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ample a white dwarf is the dead core left over after a star has shed its outer layers and is much smaller than a main sequence star roughly the size of earth these represent the final evolutionary stage of many main sequence stars 22 parameters edit comparison of main sequence stars of each spectral class by treating the star as an idealized energy radiator known as a black body the luminosity l and radius r can be related to the effective temperature t eff by the stefan boltzmann law l 4 π σ r 2 t eff 4 displaystyle l 4 pi sigma r 2 t_ text eff 4 where σ is the stefan boltzmann constant as the position of a star on the hr diagram shows its approximate luminosity this relation can be used to estimate its radius 23 the mass radius and luminosity of a star are closely interlinked and their respective values can be approximated by three relations first is the stefan boltzmann law which relates the luminosity l the radius r and the surface temperature t eff second is the mass luminosity relation which relates the luminosity l and the mass m finally the relationship between m and r is close to linear the ratio of m to r increases by a factor of only three over 2 5 orders of magnitude of m this relation is roughly proportional to the star s inner temperature t i and its extremely slow increase reflects the fact that the rate of energy generation in the core strongly depends on this temperature whereas it has to fit the mass luminosity relation thus a too high or too low temperature will result in stellar instability a better approximation is to take ε l m the energy generation rate per unit mass as ε is proportional to t i 15 where t i is the core temperature this is suitable for stars at least as massive as the sun exhibiting the cno cycle and gives the better fit r m 0 78 24 sample parameters edit the table below shows typical values for stars along the main sequence the values of luminosity l radius r and mass m are relative to the sun a dwarf star with a spectral classification of g2 v the actual values for a star may vary by as much as 20 30 from the values listed below 25 why table of main sequence stellar parameters 26 stellar class radius r r mass m m luminosity l l temp k examples 27 o2 12 100 800 000 50 000 bi 253 o6 0 9 8 0 35 180 000 38 000 theta 1 orionis c b0 0 7 4 0 18 0 20 000 30 000 phi 1 orionis b5 0 3 8 00 6 5 000 800 16 400 pi andromedae a a0 0 2 5 00 3 2 000 0 80 10 800 alpha coronae borealis a a5 0 1 7 00 2 1 000 0 20 0 8 620 beta pictoris f0 0 1 3 00 1 7 000 00 6 0 7 240 gamma virginis f5 0 1 2 00 1 3 000 00 2 5 0 6 540 eta arietis g0 0 1 05 00 1 10 000 00 1 26 0 5 920 beta comae berenices g2 0 1 00 00 1 00 000 00 1 00 0 5 780 sun note 2 g5 0 0 93 00 0 93 000 00 0 79 0 5 610 alpha mensae k0 0 0 85 00 0 78 000 00 0 40 0 5 240 70 ophiuchi a k5 0 0 74 00 0 69 000 00 0 16 0 4 410 61 cygni a 28 m0 0 0 51 00 0 60 000 00 0 072 0 3 800 lacaille 8760 m5 0 0 18 00 0 15 000 00 0 0027 0 3 120 ez aquarii a m8 0 0 11 00 0 08 000 00 0 0004 0 2 650 van biesbroeck s star 29 l1 0 0 09 00 0 07 000 00 0 00017 0 2 200 2mass j0523 1403 representative lifetimes of stars as a function of their masses energy generation edit see also stellar nucleosynthesis logarithm of the relative energy output ε of proton proton pp cno and triple α fusion processes at different temperatures t the dashed line shows the combined energy generation of the pp and cno processes within a star at the sun s core temperature the pp process is more efficient all main sequence stars have a core region where energy is generated by nuclear fusion the temperature and density of this core are at the levels necessary to sustain the energy production that will support the remainder of the star a reduction of energy production would cause the overlaying mass to compress the core resulting in an increase in the fusion rate because of higher temperature and pressure likewise an increase in energy production would cause the star to expand lowering the pressure at the core thus the star forms a self regulating system in hydrostatic equilibrium that is stable over the course of its main sequence lifetime 30 main sequence stars employ two types of hydrogen fusion processes and the rate of energy generation from each type depends on the temperature in the core region astronomers divide the main sequence into upper and lower parts based on which of the two is the dominant fusion process in the lower main sequence energy is primarily generated as the result of the proton proton chain which directly fuses hydrogen together in a series of stages to produce helium 31 stars in the upper main sequence have sufficiently high core temperatures to efficiently use the cno cycle see chart this process uses atoms of carbon nitrogen and oxygen as intermediaries in the process of fusing hydrogen into helium at a stellar core temperature of 18 million kelvin the pp process and cno cycle are equally efficient and each type generates half of the star