200,000 Quasars Confirm Einstein's Prediction

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Would 200,000 quasars qualify as enough of a statistical sampling to bury intrinsic red shift in shattered pieces in a concrete slab at the bottom of Yucca Mountain?

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The last time I felt a warm fuzzy feeling, I was informed by my doctor that it was just gas.

That's what I was thinking.

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Everything I need to know I learned through Googling.

Sure as a sample size, 200,000 quasars could potentially bury the local quasars/intrinsic redshift theory. However, the question is whether or not the assumptions of this study actually allow a refutation of intrinsic redshifts. For any scientific investigation you must know exactly what it can "prove" and what it can falsify. I'll explain more about this later - maybe this weekend if not sooner, but this study is not a study that can falsify the hypothesis that quasars are local and contain intrinsic redshifts.

Perhaps not as a direct measure of redshift, but if you consider each quasar and the number/distance of the various galaxies which amplify the light emitted by each individually, you can dismiss the concept of locality, which undermines the idea of wildly different redshifts at equivalent distances.

That does appear to be one aspect of the intrinsic redshift arguement that was quantified sufficiently in this study to be applicable.


Edit: typo correction

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The last time I felt a warm fuzzy feeling, I was informed by my doctor that it was just gas.

Again, you have to look at the actual assumptions underlying this study. I'm still reading the research article that was posted on astro-ph, so as soon as I've had a chance to digest that I'll clarify what I mean.

Would one of you gents be good enough to explain the idea of "intrinsic" red shift and why this quasar study may put it to rest. I understand the concept of redshift and blueshift of light (basicaly dopler effect translated to light) but the intrinsic part is lost to me.

Also if someone could briefly explain how quasars are expected to magnify light that would be great. Is it a gravitational lensing sort of deal?

Thanks in advance.

K

[hand on forehead, shielding eyes]
Hmm. I don't see any John Kiernan around. Odd.
John Kiernan? John?
Hmmf.
[shrug]

;-)

CJSF

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I was looking up past the city lights
But the city lights got in my way

See the constellation ride across the sky
No cigar, no lady on his arm
Just a guy made of dots and lines

-from "See The Constellation"
by They Might Be Giants

Just to be clear - intrinsic redshifts are not a phenomenon that is accepted by mainstream astronomers. So we're talking about a controversial topic.

I'll try to keep the explanation short. In mainstream cosmology it is assumed that almost the entire observed redshift of a quasar or galaxy is cosmological - resulting from expansion of the universe. However, shortly after quasars were discovered the Astronomer Halton Arp noticed that many of the quasars appeared to be placed in the sky near active and disturbed low redshift galaxies. Since some of the quasars were aligned in pairs across the galaxies Arp put forward the interpretation that the quasars were ejected from the nuclei of the active galaxies.

Since quasars have very large redshifts in mainstream theory they are interpreted to be very distant. If Arp is right, they are not very distant – they are local. However that would mean that most of their redshift is not from expansion but must have some other cause. This other cause is generically referred to as “intrinsic redshift” by those of us that support this interpretation because the redshift would most likely be due to some intrinsic property of the quasars.

If intrinsic redshifts are real, the cause is unknown. Asking what intrinsic redshifts are is similar to asking what dark energy or dark matter is in that there is some theory and speculation, but a specific answer has not been scientifically proven.

At any rate, there have been numerous papers published by Arp and others presenting evidence supporting the interpretation that some high redshift objects can be associated with much lower redshift objects. The mainstream response is that these associations are not real, but simply accidental alignments of background objects with nearby lower redshift galaxies.

Here are two recent papers that discuss several of the strongest candidates for real associations between high and low redshift objects. You can download the papers by clicking on “PDF” and look at the images in the papers to get the quick picture of the evidence:

NGC 7603 and NEQ3

What the papers is proposing is that the quasars are very distant as the mainstream interpretation of redshift would require and that the light from those quasars is magnified by gravitational lensing from intervening masses.

Ok I've had a chance to read the article on astro-ph . The reason the study does not refute the local quasars hypothesis is that they assumed the quasars are background objects relative to the galaxies in conducting the analysis. As such their analysis and conclusions depend upon the interpretation that the quasars are not local. They were not testing local vs cosmological quasar distances.

It is also important to note that the study does not present evidence that this or that specific quasar is lensed. Rather they can conclude that if the quasars are background objects, their distribution is consistent with the concordance model parameters.

