By: Mandeep S.S. Gill and Michael Baumer
Editors: Rachel Wolf, Ross Cawthon, Kathy Romer, Anthony Kremin
For decades, cosmologists have been attempting to piece together the history and composition of the Universe. Since we now know that ~95% of the Universe’s mass-energy content takes the form of invisible dark matter and dark energy, this is a very difficult task indeed. However, with such enormous catalogs of galaxies such as those produced by the Dark Energy Survey (DES), we can use what we observe about the visible matter in the Universe (in the form of stars and galaxies) to infer the behavior of dark matter and dark energy.
Since galaxies form from the gravitational pull of regions with above-average amounts of dark matter, we can infer where over- and under-densities of dark matter must exist from the locations of galaxies on the sky (more galaxies imply regions of more dark matter). In addition, although dark matter is itself invisible, its effect on light from galaxies that we can see can also make its presence known via gravitational lensing. This effect causes all matter (including dark matter) to distort the images of distant galaxies in a characteristic way, which can be detected by precisely measuring the shapes of galaxies.
Several earlier posts in the DES DArchives series (Weak lensing by galaxy troughs in DES SV data, CMB lensing tomography with DES SV, A new method of measuring galaxy bias combining density and weak lensing, Cross correlation of gravitational lensing from DES SV with SPT and Planck) have described the technique of weak gravitational lensing in more detail. These earlier DArchives were based on results from the early "Science Verification Data," the first dataset analyzed by DES—which is now publicly available. Now, with the much larger Year 1 (Y1) DES dataset fully in hand and the images carefully processed into a format where further analyses can be performed, the collaboration is presenting its first Y1 results for constraining cosmological parameters (quantities that describe the behavior of dark matter and dark energy).
Powered by the additional data from the Y1 dataset and the hard work of hundreds of DES scientists, these are the most stringent results to date for two critical cosmological parameters: Ωm (which is a measure of the amount of matter in the Universe), and σ8(a measure of the initial "clumpiness" of matter in the Universe, just after the Big Bang era). To get such precise results represents a resounding and tremendous success for the technique of gravitational lensing—one of the newest cosmological analysis methods in our quiver.
Two-point correlation functions: the ingredients to our combined analysis
This specific paper presents the results of the so-called "3x2pt" analysis of the data, and builds on the work of no less than a dozen other DES papers (all of these papers are referenced within the 3x2pt analysis paper itself, and most were publicly released at the same time as the 3x2pt result became public—5 pm CDT on Thurs Aug 3, 2017).
"3x2pt" refers to the three different types of two-point correlation function measurements we use in DES to summarize our observations of galaxies, and the shapes of those galaxies turned into measurements that we can compare to a theoretical model.
1. Galaxy Clustering: The first of these, known as "galaxy-galaxy" correlations compares the position of each galaxy with the position of every other one. Galaxies, due to the attractive force of gravity, like to clump into structures, like to clump together into structures, rather than to distribute themselves at random. Therefore, we are statistically much more likely to find two galaxies close to one another than far apart. We measure this closeness (or technically, "correlation") through a parameter called w(θ), where higher w is more galaxy correlation, and w(θ)=0 would represent a random universe (θ is the separation between the galaxies). Changing the amount of matter or how clumpy the matter is would change the value of w(θ).
This is what we then see in the above plot from the paper, where the horizontal axis is the galaxy separation (in arcminutes), the vertical axis is the correlation w times the separation θ (this multiplication by θ causes the plotted values to increase and then decrease, despite w decreasing from left to right). The numbers in the upper left indicate which distance bin (where distance is measured from us to the object) we are looking at the correlation function in, from nearest on the left to farthest on the right. The points are our observations, and the blue line is from a ΛCDM model (i.e. our current best picture of the Universe) after the best fit value is extracted from combining information from this analysis with that of the other two techniques discussed below. The grey band shaded area has been excluded from our final analysis, because when galaxies are close together (where θ is small), complex interactions between galaxies (sometimes termed ‘gastrophysics’) introduce large uncertainties into the model.
2. Galaxy-Galaxy Lensing: The second two-point function, known as a "galaxy-shear" correlation compares the position of each galaxy with the shapes of every other one. Because galaxies like to clump together, and because those clumps contain the largest mass concentrations (which will lead to gravitational lensing), it follows that you are likely to find galaxies with the most distorted shapes in places where there are lots of other galaxies aligned with them.
