# Stars/Sun

A natural division of astronomical objects, between rocky objects, astronomical objects with solid surfaces, or solids and liquids predominately on the surface, and gas objects, astronomical objects with gases predominately detected and apparently constituting a surface, may be an informative approach toward stellar science. The Earth is an apparent rocky object that has a gaseous envelope. When viewed under certain conditions in radiation astronomy, the Earth appears as a gas object.

The GOES 14 spacecraft carries a Solar X-ray Imager that took this image of the Sun during the most recent quiet period. The Sun appears dark because of the wavelength band of observation. Credit: NOAA/Space Weather Prediction Center and the NWS Internet Services Team.

Depending primarily upon gas temperature, the presence of gas may be used to determine the composition of the gas object observed, at least the outer layer. Early spectroscopy[1] of the Sun using estimates of "the line intensities of several lines by eye [to derive] the abundances of ... elements ... [concluded] that the Sun [is] largely made of hydrogen."[2]

At right is an image from the GOES 14 Solar X-ray Imager during the most recent quiet period on or above the Sun. Except for X-ray emission that suggests a circular disc with some isolated X-ray sources at specific locations, the Sun is almost invisible. X-rays are primarily emitted from plasmas near 106 K.

## Helionomy

Solar astronomy (Helionomy) includes the various radiation astronomies focused on the Sun and the effects on the Sun of revolving around the center of the Milky Way. The Sun is first and locally foremost a gas giant.

## Stars

Def. the "star at the center of our solar system"[3] is called the Sun.

Def. a "luminous celestial body, made up of plasma (particularly hydrogen and helium) and having a spherical shape"[4] is called a star.

On Wiktionary, after the above definition for a star is the comment, "Depending on context the sun may or may not be included."[4]

Def. "[a]ny small luminous dot appearing in the cloudless portion of the night sky, especially with a fixed location relative to other such dots"[4] is called a star.

## Colors

Def. "the natural medium emanating from the sun and other very hot sources (now recognised as electromagnetic radiation with a wavelength of 400-750 nm), within which vision is possible"[5] is called light.

Def. "emitting light"[6] is called luminous.

## Theory of the Sun

This image is a theory for the interior of the Sun. Credit: NASA.

In the model shown at right the Sun and regions around it are labeled.

The core of the Sun is considered to extend from the center to about 0.2 to 0.25 solar radius.[7] It is the hottest part of the Sun and of the Solar System. It has a density of up to 150 g/cm³ (150 times the density of liquid water) and a temperature of close to 15,000,000 kelvin 15 MK. The core is made of hot, dense gas in the plasmic state. The core, inside 0.24 solar radius, generates 99% of the fusion power of the Sun. It is in the core region that solar neutrinos may be produced.

The radiation zone or radiative zone is a layer of a star's interior where energy is primarily transported toward the exterior by means of radiative diffusion, rather than by convection.[8] Energy travels through the radiation zone in the form of electromagnetic radiation as photons. Within the Sun, the radiation zone is located in the intermediate zone between the solar core at .2 of the Sun's radius and the outer convection zone at .71 of the Sun's radius.[8]

Matter in a radiation zone is so dense that photons can travel only a short distance before they are absorbed or scattered by another particle, gradually shifting to longer wavelength as they do so. For this reason, it takes an average of 171,000 years for gamma rays from the core of the Sun to leave the radiation zone. Over this range, the temperature of the plasma drops from 15 million K near the core down to 1.5 million K at the base of the convection zone.[9]

Within a radiative zone, the temperature gradient—the change in temperature (T) as a function of radius (r)—is given by:

${\displaystyle {\frac {{\text{d}}T(r)}{{\text{d}}r}}\ =\ -{\frac {3\kappa (r)\rho (r)L(r)}{(4\pi r^{2})(16\sigma )T^{3}(r)}}}$

where κ(r) is the opacity, ρ(r) is the matter density, L(r) is the luminosity, and σ is the Stefan–Boltzmann constant.[8] Hence the opacity (κ) and radiation flux (L) within a given layer of a star are important factors in determining how effective radiative diffusion is at transporting energy. A high opacity or high luminosity can cause a high temperature gradient, which results from a slow flow of energy. Those layers where convection is more effective than radiative diffusion at transporting energy, thereby creating a lower temperature gradient, will become convection zones.[10]

The convection zone of a star is the range of radii in which energy is transported primarily by convection. Stellar convection consists of mass movement of plasma within the star which usually forms a circular convection current with the heated plasma ascending and the cooled plasma descending. This is the granular zone in the outer layer of a star.

The solar dynamo is the physical process that generates the Sun's magnetic field. The Sun is permeated by an overall dipole magnetic field, as are many other celestial bodies such as the Earth. The dipole field is produced by a circular electric current flowing deep within the star, following Ampère's law. The current is produced by shear (stretching of material) between different parts of the Sun that rotate at different rates, and the fact that the Sun itself is a very good electrical conductor (and therefore governed by the laws of magnetohydrodynamics).

## Standard solar model

The Standard Solar Model (SSM) refers to a mathematical treatment of the Sun as a spherical ball of gas (in varying states of ionisation, with the hydrogen in the deep interior being a completely ionised plasma). This model, technically the spherically symmetric quasi-static model of a star, has stellar structure described by several differential equations derived from basic physical principles. The model is constrained by boundary conditions, namely the luminosity, radius, age and composition of the Sun, which are well determined. The age of the Sun cannot be measured directly; one way to estimate it is from the age of the oldest meteorites, and models of the evolution of the solar system.[11] The composition in the photosphere of the modern-day Sun, by mass, is 74.9% hydrogen and 23.8% helium.[12] All heavier elements, called metals in astronomy, account for less than 2 percent of the mass. The SSM is used to test the validity of stellar evolution theory. In fact, the only way to determine the two free parameters of the stellar evolution model, the helium abundance and the mixing length parameter (used to model convection in the Sun), are to adjust the SSM to "fit" the observed Sun.

The differential equations of stellar structure, such as the equation of hydrostatic equilibrium, are integrated numerically. The differential equations are approximated by difference equations. The star is imagined to be made up of spherically symmetric shells and the numerical integration carried out in finite steps making use of the equations of state, giving relationships for the pressure, the opacity and the energy generation rate in terms of the density, temperature and composition.[13]

## Evolutionary model

Neutrino flux at Earth predicted by the Standard Solar Model of 2005. The neutrinos produced in the pp chain are shown in black, neutrinos produced by the CNO cycle are shown in blue. The solar neutrino spectrum predicted by the BS05(OP) standard solar model. The neutrino fluxes from continuum sources are given in units of number cm−2 s−1 MeV−1 at one astronomical unit, and the line fluxes are given in number cm−2 s−1. Credit: .

