An Updated View of the Milky Way from Maser Astrometry

Round 1

Reviewer 1 Report

The proposed manuscript is a review, so one would expect to find all relevant references within the topic. However the list of authors referenced is still rather narrow. In particular, I can propose to mention the papers treated just the statistics of the VLBI maser observations to clarify the Milky Way structure and kinematics:

Bobylev, Bajkova 2014 MNRAS v.437, p.1549 (the pitch angle of spirals)

Bobylev, Bajkova 2016, Astronomy Letters v.42, p. 182 (the Sun position above the MW plane)

Rastorguev et al. 2017, Astrophys. Bull. v.72, p. 122 (the kinematical parameters, four-armed spiral pattern, and even the disk exponential scalelength)

Bobylev, Krisanova, Bajkova 2020, Astronomy Letters v.46, p.439 (V_rot refinement).

I must stress that the results of all works mentioned above are in full agreement with the recent conclusions of the BeSSeL and VERA teams (the papers of 2019 and 2020, respectively).

Author Response

We thank the reviewer for suggesting these references which certainly render the review more complete.  Below each given reference, we specify the changes we made in the manuscript and the text we added. All changes to the text (also in response to the other referees) are marked in bold in the revised manuscript.

• Bobylev, Bajkova 2014 MNRAS v.437, p.1549 (the pitch angle of spirals)
  • We added the pitch angles for the Outer, Sagittarius, Scutum and Perseus spiral arms to Table 1. We also added the following sentence in the Local arm subsection: “\cite{Bobylev:2014} showed that there is no significant difference in pitch angle for low- and high-mass stars in the arm.”
• Bobylev, Bajkova 2016, Astronomy Letters v.42, p. 182 (the Sun position above the MW plane)
  • We added the following text in Section 7.2: “\textbf{\cite{Bobylev:2016} in their Figure 5 showed how methanol masers trace the Galactic plane better than H{\sc ii} regions or giant molecular clouds.}” and “The result of \cite{Reid:2019} is in agreement with the value for the Sun's height above the Galactic plane of $5.7\pm0.5$\,pc and $7.6\pm0.4$ derived using methanol masers and H{\sc ii} regions, respectively, from the inner Galaxy (galacto-centric distances $< R_0$) excluding the Local-arm masers \citep[][]{Bobylev:2016}. Also the results of \cite{Anderson:2019}, based on H{\sc ii} regions in First Galactic Quadrant and Inner Galaxy, yield results between 3 and 6 pc for different rotation curves and spatial sub-selections. Interestingly, literature values of $Z_\odot$ vary between 5 to 40 pc \citep[see][and references therein]{Reid:2019}. Potential origins for this variation can be the extinction in the Galactic plane and Galactic warping \citep{Reid:2019} and the Local arm which was found to affect the Z distribution pattern \citep{Bobylev:2016}.”
• Rastorguev et al. 2017, Astrophys. Bull. v.72, p. 122 (the kinematical parameters, four-armed spiral pattern, and even the disk exponential scalelength)
  • As Bobylev et al. 2020 did a similar analysis but with a much larger sample size we decided to discuss only the results from Bobylev et al. 2020. Similarly as we do for the BeSSeL papers, where we do not cite Reid et al. 2009 and 2014 for the distance to the Galactic Centre and the rotation speed.
  • Both papers, Rastoguev et al. 2017 and Bobylev et al. 2020, contain very interesting results on the spiral density wave parameters. However, we do not discuss these aspects of spiral structure in the review and thus we did not include these results in the review.  
• Bobylev, Krisanova, Bajkova 2020, Astronomy Letters v.46, p.439 (V_rot refinement).
  • We added in Sec: 7.1.1 (Distance to the Galactic Centre) for R0: “A further analysis by \cite{Bobylev:2020} combined maser VLBI astrometry  \citep{Reid:2019, VERA:2020, Sakai:2020, Ortiz-Leon:2020} with stellar continuum VLBI astrometry from the GOBELIN programme \citep{Kounkel:2017,Galli:2018, Ortiz-Leon:2018} and obtained a distance to the Galactic Centre of $8.15^{+0.04}_{-0.20}$ kpc, in full agreement with the maser astrometry results.”
  • In section 7.1.2, about Solar rotation speed: “Also the result obtained from maser astrometry and radio star astrometry (using, among others, BeSSeL and VERA data, see Section~\ref{subsec:dgc} for a data provenance list), $236.4\pm3.3$\,\kms\ \citep{Bobylev:2020}, is consistent.”
  • In the Table we added the value for R0 and the values for theta_0 and omega_sun from Bobylev et al. 2020. 
• Additionally, we added in section 7.1.2  on Solar rotation speed: “{\em Gaia} EDR3 data of OB stars find $240.7\pm3.0$\,\kms\ \citep{Bobylev:2022}, notably close to the {\em Gaia} O-star result \citep{Xu:2018b}.”

