The referee’s report is favorable, but a lot of little things to address.  I am 
going to shoot for having this back to the referee by Wednesday next week.  Let 
me know if you want to weigh in on any of the comments.

The statistics report at the end is new to me … I don’t think the comments are 
very useful, but it’s interesting that they’re doing this, and curious that 
Zaki’s paper didn’t get this treatment.  :)

James Aguirre
Assistant Professor 
Department of Physics and Astronomy 
University of Pennsylvania 
209 South 33rd Street Philadelphia, PA 19104 
(215) 898-9596 (office) 
(215) 898-9646 (lab)
http://www.sas.upenn.edu/~jaguirre/ 

> Begin forwarded message:
> 
> Date: March 30, 2015 at 11:03:20 AM EDT
> To: [email protected]
> Subject: Your ApJ Submission MS#ApJ98178
> Cc: [email protected]
> From: [email protected]
> Reply-To: [email protected], [email protected]
> 
> March 30, 2015 
> 
> Prof. James E. Aguirre
> University of Pennsylvania
> Department of Physics and Astronomy
> 209 South 33rd Street Philadelphia, PA 19104-6396, USA
> Philadelphia, PA 19104-6396
> 
> 
> Title: New Limits on Polarized Power Spectra at 126 and 164 MHz: Relevance to 
> Epoch of Reionization Measurements
> 
> Dear Prof. Aguirre,
> 
> I have received the referee's report on your above submission to The 
> Astrophysical Journal, and appended it below. As you will see, the referee 
> thinks that your article is interesting and that it will merit publication 
> once you have addressed the issues raised in the report.
> 
> I have also shown your paper to our statistics editor, whose comments are 
> attached below. They are not part of the referee report, but I include them 
> in the hope that you will find them useful.
> 
> When you resubmit the manuscript, please include a detailed cover letter 
> containing the (mandatory) listing of the changes you've made to the text and 
> your responses to the report.
> 
> Click the link below to upload your revised manuscript; 
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>  
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> 
> Regards,
> Ethan T. Vishniac
> Editor-in-Chief
> The Astrophysical Journal
> University of Saskatchewan
> ---------------------------------------------------------------------- 
> Referee Report 
> Reviewer's Comments:
> This is a very worthwhile investigation into the effects of polarisation 
> leakage and its effect on epoch of reionoization experiments. The results and 
> analysis are both highly relevant not only for PAPER but also for LOFAR, MWA, 
> SKA-Low and any other low frequency radio observatories. Overall, the paper 
> is well written, however, better use of known data, rather than conjecture, 
> would greatly enhance the quality and confidence in the final results and 
> conclusions. Some aspects of the paper are also difficult to judge as 
> specific details associated with the observations/instrument are not entirely 
> clear e.g. available bandwidth per band, channel size, hours observed, etc.
> 
> One aspect that is not entirely clear to me, as admittedly I am not entirely 
> familiar with the non-imaging methods described in the paper, is what affect 
> assuming the rather simple Stokes definition in Eq. 4 has in terms of overall 
> leakage. If the instrument has a wide-field of view then taking this simple 
> approach will result in position dependent behaviour in polarimetry i.e. 
> sources that are not directly at zenith will appear polarised in different 
> ways depending on where they are in the sky. It may be worthwhile reassuring 
> readers that this will not have a detrimental effect on the analysis (as is 
> mentioned throughout the document these are normally corrected for in the 
> image plane and yet there is not imaging performed here).
> 
> p.1, section 1: It may be worth noting that historically Mathewson & Milne 
> (1965, AuJPh, 18, 635) mapped diffuse linear polarisation in the southern sky 
> at 408 MHz (generally between 2-5 K).
> p.2, section 2: "rotation measure of 20 m^-2" - do you mean 20 rad m^-2?
> p.2, section 2: Is it techincally correct to refer to the linearly-polarised 
> visibilities as Vxx, etc as in reality these are instrumental polarisations 
> (where the polarimetric behaviour changes as a function of sky position) 
> rather than true linear polarisations? See Ord et al. (2010) where they refer 
> to generally nonorthogonal projected receptors (p, q). With this convention 
> the Vpp and Vqq approach Vxx and Vyy only for a source directly at zenith 
> (assuming the dipoles are orthogonal).
> p.2, section 2: What field of view is PAPER sensitive to and what affect does 
> this have on the validity of Eq. 4?
