Super-Resolved Image of M87 Observed with East Asian VLBI Network

Round 1

Reviewer 1 Report

This paper describes the application of RML imaging to a 22 GHz M87 EAVN data set. The paper is topical and well written and I recommend publication after the authors have addressed the following points.

 

Line 15:

This would be better with "super-massive black hole" added before "at its center".

 

Line 22:

"... but [EHT] did not detect the jet."

It would be worth expanding on this point. It is true they did not, but they offer an explanation of why they did not expect to -- see sec. 7.1 of EHT et al. 2019, paper IV.

 

Line 30:

"i.e." should be "e.g.", as VSOP is one example of a space VLBI mission.

 

Line 35:

"used" or "applied" would be better than "introduced", as the latter carries some suggestion that this is the first time the method has ever been used.

 

Line 48:

"These densely monitoring observations..." would be better as "These high-cadence monitoring observations..." or "This dense monitoring campaign..."

 

Line 58:

As not all readers may be familiar with the EAVN, it would be useful to list all participating telescopes (including the elements of the KVN and VERA), together with their size and abbreviation. (This is partly necessary to explain URU and TIA in line 100.)

 

Line 76:

"...for imaging from EHT data set" would be better as "...for imaging EHT data"

 

Line 85:

"This allows to the production..." should be "This allows the production..."

 

Line 90:

It is not clear what is meant by "of sufficient size" -- perhaps that phrase could be dropped? (Although, some justification for choosing that size would be useful.)

 

Line 91:

"L1w" is used here, but is introduced as wL1 on line 83.

 

Line 94:

"41 x 20 mas square" is odd (as it is a rectangle not a square!). I suggest "41 mas x 20 mas". (Simimlarly, the previous sentence could end with "a pixel size of 80 mu-as.")

 

Line 116:

How were these values of chi-squared determined? And were they chosen in advance?

 

Line 118:

Some journal styles require that sentences start with a word rather than a number. So, an alternative like "In total, 48 final images..." or simply "Forty-eight final images..."

may be better.

 

Line 121:

"...a dark jet" seems odd -- perhaps "...a fainter jet"?

 

Line 124:

The counterjet-like structure is, as stated, faint and short, but I suspect that is consistent with previously published reports of a counterjet in M87 -- it would be useful to add a sentence or two comparing this result with others.

 

Figure 4:

It might be useful to add the observation epochs of the 43 and 86 GHz data.

Author Response

Thank you very much for providing important comments. We are thankful for the time and energy you expended. The paper has been revised in response to all referees' comments. Revised sections are highlighted in blue. We have also revised the sections not pointed out by referees in order to comply with the rule of 4000 words or more in total, which are highlighted in green. The resubmitted manuscript will be submitted for English editing.

Our responses to the referee’s comments are as follow:

This paper describes the application of RML imaging to a 22 GHz M87 EAVN data set. The paper is topical and well written and I recommend publication after the authors have addressed the following points.

 

Line 15:

This would be better with "super-massive black hole" added before "at its center".

Done. Thank you for pointing it out.

 

Line 22:

"... but [EHT] did not detect the jet."

It would be worth expanding on this point. It is true they did not, but they offer an explanation of why they did not expect to -- see sec. 7.1 of EHT et al. 2019, paper IV.

Done.

 

Line 30:

"i.e." should be "e.g.", as VSOP is one example of a space VLBI mission.

Done.

 

Line 35:

"used" or "applied" would be better than "introduced", as the latter carries some suggestion that this is the first time the method has ever been used.

Done. Thank you for the suggestion.

 

Line 48:

"These densely monitoring observations..." would be better as "These high-cadence monitoring observations..." or "This dense monitoring campaign..."

Done.

 

Line 58:

As not all readers may be familiar with the EAVN, it would be useful to list all participating telescopes (including the elements of the KVN and VERA), together with their size and abbreviation. (This is partly necessary to explain URU and TIA in line 100.)

Names and abbreviations of each station are added. For the size of the telescope, we direct readers to Cui et al. (2021), the first paper to study jets with the EAVN.

 

Line 76:

"...for imaging from EHT data set" would be better as "...for imaging EHT data"

Corrected.

