Luminosity

Luminosity has different meanings in several different fields of science.

1 In photometry and color imaging
2 In astronomy
- 2.1 Computing between brightness and luminosity
- 2.2 Computing between luminosity and magnitude
3 In scattering theory and accelerator physics
- 3.1 Elementary relations for luminosity

In photometry and color imaging

Main article: luminance

In photometry, luminosity is sometimes incorrectly used to refer to luminance, which is the density of luminous intensity in a given direction. Luminance is a photometric measure of the density of Luminous intensity in a given direction Luminance is a photometric measure of the density of Luminous intensity in a given direction In photometry, luminous intensity is a measure of the wavelength-weighted power emitted by a Light source in a particular direction per unit Solid The SI unit for luminance is candela per square metre. The candela (kanˈdɛlə /-ˈdiːlə/ symbol cd) is the SI base unit of Luminous intensity; that is power emitted by a light source in a particular M^2 redirects here For other uses see M². CM2 redirects here

Main article: luma (video)

In Adobe Photoshop's imaging operations, luminosity is the term used incorrectly to refer to the luma component of a color image signal; that is, a weighted sum of the nonlinear red, green, and blue signals. As applied to video signals luma represents the brightness in an image (the "black and white" or achromatic portion of the image As applied to video signals luma represents the brightness in an image (the "black and white" or achromatic portion of the image It seems to be calculated with the Rec. 601 luma co-efficients (Rec. 601: Luma (Y’) = 0. 299 R’ + 0. 587 G’ + 0. 114 B’).

Main article: HSL color space

The "L" in HSL color space is sometimes said to stand for luminosity. HSL and HSV are two related representations of points in an RGB color space, which attempt to describe perceptual color relationships more accurately than HSL and HSV are two related representations of points in an RGB color space, which attempt to describe perceptual color relationships more accurately than "L" in this case is calculated as 1/2 (MAX + MIN), where MAX and MIN refer to the highest and lowest of the R'G'B' components to be converted into HSL color space.

In astronomy

In astronomy, luminosity is the amount of energy a body radiates per unit time. Astronomy (from the Greek words astron (ἄστρον "star" and nomos (νόμος "law" is the scientific study

The luminosity of stars is measured in two forms: apparent (counting visible light only) and bolometric (total radiant energy); a bolometer is an instrument that measures radiant energy over a wide band by absorption and measurement of heating. A bolometer is a device for measuring the energy of incident Electromagnetic radiation. When not qualified, luminosity means bolometric luminosity, which is measured in the SI units watts, or in terms of solar luminosities, $L_{\odot}$ ; that is, how many times as much energy the object radiates than the Sun, whose luminosity is 3. The watt (symbol W) is the SI derived unit of power, equal to one Joule of energy per Second. The solar luminosity, L_\odot is a unit of Luminosity ( power emitted in the form of Photons conventionally used by Astronomers to The Sun (Sol is the Star at the center of the Solar System. 846×10²⁶ W.

Luminosity is an intrinsic constant independent of distance, and is measured as absolute magnitude corresponding to apparent luminosity, or bolometric magnitude corresponding to bolometric luminosity. In Astronomy, absolute magnitude (also known as absolute visual magnitude) is the Apparent magnitude an object would have if it were at a standard In contrast, apparent brightness is related to distance by an inverse square law. Visible brightness is usually measured by apparent magnitude, which is on a logarithmic scale. The apparent magnitude ( m) of a celestial body is a measure of its Brightness as seen by an observer on Earth, normalized to the value

In measuring star brightnesses, visible luminosity (not total luminosity at all wave lengths), apparent magnitude (visible brightness), and distance are interrelated parameters. The apparent magnitude ( m) of a celestial body is a measure of its Brightness as seen by an observer on Earth, normalized to the value Distance is a numerical description of how far apart objects are If you know two, you can determine the third. Since the sun's luminosity is the standard, comparing these parameters with the sun's apparent magnitude and distance is the easiest way to remember how to convert between them.

Computing between brightness and luminosity

Imagine a point source of light of luminosity $L$ that radiates equally in all directions. A hollow sphere centered on the point would have its entire interior surface illuminated. "Globose" redirects here See also Globose nucleus. A sphere (from Greek σφαίρα - sphaira, "globe As the radius increases, the surface area will also increase, and the constant luminosity has more surface area to illuminate, leading to a decrease in observed brightness.

