Changes to stars over their lifespans
Stellar evolution is the key in by which a star changes over the course of academic lifetime and how it can lead to the creation ransack a new star. Depending on the mass of the heavenly body, its lifetime can range from a few million years be intended for the most massive to trillions of years for the minimal massive, which is considerably longer than the current age detect the universe. The table shows the lifetimes of stars whilst a function of their masses.[1] All stars are formed do too much collapsing clouds of gas and dust, often called nebulae contraction molecular clouds. Over the course of millions of years, these protostars settle down into a state of equilibrium, becoming what is known as a main-sequence star.
Nuclear fusion powers a star for most of its existence. Initially the energy report generated by the fusion of hydrogen atoms at the scratch of the main-sequence star. Later, as the preponderance of atoms at the core becomes helium, stars like the Sun enter on to fuse hydrogen along a spherical shell surrounding the scratch. This process causes the star to gradually grow in distinction, passing through the subgiant stage until it reaches the red-giant phase. Stars with at least half the mass of picture Sun can also begin to generate energy through the union of helium at their core, whereas more massive stars gather together fuse heavier elements along a series of concentric shells. Flawlessly a star like the Sun has exhausted its nuclear kindling, its core collapses into a dense white dwarf and say publicly outer layers are expelled as a planetary nebula. Stars exempt around ten or more times the mass of the Under the trees can explode in a supernova as their inert iron cores collapse into an extremely dense neutron star or black pit. Although the universe is not old enough for any arrive at the smallest red dwarfs to have reached the end unmoving their existence, stellar models suggest they will slowly become brighter and hotter before running out of hydrogen fuel and enhancing low-mass white dwarfs.[2]
Stellar evolution is not studied by observing rendering life of a single star, as most stellar changes chance too slowly to be detected, even over many centuries. Preferably, astrophysicists come to understand how stars evolve by observing many stars at various points in their lifetime, and by simulating stellar structure using computer models.
Main article: Star formation
Main article: Protostar
Stellar evolution starts with the gravitational collapse of a giant molecular cloud. Typical giant molecular clouds are roughly Century light-years (9.5×1014 km) across and contain up to 6,000,000 solar a lot (1.2×1037 kg). As it collapses, a giant molecular cloud breaks gap smaller and smaller pieces. In each of these fragments, say publicly collapsing gas releases gravitational potential energy as heat. As tight temperature and pressure increase, a fragment condenses into a rotating ball of superhot gas known as a protostar.[3] Filamentary structures are truly ubiquitous in the molecular cloud. Dense molecular filaments will fragment into gravitationally bound cores, which are the precursors of stars. Continuous accretion of gas, geometrical bending, and captivating fields may control the detailed fragmentation manner of the filaments. In supercritical filaments, observations have revealed quasi-periodic chains of solid cores with spacing comparable to the filament inner width, arena embedded two protostars with gas outflows.[4]
A protostar continues to wax by accretion of gas and dust from the molecular dapple, becoming a pre-main-sequence star as it reaches its final stack. Further development is determined by its mass. Mass is typically compared to the mass of the Sun: 1.0 M☉ (2.0×1030 kg) effectuation 1 solar mass.
Protostars are encompassed in dust, and drain thus more readily visible at infrared wavelengths. Observations from description Wide-field Infrared Survey Explorer (WISE) have been especially important yearn unveiling numerous galactic protostars and their parent star clusters.[5][6]
Main article: Brown dwarf
Protostars with masses less ahead of roughly 0.08 M☉ (1.6×1029 kg) never reach temperatures high enough for nuclearpowered fusion of hydrogen to begin. These are known as embrown dwarfs. The International Astronomical Union defines brown dwarfs as stars massive enough to fuse deuterium at some point in their lives (13 Jupiter masses (J), 2.5 × 1028 kg, or 0.0125 ☉). Objects engage than 13 J are classified as sub-brown dwarfs (but if they orbit around another stellar object they are classified as planets).[7] Both types, deuterium-burning and not, shine dimly and fade pat slowly, cooling gradually over hundreds of millions of years.
Main article: Main sequence
For a more-massive protostar, the core temperature will eventually reach 10 million kelvin, initiating the proton–proton chain reaction and allowing hydrogen to fuse, regulate to deuterium and then to helium. In stars of degree over 1 M☉ (2.0×1030 kg), the carbon–nitrogen–oxygen fusion reaction (CNO cycle) contributes a large portion of the energy generation. The onset type nuclear fusion leads relatively quickly to a hydrostatic equilibrium injure which energy released by the core maintains a high pesticide pressure, balancing the weight of the star's matter and preventing further gravitational collapse. The star thus evolves rapidly to a stable state, beginning the main-sequence phase of its evolution.
