Tracing Hot Spot Motion in Sagittarius A* Using the Next-Generation Event Horizon Telescope (ngEHT)

Round 1

Reviewer 1 Report

Overall:

This is a very interesting paper on the visibility of hot-spots in the strongly-lensed Sgr A* disk with the Event Horizon Telescope, a Earth-spanning millimetre array, and its augmented future as the ngEHT - under various configurations.  Improved U-V coverage is translated into the real effects on the tracking of dynamics of a hotspot, which is shown to have implications for understanding the physical mechanisms and magnetic environment within the disk. This could be used to guide the development of the facility, so it is an important work within the field of interferometry. But it is also of more general interest to the physics community, and timely regarding the current excitement surrounding BH direct imaging efforts.

It is a generally well-written report: I found mostly grammatical mistakes, with some instances where text and tables could be clarified. I was actually a little surprised that the main conclusion of this was not stronger, making a clear quantitative statement regarding ngEHT (and which array stations) are necessary to disentangle effects in the disk; but I don't think it is a harm to the paper: a suggestion is made regarding this. Detailed comments are provided below, and with those suggestions considered and minor corrections made, my view is that it can be published in Galaxies.

Detailed comments:

Abstract: "in which few new additional sites are added" -> "into which a few new additional sites are added."  I think.

Section 1, first par: "... across *the* electromagnetic spectrum." later, "... and X-rays" (plural, to be grammatically correct).  Further instances later.

Same par, later: Possibly the proper form, when using a reference as an example, is to put "e.g." within the bracket [e.g. 31]; this reads oddly otherwise.  Perhaps drop.

Same, third par. "... these flares (hot spots)" perhaps, for consistency.

Figure 1: Define HAMR, either here, as it appears first, or in the text; I don't see a definition in the text.

Section 2, second sent.: MAD state.  What is that? This is the first instance, and needs to be defined.

Same, last sent. "... relativistically hot blobs of plasma that are surrounded by more magnetized gas."  Not clear: blobs are surrounded by cooler but magnetized gas, I think; but "cooler" gas being the operative thing here, yes?

Section 3. A split-infinitive. Second sent. begins with reference tag, so maybe: "Others [54] extended..." Perhaps.  I notice that this mixing of the two referencing styles (tags versus label by first-author) appears elsewhere too.

Equation 1:  For clarity, it should be possible to understand any equation presented without going to the references, so please formally define g (and units).  And so also state that G=c=1 here, I think, if e- number density is an absolute number. The negative numerator and denominator (within the square-root) was chosen to help clarify orientation of the vectors, I assume, but it might be helpful to just say that. Less important, but putting a multiply symbol (either an X or a dot) between that term and the third multiplicative term might also help the reader parse this. Tracking those positions relative to U-V coverage is the crux of the rest of the paper, I interpret.

Same, fifth par.: "We use a few different observational arrays ..."  and ending "... any type of dynamical motion."

Section 4:

Table 1. Referring to sites used in generating simulated data: the observatory acronyms are not defined, and should be.  It would also be helpful to understand how the arrays are situated on Earth - as this is seemingly the whole point of further extending it, to improve U-V coverage.  One of many possible approaches (that are done in different ways in prior publications) could be simply to list lat. and long. of each station here too, although a map might work well.  I don't have a strong view that this map is required, but each station at minimum should be defined: GARS, GAM, CAT, etc.  It is surprising to see GLT (if I'm correct in assuming that means the Greenland Telescope) in a simulation of Sgr A*, as that target must below its horizon (in April, or otherwise) and so is unphysical. Can that be clarified?

Just noting how nicely Figure 4 provides the main take-away of the paper: the fidelity with which the hot-spots are returned, best done with ngEHT - I think most notably at 7.62 UT, as ngEHTp1 does not seem to recover this correctly, even viewed qualitatively it seems to fail at that point by putting the hotspot near the center of the image, where one expects rather the shadow. A suggestion is to point to that in the caption as well.

There seems to be a pagination issue: Figure 4 strangely appears to interrupt the equations, prior to end of text describing equation (4) and the related image reconstruction technique.  This figure should come after, presumably.

After Figure 5, which shows the recovery of intensity and angle of the bright spot, first par. beginning "StarWarps" solves for N-D image array ..." This is the first appearance of the term: what is "N-D"?  Later, "I this method..." --> "In this method..."

Next par.: "2% systematic noise is added on the top of this..." If systematic, it could be subtracted, so possibly "random noise" is what is meant here. Please clarify what kind of noise is added, truly Gaussian noise with a standard deviation of 2%, or what?  Also, why 2%?  Is it thought to be realistic, or does it represent what you can expect in future with the improved array?  If so, state that.

Section 6:

Correlation methods: Just to say that I feel less confident in reviewing these statistical analyses, but they seem to be sound methods, and I don't find faults in them.


Figure 7, caption, second-last and last sent.: "quite good" --> "quite well"  and "It's performance ..." - "Its performance ..."

