How and why do sunspots affect propagation in HF bands?
The sunspots do not cause changes in propagation, but increase and decrease with other solar phenomena. Another way to say this is that sunspots are correlated with solar activity.
The amount of solar activity seems to vary on an 11 year cycle. Charged particles from the sun streaming by Earth affect the ability of the ionosphere to refract radio signals back to Earth.
You will see sometimes see hams use the word reflection to describe what happens at the ionosphere where signals below the MUF, or Maximum Usable Frequency, return to Earth. This is a simplification. The ionopshere is not a mirror, where there is a sudden pronounced change of materials, but rather varies in density bending the signal. This bending is called refraction. For more on this, including illustrations, see this page on Refraction in the ionosphere
HF propagation occurs by way of the ionosphere. The signal from the transmitting antenna travels up to the ionosphere, is bent (or refracted) back to Earth and is then audible hundreds or thousands of miles away. The ionosphere consists of several layers, and the distance traveled by the radio signal in one hop depends on the height of the layer of the ionosphere that is involved.
Roughly, the effect of increased solar activity is to increase the usability of the bands from 14-28 Mhz, and sometimes 50 Mhz.
However, solar "storms" can cause other effects, such as seeing aurora at lower latitudes, causing the ionosphere to absorb rather than refract signals (making bands unusable), or cause unusual phenomena such as 50 Mhz or even 144Mhz to be temporarily useful for long distance communications.
These spots are cool areas (relatively speaking) on the surface of the sun. The temperature is around only 3000C against a sizzling 6000C for the rest of the surface. It is much hotter under the surface reaching temperatures in excess of a million degrees Celsius.
These sunspots are areas where there is intense magnetic activity. The fields in these areas are enormous and as a result the surface of the sun is disrupted. In these areas the surface cools dramatically causing a darker region to be perceived.
Around the sunspot there is an area called a plage. This is slightly brighter than the surrounding area and it is a large radiator of cosmic rays, ultra-violet light and X-rays. In fact it results in the overall level of radiation coming from the sun to increase. In turn this increased radiation level from around the sunspots causes the ionosphere to become ionised to a greater extent. This means that higher frequencies can be reflected from the ionosphere.
Sun spots affect radio propagation by affecting the layer of the atmosphere called the ionosphere. The ionosphere contains electrified layers of ions. The layers are formed by the sun bombarding them with ultraviolet light. The intensity of the sun's bombardment of these layers with ultraviolet radiation varies depending on the hour of the day, the season of the year, and year to year resulting in great variations in the amount of energy in these layers. Enter sunspots, they also add to ionization. Why do they add to ionization? The same reason as above - because they create ultraviolet radiation, a considerable amount of it. The more sun spots there are the greater the level of ultraviolet radiation emitted by the sun. Greater levels of ultraviolet radiation means more ultraviolet energy pumped into the ionosphere. Higher levels of ionization in the electrified layers encircling the earth increases its ability to bend HF radio waves and return them to the earth at great distances from their source. That's why when the sun surface is covered with a great number of sun spots that communications has a positive effect on propagation in HF bands.