Analysis

Introduction

Abstract

Content

Analysis

Personal Comments

Organization

This paper did a very good job of motivating its research. The specific problem was clearly addressed: how does one reconcile the z~6 quasars in the SDSS? It first outlined the other hypotheses that had been tested and rejected (see the diagram in the content section). It then addressed one that had not been rejected yet: that the quasars' brightness could be attributable to gravitational lensing magnification occurring without multiple images being detected. In this way, it placed itself among those trying to use one of Sherlock Holmes's principles to find out what is the truth. Namely:

“When you have eliminated the impossible, whatever remains, however improbable, must be the truth.”
- Sir Arthur Conan Doyle, The Sign of Four, ch 6.

Once this paper's conclusion is accepted, and it is believed there are no other reasonable hypothesis that could explain this, it implicates that there could be something wrong with LCDM cosmology. Metaphorically, this paper tightens the noose around LCDM cosmology, forcing it to reconcile these improbable results under its theory with observational evidence.

The paper itself is very well organized. It begins in the beginning: reviewing gravitational lensing and defining its own terms, like A_sing, the single image cross-section function with magnification above a certain limit. Then it uses these functions and analyzes both isothermal halos and NFW halos. The isothermal model was allowed to have an elliptical shape, and shear, which made the model more realistic. Then qualitative observations where made about these models, and then backed up with numerical evidence. Finally, these models were combined with other research about the mass function and the function defined in the paper f_SIS, describing the type of halo, to get statistics about the ratio of apparent single imaging to true multiple imaging. All the parts stood independent of the secondary goal of analyzing the likelihood of the SDSS quasars being apparently singly imaged, but pointed towards that goal.

Readability

For a technical paper, I was surprised at how easily I understood on a conceptual level what was going on. Although there was some discussion about lensing which was above my level, if it was simply treated as a black-box then it was comprehensible (as was somewhat the case in this paper; they did use GRAVLENS as black-box for most of their calculations). However, jargon was still an issue, particularly the word caustics, even for someone with a slight astrophysics background. If one was completely unfamiliar with the topic but knew even a bit about gravity and lenses, at least the broad strokes of the paper would have been visible, but a lot of the detail about halos, clusters, groups, and mass distributions would have been lost. Yet the information about the methodology would have remained clear, and logical. To a layman, if he or she had been able to surmount the amount of technical physics speak (isothermal, ellipticity) then I think the broad strokes would have still made sense to the reader. It does the article credit that it can be so broadly understood.

The writing style, while terse, was logical and straightforward. There were no wasted words or time in preparing this paper. Everything was directed towards the goal of examining this type of lensing. The quality of their organization added to the readability because questions in the reader's mind were answered soon after they were raised by the text. Additionally, I did not find any errors in grammar or logic, and their sentence structure was generally clear and to the point.

Convincingness of Results and Conclusions

There is one thing in particular that bothered me about this paper. A lot of the analysis went on inside of a numerical simulation to which I did not have access to the source code. Without that, there is no way besides for replicating their work by following the paper to check their work.

Although I was generally convinced by their isothermal treatment, the one part that stuck out was their lack of mention of higher order effects caused by multiple lenses in sequence. Although this is improbable, mention of the effect of this could be important, especially if the line of sight is along a filament somewhere between the present and z~6.

Otherwise, I found the analysis very thorough, especially in the models, which frequently cited earlier works on the topic. I assume those results could be trusted, since they were also published in reputable journals.

Most Informative and Most Surprising Parts

The most scientifically enlightening part was how they showed it was improbable that the SDSS quasars were singly lensed and magnified. I imagined that there would have to be a very complicated analysis to show that lensing could not be responsible in a magnitude limited sample. Yet their method was elegant. They only showed that if lensing was responsible for the apparent brightness of the quasars, then it was extremely improbable that there were no other lensed quasars with multiple images at the same redshift (from their analysis of apparently single imaging vs total lensing at the same magnification). This clearly showed that these quasars probably were not all singly imaged and magnified.

The most surprising part was how robust their model turned out to be. Although I have seen robust models in my computational experience, the stability of their model was quite impressive to only vary ~10% on a completely different data set.

Most Confusing Parts

The most confusing part of this paper was getting used to the terminology. One term that eluded my definition for some time was “caustic,” which defines a bound between different types of imaging, such as the one between two images and four, or two and a single. Another effect which was hard to understand was the presence of dwarf halos physically. Although it seems to make sense, understanding the underlying process is a bit advanced. I do find the idea of dwarf halos appealing since their presence in the calculations effectively add a “dark lens” that could be responsible. These halos are ruled out as a possible source of magnification of the z~6 quasars since their profiles do not make them likely candidates for satisfying the single detectable image criterion.

Relationship with the Rest of Astronomical Knowledge

This paper connects with astronomical knowledge in three places: gravitational lenses, quasars, and cosmology.

• With gravitational lenses, this paper presents a more complicated analysis of the probabilities associated with lensing. It presents functions for determining the occurrence of multiple images as being unidentifiable by either the dimness of the other images or by their close proximity. It also analyzes elliptical isothermal lenses and NFW lenses and presents a thorough analysis of the lensing that due to instrumentation limitations appears as one image.

• With cosmology, it helps remove the possible explanations for these quasars brightness. With this addition, it becomes more likely that there is no explanation that follows the Principle of Least Astonishment, but instead the results really are incredible. They also create problems for the LCDM cosmology. These results, will in turn, influence future generations of cosmological models, and models that come after LCDM must account for such massive black holes in the early universe.

• With quasars, it provides support for very large, massive quasars in the early universe, which has a great effect on the quasar luminosity function.

How the Paper Could Have Been Made Better

One of my nits about this paper, is that they did not provide the source code for the software they used. If they were using closed source, pay ware, I would have understood them not providing the source code. However, since they use GRAVLENS which is open source and free, there was nothing to prevent them from attaching a link to a website where the code could be downloaded and run by anyone who chose to use it. It would also have provided fellow scientists an easy way of tweaking the generalized results to subjects of their own interest.

Secondly, I had to read through the article several times before I realized they did specify which mass function they used in connection with their function f_SIS which described the fraction of halos with isothermal profiles. It was hidden in a footnote, and seemed an afterthought. Perhaps the mass function is standard, but it still deserves attribution to the authors in the text of the paper, like the rest of the sources they used.