Another Rung on the Ladder

One of the most fundamental problems in all of astronomy is to determine the distance to objects. To be able to do this, astronomers have developed what's known as the cosmic distance ladder. The base is built with extremely reliable methods, like parallax, which is then used to calibrate distance indicators for objects further away, which are then used to calibrate even further objects, etc....

In this ladder, one of the most helpful and commonly used types of distance measurement is based on a type of star known as Cepheid Variables. These stars are stars towards the end of their lives, off the main sequence, in what's known as the instability strip. Because of their unstable nature, they change their brightness in a regular way. In particular, the average brightness is directly related to the amount of time it takes to make one full cycle (the period) by the equation

M_V = -1.34 – 2.85 logP.
Thus, by observing a Cepheid type variable's period, we can determine the overall brightness, which we can then compare to how bright it actually looks to determine distance via the distance modulus.

As with all things, there is some inherent error in this equation. It's well established that the amount of heavy elements in a star (the “metals”) will change the overall brightness. As a result, it's suggested that Cepheids in the Large Magellanic Cloud are about 0.4 magnitudes fainter than stars with metallicities similar to the sun (Sekiguchi & Fukugita). Additionally, the calibration of the equation I listed also has general error associated with it as well, but in general it's nothing too outstanding. In general, Cepheids are a wonderfully reliable distance indicator that works over a large range of distances.

However, there's a limit. The problem is that this type of variation only occurs with the more massive stars. Since more massive stars burn through their lives faster, Cepheids are relatively speaking, young. As a result, they tend to be concentrated in clusters since they have not yet had time to disperse. The problem then becomes that, eventually, you simply can't reliably resolve the star you want and be certain you're not getting light contamination from other stars of a similar brightness contaminating your data. Due to this Cepheids only end up being useful to a distance of about 25-30 million parsecs.

A recent paper in the Astrophysical Journal provides a potentially new way to extend that distance to as much as 100 million parsecs (Bird, Stanek, Prieto)! Their trick is to use Cepheids that aren't the prototypical variety. Normal Cepehids are considered to have periods of about 3 days to about 100. But the ones looked at in this study exist at the upper edge of that limit and well beyond, going from 80 days to as much as 210 for the 18 stars they analyzed. They call these stars, “Ultra Long Period” (ULP) Cepheids.

The advantage to these stars is that they're about 2.5 magnitudes brighter than their classical companions (remember that the magnitude system is a logarithmic scale so that's actually about 23 times as bright!). This means that (1) we can see them further away and (2) it's less likely that there will be stars of a similar brightness to contaminate the field. Sounds like it solves all our problems, right?

As of yet, I'd still be somewhat skeptical to fully rely on this system. The issue is that, although promising, the statistical certainty just isn't there yet. The authors of this new paper looked for a new period-luminosity relation in three different filter systems. In all three, the root mean squared values (in essence, the amount of uncertainty) was at least twice as high as it was for classical Cepheids. While twice the error can be dealt with and doesn't ruin the science done with such a method (assuming that the error is properly figured in), it does not yet match the statistical certainty of other available methods available up to 100 million parsecs (namely the use of Type Ia supernovae).

But could it get there?

The authors suggest (and I'm prone to agree) that their uncertainty is not too much higher than that of the Type Ia supernovae. But to get the certainty of the supernovae method as low as it is, significant effort has been invested in beating down the statistical errors. If a larger survey was conducted and the baseline was expanded it's entirely possible that the errors for this ULP Cepheid method would decrease as well. It's not a guarantee, of course. It's entirely possible that in expanding the sample size may begin to reveal other variables they had not yet considered, but it's a good possibility.

So in the end, this paper is giving us the very real possibility of adding a new rung to our cosmic distance ladder. Each step makes us more certain of where we fit in our universe.

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Sekiguchi, M.; Fukugita, M. (1998). Metallicity dependence of the Cepheid calibration The Observatory, 118, 73-77

Bird, J., Stanek, K., & Prieto, J. (2009). USING ULTRA LONG PERIOD CEPHEIDS TO EXTEND THE COSMIC DISTANCE LADDER TO 100 Mpc AND BEYOND The Astrophysical Journal, 695 (2), 874-882 DOI: 10.1088/0004-637X/695/2/874