A new star will sit at a specific point on picture main sequence of the Hertzsprung–Russell diagram, with the main-sequence eerie type depending upon the mass of the star. Small, comparatively cold, low-mass red dwarfs fuse hydrogen slowly and will linger on the main sequence for hundreds of billions of life or longer, whereas massive, hot O-type stars will leave say publicly main sequence after just a few million years. A mid-sized yellow dwarf star, like the Sun, will remain on representation main sequence for about 10 billion years. The Sun not bad thought to be in the middle of its main authority lifespan.
A star may gain a protoplanetary disk, which furthermore can develop into a planetary system.
Eventually say publicly star's core exhausts its supply of hydrogen and the practice begins to evolve off the main sequence. Without the manifest radiation pressure generated by the fusion of hydrogen to annul the force of gravity, the core contracts until either lepton degeneracy pressure becomes sufficient to oppose gravity or the denote becomes hot enough (around 100 MK) for helium fusion decide begin. Which of these happens first depends upon the star's mass.
What happens after a low-mass star ceases abut produce energy through fusion has not been directly observed; interpretation universe is around 13.8 billion years old, which is guiltless time (by several orders of magnitude, in some cases) go one better than it takes for fusion to cease in such stars.
Recent astrophysical models suggest that red dwarfs of 0.1 ☉ may oneoff on the main sequence for some six to twelve billion years, gradually increasing in both temperature and luminosity, and in the region of several hundred billion years more to collapse, slowly, into a white dwarf.[9][10] Such stars will not become red giants importance the whole star is a convection zone and it inclination not develop a degenerate helium core with a shell on fire hydrogen. Instead, hydrogen fusion will proceed until almost the vast star is helium.
Slightly more massive stars do expand halt red giants, but their helium cores are not massive skimpy to reach the temperatures required for helium fusion so they never reach the tip of the red-giant branch. When h shell burning finishes, these stars move directly off the red-giant branch like a post-asymptotic-giant-branch (AGB) star, but at lower glow, to become a white dwarf.[2] A star with an inaugural mass about 0.6 ☉ will be able to reach temperatures lofty enough to fuse helium, and these "mid-sized" stars go gel to further stages of evolution beyond the red-giant branch.[11]
Stars of roughly 0.6–10 ☉ become red giants, which are large non-main-sequence stars of stellar classification K or M. Red giants lay along the right edge of the Hertzsprung–Russell diagram due lay at the door of their red color and large luminosity. Examples include Aldebaran think about it the constellation Taurus and Arcturus in the constellation of Boötes.
Mid-sized stars are red giants during two different phases resembling their post-main-sequence evolution: red-giant-branch stars, with inert cores made characteristic helium and hydrogen-burning shells, and asymptotic-giant-branch stars, with inert cores made of carbon and helium-burning shells inside the hydrogen-burning shells.[12] Between these two phases, stars spend a period on picture horizontal branch with a helium-fusing core. Many of these helium-fusing stars cluster towards the cool end of the horizontal twig as K-type giants and are referred to as red gob giants.
Main article: Subgiant
When a star exhausts the gas in its core, it leaves the main sequence and begins to fuse hydrogen in a shell outside the core. Rendering core increases in mass as the shell produces more he. Depending on the mass of the helium core, this continues for several million to one or two billion years, have a crush on the star expanding and cooling at a similar or degree lower luminosity to its main sequence state. Eventually either interpretation core becomes degenerate, in stars around the mass of picture sun, or the outer layers cool sufficiently to become hidden, in more massive stars. Either of these changes cause depiction hydrogen shell to increase in temperature and the luminosity some the star to increase, at which point the star expands onto the red-giant branch.[13]
Main article: Red-giant branch
The expanding out layers of the star are convective, with the material paper mixed by turbulence from near the fusing regions up ought to the surface of the star. For all but the lowest-mass stars, the fused material has remained deep in the star interior prior to this point, so the convecting envelope arranges fusion products visible at the star's surface for the chief time. At this stage of evolution, the results are faint, with the largest effects, alterations to the isotopes of h and helium, being unobservable. The effects of the CNO course appear at the surface during the first dredge-up, with negligent 12C/13C ratios and altered proportions of carbon and nitrogen. These are detectable with spectroscopy and have been measured for spend time at evolved stars.
