Absolute magnitude

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Absolute_magnitude#Bolometric_magnitude

Absolute magnitude (M) is a measure of the luminosity of a celestial object, on an inverse logarithmic astronomical magnitude scale. An object's absolute magnitude is defined to be equal to the apparent magnitude that the object would have if it were viewed from a distance of exactly 10 parsecs (32.6 light-years), without extinction (or dimming) of its light due to absorption by interstellar matter and cosmic dust. By hypothetically placing all objects at a standard reference distance from the observer, their luminosities can be directly compared on a magnitude scale.

As with all astronomical magnitudes, the absolute magnitude can be specified for different wavelength ranges corresponding to specified filter bands or passbands; for stars a commonly quoted absolute magnitude is the absolute visual magnitude, which uses the visual (V) band of the spectrum (in the UBV photometric system). Absolute magnitudes are denoted by a capital M, with a subscript representing the filter band used for measurement, such as M_V for absolute magnitude in the V band.

The more luminous an object, the smaller the numerical value of its absolute magnitude. A difference of 5 magnitudes between the absolute magnitudes of two objects corresponds to a ratio of 100 in their luminosities, and a difference of n magnitudes in absolute magnitude corresponds to a luminosity ratio of 100^(n/5). For example, a star of absolute magnitude M_V=3.0 would be 100 times as luminous as a star of absolute magnitude M_V=8.0 as measured in the V filter band. The Sun has absolute magnitude M_V=+4.83. Highly luminous objects can have negative absolute magnitudes: for example, the Milky Way galaxy has an absolute B magnitude of about −20.8.

An object's absolute bolometric magnitude (M_bol) represents its total luminosity over all wavelengths, rather than in a single filter band, as expressed on a logarithmic magnitude scale. To convert from an absolute magnitude in a specific filter band to absolute bolometric magnitude, a bolometric correction (BC) is applied.

For Solar System bodies that shine in reflected light, a different definition of absolute magnitude (H) is used, based on a standard reference distance of one astronomical unit.

Stars and galaxies

In stellar and galactic astronomy, the standard distance is 10 parsecs (about 32.616 light-years, 308.57 petameters or 308.57 trillion kilometres). A star at 10 parsecs has a parallax of 0.1″ (100 milliarcseconds). Galaxies (and other extended objects) are much larger than 10 parsecs, their light is radiated over an extended patch of sky, and their overall brightness cannot be directly observed from relatively short distances, but the same convention is used. A galaxy's magnitude is defined by measuring all the light radiated over the entire object, treating that integrated brightness as the brightness of a single point-like or star-like source, and computing the magnitude of that point-like source as it would appear if observed at the standard 10 parsecs distance. Consequently, the absolute magnitude of any object equals the apparent magnitude it would have if it were 10 parsecs away.

The measurement of absolute magnitude is made with an instrument called a bolometer. When using an absolute magnitude, one must specify the type of electromagnetic radiation being measured. When referring to total energy output, the proper term is bolometric magnitude. The bolometric magnitude usually is computed from the visual magnitude plus a bolometric correction, M_bol = M_V + BC. This correction is needed because very hot stars radiate mostly ultraviolet radiation, whereas very cool stars radiate mostly infrared radiation (see Planck's law).

Some stars visible to the naked eye have such a low absolute magnitude that they would appear bright enough to outshine the planets and cast shadows if they were at 10 parsecs from the Earth. Examples include Rigel (−7.0), Deneb (−7.2), Naos (−6.0), and Betelgeuse (−5.6). For comparison, Sirius has an absolute magnitude of only 1.4, which is still brighter than the Sun, whose absolute visual magnitude is 4.83. The Sun's absolute bolometric magnitude is set arbitrarily, usually at 4.75. Absolute magnitudes of stars generally range from −10 to +17. The absolute magnitudes of galaxies can be much lower (brighter). For example, the giant elliptical galaxy M87 has an absolute magnitude of −22 (i.e. as bright as about 60,000 stars of magnitude −10). Some active galactic nuclei (quasars like CTA-102) can reach absolute magnitudes in excess of −32, making them the most luminous objects in the observable universe.

Apparent magnitude

The Greek astronomer Hipparchus established a numerical scale to describe the brightness of each star appearing in the sky. The brightest stars in the sky were assigned an apparent magnitude m = 1, and the dimmest stars visible to the naked eye are assigned m = 6. The difference between them corresponds to a factor of 100 in brightness. For objects within the immediate neighborhood of the Sun, the absolute magnitude M and apparent magnitude m from any distance d (in parsecs, with 1 pc = 3.2616 light-years) are related by

${\displaystyle 100^{\frac {m-M}{5}}={\frac {F_{10}}{F}}=\left({\frac {d}{10\;\mathrm {pc} }}\right)^{2},}$

where F is the radiant flux measured at distance d (in parsecs), F₁₀ the radiant flux measured at distance 10 pc. Using the common logarithm, the equation can be written as

${\displaystyle M=m-5\log _{10}(d_{\text{pc}})+5=m-5\left(\log _{10}d_{\text{pc}}-1\right),}$

where it is assumed that extinction from gas and dust is negligible. Typical extinction rates within the Milky Way galaxy are 1 to 2 magnitudes per kiloparsec, when dark clouds are taken into account.

For objects at very large distances (outside the Milky Way) the luminosity distance d_L (distance defined using luminosity measurements) must be used instead of d, because the Euclidean approximation is invalid for distant objects. Instead, general relativity must be taken into account. Moreover, the cosmological redshift complicates the relationship between absolute and apparent magnitude, because the radiation observed was shifted into the red range of the spectrum. To compare the magnitudes of very distant objects with those of local objects, a K correction might have to be applied to the magnitudes of the distant objects.

The absolute magnitude M can also be written in terms of the apparent magnitude m and stellar parallax p:

${\displaystyle M=m+5\left(\log _{10}p+1\right),}$

or using apparent magnitude m and distance modulus μ:

${\displaystyle M=m-\mu }$.

Examples

Rigel has a visual magnitude m_V of 0.12 and distance of about 860 light-years:

${\displaystyle M_{\mathrm {V} }=0.12-5\left(\log _{10}{\frac {860}{3.2616}}-1\right)=-7.0.}$

Vega has a parallax p of 0.129″, and an apparent magnitude m_V of 0.03:

${\displaystyle M_{\mathrm {V} }=0.03+5\left(\log _{10}{0.129}+1\right)=+0.6.}$

The Black Eye Galaxy has a visual magnitude m_V of 9.36 and a distance modulus μ of 31.06:

${\displaystyle M_{\mathrm {V} }=9.36-31.06=-21.7.}$

Bolometric magnitude

The bolometric magnitude M_bol, takes into account electromagnetic radiation at all wavelengths. It includes those unobserved due to instrumental passband, the Earth's atmospheric absorption, and extinction by interstellar dust. It is defined based on the luminosity of the stars. In the case of stars with few observations, it must be computed assuming an effective temperature.

Classically, the difference in bolometric magnitude is related to the luminosity ratio according to:

${\displaystyle M_{\mathrm {bol,\star } }-M_{\mathrm {bol,\odot } }=-2.5\log _{10}\left({\frac {L_{\star }}{L_{\odot }}}\right)}$

which makes by inversion:

${\displaystyle {\frac {L_{\star }}{L_{\odot }}}=10^{0.4\left(M_{\mathrm {bol,\odot } }-M_{\mathrm {bol,\star } }\right)}}$

where

L_⊙ is the Sun's luminosity (bolometric luminosity)

L_★ is the star's luminosity (bolometric luminosity)

M_bol,⊙ is the bolometric magnitude of the Sun

M_bol,★ is the bolometric magnitude of the star.