A star is considered to be at zero age (protostellar) when it is assumed to have a homogeneous composition and to be just beginning to derive most of its luminosity from nuclear reactions (so neglecting the period of contraction from a cloud of gas and dust). To obtain the SSM, a one solar mass stellar model at zero age is evolved numerically to the age of the Sun. The abundance of elements in the zero age solar model is estimated from primordial meteorites.[12] Along with this abundance information, a reasonable guess at the zero-age luminosity (such as the present-day Sun's luminosity) is then converted by an iterative procedure into the correct value for the model, and the temperature, pressure and density throughout the model calculated by solving the equations of stellar structure numerically assuming the star to be in a steady state. The model is then evolved numerically up to the age of the Sun. Any discrepancy from the measured values of the Sun's luminosity, surface abundances, etc. can then be used to refine the model. For example, since the Sun formed, the helium and heavy elements have settled out of the photosphere by diffusion. As a result, the Solar photosphere now contains about 87% as much helium and heavy elements as the protostellar photosphere had; the protostellar Solar photosphere was 71.1% hydrogen, 27.4% helium, and 1.5% metals.[12] A measure of heavy-element settling by diffusion is required for a more accurate model.

Nuclear reactions in the core of the Sun change its composition, by converting hydrogen nuclei into helium nuclei by the proton-proton chain and (to a lesser extent in the Sun than in more massive stars) the CNO cycle. This decreases the mean molecular weight in the core of the Sun, which should lead to a decrease in pressure. This does not happen as instead the core contracts. By the Virial Theorem half of the gravitational potential energy released by this contraction goes towards raising the temperature of the core, and the other half is radiated away. By the ideal gas law this increase in temperature also increases the pressure and restores the balance of hydrostatic equilibrium. The luminosity of the Sun is increased by the temperature rise, increasing the rate of nuclear reactions. The outer layers expand to compensate for the increased temperature and pressure gradients, so the radius also increases.[13]

Most of the neutrinos produced in the sun come from the first step of the pp chain but their energy is so low (<0.425 MeV)[14] they are very difficult to detect. A rare side branch of the pp chain produces the "boron-8" neutrinos with a maximum energy of roughly 15 MeV, and these are the easiest neutrinos to detect. A very rare interaction in the pp chain produces the "hep" neutrinos, the highest energy neutrinos predicted to be produced by our sun. They are predicted to have a maximum energy of about 18 MeV.

All of the interactions described above produce neutrinos with a spectrum of energies. The electron capture of 7Be produces neutrinos at either roughly 0.862 MeV (~90%) or 0.384 MeV (~10%).[14]

## Meteors

This movie of the Sun shows a coronal mass ejection. Credit: .

"Sun-grazing comets almost never re-emerge, but their sublimative destruction near the sun has only recently been observed directly, while chromospheric impacts have not yet been seen, nor impact theory developed."[15] "[N]uclei are ... destroyed by ablation or explosion ... in the chromosphere, producing flare-like events with cometary abundance spectra."[15]

"The death of a comet at r ~ R has been seen directly only very recently (Schrijver et al 2011) using the SDO AIA XUV instrument. This recorded sublimative destruction of Comet C/2011 N3 as it crossed the solar disk very near periheloin q = 1.139Rʘ."[15]

"The phenomenon of flare induced sunquakes - waves in the photosphere - discovered by Kosovichev and Zharkova (1998) and now widely studied (e.g. Kosovichev 2006) should also result from the momentum impulse delivered by a cometary impact."[15]

"Coronal clouds, type IIIg, form in space above a spot area and rain streamers upon it."[16]

The solar wind originates through the polar coronal holes.

## Cosmic rays

The surface of the Sun has not been detected with cosmic rays.

"[T]he relative abundances of solar cosmic rays reflect those of the solar photosphere for multicharged nuclei with approximately the same nuclear charge-to-mass ratio."[17]

## Neutrons

The surface of the Sun is not a known source of neutrons. No neutron probes have been used to detect the Sun.

## Protons

This graph displays the flux of high energy protons measured by GOES 11 over four days from November 2, 2004, to November 4, 2003. Credit: NOAA.

The Sun and the solar wind, at least that portion that originates through the polar coronal holes apparently from the photosphere, may be major sources of protons within the solar system.

At right is a temporal distribution of solar proton flux in units of particles cm-2 s-1 sr-1 as measured by GOES 11 over the four days from November 2, 2003, to November 4, 2003, in three windows of energy: ≥ 100 MeV (green), ≥ 50 MeV (blue), and ≥ 10 MeV (red). The percentage originating from the surface of the Sun either directly or through the contribution to the solar wind is not indicated.

## Electrons

"Energetic photons, ions and electrons from the solar wind, together with galactic and extragalactic cosmic rays, constantly bombard surfaces of planets, planetary satellites, dust particles, comets and asteroids."[18]

Jovian electrons propagate "along the spiral magnetic field of the interplanetary medium [from Jupiter and its magnetosphere to the Sun]".[1]

## Positrons

RHESSI observes high-energy phenomena from a solar flare. Credit: NASA/Goddard Space Flight Center Scientific Visualization Studio.

The solar flare at Active Region 10039 on July 23, 2002, exhibits many exceptional high-energy phenomena including the 2.223 MeV neutron capture line and the 511 keV electron-positron (antimatter) annihilation line. In the image at right, the RHESSI low-energy channels (12-25 keV) are represented in red and appear predominantly in coronal loops. The high-energy flux appears as blue at the footpoints of the coronal loops. Violet is used to indicate the location and relative intensity of the 2.2 MeV emission.

During solar flares “[s]everal radioactive nuclei that emit positrons are also produced; [which] slow down and annihilate in flight with the emission of two 511 keV photons or form positronium with the emission of either a three gamma continuum (each photon < 511 keV) or two 511 keV photons."[19] The Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) made the first high-resolution observation of the solar positron-electron annihilation line during the July 23, 2003 solar flare.[19] The observations are somewhat consistent with electron-positron annihilation in a quiet solar atmosphere via positronium as well as during flares.[19] Line-broadening is due to "the velocity of the positronium."[19] "The width of the annihilation line is also consistent ... with thermal broadening (Gaussian width of 8.1 ± 1.1 keV) in a plasma at 4-7 x 105 K. ... The RHESSI and all but two of the SMM measurements are consistent with densities ≤ 1012 H cm-3 [but] <10% of the p and α interactions producing positrons occur at these low densities. ... positrons produced by 3He interactions form higher in the solar atmosphere ... all observations are consistent with densities > 1012 H cm-3. But such densities require formation of a substantial mass of atmosphere at transition region temperatures."[19]

## Neutrinos

This "neutrino image" of the Sun is produced by using the Super-Kamiokande to detect the neutrinos from nuclear fusion coming from the Sun. Credit: R. Svoboda and K. Gordan (LSU).

This figure shows a detected 94 % correlation between scaled sunspot numbers and neutrino detections. Credit: John N. Bahcall.

Neutrinos are hard to detect. The Super-Kamiokande, or "Super-K" is a large-scale experiment constructed in an unused mine in Japan to detect and study neutrinos. The image at right required 500 days worth of data to produce the "neutrino image" of the Sun. The image is centered on the Sun's calculated position. It covers a 90° x 90° octant of the sky (in right ascension and declination). The higher the brightness of the color, the larger is the neutrino flux.

The surface of the Sun is not a known source of neutrinos. Those detected may be from nucleosynthesis within the coronal cloud in the near vicinity of the Sun or perhaps from nucleosynthesis occurring interior to the Sun.

"[N]eutrino flux increases noted in Homestake results [coincide] with major solar flares [14]."[20]

This result together with those in the next two paragraphs establishes that neutrinos are being produced by processes above the photosphere and probably within 2-4 solar radii as most solar flares give off energy close to and into the chromosphere.