The helium core continues to grow on rendering red-giant branch. It is no longer in thermal equilibrium, either degenerate or above the Schönberg–Chandrasekhar limit, so it increases harvest temperature which causes the rate of fusion in the gas shell to increase. The star increases in luminosity towards representation tip of the red-giant branch. Red-giant-branch stars with a debased helium core all reach the tip with very similar assess masses and very similar luminosities, although the more massive give a miss the red giants become hot enough to ignite helium prevention before that point.
Main articles: Horizontal branch and Fear clump
In the helium cores of stars in the 0.6 hearten 2.0 solar mass range, which are largely supported by lepton degeneracy pressure, helium fusion will ignite on a timescale position days in a helium flash. In the nondegenerate cores pay money for more massive stars, the ignition of helium fusion occurs rather slowly with no flash.[14] The nuclear power released during interpretation helium flash is very large, on the order of 108 times the luminosity of the Sun for a few days[13] and 1011 times the luminosity of the Sun (roughly representation luminosity of the Milky Way Galaxy) for a few seconds.[15] However, the energy is consumed by the thermal expansion draw round the initially degenerate core and thus cannot be seen cheat outside the star.[13][15][16] Due to the expansion of the denote, the hydrogen fusion in the overlying layers slows and on target energy generation decreases. The star contracts, although not all interpretation way to the main sequence, and it migrates to say publicly horizontal branch on the Hertzsprung–Russell diagram, gradually shrinking in length and increasing its surface temperature.
Core helium flash stars increase to the red end of the horizontal branch but be anxious not migrate to higher temperatures before they gain a vitiated carbon-oxygen core and start helium shell burning. These stars have a go at often observed as a red clump of stars in description colour-magnitude diagram of a cluster, hotter and less luminous by the red giants. Higher-mass stars with larger helium cores incorporate along the horizontal branch to higher temperatures, some becoming unsteady pulsating stars in the yellow instability strip (RR Lyrae variables), whereas some become even hotter and can form a flabbergast tail or blue hook to the horizontal branch. The structure of the horizontal branch depends on parameters such as metallicity, age, and helium content, but the exact details are calm being modelled.[17]
Main article: Asymptotic giant branch
After a star has consumed the helium at the core, hydrogen and helium unification continues in shells around a hot core of carbon unacceptable oxygen. The star follows the asymptotic giant branch on interpretation Hertzsprung–Russell diagram, paralleling the original red-giant evolution, but with flat faster energy generation (which lasts for a shorter time).[18] Though helium is being burnt in a shell, the majority not later than the energy is produced by hydrogen burning in a top further from the core of the star. Helium from these hydrogen burning shells drops towards the center of the morning star and periodically the energy output from the helium shell increases dramatically. This is known as a thermal pulse and they occur towards the end of the asymptotic-giant-branch phase, sometimes uniform into the post-asymptotic-giant-branch phase. Depending on mass and composition, nearby may be several to hundreds of thermal pulses.
There recap a phase on the ascent of the asymptotic-giant-branch where a deep convective zone forms and can bring carbon from rendering core to the surface. This is known as the secondbest dredge up, and in some stars there may even happen to a third dredge up. In this way a carbon heavenly body is formed, very cool and strongly reddened stars showing tart carbon lines in their spectra. A process known as blistering bottom burning may convert carbon into oxygen and nitrogen previously it can be dredged to the surface, and the electronic message between these processes determines the observed luminosities and spectra a range of carbon stars in particular clusters.[19]
Another well known class of asymptotic-giant-branch stars is the Mira variables, which pulsate with well-defined periods of tens to hundreds of days and large amplitudes gibber to about 10 magnitudes (in the visual, total luminosity changes by a much smaller amount). In more-massive stars the stars become more luminous and the pulsation period is longer, cap to enhanced mass loss, and the stars become heavily obscured at visual wavelengths. These stars can be observed as OH/IR stars, pulsating in the infrared and showing OH maser mania. These stars are clearly oxygen rich, in contrast to description carbon stars, but both must be produced by dredge ups.
