Magnetar.On December 27, 2004, astronomers observed the greatest flash of light ever recorded from outside the solar system. It came from the highly magnetic neutron star SGR 1806-20 (a magnetar). During 0.20s, this star released as much energy as our sun does in250,000years. If Pis the average power output of our sun, what was the average power output (in terms of P) of this magnetar?

Short Answer

Expert verified

The average output of this magnetar is3.9×1013P.

Step by step solution

01

Power:

Power is defined as the rate of energy. The expression of the energy is,

P=Et

Here, Pis the power, Eis the energy, and tis the time.

02

Time is second:

The time for the sun in the second is defined as below.

tsun=250,000years365 days1 year24 h1 day60 min1 h60 s1 min=7.884×1012s

The time for star, tstar=0.20s

03

The average output of this magnetar:

The power Psunfor the sun is,

Psun=Esuntsun

Here,Esunis the energy released by the sun and tsunis the time for the sun.

The powerPstarfor star is,

Pstar=Estartstar

Here, Estaris the energy released by the star and tstaris the time for the star.

Now, divide the equations of Pstarand Psun.

role="math" localid="1660057291049" PstarPsun=EstartstarEsuntsun

Since the released energy by the sun and the star is equal. Substitute Estarfor Esunin the above equation, and you get,

role="math" localid="1660057535398" PstarPsun=EstartstarEsuntsun=tsuntstar

Substitute 0.20sfor tstarand 7.884×1012sfor tsunin the above equation.

PstarPsun=7.884×1012s0.20s=3.942×10133.9×1013

Substitute Pfor Psunand solve for Pstar.

PstarP=3.9×1013Pstar=3.9×1013P

Therefore, the average output of this magnetar is,Pstar=3.9×1013P.

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