In August 2015, the International Astronomical Union passed Resolution B2 defining the zero points of the absolute and apparent bolometric magnitude scales in SI units for power (watts) and irradiance (W/m²), respectively. Although bolometric magnitudes had been used by astronomers for many decades, there had been systematic differences in the absolute magnitude-luminosity scales presented in various astronomical references, and no international standardization. This led to systematic differences in bolometric corrections scales. Combined with incorrect assumed absolute bolometric magnitudes for the Sun, this could lead to systematic errors in estimated stellar luminosities (and other stellar properties, such as radii or ages, which rely on stellar luminosity to be calculated).

Resolution B2 defines an absolute bolometric magnitude scale where M_bol = 0 corresponds to luminosity L₀ = 3.0128×10²⁸ W, with the zero point luminosity L₀ set such that the Sun (with nominal luminosity 3.828×10²⁶ W) corresponds to absolute bolometric magnitude M_bol,⊙ = 4.74. Placing a radiation source (e.g. star) at the standard distance of 10 parsecs, it follows that the zero point of the apparent bolometric magnitude scale m_bol = 0 corresponds to irradiance f₀ = 2.518021002×10⁻⁸ W/m². Using the IAU 2015 scale, the nominal total solar irradiance ("solar constant") measured at 1 astronomical unit (1361 W/m²) corresponds to an apparent bolometric magnitude of the Sun of m_bol,⊙ = −26.832.

Following Resolution B2, the relation between a star's absolute bolometric magnitude and its luminosity is no longer directly tied to the Sun's (variable) luminosity:

${\displaystyle M_{\mathrm {bol} }=-2.5\log _{10}{\frac {L_{\star }}{L_{0}}}\approx -2.5\log _{10}L_{\star }+71.197425}$

where

L_★ is the star's luminosity (bolometric luminosity) in watts

L₀ is the zero point luminosity 3.0128×10²⁸ W

M_bol is the bolometric magnitude of the star

The new IAU absolute magnitude scale permanently disconnects the scale from the variable Sun. However, on this SI power scale, the nominal solar luminosity corresponds closely to M_bol = 4.74, a value that was commonly adopted by astronomers before the 2015 IAU resolution.

The luminosity of the star in watts can be calculated as a function of its absolute bolometric magnitude M_bol as:

${\displaystyle L_{\star }=L_{0}10^{-0.4M_{\mathrm {bol} }}}$

using the variables as defined previously.

Solar System bodies (H)

Abs Mag (H)
and Diameter
for asteroids
(albedo=0.15)

H	Diameter
10	34 km
12.6	10 km
15	3.4 km
17.6	1 km
19.2	500 meter
20	340 meter
22.6	100 meter
24.2	50 meter
25	34 meter
27.6	10 meter
30	3.4 meter

For planets and asteroids, a definition of absolute magnitude that is more meaningful for non-stellar objects is used. The absolute magnitude, commonly called ${\displaystyle H}$, is defined as the apparent magnitude that the object would have if it were one astronomical unit (AU) from both the Sun and the observer, and in conditions of ideal solar opposition (an arrangement that is impossible in practice). Solar System bodies are illuminated by the Sun, therefore the magnitude varies as a function of illumination conditions, described by the phase angle. This relationship is referred to as the phase curve. The absolute magnitude is the brightness at phase angle zero, an arrangement known as opposition, from a distance of one AU.

Apparent magnitude

The phase angle ${\displaystyle \alpha }$ can be calculated from the distances body-sun, observer-sun and observer-body, using the law of cosines.

The absolute magnitude ${\displaystyle H}$ can be used to calculate the apparent magnitude ${\displaystyle m}$ of a body. For an object reflecting sunlight, ${\displaystyle H}$ and ${\displaystyle m}$ are connected by the relation

${\displaystyle m=H+5\log _{10}{\left({\frac {d_{BS}d_{BO}}{d_{0}^{2}}}\right)}-2.5\log _{10}{q(\alpha )},}$

where ${\displaystyle \alpha }$ is the phase angle, the angle between the body-Sun and body–observer lines. ${\displaystyle q(\alpha )}$ is the phase integral (the integration of reflected light; a number in the 0 to 1 range).

By the law of cosines, we have:

${\displaystyle \cos {\alpha }={\frac {d_{\mathrm {BO} }^{2}+d_{\mathrm {BS} }^{2}-d_{\mathrm {OS} }^{2}}{2d_{\mathrm {BO} }d_{\mathrm {BS} }}}.}$

Distances:

• d_BO is the distance between the body and the observer
• d_BS is the distance between the body and the Sun
• d_OS is the distance between the observer and the Sun
• d₀ is 1 AU, the average distance between the Earth and the Sun

Approximations for phase integral ${\displaystyle q(\alpha )}$

The value of ${\displaystyle q(\alpha )}$ depends on the properties of the reflecting surface, in particular on its roughness. In practice, different approximations are used based on the known or assumed properties of the surface.

Planets

Diffuse reflection on sphere and flat disk

 

Brightness with phase for diffuse reflection models. The sphere is 2/3 as bright at zero phase, while the disk can't be seen beyond 90 degrees.

Planetary bodies can be approximated reasonably well as ideal diffuse reflecting spheres. Let ${\displaystyle \alpha }$ be the phase angle in degrees, then

${\displaystyle q(\alpha )={\frac {2}{3}}\left(\left(1-{\frac {\alpha }{180^{\circ }}}\right)\cos {\alpha }+{\frac {1}{\pi }}\sin {\alpha }\right).}$

A full-phase diffuse sphere reflects two-thirds as much light as a diffuse flat disk of the same diameter. A quarter phase (${\displaystyle \alpha =90^{\circ }}$) has ${\displaystyle {\frac {1}{\pi }}}$ as much light as full phase (${\displaystyle \alpha =0^{\circ }}$).

For contrast, a diffuse disk reflector model is simply ${\displaystyle q(\alpha )=\cos {\alpha }}$, which isn't realistic, but it does represent the opposition surge for rough surfaces that reflect more uniform light back at low phase angles.

The definition of the geometric albedo ${\displaystyle p}$, a measure for the reflectivity of planetary surfaces, is based on the diffuse disk reflector model. The absolute magnitude ${\displaystyle H}$, diameter ${\displaystyle D}$ (in kilometers) and geometric albedo ${\displaystyle p}$ of a body are related by

${\displaystyle D={\frac {1329}{\sqrt {p}}}\times 10^{-0.2H}}$ km.

Example: The Moon's absolute magnitude ${\displaystyle H}$ can be calculated from its diameter ${\displaystyle D=3474{\text{ km}}}$ and geometric albedo ${\displaystyle p=0.113}$:

${\displaystyle H=5\log _{10}{\frac {1329}{3474{\sqrt {0.113}}}}=+0.28.}$

We have ${\displaystyle d_{BS}=1{\text{ AU}}}$, ${\displaystyle d_{BO}=384400{\text{ km}}=0.00257{\text{ AU}}.}$ At quarter phase, ${\displaystyle q(\alpha )\approx {\frac {2}{3\pi }}}$ (according to the diffuse reflector model), this yields an apparent magnitude of ${\displaystyle m=+0.28+5\log _{10}{\left(1\cdot 0.00257\right)}-2.5\log _{10}{\left({\frac {2}{3\pi }}\right)}=-10.99.}$ The actual value is somewhat lower than that, ${\displaystyle m=-10.0.}$ The phase curve of the Moon is too complicated for the diffuse reflector model.