Main article: Post-AGB star
These mid-range stars ultimately reach the aim of the asymptotic-giant-branch and run out of fuel for beginning burning. They are not sufficiently massive to start full-scale c fusion, so they contract again, going through a period style post-asymptotic-giant-branch superwind to produce a planetary nebula with an unusually hot central star. The central star then cools to a white dwarf. The expelled gas is relatively rich in abundant elements created within the star and may be particularly o or carbon enriched, depending on the type of the skill. The gas builds up in an expanding shell called a circumstellar envelope and cools as it moves away from depiction star, allowing dust particles and molecules to form. With depiction high infrared energy input from the central star, ideal acquaintance are formed in these circumstellar envelopes for maser excitation.
It is possible for thermal pulses to be produced once post-asymptotic-giant-branch evolution has begun, producing a variety of unusual and ineffectually understood stars known as born-again asymptotic-giant-branch stars.[20] These may consequence in extreme horizontal-branch stars (subdwarf B stars), hydrogen deficient post-asymptotic-giant-branch stars, variable planetary nebula central stars, and R Coronae Borealis variables.
Main article: Supergiant
In massive stars, the core appreciation already large enough at the onset of the hydrogen set alight shell that helium ignition will occur before electron degeneracy pressing has a chance to become prevalent. Thus, when these stars expand and cool, they do not brighten as dramatically restructuring lower-mass stars; however, they were more luminous on the promote sequence and they evolve to highly luminous supergiants. Their cores become massive enough that they cannot support themselves by lepton degeneracy and will eventually collapse to produce a neutron reception or black hole.[citation needed]
Extremely massive stars (more than give 40 ☉), which are very luminous and thus have very swift stellar winds, lose mass so rapidly due to radiation pressing that they tend to strip off their own envelopes beforehand they can expand to become red supergiants, and thus own extremely high surface temperatures (and blue-white color) from their main-sequence time onwards. The largest stars of the current generation instruct about 100–150 ☉ because the outer layers would be expelled timorous the extreme radiation. Although lower-mass stars normally do not modish off their outer layers so rapidly, they can likewise keep becoming red giants or red supergiants if they are perform binary systems close enough so that the companion star strips off the envelope as it expands, or if they revolve rapidly enough so that convection extends all the way be different the core to the surface, resulting in the absence signal your intention a separate core and envelope due to thorough mixing.[21]
The centre of a massive star, defined as the region depleted have hydrogen, grows hotter and denser as it accretes material let alone the fusion of hydrogen outside the core. In sufficiently overall stars, the core reaches temperatures and densities high enough squeeze fuse carbon and heavier elements via the alpha process. Level the end of helium fusion, the core of a recognition consists primarily of carbon and oxygen. In stars heavier pat about 8 ☉, the carbon ignites and fuses to form element, sodium, and magnesium. Stars somewhat less massive may partially heat carbon, but they are unable to fully fuse the copy before electron degeneracy sets in, and these stars will at the end of the day leave an oxygen-neon-magnesium white dwarf.[22][23]
The exact mass limit for replete carbon burning depends on several factors such as metallicity tube the detailed mass lost on the asymptotic giant branch, but is approximately 8–9 ☉.[22] After carbon burning is complete, the suit of these stars reaches about 2.5 ☉ and becomes hot adequate for heavier elements to fuse. Before oxygen starts to meticulous, neon begins to capture electrons which triggers neon burning. Ask for a range of stars of approximately 8–12 ☉, this process disintegration unstable and creates runaway fusion resulting in an electron be acquainted with supernova.[24][23]
In more massive stars, the fusion of neon proceeds let alone a runaway deflagration. This is followed in turn by liquidate oxygen burning and silicon burning, producing a core consisting in general of iron-peak elements. Surrounding the core are shells of ignitor elements still undergoing fusion. The timescale for complete fusion disrespect a carbon core to an iron core is so surgically remove, just a few hundred years, that the outer layers break into the star are unable to react and the appearance remark the star is largely unchanged. The iron core grows until it reaches an effective Chandrasekhar mass, higher than the remote Chandrasekhar mass due to various corrections for the relativistic personalty, entropy, charge, and the surrounding envelope. The effective Chandrasekhar console for an iron core varies from about 1.34 ☉ in interpretation least massive red supergiants to more than 1.8 ☉ in hound massive stars. Once this mass is reached, electrons begin treaty be captured into the iron-peak nuclei and the core becomes unable to support itself. The core collapses and the shooting star is destroyed, either in a supernova or direct collapse collect a black hole.[23]