s net luminosity as this is the core temperature of a star with about 1 5 m the upper main sequence consists of stars above this mass thus roughly speaking stars of spectral class f or cooler belong to the lower main sequence while a type stars or hotter are upper main sequence stars 15 the transition in primary energy production from one form to the other spans a range difference of less than a single solar mass in the sun a one solar mass star only 1 5 of the energy is generated by the cno cycle 32 by contrast stars with 1 8 m or above generate almost their entire energy output through the cno cycle 33 the observed upper limit for a main sequence star is 120 200 m 34 the theoretical explanation for this limit is that stars above this mass can not radiate energy fast enough to remain stable so any additional mass will be ejected in a series of pulsations until the star reaches a stable limit 35 the lower limit for sustained proton proton nuclear fusion is about 0 08 m or 80 times the mass of jupiter 31 below this threshold are sub stellar objects that can not sustain hydrogen fusion known as brown dwarfs 36 structure edit main article stellar structure this diagram shows a cross section of a sun like star showing the internal structure because there is a temperature difference between the core and the surface or photosphere energy is transported outward the two modes for transporting this energy are radiation and convection a radiation zone where energy is transported by radiation is stable against convection and there is very little mixing of the plasma by contrast in a convection zone the energy is transported by bulk movement of plasma with hotter material rising and cooler material descending convection is a more efficient mode for carrying energy than radiation but it will only occur under conditions that create a steep temperature gradient 30 37 in massive stars above 10 m 38 the rate of energy generation by the cno cycle is very sensitive to temperature so the fusion is highly concentrated at the core consequently there is a high temperature gradient in the core region which results in a convection zone for more efficient energy transport 31 this mixing of material around the core removes the helium ash from the hydrogen burning region allowing more of the hydrogen in the star to be consumed during the main sequence lifetime the outer regions of a massive star transport energy by radiation with little or no convection 30 intermediate mass stars such as sirius may transport energy primarily by radiation with a small core convection region 39 medium sized low mass stars like the sun have a core region that is stable against convection with a convection zone near the surface that mixes the outer layers this results in a steady buildup of a helium rich core surrounded by a hydrogen rich outer region by contrast cool very low mass stars below 0 4 m are convective throughout 11 thus the helium produced at the core is distributed across the star producing a relatively uniform atmosphere and a proportionately longer main sequence lifespan 30 luminosity color variation edit the sun is the most familiar example of a main sequence star as non fusing helium accumulates in the core of a main sequence star the reduction in the abundance of hydrogen per unit mass results in a gradual lowering of the fusion rate within that mass since it is fusion supplied power that maintains the pressure of the core and supports the higher layers of the star the core gradually gets compressed this brings hydrogen rich material into a shell around the helium rich core at a depth where the pressure is sufficient for fusion to occur the high power output from this shell pushes the higher layers of the star further out this causes a gradual increase in the radius and consequently luminosity of the star over time 15 for example the luminosity of the early sun was only about 70 of its current value 40 as a star ages it thus changes its position on the hr diagram this evolution is reflected in a broadening of the main sequence band which contains stars at various evolutionary stages 41 other factors that broaden the main sequence band on the hr diagram include uncertainty in the distance to stars and the presence of unresolved binary stars that can alter the observed stellar parameters however even perfect observation would show a fuzzy main sequence because mass is not the only parameter that affects a star s color and luminosity variations in chemical composition caused by the initial abundances the star s evolutionary status 42 interaction with a close companion 43 rapid rotation 44 or a magnetic field can all slightly change a main sequence star s hr diagram position to name just a few factors as an example there are metal poor stars with a very low abundance of elements with higher atomic numbers than helium that lie just below the main sequence and are known as subdwarfs these stars are fusing hydrogen in their cores and so they mark the lower edge of the main