Brightness without extra mass:
If Jupiter only starts emitting light, and doesn't become more massive (hadwavium alien technology), 15% of Sol's luminosity at a closest approach of (5.2-1) AU makes it 15%/(4.22) = 0.15*5.66…% = 0.85…% the apparent brightness of Sol. Given that anthropogenic climate change (currently about 1°C) has the same effect as 0.15% of solar luminosity, this will be Bad. Not wipe out all life bad, but definitely very bad — but humans are adaptable and would probably make do.
(Given humanity could fly to Jupiter without much difficulty in the 2001 and 2010 films, a massive sun-shield is not entirely implausible, which would mitigate the climate problems of two stars much more effectively than the climate-and-pollution problems of CO2, but I'm not sure if you want that from your question).
Brightness by becoming heavy enough to start fusion:
Now, what happens if Jupiter does get more massive, enough so to produce 15% Sol luminosity? I happen to have just written an orbital simulator for the story I'm writing to make sure the specifics of my plot device doesn't accidentally break the entire system.
Assuming 15% solar luminosity requires 500 Jupiter masses, as per comment from @userLTK, this is how it turned out:
At ten years, it's not looking too bad:
- Mercury: 0.24677… AU
- Venus: 0.67828… AU
- Earth: 0.99387… AU
- Mars: 1.8782… AU
- Jupiter: 4.8489… AU
- Saturn: 10.259… AU
- Uranus: 14.408… AU
- Neptune: 38.403… AU
The problems happen (in this run of the simulation) at about 53 years, where the Earth is now 1.1 AU from Sol, getting 83% of the warmth from Sol that it currently gets. But that's just a cold snap, it doesn't even last to the end of the year. Regardless, long enough for one or two more generations if perhaps not two or three.
- 54 years, six months: 0.77… AU, 165.8…% Sol apparent luminosity
- 60 years, three months: 0.715… AU (inside Venus' orbit), nearly doubles the apparent luminosity of Sol
- 63y3m: 1.138… AU, 77% Sol brightness
- 65y2m: 1.279… AU, 61% Sol brightness
- 104y: 2.780… AU, 13% Sol brightness
- 105y: 3.712… AU, 7.2% Sol brightness
- 106y: 5.379… AU (further from Sol than from Jupiter), 3.5% Sol brightness
And, in the far future:
- 200 years: 587.3… AU, Sol is a tiny speck of light almost like any other star, 0.00029% of its current apparent luminosity. The atmosphere of Earth has now condensed into a 12m thick layer of solid nitrogen, solid oxygen, solid everything. All structures more than 12m above sea level are now in hard vacuum.
(I stopped the simulation after 1000 years, by which point Earth is 0.6 light years away from Sol, further than all of the other planets).