 

Line 85:

"This allows to the production..." should be "This allows the production..."

Corrected.

 

Line 90:

It is not clear what is meant by "of sufficient size" -- perhaps that phrase could be dropped? (Although, some justification for choosing that size would be useful.)

We added more detailed explanation.

 

Line 91:

"L1w" is used here, but is introduced as wL1 on line 83.

The notation is unified to wL1.

 

Line 94:

"41 x 20 mas square" is odd (as it is a rectangle not a square!). I suggest "41 mas x 20 mas". (Simimlarly, the previous sentence could end with "a pixel size of 80 mu-as.")

Done.

 

Line 116:

How were these values of chi-squared determined? And were they chosen in advance?

It was determined based on the distribution of reduced chi^2 of the images obtained. With this selection criteria, it is possible to select images of the distribution with a peak near 1.

 

Line 118:

Some journal styles require that sentences start with a word rather than a number. So, an alternative like "In total, 48 final images..." or simply "Forty-eight final images..."

may be better.

Thank you for the suggestion. Corrected.

 

Line 121:

"...a dark jet" seems odd -- perhaps "...a fainter jet"?

Corrected.

 

Line 124:

The counterjet-like structure is, as stated, faint and short, but I suspect that is consistent with previously published reports of a counterjet in M87 -- it would be useful to add a sentence or two comparing this result with others.

Done.

 

Figure 4:

It might be useful to add the observation epochs of the 43 and 86 GHz data.

Done.

 

Reviewer 2 Report

This paper describes a re-analysis of the observations of the jet of M87 conducted with the East Asian VLBI Network at 22 GHz. The authors use a relatively novel method of imaging, the regularized maximum likelihood method to surpass the resolution limit of the conventional CLEAN method and thus study the cross-section of the jet.

This paper is definitely worth publishing but before that, a couple of modifications should be implemented.

Below I give my comments mostly in order of appearance in the text.

 

Introduction, line 15: The phrase "black hole" is missing from this sentence. 

Line 16: I suggest "emitting radiation" instead of "emitting wavelengths".

Line 18: The term "low-frequency" means very different things for radio astronomers working at different fields. I suggest to change this something more quantitative (also in the abstract, and later in the Introduction e.g. line 24) or rewrite the sentence.

Line 34: Here again low-frequency should be quantified. Also the message of the sentence is not conveyed the best way. Did the authors want to say something like that "to image the fine structure of the jet further from the central region, high resolution observations are needed at those frequencies where the jet is the brightest"?

The last paragraph of the Introduction (about the extension of EAVN) seems a bit out of place here. I would move that to the summary and also provide some details how these expansions of the arrays can be used in the investigations of the jets and/or M87 specifically.

Section 2: If I understand correctly (after looking at Cui et al. 2021), the here described observations were introduced and analysed by Cui et al. using the conventional CLEAN method. This should be clearly stated in the beginning of this section, and the authors have to decide whether they only refer Cui et al. for the details of the observation and the data reduction, and here they give only a very brief summary. Or provide a detailed description of both observation and data reduction part. In its current form, the manuscript uses a mixed approach, which is confusing.

 

In Section 3, the authors describes the process of imaging. Here I think a few more details can be added:

- the description of regularisation terms (weighted L1, total variation, total squared variations, and maximum entropy method, line 83-84) require either a brief explanation or a reference. If these terms are used in the same way as for the EHT data reduction, this can be mentioned here together with the reference number [19] currently in the manuscript.

- in line 89, what is "big drop" means in this context? The visibility amplitudes in the listed baselines are with n percent below the values at other baselines? Or is it a time/frequency-dependent change?

- in line 89, "We used a CLEAN image [10]" means that the authors used the clean image of M87 obtained by Cui et al. (2021)? I wonder if the clean image of Cui et al. have been used or the clean model components of Cui et al. but convolved with a different beam? (See my next point)

- in line 90, what "sufficient size" of the circular Gaussian means? How was this derived?

- what is the difference (or definition) of a soft mask (line 91) and a hard mask (line 94)?

- in line 93 "The image properties are set to a pixel size of 80 μas square, and a field of view of 41 × 20 mas square." Why were these particular values selected?