sequence fuzziness caused by variance in chemical composition 45 a nearly vertical region of the hr diagram known as the instability strip is occupied by pulsating variable stars known as cepheid variables these stars vary in magnitude at regular intervals giving them a pulsating appearance the strip intersects the upper part of the main sequence in the region of class a and f stars which are between one and two solar masses pulsating stars in this part of the instability strip intersecting the upper part of the main sequence are called delta scuti variables main sequence stars in this region experience only small changes in magnitude so this variation is difficult to detect 46 other classes of unstable main sequence stars like beta cephei variables are unrelated to this instability strip lifetime edit this plot gives an example of the mass luminosity relationship for zero age main sequence stars the mass and luminosity are relative to the present day sun the total amount of energy that a star can generate through nuclear fusion of hydrogen is limited by the amount of hydrogen fuel that can be consumed at the core for a star in equilibrium the thermal energy generated at the core must be at least equal to the energy radiated at the surface since the luminosity gives the amount of energy radiated per unit time the total life span can be estimated to first approximation as the total energy produced divided by the star s luminosity 47 for a star with at least 0 5 m when the hydrogen supply in its core is exhausted and it expands to become a red giant it can start to fuse helium atoms to form carbon the energy output of the helium fusion process per unit mass is only about a tenth the energy output of the hydrogen process and the luminosity of the star increases 48 this results in a much shorter length of time in this stage compared to the main sequence lifetime for example the sun is predicted to spend 130 million years burning helium compared to about 12 billion years burning hydrogen 49 thus about 90 of the observed stars above 0 5 m will be on the main sequence 50 on average main sequence stars are known to follow an empirical mass luminosity relationship 51 the luminosity l of the star is roughly proportional to the total mass m as the following power law l m 3 5 displaystyle l propto m 3 5 this relationship applies to main sequence stars in the range 0 1 50 m 52 the amount of fuel available for nuclear fusion is proportional to the mass of the star thus the lifetime of a star on the main sequence can be estimated by comparing it to solar evolutionary models the sun has been a main sequence star for about 4 5 billion years and it will start to expand rapidly towards a red giant in 6 5 billion years 53 for a total main sequence lifetime of roughly 10 10 years hence 54 τ ms 10 10 years m m l l 10 10 years m m 2 5 displaystyle tau _ text ms approx 10 10 text years left frac m m_ bigodot right left frac l_ bigodot l right 10 10 text years left frac m m_ bigodot right 2 5 where m and l are the mass and luminosity of the star respectively m displaystyle m_ bigodot is a solar mass l displaystyle l_ bigodot is the solar luminosity and τ ms displaystyle tau _ text ms is the star s estimated main sequence lifetime although more massive stars have more fuel to burn and might intuitively be expected to last longer they also radiate a proportionately greater amount with increased mass this is required by the stellar equation of state for a massive star to maintain equilibrium the outward pressure of radiated energy generated in the core not only must but will rise to match the titanic inward gravitational pressure of its envelope thus the most massive stars may remain on the main sequence for only a few million years while stars with less than a tenth of a solar mass may last for over a trillion years 55 the exact mass luminosity relationship depends on how efficiently energy can be transported from the core to the surface a higher opacity has an insulating effect that retains more energy at the core so the star does not need to produce as much energy to remain in hydrostatic equilibrium by contrast a lower opacity means energy escapes more rapidly and the star must burn more fuel to remain in equilibrium 56 a sufficiently high opacity can result in energy transport via convection which changes the conditions needed to remain in equilibrium 15 in high mass main sequence stars the opacity is dominated by electron scattering which is nearly constant with increasing temperature thus the luminosity only increases as the cube of the star s mass 48 for stars below 10 m the opacity becomes dependent on temperature resulting in the luminosity varying approximately as the fourth power of the star s mass 52 for very low mass stars molecules in the atmosphere also contribute to the opacity below about 0 5 m the luminosity of the star varies as the mass to the power of 2 3 producing a flattening of the slope 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