# Can the distance of a quasar be determined accurately?

As noted in How can a quasar be 29 billion light-years away from Earth if Big Bang happened only 13.8 billion years ago?, the wiki about quasars still contains the following misleading sentence:

"The highest redshift quasar known (as of June 2011) is ULAS_J1120+0641, with a redshift of 7.085, which corresponds to a proper distance of approximately 29 billion light-years from Earth."

But even if the "strange 29 billion" is replaced by the "correct 12.9 billion", the fact remains that the actual measurement is "a redshift of 7.085". The "proper distance" is only a different way to express that measurement. It's not clear to me how "accurately" this describes the distance of the quasar, because the quasar surrounds a black hole and rotates quite fast. So there are at least two additional sources for the redshift, but how significant is their contribution?

• My general impression is that where light is emitted in the quasar is far enough away from the black-hole proper that rotation and gravitational redshift can be mostly negated. Commented Aug 8, 2011 at 1:32
• I would suggest closing this, since it's pretty much redundant with this physics.stackexchange.com/q/11803 and this physics.stackexchange.com/q/12049
– user4552
Commented Aug 8, 2011 at 2:14
• The question only looks redundant, because I read the mentioned questions during my research, and tried to formulate the question in a similar way (and because the 29/12.9 thing really confused me a bit). But this question is about the magnitude of "corrections for redshift effects", which are hinted at in the wiki about Halton Arp: "Moreover, the spectra of the high-redshift galaxies, as seen from X-ray to radio wavelengths, match the spectra of nearby galaxies (...) when corrected for redshift effects." Commented Aug 8, 2011 at 9:40
• Here is some information re Arp's crackpottery: physicsforums.com/showthread.php?t=506994 The "intrinsic" redshifts proposed by kooks like Arp are not gravitational or kinematic Doppler shifts; they are shifts that they propose occur due to some entirely unknown physical process, for which there is no evidence.
– user4552
Commented Aug 8, 2011 at 15:14
• That link sort of provided an answer to my "real" question: [Stockton, 1978] "Redshifts have been obtained for 25 of the 29 galaxies, and 13 galaxies in eight fields have redshifts within 1000 km/s of that of the QSO in the field." This indicates to me, that the measured redshift values are often accurate to more than 0.3%, even without correcting any redshift effects. Later papers also report velocity dispersion around 1000 km/s (at z~0.9), whatever that means. Based on the papers, Arp's suggestions weren't crackpottery back then, only that he still believes in them today is foolish. Commented Aug 10, 2011 at 11:31

You may gain some intuition on cosmological distances by exploring cosmocalc which gives a light travel time of 12.9 Gyrs for the redshift of 7. This site is nice because it shows you the parameters for the "concordant" cosmology that describe our Universe. These parameters describe how the universe is expanding and how it expanded in the past. One cool thing to try out is varying the redshift and seeing what ages for the universe you get at that redshift. This gives you a feeling for how a big change in redshift at high $z$ gives you little change in the age of the universe. For example a change from $z=7$ to $z=8$. But this represents a pretty big shift in the spectrum (challenging detection). A decade ago astronomers did not know whether the universe was flat or what $\Omega_M$ was (density in units of a flat universe). But now there are a number of different astronomical measurements that have all agreed on (or given small error bars around) these parameters. Hence the term "concordant."