> p.2, section 3: "82 days of observation" - What does this represent in terms 
> of on sky observing time? i.e. approximately how many hours per day were 
> observed?
> p.3, table 1: it's unusual to refer to a centre frequency as \nu_0 (which is 
> more often used to represent a frequency at one edge of a band) perhaps \nu_c 
> is more intuitive? It would be useful to explain some of the parameters in 
> this table e.g. does delta_\nu represent the bandwidth or the channel width? 
> (presumably this can't be the channel width otherwise the polarised signal 
> would be highly depolarised. It would thus be useful to indicate the channel 
> width and thus what RM range the observation is sensitive to.
> p.3, section 3.1: What proportion of the data survives the flagging process?
> p.3, section 3.2: How valid is the solution at Pictor A to the rest of the 
> field of view?
> p.3, section 3.3: Averaging over multiple days could weaken the true 
> polarised signal if ionospheric Faraday rotation isn't taken into 
> consideration.
> p.4, section 3.4: "roughly the area between the south celestial pole and the 
> southern horizon
> p.4, Eq.7 and Eq.8 use the same symbol for different definitions i.e. 
> \delta_nu is either the channel width or the bandwidth - it would be better 
> to clarify this by using different symbols.
> p.5, section 3.7: It is unclear why the authors have not used readily 
> available archival TEC data to determine the actual effect of the ionosphere 
> during the observing programme - several tools are available specifically for 
> this purpose e.g. ionFR, RMextract and ALBUS. They are relatively easy to 
> obtain and can also estimate the ionospheric RM component and this would 
> allow an more physical (and with greater degree of certainty) estimate of the 
> ionospheric effect.
> p.5, section 4: "Stokes V ... excess below ~0.15 ... unknown origin" - it may 
> be useful to examine Q and U power spectra individually, rather than P which 
> merges the effects on Q and U, as this may highlight the origin of this 
> excess. U should generally be cleaner than Q as it is unaffected by leakage 
> from I (which is a major effect on Q). Could this be a pulsar? Some pulsars 
> can be highly circularly polarised even at long wavelengths.
> p.6, fig 3: The left-hand figure is missing the y axes, label and units 
> (presumably LST in hr).
> p.6, section 4.1: "RA 6h52m Dec -30 ... -50 rad m^-2" is this known to 
> correspond to any known polarised sources in the region - a quick search 
> through Taylor et al. could verify this. Perhaps also check for pulsars in 
> the region (these could conceivable achieve a higher fractional polarisation 
> than AGN and thus may not necessarily be as bright in total intensity). If it 
> is physical then it must be associated with a known source. 
> p.7, fig 5: the colour scheme makes it very difficult to see PMN J0351-2744, 
> adjust the colours or perhaps try a log intensity scale to make it clearer 
> where the source sits.
> p.8, section 5: "place on these simulation" ->"place on these simulations".
> p.9, section 5: "only published observational constraint" - Jelic et al. 
> (2014) and Mulcahy et al. (2014) LOFAR observations can also be used to place 
> some limits on polarised source characteristics at these wavelengths. It 
> might also be worthwhile using the Taylor et al. catalogue coverage of these 
> survey regions and based on some anticipated spectral index and level of 
> depolarisation how many should have been detected in the LOFAR/MWA/PAPER 
> observations. Once again, this matches characteristics of the real sky 
> observed by PAPER against known observations.
> 
> *************
> Statistics Report
> *************
> 
> ) In Fig 3, while the reader benefits from seeing the noise, the signal can 
> be enhanced by kernel smoothing. The kernel bandwidth need not be the same in 
> the two variables.
> 
> b) In Fig 4 and later figures, I do not see the value in binning the signal 
> so that the S/N ratio is extremely low. There is no mathematical reason why 
> evenly spaced bins (or any other grouping algorithm) should be used ... any 
> choice that improves the visualization of the signal can be used. Please 
> confirm that the scientific result (Table 2) does not depend on the arbitrary 
> choice of k, the number of bins.
> 
> c) Around eqn 21, there is no basis for choosing a Jeffery's prior, or any 
> other. I suggest that the analysis first be done by maximizing the likelihood 
> in eqn 20 and, if new insights emerge, secondly using Bayes' theorem with 
> different reasonable priors. The scientific result should not depend on 
> choice of arbitrary priors. 
> 
> 

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