$b = \frac{L}{A}$

where

A

is the area of the illuminated surface.

For stars and other point sources of light, $A = 4π r 2$ so

$b = \frac{L}{4\pi r^2} \,$

where

r

is the distance from the observer to the light source.

It has been shown that the luminosity of a star $L$ (assuming the star is a black body, which is a good approximation) is also related to temperature $T$ and radius $R$ of the star by the equation:

$L = 4\pi R^2\sigma T^4 \,$

where

σ is the Stefan-Boltzmann constant 5. In Physics, a black body is an object that absorbs all light that falls on it The Stefan–Boltzmann constant (also Stefan's constant) a Physical constant denoted by the Greek letter σ, is the Constant of proportionality 67×10⁻⁸ W·m^-2·K^-4

Dividing by the luminosity of the sun $L_{\odot}$ and cancelling constants, we obtain the relationship

$\frac{L}{L_{\odot}} = {\left ( \frac{R}{R_{\odot}} \right )}^2 {\left ( \frac{T}{T_{\odot}} \right )}^4$ . The watt (symbol W) is the SI derived unit of power, equal to one Joule of energy per Second.

For stars on the main sequence, luminosity is also related to mass:

$\frac{L}{L_{\odot}} \sim {\left ( \frac{M}{M_{\odot}} \right )}^{3.9}$

It is easy to see that a star's luminosity, temperature, radius, and mass are all related. The main sequence is the name for a continuous and distinctive band of stars that appear on a plot of stellar color versus brightness

The magnitude of a star is a logarithmic scale of observed visible brightness. The apparent magnitude is the observed visible brightness from Earth, and the absolute magnitude is the apparent magnitude at a distance of 10 parsecs. The apparent magnitude ( m) of a celestial body is a measure of its Brightness as seen by an observer on Earth, normalized to the value EARTH was a short-lived Japanese vocal trio which released 6 singles and 1 album between 2000 and 2001 In Astronomy, absolute magnitude (also known as absolute visual magnitude) is the Apparent magnitude an object would have if it were at a standard The apparent magnitude ( m) of a celestial body is a measure of its Brightness as seen by an observer on Earth, normalized to the value History The first direct measurements of an object at interstellar distances were undertaken by German Astronomer Friedrich Wilhelm Bessel in 1838 Given a visible luminosity (not total luminosity), one can calculate the apparent magnitude of a star from a given distance:

$m_{\rm star}=m_{\rm sun}-2.5\log_{10}\left({ L_{\rm star} \over L_{\odot} } \cdot \left(\frac{ r_{\rm sun} }{ r_{\rm star} }\right)^2\right)$

where

m_star is the apparent magnitude of the star (a pure number)

m_sun is the apparent magnitude of the sun (also a pure number)

L_star is the visible luminosity of the star

$L_{\odot}$ is the solar visible luminosity

r_star is the distance to the star

r_sun is the distance to the sun

Or simplified, given m_sun = −26. The apparent magnitude ( m) of a celestial body is a measure of its Brightness as seen by an observer on Earth, normalized to the value 73, dist_sun = 1. 58 × 10⁻⁵ lyr:

m_star = − 2. 72 − 2. 5 · log(L_star/dist_star²)

Example:

How bright would a star like the sun be from 4. 3 light years away? (The distance to the next closest star Alpha Centauri)

m_sun (@4. Alpha Centauri (α Centauri / α Cen also known as Rigil Kentaurus, Rigil Kent, or Toliman, is the brightest Star in the southern Constellation 3lyr) = −2. 72 − 2. 5 · log(1/4. 3²) = 0. 45

0. 45 magnitude would be a very bright star, but not quite as bright as Alpha Centauri.

Also you can calculate the luminosity given a distance and apparent magnitude:

L_star/ $L_{\odot}$ = (dist_star/dist_sun)² · 10^{[(m_sun −m_star) · 0. 4]}

L_star = 0. 0813 · dist_star² · 10^{(−0. 4 · m_star)} · $L_{\odot}$

Example:

What is the luminosity of the star Sirius?

Sirius is 8. Sirius is the brightest star in the night sky with a visual Apparent magnitude of &minus1 6 lyr distant, and magnitude −1. 47.