To answer your question, a light travel time is a proxy for distance, it is an integrated quantity and so a meaningful metric for distance. However you can't really send a message back as the universe has been expanding since the quasar emitted the light that we are detecting. The second part of your question concerned accuracy. Probably the most meaningful error is the error in the estimated redshift. As you mention the emission lines can be broad and this would contribute to the error. The emission lines could be misidentified though since there is a Lyman alpha forest giving absorption lines from material in between us and the quasar this is unlikely for this object. The quasar could be moving w.r.t to the `Hubble flow' or mean expansion of the universe. For example the quasar could be a black hole that ejected from a galaxy. This type of error is likely to be less than the speed of light and so would at most contribute something like an error of 1 to the redshift (and that would be a really big error and so it's probably less than this). Likewise the emission lines could be broad but at most giving an error of about this size. At most. You can turn an error in redshift into an error in the frequency or wavelength shift of the spectrum. Even for low resolution spectra an error of 0.1 in $z$ would be just enormous. Errors in the concordant cosmology parameters would also affect the estimated light travel time. These days these parameters have errors of a few percent or so, -- using the cosmocalc you can figure out what affect variations in these ($\Omega_M$, $\Lambda$, and the hubble constant) would have on the light travel time.

• "BTW the mistake in the travel time is suspiciously close to a factor of 3. The factor of three comes from the rule of multiplying distances in parsecs by about 3 to get lightyears." This is incorrect. It's not a mistake, and it has nothing to do with parsecs. Here is an explanation of where the 3 comes from: physicsforums.com/showthread.php?t=506987 It's basically because $a\propto t^{2/3}$ for a matter-dominated FRW solution.
– user4552
Commented Aug 8, 2011 at 20:19
• @Ben thanks for clarifying, however this seems to me conceptually even worse than multiplying by 3. Yikes! ;) Commented Aug 8, 2011 at 21:03
• Undid my -1 vote since you fixed the mistake.
– user4552
Commented Aug 8, 2011 at 21:51

First off, you seem to be getting confused over the same issue that the OP in How can a quasar be 29 billion light-years away from Earth if Big Bang happened only 13.8 billion years ago? . As far as I can tell, both you and that person believed that the proper distance x traveled by light over an interval of cosmological time t should be x=ct. This is incorrect, because while the photon is in flight, the universe expands. Here http://physicsforums.com/showthread.php?t=506987 is a more detailed explanation of that point. Both the 29 billion l.y. figure and the 12.9 billion years are correct.

The line spectra used to determine the redshifts are emission spectra from clouds of gas that lie between us and the quasar. There will be a gravitational redshift, but believe it or not, the astronomers in this business are not complete idiots, and this has occurred to them, and they know how to handle it. I believe the gas is far enough from the event horizon that the effect is actually negligible.

Similar considerations apply to the rotation. The infalling gas may be moving quite fast, but the emission spectrum is from gas that is much farther out, and is not moving as fast. In addition, there will tend to be a cancellation of the kinematic Doppler shift on the average, since equal amounts of emission occurs for gas moving away from us and gas moving toward us. (It won't be an exact cancellation, because SR has transverse as well as longitudinal Doppler shifts.)

• Thanks for clearing up my confusion about the 29/12.9 thing, it's clearer now. However, your explanation with respect to the redshift contradicts a bit what the wiki about quasars says: "Quasar redshifts are measured from the strong spectral lines that dominate their optical and ultraviolet spectra. These lines are brighter than the continuous spectrum, so they are called 'emission' lines." Commented Aug 8, 2011 at 9:55
• It's sad that you got the impression I think astronomers are idiots. My point was that normally the actual measured redshift without any correction will be reported, even if it is also expressed as "proper distance" or another intuitive physical quantity. Possible redshift corrections would be less unique, so they will only be applied for comparisons with nearby galaxies. Commented Aug 8, 2011 at 10:01
• @Thomas Klimpel: Thanks for the correction re emission versus absorption. I'll edit my post.
– user4552
Commented Aug 8, 2011 at 15:10
• You replaced 'absorption' by 'emission', but that makes your answer inconsistent. The statement "The line spectra used to determine the redshifts are emission spectra from clouds of gas that lie between us and the quasar." is certainly wrong, because this type of "spectra from clouds of gas" would be absorption spectra. For me, the quote from wiki about quasars indicates that the measured spectrum is emitted by the quasar itself. Commented Aug 10, 2011 at 11:43