Thursday, August 6, 2009

Redshift Z In The Wild

Redshift z is used in astronomy to determine how far away an object is. The more the light from that object shifts to red, the farther away it is. Wikipedia has a good description of redshift.

While surfing NASA's site, I decided to record the redshift z and distance of objects when they were provided in the description. The distances of these objects ranged from 250 million light years away to 12 billion light years away.

What I found was rather surprising. The data don't seem to correlate very well. The redshift z doesn't seem to have an algorithmic relationship to distance.

You can see this for yourself in the charts above. The first chart shows redshift z as a blue line overlaying green distance bars. The two curves don't match up! The next two charts divide distance by redshift z and redshift z by distance. These two charts highlight that there is no smooth curve relating the values of redshift z and distance.

I also tried normalizing the redshift z and distance values to a scale of 0 to 1. This didn't change the results, as you can see in the image below.

I don't know if these numbers simply represent errors in the values provided on NASA's website, if there's something I'm misunderstanding, or if the redshift z theory really uses these unusual values. I think I'll shoot an e-mail to NASA and try to get an explanation.

Here is what the relationship between redshift z and distance looks like in theory. You can see how smooth the curve is in theory. Not at all what the curve looks like in practice.

Redshift z values are multiplied by 10,000 in the charts I provided. This was done so they'd be on a similar scale to distance values, otherwise you wouldn't be able to see them in the charts that had scales large enough to show distances. Scaling the redshift z values in this way does not affect the results I discuss here.

Data (Late Edit: By request, chart modified to include object names)

Wikipedia Cosmology Distance Measures


  1. Your inputs range from 1999 to 2009, during which time the preferred estimates of the Hubble constant and omegaM may have changed (John Huchra's website gives a good intro to the former (; Ned Wright's gives a good intro to cosmology ( In any case, what is observed is z; distance is estimated from z via a calculation like that found on Ned Wright's site (some nearby objects may have distances estimated independently of z).

  2. Thank you jeant8. I did a search on the net and it turns out the Hubble constant has changed several between 1999 and 2009.

    However, all of the changes were rather minor, so I'm not sure if they're strong enough to account for the data here. I'll do an analysis based on year and post the results.

  3. It's not just the Hubble constant, but the set of cosmological parameters (see Ned Wright's tutorial). Today's standard is "737", with the Hubble constant 70 km/s/Mpc, OmegaM 0.3, and Omegavacuum 0.7 (this is a flat universe). At the inferred precision of the distance estimates (~1 or 2 significant figures), using the best fit parameters from the WMAP Fifth-Year results won't make anything other than a trivial difference (70, 0.28, and 0.72 IIRC). Let's not forget that strong observational evidence for lambda ("dark energy") was first reported only in 1998/1999, so perhaps the earliest datapoints in your table come from cosmological models with quite different parameters.

    Some of the data seem wildly wrong (z = 0.89/3500 Mly, for example), which may be due to some errors in the originals (e.g. 3500 Mpc vs 3500 Mly, typos), or ambiguity over which 'distance' is being estimated (light travel time vs comoving radial distance perhaps?).

    Perhaps you could update the table by indicating which object(s) is associated with each redshift/row?

  4. Of the 20 datapoints, 7 are discrepant, in the sense of the stated distance being >~10% different (+ or -) from the "737" cosmological model estimated distance.

    One of those is the sole non-Chandra record (so it's highly doubtful NASA's reply will help with this).

    Four are from the same 2006 Chandra PR (five objects, of six, mentioned in it have both z and estimated distances).

    The remaining two are HydraA and the central region of the Coma cluster; IIRC there are estimates of the distances to galaxies in both clusters derived using methods quite independent of z.

  5. Here is a sample of estimates of the distance to the Coma cluster, published before 2002 (the date of the Chandra PR):

    Distances of the Virgo and Coma clusters of galaxies through novae and supernovae ( result expressed as a Coma cluster distance modulus (35.05 mag, considerable +/-), together with an estimate of "Virgocentric infall velocity", based on novae and supernovae; this is a direct distance determination, using the 'distance ladder' method (i.e. a way to estimate the Hubble constant). H0 = 70 +/- 15 km/s/Mpc.

    Distance to the Coma cluster and the value of H0 ( distance estimate based on the B band Tully-Fisher relationship (distance modulus 34.5 +/- 0.4); H0 = 92 +/- 16 km/s/Mpc.

    Distance to the Coma Cluster and a Value for H_0 ( estimated luminosity distance of 107 +/- 3 Mpc and 103 +/- 8 Mpc (both are model-dependent); based on globular cluster luminosity function.

    The Distance to the Coma Cluster from Surface Brightness Fluctuations ( distance estimate of 102 +/- 14 Mpc, based on surface brightness fluctuations method.