L_Sirius = 0. 0813 · 8. 6² · 10^{−0. 4·(−1. 47)} = 23. 3 × $L_{\odot}$

You can say that Sirius is 23 times brighter than the sun, or it radiates 23 suns.

A bright star with bolometric magnitude −10 has a luminosity of 10⁶ $L_{\odot}$ , whereas a dim star with bolometric magnitude +17 has luminosity of 10⁻⁵ $L_{\odot}$ . A star is a massive luminous ball of plasma. The nearest star to Earth is the Sun, which is the source of most of the Energy on Earth In Astronomy, absolute magnitude (also known as absolute visual magnitude) is the Apparent magnitude an object would have if it were at a standard Note that absolute magnitude is directly related to luminosity, but apparent magnitude is also a function of distance. In Astronomy, absolute magnitude (also known as absolute visual magnitude) is the Apparent magnitude an object would have if it were at a standard The apparent magnitude ( m) of a celestial body is a measure of its Brightness as seen by an observer on Earth, normalized to the value Since only apparent magnitude can be measured observationally, an estimate of distance is required to determine the luminosity of an object.

Computing between luminosity and magnitude

A magnitude difference is related to stellar luminosity ratio according to:

$M_1 - M_2 = -2.5 \log{\frac{L_1}{L_2}}$

which makes by inversion:

$\frac{L_1}{L_2} = 10^{(M_2 - M_1)/2.5}.$

In scattering theory and accelerator physics

In scattering theory and accelerator physics, luminosity is the number of particles per unit area per unit time times the opacity of the target, usually expressed in either the cgs units cm^-2 s^-1 or b^-1 s^-1. In Mathematics and Physics, scattering theory is a framework for studying and understanding the Scattering of Waves and particles. Area is a Quantity expressing the two- Dimensional size of a defined part of a Surface, typically a region bounded by a closed Curve. For other uses see Time (disambiguation Time is a component of a measuring system used to sequence events to compare the durations of Opacity is the measure of impenetrability to electromagnetic or other kinds of radiation especially visible Light. The centimetre-gram-second system ( CGS) is a system of physical units. A centimetre ( American spelling: centimeter, symbol cm) is a unit of Length in the Metric system, equal to one hundredth The second ( SI symbol s) sometimes abbreviated sec, is the name of a unit of Time, and is the International System of Units A barn (symbol b) is a unit of Area. While the barn is not an SI unit it is accepted (although discouraged for use with the SI The integrated luminosity is the integral of the luminosity with respect to time. The European Space Agency 's INTErnational Gamma-Ray Astrophysics Laboratory ( INTEGRAL) is detecting some of the most energetic radiation that comes from space The luminosity is an important value to characterize the performance of an accelerator.

Elementary relations for luminosity

The following relations hold

$L = \rho v \,$ (if the target is perfectly opaque)

$\frac{dN}{dt} = L \sigma$

$\frac{d\sigma}{d\Omega} = \frac{1}{L} \frac{d^{2}N}{d\Omega dt}$

where

L

is the Luminosity.

N

is the number of interactions.

ρ

is the number density of a particle beam.

σ

is the total cross section. In nuclear and Particle physics, the concept of a cross section is used to express the likelihood of interaction between particles

d Ω

is the differential solid angle. The solid angle, Ω, is the angle in three-dimensional space that an object Subtends at a point

$\frac{d\sigma}{d\Omega}$ is the differential cross section. In nuclear and Particle physics, the concept of a cross section is used to express the likelihood of interaction between particles

For an intersecting storage ring collider:

$L = f n \frac{N_{1} N_{2}}{A}$

where

f

is the revolution frequency

n

is the number of bunches in one beam in the storage ring.

N i

is the number of particles in each bunch

A

is the cross section of the beam.

Dictionary

-noun

(uncountable) the state of being luminous, or a luminous object; brilliance or radiance
(physics) the ratio of luminous flux to radiant flux at the same wavelength; the luminosity factor
(astronomy) the rate at which a star radiates energy in all directions

Contents

In photometry and color imaging

In astronomy

Computing between brightness and luminosity

Computing between luminosity and magnitude

In scattering theory and accelerator physics

Elementary relations for luminosity

Dictionary

luminosity

-noun