There are two tests that could definitively falsify Arp's hypothesis that quasars are local. Time dilation - which it has been found quasars do not exhibit - a result consistent with them being local. If time dilation was identified in QSO's that would place them at cosmological distances and therefore falsify Arp's proposal. Proper motions provide another test. If quasars are local ejected objects, then proper motions will be detected in reasonable time frames. If Arp is wrong than such studies will not find proper motions.

You seem to be dissembling a bit here, dgruss. While it's true that this paper does not set out to address the "intrinsic redshift question" at all (probably because it's not even considered to be a question to this substantial list of astrophysicists*), NEVERTHELESS, the findings of this paper go quite a bit beyond being "consistent with the concordance model parameters", as you so euphemistically put it. This paper provides a perfectly logical explanation strongly supported by millions of observations for the reason we often find bright quasars near the same line of sight as galaxies. This explanation simply relies on General Relativity. This explanation does not require us to abandon the redshift-distance relation (as Arp's explanation does), a relation that has been one of the key tools of astronomy and astrophysics over the last 80 years. This explanation does not require us to accept any of the wildly speculative explanations about "mass varying with age" etc. put forward by Arp & Narlikar. You're right - this paper does not "refute" the local quasar hypothesis, but it does appear to make it unnecessary.

* Ryan Scranton, Brice M´enard, Gordon T. Richards, Robert C. Nichol, Adam D. Myers, Bhuvnesh Jain, Alex Gray, Matthias Bartelmann, Robert J. Brunner, Andrew J. Connolly, James E. Gunn3, Ravi K. Sheth, Neta A. Bahcall, John Brinkman, Jon Loveday, Donald P. Schneider, Aniruddha Thakar, Donald G. York

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Everyone is entitled to his own opinion, but not his own facts.

This is not true, there is a distance related redshift component in Arp's model. Only part of the redshift is intrinsic.

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Once again you try to characterize my motives - as usual incorrectly.

Cougar, the paper does not refute the local quasar hypothesis because it was not designed to test the local quasar hypothesis. The authors assumed from the redshifts that the quasars were background to the galaxies. So to draw any conclusions about implications for the local quasar hypothesis would be circular reasoning.

Which is also why their results do not make the local quasar hypothesis unnecessary. Their paper has absolutely no implications for the local quasar hypothesis one way or the other. What their paper indicates is that if the quasars are background to the galaxies, then their distribution is consistent with GR.

I've specified above which tests can verify/refute the local quasars hypothesis.

Do you read into your scientific data as much as you (erroneously) read into BABB postings?
That's what I said.
dgruss, over the last 80 years of astronomical observations, it has been well established that redshift correlates with distance. Higher redshift means more distance. It's not like these authors are making some assumption out of the blue, as in "Let's assume for the sake of argument..." They are simply working from the knowledge base of the astronomical community compiled over the past 80 years. So if you want to say, "They're assuming the knowledge base of the astronomical community is correct!", then fine. But if you want to claim that there's some problem with that, you'll have to convince the community that it's been wrong these past 80 years, and you haven't done that.
I disagree on both counts. Why is there a "local quasar hypothesis"? Because Arp found a number of high redshift quasars close to the line of sight of lower redshift galaxies, and ever since he's been trying to fit the square high redshift quasar into the round hole of the low redshift galaxy. Now Scranton et al, with an extraordinarily large sample using nothing other than GR, have explained why one would see a number of high redshift quasars close to the line of sight of lower redshift galaxies. You claim this paper "has absolutely no implications for the local quasar hypothesis", but I think the implication is clear... to anyone not sticking his head in the sand.

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Everyone is entitled to his own opinion, but not his own facts.

As a matter of habit you constantly characterize my motives . Perhaps then you might explain your use of the word "dissembling": "Dissembling: To disguise or conceal one's real nature, motives, or feelings behind a false appearance."

Your use of the word dissembling is an accusation that I am being misleading. Once again you're walking that line between discussion and ad-hominem.

But seem not to understand or you would not have stated that it makes the local quasar hypothesis irrelevant.

We've already discussed all this not that long ago. And you abandoned the discussion. Since you scoff rather than discuss I see little reason to repeat discussions we've already had on these matters.