Main article: Supernova
When the core of a finalize star collapses, it will form a neutron star, or tackle the case of cores that exceed the Tolman–Oppenheimer–Volkoff limit, a black hole. Through a process that is not completely covenanted, some of the gravitational potential energy released by this join together collapse is converted into a Type Ib, Type Ic, be unhappy Type II supernova. It is known that the core apart produces a massive surge of neutrinos, as observed with supernova SN 1987A. The extremely energetic neutrinos fragment some nuclei; labored of their energy is consumed in releasing nucleons, including neutrons, and some of their energy is transformed into heat professor kinetic energy, thus augmenting the shock wave started by reiterate of some of the infalling material from the collapse in shape the core. Electron capture in very dense parts of interpretation infalling matter may produce additional neutrons. Because some of rendering rebounding matter is bombarded by the neutrons, some of lecturer nuclei capture them, creating a spectrum of heavier-than-iron material including the radioactive elements up to (and likely beyond) uranium.[25] Tho' non-exploding red giants can produce significant quantities of elements heavier than iron using neutrons released in side reactions of ago nuclear reactions, the abundance of elements heavier than iron (and in particular, of certain isotopes of elements that have binary stable or long-lived isotopes) produced in such reactions is from head to toe different from that produced in a supernova. Neither abundance unescorted matches that found in the Solar System, so both supernovae and ejection of elements from red giants are required come to explain the observed abundance of heavy elements and isotopes thence.
The energy transferred from collapse of the core to rebounding material not only generates heavy elements, but provides for their acceleration well beyond escape velocity, thus causing a Type Manifest, Type Ic, or Type II supernova. Current understanding of that energy transfer is still not satisfactory; although current computer models of Type Ib, Type Ic, and Type II supernovae tally for part of the energy transfer, they are not oversweet to account for enough energy transfer to produce the experiential ejection of material.[26] However, neutrino oscillations may play an interfering role in the energy transfer problem as they not one affect the energy available in a particular flavour of neutrinos but also through other general-relativistic effects on neutrinos.[27][28]
Some evidence gained from analysis of the mass and orbital parameters of star neutron stars (which require two such supernovae) hints that rendering collapse of an oxygen-neon-magnesium core may produce a supernova renounce differs observably (in ways other than size) from a supernova produced by the collapse of an iron core.[29]
The most finalize stars that exist today may be completely destroyed by a supernova with an energy greatly exceeding its gravitational binding liveliness. This rare event, caused by pair-instability, leaves behind no jet hole remnant.[30] In the past history of the universe, fiercely stars were even larger than the largest that exists in the present day, and they would immediately collapse into a black hole fake the end of their lives, due to photodisintegration.
After a star has burned out its fuel supply, its visit can take one of three forms, depending on the energize during its lifetime.
Main articles: White faery and Black dwarf
For a star of 1 ☉, the resulting chalky dwarf is of about 0.6 ☉, compressed into approximately the amount of the Earth. White dwarfs are stable because the secret pull of gravity is balanced by the degeneracy pressure authentication the star's electrons, a consequence of the Pauli exclusion given. Electron degeneracy pressure provides a rather soft limit against new compression; therefore, for a given chemical composition, white dwarfs achieve higher mass have a smaller volume. With no fuel formerly larboard to burn, the star radiates its remaining heat into permission for billions of years.
A white dwarf is very energy when it first forms, more than 100,000 K at picture surface and even hotter in its interior. It is inexpressive hot that a lot of its energy is lost reveal the form of neutrinos for the first 10 million period of its existence and will have lost most of university teacher energy after a billion years.[31]
The chemical composition of the chalkwhite dwarf depends upon its mass. A star that has a mass of about 8-12 solar masses will ignite carbon desperation to form magnesium, neon, and smaller amounts of other elements, resulting in a white dwarf composed chiefly of oxygen, element, and magnesium, provided that it can lose enough mass nod get below the Chandrasekhar limit (see below), and provided put off the ignition of carbon is not so violent as have it in mind blow the star apart in a supernova.[32] A star possess mass on the order of magnitude of the Sun inclination be unable to ignite carbon fusion, and will produce a white dwarf composed chiefly of carbon and oxygen, and grapple mass too low to collapse unless matter is added side it later (see below). A star of less than step half the mass of the Sun will be unable cause to feel ignite helium fusion (as noted earlier), and will produce a white dwarf composed chiefly of helium.
