Cosmology: Cepheid Variables – or why Henrietta couldn’t Leavitt alone …(Post #4)

Having exhausted the measurement capabilities for small angles, to proceed further, scientists really needed to use the one thing galaxies and stars put out in plenty – light. The trouble is, to do so, we either need detailed, correct theories of galaxy and star life-cycles (so we know when they are dim or bright) or we need a “standard candle”. That term needs explanation.

If I told you to estimate how far away a bulb was, you could probably make an estimate based on how bright the bulb seemed. For this you need two things. You need to know how bright the bulb is {\bf intrinsically} – this is the absolute luminosity and its measured in watts which is Joules \: per \: second. Remember, however, that a 100 watt bulb right next to you appears brighter (and hotter) than the same 100 watt bulb ten miles away! To account for that, you could use the fact that the bulb distributes its light almost uniformly into a sphere around itself, to compute what fraction of the light energy you are actually able to intercept – we might have a patch of CCD (like the little sensor inside your video camera), of area A capturing the light emitted by the bulb. Putting these together, as in the figure below, the amount of light captured is I_{Apparent} watts while the bulb puts out I_{Intrinsic} watts.

Luminosity Falls Off

I_{Apparent} = I_{Intrinsic} \frac{CCD \: Area}{Sphere \: Surface \: Area}

I_{Apparent} = A \frac {I_{Intrinsic}}{4 \pi R^2}

where if you dig into your memory, you should recall that the area of a sphere of radius R is 4 \pi R^2!

you can compute R

R = \sqrt{A \frac {I_{Intrinsic}}{4 \pi I_{Apparent}}}

You know how big your video camera’s sensor area is (it is in that manual that you almost threw away!) You know how much energy you are picking up every second (the apparent luminosity) – you’d need to buy a multimeter from Radio Shack for that (if you can find one now). But to actually compute the distance, you need to know the {\bf Intrinsic} or {\bf actual} luminosity of the light source!

That’s the problem! To do this, we need a set of “standard candles” (a light source of known actual luminosity in watts!) distributed around the universe. In fact the story of cosmology really revolves around the story of standard candles.

The first “standard candles” could well be the stars. If you assume you know how far away the Sun is, and if you assume other stars are just like our Sun, then you could make the first estimates of the size of the Universe.

We already know that the method of parallax could be used with the naked eye to calculate the distance to the moon. Hipparchus calculated that distance to be 59 earth radii. Aristarchus measured the distance to the sun (the method is a tour de force of elementary trigonometry and I will point to a picture here as an exercise!)

Aristarchus Figures out the Distance to the Sun

His calculation of the Earth-Sun distance was only 5 million miles, a fine example of a large experimental error – the one angle he had to measure was \alpha, he got wrong by a factor of 20. Of course, he was wise – he would have been blinded if he had tried to be very accurate and look at the sun’s geometric center!

Then, if you blindly used this estimate and ventured bravely on to calculate distances to other stars based on their apparent brightness relative to the sun, the results were startlingly large (and of course, still too small!) and people knew this as early as 200 B.C. The history of the world might have well been different if people had taken these observers seriously. It was quite a while and not till the Renaissance in Europe that quantitative techniques were re-discovered for distance measurements to the stars.

The problem with the technique of using the Sun as a “standard candle” is that stars differ quite a bit in their luminosity based on their composition, their size, their age and so on. The classification of stars and the description of their life-cycle was completed with the Hertzsprung-Russell diagram in 1910. In addition, the newly discovered nebulae had been resolved into millions of stars, so it wasn’t clear there was a simple way to think of stellar “standard candles” unless someone had a better idea of the size of these stellar clusters. However, some of the nearby galaxy companions of the Milky Way could have their distances estimated approximately (the Magellanic Cloud, for instance).

Enter Henrietta Leavitt. Her story is moving and representative of her time, from her Radcliffe college education to her $0.30 / hour salary for her work studying variable stars (she was a human computer for her academic boss), as well as the parsimonious recognition for her work while she was alive. She independently discovered that a class of variable stars called Cepheids in the Magellanic clouds appeared to have a universal connection between their intrinsic luminosity and the time period of their brightness oscillation. Here’s a typical graph (Cepheids are much brighter than the Sun and can be observed separately in many galaxies)

t1_cepheid_PL_relation

If you inverted the graph, you simply had to observe a Cepheid variable’s period to determine the absolute luminosity. Voila! You had a standard candle.

A little blip occurred in 1940, when Walter Baade discovered that Cepheids in the wings of  the Andromeda galaxy were older stars (called Population II, compared to the earlier ones that are now referred to as Population I) and were in general dimmer than Population I Cepheids.  When the Luminosity vs. Period graph was drawn for those, it implied the galaxy they were in was actually even further away! The size of the universe quadrupled (as it turned out) overnight!

Henrietta Leavitt invented the first reliable light-based distance measurement method for galaxies. Edwin Hubble and Milton Humason used data collected mainly from an analysis of Cepheids to derive the equation now known as Hubble’s law.

Next post will be about something called Olbers’ paradox before we start studying the expansion of the Universe, the Cosmic Microwave background and the current belief that we constitute just 4% of the universe  – the rest being invisible to us and not (as far as we can tell) interacting with us.

 

 

 

 

 

 

 

 

 

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