More advanced models

Because Solar System bodies are never perfect diffuse reflectors, astronomers use different models to predict apparent magnitudes based on known or assumed properties of the body. For planets, approximations for the correction term ${\displaystyle -2.5\log _{10}{q(\alpha )}}$ in the formula for m have been derived empirically, to match observations at different phase angles. The approximations recommended by the Astronomical Almanac are (with ${\displaystyle \alpha }$ in degrees):

Planet	${\displaystyle H}$	Approximation for ${\displaystyle -2.5\log _{10}{q(\alpha )}}$
Mercury	−0.613	${\displaystyle +6.328\times 10^{-2}\alpha -1.6336\times 10^{-3}\alpha ^{2}+3.3644\times 10^{-5}\alpha ^{3}-3.4265\times 10^{-7}\alpha ^{4}+1.6893\times 10^{-9}\alpha ^{5}-3.0334\times 10^{-12}\alpha ^{6}}$
Venus	−4.384	${\displaystyle -1.044\times 10^{-3}\alpha +3.687\times 10^{-4}\alpha ^{2}-2.814\times 10^{-6}\alpha ^{3}+8.938\times 10^{-9}\alpha ^{4}}$ (for ${\displaystyle 0^{\circ }<\alpha \leq 163.7^{\circ }}$) ${\displaystyle +240.44228-2.81914\alpha +8.39034\times 10^{-3}\alpha ^{2}}$ (for ${\displaystyle 163.7^{\circ }<\alpha <179^{\circ }}$)
Earth	−3.99	${\displaystyle -1.060\times 10^{-3}\alpha +2.054\times 10^{-4}\alpha ^{2}}$
Mars	−1.601	${\displaystyle +2.267\times 10^{-2}\alpha -1.302\times 10^{-4}\alpha ^{2}}$ (for ${\displaystyle 0^{\circ }<\alpha \leq 50^{\circ }}$) ${\displaystyle +1.234-2.573\times 10^{-2}\alpha +3.445\times 10^{-4}\alpha ^{2}}$ (for ${\displaystyle 50^{\circ }<\alpha \leq 120^{\circ }}$)
Jupiter	−9.395	${\displaystyle -3.7\times 10^{-4}\alpha +6.16\times 10^{-4}\alpha ^{2}}$ (for ${\displaystyle \alpha \leq 12^{\circ }}$) ${\displaystyle -0.033-2.5\log _{10}{\left(1-1.507\left({\frac {\alpha }{180^{\circ }}}\right)-0.363\left({\frac {\alpha }{180^{\circ }}}\right)^{2}-0.062\left({\frac {\alpha }{180^{\circ }}}\right)^{3}+2.809\left({\frac {\alpha }{180^{\circ }}}\right)^{4}-1.876\left({\frac {\alpha }{180^{\circ }}}\right)^{5}\right)}}$ (for ${\displaystyle \alpha >12^{\circ }}$)
Saturn	−8.914	${\displaystyle 1.825\sin {\left(\beta \right)}+2.6\times 10^{-2}\alpha -0.378\sin {\left(\beta \right)}e^{-2.25\alpha }}$ (for planet and rings, ${\displaystyle \alpha <6.5^{\circ }}$ and ${\displaystyle \beta <27^{\circ }}$) ${\displaystyle -0.036-3.7\times 10^{-4}\alpha +6.16\times 10^{-4}\alpha ^{2}}$ (for the globe alone, ${\displaystyle \alpha \leq 6^{\circ }}$) ${\displaystyle +0.026+2.446\times 10^{-4}\alpha +2.672\times 10^{-4}\alpha ^{2}-1.505\times 10^{-6}\alpha ^{3}+4.767\times 10^{-9}\alpha ^{4}}$ (for the globe alone, ${\displaystyle 6^{\circ }<\alpha <150^{\circ }}$)
Uranus	−7.110	${\displaystyle -8.4\times 10^{-4}\phi '+6.587\times 10^{-3}\alpha +1.045\times 10^{-4}\alpha ^{2}}$ (for ${\displaystyle \alpha <3.1^{\circ }}$)
Neptune	−7.00	${\displaystyle +7.944\times 10^{-3}\alpha +9.617\times 10^{-5}\alpha ^{2}}$ (for ${\displaystyle \alpha <133^{\circ }}$ and ${\displaystyle t>2000.0}$)

Here ${\displaystyle \beta }$ is the effective inclination of Saturn's rings (their tilt relative to the observer), which as seen from Earth varies between 0° and 27° over the course of one Saturn orbit, and ${\displaystyle \phi '}$ is a small correction term depending on Uranus' sub-Earth and sub-solar latitudes. ${\displaystyle t}$ is the Common Era year. Neptune's absolute magnitude is changing slowly due to seasonal effects as the planet moves along its 165-year orbit around the Sun, and the approximation above is only valid after the year 2000. For some circumstances, like ${\displaystyle \alpha \geq 179^{\circ }}$ for Venus, no observations are available, and the phase curve is unknown in those cases.

Example: On 1 January 2019, Venus was ${\displaystyle d_{BS}=0.719{\text{ AU}}}$ from the Sun, and ${\displaystyle d_{BO}=0.645{\text{ AU}}}$ from Earth, at a phase angle of ${\displaystyle \alpha =93.0^{\circ }}$ (near quarter phase). Under full-phase conditions, Venus would have been visible at ${\displaystyle m=-4.384+5\log _{10}{\left(0.719\cdot 0.645\right)}=-6.09.}$ Accounting for the high phase angle, the correction term above yields an actual apparent magnitude of ${\displaystyle m=-6.09+\left(-1.044\times 10^{-3}\cdot 93.0+3.687\times 10^{-4}\cdot 93.0^{2}-2.814\times 10^{-6}\cdot 93.0^{3}+8.938\times 10^{-9}\cdot 93.0^{4}\right)=-4.59.}$ This is close to the value of ${\displaystyle m=-4.62}$ predicted by the Jet Propulsion Laboratory.

Earth's albedo varies by a factor of 6, from 0.12 in the cloud-free case to 0.76 in the case of altostratus cloud. The absolute magnitude here corresponds to an albedo of 0.434. Earth's apparent magnitude cannot be predicted as accurately as that of most other planets.

Asteroids

Asteroid 1 Ceres, imaged by the Dawn spacecraft at phase angles of 0°, 7° and 33°. The left image at 0° phase angle shows the brightness surge due to the opposition effect.

 

Phase integrals for various values of G

 

Relation between the slope parameter ${\displaystyle G}$ and the opposition surge. Larger values of ${\displaystyle G}$ correspond to a less pronounced opposition effect. For most asteroids, a value of ${\displaystyle G=0.15}$ is assumed, corresponding to an opposition surge of ${\displaystyle 0.3{\text{ mag}}}$.

If an object has an atmosphere, it reflects light more or less isotropically in all directions, and its brightness can be modelled as a diffuse reflector. Atmosphereless bodies, like asteroids or moons, tend to reflect light more strongly to the direction of the incident light, and their brightness increases rapidly as the phase angle approaches ${\displaystyle 0^{\circ }}$. This rapid brightening near opposition is called the opposition effect. Its strength depends on the physical properties of the body's surface, and hence it differs from asteroid to asteroid.

In 1985, the IAU adopted the semi-empirical ${\displaystyle HG}$-system, based on two parameters ${\displaystyle H}$ and ${\displaystyle G}$ called absolute magnitude and slope, to model the opposition effect for the ephemerides published by the Minor Planet Center.

${\displaystyle m=H+5\log _{10}{\left({\frac {d_{BS}d_{BO}}{d_{0}^{2}}}\right)}-2.5\log _{10}{q(\alpha )},}$

where

the phase integral is ${\displaystyle q(\alpha )=\left(1-G\right)\phi _{1}\left(\alpha \right)+G\phi _{2}\left(\alpha \right)}$

and

${\displaystyle \phi _{i}\left(\alpha \right)=\exp {\left(-A_{i}\left(\tan {\frac {\alpha }{2}}\right)^{B_{i}}\right)}}$ for ${\displaystyle i=1}$ or ${\displaystyle 2}$, ${\displaystyle A_{1}=3.332}$, ${\displaystyle A_{2}=1.862}$, ${\displaystyle B_{1}=0.631}$ and ${\displaystyle B_{2}=1.218}$.

This relation is valid for phase angles ${\displaystyle \alpha <120^{\circ }}$, and works best when ${\displaystyle \alpha <20^{\circ }}$.