- the regularisation parameters are first given in line 104-105 and later also in line 112-113. However the two sets of parameters are different. This has to be clarified.

- in line 115, the authors mean the reduced chi2? Why were these particular values selected?

 

The role of Figure 3 is currently to show the selected 48 images which were used to create the average final image. However, I think this figure cannot accomplish its goal in its current format as it is hard to find any difference among the shown images. In one hand, this is exactly the reason that they are shown as "there are minor differences in the images", however to illustrate that I do not think so many images are necessary. I suggest a different approach, either

(i) show a one of the 48 final images (a representative one) together with a few of the not selected images to highlight the selection mechanism or

(ii) show some image differences (created by subtraction or division) to highlight the largest, most prominent differences among the 48 selected ones.

 

In line 123-124, when the counterjet emission is mentioned, it would be better if its comparison with the jet can be quantified. Also for the phrase "solid detection" a quantity can be added (e.g. how much above the noise level).

"The width that is half of the peak value is defined here as the jet width." This sentence (line 128-129) is not clear to me. It has to be rephrased.

Figure 4: The tick marks at the axes are hard to see. I suggest to make them bigger. Also the value of the slope is better to give in the caption and in the text and not in the figure itself.

Line 139: The best-fit parameters were obtained by fitting _the profile_ with three Gaussian components.

In line 143 and further down in this paragraph, the authors mention a CLEAN image (where there are no triple ridge). It should be stated here which CLEAN image they are referring to, the one from Cui et al., or the images from the Hada et al. publications shown in Figure 4?

Sect. 5: The phrase EATING VLBI is not defined, used here the first time.

 

Line 134-135: Finally, this may have been a stylistic issue, but I suggest to write the following sentence differently. Instead:

"The width of the jet was found to be proportional to the 0.54 ± 0.09 (95% confidence level) power of the apparent distance from the core."

I would write something like:

The jet width dependence on the core distance can be fitted with a power law with an exponent of ....

Author Response

 

Thank you very much for providing important comments. We are thankful for the time and energy you expended. The paper has been revised in response to all referees' comments. Revised sections are highlighted in blue. We have also revised the sections not pointed out by referees in order to comply with the rule of 4000 words or more in total, which are highlighted in green. The resubmitted manuscript will be submitted for English editing.

Our responses to the referee’s comments are as follow:

This paper describes a re-analysis of the observations of the jet of M87 conducted with the East Asian VLBI Network at 22 GHz. The authors use a relatively novel method of imaging, the regularized maximum likelihood method to surpass the resolution limit of the conventional CLEAN method and thus study the cross-section of the jet.

This paper is definitely worth publishing but before that, a couple of modifications should be implemented.

Below I give my comments mostly in order of appearance in the text.

 

Introduction, line 15: The phrase "black hole" is missing from this sentence.

Done. Thank you for pointing it out.

 

Line 16: I suggest "emitting radiation" instead of "emitting wavelengths".

Done.

 

Line 18: The term "low-frequency" means very different things for radio astronomers working at different fields. I suggest to change this something more quantitative (also in the abstract, and later in the Introduction e.g. line 24) or rewrite the sentence.

We corrected to "VLBI at centimeter or longer wavelengths" instead of "low-frequency VLBI." Other parts of the manuscript were revised accordingly.

 

Line 34: Here again low-frequency should be quantified. Also the message of the sentence is not conveyed the best way. Did the authors want to say something like that "to image the fine structure of the jet further from the central region, high resolution observations are needed at those frequencies where the jet is the brightest"?

Your point is correct. We rephrased it.

 

The last paragraph of the Introduction (about the extension of EAVN) seems a bit out of place here. I would move that to the summary and also provide some details how these expansions of the arrays can be used in the investigations of the jets and/or M87 specifically.

Done.

 

Section 2: If I understand correctly (after looking at Cui et al. 2021), the here described observations were introduced and analysed by Cui et al. using the conventional CLEAN method. This should be clearly stated in the beginning of this section, and the authors have to decide whether they only refer Cui et al. for the details of the observation and the data reduction, and here they give only a very brief summary. Or provide a detailed description of both observation and data reduction part. In its current form, the manuscript uses a mixed approach, which is confusing.

