Saturday, November 7, 2009

Radiation

The energy produced by stars, as a by-product of nuclear fusion, radiates into space as both electromagnetic radiation and particle radiation. The particle radiation emitted by a star is manifested as the stellar wind[94] (which exists as a steady stream of electrically charged particles, such as free protons, alpha particles, and beta particles, emanating from the star’s outer layers) and as a steady stream of neutrinos emanating from the star’s core.

The production of energy at the core is the reason why stars shine so brightly: every time two or more atomic nuclei of one element fuse together to form an atomic nucleus of a new heavier element, gamma ray photons are released from the nuclear fusion reaction. This energy is converted to other forms of electromagnetic energy, including visible light, by the time it reaches the star’s outer layers.

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.[95] Besides visible light, stars also emit forms of electromagnetic radiation that are invisible to the human eye. In fact, stellar electromagnetic radiation spans the entire electromagnetic spectrum, from the longest wavelengths of radio waves and infrared to the shortest wavelengths of ultraviolet, X-rays, and gamma rays. All components of stellar electromagnetic radiation, both visible and invisible, are typically significant.

Using the stellar spectrum, astronomers can also determine the surface temperature, surface gravity, metallicity and rotational velocity of a star. If the distance of the star is known, such as by measuring the parallax, then the luminosity of the star can be derived. The mass, radius, surface gravity, and rotation period can then be estimated based on stellar models. (Mass can be measured directly for stars in binary systems. The technique of gravitational microlensing will also yield the mass of a star.) With these parameters, astronomers can also estimate the age of the star.

Luminosity

In astronomy, luminosity is the amount of light, and other forms of radiant energy, a star radiates per unit of time. The luminosity of a star is determined by the radius and the surface temperature. However, many stars do not radiate a uniform flux—the amount of energy radiated per unit area—across their entire surface. The rapidly rotating star Vega, for example, has a higher energy flux at its poles than along its equator.[98]

Surface patches with a lower temperature and luminosity than average are known as starspots. Small, dwarf stars such as the Sun generally have essentially featureless disks with only small starspots. Larger, giant stars have much bigger, much more obvious starspots,and they also exhibit strong stellar limb darkening. That is, the brightness decreases towards the edge of the stellar disk.Red dwarf flare stars such as UV Ceti may also possess prominent starspot features.

Magnitude

The apparent brightness of a star is measured by its apparent magnitude, which is the brightness of a star with respect to the star’s luminosity, distance from Earth, and the altering of the star’s light as it passes through Earth’s atmosphere. Intrinsic or absolute magnitude is what the apparent magnitude a star would be if the distance between the Earth and the star were 10 parsecs (32.6 light-years), and it is directly related to a star’s luminosity.

Number of stars brighter than magnitude
Apparent
magnitude
Number
of Stars
0 4
1 15
2 48
3 171
4 513
5 1,602
6 4,800
7 14,000

Both the apparent and absolute magnitude scales are logarithmic units: one whole number difference in magnitude is equal to a brightness variation of about 2.5 times (the 5th root of 100 or approximately 2.512). This means that a first magnitude (+1.00) star is about 2.5 times brighter than a second magnitude (+2.00) star, and approximately 100 times brighter than a sixth magnitude (+6.00) star. The faintest stars visible to the naked eye under good seeing conditions are about magnitude +6.

On both apparent and absolute magnitude scales, the smaller the magnitude number, the brighter the star; the larger the magnitude number, the fainter. The brightest stars, on either scale, have negative magnitude numbers. The variation in brightness (ΔL) between two stars is calculated by subtracting the magnitude number of the brighter star (mb) from the magnitude number of the fainter star (mf), then using the difference as an exponent for the base number 2.512; that is to say:

Δm = mfmb
2.512Δm = ΔL

Relative to both luminosity and distance from Earth, absolute magnitude (M) and apparent magnitude (m) are not equivalent for an individual star; for example, the bright star Sirius has an apparent magnitude of −1.44, but it has an absolute magnitude of +1.41.

The Sun has an apparent magnitude of −26.7, but its absolute magnitude is only +4.83. Sirius, the brightest star in the night sky as seen from Earth, is approximately 23 times more luminous than the Sun, while Canopus, the second brightest star in the night sky with an absolute magnitude of −5.53, is approximately 14,000 times more luminous than the Sun. Despite Canopus being vastly more luminous than Sirius, however, Sirius appears brighter than Canopus. This is because Sirius is merely 8.6 light-years from the Earth, while Canopus is much farther away at a distance of 310 light-years.

As of 2006, the star with the highest known absolute magnitude is LBV 1806-20, with a magnitude of −14.2. This star is at least 5,000,000 times more luminous than the Sun. The least luminous stars that are currently known are located in the NGC 6397 cluster. The faintest red dwarfs in the cluster were magnitude 26, while a 28th magnitude white dwarf was also discovered. These faint stars are so dim that their light is as bright as a birthday candle on the Moon when viewed from the Earth.

