Which surface has a higher temperature - the surface of a yellow star or that of a red star?

When we look at the stars, we're observing not just points of light, but powerhouses of electromagnetic radiation. A particular type known as blackbody radiation plays a crucial role in our understanding of celestial temperatures. Imagine an idealized object that absorbs all incoming light and doesn't reflect or transmit any of it; this is a blackbody. Such objects emit radiation in a spectrum that is determined solely by their intrinsic temperature, and that emission is what scientists refer to as blackbody radiation.

The sun, along with other stars, is a near-perfect example of a blackbody because their dense gases absorb and emit radiation across a broad spectrum. Therefore, when scientists want to understand the thermal properties of a star, they model it as a blackbody. This simple model gives us surprisingly accurate insights into the relationships between temperature, color, and luminosity of stars.

The light we see from stars is part of the wider spectrum of electromagnetic radiation, which covers everything from gamma rays to radio waves. This radiation is a form of energy that travels through space at the speed of light and can have a range of wavelengths and frequencies. The visual splendor we associate with stars—colors from red to blue—is actually electromagnetic radiation in the visible spectrum.

The Spectrum of Colors

Our sun emits a white light, but when passed through a prism, it disperses into a spectrum of colors, each corresponding to different wavelengths. Likewise, stars emit ranges of colors based on their surface temperature, with cooler stars emitting more towards the red end of the spectrum and hotter stars shining bluer. To determine these temperatures, astronomers use instruments that function like ultra-precise prisms to analyze the light from stars and understand their properties.

The temperature of a star fascinatingly dictates its color and spectral classification. Stars, as we've mentioned, act like blackbodies, and their temperatures can range from a few thousand to tens of thousands of Kelvin. Astronomers classify stars into spectral types based on their temperatures using the mnemonic 'OBAFGKM', running from the hottest 'O' stars, which are blue, to the coolest 'M' stars, which appear red.

Understanding a star's temperature helps scientists interpret its life cycle, age, and even the potential existence of orbiting planets. By studying its spectrum, we can estimate a star's temperature; hotter stars have peak emissions at shorter wavelengths, which correspond to blue or white colors. Conversely, cooler stars peak at longer wavelengths, and hence they seem more red. Yellow stars, like our Sun, are intermediate in temperature.

To tie temperature and color together, we use Wien's Law, which provides a mathematical way to connect the dots. According to this law, the peak emission wavelength of a star—the wavelength at which it emits the most light—is inversely proportional to its temperature.

Mathematically, Wien's Law is expressed as \( T = \frac{b}{{\lambda_{max}}} \), where \(T\) is the temperature in Kelvin, \(b\) is the constant approximately equal to \(2.9 \times 10^{-3} m \cdot K\), and \(\lambda_{max}\) is the peak emission wavelength in meters.

Thus, by knowing the color of the star, and therefore its peak emission wavelength, we can calculate its surface temperature. A yellow star with its shorter wavelength will have a higher temperature under this law compared to a red star, which has a longer wavelength and hence a cooler temperature. Wien's Law allows astronomers to deduce the surface temperatures of stars millions of miles away, just from observing their color.