When a lightbulb is brighter than a star

"Far more marvelous is the truth than any artists of the past imagined it"

Richard Feynman

"Here comes the science bit"

Jennifer Aniston

Recently the Brooklyn based artist Rob MacInnis set up a camera near a hill and took an LED light bulb up the hill to a location near the top whose distance from the camera was far enough for the light bulb to be the same size as a star.

This is shown in this video he took with the camera which is found on his website here:
http://www.robmacinnis.com/the-brightest-star-in-the-night-sky/

The angular extent of the light bulb is the same as the star Alpha Centauri. But what can be seen clearly in the video is that the light bulb appears brighter than the star. The difference in the physical size of the light bulb and star should have been compensated by the difference in the distances that results in them both covering the same amount of the sky.  

So how can the light bulb be brighter than a star under these circumstances?

The answer is to consider the different ways they make light.

The star radiates energy over a broad spectrum of electromagnetic frequencies. This includes the visible spectrum we can see, but the star is also "radio bright", emits infra-red, ultraviolet, and so on. The variation in intensity over this spectrum is related to the star's temperature and the thermodynamic equilibrium between the electromagnetic radiation it emits and the star's photosphere, heated by nuclear fusion reactions within its core.

If the Sun was a different temperature, the relative brightness of the colours in a rainbow would be different because the spectrum would be different. The peak in the Sun's spectrum - the brightest colour in the rainbow - is bluey-green. The Sun appears yellow because of our colour perception of combinations of multiple frequencies of light. A shift in this peak as a result of a change in temperature would result in a different perceived colour.  

The LED light bulb concentrates its emissions into a much narrower range of frequencies, almost entirely within the visible spectrum. The frequency of the LED emissions is completely determined by the difference in energy between valence and conduction bands in the semiconductor material from which the LED is made.

The light bulb appears white because it contains a single blue LED coated with phosphor which absorbs and re-emits the light produced by the LED over a slightly broader spectrum of frequencies. But, unlike the star, temperature does not affect the colour of the LED. The populations of electrons in the conduction and valence energy bands may change with temperature, but the energy gap between them does not. The rate at which electrons change energy levels in the phosphor may change with temperature, but the energies associated with those levels do not.

The star is bright because it is hot. The LED is bright despite being cold.

Imagine, instead, you had a hypothetical star made entirely of LED light bulb stuff, to compare directly with a similarly sized star made of typical star stuff. You can hold an LED light bulb in your hand. It would be difficult to scoop up a handful of star to do the same thing.

The LED star would be brighter but colder. If we had to plot the LED light bulb star on a Hertzsprung-Russell diagram, it would be an extreme outlier.

Why is this important?

An instructive contrast would be to consider a tungsten filament light bulb instead of an LED light bulb, one which consumed the same amount of power as the LED light bulb. It would be fainter than the LED light bulb. Just like the star.

Since the light from the tungsten filament is generated by heating it, it behaves similarly to the star. One of the advantages of LEDs over tungsten filament is their lower power consumption for the same luminosity at visible wavelengths. The LED turns more of the power it consumes into visible light and stays cold, whereas the tungsten filament (and the star) generate light as a by-product of heat as they become "white hot", for a given power consumption.

In the video above the comparison between the LED light bulb and the star is the same as if, instead of a star, a giant tungsten filament bulb the size of a star had been placed at the same distance as the star.

Rob MacInnis could have achieved the same thing by taking two similarly sized and rated light bulbs, one tungsten filament and one LED, and holding them up next to each other.

Still, it is nice to climb a hill at night.