"The correlation between a great solar flare and Homestake neutrino enhancement was tested in 1991. Six major flares occurred from May 25 to June 15 including the great June 4 flare associated with a coronal mass ejection and production of the strongest interplanetary shock wave ever recorded (later detected from spacecraft at 34, 35, 48, and 53 AU) [15]. It also caused the largest and most persistent (several months) signal ever detected by terrestrial cosmic ray neutron monitors in 30 years of operation [16]. The Homestake exposure (June 1–7) measured a mean 37Ar production rate of 3.2 ± 1.5 atoms/day (≈19 37Ar atoms produced in 6 days) [13]; about 5 times the rate of ≈ 0.65 day −1 for the preceding and following runs, > 6 times the long term mean of ≈ 0.5 day−1 and > 2 1/2 times the highest rates recorded in ∼ 25 operating years."[20]

The highest flux of solar neutrinos come directly from the proton-proton interaction, and have a low energy, up to 400 keV. There are also several other significant production mechanisms, with energies up to 18 MeV.[21]

The parts of the Sun above the photosphere are referred to collectively as the solar atmosphere.[22]

"Neutrinos can be produced by energetic protons accelerated in solar magnetic fields. Such protons produce pions, and therefore muons, hence also neutrinos as a decay product, in the solar atmosphere."[23]

"Energetic protons in the solar corona could explain Figure 2 [at right] only if (1) they tap a substantial fraction of the entire energy generated in the corona, (2) the energy generated in the corona is at least 3 times what has been deduced from the observations, (3) the vast majority of energetic protons do not escape the Sun, (4) the proton energy spectrum is unusually hard (p0 = 300 MeV c-1, and (5) the sign of the variation is opposite to what one would predict. As the likelihood of all of these conditions being fulfilled seems extremely small, we do not believe that neutrinos produced by energetic protons in the solar atmosphere contribute significantly to the neutrino capture in the 37Cl experiment."[23]

"The total number of neutrinos of all types agrees with the number predicted by the computer model of the Sun. Electron neutrinos constitute about a third of the total number of neutrinos. [...] The missing neutrinos were actually present, but in the form of the more difficult to detect muon and tau neutrinos."[24]

The reactions that produce the higher energy neutrinos: νµ and ντ are.

For antiproton-proton annihilation at rest, a meson result is, for example,

${\displaystyle p^{+}+{\bar {p}}^{-}\rightarrow \pi ^{+}+\pi ^{-},}$ [25]
${\displaystyle {\pi }^{+}\rightarrow {\mu }^{+}+{\nu }_{\mu }\rightarrow e^{+}+{\nu }_{e}+{\bar {\nu }}_{\mu }+{\nu }_{\mu },}$ [26] and
${\displaystyle D_{S}\rightarrow \tau +{\bar {\nu }}_{\tau }\rightarrow \nu _{\tau }+{\bar {\nu }}_{\tau }.}$ [27]

"All other sources of ντ are estimated to have contributed an additional 15%."[27]

${\displaystyle \tau \rightarrow e+\nu _{\tau }+\nu _{e},}$ [27]

for two neutrinos.[27]

${\displaystyle \tau \rightarrow h+\nu _{\tau }+X,}$ [27]

where ${\displaystyle h}$  is a hadron, for two neutrinos.[27]

## Gamma rays

The Sun is seen in gamma rays by COMPTEL during a June 15, 1991, solar flare. Credit: COMPTEL team, University of New Hampshire.

The surface of the Sun has yet to be detected as a gamma ray source, reflector, or in fluorescence.

RHESSI was the first satellite to image solar gamma rays from a solar flare.[28]

## X-rays

The coronal clouds of the Sun are captured with X-rays. Credit: NASA Goddard Laboratory for Atmospheres.

The image at top shows that the surface of the Sun, its photosphere, apparently neither emits, reflects, nor fluoresces X-rays.

"X-ray photons can be effectively backscattered by photosphere atoms and electrons (Tomblin 1972; Bai & Ramaty 1978). ... [A]t energies not dominated by absorption the backscattered albedo flux must be seen virtually in every solar flare spectrum, the degree of the albedo contribution depending on the directivity of the primary X-ray flux (Kontar et al. 2006). The solar flare photons backscattered by the solar photosphere can contribute significantly (the reflected flux is 50-90 % of the primary in the 30 - 50 keV range for isotropic sources) to the total observed photon spectrum. for the simple case of a power-law-like primary solar flare spectrum (without albedo), the photons reflected by the photosphere produce a broad 'hump' component. Photospheric albedo makes the observed spectrum flatter below ~ 35 keV and slightly steeper above, in comparison with the primary spectrum."[29]

## Opticals

Sample calibration colors[30]
Class B–V U–B V–R R–I Teff (K)
O5V –0.33 –1.19 –0.15 –0.32 42,000
B0V –0.30 –1.08 –0.13 –0.29 30,000
A0V –0.02 –0.02 0.02 –0.02 9,790
F0V 0.30 0.03 0.30 0.17 7,300
G0V 0.58 0.06 0.50 0.31 5,940
K0V 0.81 0.45 0.64 0.42 5,150
M0V 1.40 1.22 1.28 0.91 3,840

The color index is a simple numerical expression that determines the color of an object, which in the case of a star gives its temperature. To measure the index, one observes the magnitude of an object successively through two different filters, such as U and B, or B and V, where U is sensitive to ultraviolet rays, B is sensitive to blue light, and V is sensitive to visible (green-yellow) light (see also: UBV system). The set of passbands or filters is called a photometric system. The difference in magnitudes found with these filters is called the U-B or B–V color index, respectively. The smaller the color index, the more blue (or hotter) the object is. Conversely, the larger the color index, the more red (or cooler) the object is. This is a consequence of the logarithmic magnitude scale, in which brighter objects have smaller (more negative) magnitudes than dimmer ones. The passbands most optical astronomers use are the UBVRI filters, where the U, B, and V filters are as mentioned above, the R filter passes red light, and the I filter passes infrared light. These filters were specified as particular combinations of glass filters and photomultiplier tubes.

## Ultraviolets

The chromosphere of the Sun shows in ultraviolets. Credit: STEREO (NASA).

The Sun's photosphere probably generates little or no ultraviolet rays.

## Visuals

A visual image is shown in black and white. Credit: Big Bear Solar Observatory.

This is the appearance of the Sun in visual radiation centered in the yellow-green. Credit: Jim E. Brau, Pearson Prentice Hall, Inc.
Sample calibration colors[30]
Class B–V V–R Teff (K)
O5V –0.33 –0.15 42,000
B0V –0.30 –0.13 30,000
A0V –0.02 0.02 9,790
F0V 0.30 0.30 7,300
G0V 0.58 0.50 5,940
K0V 0.81 0.64 5,150
M0V 1.40 1.28 3,840

The visual color index is a simple numerical expression that determines the color of an object, which in the case of a star gives its temperature. To measure the visual index, one observes the magnitude of an object successively through two different filters, such as B and V, where B is sensitive to blue light, and V is sensitive to visible (green-yellow) light. The difference in magnitudes found with these filters is called the B–V color index. The smaller the color index, the more blue (or hotter) the object is. Conversely, the larger the color index, the more red (or cooler) the object is. For comparison, the yellowish Sun has a B–V index of 0.656 ± 0.005,[31] while the bluish Rigel has a B–V of –0.03 (its B magnitude is 0.09 and its V magnitude is 0.12, B–V = –0.03).[32]

## Violets

The Sun in purple or violet is shown. Credit: .