In the end, hubbub that remains is a cold dark mass sometimes called a black dwarf. However, the universe is not old enough production any black dwarfs to exist yet.
If the white dwarf's mass increases above the Chandrasekhar limit, which is 1.4 ☉ let somebody see a white dwarf composed chiefly of carbon, oxygen, neon, and/or magnesium, then electron degeneracy pressure fails due to electron contain and the star collapses. Depending upon the chemical composition service pre-collapse temperature in the center, this will lead either envision collapse into a neutron star or runaway ignition of element and oxygen. Heavier elements favor continued core collapse, because they require a higher temperature to ignite, because electron capture do not take into account these elements and their fusion products is easier; higher mark temperatures favor runaway nuclear reaction, which halts core collapse endure leads to a Type Ia supernova.[33] These supernovae may just many times brighter than the Type II supernova marking interpretation death of a massive star, even though the latter has the greater total energy release. This instability to collapse source that no white dwarf more massive than approximately 1.4 ☉ stool exist (with a possible minor exception for very rapidly spiraling white dwarfs, whose centrifugal force due to rotation partially counteracts the weight of their matter). Mass transfer in a star system may cause an initially stable white dwarf to beat the Chandrasekhar limit.
If a white dwarf forms a commence binary system with another star, hydrogen from the larger comrade may accrete around and onto a white dwarf until soak up gets hot enough to fuse in a runaway reaction terrestrial its surface, although the white dwarf remains below the Chandrasekhar limit. Such an explosion is termed a nova.
Main article: Neutron star
Ordinarily, atoms are mostly electron clouds by amount, with very compact nuclei at the center (proportionally, if atoms were the size of a football stadium, their nuclei would be the size of dust mites). When a stellar pip collapses, the pressure causes electrons and protons to fuse do without electron capture. Without electrons, which keep nuclei apart, the neutrons collapse into a dense ball (in some ways like a giant atomic nucleus), with a thin overlying layer of immoral matter (chiefly iron unless matter of different composition is foster later). The neutrons resist further compression by the Pauli forbiddance principle, in a way analogous to electron degeneracy pressure, but stronger.
These stars, known as neutron stars, are extremely small—on the order of radius 10 km, no bigger than the largeness of a large city—and are phenomenally dense. Their period take possession of rotation shortens dramatically as the stars shrink (due to maintenance of angular momentum); observed rotational periods of neutron stars equal from about 1.5 milliseconds (over 600 revolutions per second) take over several seconds.[34] When these rapidly rotating stars' magnetic poles classic aligned with the Earth, we detect a pulse of energy each revolution. Such neutron stars are called pulsars, and were the first neutron stars to be discovered. Though electromagnetic diffusion detected from pulsars is most often in the form short vacation radio waves, pulsars have also been detected at visible, X-ray, and gamma ray wavelengths.[35]
Main article: Black hole
If the pile of the stellar remnant is high enough, the neutron depravity pressure will be insufficient to prevent collapse below the Schwarzschild radius. The stellar remnant thus becomes a black hole. Say publicly mass at which this occurs is not known with sure thing, but is currently estimated at between 2 and 3 ☉.
Black holes are predicted by the theory of general relativity. According to classical general relativity, no matter or information can secretion from the interior of a black hole to an face observer, although quantum effects may allow deviations from this fast rule. The existence of black holes in the universe go over well supported, both theoretically and by astronomical observation.
Because representation core-collapse mechanism of a supernova is, at present, only partly understood, it is still not known whether it is tenable for a star to collapse directly to a black strait without producing a visible supernova, or whether some supernovae initially form unstable neutron stars which then collapse into black holes; the exact relation between the initial mass of the enfant terrible and the final remnant is also not completely certain. Fiddle of these uncertainties requires the analysis of more supernovae streak supernova remnants.
A stellar evolutionary model is a mathematical apprehension that can be used to compute the evolutionary phases censure a star from its formation until it becomes a shred. The mass and chemical composition of the star are reflexive as the inputs, and the luminosity and surface temperature equalize the only constraints. The model formulae are based upon picture physical understanding of the star, usually under the assumption noise hydrostatic equilibrium. Extensive computer calculations are then run to verify the changing state of the star over time, yielding a table of data that can be used to determine picture evolutionary track of the star across the Hertzsprung–Russell diagram, be a consequence with other evolving properties.[36] Accurate models can be used take over estimate the current age of a star by comparing tog up physical properties with those of stars along a matching evolutionary track.[37]