The slope parameter ${\displaystyle G}$ relates to the surge in brightness, typically 0.3 mag, when the object is near opposition. It is known accurately only for a small number of asteroids, hence for most asteroids a value of ${\displaystyle G=0.15}$ is assumed. In rare cases, ${\displaystyle G}$ can be negative. An example is 101955 Bennu, with ${\displaystyle G=-0.08}$.

In 2012, the ${\displaystyle HG}$-system was officially replaced by an improved system with three parameters ${\displaystyle H}$, ${\displaystyle G_{1}}$ and ${\displaystyle G_{2}}$, which produces more satisfactory results if the opposition effect is very small or restricted to very small phase angles. However, as of 2019, this ${\displaystyle HG_{1}G_{2}}$-system has not been adopted by either the Minor Planet Center nor Jet Propulsion Laboratory.

The apparent magnitude of asteroids varies as they rotate, on time scales of seconds to weeks depending on their rotation period, by up to ${\displaystyle 2{\text{ mag}}}$ or more. In addition, their absolute magnitude can vary with the viewing direction, depending on their axial tilt. In many cases, neither the rotation period nor the axial tilt are known, limiting the predictability. The models presented here do not capture those effects.

Cometary magnitudes

The brightness of comets is given separately as total magnitude (${\displaystyle m_{1}}$, the brightness integrated over the entire visible extend of the coma) and nuclear magnitude (${\displaystyle m_{2}}$, the brightness of the core region alone). Both are different scales than the magnitude scale used for planets and asteroids, and can not be used for a size comparison with an asteroid's absolute magnitude H.

The activity of comets varies with their distance from the Sun. Their brightness can be approximated as

${\displaystyle m_{1}=M_{1}+2.5\cdot K_{1}\log _{10}{\left({\frac {d_{BS}}{d_{0}}}\right)}+5\log _{10}{\left({\frac {d_{BO}}{d_{0}}}\right)}}$

${\displaystyle m_{2}=M_{2}+2.5\cdot K_{2}\log _{10}{\left({\frac {d_{BS}}{d_{0}}}\right)}+5\log _{10}{\left({\frac {d_{BO}}{d_{0}}}\right)},}$

where ${\displaystyle m_{1,2}}$ are the total and nuclear apparent magnitudes of the comet, respectively, ${\displaystyle M_{1,2}}$ are its "absolute" total and nuclear magnitudes, ${\displaystyle d_{BS}}$ and ${\displaystyle d_{BO}}$ are the body-sun and body-observer distances, ${\displaystyle d_{0}}$ is the Astronomical Unit, and ${\displaystyle K_{1,2}}$ are the slope parameters characterising the comet's activity. For ${\displaystyle K=2}$, this reduces to the formula for a purely reflecting body.

For example, the lightcurve of comet C/2011 L4 (PANSTARRS) can be approximated by ${\displaystyle M_{1}=5.41{\text{, }}K_{1}=3.69.}$ On the day of its perihelion passage, 10 March 2013, comet PANSTARRS was ${\displaystyle 0.302{\text{ AU}}}$ from the Sun and ${\displaystyle 1.109{\text{ AU}}}$ from Earth. The total apparent magnitude ${\displaystyle m_{1}}$ is predicted to have been ${\displaystyle m_{1}=5.41+2.5\cdot 3.69\cdot \log _{10}{\left(0.302\right)}+5\log _{10}{\left(1.109\right)}=+0.8}$ at that time. The Minor Planet Center gives a value close to that, ${\displaystyle m_{1}=+0.5}$.

Absolute magnitudes and sizes of comet nuclei

Comet	Absolute magnitude ${\displaystyle M_{1}}$	Nucleus diameter
Comet Sarabat	−3.0	≈100 km?
Comet Hale-Bopp	−1.3	60 ± 20 km
Comet Halley	4.0	14.9 x 8.2 km
average new comet	6.5	≈2 km
289P/Blanpain (during 1819 outburst)	8.5	320 m
289P/Blanpain (normal activity)	22.9	320 m

The absolute magnitude of any given comet can vary dramatically. It can change as the comet becomes more or less active over time, or if it undergoes an outburst. This makes it difficult to use the absolute magnitude for a size estimate. When comet 289P/Blanpain was discovered in 1819, its absolute magnitude was estimated as ${\displaystyle M_{1}=8.5}$. It was subsequently lost, and was only rediscovered in 2003. At that time, its absolute magnitude had decreased to ${\displaystyle M_{1}=22.9}$, and it was realised that the 1819 apparition coincided with an outburst. 289P/Blanpain reached naked eye brightness (5–8 mag) in 1819, even though it is the comet with the smallest nucleus that has ever been physically characterised, and usually doesn't become brighter than 18 mag.

For some comets that have been observed at heliocentric distances large enough to distinguish between light reflected from the coma, and light from the nucleus itself, an absolute magnitude analogous to that used for asteroids has been calculated, allowing to estimate the sizes of their nuclei.

Meteors

For a meteor, the standard distance for measurement of magnitudes is at an altitude of 100 km (62 mi) at the observer's zenith.

Luminosity

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Luminosity 

 

The Sun has an intrinsic luminosity of 3.83×10²⁶ Watts. In astronomy, this amount is equal to one solar luminosity, represented by the symbol L_⊙. A star with four times the radiative power of the sun has a luminosity of 4 L_⊙.

Luminosity is an absolute measure of radiated electromagnetic power (light), the radiant power emitted by a light-emitting object.

In astronomy, luminosity is the total amount of electromagnetic energy emitted per unit of time by a star, galaxy, or other astronomical object.

In SI units, luminosity is measured in joules per second, or watts. In astronomy, values for luminosity are often given in the terms of the luminosity of the Sun, L_⊙. Luminosity can also be given in terms of the astronomical magnitude system: the absolute bolometric magnitude (M_bol) of an object is a logarithmic measure of its total energy emission rate, while absolute magnitude is a logarithmic measure of the luminosity within some specific wavelength range or filter band.

In contrast, the term brightness in astronomy is generally used to refer to an object's apparent brightness: that is, how bright an object appears to an observer. Apparent brightness depends on both the luminosity of the object and the distance between the object and observer, and also on any absorption of light along the path from object to observer. Apparent magnitude is a logarithmic measure of apparent brightness. The distance determined by luminosity measures can be somewhat ambiguous, and is thus sometimes called the luminosity distance.

Measurement

When not qualified, the term "luminosity" means bolometric luminosity, which is measured either in the SI units, watts, or in terms of solar luminosities (L_☉). A bolometer is the instrument used to measure radiant energy over a wide band by absorption and measurement of heating. A star also radiates neutrinos, which carry off some energy (about 2% in the case of our Sun), contributing to the star's total luminosity. The IAU has defined a nominal solar luminosity of 3.828×10²⁶ W to promote publication of consistent and comparable values in units of the solar luminosity.

While bolometers do exist, they cannot be used to measure even the apparent brightness of a star because they are insufficiently sensitive across the electromagnetic spectrum and because most wavelengths do not reach the surface of the Earth. In practice bolometric magnitudes are measured by taking measurements at certain wavelengths and constructing a model of the total spectrum that is most likely to match those measurements. In some cases, the process of estimation is extreme, with luminosities being calculated when less than 1% of the energy output is observed, for example with a hot Wolf-Rayet star observed only in the infrared. Bolometric luminosities can also be calculated using a bolometric correction to a luminosity in a particular passband.

The term luminosity is also used in relation to particular passbands such as a visual luminosity of K-band luminosity. These are not generally luminosities in the strict sense of an absolute measure of radiated power, but absolute magnitudes defined for a given filter in a photometric system. Several different photometric systems exist. Some such as the UBV or Johnson system are defined against photometric standard stars, while others such as the AB system are defined in terms of a spectral flux density.

