An Etymological Dictionary of Astronomy and Astrophysics
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A theorem relating the → Fourier coefficients to the function that they describe. It states that: (1/L) ∫ |f(x)|²dx (integrated from x₀ to x₀ + L) = (a₀/2)² + (1/2) Σ (a_r² + b_r²) (summed from r = 1 to ∞). In other words, the sum of the moduli squared of the complex Fourier coefficients is equal to the average value of |f(x)|² over one period.

Named after Marc-Antoine Parseval (1755-1836), French mathematician; → theorem.

A type of differential equation involving an unknown function (or functions) of several independent variables and its (or their) partial derivatives with respect to those variables.

→ partial; → differential; → equation.

A general term to describe → light involving the following phenomena: → reflection, → refraction, and → photoelectric effect. Compare → wave nature.

→ particle; → nature.

An experiment carried out by Blaise Pascal in 1646 to demonstrate the hydraulic pressure. A long and narrow vertical pipe was connected to the content of a closed wooden barrel already full of water. He poured a small quantity of water into the pipe, whereby the height of the fluid within the pipe sharply increased. Due to the increase in hydrostatic pressure and → Pascal's law, the barrel could leak and even burst.

→ pascal (Pa); M.E. barel, from M.Fr. baril, O.Fr. barril; → experiment

A planet formation concept that concerns the → accretion of small objects of negligible gravitational mass (ranging from centimeters up to meters in diameter) onto large, gravitating bodies: → planetesimals, → protoplanets, or → planets. In a more narrow sense, pebble accretion is an accretion process where (gas) drag and gravity play major roles. Simply put, this means that the pebble has to be aerodynamically small and the planet to be gravitationally large (C. W. Ormel, in Formation, Evolution, and Dynamics of Young Solar Systems, p. 197, eds. M. Pessah, O. Gressel, Springer, 2017).

→ pebble; → accretion.

A collapsing object whose radius is less than its Schwarzschild radius must collapse into a singularity.

→ Penrose process; → theorem.

An → integer of the form n², where n is a → positive number. In other words, a → perfect power when k = 2.

→ perfect; → square.

→ advance of perihelion.

→ perihelion; → precession.

A → correlation between the periods and luminosities of → Cepheid variable stars: Cepheids with longer periods are intrinsically more luminous than those with shorter periods. The relation was discovered by Henrietta Leavitt in 1912 when studying Cepheids in the → Small Magellanic Cloud. Once the period of a Cepheid variable is determined from observations, the period-luminosity relation can be used to derive its luminosity. Since luminosity is a function of → distance, the distance can then be calculated with the luminosity. The period-luminosity relation is an invaluable tool for the measurements of distances out to the nearest galaxies and thus for studying the structure of our own Galaxy and of the Universe.

→ period; → luminosity; → relation.

A relation that gives a rough estimate of the oscillation period of a → pulsating star as a function of its mean density. This relation is obtained by considering how long it would take a sound wave to travel across the diameter of a model star: Π ≅ (3π/2γGρ)^1/2, where ρ is the mean density, γ the ratio of → specific heats (C_p/C_v), and G the → gravitational constant. This relation shows that the pulsation period of a star is inversely proportional to the square root of its mean density. And this is the reason why the pulsation periods decrease along the → instability strip from the luminous, very tenuous → supergiants to the faint, very dense → white dwarfs.

→ period; → mean; → density; → relation.

In a charge-coupled device, the detection of charge collected by the transport register rather than by the image-sensing elements.

→ peripheral; → response.

The → moment of inertia of a plane object (→ lamina) about an axis perpendicular to the plane is equal to the sum of the moments of inertia about any two perpendicular axes in the plane. Thus if x and y axes are in the plane, I_z = I_x + I_y.

→ perpendicular; → axis; → theorem.

The difference of phase (usually expressed as a time or an angle) between two periodic quantities which vary sinusoidally and have the same frequency.

→ phase; → difference.

An angular shift in phase by 180°.

→ phase; → reversal.

A correlation between the peak brightness of → Type Ia supernovae and the decline rate of their → light curve (15 days after the maximum). The decline rate is also correlated to the width of the peak brightness of the supernova. The brightest events are the broadest in time and brighter SNe Ia decline more slowly than dimmer ones. Applying the Phillips relation reduces the dispersion in the light curves of Type Ia SNe thus making them precise distance indicators which can be observed over large distances.

Named after Mark M. Phillips (1951-), American astronomer (Phillips et al. 1993, ApJ 413, L105); → relation.

A specific type of → photoluminescence that continues for an appreciable time after the stimulating process has ceased. Phosphorescence is due to the existence of metastable → excited states of the atoms and molecules from which a change to the normal state is hindered for some reason or other. The change from the → metastable metastable state to the normal one becomes possible only as a result of some additional excitation, for example the application of heat.

→ phosphorus; → -escence.

A neutral region at the boundary of a → molecular cloud created by the penetration of → far ultraviolet (FUV) radiation from associated stars. The FUV radiation (6 eV ≤ hν ≤ 13.6 eV) dissociates the molecules and heats the gas and dust. A warm, atomic → H I region is thus created and the chemistry and thermal balance of the region are determined by the penetrating FUV photons. The progressive absorption of FUV photons leads to the occurrence of transitions between atomic and molecular phases, such as H I/H₂ and C II/C I/CO transitions. By extension, any neutral region where the physics is controlled by FUV photons can be called a PDR, as it is the case for → diffuse interstellar clouds or the edge of → circumstellar disks. The PDR concept was first studied by A. G. G. M. Tielens and D. Hollenbach (1985, ApJ 291, 722).

→ photodissociation + → region.

The current produced in an → photoelectric effect process when → photoelectrons are received at the positive electrode.

→ photoelectric; → current.

A surface where if a photon is emitted from one of its points the photon follows a closed orbit and returns periodically to its departure point. Such a surface exists only near sufficiently → compact objects where the → curvature of → space-time is very important. In other words, a body can take a stable orbit around a → black hole provided that it moves with the → speed of light. However, only photons can have such a velocity; hence the term "photon sphere." For a non-rotating → Schwarzschild black hole, the photon sphere has a radius of R = 3GM/c² = 3 R_S/2, where G is the → gravitational constant, M is the mass, c is the → speed of light, and R_S is the → Schwarzschild radius. For a rotating, → Kerr black hole, the situation is much more complex due to the → Lense-Thirring effect. In that case circular paths exist for radii whose values depend on the rotation direction. More specifically, in the equatorial plane there are two possible circular light paths: a smaller one in the direction of the rotation, and a larger one in the opposite direction.

→ photon; → sphere.

1) The visible surface of the Sun (temperature 5700 K), just below the → chromosphere and just above the → convective zone. The solar photosphere is a thin layer of roughly 300 km wide. Its temperature decreases uniformly with height, from about 6,600 K (pressure 0.868 → millibars) at its bottom, to about 4,400 K (pressure 125 mb), where it merges with the chromosphere. The photosphere has a "rice-grain" appearance, called → granulation, caused by rising (hot) and falling (cool) material in the → convective cells just below the photosphere. Other main features of the photosphere are → sunspots, → faculae, and → supergranulation.
2) The region of a star which gives rise to the continuum radiation emitted by the star.

→ photo- + → sphere.