▁increased ▁by ▁the ▁temperature ▁rise , ▁increasing ▁the ▁rate ▁of ▁nuclear ▁re actions . ▁The ▁outer ▁layers ▁expand ▁to ▁compens ate ▁for ▁the ▁increased ▁temperature ▁and ▁pressure ▁grad ients , ▁so ▁the ▁radius ▁also ▁increases . ▁ ▁No ▁star ▁is ▁completely ▁static , ▁but ▁stars ▁stay ▁on ▁the ▁main ▁sequence ▁( burn ing ▁hydro gen ▁in ▁the ▁core ) ▁for ▁long ▁periods . ▁In ▁the ▁case ▁of ▁the ▁Sun , ▁it ▁has ▁been ▁on ▁the ▁main ▁sequence ▁for ▁roughly ▁ 4 . 6 ▁billion ▁years , ▁and ▁will ▁become ▁a ▁red ▁giant ▁in ▁roughly ▁ 6 . 5 ▁billion ▁years ▁for ▁a ▁total ▁main ▁sequence ▁lifetime ▁of ▁roughly ▁ 1 1 ▁billion ▁( 1 0 1 0 ) ▁years . ▁Thus ▁the ▁assumption ▁of ▁steady ▁state ▁is ▁a ▁very ▁good ▁approximation . ▁For ▁simplicity , ▁the ▁stell ar ▁structure ▁equations ▁are ▁written ▁without ▁explicit ▁time ▁dependence , ▁with ▁the ▁exception ▁of ▁the ▁lum inos ity ▁gradient ▁equation : ▁ ▁Here ▁L ▁is ▁the ▁lum inos ity , ▁ ε ▁is ▁the ▁nuclear ▁energy ▁generation ▁rate ▁per ▁unit ▁mass ▁and ▁ ε ν ▁is ▁the ▁lum inos ity ▁due ▁to ▁neut r ino ▁emission ▁( see ▁below ▁for ▁the ▁other ▁quantities ). ▁The ▁slow ▁evolution ▁of ▁the ▁Sun ▁on ▁the ▁main ▁sequence ▁is ▁then ▁determined ▁by ▁the ▁change ▁in ▁the ▁nuclear ▁species ▁( pr inci p ally ▁hydro gen ▁being ▁consum ed ▁and ▁hel ium ▁being ▁produced ). ▁The ▁rates ▁of ▁the ▁various ▁nuclear ▁re actions ▁are ▁estimated ▁from ▁particle ▁physics ▁experiments ▁at ▁high