Stellar luminosity

A star's luminosity can be determined from two stellar characteristics: size and effective temperature. The former is typically represented in terms of solar radii, R_⊙, while the latter is represented in kelvins, but in most cases neither can be measured directly. To determine a star's radius, two other metrics are needed: the star's angular diameter and its distance from Earth. Both can be measured with great accuracy in certain cases, with cool supergiants often having large angular diameters, and some cool evolved stars having masers in their atmospheres that can be used to measure the parallax using VLBI. However, for most stars the angular diameter or parallax, or both, are far below our ability to measure with any certainty. Since the effective temperature is merely a number that represents the temperature of a black body that would reproduce the luminosity, it obviously cannot be measured directly, but it can be estimated from the spectrum.

An alternative way to measure stellar luminosity is to measure the star's apparent brightness and distance. A third component needed to derive the luminosity is the degree of interstellar extinction that is present, a condition that usually arises because of gas and dust present in the interstellar medium (ISM), the Earth's atmosphere, and circumstellar matter. Consequently, one of astronomy's central challenges in determining a star's luminosity is to derive accurate measurements for each of these components, without which an accurate luminosity figure remains elusive. Extinction can only be measured directly if the actual and observed luminosities are both known, but it can be estimated from the observed colour of a star, using models of the expected level of reddening from the interstellar medium.

In the current system of stellar classification, stars are grouped according to temperature, with the massive, very young and energetic Class O stars boasting temperatures in excess of 30,000 K while the less massive, typically older Class M stars exhibit temperatures less than 3,500 K. Because luminosity is proportional to temperature to the fourth power, the large variation in stellar temperatures produces an even vaster variation in stellar luminosity. Because the luminosity depends on a high power of the stellar mass, high mass luminous stars have much shorter lifetimes. The most luminous stars are always young stars, no more than a few million years for the most extreme. In the Hertzsprung–Russell diagram, the x-axis represents temperature or spectral type while the y-axis represents luminosity or magnitude. The vast majority of stars are found along the main sequence with blue Class O stars found at the top left of the chart while red Class M stars fall to the bottom right. Certain stars like Deneb and Betelgeuse are found above and to the right of the main sequence, more luminous or cooler than their equivalents on the main sequence. Increased luminosity at the same temperature, or alternatively cooler temperature at the same luminosity, indicates that these stars are larger than those on the main sequence and they are called giants or supergiants.

Blue and white supergiants are high luminosity stars somewhat cooler than the most luminous main sequence stars. A star like Deneb, for example, has a luminosity around 200,000 L_⊙, a spectral type of A2, and an effective temperature around 8,500 K, meaning it has a radius around 203 R_☉ (1.41×10¹¹ m). For comparison, the red supergiant Betelgeuse has a luminosity around 100,000 L_⊙, a spectral type of M2, and a temperature around 3,500 K, meaning its radius is about 1,000 R_☉ (7.0×10¹¹ m). Red supergiants are the largest type of star, but the most luminous are much smaller and hotter, with temperatures up to 50,000 K and more and luminosities of several million L_⊙, meaning their radii are just a few tens of R_⊙. For example, R136a1 has a temperature over 50,000 K and a luminosity of more than 8,000,000 L_⊙ (mostly in the UV), it is only 35 R_☉ (2.4×10¹⁰ m).

Radio luminosity

The luminosity of a radio source is measured in W Hz⁻¹, to avoid having to specify a bandwidth over which it is measured. The observed strength, or flux density, of a radio source is measured in Jansky where 1 Jy = 10⁻²⁶ W m⁻² Hz⁻¹.

For example, consider a 10W transmitter at a distance of 1 million metres, radiating over a bandwidth of 1 MHz. By the time that power has reached the observer, the power is spread over the surface of a sphere with area 4πr² or about 1.26×10¹³ m², so its flux density is 10 / 10⁶ / 1.26×10¹³ W m⁻² Hz⁻¹ = 10⁸ Jy.

More generally, for sources at cosmological distances, a k-correction must be made for the spectral index α of the source, and a relativistic correction must be made for the fact that the frequency scale in the emitted rest frame is different from that in the observer's rest frame. So the full expression for radio luminosity, assuming isotropic emission, is

${\displaystyle L_{\nu }={\frac {S_{\mathrm {obs} }4\pi {D_{L}}^{2}}{(1+z)^{1+\alpha }}}}$

where L_ν is the luminosity in W Hz⁻¹, S_obs is the observed flux density in W m⁻² Hz⁻¹, D_L is the luminosity distance in metres, z is the redshift, α is the spectral index (in the sense ${\displaystyle I\propto {\nu }^{\alpha }}$, and in radio astronomy, assuming thermal emission the spectral index is typically equal to 2.)

For example, consider a 1 Jy signal from a radio source at a redshift of 1, at a frequency of 1.4 GHz. Ned Wright's cosmology calculator calculates a luminosity distance for a redshift of 1 to be 6701 Mpc = 2×10²⁶ m giving a radio luminosity of 10⁻²⁶ × 4π(2×10²⁶)² / (1+1)⁽¹⁺²⁾ = 6×10²⁶ W Hz⁻¹.

To calculate the total radio power, this luminosity must be integrated over the bandwidth of the emission. A common assumption is to set the bandwidth to the observing frequency, which effectively assumes the power radiated has uniform intensity from zero frequency up to the observing frequency. In the case above, the total power is 4×10²⁷ × 1.4×10⁹ = 5.7×10³⁶ W. This is sometimes expressed in terms of the total (i.e. integrated over all wavelengths) luminosity of the Sun which is 3.86×10²⁶ W, giving a radio power of 1.5×10¹⁰ L_⊙.

Luminosity formulae

Point source S is radiating light equally in all directions. The amount passing through an area A varies with the distance of the surface from the light.

The Stefan–Boltzmann equation applied to a black body gives the value for luminosity for a black body, an idealized object which is perfectly opaque and non-reflecting:

${\displaystyle L=\sigma AT^{4}}$ ,

where A is the surface area, T is the temperature (in Kelvins) and σ is the Stefan–Boltzmann constant, with a value of 5.670374419...×10⁻⁸ W⋅m⁻²⋅K⁻⁴.

Imagine a point source of light of luminosity ${\displaystyle L}$ that radiates equally in all directions. A hollow sphere centered on the point would have its entire interior surface illuminated. 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.

${\displaystyle F={\frac {L}{A}}}$ ,

where

${\displaystyle A}$ is the area of the illuminated surface.

${\displaystyle F}$ is the flux density of the illuminated surface.

The surface area of a sphere with radius r is ${\displaystyle A=4\pi r^{2}}$, so for stars and other point sources of light:

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

where ${\displaystyle r}$ is the distance from the observer to the light source.

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

${\displaystyle {\frac {L}{L_{\odot }}}\approx {\left({\frac {M}{M_{\odot }}}\right)}^{3.5}}$ .

If we define ${\displaystyle M}$ as the mass of the star in terms of solar masses, the above relationship can be simplified as follows:

${\displaystyle L\approx M^{3.5}}$ .

Relationship to magnitude

Luminosity is an intrinsic measurable property of a star independent of distance. The concept of magnitude, on the other hand, incorporates distance. The apparent magnitude is a measure of the diminishing flux of light as a result of distance according to the inverse-square law. The Pogson logarithmic scale is used to measure both apparent and absolute magnitudes, the latter corresponding to the brightness of a star or other celestial body as seen if it would be located at an interstellar distance of 10 parsecs (3.1×10¹⁷ metres). In addition to this brightness decrease from increased distance, there is an extra decrease of brightness due to extinction from intervening interstellar dust.

By measuring the width of certain absorption lines in the stellar spectrum, it is often possible to assign a certain luminosity class to a star without knowing its distance. Thus a fair measure of its absolute magnitude can be determined without knowing its distance nor the interstellar extinction.

In measuring star brightnesses, absolute magnitude, apparent magnitude, and distance are interrelated parameters—if two are known, the third can be determined. 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, although officially, zero point values are defined by the IAU.

