Season 17, Episode 8: The “Red Hot” Debate, Betelgeuse and Rigel

Hey StarTalkians! Season 17, Episode 8 was a “Thing you thought you knew” edition, where Neil and Chuck sat down to chat about a few interesting facts. The highlight of the episode – at least for me – was Neil’s science-inspired rant about people saying things are “red hot.”

Thing You Thought You Knew – Red Hot, Blue Hot - StarTalk Radio 

(The discussion starts at 13:45)

He’s right… Kind of. As you’d expect, the physics is right. But when we move over to the real world, the reason we say “red hot” is baked right into the equations.

Black Body Radiation and the Temperature of Stars – Neil’s Point

This whole discussion comes down to what physicists call “black body radiation.” This is the light that something emits as a result of its temperature.

As Neil explains, when this emitted energy gets to the visible part of the spectrum, red is the lowest energy – coolest – colour of light we can see. If the temperature increases, it goes through orange, yellow, green and (theoretically) all the way to blue.

With some simplifying assumptions, physicists use Wien’s displacement law (Wavelength- and Frequency-Dependent Formulations of Wien’s Displacement Law) to describe this:

λ T = (a constant)

Here, λ is the wavelength with the peak output, and T is the corresponding temperature. This is all equal to a constant (2.898 × 10^(−3) meters-Kelvin), so we can do a little trick. Let’s say we’re looking at two stars in Orion: Rigel (blue) and Betelgeuse (red). Both of them fulfill Wien’s law, so we can write:

 λ(Rigel) T(Rigel) = (a constant) = λ(Betelgeuse) T(Betelgeuse)

But we know Rigel is blue (short wavelength) and Betelgeuse is red (long wavelength). So since λ(Rigel) <  λ(Betelgeuse), the only way this could all work is if T(Rigel) > T(Betelgeuse). And it’s true! (Colour evolution of Betelgeuse and Antares over two millennia, derived from historical records, as a new constraint on mass and age )

This is Neil’s point.

Why We Still Say “Red Hot”

You give off black body radiation too. But you’re so cold compared to a star that the wavelength is way too high for our visual range. The same goes for an unheated bit of iron.

But if it gets really hot, it will actually enter the visible range for the first time, glowing red.

Wein’s law shows that for something to go “blue hot,” it would have to reach about 7,000 degrees Celsius. No metal could get this hot without melting (Melting Point of Common Metals, Alloys, & Other Materials | AMERICAN ELEMENTS ®). So it makes sense we would never say that.