A quasar consumes 1 solar mass of material per year converting 15 percent of it directly into energy
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August 4, 2020A quasar consumes 1 solar mass of material per year converting 15 percent of it directly into energy
##L = 1.478 xx 10^13 L_o.##
Quasars are created as a result of mas being swallowed by the supermassive black hole at the center of an active galactic nucleus. The luminosity of a quasar is the rate at which energy is emitted by the quasar. We are given the rate of ##1 M_o. / yr## and Einstein gave us the formula to convert mass into energy.
##E=mc^2##
Here ##m## is the mass converted and ##c## is the speed of light. One solar mass is equal to ##1.989 xx 10^30kg##. Using the mass conversion formula;
##E = (1.989xx10^30kg)(3 xx 10^8 m/s)^2##
##E = 1.790 xx 10^47J##
Luminosity is measured in watts ##W## or ##J/s## so we need to convert years into seconds.
##1year = 365days = 8760 hours = 525600 minutes ##
##= 31536000 seconds##
So the luminosity of the quasar is;
##L = (1.790 xx 10^47 J)/(3.154 xx 10^7 s) = 5.675 xx 10^39 W##
For comparison the luminosity of is;
##L_o. = 3.828 xx 10^26 W##
Which is about 1 ten-billionth of the luminosity of the quasar.
##L = (5.675 xx 10^39W)/(3.282 xx 10^26W)=1.478 xx 10^13 L_o.##
