Of Galaxies, Stars, and Rainbows

By Josh Meyers

One of the chief goals of current and planned astronomy surveys is to determine the nature of dark energy - the name given to the mysterious ‘substance’ that appears to be making the expansion of the Universe proceed faster and faster over time in surprising opposition to the expectations of nearly all cosmologists only a couple of short decades ago.  One technique to probe the nature of dark energy is to examine the distribution of matter in the Universe -- essentially the universe’s clumpiness -- and see how that distribution changes as we look farther and farther away from the Milky Way galaxy (which becomes further and further into the past, once we take into account the finite speed of light).  The tricky thing is that the large majority of the mass in the Universe is in the form of dark matter, which does not emit, reflect, or even absorb light.  

Fortunately, astronomers are clever -- and even more fortunately, the Universe has given us a few ways to indirectly map the dark matter, including a wonderfully exotic-sounding effect called “weak gravitational lensing”.  In a nutshell: as light rays from distant galaxies pass by clumps of matter on their way toward Earth, their trajectories bend a tiny bit.  This bending is slightly different for light coming from different parts of the distant galaxy, which subtly distorts the galaxy images when observed with our telescopes.

The image above shows how dark matter, shown in red, distorts the light path from and apparent shape of distant galaxies, depicted in blue (http://www.astronet.ru/db/xware/msg/1227050).   By measuring the distortions of multitudes of galaxies, astronomers can ‘reverse engineer’ the location of the matter clumps that warped the light rays from those galaxies.  By mapping the matter clumps at multiple distances from the Earth, we can learn about the history of large scale structure formation and the expansion history of the Universe, which can ultimately tell us something about dark energy itself.


Other distortions from the atmosphere and the telescope

Whew!  OK, let’s assume for now we can reconstruct the matter distribution over time if we measure the galaxy shapes perfectly.

Unfortunately, there’s a catch: turbulence in the atmosphere and optical imperfections in the telescope and camera produce distortions much larger than the gravitational signal of interest.  However, the Universe has kindly provided a solution to this conundrum as well.  The images of stars can be used to learn -- exposure by exposure -- what the distortions caused by the atmosphere and the optics are; the distortions can then be removed from the images of the galaxies.

This technique of using images of stars to remove the effects of the atmosphere and optical imperfections on images of galaxies (but, importantly, not the effects of gravitational lensing!) has been standard practice for more than a decade now. However, new surveys such as the Dark Energy Survey, currently in its second year of taking data, and especially surveys at future facilities such as the Large Synoptic Survey Telescope, which has just begun construction this last summer, will strain this technique to its limits.


Accurately measuring how tall the average astronomer is

To see why, we need to understand something about how different types of uncertainties enter into scientific results.  Imagine that you are tasked with needing to know very accurately what the average height of astronomers is worldwide.  You might measure the height of a few of your astronomer friends and combine them together by taking the average.  Of course, if you only measure the heights of a few astronomers, then there’s a chance that the astronomers you pick might happen to be uncharacteristically tall.  To compensate for this, you can make measurements of more and more astronomers, which should slowly reduce the probability that anything is unusual with your sample.  Astronomers label the uncertainties arising due to the possibility of a chance encounter with an atypical data point or two “statistical uncertainties”.  When averaging together a large number of observations, these uncertainties decrease.  A different type of uncertainty can arise, however, which does not average away with more measurements.  Say, for example, that the meter stick you use to measure the heights of astronomers is accidentally short by 1%.  In this case, averaging the heights of more and more astronomers will simply get you closer and closer to the wrong value -- a 1% too-short value.  Astronomers label this kind of uncertainty a “systematic uncertainty”.

Part of the current push for larger and larger astronomical surveys is that we will be able to measure the distortions of more and more galaxies, and thus substantially reduce the *statistical* uncertainties on the inferred gravitational lensing matter maps. Part of the work that we have been engaged in lately has been to make sure that *systematic* uncertainties will be small enough that they don’t degrade the benefits of surveying billions of galaxies.


Color vision is great -- chromatic aberration not so much though

The particular effect keeping me occupied recently is the difference in distortions caused by the atmosphere for different colors of light.  The atmosphere bends light like a prism for light rays that hit it at an angle, bending blue light slightly more than red light.  It also tends to spread blue light out a bit more than red light.  

The colored lines in the image above show how much a light ray of a given color and at a given entry angle at the surface of the atmosphere will bend relative to one at 500 nm (perceived as blue-green by humans).  The different shaded regions show the wavelength coverage of each of the planned color filters for LSST.

The concern is that if you learn about atmospheric distortions from a blue star, and then try to remove those distortions from a red galaxy, then you will actually remove the wrong distortions at a subtle level.  This hasn’t been a concern for gravitational lensing experiments to date simply because it is a relatively small effect and the number of galaxy distortions available to measure has not yet been so large.  Up till now, to have worried about this would have been roughly the equivalent of worrying that your meter stick might be 0.1% too small when you only get to average the heights of 10 astronomers.  Since the variation of heights of astronomers is much larger than 0.1% and you only get 10 measurements, it doesn’t really matter if your meter stick is off by this amount.  On the other hand, if you suddenly had the opportunity to average together the heights of a billion astronomers, you might want to make sure your meter stick was accurate to better than 0.1%.


Correcting the rainbow

To solve the riddle of color-dependent distortion, we can take advantage of a feature in the design of essentially all future large imaging surveys: they take images through a variety of different color filters.  By comparing the amount of light received through a blue filter to the amount of light received through a red filter, for both stars and galaxies, we can estimate how far off the distortion correction we learn from the star is from the correct distortion correction to apply to the galaxy.  In fact, DES is using five color filters and LSST will use six color filters (these span the range from somewhat bluer than the human eye can see to somewhat redder than the human eye can see), all of which can be used to make this estimate.  By running simulations of many potential stars and galaxies, it’s possible to train a machine learning algorithm to predict the correction to the distortion correction (yes, you read that right) due to color-dependence.  We showed that this approach should be sufficient to reduce this particular systematic uncertainty to well below the statistical uncertainties of future experiments.

The left figure shows the color-dependent distortions for a variety of simulated galaxies before any correction is applied.  The right figure shows the distortions after a machine learning algorithm is applied to the data.  The horizontal bands are requirements for DES (wide band) and LSST (narrow band).  The fact that nearly all the data points land well within the LSST band on the right is good evidence that we can greatly reduce this systematic uncertainty to make it unimportant to the final LSST results.


Towards Accurate Cosmology

The goals of future surveys, which include measuring dark energy properties with the hope that we can narrow in on specific theoretical models, are ambitious.  We require high-fidelity simulations and catalogs, checks with real data, and an image analysis ‘pipeline’ that can precisely correct for tiny effects much smaller than have ever before been corrected before.  All of these take time to develop, which is why hundreds of astronomers are working on this now -- while DES is still recording data and over five years before LSST will begin.  When the final analyses do come around, we want to be sure that our meter sticks really do measure precisely one meter.

This work is supported by National Science Foundation grants PHY-0969487 and PHY-1404070.


------------ For more details see:

Impact of Atmospheric Chromatic Effects on Weak Lensing Measurements