I never said they did Cougar, but its not that hard a concept to grasp that if your analysis depends upon a certain set of assumptions or interpretations of the data (cosmological quasar distances in this case), then the conclusions of the study are only valid if the assumptions are valid. More important to this discussion: the conclusions do not and cannot prove the assumptions upon which the analysis depends. That would be circular reasoning.

No, that's for other discussions. If you'd stop interpreting more into what I'm saying than what I'm actually saying, we'd be able to shorten these discussions. What I said earlier on this thread, and what I'm saying to you is very clearly stated right above. Why don't you try telling me what you think is wrong with my above point rather than complicate the discussion by implying I'm saying this or that that I haven't stated. I never said that the knowledge base of the last 80 years is incorrect. And I never said I'm trying to convince everybody that the last 80 years has been wrong.

This is something you're constantly doing. It happened in this thread and now you're doing it again here. Here let me help you for future reference:

I'm not saying:

Big Bang is wrong.
Universe is not expanding.

I am saying:

Evidence exists that there may be a component of intrinsic redshifts in normal galaxies superimposed upon the cosmological component (which could be from expansion). See my papers.

Evidence exists that QSO's and some other very high redshift objects may be local rather than at cosmological distances. I've specifically defined (on this thread again) tests that could falsify this possibility for local QSO's: (1) Time dilation; (2) QSO proper motions.

What would that implication be Cougar? That a test which assumes quasars are at cosmological distances can prove its own assumption? If that's where scientific reasoning is headed then perhaps I'll put my head in the sand.

You know what? I think you're wrong that the authors of this study "assumed" that quasars are at cosmological distances. Of course everybody knows that they are (except a few diehards of one offbeat theoretical persuasion or another), but the view that quasars are at cosmological distances is not actually an assumption of Scranton's paper. It's not needed as an assumption. The authors took a ton of data from the SDSS. The SDSS assumes nothing - it's just data. With their huge sample they found that quasars near galaxies were typically brighter, and there were hardly any dim quasars near galaxies. This finding assumes nothing about foreground/background; however, this finding is perfectly consistent with the explanation that the quasars near the galaxies are being weakly lensed by the galaxy, magnifying the quasar image and making it brighter. This also explains why there are hardly any dim quasars near galaxies. Of course, to be lensed the quasar must be in the distant background, with the galaxy in the foreground. This means the quasar is not local.

Scranton's paper does not assume quasars are at cosmological distances, but the paper's findings do provide significant support for that view.

The key foundation of your argument is incorrect. That Scranton's paper supports the view that quasars are at cosmological distances is not circular reasoning. Scranton's findings explain Arp's anecdotal quasar-galaxy associations better than Arp's attempts at explanation. This paper does indeed damage the local-quasar, intrinsic-redshift hypotheses.

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Everyone is entitled to his own opinion, but not his own facts.

Dgruss, to explain why I felt this study might provide ammunition to refute intrinsic redshift. One of the arguements I've heard repeatedly with Arp was that there always seemed to be a line of sight correlation with a known, low red shift galaxy and a known quasar or two. I acknowledge full well that the necessary direct observations needed to determine specific redshifts were not taken, but I was reaching for the idea that with over 200,000 different data points to use, the so-called line of site correlation arguement could be refuted.

If it could be determined by this study that the apparent relationship between quasars and low red shift galaxies is not statistically consistent, one of Arp's legs could be abruptly removed from beneath him.

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The last time I felt a warm fuzzy feeling, I was informed by my doctor that it was just gas.

Cougar emailed me about this thread and I thought it would be appropriate to comment on the discussion here.

Contrary to the dgruss23's reading of the paper, our measurement does not implicitly assume that the quasars were background objects. Rather, we merely selected the quasars based on photometric redshifts so that they were distintinctly separated in redshift from our galaxy sample (see our Figure 1). The cross-correlation is based on angular distance on the the sky, so there's no assumption of cosmology there. Likewise, the weighting scheme we used in the second series of measurements was based on the slope of the quasar number counts as a function of magnitude. As with the redshift selection, this was done because it's relevant to the lensing hypothesis, but we don't have to assume anything about cosmology to measure the slope.

Now, when it comes to calculating the expected weak lensing signal to compare to the measurement, yes, we are assuming a standard cosmological redshift relation for quasars. Obviously, we could have calculated the expected signal based on a non-cosmological model, but the main thrust of this paper was to address the discrepancy between the various previous measurements of this cross-correlation. If anyone were interested in doing such a calculation to compare to our measurements, I'd be happy to share the raw numbers from our results for a comparison along the lines of our Figures 3, 7 and 8.

