Imagine that the source of energy in the interior of the Sun changed abruptly. a. How long would it take before a neutrino telescope detected the event? b. When would a visible-light telescope see evidence of the change?

Neutrinos are tiny particles generated during nuclear reactions in the Sun's core. Since they interact very weakly with other matter, they can escape the Sun's core and travel across space almost without hindrance. This property makes neutrinos fascinating for scientists because they can carry direct information from the core of the Sun to Earth.
When there is a change in the energy source in the Sun's core, neutrinos are among the first particles to react. These particles zip through the Sun and arrive at Earth after traveling a distance of 1 AU (astronomical unit).

Using their speed, which is approximately the speed of light, we can calculate the time it takes for a neutrino to travel from the Sun to Earth:
\(\text{Time} = \frac{1 \text{ AU}}{c} \approx 8 \text{ minutes} \)
So, if there was an abrupt change in the Sun's energy source, a neutrino telescope on Earth would detect the event in about 8 minutes.

Energy produced in the Sun's core travels to the surface in a slow and arduous process called radiative diffusion. Instead of traveling in a straight line, energy particles are constantly absorbed and re-emitted by atoms within the Sun, making their path unpredictable.
This random walk through the Sun's dense, opaque material means that light-energy particles (photons) take an extraordinarily long time to travel from the core to the photosphere—the Sun's visible surface.

In fact, it can take hundreds of thousands to millions of years for energy to complete this journey. Each photon travels a tiny distance before it's absorbed and then radiated again in a new direction. This lengthy process is a critical reason why changes in the Sun's core take so long to affect the visible light we see.
So, if the energy source at the Sun's core changed abruptly, it would take an immense amount of time before any evidence appeared to a visible-light telescope on Earth.

The photosphere is the outer shell of the Sun from which visible light is emitted. It’s essentially what we see as the Sun’s surface despite being around 500 kilometers thick.
Compared to other layers of the Sun, the photosphere is relatively cool, with a temperature of about 5,500 degrees Celsius. However, this temperature is enough to emit light that is visible to us on Earth.

When energy finally reaches the photosphere through radiative diffusion, it escapes into space as the light we see. This visible light can show us changes occurring on the Sun's surface, such as sunspots, solar flares, or other solar activities.
The photosphere marks the transition between the dense interior of the Sun and the outer atmosphere (corona), which is much hotter but less dense.
Considering the radiative diffusion time, any abrupt changes in the Sun's core energy source wouldn't appear in the photosphere—and hence be visible to Earth's telescopes—for hundreds of thousands to millions of years.
This highlights how deeply hidden the source of solar energy is and why changes there take so long to manifest visually.