Technically speaking, this galaxy-shear correlation function is a correlation between the locations of lens galaxies (which act as cosmic magnifying glasses), and the "tangential shear" (called γt) of galaxies around them. This is called tangential shear because the image of galaxies gets stretched tangentially relative to a central mass, as illustrated in the right-hand panels of this image: https://upload.wikimedia.org/wikipedia/commons/9/9c/Shapenoise.svg
This effect is seen in this figure adapted from Prat et al., which is a bit dense, but let’s break it down: in each of the five plots (each of which represents an analysis of lens galaxies at different distances from us), the horizontal axis is the separation of the lens and the galaxy whose shape it is distorting, in arcminutes, and the vertical axis is the tangential shear (the strength of the shape distortion).
The different colors represent different distances of the distorted galaxies, with blue being the closest and orange being the farthest. Just as the magnification of a magnifying glass changes as you move back and forth from the object you’re looking at, the strength of these galaxy shape distortions depend on the distance from the lens to the object. In this case, we observe that the farthest away galaxies are distorted more strongly than nearby ones.
As with the previous two-point function, the points represent our observations, and the line is the prediction of our ΛCDM model after the best fit value is extracted from combining all three techniques. The gray shaded region is excluded again for similar reasons to the previous two-point function.
3. Cosmic Shear: The third and final two-point function, known as a "shear-shear" correlation, compares the shape of each galaxy with the shap of every other one. By the same rationale as above, you would expect to find a highly distorted galaxy close to another highly distorted galaxy.
This is shown in this figure adapted from Troxel et al. Each plot shows the same measurement, using galaxy shapes measured via two different methods as described in Zuntz et al. The horizontal axis is again the separations between the pairs of galaxies whose shapes we are comparing, and the quantity on the vertical axis, χ+, is a measure of the correlation between the galaxies' shapes. As expected, we observe the shapes of close-together galaxies (small θ) to be more correlated that pairs that are further apart. The fact that these measurements come out the same for each of our methods of measuring galaxy shape (metacalibration and im3shape) is very encouraging!
Having put in all this effort to measure cosmological parameters, we want to be sure that the results we report reflect how the Universe actually is, rather than what any of us want it to be, or think it should be. History has shown that, despite our best efforts to remain objective, scientists are susceptible to biases that lead us to prefer results that agree with what’s been found previously (for examples and more details, check out the KIPAC blog post, They blinded it for science.
To avoid such biases, our analysis was "blinded" in several ways, much like a clinical trial of medicine. In a medical trial, the company that made the new drug would prefer results that show the drug works very well, so in order for a trial of a new drug versus placebo to be credible, the patients shouldn’t know which treatment they are receiving, the doctors shouldn’t know which patients are receiving the real treatment (if possible), and the data analysts shouldn’t know which treatment each patient received until the last possible moment, when the results are revealed. Critically, after the results are revealed, they can only be edited for pre-determined reasons, not just because people "don't like" the outcome.
For DES, in order to keep ourselves blind, before revealing the real results, we:
- Rescaled the galaxy shapes by a random amount that was not known to any of the scientists doing the analysis
- Never plotted theory expectations and data on the same plots (such a direct comparison would have let us "see how we were doing" along the way)
- Offset the extracted parameters by another unknown amount whenever the analysis codes were run, so we could see how small our error bars were but not what our final answers were.
The allowed changes to catalogs and analyses after unblinding were very minimal and were fully agreed upon beforehand (and are listed in Sec V of the paper).
One of the primary results is that the constraints achieved on two fundamental cosmology parameters: σ8 (which again indicates how much matter clusters in the Universe), and Ωm (the overall density of matter in Universe), are the most precise results on these parameters (i.e. the results have the smallest "error bars") ever achieved by optical astronomy.
[Technical note: all the plots we show here will list results on vertical axis says S8, not σ8, here. This is simply because S8 is a combination of σ8 and Ωm that is best constrained in lensing, and thus is the 'version' of σ8 often used in analyses.]