The magnitude of a star, a unitless measure, is a logarithmic scale of observed visible brightness. The apparent magnitude is the observed visible brightness from Earth which depends on the distance of the object. The absolute magnitude is the apparent magnitude at a distance of 10 pc (3.1×10¹⁷ m), therefore the bolometric absolute magnitude is a logarithmic measure of the bolometric luminosity.

The difference in bolometric magnitude between two objects is related to their luminosity ratio according to:

${\displaystyle M_{\text{bol1}}-M_{\text{bol2}}=-2.5\log _{10}{\frac {L_{\text{1}}}{L_{\text{2}}}}}$

where:

${\displaystyle M_{\text{bol1}}}$ is the bolometric magnitude of the first object

${\displaystyle M_{\text{bol2}}}$ is the bolometric magnitude of the second object.

${\displaystyle L_{\text{1}}}$ is the first object's bolometric luminosity

${\displaystyle L_{\text{2}}}$ is the second object's bolometric luminosity

The zero point of the absolute magnitude scale is actually defined as a fixed luminosity of 3.0128×10²⁸ W. Therefore, the absolute magnitude can be calculated from a luminosity in watts:

${\displaystyle M_{\mathrm {bol} }=-2.5\log _{10}{\frac {L_{*}}{L_{0}}}\approx -2.5\log _{10}L_{*}+71.1974}$

where L₀ is the zero point luminosity 3.0128×10²⁸ W

and the luminosity in watts can be calculated from an absolute magnitude (although absolute magnitudes are often not measured relative to an absolute flux):

${\displaystyle L_{*}=L_{0}\times 10^{-0.4M_{\mathrm {bol} }}}$

 

Divine light

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Divine_light 

In theology, divine light (also called divine radiance or divine refulgence) is an aspect of divine presence, specifically an unknown and mysterious ability of angels or human beings to express themselves communicatively through spiritual means, rather than through physical capacities.

Spirituality

The term light has been used in spirituality (vision, enlightenment, darshan, Tabor Light). Bible commentators such as John W. Ritenbaugh see the presence of light as a metaphor of truth, good and evil, knowledge and ignorance. In the first Chapter of the Bible, Elohim is described as creating light by fiat and seeing the light to be good. In Hinduism, Diwali — the festival of lights — is a celebration of the victory of light over darkness. A mantra in Bṛhadāraṇyaka Upaniṣad (1.3.28) urges God to 'from darkness, lead us unto Light'. The Rig Veda includes nearly two dozen hymns to the dawn and its goddess, Ushas. And Buddhist scripture speaks of numerous buddhas of light, including a Buddha of Boundless Light, a Buddha of Unimpeded Light, and Buddhas of Unopposed Light, of Pure Light, of Incomparable Light, and of Unceasing Light.

Various local religious concepts exist:

• Inner light – Christian concept and Quaker doctrine
• Prakasa – Kashmiri Saiva concept of the light of Divine Consciousness of Siva
• An Noor – Islamic term and concept
• Ein Sof – in Rabbinic Judaism
• Tabor Light – in Eastern Orthodox theology
• Theoria – in Christian theology, illumination on the path to theosis
• Ayat an-Nur – in Arabic, the Sign of Light

Zoroastrianism

Light is the core concept in Iranian mysticism. The main roots of this thought is in the Zoroastrian beliefs, which defines The Supreme God Ahura Mazda as the source of light. This very essential attribute is manifested in various schools of thought in Persian mysticism and philosophy. Later this notion has been dispensed into the whole Middle East, having a great effect of shaping the paradigms of different religions and philosophies emerging one after another in the region. After the Arab invasion, this concept has been incorporated into the Islamic teachings by Iranian thinkers, most famous of them Shahab al-Din Suhrawardi, who is the founder of the illumination philosophy.

Although this school had stemmed from the Iranian culture and beliefs, it has spread far into Europe and can be seen and traced in the teachings of the Enlightenment era, Renaissance movement, and even the secret cults as early Illuminati.

Manichaeism

Manichaeism, the most widespread Western religion prior to Christianity, was based on the belief that god was, literally, light. From about 250-350 CE devout Manichees followed the teachings of self-proclaimed prophet Mani. Mani's faithful, who could be found from Greece to China, believed in warring kingdoms of Light and Darkness, in "beings of light," and in a Father of Light who would conquer the demons of darkness and remake the earth through shards of light found in human souls. Manichaeism also co-opted other religions, including Buddhist teachings in its scripture and worshipping a Jesus the Luminous who was crucified on a cross of pure light. Among the many followers of Manicheaism was the young Augustine, who later wrote, "I thought that you, Lord God and Truth, were like a luminous body of immense size, and myself a bit of that body." When he converted to Christianity in 386 CE, Augustine denounced Manicheaism. But by then, the faith had been supplanted by ascendant Christianity. Manichaeism's legacy is the word Manichaean -- relating to a dualistic view of the world, dividing things into either good or evil, light or dark, black or white.

Sant Mat

In the terminology of Sant Mat, Light and Sound are the two main and expressions of God and from them all the creation comes into existence. Inner Light (and Inner Sound) can be experienced with and after an initiation by a competent Guru during meditation, and are considered the better way to reach Enlightenment.

Eastern Orthodox Church

In the Eastern Orthodox tradition, the Divine Light illuminates the intellect of man through "theoria" or contemplation. In the Gospel of John, the opening verses describe God as Light: "In Him was life and the life was the light of men. And the light shines in the darkness and the darkness did not comprehend it." (John 1:5)

In John 8:12, Christ proclaims "I am the light of the world", bringing the Divine Light to mankind. The Tabor Light, also called the Uncreated Light, was revealed to the three apostles present at the Transfiguration.

Blindsight

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Blindsight 

Blindsight is the ability of people who are cortically blind due to lesions in their striate cortex, also known as the primary visual cortex or V1, to respond to visual stimuli that they do not consciously see. The majority of studies on blindsight are conducted on patients who have the conscious blindness on only one side of their visual field. Following the destruction of the striate cortex, patients are asked to detect, localize, and discriminate amongst visual stimuli that are presented to their blind side, often in a forced-response or guessing situation, even though they do not consciously recognize the visual stimulus. Research shows that blind patients achieve a higher accuracy than would be expected from chance alone. Type 1 blindsight is the term given to this ability to guess—at levels significantly above chance—aspects of a visual stimulus (such as location or type of movement) without any conscious awareness of any stimuli. Type 2 blindsight occurs when patients claim to have a feeling that there has been a change within their blind area—e.g. movement—but that it was not a visual percept. Blindsight challenges the common belief that perceptions must enter consciousness to affect our behavior; showing that our behavior can be guided by sensory information of which we have no conscious awareness. It may be thought of as a converse of the form of anosognosia known as Anton–Babinski syndrome, in which there is full cortical blindness along with the confabulation of visual experience.

History

We owe much of our current understanding of blindsight to early experiments on monkeys. One monkey in particular, Helen, could be considered the "star monkey in visual research" because she was the original blindsight subject. Helen was a macaque monkey that had been decorticated; specifically, her primary visual cortex (V1) was completely removed, blinding her. Nevertheless, under certain specific situations, Helen exhibited sighted behavior. Her pupils would dilate and she would blink at stimuli that threatened her eyes. Furthermore, under certain experimental conditions, she could detect a variety of visual stimuli, such as the presence and location of objects, as well as shape, pattern, orientation, motion, and color. In many cases, she was able to navigate her environment and interact with objects as if she were sighted.

A similar phenomenon was also discovered in humans. Subjects who had suffered damage to their visual cortices due to accidents or strokes reported partial or total blindness. In spite of this, when they were prompted they could "guess" with above-average accuracy about the presence and details of objects, much like the animal subjects, and they could even catch objects that were tossed at them. The subjects never developed any kind of confidence in their abilities. Even when told of their successes, they would not begin to spontaneously make "guesses" about objects, but instead still required prompting. Furthermore, blindsight subjects rarely express the amazement about their abilities that sighted people would expect them to express.