The Sun's photosphere emits over the violet (380-450 nm) band.

## Blues

This an image of the Sun demonstrating blue emission. Credit: A. Friedman.

The surface of the Sun emits blue (450-475 nm) electromagnetic radiation.

## Cyans

The surface of the Sun emits cyan (475-495 nm) electromagnetic radiation.

## Greens

This is a video of the Sun in yellow-green. Credit: NASA/SDO.

This is the latest image of the Sun by SDO for 03 December 2015. Credit: SDO, NASA.

The Na I green lines at 568.2 and 568.8 nm arise "in the photospheric layers between log τ5000 ≈ -1 and -2."[33]

The latest image of the Sun on the left in yellow-green shows no sunspots.

## Yellows

The Sun often appears yellow. Credit: NASA.

Seeing the yellow Sun and feeling the warmth of its rays is probably a student's first encounter with an astronomical yellow radiation source.

The surface of the Sun emits yellow (570-590 nm) radiation.

"Stars of spectral classes F and G, such as our sun Sol, have color temperatures that make them look "yellowish".[34]

## Oranges

Atmospheric effects may produce an orange Sun. Credit: .

This is an orange colorized intensity gram of the Sun. Credit: NASA, Solar Dynamics Observatory.

Image at 617.3 nm taken on 5 March 2013, 10:00:20. Credit: NASA/SDO.

The surface of the Sun emits in the orange (590 to 620 nm) wavelengths.

The Na I lines at 615.4 and 616.0 nm arise "in the photospheric layers between log τ5000 ≈ -1 and -2."[33]

The second image down on the right is an orange colorized intensity gram of the Sun using the Helioseismic and Magnetic Imager (HMI) on NASA's Solar Dynamics Observatory. HMI observes the solar disk at 6173 Ångstroms which is the source of the orange color. The image was taken on 16 August 2012. Compare this with the image on the left taken almost 2 years later. The second has far fewer sunspots.

## Reds

The Sun is observed through a telescope with an H-alpha filter. Credit: Marshall Space Flight Center, NASA.

This is a red sun. Credit: Totallyhaywire2.

The sun with Venus in transit, from Mount Wilson Observatory, June 5, 2012. Credit: Alan Friedman, Mount Wilson Observatory.

The surface of the Sun emits in the red (621 to 750 nm) wavelengths.

"[S]ome observed properties of the Sun still defy explanation, such as the degree of Li depletion" [the "solar Li abundance is roughly a factor of 200 below the meteoritic abundance"].[35]

The second image down on the right is an image of the Sun during a transit of Venus at a wavelength close 620 nm.

## Infrareds

This graph depicts the expected intensity of infrared emission versus wavelength at various radial distances from the Sun. Credit: NASA (Dr. Paulett Liewer).

The surface of the Sun emits infrared. Credit: .

This is an image of the Sun in infrared. Credit: Jim E. Brau, Pearson Prentice Hall, Inc.

The surface of the Sun emits in the infrared.

At right is a graph of the expected solar and interstellar infrared emission versus wavelength at various radial distances from the Sun.

The Na I lines at 818.3, 819.4, and 1140 nm in the near infrared arise "in the photospheric layers between log τ5000 ≈ -1 and -2."[33]

The second image down on the right shows the Sun imaged in the infrared.

## Microwaves

This is the Sun at 5 GHz. Credit: .

The surface of the Sun emits radio waves, including microwaves.

This is a radio image of the Sun. Credit: Jim E. Brau, Pearson Prentice Hall, Inc.

The Sun does emit radio waves as shown in the image on the right.

## Superluminals

The surface of the Sun is not a known source of superluminal radiation.

## Plasma objects

Plasma is a state of matter similar to gas in which a certain portion of the particles are ionized. Heating a gas may ionize its molecules or atoms (reduce or increase the number of electrons in them), thus turning it into a plasma, which contains charged particles: positive ions and negative electrons or ions.[36]

For plasma to exist, ionization is necessary. The term "plasma density" by itself usually refers to the "electron density", that is, the number of free electrons per unit volume. The degree of ionization of a plasma is the proportion of atoms that have lost or gained electrons, and is controlled mostly by the temperature. Even a partially ionized gas in which as little as 1% of the particles are ionized can have the characteristics of a plasma (i.e., response to magnetic fields and high electrical conductivity). The degree of ionization, α is defined as α = ni/(ni + na) where ni is the number density of ions and na is the number density of neutral atoms. The electron density is related to this by the average charge state <Z> of the ions through ne = <Z> ni where ne is the number density of electrons.

## Solar flares

"[A] medium-strength flare erupted from the sun on July 19, 2012. The blast also generated the enormous, shimmering plasma loops, which are an example of a phenomenon known as "coronal rain," agency officials said."[37]

## Rain

"Hot plasma in the corona cooled and condensed along strong magnetic fields in the region" slowly falling back to the solar surface as plasma "rain".[37]

## Coronal mass ejections

Arcs rise above an active region on the surface of the Sun in this series of images taken by the STEREO (Behind) spacecraft. Credit: Images courtesy of the NASA STEREO Science Center.

"Many CMEs have also been observed to be unassociated with any obvious solar surface activity"[38].

In the images at right, a CME, or "arcs rise above an active region on the surface of the Sun in this series of images taken by the STEREO (Behind) spacecraft on January 27, 2010. The arcs are plasma, superheated matter made up of moving charged particles (electrons and ions). Just as iron filings arc from one end of a magnet to another, the plasma is sliding in an arc along magnetic field lines. In a movie of STEREO observations made between January 26 and January 29, the dynamic streams were initially just over the Sun’s edge and readily spotted as the Sun rotated them more into view."[39]

"About mid-way through the movie clip, a small coronal mass ejection (a stream of charged particles from the Sun) shoots out and into space at about a million miles per hour, carrying some magnetic field with it. The [first] image shows the beginning of the coronal mass ejection, while the [second] image shows the solar matter leaving the Sun’s corona. Most coronal mass ejections are more bulbous and wide: this one is quite narrow and contained. Nonetheless, NASA solar scientists agree that its speed and characteristics suggest that it was indeed a non-typical coronal mass ejection."[39]

## Solar clouds

The February 10, 1956, event "was observed at Sacramento Peak. A bright ball appears above the [Sun's] surface, grows in size and Hα brightness, and explodes upward and outward."[40]

## Photospheres

The solar photosphere is a "weakly ionized [ni/(ni + na)] ~ 10-4, relatively cold and dense plasma".[41]

## Gaseous objects

Gaseous objects have been used to approximate a location for the Sun based on Kepler's laws.

No gaseous objects are known to have been emitted, reflected, or deflected by the Sun. No gaseous objects have impacted the surface of the Sun.