Without doing such a calculation, however, my guess is that, if quasars were physically associated with galaxies, the cross-correlation between galaxies and quasars should be on order the auto-correlation of galaxies, rather than down by at least two orders of magnitude as we found in our measurement. Likewise, I wouldn't expect the amplitude of the signal to scale with the slope of the quasar number counts, as we demonstrated in our paper, although I'm not familar enough with the details of Arp's model to say for certain.

Hope this helps to clarify things...

Let me qualify my previous statement. Considering the cross-correlation of galaxies and quasars, Scranton et al found a positive correlation with bright quasars and a negative correlation with faint quasars. This correlation makes no assumption about foreground galaxies/background quasars. It may have been expected, but it was not assumed.

Q. What is the natural explanation for such a finding?
A. Gravitational lensing.

Thereafter, Scranton et al did suppose, "Well, if this finding is due to lensing, we would have certain mathematical expectations according to the physics of lensing." So they tried weighting each quasar by the expected lensing signal and found that the result matched the expected lensing signature extremely well.

I continue to assert that this finding does serious damage to the idea that quasars are physically associated with local galaxies.

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Everyone is entitled to his own opinion, but not his own facts.

Oops. Didn't notice your post, Dr. Scranton. I'm sure we all appreciate your input.

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Everyone is entitled to his own opinion, but not his own facts.

I'm just glad to see people interested in the paper; the disagreements between the various earlier attempts kept the measurement kind of obscure. Lensing people had originally looked at the magnification effect because the optics necessary to measure lensing shear weren't widely available. When it turned out that the non-uniformities in galaxy and quasar selection were really difficult to overcome, people lost interest.

The primary authors on the paper have been working on the measurement on and off for the last five years, so we've all been very pleased by the results we got when we switched from using spectroscopically selected quasars to the photometric sample in the paper. The behavior was the same in both cases, but the much, much larger photometric sample shrunk the error bars considerably.

Now that we've shown it can be done reliably and basically comes for free for all of the planned multi-band large-area surveys that will follow the SDSS, we're busy working out new applications and making predictions for its future use in larger surveys.

Dr. Scranton, Thank you for taking the time to clarify some details for us. I do genuinely appreciate your comments on this. From the beginning of this thread I have not had a dispute with the analysis methods or conclusions in your paper. My issue is that it has been suggested here by Cougar and others that your study specifically refutes the possibility of local quasars.

I understand that your correlation analysis is a matter of quasar/galaxy distribution on the sky and can be analyzed independently of cosmological models. However, as you noted above - when you calculated the lensing signal - which is what Cougar and others seem to think refutes the local quasars hypothesis, then you did have to assume the standard cosmological redshift-distance relation for the quasars. I obviously was not specific enough as to when that assumption was brought into play in your analysis. My apologies for that. But my point to Cougar is that your conclusions about the lensing are dependent upon the quasars being at cosmological distances. So the lensing part of the analysis is not designed to refute the local quasars hypothesis. Yet he keeps insisting that it does refute the local quasars hypothesis.

As for the correlation analysis, since Arp expects a correlation between the distribution of galaxies and higher redshift quasars, it would depend upon specific theoretical predictions as to whether the correlations in your paper specifically refute local quasars. In our discussions on this board I've tried to make clear the distinction between Arp's empirical model for ejection of quasars and the development of a theoretical explanation if he's right. What seems to get lost in these discussions is that the specific mathematical predictions such as those in your lensing analysis require a theoretical model. Unfortunately, Arp lacks a theoretical model that would allow such specific predictions about QSO-galaxy associations. The best that can be done at this time is general trends from the empirical relationships.

However, as I did point out in an earlier post above (and on plenty of other threads in which I've discussed this with Cougar), there are several tests that can falsify the possibility of local quasars even without developing a specifical theoretical mechanism for ejection of quasars and intrinsic redshifts. Those tests are Time dilation and proper motions. Hawkins found that quasar variability does not exhibit time dilation as expected if they are at cosmological distances. Microlensing was initially advanced as an explanation, but more recent studies have shown microlensing is too small a player in QSO variability to account for the lack of time dilation. So this test is consistent with quasars being local - or at least the quasars studied by Hawkins.