Describing blindsight

Patients with blindsight have damage to the system that produces visual perception (the visual cortex of the brain and some of the nerve fibers that bring information to it from the eyes) rather than to the underlying brain system controlling eye movements. The phenomenon shows how, after the more complex perception system is damaged, people can use the underlying control system to guide hand movements towards an object even though they cannot see what they are reaching for. Hence, visual information can control behavior without producing a conscious sensation. This ability of those with blindsight to act as if able to see objects that they are unconscious of suggests that consciousness is not a general property of all parts of the brain, but is produced by specialised parts of it.

Blindsight patients show awareness of single visual features, such as edges and motion, but cannot gain a holistic visual percept. This suggests that perceptual awareness is modular and that—in sighted individuals—there is a "binding process that unifies all information into a whole percept", which is interrupted in patients with such conditions as blindsight and visual agnosia. Therefore, object identification and object recognition are thought to be separate processes and occur in different areas of the brain, working independently from one another. The modular theory of object perception and integration would account for the "hidden perception" experienced in blindsight patients. Research has shown that visual stimuli with the single visual features of sharp borders, sharp onset/offset times, motion, and low spatial frequency contribute to, but are not strictly necessary for, an object's salience in blindsight.

Cause

There are three theories for the explanation of blindsight. The first states that after damage to area V1, other branches of the optic nerve deliver visual information to the superior colliculus and several other areas, including parts of the cerebral cortex. In turn, these areas might then control the blindsight responses.

Another explanation for the phenomenon of blindsight is that even though the majority of a person's visual cortex may be damaged, tiny islands of functioning tissue remain. These islands aren't large enough to provide conscious perception, but nevertheless enough for some unconscious visual perception.

A third theory is that the information required to determine the distance to and velocity of an object in object space is determined by the lateral geniculate nucleus before the information is projected to the visual cortex. In a normal subject, these signals are used to merge the information from the eyes into a three-dimensional representation (which includes the position and velocity of individual objects relative to the organism), extract a vergence signal to benefit the precision (previously auxiliary) optical system, and extract a focus control signal for the lenses of the eyes. The stereoscopic information is attached to the object information passed to the visual cortex.

Evidence of blindsight can be indirectly observed in children as young as two months, although there is difficulty in determining the type in a patient who is not old enough to answer questions.

Evidence in animals

In a 1995 experiment, researchers attempted to show that monkeys with lesions in or even wholly removed striate cortexes also experienced blindsight. To study this, they had the monkeys complete tasks similar to those commonly used on human subjects. The monkeys were placed in front of a monitor and taught to indicate whether a stationary object or nothing was present in their visual field when a tone was played. Then the monkeys performed the same task except the stationary objects were presented outside of their visual field. The monkeys performed very similar to human participants and were unable to perceive the presence of stationary objects outside of their visual field.

Another 1995 study by the same group sought to prove that monkeys could also be conscious of movement in their deficit visual field despite not being consciously aware of the presence of an object there. To do this, researchers used another standard test for humans which was similar to the previous study except moving objects were presented in the deficit visual field. Starting from the center of the deficit visual field, the object would either move up, down, or to the right. The monkeys performed identically to humans on the test, getting them right almost every time. This showed that the monkey's ability to detect movement is separate from their ability to consciously detect an object in their deficit visual field, and gave further evidence for the claim that damage to the striate cortex plays a large role in causing the disorder.

Several years later, another study compared and contrasted the data collected from monkeys and that of a specific human patient with blindsight, GY. GY's striate cortical region was damaged through trauma at the age of eight, though for the most part he retained full functionality, GY was not consciously aware of anything in his right visual field. In the monkeys, the striate cortex of the left hemisphere was surgically removed. By comparing the test results of both GY and the monkeys, the researchers concluded that similar patterns of responses to stimuli in the "blind" visual field can be found in both species.

Research

Lawrence Weiskrantz and colleagues showed in the early 1970s that if forced to guess about whether a stimulus is present in their blind field, some observers do better than chance. This ability to detect stimuli that the observer is not conscious of can extend to discrimination of the type of stimulus (for example, whether an 'X' or 'O' has been presented in the blind field).

Electrophysiological evidence from the late 1970s has shown that there is no direct retinal input from S-cones to the superior colliculus, implying that the perception of color information should be impaired. However, more recent evidence point to a pathway from S-cones to the superior colliculus, opposing previous research and supporting the idea that some chromatic processing mechanisms are intact in blindsight.

Patients shown images on their blind side of people expressing emotions correctly guessed the emotion most of the time. The movement of facial muscles used in smiling and frowning were measured and reacted in ways that matched the kind of emotion in the unseen image. Therefore, the emotions were recognized without involving conscious sight.

A 2011 study found that a young woman with a unilateral lesion of area V1 could scale her grasping movement as she reached out to pick up objects of different sizes placed in her blind field, even though she could not report the sizes of the objects. Similarly, another patient with unilateral lesion of area V1 could avoid obstacles placed in his blind field when he reached toward a target that was visible in his intact visual field. Even though he avoided the obstacles, he never reported seeing them.

A study reported in 2008 asked patient GY to misstate where in his visual field a distinctive stimulus was presented. If the stimulus was in the upper part of his visual field, he was to say it was in the lower part, and vice versa. He was able to misstate, as requested, in his left visual field (with normal conscious vision); but he tended to fail in the task—to state the location correctly—when the stimulus was in his blindsight (right) visual field. This failure rate worsened when the stimulus was clearer, indicating that failure was not simply due to unreliability of blindsight.

Case studies

Researchers applied the same type of tests that were used to study blindsight in animals to a patient referred to as DB. The normal techniques that were used to assess visual acuity in humans involved asking them to verbally describe some visually recognizable aspect of an object or objects. DB was given forced-choice tasks to complete instead. The results of DB's guesses showed that DB was able to determine shape and detect movement at some unconscious level, despite not being visually aware of this. DB themselves chalked up the accuracy of their guesses to be merely coincidental.

The discovery of the condition known as blindsight raised questions about how different types of visual information, even unconscious information, may be affected and sometimes even unaffected by damage to different areas of the visual cortex. Previous studies had already demonstrated that even without conscious awareness of visual stimuli humans could still determine certain visual features such as presence in the visual field, shape, orientation and movement. But, in a newer study evidence showed that if the damage to the visual cortex occurs in areas above the primary visual cortex the conscious awareness of visual stimuli itself is not damaged. Blindsight is a phenomenon that shows that even when the primary visual cortex is damaged or removed a person can still perform actions guided by unconscious visual information. So even when damage occurs in the area necessary for conscious awareness of visual information, other functions of the processing of these visual percepts are still available to the individual. The same also goes for damage to other areas of the visual cortex. If an area of the cortex that is responsible for a certain function is damaged, it will only result in the loss of that particular function or aspect, functions that other parts of the visual cortex are responsible for remain intact.

Alexander and Cowey investigated how contrasting brightness of stimuli affects blindsight patients' ability to discern movement. Prior studies have already shown that blindsight patients are able to detect motion even though they claim they do not see any visual percepts in their blind fields. The subjects of the study were two patients who suffered from hemianopsia—blindness in more than half of their visual field. Both of the subjects had displayed the ability to accurately determine the presence of visual stimuli in their blind hemifields without acknowledging an actual visual percept previously.

To test the effect of brightness on the subject's ability to determine motion they used a white background with a series of colored dots. They would alter the contrast of the brightness of the dots compared to the white background in each different trial to see if the participants performed better or worse when there was a larger discrepancy in brightness or not. Their procedure was to have the participants face the display for a period of time and ask them to tell the researchers when the dots were moving. The subjects focused on the display through two equal length time intervals. They would tell the researchers whether they thought the dots were moving during the first or the second time interval.

