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den 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 on a graph of mass versus luminosity even these refinements are only an approximation however and the mass luminosity relation can vary depending on a star s composition 11 evolutionary tracks edit main article stellar evolution evolutionary track of a star like the sun when a main sequence star has consumed the hydrogen at its core the loss of energy generation causes its gravitational collapse to resume and the star evolves off the main sequence the path which the star follows across the hr diagram is called an evolutionary track 57 a track known as the zero age main sequence zams is where stars of different masses begin their main sequence lives while a track known as the terminal age main sequence tams is where stars of different masses end their main sequence lives when hydrogen is depleted in their cores 58 h r diagram for two open clusters ngc 188 blue is older and shows a lower turn off from the main sequence than m67 yellow the dots outside the two sequences are mostly foreground and background stars with no relation to the clusters stars with less than 0 23 m 59 are predicted to directly become white dwarfs when energy generation by nuclear fusion of hydrogen at their core comes to a halt but stars in this mass range have main sequence lifetimes longer than the current age of the universe so no stars are old enough for this to have occurred in stars more massive than 0 23 m the hydrogen surrounding the helium core reaches sufficient temperature and pressure to undergo fusion forming a hydrogen burning shell and causing the outer layers of the star to expand and cool the stage as these stars move away from the main sequence is known as the subgiant branch it is relatively brief and appears as a gap in the evolutionary track since few stars are observed at that point when the helium core of low mass stars becomes degenerate or the outer layers of intermediate mass stars cool sufficiently to become opaque their hydrogen shells increase in temperature and the stars start to become more luminous this is known as the red giant branch it is a relatively long lived stage and it appears prominently in h r diagrams these stars will eventually end their lives as white dwarfs 60 61 the most massive stars do not become red giants instead their cores quickly become hot enough to fuse helium and eventually heavier elements and they are known as supergiants they follow approximately horizontal evolutionary tracks from the main sequence across the top of the h r diagram supergiants are relatively rare and do not show prominently on most h r diagrams their cores will eventually collapse usually leading to a supernova and leaving behind either a neutron star or black hole 62 when a cluster of stars is formed at about the same time the main sequence lifespan of these stars will depend on their individual masses the most massive stars will leave the main sequence first followed in sequence by stars of ever lower masses the position where stars in the cluster are leaving the main sequence is known as the turnoff point by knowing the main sequence lifespan of stars at this point it 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mass loss and overshooting in mas...
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