Stars/Sun/Heliography

As geography describes the features of the surface of the Earth, heliography describes the surface features of Helios or the Sun, Sol.

Helionomy
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.

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


 * $$\lambda_2=\left\{\frac{\lambda_1}{360^\circ}-\frac{{\rm JD}-2398220}{27.2753}\right\}\cdot360^\circ$$.

The Sun has an equatorial radius of 695,500 km

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

"When we speak of the surface of the Sun, we normally mean the photosphere." "[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." 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).

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. Conversely, the visible light we see is produced as electrons react with hydrogen atoms to produce H− ions. 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).

Physical features
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:


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

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" 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."

Theoretical heliography
Def. the "scientific study of the sun" is called heliography.

Here's a theoretical definition:

Def. the study of the physical features of the Sun and its atmosphere is called heliography.

Objects
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.

Emissions
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.

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'. 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.

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".

Reds
"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."

"[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".

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

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

Def. "[a]n opening through which [entities such as] gases ... can pass" 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. 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." "Spöerer's law ... involves that in a minimum year the zone about 15° should be entirely barren".

"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."" 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." 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."

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

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. This would presume annual layering; however, alternate explanations (diurnal) have also been proposed.

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.

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

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]."

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.

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


 * $$\frac{dH}{dt} = -2 \oint ( \mathbf{v} \cdot \mathbf{A_p}) \mathbf{B_n} \mathrm{d}\mathbf{S},$$

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

"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."

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.

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)."

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

"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 $$R$$ is computed using the formula (collected as a daily index of sunspot activity):


 * $$R = k(10g + s) \, $$

where


 * $$s$$ is the number of individual spots,
 * $$g$$ is the number of sunspot groups, and
 * $$k$$ is a factor that varies with location and instrumentation (also known as the observatory factor or the personal reduction coefficient $$K$$).

Hypotheses

 * 1) As the surface of the Sun is bombarded by incoming electrons the rotational speed is decreased.
 * 2) The Sun rotates at its slowest during the peak of the solar cycle and fastest at the cycle minimum.
 * 3) As the rotational rate of the Sun is set by convention, the actual rate is detectably different.