# How bright would a magically created 13.7B years ago white dwarf be now?

I assumed that the initial brightness is $$1$$, and at death it is $$10^{-20}$$ (since I can't reach 0 with exponentiation, it will be close enough to 0), and it lived $$10^{15}$$ years.

Then I solved an equation $$x=-\frac{10^{15}}{ln(10^{-20})}$$ to get the right results at $$10^{15}$$ years.

And lastly I made a graph: $$y=e^{\frac{-x}{-\frac{10^{15}}{\ln(10^{20})}}}$$, that gives me $$y=10^{-20}$$ at $$x=10^{15}$$ or a quadrillion years after its creation.

I got $$y=0.999$$ at $$x=13.7\cdot10^{9}$$ or 13.7 billion years, or now, which means the white dwarf is 0.999 the brightness it was when it was created during the big bang somehow.

Do these results make sense?

• No they don't. That isn't how WD cooling works and it isn't an exponential decay. I don't understand where you get your 1e-20 at 1e15 years. The faintest white dwarfs are about 1 millionth of a solar luminosity – ProfRob Oct 22 '20 at 18:35