The photosphere is not smooth and steady. Dark sunspots come and go, and their number rises and falls in a cycle of about 11 years. The cause is magnetism. You know from Magnets and Magnetic Fields that magnets have field lines running from north to south poles. The Sun is a giant, churning magnet.
Why it works
The Sun's gas is a plasma, full of charged particles, so it drags magnetic field lines along as it moves. The Sun also spins faster at its equator (about 25 days) than near its poles (about 35), and its convective zone boils. Together these wind up and twist the field until bundles of it burst through the surface in loops. Where a strong loop comes out, its field pushes back on the hot gas rising from below and slows the flow of heat. That patch cools to about $3800$ to $4500$ K, against about $5800$ K around it, and so it looks dark. Every 11 years or so the tangled field reorganizes, and the Sun's magnetic poles flip; the full magnetic cycle takes about 22 years.
Key idea
Sunspots are cooler, darker patches where strong magnetic fields block the heat coming up from below. Their number rises and falls about every 11 years, along with flares and other solar activity.
Worked examples
Worked example: How dark is a sunspot?
A sunspot is at $4000$ K and the photosphere around it at $5800$ K. Power per square meter goes as $T^4$. How bright is the spot compared with its surroundings?
- $\left(\frac{4000}{5800}\right)^4 = 0.690^4 = 0.23$.
- The spot gives off about a quarter as much light per square meter, so it looks dark by contrast, though on its own it would still glow brighter than the filament of a light bulb.
Answer: About $23\%$ as bright.
Worked example: Watching the Sun turn
A sunspot near the equator takes about $27$ days to go once around as seen from Earth. How long does it take to cross the visible half of the disk?
- The visible half is half a turn: $27 \div 2 = 13.5$ days.
- Galileo used sunspots this way to show that the Sun rotates.
Answer: About $13.5$ days.
Common mistake
Sunspots are neither holes in the Sun nor hotter spots. They are cooler, by well over a thousand kelvins, which is why they look dark next to the brighter gas around them. Check with $T^4$: a $4000$ K patch beside a $5800$ K surface gives off only about a quarter as much light per square meter.
Above active regions, twisted fields can snap and reconnect, releasing flares and huge clouds of plasma (coronal mass ejections). When these reach Earth they cause auroras and can disturb satellites and power grids. NOAA's Space Weather Prediction Center tracks them.