Magnetic clouds represent about one third of ejecta observed by satellites at Earth. Other types of ejecta are multiple-magnetic cloud events (a single structure with multiple subclouds distinguishable)[42][43] and complex ejecta, which can be the result of the interaction of multiple [Coronal Mass Ejection] CMEs.

## Rocky objects

Rocky objects have been used to approximate a location for the Sun based on Kepler's laws. No rocky objects are known to have been emitted, reflected, or deflected by the Sun. Nor, have any rocky objects impacted the surface of the Sun.

"Sun-grazing comets almost never re-emerge, but their sublimative destruction near the sun has only recently been observed directly, while chromospheric impacts have not yet been seen, nor impact theory developed."[15] "[N]uclei are ... destroyed by ablation or explosion ... in the chromosphere, producing flare-like events with cometary abundance spectra."[15]

"The death of a comet at r ~ R has been seen directly only very recently (Schrijver et al 2011) using the SDO AIA XUV instrument. This recorded sublimative destruction of Comet C/2011 N3 as it crossed the solar disk very near periheloin q = 1.139Rʘ."[15]

"The phenomenon of flare induced sunquakes - waves in the photosphere - discovered by Kosovichev and Zharkova (1998) and now widely studied (e.g. Kosovichev 2006) should also result from the momentum impulse delivered by a cometary impact."[15]

## Heliognosy

This graph shows the temperature and density of the Sun's atmosphere from Skylab observations. Credit: John A. Eddy, NASA.

The Sun as a star has a composition. Hydrogen has been detected on the surface of the Sun.

For stars, the metallicity is often expressed as "[Fe/H]", which represents the logarithm of the ratio of a star's iron abundance compared to that of the Sun (iron is not the most abundant heavy element, but it is among the easiest to measure with spectral data in the visible spectrum). The formula for the logarithm is expressed thus:

${\displaystyle [\mathrm {Fe} /\mathrm {H} ]=\log _{10}{\left({\frac {N_{\mathrm {Fe} }}{N_{\mathrm {H} }}}\right)_{star}}-\log _{10}{\left({\frac {N_{\mathrm {Fe} }}{N_{\mathrm {H} }}}\right)_{sun}}}$

where ${\displaystyle N_{\mathrm {Fe} }}$  and ${\displaystyle N_{\mathrm {H} }}$  are the number of iron and hydrogen atoms per unit of volume respectively. The unit often used for metallicity is the "dex" which is a (now-deprecated) contraction of decimal exponent.[44] By this formulation, stars with a higher metallicity than the Sun have a positive logarithmic value, while those with a lower metallicity than the Sun have a negative value. The logarithm is based on powers of ten; stars with a value of +1 have ten times the metallicity of the Sun (101). Conversely, those with a value of -1 have one tenth (10 −1), while those with -2 have a hundredth (10−2), and so on.[45] Young Population I stars have significantly higher iron-to-hydrogen ratios than older Population II stars. Primordial Population III stars are estimated to have a metallicity of less than −6.0, that is, less than a millionth of the abundance of iron which is found in the Sun.

The image at right describes graphically the temperature and density of the Sun's atmosphere from the photosphere upwards. "The Sun's photosphere has a temperature between 4500 and 6000 K[46] (with an effective temperature of 5777 K) and a density of about [2 x 10-4kg/m3;[47] other stars may have hotter or cooler photospheres.

## Hydrogens

The Balmer series of emission lines from hydrogen occur in the visible spectrum of the Sun at: 397, 410, 434, 486, and 656 nm. Hα is the red line (656 nm).

## Heliums

Helium was first detected as an unknown yellow spectral line signature in sunlight during a solar eclipse in 1868 by French astronomer Jules Janssen. Janssen is jointly credited with detecting the element along with Norman Lockyer during the solar eclipse of 1868, and Lockyer was the first to propose that the line was due to a new element, which he named.

## Heliography

This is a rotating projection of the entire surface of the Sun on February 10, 2011, as seen by the twin STEREO satellites. Credit: NASA STEREO mission.

This computer-generated diagram of internal rotation in the Sun shows differential rotation in the outer convective region and almost uniform rotation in the central radiative region. Credit: Global Oscillation Network Group (GONG).

Use of Stonyhurst disk is shown to determine the heliographic coordinates of sunspots. Credit: Cortie, A. L. 1908.

The surface of the Sun is often described by features observed. These are located using heliographic coordinates based on heliographic north and south poles. The surface of the Sun rotates, has a rotational north and south pole, and there is a central meridian.

Different parts of the Sun rotate at different rates.

At right is a diagram of the internal rotation in the Sun, showing differential rotation in the outer convective region and almost uniform rotation in the central radiative region. The transition between these regions is called the tachocline.

Until the advent of helioseismology, the study of wave oscillations in the Sun, very little was known about the internal rotation of the Sun. The differential profile of the surface was thought to extend into the solar interior as rotating cylinders of constant angular momentum.[48] Through helioseismology this is now known not to be the case and the rotation profile of the Sun has been found. On the surface the Sun rotates slowly at the poles and quickly at the equator. This profile extends on roughly radial lines through the solar convection zone to the interior. At the tachocline the rotation abruptly changes to solid body rotation in the solar radiation zone.[49]

The Stonyhurst Disk is superimposed on an image of the Sun to determine the heliographic coordinates. These are constructed by analogy with the geographical and are characterized by two values, latitude (Φ) and longitude (λ). Latitude is measured from the plane of the solar equator. The first longitude (λ1) is measured from the plane of the "central meridian" as it passes through the rotation axis of the Sun and the line connecting the center of the Sun to the observer. The Carrington longitude (λ2) is measured from the central meridian as it passes through the ascending node of the solar equator at Greenwich noon on January 1, 1854 (JD 2398220.0) and rotating with the sidereal period of 25.38 Earth days.

The two longitudes are associated approximately by the ratio

${\displaystyle \lambda _{2}=\left\{{\frac {\lambda _{1}}{360^{\circ }}}-{\frac {{\rm {JD}}-2398220}{27.2753}}\right\}\cdot 360^{\circ }}$ .

The Sun has an equatorial radius of 695,500 km[50]

## Surfaces

This is a visual image of the Sun with some sunspots visible on the photosphere. The two small spots in the middle have about the same diameter as our planet Earth. Credit: NASA.

Def. a "visible surface layer of a star, and especially that of a sun"[51] is called a photosphere.

"When we speak of the surface of the Sun, we normally mean the photosphere."[52] "[T]he photosphere may be thought of as the imaginary surface from which the solar light that we see appears to be emitted. The diameter quoted for the Sun usually refers to the diameter of the photosphere."[52] The photosphere emits visual, or visible, radiation.

Illumination of the Sun's photosphere is in part by gamma rays. "Each gamma ray [that interacts with the photosphere] is converted into several million photons of visible light. At the visible surface of the Sun, the temperature has dropped to 5,700 K and the density to only 0.2 g/m3 (about 1/6,000th the density of air at sea level).[53]

The tremendous power output of the Sun is not due to its high power per volume, but instead due to its large size. Above the photosphere visible sunlight is free to propagate into space, and its energy escapes the Sun entirely. The change in opacity is due to the decreasing amount of H ions, which absorb visible light easily.[22] Conversely, the visible light we see is produced as electrons react with hydrogen atoms to produce H ions.[54][55] The photosphere has a particle density of ~1023 m−3 (this is about 0.37% of the particle number per volume of Earth's atmosphere at sea level; however, photosphere particles are electrons and protons, so the average particle in air is 58 times as heavy).

