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Dim and Dimmer

To the Editors:

In the article “Illuminating Dark Energy with Supernovae” (July–August), D. Andrew Howell indicates that the brighter supernovae take longer to reach maximum brightness—three weeks for the brightest, two weeks for the dimmest. The time to reach maximum brightness, as measured on Earth, needs to be adjusted by the value of redshift, due to the expansion of the universe. (As is detailed in the article, the wavelengths of photons from more distant supernovae are stretched more, making them redder—this is called redshift.) For example, suppose a Type Ia supernova was observed to take three weeks to reach maximum brightness. Using the observed data from our example supernova as it stands would indicate that it was intrinsically one of the brightest supernovae and therefore, for a given observed brightness, farther away. However, this assumption is not necessarily true.

Assume the observed optical spectrum was shifted toward the red by a factor of 1.5. That means that everything that we see occurring at the supernova takes 1.5 times longer, from our perspective. So this supernova actually only took two weeks to reach maximum brightness and was therefore one of the dimmer supernovae and therefore closer.

Because we are viewing the distant supernova in “slow motion,” as it were, it appears even dimmer. The explosion releases a given amount of light but if, from our viewpoint, it is “strung out” over a longer period (three weeks rather than two), the intensity would be less and therefore, it appears less bright. No doubt, this effect is also compensated for when using supernovae to measure the expansion history of the universe.

Paul White
Portsmouth, RI

Dr. Howell responds:

This is true. Due to the effects of time dilation from the expansion of the universe, distant supernovae do seem to evolve more slowly than nearby ones, from our perspective on Earth. This phenomenon is similar to the twin paradox: If one twin speeds away from Earth at or near the speed of light, he or she will age more slowly than the Earth-bound twin. To keep the two straight, astronomers refer to time in the “rest frame” (time as measured at the supernova), and in the “observer frame” (time as measured by us on Earth moving relative to the distant supernova). They are related by an equation: tobserver = trest (1 + z), where z is the redshift. In the article I referred to restframe time, and indeed all observed times are corrected with this equation in cosmological papers on the subject (such as Perlmutter et al. 1999, Riess et al. 1998, and Sullivan et al. 2011 in the feature’s bibliography). Supernovae have even been used to confirm this relativistic time dilation, for example in the work of Stéphane Blondin of the Laboratoire d’Astrophysique de Marseille and his colleagues as published in 2008 in the Astrophysical Journal.

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