Classification

Surface Temperature Ranges for
Different Stellar Classes
Class Temperature Sample star
O 33,000 K or more Zeta Ophiuchi
B 10,500–30,000 K Rigel
A 7,500–10,000 K Altair
F 6,000–7,200 K Procyon A
G 5,500–6,000 K Sun
K 4,000–5,250 K Epsilon Indi
M 2,600–3,850 K Proxima Centauri

The current stellar classification system originated in the early 20th century, when stars were classified from A to Q based on the strength of the hydrogen line It was not known at the time that the major influence on the line strength was temperature; the hydrogen line strength reaches a peak at around 9000 K, and is weaker at both hotter and cooler temperatures. When the classifications were reordered by temperature, it more closely resembled the modern scheme.

There are different single-letter classifications of stars according to their spectra, ranging from type O, which are very hot, to M, which are so cool that molecules may form in their atmospheres. The main classifications in order of decreasing surface temperature are: O, B, A, F, G, K, and M. A variety of rare spectral types have special classifications. The most common of these are types L and T, which classify the coldest low-mass stars and brown dwarfs. Each letter has 10 sub-divisions, numbered from 0 to 9, in order of decreasing temperature. However, this system breaks down at extreme high temperatures: class O0 and O1 stars may not exist.[109]

In addition, stars may be classified by the luminosity effects found in their spectral lines, which correspond to their spatial size and is determined by the surface gravity. These range from 0 (hypergiants) through III (giants) to V (main sequence dwarfs); some authors add VII (white dwarfs). Most stars belong to the main sequence, which consists of ordinary hydrogen-burning stars. These fall along a narrow, diagonal band when graphed according to their absolute magnitude and spectral type. Our Sun is a main sequence G2V yellow dwarf, being of intermediate temperature and ordinary size.

Additional nomenclature, in the form of lower-case letters, can follow the spectral type to indicate peculiar features of the spectrum. For example, an "e" can indicate the presence of emission lines; "m" represents unusually strong levels of metals, and "var" can mean variations in the spectral type.

White dwarf stars have their own class that begins with the letter D. This is further sub-divided into the classes DA, DB, DC, DO, DZ, and DQ, depending on the types of prominent lines found in the spectrum. This is followed by a numerical value that indicates the temperature index.

Variable stars


The asymmetrical appearance of Mira, an oscillating variable star. NASA HST image

Variable stars have periodic or random changes in luminosity because of intrinsic or extrinsic properties. Of the intrinsically variable stars, the primary types can be subdivided into three principal groups.

During their stellar evolution, some stars pass through phases where they can become pulsating variables. Pulsating variable stars vary in radius and luminosity over time, expanding and contracting with periods ranging from minutes to years, depending on the size of the star. This category includes Cepheid and cepheid-like stars, and long-period variables such as Mira.

Eruptive variables are stars that experience sudden increases in luminosity because of flares or mass ejection events. This group includes protostars, Wolf-Rayet stars, and Flare stars, as well as giant and supergiant stars.

Cataclysmic or explosive variables undergo a dramatic change in their properties. This group includes novae and supernovae. A binary star system that includes a nearby white dwarf can produce certain types of these spectacular stellar explosions, including the nova and a Type 1a supernova. The explosion is created when the white dwarf accretes hydrogen from the companion star, building up mass until the hydrogen undergoes fusion. Some novae are also recurrent, having periodic outbursts of moderate amplitude.

Stars can also vary in luminosity because of extrinsic factors, such as eclipsing binaries, as well as rotating stars that produce extreme starspots A notable example of an eclipsing binary is Algol, which regularly varies in magnitude from 2.3 to 3.5 over a period of 2.87 days.

Structure

The interior of a stable star is in a state of hydrostatic equilibrium: the forces on any small volume almost exactly counterbalance each other. The balanced forces are inward gravitational force and an outward force due to the pressure gradient within the star. The pressure gradient is established by the temperature gradient of the plasma; the outer part of the star is cooler than the core. The temperature at the core of a main sequence or giant star is at least on the order of 107 K. The resulting temperature and pressure at the hydrogen-burning core of a main sequence star are sufficient for nuclear fusion to occur and for sufficient energy to be produced to prevent further collapse of the star

As atomic nuclei are fused in the core, they emit energy in the form of gamma rays. These photons interact with the surrounding plasma, adding to the thermal energy at the core. Stars on the main sequence convert hydrogen into helium, creating a slowly but steadily increasing proportion of helium in the core. Eventually the helium content becomes predominant and energy production ceases at the core. Instead, for stars of more than 0.4 solar masses, fusion occurs in a slowly expanding shell around the degenerate helium core.

In addition to hydrostatic equilibrium, the interior of a stable star will also maintain an energy balance of thermal equilibrium. There is a radial temperature gradient throughout the interior that results in a flux of energy flowing toward the exterior. The outgoing flux of energy leaving any layer within the star will exactly match the incoming flux from below.