When the contrast in brightness between the background and the dots was higher, both of the subjects could discern motion more accurately than they would have statistically by just guessing. However one of the subjects was not able to accurately determine whether or not blue dots were moving regardless of the brightness contrast, but he/she was able to do so with every other color dot. When the contrast was highest the subjects were able to tell whether or not the dots were moving with very high rates of accuracy. Even when the dots were white, but still of a different brightness from the background, the subjects could still determine if they were moving or not. But, regardless of the dots' color the subjects could not tell when they were in motion or not when the white background and the dots were of similar brightness.

Kentridge, Heywood, and Weiskrantz used the phenomenon of blindsight to investigate the connection between visual attention and visual awareness. They wanted to see if their subject—who exhibited blindsight in other studies—could react more quickly when his/her attention was cued without the ability to be visually aware of it. The researchers wanted to show that being conscious of a stimulus and paying attention to it was not the same thing.

To test the relationship between attention and awareness, they had the participant try to determine where a target was and whether it was oriented horizontally or vertically on a computer screen. The target line would appear at one of two different locations and would be oriented in one of two directions. Before the target would appear an arrow would become visible on the screen and sometimes it would point to the correct position of the target line and less frequently it would not, this arrow was the cue for the subject. The participant would press a key to indicate whether the line was horizontal or vertical, and could then also indicate to an observer whether or not he/she actually had a feeling that any object was there or not—even if they couldn't see anything. The participant was able to accurately determine the orientation of the line when the target was cued by an arrow before the appearance of the target, even though these visual stimuli did not equal awareness in the subject who had no vision in that area of his/her visual field. The study showed that even without the ability to be visually aware of a stimulus the participant could still focus his/her attention on this object.

In 2003, a patient known as TN lost use of his primary visual cortex, area V1. He had two successive strokes, which knocked out the region in both his left and right hemispheres. After his strokes, ordinary tests of TN's sight turned up nothing. He could not even detect large objects moving right in front of his eyes. Researchers eventually began to notice that TN exhibited signs of blindsight and in 2008 decided to test their theory. They took TN into a hallway and asked him to walk through it without using the cane he always carried after having the strokes. TN was not aware at the time, but the researchers had placed various obstacles in the hallway to test if he could avoid them without conscious use of his sight. To the researchers' delight, he moved around every obstacle with ease, at one point even pressing himself up against the wall to squeeze past a trashcan placed in his way. After navigating through the hallway, TN reported that he was just walking the way he wanted to, not because he knew anything was there.

In another case study, a girl had brought her grandfather in to see a neuropsychologist. The girl's grandfather, Mr. J., had had a stroke which had left him completely blind apart from a tiny spot in the middle of his visual field. The neuropsychologist, Dr. M., performed an exercise with him. The doctor helped Mr. J. to a chair, had him sit down, and then asked to borrow his cane. The doctor then asked, "Mr. J., please look straight ahead. Keep looking that way, and don't move your eyes or turn your head. I know that you can see a little bit straight ahead of you, and I don't want you to use that piece of vision for what I'm going to ask you to do. Fine. Now, I'd like you to reach out with your right hand [and] point to what I'm holding." Mr. J. then replied, "But I don't see anything—I'm blind!" The doctor then said, "I know, but please try, anyway." Mr. J then shrugged and pointed, and was surprised when his finger encountered the end of the cane which the doctor was pointing toward him. After this, Mr. J. said that "it was just luck". The doctor then turned the cane around so that the handle side was pointing towards Mr. J. He then asked for Mr. J. to grab hold of the cane. Mr. J. reached out with an open hand and grabbed hold of the cane. After this, the doctor said, "Good. Now put your hand down, please." The doctor then rotated the cane 90 degrees, so that the handle was oriented vertically. The doctor then asked Mr. J. to reach for the cane again. Mr. J. did this, and he turned his wrist so that his hand matched the orientation of the handle. This case study shows that—although (on a conscious level) Mr. J. was completely unaware of any visual abilities that he may have had—he was able to orient his grabbing motions as if he had no visual impairments.

Brain regions involved

Visual processing in the brain goes through a series of stages. Destruction of the primary visual cortex leads to blindness in the part of the visual field that corresponds to the damaged cortical representation. The area of blindness – known as a scotoma – is in the visual field opposite the damaged hemisphere and can vary from a small area up to the entire hemifield. Visual processing occurs in the brain in a hierarchical series of stages (with much crosstalk and feedback between areas). The route from the retina through V1 is not the only visual pathway into the cortex, though it is by far the largest; it is commonly thought that the residual performance of people exhibiting blindsight is due to preserved pathways into the extrastriate cortex that bypass V1. What is surprising is that activity in these extrastriate areas is apparently insufficient to support visual awareness in the absence of V1.

To put it in a more complex way, recent physiological findings suggest that visual processing takes place along several independent, parallel pathways. One system processes information about shape, one about color, and one about movement, location and spatial organization. This information moves through an area of the brain called the lateral geniculate nucleus, located in the thalamus, and on to be processed in the primary visual cortex, area V1 (also known as the striate cortex because of its striped appearance). People with damage to V1 report no conscious vision, no visual imagery, and no visual images in their dreams. However, some of these people still experience the blindsight phenomenon, though this too is controversial, with some studies showing a limited amount of consciousness without V1 or projections relating to it.

The superior colliculus and prefrontal cortex also have a major role in awareness of a visual stimulus.

Lateral geniculate nucleus

Mosby's Dictionary of Medicine, Nursing & Health Professions defines the LGN as "one of two elevations of the lateral posterior thalamus receiving visual impulses from the retina via the optic nerves and tracts and relaying the impulses to the calcarine (visual) cortex".

What is seen in the left and right visual field is taken in by each eye and brought back to the optic disc via the nerve fibres of the retina. From the optic disc, visual information travels through the optic nerve and into the optic chiasm. Visual information then enters the optic tract and travels to four different areas of the brain including the superior colliculus, pretectum of the mid brain, the suprachiasmatic nucleus of the hypothalamus, and the lateral geniculate nucleus (LGN). Most axons from the LGN will then travel to the primary visual cortex.

Injury to the primary visual cortex, including lesions and other trauma, leads to the loss of visual experience. However, the residual vision that is left cannot be attributed to V1. According to Schmid et al., "thalamic lateral geniculate nucleus has a causal role in V1-independent processing of visual information". This information was found through experiments using fMRI during activation and inactivation of the LGN and the contribution the LGN has on visual experience in monkeys with a V1 lesion. These researchers concluded that the magnocellular system of the LGN is less affected by the removal of V1, which suggests that it is because of this system in the LGN that blindsight occurs.

Furthermore, once the LGN was inactivated, virtually all of the extrastriate areas of the brain no longer showed a response on the fMRI. The information leads to a qualitative assessment that included "scotoma stimulation, with the LGN intact had fMRI activation of ~20% of that under normal conditions". This finding agrees with the information obtained from, and fMRI images of, patients with blindsight. The same study also supported the conclusion that the LGN plays a substantial role in blindsight. Specifically, while injury to V1 does create a loss of vision, the LGN is less affected and may result in the residual vision that remains, causing the "sight" in blindsight. 

Functional magnetic resonance imaging was has also been employed to conduct brain scans in normal, healthy human volunteers to attempt to demonstrate that visual motion can bypass V1, through a connection from the LGN to the human middle temporal complex. Their findings concluded that there was an indeed a connection of visual motion information that went directly from the LGN to the hMT+ bypassing V1 completely. Evidence also suggests that, following a traumatic injury to V1, there is still a direct pathway from the retina through the LGN to the extrastriate visual areas. The extrastriate visual areas include parts of the occipital lobe that surround V1. In non-human primates, these often include V2, V3, and V4.

In a study conducted in primates, after partial ablation of area V1, areas V2 and V3 were still excited by visual stimulus. Other evidence suggests that "the LGN projections that survive V1 removal are relatively sparse in density, but are nevertheless widespread and probably encompass all extrastriate visual areas," including V2, V4, V5 and the inferotemporal cortex region.