We will show these results in a type of graph called a ‘contour plot’ where usually 2 contours are shown: an innermost one (called the "1-σ contour") within which the likelihood of finding the result of the parameters plotted is 68%, and then an outer one (called the "2-σ contour") within which the likelihood of finding the result of the parameters plotted is 95%. The most likely point, and the one usually quoted as the resultant central value of the analysis, is somewhere close to the center of the innermost contour. In general, when we use the word "better results," we mean ones where the area of the contours of the allowed region for the parameters is smaller.
So now, in comparing the first two methods vs. all three combined, we achieve the results in the contour plot shown below, where: green is cosmic shear (our 3rd two-point function) only, red is clustering with galaxy-galaxy lensing (the 1st and 2nd two-point function combined), and blue is the combination of all three two-point correlations.
Comparison with external data
To test consistency with previously achieved results, we combine DES results with those from other observatories and surveys. The most constraining of these previous results are those from the Planck cosmic microwave background (CMB) satellite telescope. Below are the results if we combine DES and Planck information:
In the figure, the "Planck (No Lensing)" results show parameter estimates from Planck’s measurements of the cosmic microwave background (CMB). This figure allows us to make a pure comparison of cosmological parameters inferred from light from the early Universe (380,000 years post-Big Bang) to those determined from structures in the relatively modern Universe that have evolved over the past 13.7 billion years (as measured by DES).
We also combine results with data from other cosmological probes and surveys, including BAO (Baryon Acoustic Oscillations, another form of galaxy clustering) and Type Ia supernovae (whose brightness as a function of distance were used to discover the accelerating expansion of the Universe in 1998). Results from this combination of DES data, BAO measurements, and supernova data (from the Joint Light-curve Analysis), are shown below in blue.
S8 vs. Omega_m plot incorporating multiple data sources, courtesy of the DES collaboration." src="https://kipac-web.stanford.edu/sites/default/files/images/BAOSN.PNG" />
What we see on the left is that the "nearby" Universe (i.e. all the "stuff" closer than the CMB) taken all together now constrains S8vs. Ωm better than the CMB alone—and also just slightly disagrees with it, since the "1-σ contours" (i.e. again, the innermost curves for each color) do not overlap. Because they are so close, however, only just a slight disagreement with one other is indicated (i.e. something that would happen a bit less than 30% of the time, for a random Universe drawn with all the same exact properties).
Finally, the paper includes a summary of DES results in numerical form:
In this figure, the inferred values of S8 (a slightly rescaled version of σ8), Ωm, and w (the so-called "equation of state parameter" of dark energy—which is a parameter that describes how dark energy changes over time with -1 representing a model where the density of dark energy does not change at all) are shown. The first three lines are results using DES data only, but the two following lines in green, where the error bars are much smaller, show the power of combining DES with other datasets. Included for reference in the last four lines are, respectively, previous results from DES ("DES SV"), results from another recent galaxy survey (KIDS-450), Planck CMB results alone ("Planck No Lensing") and a combination of Planck with BAO and supernova data ("Planck+BAO+JLA").
The final outcome from this enormous amount of work on multiple fronts is that using data from Y1 alone, DES has had a very significant impact on our picture of cosmology. After many human-years of painstaking work from hundreds of contributing scientists, DES has now achieved some of the best precision on the specific cosmological parameters σ8 and Ωm that before had only been attainable from the "gold standard" in cosmology: the CMB.
We now rival that precision, and do not yet know if the small discrepancy we observe will resolve itself over time as we collect more statistics. As we lower our systematic errors in the future and these contours shrink, we will see whether they eventually overlap—or harden into separate areas that indicate something we do not yet understand about the Universe. Ahead of us are the Year 3 analyses, and in 2017–2018, the next observing season of DES. What will an analysis of all five years of data reveal? Will it show closer agreement to Planck and other observables? Or steadily diverge as the "error bars" continue to shrink? No one yet knows. And therein lies the beauty, magic, mystery, and adventure of doing experimental science.
We are an intrepid and unstoppable species, irrepressible in our drive to stumble about in the dark and trying to do the best we can while bruising our shins and bloodying our knuckles on the rocks about us, trying to figure out: where we are, where we came from, where we are going—and why. And the DES Y1 results are a significant step in elucidating all of that, shining a light in one particular direction, revealing that our previous mental image of what was out there doesn’t yet fully match what our flashlight is illuminating.
Work remains. More exploration must be done.