This diagram shows a cross-section of a solar-type star. NASA image

The radiation zone is the region within the stellar interior where radiative transfer is sufficiently efficient to maintain the flux of energy. In this region the plasma will not be perturbed and any mass motions will die out. If this is not the case, however, then the plasma becomes unstable and convection will occur, forming a convection zone. This can occur, for example, in regions where very high energy fluxes occur, such as near the core or in areas with high opacity as in the outer envelope.

The occurrence of convection in the outer envelope of a main sequence star depends on the mass. Stars with several times the mass of the Sun have a convection zone deep within the interior and a radiative zone in the outer layers. Smaller stars such as the Sun are just the opposite, with the convective zone located in the outer layers. Red dwarf stars with less than 0.4 solar masses are convective throughout, which prevents the accumulation of a helium core.For most stars the convective zones will also vary over time as the star ages and the constitution of the interior is modified.

The portion of a star that is visible to an observer is called the photosphere. This is the layer at which the plasma of the star becomes transparent to photons of light. From here, the energy generated at the core becomes free to propagate out into space. It is within the photosphere that sun spots, or regions of lower than average temperature, appear.

Above the level of the photosphere is the stellar atmosphere. In a main sequence star such as the Sun, the lowest level of the atmosphere is the thin chromosphere region, where spicules appear and stellar flares begin. This is surrounded by a transition region, where the temperature rapidly increases within a distance of only 100 km. Beyond this is the corona, a volume of super-heated plasma that can extend outward to several million kilometres. The existence of a corona appears to be dependent on a convective zone in the outer layers of the star. Despite its high temperature, the corona emits very little light. The corona region of the Sun is normally only visible during a solar eclipse.

From the corona, a stellar wind of plasma particles expands outward from the star, propagating until it interacts with the interstellar medium. For the Sun, the influence of its solar wind extends throughout the bubble-shaped region of the heliosphere.

Nuclear fusion reaction pathways


Overview of the proton-proton chain

The carbon-nitrogen-oxygen cycle

A variety of different nuclear fusion reactions take place inside the cores of stars, depending upon their mass and composition, as part of stellar nucleosynthesis. The net mass of the fused atomic nuclei is smaller than the sum of the constituents. This lost mass is released as electromagnetic energy, according to the mass-energy equivalence relationship E = mc².

The hydrogen fusion process is temperature-sensitive, so a moderate increase in the core temperature will result in a significant increase in the fusion rate. As a result the core temperature of main sequence stars only varies from 4 million K for a small M-class star to 40 million K for a massive O-class star.

In the Sun, with a 10 million K core, hydrogen fuses to form helium in the proton-proton chain reaction:

41H → 22H + 2e+ + 2νe (4.0 MeV + 1.0 MeV)
21H + 22H → 23He + 2γ (5.5 MeV)
23He → 4He + 21H (12.9 MeV)

These reactions result in the overall reaction:

41H → 4He + 2e+ + 2γ + 2νe (26.7 MeV)

where e+ is a positron, γ is a gamma ray photon, νe is a neutrino, and H and He are isotopes of hydrogen and helium, respectively. The energy released by this reaction is in millions of electron volts, which is actually only a tiny amount of energy. However enormous numbers of these reactions occur constantly, producing all the energy necessary to sustain the star's radiation output.

Minimum stellar mass required for fusion
Element Solar
masses
Hydrogen 0.01
Helium 0.4
Carbon 5[120]
Neon 8

In more massive stars, helium is produced in a cycle of reactions catalyzed by carbon—the carbon-nitrogen-oxygen cycle.[119]

In evolved stars with cores at 100 million K and masses between 0.5 and 10 solar masses, helium can be transformed into carbon in the triple-alpha process that uses the intermediate element beryllium:[119]

4He + 4He + 92 keV → 8*Be
4He + 8*Be + 67 keV → 12*C
12*C → 12C + γ + 7.4 MeV

For an overall reaction of:

34He → 12C + γ + 7.2 MeV

In massive stars, heavier elements can also be burned in a contracting core through the neon burning process and oxygen burning process. The final stage in the stellar nucleosynthesis process is the silicon burning process that results in the production of the stable isotope iron-56. Fusion can not proceed any further except through an endothermic process, and so further energy can only be produced through gravitational collapse.

The example below shows the amount of time required for a star of 20 solar masses to consume all of its nuclear fuel. As an O-class main sequence star, it would be 8 times the solar radius and 62,000 times the Sun's luminosity.


Fuel
material
Temperature
(million kelvins)
Density
(kg/cm³)
Burn duration
(τ in years)
H 37 0.0045 8.1 million
He 188 0.97 1.2 million
C 870 170 976
Ne 1,570 3,100 0.6
O 1,980 5,550 1.25
S/Si 3,340 33,400 0.0315

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