The proper motion test should be relatively simple but will probably take a decade or two if somebody actually conducts the study. The best candidates would be the quasars in the vicinity of M-82 which Arp has suggested are ejected from that galaxy. Since M-82 is a local galaxy, the proper motions will be detectable much sooner if the quasars are in fact local.

Personally, I wouldn't be surprised if the basic cosmological picture is correct, but that intrinsic redshifts are an additional phenomenon superimposed upon any cosmological redshift from expansion.

Anyway, congratulations on your results! It is obviously no small task to conduct the analysis and reductions on 200,000 QSO's and 13 million galaxies.

And you continue to be wrong. As I said in my comments to Dr. Scranton, Arp lacks a theoretical mechanism to explain ejection of quasars. Obviously that doesn't help him win support, but the purpose of these discussions is to consider the tests that could refute or verify the various hypotheses. In the case of the local quasars hypothesis derived from the empirical results: Time dilation and proper motions are the valid tests.

One of the greatest difficulties in testing the local quasars hypothesis is the lack of a mechanism for ejections. So its hard to make specific numerical predictions about QSO distributions. That's why the time dilation and proper motion tests are so critical. They are completely independent of any theoretical mechanisms. If quasars are local they will not exhibit time dilation (see above posts).

It also helps if you know the distances to the proposed parent galaxies of the quasars. That requires redshift independent distances - which for very distant galaxies are hard to come by.

I still disagree with many of the points in your last post, but let's just discuss this: Isn't it correct that Arp's theory would predict that the closer a quasar appears to a galaxy, its redshift should be higher (when compared to the redshift of the galaxy)? Quasars farther from the galaxy should have less of a redshift differential? I am far from being an expert on gravitational lensing, but I expect a significant sample from SDSS would show this is not the case. So here's another way to falsify Arp's intrinsic redshift-quasar ejection hypothesis.

Has this finding been duplicated? I still have major problems with this method since quasars are so widely variable themselves - something that works against any test for time dilation, which requires a standard variation, like Supernova Ia light curves .

Why hasn't he or you checked the Harvard College Observatory full-sky archives that extend from 1889 to the present? This solution wouldn't even require telescope time.

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Everyone is entitled to his own opinion, but not his own facts.

In your opinion. Which is wrong. I hope Dr. Scranton will not mind too much if I quote a small section of his correspondence to me:
Now, this was not the point of his paper, and I'm sure he didn't want this controversy to overshadow his results, which are significant in their own right. Still, like Einstein's initial publications, the implications are not limited to his initial intent.
Do you agree with the other test I suggested? I shouldn't think these two are the only possible tests.

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Everyone is entitled to his own opinion, but not his own facts.

My pleasure. Please call me Ryan.

Well, as I said in my first post, I think the behavior that we're seeing strongly disagrees with what one would expect from the simplest form of Arp's model, with quasars recently ejected from local galaxies and somehow possessed of intrinsic redshifts. Obviously, one could come up with variations on this theme that could reduce the signal, but I think it'd be tricky to have it match the proportionality to the quasar number count slope that we see in our measurement. You'd have to have some reason to relate the gravitational clustering (and anti-clustering) to the intrinsic brightness of the quasars and their luminosity function. Tough to do.

Again, it's tough to get a signal that looks like lensing accidentally. As we mentioned in the paper, if you cross-correlate stars with quasars using the optimal weighting scheme, you don't get anything like the curves in Figure 8 of the paper.

[Skipping a bit; I agree that this whole discussion would be easier if Arp had some concrete mechanism to test.]

Are you referring to Hawkins, 2001, ApJ, 553, 97? I'll have to give it a closer read, but I'm initially a bit skeptical given that he's working off of photographic plates (young-ish astronomer bias, I suppose). Of course, I'm also not terribly keen on our current understanding of quasar dynamics being up to the task of predicting what quasar variability time scales should be. Still, I suppose there's no reason not to assume that the rest-frame time scale is independent of redshift as a first guess, but that is a potentially very strong assumption.

By coincidence, I'm also part of a group working on a project tracking quasar variability using the repeat scans that have been done with the SDSS (an earlier attempt with SDSS data was done by Vanden Berk et al, 2004, ApJ, 601, 692, but we'll have many more epochs per object). We won't have quite the time base line (only 5-6 years), but we should be able to do much better on number of quasars and photometric accuracy. Time dilation should definitely be on the list of things to check, but one could easily imagine something like quasar duty cycle variations screwing things up. Given enough quasars, you could probably find a set where you're matching a lot of emission line strengths, but you'd have a hard time getting much redshift range. Tough problem.

