrum that is nearly blackbody. However, highly energetic phenomena in the Sun’s photosphere, chromospheres, and corona superimpose nonthermal features on the blackbody spectrum. The planets, too, are sources of thermal emissions, not only because of their warmth in absorbing and then reemitting solar radiation but also because of the residual radiating energy left over from their formation and internal heat generated by the decay of radioactive nuclei. Scattered throughout the solar system, dust fills much of the space between planets and is plentiful in its outer regions. Far from the Sun, the temperature of the dust falls to just a few tens of degrees above absolute zero, resulting in thermal emissions in the far-infrared region of the spectrum. Detecting thermal emissions from cold objects presents a challenge, however. To prevent the thermal emissions from the detector itself from overwhelming the signal from the object studied, the detector, with its electronics, must be cooled to temperatures very near absolute zero.
Knowledge Gained
Thermal spectra provide a wealth of fundamental information regarding objects in the solar system. The Sun’s spectrum is particularly informative. From satellite observations outside the complicating effects of Earth’s atmosphere, the wavelength of the peak intensity is approximately 470 nanometers. Wien’s law indicates that the corresponding temperature of the visible portion of the Sun, its photosphere, is 6,170 kelvins. Another estimate of the Sun’s temperature may be obtained from the Stefan-Boltzmann law, which links the irradiance of the Sun to its temperature. From satellite measurements outside Earth’s atmosphere, 1,368 watts of electromagnetic power are delivered to each square meter of detector surface. Because the distance to the Sun is known, the total power output of the Sun can be computed to be 3.85 1026 watts, and from its size, the irradiance is determined to be 6.34 107 watts/meter2. The Stefan-Boltzmann law implies that the Sun’s temperature is 5,780 kelvins. The temperatures determined by these two methods differ because the Sun is not a perfect blackbody. Nonthermal absorption features created by atoms and ions in its atmosphere remove energy from one part of the spectrum, and that energy reappears in other parts, thus producing a spectrum slightly distorted from that of a blackbody.
A combination of Wien’s law and the Stefan-Boltzmann law yields an equilibrium temperature profile within the solar system illuminated by the central Sun. Thus, objects farther from the Sun capture less of the Sun’s radiant energy, are cooler than objects nearer the Sun, and possess thermal spectra whose peak wavelengths are longer than objects nearer the Sun. As an example of applying this principle, the location of most dust in the solar system can be deduced. Visual observations from Earth have long recognized that the zodiacal light was likely due to dust lying in the ecliptic plane. Infrared satellite observations of the dust indicate that the peak in the thermal spectrum of the dust occurs at approximately 12 microns (1 micron = 10-6 meters). The twelve-micron peak in the thermal spectrum of the dust in the solar system corresponds to a distance of 4.0 1011 meters, or about 2.7 AU (one astronomical unit, or AU, being the mean distance between Earth and the Sun), a location at the inner region of the asteroid belt. Most likely, collisions among objects within the asteroid belt generate the observed dust.
Context
An idealized blackbody spectrum closely mimics the thermal electromagnetic radiation produced by a real object for the corresponding temperature. In this case, the wealth of theoretical results associated with blackbody radiation can be used to tease out information from the object under study. Within our solar system, images of rocky worlds taken through two or three filters in different parts of their thermal spectra produce a composite image displaying the minerals' distribution on their surfaces. Sometimes, such a composite image identifies the minerals without retrieving a sample. This helps planetary scientists understand the relation between the mineralogy and the landforms, providing valuable clues as to the processes that produced the visible landscape. In other cases, thermal emission images of the surface of a planet, satellite, or asteroid serve as an essential prelude to identifying the best target areas for a landing and site exploration, as in the case of many missions to the Moon and Mars.
The same information gleaned from the thermal spectra of objects within the solar system can be retrieved from a study of the spectra of objects and systems throughout the cosmos. Dust around young stars sometimes points to the formation of new solar systems beyond our own. Finally, the universe itself announces itself in subtle, omnipresent thermal emissions corresponding to a blackbody at a temperature of 2.725 kelvins, the radiation left over from the hot, dense creation of the cosmos 13.7 billion years ago.
Bibliography
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