Yes, we are using the initial calibration data from Cui et al. This was properly explained in the first paragraph.

 

In Section 3, the authors describes the process of imaging. Here I think a few more details can be added:

- the description of regularisation terms (weighted L1, total variation, total squared variations, and maximum entropy method, line 83-84) require either a brief explanation or a reference. If these terms are used in the same way as for the EHT data reduction, this can be mentioned here together with the reference number [19] currently in the manuscript.

Done.

 

- in line 89, what is "big drop" means in this context? The visibility amplitudes in the listed baselines are with n percent below the values at other baselines? Or is it a time/frequency-dependent change?

"Big drop" means that the visibility amplitude in the baselines of TNRT, NSRT, and HIT are systematically lower than that of KaVA baselines.We have revised the manuscript to make this clearer.

 

- in line 89, "We used a CLEAN image [10]" means that the authors used the clean image of M87 obtained by Cui et al. (2021)? I wonder if the clean image of Cui et al. have been used or the clean model components of Cui et al. but convolved with a different beam? (See my next point)

Yes, we used a CLEAN map obtained in Cui et al. (2021) as a prior image. Penalties by pixel intensity are applied so that darker areas in the prior image are also darker in the restored image. We only need loose constraints on the intensity distribution of the core and the jet, so we convolve the map with a large enough circular Gaussian. Therefore, our images are not affected by the detailed CLEAN model. We have revised the manuscript to make this clearer.

 

- in line 90, what "sufficient size" of the circular Gaussian means? How was this derived?

This means that the fine structure of the jets seen in the CLEAN map is blurred so that it does not affect the RML imaging. We have revised the manuscript as per the response above.

 

- what is the difference (or definition) of a soft mask (line 91) and a hard mask (line 94)?

“Soft mask” means that the prior image serves as a penalty for pixel intensity. “Hard mask” means that the intensity is calculated only inside the image window. We decided not to use the terms soft mask or hard mask.

 

- in line 93 "The image properties are set to a pixel size of 80 μas square, and a field of view of 41 × 20 mas square." Why were these particular values selected?

The CLEAN map shown in Fig. 9 of Cui et al. was used as a reference to ensure that the field of view was sufficient to restore the jet. We added an explanation.

 

- the regularisation parameters are first given in line 104-105 and later also in line 112-113. However the two sets of parameters are different. This has to be clarified.

The first regularized parameter set was used for the very first imaging. By self-calibrating with that image, the visibility amplitudes of HIT, NSRT, and TMRT were aligned with the other baselines. The next set of regularized parameters was used in the iterative pipeline of imaging and self-calibration. We have revised the manuscript to make this clearer.

 

- in line 115, the authors mean the reduced chi2? Why were these particular values selected?

Yes, reduced chi^2. Corrected. The reduced chi^2 of all images was distributed from around 1 to about 4. This selection criteria were set in order to select images with reduced chi^2 around 1.

 

The role of Figure 3 is currently to show the selected 48 images which were used to create the average final image. However, I think this figure cannot accomplish its goal in its current format as it is hard to find any difference among the shown images. In one hand, this is exactly the reason that they are shown as "there are minor differences in the images", however to illustrate that I do not think so many images are necessary. I suggest a different approach, either

(i) show a one of the 48 final images (a representative one) together with a few of the not selected images to highlight the selection mechanism or

(ii) show some image differences (created by subtraction or division) to highlight the largest, most prominent differences among the 48 selected ones.

We agree with your point. In addition to posting the average image as a representative, we also include three images as examples so that you can see how much difference there is between the selected images.

 

In line 123-124, when the counterjet emission is mentioned, it would be better if its comparison with the jet can be quantified. Also for the phrase "solid detection" a quantity can be added (e.g. how much above the noise level).

The brightest part of the counter feature in the average RML image, which is located 1.7 mas southeast of the core, has about 23% of the brightness of the main jet symmetrically located relative to the core. The counter-jet-like structure is about 6 times brighter than the image noise rms. We explained these in the revised manuscript. 

