There are several scientific papers that claim that the variability in luminosity of young stars can be explained by the collisions of these stars with comet-like bodies, and that during such collisions, energy release would be rapid and explosive in the upper layers of the solar atmosphere (similar to the explosion of the Chelyabinsk meteorite).

Furthermore, it is known that Kreutz comet progenitor with a diameter of 100-200 kilometers passed at a distance of 1.3 solar radii from the Sun around 2,300 years ago. Due to the very high escape velocity at the Sun, a body falling from infinity would have a velocity of 618 kilometers per second at its surface. This gives us energy estimates: when a body with a diameter of 100 km falls, the flare energy would be 100 times greater than the energy radiated by the Sun per second, and if a 1000-kilometer body falls, it would be 100,000 times greater. If a significant portion of this energy converts to light, this would lead to burns and fires on the Sun-facing side of Earth, as well as effects similar to a magnetic superflare. Comet impacts on the Sun can explain some of Miyaki events – 5 superflares in last 10 000 years which are observed via radioactive materials in tree rings.  

There are also remnants of global fires 12800 ya, but not coinciding with radioactive traces of the solar flare 14700 ya. This can be explained by disintegration of a large comet near the Sun, part of which impacted the Sun and part of it formed a large tail which Earth later passed through and experienced many small impacts mostly in North America. 

Based on this, we can assume that collisions of comets with the Sun large enough to have consequences on Earth occur approximately once every 10,000 years in current epoch, while collisions that lead to catastrophic consequences (mass extinction) occur once every several million years. 

The overall intensity of comet influx from the Oort cloud depends on the influence of nearby star passages and periodic passage through the galactic disk. Since there was a recent passage of stars (HD 7977 3 millions of years ago and Scholz's Star 80,000 years ago) and the Sun's passage through the disk plane happened 3 million years ago, we may be living in a period of more intense comet bombardment than the average throughout history. Thus, the risk of a bright flare from a comet falling on the Sun equals approximately 1 percent per century. Necessary protective measures include observation, creating stockpiles of food and light-reflecting materials.

TL;DR: Large comets (100-200 km in diameter) probably collide with the Sun approximately every 10,000 years. These collisions release energy equivalent to 0.25-3 hours of the Sun's total radiation in the form of a short flare lasting 0.1-10 minutes, which could cause significant damage and fires on Earth.

Disclaimer: abstract above, content and main ideas are human-written; the full text below is written with significant help of AI but is human-verified as well as by other AIs. 

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