## Disc edge

Def. a shape or surface that is round and flat in appearance (middle 17th century usage referring to the seemingly flat round form of the Sun) is called a disc, or disk.

Def. "the radial distance q from the Sun's center such that the following finite Fourier transform is zero:

${\displaystyle F(G;q,a)=\int _{-1/2}^{+1/2}G(q+a\sin \pi s)\cos(2\pi s)ds,}$

where s is a dummy variable, G is the observed solar intensity as a function of the radius, and the parameter a determines the extent of the solar limb used"[56] is called the solar edge.

"When F(G; q, a) = 0, the a dependence of q can be used to choose different points as the edge."[56]

## Granulation

This visual image using the Vacuum Tower Telescope shows solar granulation around and outward from a sunspot or hole. Credit: Vacuum Tower Telescope, NASA.

There is turbulence and granulation in the Sun's photosphere. A typical granule has a diameter on the order of 1,000 kilometers and lasts 8 to 20 minutes before dissipating. At any one time, the Sun's surface is covered by about 4 million granules.

Supergranulation is a particular pattern of granules on the Sun's surface that was discovered in the 1950s by A.B.Hart using Doppler velocity measurements showing horizontal flows on the photosphere (flow speed about 300 to 500 m/s, a tenth of that in the smaller granules). Later work (1960s) by Leighton, Noyes and Simon established a typical size of about 30000 km for supergranules with a lifetime of about 24 hours.[57]

## Faculae

Solar faculae are bright spots that form in the canyons between solar granules.

The emission of higher than average amounts of radiation later were observed from the solar faculae.[58]

Correlations are now known to exist with decreases in luminosity caused by sunspots (generally < - 0.3%) and increases (generally < + 0.05%) caused both by faculae that are associated with active regions as well as the magnetically active 'bright network'.[59] Faculae in magnetically active regions are hotter and 'brighter' than the average photosphere and cause temporary increases in [total solar irradiance] TSI. Luminosity has also been found to decrease by as much as 0.3% on a 10 day timescale when large groups of sunspots rotate across the Earth's view and increase by as much as 0.05% for up to 6 months due to faculae associated with the large sunspot groups.[59]

The net effect during periods of enhanced solar magnetic activity is increased radiant output of the sun because faculae are larger and persist longer than sunspots.

"Though sunspots themselves are darker, they form when there are particularly magnetically active regions, which is when larger, brighter, longer-duration Faculae are more common as well"[60].

## Holes

The image shows a drawing of a sunspot in the Chronicles of John of Worcester. Credit: Original work by John of Worcester.

This drawing of a group of sun spots and veiled spots is as observed on June 17, 1875, at 7 h 30 m a.m. Credit: Étienne Léopold Trouvelot.

This spiral sunspot was seen at Rome on May 5, 1857. Credit: Secchi.

A sunspot is a depression on the Sun's face that is slightly cooler and less luminous than the rest of the Sun. Credit: Vacuum Tower Telescope, NSO, NOAO.

A planet-sized sunspot showing for the first time dark cores of the filaments extending into the sunspot. These filaments are thousands of km long by about 100 km wide. Recorded on July 15, 2002, using the Swedish Solar Telescope (SST). Solar active region AR 10030. Credit: SST, Royal Swedish Academy of Sciences.

Measurements of solar cycle variation are included for the last 30 years. Credit: Robert A. Rohde.

History of the number of observed sunspots during the last 250 years shows the ~11-year solar cycle. Credit: Leland McInnes.

This figure summarizes sunspot number observations. Credit: Robert A. Rohde.

Changes in 14C concentration in the Earth's atmosphere serve as a long term proxy of solar activity. Note the present day is on the right-hand side. Credit: USGS.

Def. a "hollow spot in a surface"[61] is called a hole.

Def. "[a]n opening in a solid[, liquid, gas, or plasma]"[61] is called a hole.

Def. a "round or irregular patch on [or apparently on] the surface of [an entity] having a different color, texture etc. and generally round in shape"[62] is called a spot.

Def. "[a]n opening through which [entities such as] gases ... can pass"[63] is called a vent.

Sunspots are temporary phenomena on the photosphere of the Sun that appear visibly as dark spots compared to surrounding regions. They are caused by intense magnetic activity, which inhibits convection by an effect comparable to the eddy current brake, forming areas of reduced surface temperature. Like magnets, they also have two poles. Although they are at temperatures of roughly 3,000–4,500 K (2,727–4,227 °C), the contrast with the surrounding material at about 5,780 K leaves them clearly visible as dark spots, as the luminous intensity of a heated black body (closely approximated by the photosphere) is a function of temperature to the fourth power. If the sunspot were isolated from the surrounding photosphere it would be brighter than an electric arc. Sunspots expand and contract as they move across the surface of the Sun and can be as large as 80,000 kilometers (49,710 mi) in diameter, making the larger ones visible from Earth without the aid of a telescope.[64] They may also travel at relative speeds ("proper motions") of a few hundred m/s when they first emerge onto the solar photosphere.

"For the greater part of the sun-spot period there is practically but one zone of spots in each hemisphere. The departure from this condition of things near or at the time of minimum, when the spots of the dying cycle are approaching the equator, and the forerunners of the new cycle are beginning to appear in high latitudes, is the only case in which the solar spots are distinctly separated into more than a single zone in each hemisphere."[65] "Spöerer's law ... involves that in a minimum year the zone about 15° should be entirely barren".[65]

"First of all there were only fifteen groups seen during the entire year [1901], north and south put together. Of these, seven were in the north, and the mean latitude for the north was 8.6°, exactly the latitude of one spot of the seven, and this very naturally, seeing that it was by far the greatest group of the year, the celebrated "eclipse group.""[65] Bold added. "Greatest group" and "eclipse group" are both relative synonyms for "dominant group".

"[T]he spot-groups have been carefully examined for cases of return, and where it appeared clear that the same group has returned a second time or more frequently, without any temporary disappearance or subsidence, such a long-continued group has been treated as an entity throughout."[66] Bold added. "It has been forgotten that, whatever the cause which produces this variation of rotation rate with latitude, the causes producing difference of rate within any given latitude are more effective still."[66]

"[T]here is a slight retardation of the rotation period from the first cycle to the second, shown by both northern and southern hemispheres."[66]

Studies of stratigraphic data have suggested that the solar cycles have been active for hundreds of millions of years, if not longer; measuring varves in precambrian sedimentary rock has revealed repeating peaks in layer thickness, with a pattern repeating approximately every eleven years. It is possible that the early atmosphere on Earth was more sensitive to changes in solar radiation than today, so that greater glacial melting (and thicker sediment deposits) could have occurred during years with greater sunspot activity.[67][68] This would presume annual layering; however, alternate explanations (diurnal) have also been proposed.[69]

Analysis of tree rings has revealed a detailed picture of past solar cycles: Dendrochronologically dated radiocarbon concentrations have allowed for a reconstruction of sunspot activity dating back 11,400 years, far beyond the four centuries of available, reliable records from direct solar observation.[70]

The earliest surviving record of sunspot observation dates from 364 BC, based on comments by Chinese astronomer Gan De in a star catalogue.[71] By 28 BC, Chinese astronomers were regularly recording sunspot observations in official imperial records.[72]

The second drawing at right is of a group of sun spots and veiled spots. This group was observed on June 17, 1875, at 07:30 a.m. The interior of these spots appears to have a larger granule size than the outer surface of the photosphere itself.