 

"The width that is half of the peak value is defined here as the jet width." This sentence (line 128-129) is not clear to me. It has to be rephrased.

Done.

 

Figure 4: The tick marks at the axes are hard to see. I suggest to make them bigger. Also the value of the slope is better to give in the caption and in the text and not in the figure itself.

Done.

 

Line 139: The best-fit parameters were obtained by fitting _the profile_ with three Gaussian components.

Done.

 

In line 143 and further down in this paragraph, the authors mention a CLEAN image (where there are no triple ridge). It should be stated here which CLEAN image they are referring to, the one from Cui et al., or the images from the Hada et al. publications shown in Figure 4?

The CLEAN image is the one from Cui et al. We specified it.

 

Sect. 5: The phrase EATING VLBI is not defined, used here the first time.

Corrected.

 

Line 134-135: Finally, this may have been a stylistic issue, but I suggest to write the following sentence differently. Instead:

"The width of the jet was found to be proportional to the 0.54 ± 0.09 (95% confidence level) power of the apparent distance from the core."

I would write something like:

The jet width dependence on the core distance can be fitted with a power law with an exponent of ....

Done.

 

Reviewer 3 Report

This paper is likely to be a valuable contribution to the radio astronomy-AGN literature and, with modest editing, is suitable to be published in Galaxies. It introduces a novel, maximum likelihood technique for constructing images of enhanced effective resolution from VLBI data. Imaging with VLBI data generally suffers from non-regular spacings in the UV, Fourier image plane. The traditional image reconstruction algorithm for such data, "CLEAN", models the "dirty" image built directly from the inverse Fourier transform of the sampled data as a sum of Gaussian point source profiles with the Gaussian profiles set by the available UV coverage.  The method introduced here, instead, uses maximum likelihood methods on a "regularized" grid that evidently can achieve better effective angular resolution than the traditional CLEAN algorithm. A large number of "consistent images" are constructed, then averaged.

On the whole the paper is well written. There are several details that should be addressed to improve the clarity of the presentation, however. For
instance:

1) The statement on page two that the technique introduced "directly
constructs an image model that fits the observed data, resulting in
beam-size-free images" is misleading. This statement implies that the
constructed images are without diffraction-based resolution constraints, which is not the case . A more proper statement would be along the line that the constructed images have effective resolution that can exceed the nominal diffraction resolution limit determined from the UV plane coverage using conventional methods.

2) There are several places where discussion of the constructed images and/or their manipulation is not clear:

a) For instance on page 5 we are told that the constructed images were rotated clockwise by 19 degrees and vertical profiles obtained. We should be told that by the rotation mentioned, the jet becomes projected horizontally with its core to the left. Only then does the content of a vertical profile become clear. Even then, clarity would improve if we were told explicitly that these vertical profiles are transverse to the jet axis.

b) The definition that follows for the jet width is awkward. It would be
sufficient and clearer simply to state that the jet width is defined using
some version of the more conventional term "full width at half maximum intensity".

c) The reference below Figure 4 on page 6 to "the profile around 8 mas" is
ambiguous. The 8 mas surely measures displacement along the jet from the core, and that should be stated explicitly.

d) In the same paragraph, the sentence ranking peak brightness of jet ridges
is too complex to follow clearly. It would be clearer just to state a simple
ranking of their peak brightnesses, which I take to be (top to bottom) northern, southern and central, if I understood what is said.

3) For the benefit of readers who are new to the VLBI world, several acronyms for VLBI networks should be defined. For instance, please define: KVN, VERA and VSOP. Some others, like VLA have been in broad use for decades, so probably do not need to be defined here.

4) The text should be proofread by a native English speaker. There are quite a few English grammar errors.

Author Response

Thank you very much for providing important comments. We are thankful for the time and energy you expended. The paper has been revised in response to all referees' comments. Revised sections are highlighted in blue. We have also revised the sections not pointed out by referees in order to comply with the rule of 4000 words or more in total, which are highlighted in green. The resubmitted manuscript will be submitted for English editing.