Reviewer 2 Report

This review collects an extended set of useful references to the field. They are summarized with an appropriate level of details, which allows the non-expert to browse the literature without losing the main line of thought. I think this review deserves publication after minor corrections isted below.

line 14: [2], for example, ...

line 16: I would go for connecting the sentences, like:

so far, for a number of reasons: (i).. (ii),..

line 30 : show -> to show

line 32: misisng reference

Author Response

Dear reviewer,

thank you very much for your thorough review.

Here is a point-by-point response to your comments:

line 14: [2], for example, ...

Added.

line 16: I would go for connecting the sentences, like:

so far, for a number of reasons: (i).. (ii),..

We think that this makes the sentence too long and thus would prefer to leave the text as is.

line 30 : show -> to show

Added.

line 32: misisng reference

This is a cross-reference within the journal issue that needs to be added by the journal. We will inquire with the editor how to do this.

Reviewer 3 Report

The paper  'An updated view of the Milky Way from maser astrometry', is a review contribution which presents a good overview of the topic. Although it does not present new data or method, in my opinion it deserves to be published as a review paper in a Special Issue "VLBI Science Applications"  on the Universe. However, I think the manuscript needs some minor revisions.

As a general comment, I think that a few more relevant aspects of the comparison with Gaia mission could be mentioned, especially with regard to the rotation curve.

I think it is a good review but reading the text I had the impression that the subject is well established. I’m afraid that it is not the case, especially with regard to the rotation curve and location of the spiral arms.

Putting the data and results in a more global perspective can help the reader to realize that there is still a lot of work to be done on this subject. Perhaps a little more detailed comparison with the results obtained with other objects using the Gaia data can help.

I missed more details of the comparison of the results with those from the Gaia since

the authors mention it in the abstract. 

Below I present my suggestions:

Line 23-25:

It is not clear. What is the definition of solar neighborhood? 

Line 32:

Missing the reference. 

Line 50:

10s km/s. What does that mean?

Line 167:

It would be interesting for the reader a mention of the parallax accuracy for all telescopes. Perhaps a table (including for example typical Gaia values) would give an overview of the state of the art.

I noticed that authors use accuracy. But I'm not sure if precision is more suitable.

Line 243 and 244:

"error floors" instead error floors

line 257:

What is the mean and standard deviation values? How many points were used in the comparison?

Line 307:

It would be useful for the reader to present more details of this comparison including values.

Line 314-317:

I suggest including the zero-point values of the cited references. 

Line 323-326

I was a little confused because of this statement. I had understood that O-type stars did indeed trace the spiral arms similar to the masers.

Couldn't the greater scattering of the spiral pattern be due to age scattering? This can be clearly seen when using samples of objects with different ages.

Line 327-328:

Regarding migration, I had understood that typically the O-type stars should not have moved more than 0.2 kpc from their birthplaces and should still be in their birth spiral arms. See the simple calculation presented in Section 3 of Xu et al. 2018 A&A 616, L15.

In the paper published by Xu et al. 2021 the same numerical argument is given considering B-type stars, although in the conclusions the authors said: "In short, the O-type stars tend to clump together and some of them are frequently found between the major spiral arms, indicating that recent star formation does occur in the inter arm regions and/or some of them have migrated far away from their birthplaces."

I was confused. What I missed?

Line 332-334:

I think it is interesting to present to the reader the future projects of Southern Hemisphere VLBI and LBA arrays.

Line 339:

It was not clear how figure 1 shows this.

Line 354:

The first line in the paragraph is not clear.

Figure 2:

Especially in Q1 I see dots of one color on arms of another color. For example, at 5<x<10 and -5<Y<0 I see Perseus's points on the outer arm. There are also points with Sagittarius's colors on arms of other colors.

I don't understand how it is possible since first the maser is associated with the arm and then the fits are made.

What I missed?

Line 365: Table1

A few words about the cause of such a large discrepancy in values would be interesting. Are the methods and data used similar?

What does that mean? I think the spiral structures is still difficult to trace with precision. Is that correct?

Other authors find different values for the pitch angle, also using the same tracers. I think it is important for the reader to say a few words about that.

Line 373:

It is not easy to see it in the plots. For example, there is no clear difference if compared to Perseus. 

Line 385-387:

I couldn't see it in the Figure 2.

lines 396-413

I’m thinking about the role of the corotation. The explanation given by Monteiro et al. 2021 (see their Figure 4) can't be an option too?

Line 422:

suggestion: at separations of 1.5 and 2.0 kpc, respectively.