    In other words, several largely independent 'distance ladder' estimates of the distance to the Coma cluster, published before 2002, are ~100 Mpc (~330 Mly). At the +/- 10 Mly level of accuracy, which distance is estimated (light travel time, comoving radial, angular size distance, luminosity distance) doesn't matter as they vary by no more than ~15 Mly. Neither does the choice of values for the cosmological model, and even the Hubble constant is only modestly constrained.

    Now why did whoever wrote that Chandra PR decide to use 370 Mly, when the consensus of the day seems to be ~330?

  6. I can't say why NASA did what they did, Jean. I can say that I'm working with NASA now to try and get to the bottom of this. Unfortunately, it's not off to a good start. If I understood the instructions correctly, I was sent to the SRSS area of the NASA web site that has public data available. But it seems the data was taken with a camera that cannot correctly record redshift.

    I may have misunderstood the instructions I was given, of course. I've expressed my concerns in the comments to the second redshift post. We'll see what response is given.

  7. I read the comments on Red Shift Z In The Wild II, and I think it might be a good idea to take things a little more slowly (I'll also add a comment on II too).

    The redshift, or z, of an extragalactic object (distant nova, supernova, galaxy, globular cluster, quasar, ...) is relatively easy to estimate; once you have a spectrum of the object, you identify the lines in it, measure their wavelengths, and z is just a simple calculation away.

    Most often, redshifts of extra-galactic objects are obtained in the 'visual' part of the electromagnetic spectrum, which is that optical telescopes on mountaintops observe in, and stretches from the near UV to the near IR (~300 nm to 1 micron). However, redshifts can be, and have been, obtained using space-based observatories, in the part of the UV that the atmosphere blocks (down to the Lyman limit, ~90 nm), in the x-ray region, in the radio and microwave region (from here on the Earth as well as in space), and in the mid and far IR (mostly from space).

    Part of the SDSS project - which is only funded partly by NASA (the "S" stands for "Sloan", as in the Alfred P. Sloan Foundation; they are the major contributors IIRC) - involves taking spectra of objects identified as candidate galaxies (and quasars) by the main workhorse; these spectra are all in the public domain, as are details of the processing pipeline and the algorithms used to automatically make estimates of z (and estimates of the confidence of that z).

    Now the redshift of interest to cosmologists is not the z that comes from the raw spectrum. For starters, the observatory is moving around the centre of the Earth, and the Earth is moving with respect to the solar system barycentre (crudely, the Sun), and the Sun is moving with respect to the centre of mass of the galaxy we are in (the Milky Way). Fortunately, these motions are well understood and well characterised, so converting the observed z to a 'heliocentric' z, or a 'galactocentric' z, etc is quite simple and straight-forward.

    And it doesn't matter much anyway; a motion of 300 km/s is trivial, cosmologically speaking (it's a z of only 0.001) ... as long as you're working at one significant figure precision, and as long as the extra-galactic objects are further away than 50 Mpc (say). By the way, the number of published redshifts, of extragalactic objects, is now well over a million, and may be in the tens of millions (SDSS alone has published nearly a million galaxy redshifts, and over 100,000 quasar ones).

    Estimating the distance to an extragalactic object is much, much, much more difficult, especially for those > 50 Mpc distant. In my comment on the Coma cluster, I referenced four independent methods (novae+supernovae, Tully-Fisher relationship, globular cluster luminosity function, and surface brightness fluctuations); there are several others. The good news is that all independent methods give consistent estimates; the bad news is that a) it is very difficult to use more than two or three methods for the same object, and b) all estimates have considerable uncertainties (at least 10%). Historically, there was also a much bigger worry: systematic effects of unknown size (this is the primary reason why estimates of the Hubble constant changed so much from the 1920s to the 1960s).

    Now Press Releases (PRs) are not primary science documents; papers published in relevant peer-reviewed journals are (conference proceedings come a close second, but they are not usually peer-reviewed). And there's many a slip betwixt paper and PR, if I may mangle the saying, as I have demonstrated with the Coma cluster distance.

    Which brings me to this: to what extent are you interested in how and why whoever wrote the Chandra PRs screwed up (or not), vs the scientific data on distances and z?

  8. I'm not interested in going after whoever screwed up at all, other than to say that educating the public with bad data probably isn't helping anyone.

    I'm much more interested in seeing some decent red shift data come from all this.

  9. I think it's fair to say that almost no one is happy when a PR containing misleading or inaccurate info is issued by a scientific institution! I often wonder about the extent to which those who write such PRs are familiar with the scientific content; I'm sure some PR authors are very good (either quite knowledgeable about the content, or fully aware of holes in their knowledge and hence reluctant to issue a PR without adequate vetting), but it's also pretty obvious that some authors are not.

    Is it only for the objects in Chandra PRs (that you're seeking decent redshift estimates)?

    In any case, have you heard of NED (NASA/IPAC Extragalactic Database)?

    As with any database, you do need to be careful in querying it, and in interpreting its records ...