Our responses to the referee’s comments are as follow:

This paper is likely to be a valuable contribution to the radio astronomy-AGN literature and, with modest editing, is suitable to be published in Galaxies. It introduces a novel, maximum likelihood technique for constructing images of enhanced effective resolution from VLBI data. Imaging with VLBI data generally suffers from non-regular spacings in the UV, Fourier image plane. The traditional image reconstruction algorithm for such data, "CLEAN", models the "dirty" image built directly from the inverse Fourier transform of the sampled data as a sum of Gaussian point source profiles with the Gaussian profiles set by the available UV coverage.  The method introduced here, instead, uses maximum likelihood methods on a "regularized" grid that evidently can achieve better effective angular resolution than the traditional CLEAN algorithm. A large number of "consistent images" are constructed, then averaged.

On the whole the paper is well written. There are several details that should be addressed to improve the clarity of the presentation, however. For
instance:

1) The statement on page two that the technique introduced "directly
constructs an image model that fits the observed data, resulting in
beam-size-free images" is misleading. This statement implies that the
constructed images are without diffraction-based resolution constraints, which is not the case . A more proper statement would be along the line that the constructed images have effective resolution that can exceed the nominal diffraction resolution limit determined from the UV plane coverage using conventional methods.

Thank you for the suggestion. We rephrased it.

2) There are several places where discussion of the constructed images and/or their manipulation is not clear:

a) For instance on page 5 we are told that the constructed images were rotated clockwise by 19 degrees and vertical profiles obtained. We should be told that by the rotation mentioned, the jet becomes projected horizontally with its core to the left. Only then does the content of a vertical profile become clear. Even then, clarity would improve if we were told explicitly that these vertical profiles are transverse to the jet axis.

Done.

b) The definition that follows for the jet width is awkward. It would be
sufficient and clearer simply to state that the jet width is defined using
some version of the more conventional term "full width at half maximum intensity".

Done.

c) The reference below Figure 4 on page 6 to "the profile around 8 mas" is
ambiguous. The 8 mas surely measures displacement along the jet from the core, and that should be stated explicitly.

Done.

d) In the same paragraph, the sentence ranking peak brightness of jet ridges
is too complex to follow clearly. It would be clearer just to state a simple
ranking of their peak brightnesses, which I take to be (top to bottom) northern, southern and central, if I understood what is said.

We rephraced as follows: The ridges with the bright peak intensity are, in order, the northern, the southern, and the central ridges.

3) For the benefit of readers who are new to the VLBI world, several acronyms for VLBI networks should be defined. For instance, please define: KVN, VERA and VSOP. Some others, like VLA have been in broad use for decades, so probably do not need to be defined here.

We added explanation in paragraph 8 for VERA and KVN, and for VSOP in paragraph 4.

4) The text should be proofread by a native English speaker. There are quite a few English grammar errors.

Thank you for the suggestion. We will submit the revised manuscript for English editing.

Round 2

Reviewer 2 Report

The authors addressed all the issues I raised in my review. I only have one very minor comment.

The authors (following my suggestion) moved the description of EATING VLBI project at the second paragraph of the Summary section, which is great. But it is now not coherently connected to the previous text of the Summary. An introductory sentence for the EATING VLBI paragraph would be useful. This may involve only to slightly reorder the sentences in this paragraph. For example starting with the importance of imaging jets such as M87 at high resolution high sensitivity at cm wavelength and then turn to how this will be helped by the EATING VLBI project.

Author Response

Thank you for your kind review. We have made corrections based on your comments. The corrected areas are highlighted in orange. Other than addressing the comments, we have corrected the 2nd affiliation and Funding information for Yuzhu Cui. The manuscript to be submitted is after it has been submitted for English editing.

The authors (following my suggestion) moved the description of EATING VLBI project at the second paragraph of the Summary section, which is great. But it is now not coherently connected to the previous text of the Summary. An introductory sentence for the EATING VLBI paragraph would be useful. This may involve only to slightly reorder the sentences in this paragraph. For example starting with the importance of imaging jets such as M87 at high resolution high sensitivity at cm wavelength and then turn to how this will be helped by the EATING VLBI project.

Thank you for your kind remarks. As per your advice, I have rearranged the order of the sentences to state the scientific goal first and that array expansinon is needed to achieve it.