# Is God right-handed? Spiral galaxies’ rotation and isotropy

A cherished principle of cosmology is isotropy—that things look the same whatever direction you look.  The cosmic microwave background, radiation left over from 300,000 years after the Big Bang, is largely isotropic (down to one part in 10,000). Inflation, the theory that in the moments just following the Universe’s birth, space itself expanded faster than the speed of light, generically predicts isotropy, too. $^*$  Obviously, the Universe isn’t isotropic on very small scales.  For instance, if you look in one direction from Earth, you see the Sun, and in another, Uranus and Neptune (depending on the time of year, of course!).  But on what we call “cosmological scales”, on the order of 1 Megaparsec ( $3\times 10^{21}$ meters), cosmologists assume it is.  What if they’re wrong?

The paper I discuss today suggests they might be. Lior Shamir analyzes 126,501 spiral galaxies from the Sloan Digital Sky Survey (SDSS) for “handedness.”  What is the handedness of a spiral galaxy? Simply the direction in which it rotates as viewed along our line of sight.  Counterclockwise (looking at its axis of rotation along our line of sight) is right-handed, just like your right-hand fingers curl counterclockwise if your right thumb is pointing up. Clockwise is left-handed, by analogy with the left hand.  Obviously, handedness cannot be determined if the spiral galaxy is edge-on (i.e. we can’t see the spiral pattern), so Shamir eliminates edge-on spirals.  His computers convert the galaxy images to intensity (how much light is received) as a function of radius from the center, and look for peaks in that curve that correspond to the arms of the spiral galaxy. The gradient of the peaks (whether they are getting stronger or weaker) can be used to determine whether the galaxy is rotating counterclockwise or clockwise. The principle of isotropy predicts that half of the galaxies should be doing one and half the other.

However, Shamir finds that the asymmetry, measured as A=(R-L)/(R+L) (the number of right-handed minus the number of left-handed over the total), is a cosine-like function of right ascension (RA).  This means that the proportion of right- or left-handed galaxies that you find depends on which direction you look in the sky. (Recall that lines of constant right ascension are just like lines of constant longitude: see picture below.) Lines of constant right ascension; they rotate with the Earth, so stars' RA changes periodically in time. This diagram is just to remind you what RA is because in the plot from the paper below, the asymmetry of galaxies is given as a function of RA. Image credit: http://www.astronomyforbeginners.com/

This dependence may seem mysterious at first, but it would be precisely what occurred if the spin axes of spirals were all preferentially aligned parallel with one global axis.  In this case, the asymmetry would vary with the cosine of the angle between this global axis and our (well, SDSS’s) line of sight to the galaxy, because the observed spin of the galaxy is the projection of the true spin onto the line of sight.  The projection is given by the cosine of the angle between the two. Plot of the asymmetry A=(R-L)/(R+L) (see text) as a function of right ascension, with a cosine function fit to it. If the principle of isotropy is right, the best fit should be a line at y = 0---clearly not the case! From paper.

Shamir then asks what this global preferred axis is, and finds it is at RA = 132 degrees  The axis is the same for both low-z (z<.085) and higher-z (.85<z<.3), though the signal is much stronger for the low-z part of the sample.  (z is redshift, which is a measure of how quickly the galaxy is moving away from us.  As Hubble discovered in 1927, this is a proxy for distance, because z is proportional to d, where d is how far away from us the galaxy is.  In turn, how far away from us the galaxy is tells us how far back in the past we are looking, since the light from it we see now will have taken longer to travel (and hence left earlier) the larger the distance.  Hence higher redshift means “older.”) Using a $\chi^2$ analysis, Shamir finds the probability for this to occur by chance is on the order of 1 in 10,000. ( $\chi^2$ measures the probability of observing a given result by chance taking the true answer as a given—e.g., if galaxies really don’t have a preferred spin, what is the probability the observations would look like they do?)

A possible limitation he notes is that SDSS itself may be biased in detecting galaxies based on their handedness—but as he points out, even if that were the case one would not expect a cosine-like variation in handedness, but rather a horizontal line at some y not equal to zero on the plot I duplicate here.

In conclusion, it is worth noting that others have found similar results; a couple additional papers are linked below.  While Shamir does not comment on the possible explanations for the alignment, these papers speculate that it may be related to the location of galaxies on a filament along the edge of a cosmic void, as shown below in an image of large-scale structure. Image of the cosmic web---filaments along which galaxies live, and voids where there is only empty eternity. This image is probably representative of how a patch about 5% of the area of the observable Universe would look. You might notice that there is more structure in the lower left-hand corner; even on scales as large as this image, some inhomogeneity is expected, but likely not a large percentage of the average density. From http://www.astro.cornell.edu/~rbean/research.html $^*$ (that’s allowed, it’s only matter that has to honor Special Relativity’s speed limit!) I'm a 2nd year grad student in Astronomy at Harvard, working with Daniel Eisenstein on the effect of relative velocities between regular and dark matter on the baryon acoustic oscillations. I did my undergrad at Princeton, where I worked with Rich Gott on dark energy, Jeremy Goodman on dark matter, and Roman Rafikov on planetesimals. I also spent a year at Oxford getting a master's in philosophy of physics, which remains an interest.

1. So I don’t get this analysis. A straight line looks as much a fit, failing in one RA bin too, while having one less degree of freedom unless I’m mistaken.

• A straight line would have 2 degrees of freedom, a slope and an intercept. I guess a cosine would have three: amplitude, period, and phase. So yes, if a straight line can fit the data as well as a cosine, it is better. But chi^2 tests do account for this, penalizing a fit for each extra degree of freedom it introduces. For instance, an extreme case would be a fit that had the same number of free parameters as the number of data points; that could fit the data perfectly. But that wouldn’t really be what one was looking for; so the chi^2 penalizes it for having lots of degrees of freedom. So the paper here finds that, even with this accounted for, a cosine is a better fit than a line, though that might not be obvious from the graph.

2. I’m always amazed how little astronomers actually care about their data analysis. If you look at that example plot just with your bare eyes, you see that a zero-constant would be an equally good fit.

Another thing astronomers will never learn: Don’t use p-values for model comparison! Here they argue that a p-value of 0.0001 suffices to reject the 0-constant. Anyone who believes in this, I recommend to read Sect. 8.2 point (2) in Kass & Raftery:

http://www.stat.cmu.edu/~kass/papers/bayesfactors.pdf

The basic issue is very simple: A p-value is an answer to the wrong question, it doesn’t tell us anything about how well a model matches the data.

The data analysis in this work uses inappropriate statistical methods and therefore, its conclusions cannot be trusted. Just from looking at their figure, hardly any conclusion can be drawn.

• While some are critical of chi^2 tests, etc., it is a standard technique in astrophysics and I think one that basically makes sense, if there is reason to believe the assumptions about the underlying distributions are satisfied.
And in terms of rejecting the work’s conclusions, yes, I also had my doubts, as the cosmological principle is a pretty consensus position, but as I noted at the end of the post, there are several other papers, which have been published in reputable journals, that also find this kind of result. So I think what we can say is that more data is needed.

3. 