Question

Ques. Explain how sunspots survive for so long even though they are surrounded by hotter
matter.

Answer 1

Sunspots are temporary phenomena on the Sun's photosphere that appear as spots darker than the surrounding areas. They are regions of reduced surface temperature caused by concentrations of magnetic field flux that inhibit convection (and convection is the mechanism of thermal conductivity).
Magnetic fields are the reason why sunspots are colder and why they live so long. Thermal conductivity is inhibited because of strong magnetic field flux.