Great Poem.

I'll leave this for the scientists.

What it's sure is that the Sun is 8 light minutes away from Earth.

So, the last electromagnetic radiation and Gravitational effects from the Sun will reach the Earth up to 8 minutes after the Sun goes away, after that everything will be dark(?), cold(?) and chaotic.

Gravitational Effects:

Our solar system is similar to the vortex you find in the museums, where the Sun is in the center and all the planets orbit around it. If the Sun disappears, all the planets (and other cosmic bodies) will reach their maximum escape lineal speed (no more turning around), maybe crashing with each other. The Moon will crash again us and depending of the Earth position, maybe we will crash again Jupiter. (no survivors)

Electromagnetic Effects: (if we survive the previous part)

The magnetic field of the Sun has direct influence in our own magnetic field, and our MF keeps the molecules of the Atmosphere in place, so any disturbance will make part of our atmosphere to escape to the empty space.

Without the Sun's radiation, our atmosphere will stop heating the surface of the Earth, making it colder than the dark side of the Moon (around -250 F or less). Without the light from Sun, there is no photosynthesis by plants, so less Oxygen and no way to burn anything. If this is not catastrophic enough, if no light is present, the temperature will drop so quickly that big cold storms should frozen the surface and the oceans,

Finally, the closes example I can give you, is what it is supposed happen 65 million of years ago, when a comet's impact generated a big cloud of dust that cover the Earth, preventing the Sun radiation (light and heat) from reaching the surface, killing most of the plants (no photosynthesis), this make the big plant eaters to disappear, and this make most of the meat eater disappear too. That was the main reason for the disappear of the Dinosaurs.

But still there is hope:

The core of the Earth is full of Magma, this is a kind of high temperature fluid that keeps moving very slowly, and that can be used to warm some parts of the deep inner surface of the oceans, so maybe some of the micro organism (bacteria and so) can survive the longest and darkest winter.

Hope this educated (but still incomplete) answer will help here.

Itux;

The author is a former teacher of Physics with high interest in Astronomy and Biophysics.

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Itux