The spiral sunspot in the third drawing at right is a vortex seen on May 5, 1857, at Rome. "[T]he substance of the photosphere is rushing with an eddying motion [into the spot]."[73]

Starspots are equivalent to sunspots but located on other stars. Spots the size of sunspots are very hard to detect since they are too small to cause fluctuations in brightness. Observed starspots are in general much larger than those on the Sun, up to about 30 % of the stellar surface may be covered, corresponding to sizes 100 times greater than those on the Sun.

The distribution of starspots across the stellar surface varies analogous to the solar case, but differs for different types of stars, e.g., depending on whether the star is a binary or not. The same type of activity cycles that are found for the Sun can be seen for other stars, corresponding to the solar (2 times) 11-year cycle. Some stars have longer cycles, possibly analogous to the Maunder minima for the Sun.

Another activity cycle is the so called flip-flop cycle, which implies that the activity on either hemisphere shifts from one side to the other. The same phenomena can be seen on the Sun, with periods of 3.8 and 3.65 years for the northern and southern hemispheres. Flip-flop phenomena are observed for both binary [RS Canum Venaticorum variable] RS CVn stars and single stars although the extent of the cycles are different between binary and singular stars.

Manifesting intense magnetic activity, sunspots host secondary phenomena such as coronal loops (prominences) and reconnection events. Most solar flares and coronal mass ejections originate in magnetically active regions around visible sunspot groupings. Similar phenomena indirectly observed on stars are commonly called starspots and both light and dark spots have been measured.[74]

The sunspot itself can be divided into two parts:

• The central umbra, which is the darkest part, where the magnetic field is approximately vertical (normal to the Sun's surface).
• The surrounding penumbra, which is lighter, where the magnetic field is more inclined.

"[T]he rate of helicity change dH/dt due to horizontal motions is

${\displaystyle {\frac {dH}{dt}}=-2\oint (\mathbf {v} \cdot \mathbf {A_{p}} )\mathbf {B_{n}} \mathrm {d} \mathbf {S} ,}$

where Bn is the vertical component of the magnetic field on the photosphere and v the photospheric horizontal velocity."[75]

"Helicity [(H)] is a quantitative measure of the chiral properties of the structures observed in the solar atmosphere. ... [H]elicity [is] injected to the corona by photospheric horizontal shearing motions (other than differential rotation) or by [vertical] magnetic flux. ... [D]ifferential rotation cannot provide the required helicity to the [CME] field ejected to interplanetary space."[75]

Solar active region AR 10030 contained a group of sunspots including the largest one partially included in the image at the right. It is a planet-sized sunspot showing for the first time the dark cores of the filaments extending into the sunspot. These filaments are thousands of km long by about 100 km wide. The image is recorded on July 15, 2002, using the Swedish Solar Telescope (SST).

"The number of sunspots visible on the Sun is not constant, but varies over an 11-year cycle known as the solar cycle. At a typical solar minimum, few sunspots are visible, and occasionally none at all can be seen. Those that do appear are at high solar latitudes. As the sunspot cycle progresses, the number of sunspots increases and they move closer to the equator of the Sun, a phenomenon described by Spörer's law. Sunspots usually exist as pairs with opposite magnetic polarity. The magnetic polarity of the leading sunspot alternates every solar cycle, so that it will be a north magnetic pole in one solar cycle and a south magnetic pole in the next.[76]

HD 154345b has "a 9.2 year, circular orbit with radius 4.2 AU. ... We also detect a ~ 9 year activity cycle in this star [HD 154345] photometrically and in chromospheric emission. ... We note that the Sun's 11 year activity cycle has a period similar to that of Jupiter's orbit, and that the Mount Wilson survey demonstrated that decadal activity cycles are a common feature of old G stars (Baliunas et al. 1995)."[77]

## Naked sunspots

"Naked sunspots are spots seen in Hα to be devoid of associated plage. In magnetograms and K-line little if any opposite polarity field is found, and in soft X-ray images a blank appears in the region of the spot. In almost all cases ... in which naked spots resulted the spot groups had emerged in unipolar regions of the same polarity as the naked spot. At least half of the naked spots are associated with coronal holes."[78]

"[N]aked spots are long-lived and show rotation rates close to the Newton-Nunn curve. Most of the naked spots had bright rims in Hα".[78]

## Wolf numbers

This graph shows Wolf numbers since 1750. Credit: NASA.

"[T]he longest data set, the Wolf sunspot number (R), is determined from visible wavelength observations of the solar surface."[79]

The Wolf number (also known as the International sunspot number, relative sunspot number, or Zürich number) is a quantity that measures the number of sunspots and groups of sunspots present on the surface of the sun.

This number has been collected and tabulated by researchers for over 150 years.

The relative sunspot number ${\displaystyle R}$  is computed using the formula (collected as a daily index of sunspot activity):

${\displaystyle R=k(10g+s)\,}$

where

• ${\displaystyle s}$  is the number of individual spots,
• ${\displaystyle g}$  is the number of sunspot groups, and
• ${\displaystyle k}$  is a factor that varies with location and instrumentation (also known as the observatory factor or the personal reduction coefficient ${\displaystyle K}$ ).[80]

## Heliometry

The graph demonstrates the motion of the barycenter of the solar system relative to the location of the center of the Sun. Credit: Carl Smith derivative of work by Rubik-wuerfel.

The center of mass plays an important role in astronomy and astrophysics, where it is commonly referred to as the barycenter. The barycenter is the point between two objects where they balance each other; it is the center of mass where two or more celestial bodies orbit each other. When a moon orbits a planet, or a planet orbits a star, both bodies are actually orbiting around a point that lies away from the center of the primary (larger) body.

The Sun's motion about the center of mass of the Solar System is complicated by perturbations from the planets. Every few hundred years this motion switches between prograde and retrograde.[81]

Def. "the mass of the Sun" is called the astronomical unit of mass.[82]

Notation: let the symbol ${\displaystyle M_{\odot }}$  indicate the solar mass.

The solar mass (${\displaystyle {\begin{smallmatrix}M_{\odot }\end{smallmatrix}}}$ ) is a standard unit of mass in astronomy, used to indicate the masses of other stars, as well as clusters, nebulae and galaxies. It is equal to the mass of the Sun, about two nonillion kilograms:

${\displaystyle M_{\odot }=(1.98855\ \pm \ 0.00025)\ \times 10^{30}{\hbox{ kg}}}$ [83][84]

This is about 332,946 times the mass of the Earth or 1,048 times the mass of Jupiter.

Because the Earth follows an elliptical orbit around the Sun, the solar mass can be computed from the equation for the orbital period of a small body orbiting a central mass.[85] Based upon the length of the year, the distance from the Earth to the Sun (an astronomical unit or AU), and the gravitational constant (G), the mass of the Sun is given by:

${\displaystyle M_{\odot }={\frac {4\pi ^{2}\times (1\ {\rm {AU}})^{3}}{G\times (1\ {\rm {year}})^{2}}}}$ .