  10. Using NED, I learned that HydraA has many, many other IDs; the top two are MCG -02-24-007 (which is an optical galaxy catalogue number) and 3C 318 (which is from perhaps the most famous radio source catalogue).

    It does not have any redshift independent distance estimates, according to NED.

    With a bit more time spent with Google, I found a paper (preprint) that seems to be based on the Chandra observations mentioned in the PR, "CHANDRA X-RAY OBSERVATIONS OF THE HYDRA A CLUSTER: AN INTERACTION BETWEEN THE

    This source gives a luminosity distance of 240 Mpc, based on the "737" cosmological model.

    So, somewhat like with the Coma cluster, we are left with the mystery of why the person(s) who wrote the 1999 Chandra PR used an estimate of its distance that is at odds with the what astronomers working with the Chandra data used, and with what the consensus was (at the time).

  11. You raise some interesting points in comments in II, magicjava!

    Some of my own thoughts on communicating with John Q. Public: I think the way the Chandra PRs are done is particularly poor, in at least one respect. ESA, NASA's European counterpart, seems to provide a reference to the paper (if any) which its PR is related to, as does Gemini, the ESO, etc, etc, etc.

    Here is an ESA example, from 2000:

    On the other hand, the Chandra website does have quite a few Tutorials, which do seem to cover the key concepts re cosmological distances. And there is a blog!

    More generally, I think your comparison of astronomical results with yards per carry and accounting misses a critical difference; namely, the rules for the last two are made, and changed, entirely by us humans ... the 'rules' of the universe are not ours to dictate.

    Did you know that there is a journal devoted entirely to the topic of communicating astronomy with the public? In fact it's called CAP (Communicating Astronomy with the Public)!

    Have you get a reply yet? And did you consider posting a comment or two to the Chandra blog? I notice that there's a quite recent blog entry on Stephan's Quintet ...

  12. One more thing: while the Chandra X-ray Observatory might be NASA's, the Chandra website that you got the PRs from is actually operated by the Smithsonian Astrophsycial Observatory in Cambridge, Mass.

    And I think you'll find the same sort of arrangement (management, operations, etc contracted out, sometimes to more than one party) for the Hubble Space Telescope (actually the Space Telescope Science Institute reports to AURA), CLUSTER (looks like the ESA is the public face for this joint NASA/ESA mission), Spitzer, ...

  13. Wow! That's a lot of info Jean. Thanks! I'm going to start by trying to reproduce my original chart using NED.

    Once I'm done with that maybe I'll drop by the CAP site and enter a plea for more accurate info in press releases. :)

  14. You're welcome magicjava.

    (Aside: I was able to spend quite a bit of time on this due to being essentially immobile - due to an injury - and I found solving puzzles more distracting of my physical condition than reading! I expect to be back to normal tomorrow, so after today it's unlikely I'll be doing more than just dropping by occassionally to read)

    Earlier I mentioned that four of the seven (six from Chandra PRs) discrepancies came from the same 2006 PR. Well, that PR actually does give a reference! "Determination of the Cosmic Distance Scale from Sunyaev-Zel'dovich Effect and Chandra X-ray Measurements of High Redshift Galaxy Clusters, M. Bonamente, Astrophysical Journal, 2006 August 10 (astro-ph/0512349)", so reading the source should settle the question of whether, once again, the author(s) of the Chandra PR screwed up (or whether the "Distance estimates" are the same as in the paper).

    Here's a link to the ArXiV preprint:

    And here's what I found:

    A. the paper examines 38 clusters; the Chandra PR covers only six

    B. the paper presents three, somewhat independent, estimates of the angular diameter distance to each cluster, in Tables 2, 4, and 5

    C. the redshifts are taken from other papers; four different sources for the five clusters in the PR

    D. a straight average of the three estimates, converted to Mly, for the five clusters is as follows (3 sig figures): 1950 (A1914), 2640 (A665), 3930 (MACS J1149.5+2223 - the ID in the PR is wrong!), 4240 (CL0016+1609), and 3120 (CL J1226.9+3332).

    Of the five clusters, three have (angular diameter) distances close to what the 737 cosmological model predicts, based on the observed redshift. The two outliers (A665 and CL J1226.9+3332) have estimated distances that seem to be less than twice the 68% confidence level uncertainty (error analysis is quite tricky, but I think my conclusion is robust).

    So, in summary, it seems that the distance estimates in at least three Chandra PRs are wrong; they are wrong in that they do not correctly reflect what's in the scientific papers on which the PRs are (apparently) based, and wrong in terms of what the consensus of the day seems to have been (on the Coma cluster distance).

    Finally, the 2006 paper is wonderful; it works out estimates of distances using a direct technique (i.e. avoiding all the problems of the 'distance ladder' one), and finds that the value of the Hubble constant is consistent with what other astronomers have found, using completely different objects and techniques!