One thing I think should also be considered here is that Arp's model doesn't prohibit gravitational lensing. Even though quasars are said to be "local", they are not all very local, they are just generally closer than their redshift distance. What I'm wondering is that would this same result be obtained due to gravitational lensing even if we assume that local quasar hypothesis is correct? There would be small subset of closeby quasars that would probably cause some deviation to the result, but would they cause too much deviation?

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Greetings, Scranton. Much thanks for your comments here in helping us to understand your research!

There is one aspect I was interested in regarding the use of photometric redshift data. There are an abundance of studies concerning the differences in spectroscopic and photometric redshift data, but I definitely don't speak the language of any of their authors! #-o

I understand that photometric obesrvation is much more convenient, and that spectroscopy is much more accurate, but I don't understand what the specific errors are that need to be accounted for in order to 'calibrate' the photometric data to spectroscopic results.

It can be seen in a number of spectroscopic versus photometric observation studies that correcting these errors may not be so easy! Are these aberrations the result of fundamental problems related to standard earth-based astronomy; atmosphere, etc? Did you encounter any interesting problems related this sort of calibration?

If anyone else is interested, I found one readable reference on this subject: Photometric Redshifts: A Comparison of Methods

Another interesting link came up while studying this: Hyperz: a new and public photometric redshift code

The flow-chart introduction is very amusing =D>

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Ari: That's true, but runs into a couple problems. The primary one is that the gravitational clustering signal is intrinsically much stronger than the weak lensing signal. If the true distribution of quasars and galaxies was not two distinct annuli, but rather two annuli blended together, you'd quickly see the lensing signal swamped by the clustering signal (and measurements of the quasar auto-correlation function in redshift and angular space lead us to believe that quasars cluster gravitationally in much the same way as galaxies).

This leads to the second big problem, which is that the weak lensing signal is expected to change amplitude and sign as a function of quasar magnitude, while the clustering signal is always going to be positive. If you had overlap in physical space, you'd expect to see two effects (assuming that the overlap was such that you weren't completely dominating the lensing signal). At the bright end, you'd see a much stronger positive signal as you're adding both the positive clustering and lensing signals. However, the angular dependence of these two signals isn't quite the same, though, so the shape would look odd (admittedly, the error bars are probably big enough that this wouldn't be show-stopper by itself). At the faint end, you're adding two signals of opposite sign (positive clustering and negative lensing), so it's going to be a mess. Depending on how things are balanced, you could get a negative signal at small angles, transitioning to a positive signal at intermediate angles or a positive signal all around with a strong dip at small angles.

In either case, if you do use the optimal weighting as we did in section 4.2 of the paper, then any physical overlap should show up as a strong deviation from the pure lensing signal we compare against in Figure 8.


akirabakabaka: The biggest challenge in dealing with photometric redshifts is that you don't know the spectral shape a priori. Which is to say that, while all galaxy spectra are roughly similar, there is a fair bit of variation due to star formation activity and the like. As such, you can easily run into cases where you don't know if a galaxy is intrinsically a bit bluer and at a higher redshift or is intrinsically red and at a lower redshift.

The ability of a photometric system to resolve these dilemma comes down to how the filters end up interacting with the space spanned by the galaxy spectra. For example, the SDSS filters have a problem with photometric redshifts around z ~ 0.4. It's not a defect, per se, just where this particular problem happened to crop up; if the filters were slightly different, then we'd have a similar problem at some other redshift.

For the quasars, you've gotta slightly different problem. Ignoring the spectrum blue-ward of the Lyman alpha break, the main spectral shape of a quasar is a power-law. This is terrible for photometric redshifts since a red-shifted power-law remains the same power-law. Instead, the quasar photometric redshifts are mostly determined by the presence or absence of the strong emission lines. As such, instead of seeing a gradual reddening of all of the colors (g-r becoming larger and larger) as you might with galaxies, individual colors bounce around with increasing redshift, sometimes getting redder, sometimes getting bluer. When you combine all of the color information (u-g, g-r, r-i, i-z, etc.), you can get a sense of what's going on, but it's not as accurate as galaxy photometric redshifts. You also run into a lot more cases where you've gotta a good match to the colors at one redshift and but also a secondary match at another redshift. This added complication is why we adopted the method for selecting and weighting the quasars we described in the paper.