The value of the gravitational constant was derived from 1798 measurements by Henry Cavendish using a torsion balance. The value obtained differed only by about 1% from the modern value.[86] The diurnal parallax of the Sun was accurately measured during the transits of Venus in 1761 and 1769,[87] yielding a value of 9″ (compared to the present 1976 value of 8.794148″). When the value of the diurnal parallax is known, the distance to the Sun can be determined from the geometry of the Earth.[88]

Notation: let the symbol ${\displaystyle R_{\odot }}$  indicate the solar radius.

The solar radius is a unit of distance used to express the size of stars in astronomy equal to the current radius of the Sun:

${\displaystyle R_{\odot }=6.955\times 10^{8}\,{\hbox{m}}=0.0046491\,{\hbox{AU}}=2.254\times 10^{-8}\,{\hbox{pc}}}$

The solar radius is approximately 695,500 kilometres (432,450 miles) or about 110 times the radius of the Earth (${\displaystyle R_{\oplus }}$ ), or 10 times the average radius of Jupiter. It varies slightly from pole to equator due to its rotation, which induces an oblateness of order 10 parts per million.

The luminosity of stars is measured in two forms: apparent (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.) When not qualified, "luminosity" means bolometric luminosity, which is measured either in the SI units, watts; or in terms of solar luminosities, ${\displaystyle L_{\odot }}$ , that is, how many times as much energy the object radiates as the Sun.

Notation: let the symbol ${\displaystyle L_{\odot }}$  represent the solar bolometric luminosity.

The solar luminosity, [${\displaystyle L_{\odot }}$ ], is a unit of radiant flux (power emitted in the form of photons) conventionally used .. to measure the luminosity of stars. One solar luminosity is equal to the current accepted luminosity of the Sun, which is 3.839×1026
W
, or 3.839×1033
erg/s
.[89] The value is slightly higher, 3.939×1026
W
(equivalent to 4.382×109
kg/s
or 1.9×1016
M/d
) if the solar neutrino radiation is included as well as electromagnetic radiation.[90] The Sun is a weakly variable star and its luminosity therefore fluctuates. The major fluctuation is the eleven-year solar cycle (sunspot cycle), which causes a periodic variation of about ±0.1%. Any other variation over the last 200–300 years is thought to be much smaller than this.[90]

The solar luminosity is related to the solar irradiance measured at the Earth or by satellites in Earth orbit. The mean irradiance at the top of the Earth's atmosphere is sometimes known as the solar constant, [${\displaystyle I_{\odot }}$ ]. Irradiance is defined as power per unit area, so the solar luminosity (total power emitted by the Sun) is the irradiance received at the Earth (solar constant) multiplied by the area of the sphere whose radius is the mean distance between the Earth and the Sun:

${\displaystyle L_{\odot }=4\pi kI_{\odot }A^{2}\,}$

where A is the unit distance (the value of the astronomical unit in metres) and k is a constant (whose value is very close to one) that reflects the fact that the mean distance from the Earth to the Sun is not exactly one astronomical unit.

Notation: let the symbol ${\displaystyle Q_{\odot }}$  represent the net solar charge.

"[A] variety of geophysical and astrophysical phenomena can be explained by a net charge on the Sun of -1.5 x 1028 e.s.u."[91] This figure was later reduced by a factor of five.[92]

${\displaystyle Q_{\odot }=-0.3\times 10^{28}\,{\hbox{esu}}.}$

## Temperatures

This figure shows the extraterrestrial solar spectral irradiance of the Sun. Credit: Sch.

CO2, temperature, and sunspot activity are diagrammed since 1850. Credit: Leland McInnes.

The color of a star, as determined by the peak frequency of the visible light, depends on the temperature of the star's outer layers, including its photosphere.[93] The effective temperature of the surface of the Sun's photosphere is 5,778 K.[94] The "[t]emperature at [the] bottom of [the Sun's] photosphere [is] 6600 K", while the "[t]emperature at [the] top of [the] photosphere [is] 4400 K".[94] The photosphere is "~400 km" in thickness.[94]

The peak emittance wavelength of 501.5 nm (~0.5 eV) makes the photosphere a primarily green radiation source. The figure at the right shows the extraterrestrial solar spectral irradiance as compared with a blackbody spectrum. The sharper than black-body cutoff at the shorter wavelength end indicates an even lower likelihood that X-rays are emitted from the photosphere.

Solar irradiance spectrum is diagrammed above atmosphere and at the Earth's surface. Credit: Robert A. Rohde.

One composite is graphed of the last 30 years of solar variability. Credit: Robert A. Rohde.

Direct irradiance measurements have only been available during the last three cycles and are based on a composite of many different observing satellites.[95] [96] However, the correlation between irradiance measurements and other proxies of solar activity make it reasonable to estimate past solar activity. Most important among these proxies is the record of sunspot observations that has been recorded since ~1610. Since sunspots and associated faculae are directly responsible for small changes in the brightness of the sun, they are closely correlated to changes in solar output. Direct measurements of radio emissions from the Sun at 10.7 cm also provide a proxy of solar activity that can be measured from the ground since the Earth's atmosphere is transparent at this wavelength. Lastly, solar flares are a type of solar activity that can impact human life on Earth by affecting electrical systems, especially satellites. Flares usually occur in the presence of sunspots, and hence the two are correlated, but flares themselves make only tiny perturbations of the solar luminosity.

Solar irradiance and insolation are measures of the amount of sunlight that reaches the Earth. The equipment used might measure optical brightness, total radiation, or radiation in various frequencies.

## Solar evolution

As stars often occur in binaries or multiple star systems, it is likely that the Sun may have been a member of a binary system or even a multiple star system at some time in the past.

The solar antapex, the direction opposite of the solar apex, is located near the star Zeta Canis Minoris.

In 1917 the solar antapex has an equatorial location of right ascension (RA) 6h declination (Dec) -34°.[97]

The solar apex (Apex of the Sun's Way) is the direction that the Sun travels with respect to the Local Standard of Rest, the "target" within the Milky Way that the Sun appears to be "chasing" as it orbits the galaxy.

The general direction of the solar apex is southwest of the star Vega near the constellation of Hercules. There are several coordinates for the solar apex. The visual coordinates (as obtained by visual observation of the apparent motion) [are] right ascension (RA) 18h 28m 0s and declination (dec) of 30° North (in galactic coordinates: 56.24° longitude, 22.54° latitude). The radioastronomical position is RA 18h 03m 50.2s and dec 30° 00′ 16.8″ (galactic coordinates: 58.87° longitude, 17.72° latitude).

The Sun moves towards the apex at about 16.5 km/s. This is relative to the Sun's general orbital speed around the Galactic center, about 220 km/s, already included in the Local Standard of Rest. Thus the Sun gains distance towards the apex at about 1/13 its orbital speed. The sun's motion in the Milky Way is more complex than a simple orbit, it also shifts ("bobs") up and down with respect to the galactic plane.[98]

## Hypotheses

1. Images of the Sun at various wavelengths are available.

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