Summarizing bullets on reconstructed images, last item: "... we conclude that the ngEHT array helps a lot in improving the quality of the reconstructed image."  Yes, that seems true.  But the weakness of this statement is puzzling following the previous three: it seems that a quantified statement could be made. How much improvement? Moreover, the additions to the array of particular stations seemed to help more in some parts, or phases, of the reconstructed orbit of the hotspot, which seems a key result. So presumably a more definitive, and stronger conclusion could be made.  The reader must surely ask at this point: do you consider it worth the effort to employ the full ngEHT to get that improvement?  Otherwise, possibly it is not.

Conclusions: These conclusions seem complete and consistent with the text, although I will repeat that the reader is logically expecting the authors here to interpret the value of the extended arrays configurations on U-V coverage, and so the fidelity in recovering the hot spot with each of those. I think that is only to re-iterate my previous comment on a stronger conclusion regarding reconstructed and ground-truth image results, not a flaw in the paper as such.

Author Response

Dear Editor, 

Many thanks for kindly forwarding the excellent referee report to us. 

Please see the attachment for the detailed response to the reviewer comments and suggestions. 

Many thanks in advance.

 

Cheers,

Razieh Emami 

Author Response File: Author Response.pdf

Reviewer 2 Report

In this work, the authors simulate the formation and shearing of a hot-spot in a galactic center environment, and produce synthetic datasets to be analyzed using the uv-coverage of different ETH arrays, with the objective of comparing how efficiently different generations of the EHT can observe and track the orbital motion of such a hot-spot. The authors study different observational properties, e.g. intensities, angular position of the intensity peak, ellipticity, and area of the hot spot. While I believe that the results and conclusions proposed in this work are worthy of attention and are potencially of a publishing quality, it also seems to me that the conclusions are not sufficiently supported by the results, and that the paper itself is written in a rushy and unclear way. In the following, I provide some comments and suggestions for improvement:

 

1. From what I understand, the authors have conducted a single simulation of a hot-spot forming and shearing, and are using this simulation to test the efficiency of four different arrays related to four different generations of the EHT, to conclude that the more recent/future generations could provide a better observation of the hot-spot. While I do believe that this is true, otherwise the new generations would not consist of an improvement with respect to the previous ones, tracing these conclusions based on a single simulation appears to be a stretch to me. How can the authors be sure that, for a different simulation on which the formation and shearing of the hot spot is slightly different, e.g. follows a different trajectory in the observer's screen with peaks of intensity in different places, etc., that the superiority of the ngEHT prevails with respect to the other generations? If the authors had made a certain number of simulations (with statistical significance), and consistently proved that the results for the ngEHT are always better, e.g. by introducing a parameter that measures the deviation from the actual hot-spot data do the data measured by the different EHT generations, and showing that the average values of this parameter over a sample of simulations is always smaller for more recent generations, I would agree that the conclusions are supported by the results. However, with a single simulation, and although it does appear that the results from the ngEHT are better, I do not believe that the conclusions are sufficiently supported by the analysis.

 

2. Furthermore, as it is stated in several places throughout the manuscript, the authors state that their are conducting their analysis for the "first" and "second" phases of the hot-spot evolution with limited portions of the data set. For example, the authors state that at T ~ 7.65 UT, the data can not be described by a condensed hot spot, and thus they have removed this data. A similar thing happens later on, when the authors chose to remove data from Fig. 6 where the reconstruction "is not too ideal". Two comments regarding these situations: first, the authors simply state that the data is not good enough to be described by the models they propose, and that the data is thus removed, but no explanation on why this is so is given, e.g., what properties of the data after T ~ 7.65 UT imply that the model chosen for the first phase is not ideal anymore (and the same for the data removed from Fig. 6)? Second, as it is presented, and given the portions of the data set that are removed with no further or clear reasoning, how can one be sure that the results (and conclusions) are not being affected by this manipulation of the data, and choice of the data portions to apply the models to? Note that I do understand that something in Fig. 5 for example seems to be odd after T ~ 7.65 UT, because we see an increase in the intensity and a decrease in the angular position of the hot spot, but how and why is this pathological for the model, and why is this sufficient to justify the removal of data?

 

3. Finally, as stated previously, I do believe that the text is rushed, and it seems to me that the authors did not proof-read the text before submission. Several writting mistakes can be found throughout the manuscript, some quantities and abbreviations are not defined, among other problems. Some examples are: the abbreviations MAD and NIR are not defined; the quantities being plotted in Fig. 1 are not defined (I suppose that T stands for temperature and \rho for density, but it is not the job of the reader to make this guess), including I and G; There seems to be a typo in the bottom left panel of Fig. 1, where both axes are labeled as x; the function g in Eq.(1) is undefined; the unit Jy in Fig. 2 is undefined; several quantities in Eqs.(2)-(4) are undefined, e.g. \mathcal N and R_t, and even after reading the text I can not completely understand what these equations represent, I urge the authors to extend the text and clarify what these equations are and what they are used for; and Fig. 4 is not called upon in the text anywhere at all.

 

While comment 3. is minor and concerns simply the overall appearence and readibility of the manuscript, my comments 1 and 2 are more important and I would be happy to recommend the paper for publication if the authors can successfully improve on these points.

Author Response

Dear Editor,

 

Thanks a lot for kindly providing the referee reports to us.

Please see the attachment for a detailed response to the referee report.

Cheers,

Razieh Emami 

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

The authors have successfully addressed my previous comments and thus I consider that the manuscript is now suitable for publication.