Line 447:

Wouldn't it be easier to see in the figure 2? Where is the bar in figure 7?

line 565:

Missing space before 36

line 596:

suggestion: The two distances to the Galactic Centre obtained...

line 598 - 600:

These results were not redetermined with Gaia data?

Line 604:

Missing the unity

Line 605:

Missing the unity

line 606-607:

But previously you said that similar values were in agreement.

line 620:

What is the value of the uncertainty?

Figure 8: rotation curve:

Are the error bars in R (x-axis) included in the error bars presented in y-axis?

Comparing the curves on an enlarged scale I don't see them as quite similar as commented in the line 666. I notice important differences that do not appear on the scale used. For example, the universal curve is systematically higher (+~10km/s) than the other curves between 5 and 10kpc. After 12 kpc the RG and 2nd-order polynomial curves fall while the other two are flat.

There are authors who fit to the same data a gap in about 9 kpc. The gap in this region, which has smaller errors, can be seen in the maser data and even more clearly in the data from the Gaia DR2 catalog by Crosta et al. 2019.

I think it is important a mention about different tracers show different rotation curves and maybe important some comment about how it is difficult to measure.

Moreover, the text gives the impression that we know the rotation curve well, but different authors using different objects obtain different results and from what I can see in the literature this subject is in debate.

As an example, Mróz 2019 claims that gives using cepheids the most accurate

Galactic rotation curve at distances R>12 kpc constructed so far.

Line 673 - 674:

I don't see so clearly that the curves from maser and stellar astrometry give similar results. 

Line 718:

suggestion: parameters instead numbers

Author Response

We would like to thank the reviewer for the thorough read of our manuscript and for the excellent comments that allowed us to improve the manuscript significantly. Below is a point-by-point response to the reviewer's comments. All changes in the manuscript (also responding to comments from the other reviewers) are marked in bold in the revised manuscript.

• Line 23-25: It is not clear. What is the definition of solar neighborhood?
  • We modified the text to read “a few kpc from the Sun”.
•  Line 32: Missing the reference.
  • The  following text was inserted: (see, for example, the Gould's Belt Distance Survey conducted with radio stars \cite[][]{Ortiz-Leon:2017a, Kounkel:2017, Ortiz-Leon:2017b, Galli:2018, Ortiz-Leon:2018} and \cite[][]{REVIEW LAURENT}, for a review of radio star astrometry). We will also cross reference to a paper in this review issue. The reference will have to be included by the editor.
• Line 50: 10s km/s. What does that mean?
  • We meant tens of km/s and modified the text accordingly. The numbers are typically 1 to 5 km/s for methanol masers, and up to about 20 km/s for water masers.
• Line 167: It would be interesting for the reader a mention of the parallax accuracy for all telescopes. Perhaps a table (including for example typical Gaia values) would give an overview of the state of the art
  • We would like to thank the reviewer for this interesting suggestion. We decided not to put these values into a table since they could be easily misinterpreted. The uncertainties for each telescope array also depend on the maser-position reference pair and thus it is difficult to give one single number of accuracy that is valid for all observations. We instead highlight the best results in terms of parallax uncertainty for each of the surveys.
  • We added the following sentences in Sections 3.1 and 3.2, respectively: “The best parallax uncertainty of 5\,$\mu$as was reached by \cite{Zhang:2013} for a 22 GHz water maser in G048.60+0.02.” and “The best parallax uncertainty of 7\,$\mu$as was reached by \cite{Nagayama:2011} for a 22 GHz water maser in G048.61+0.02.”
  • For the Gaia values, we added a new paragraph at the beginning of Section 4 (comparison with Gaia): “The {\em Gaia} catalogue is published in various Data Releases (DR) as more information is being collected by the satellite and analysed. At the time of writing, DR3 had just been released\footnote{The {\em Gaia} archive is available at \href{https://gea.esac.esa.int/archive/}.}. In {\em Gaia} DR3, the best parallax uncertainty reached for O-type stars is 10\,$\mu$as, comparable to the maser VLBI parallax uncertainties.” 
•  I noticed that authors use accuracy. But I'm not sure if precision is more suitable.
  • We decided to change the word to uncertainty.
• Line 243 and 244: "error floors" instead error floors
  • Changed.
• line 257: What is the mean and standard deviation values? How many points were used in the comparison?
  • The number of objects were specified and the mean and standard deviation values of the parallax difference were inserted in the text.
  • The text was adjusted to: “Comparison of 28 VLBA/EVN and VERA parallaxes find that for a large majority of maser targets (21 out of 28) the parallaxes agree within 2$\sigma$ joint error \citep[][where the parallax of \cite{Wu:2019} was used for W\,48]{VERA:2020}. The mean and the standard deviation of the parallax difference are $-0.002$ and $0.318$ mas, respectively, for the sample of 28 targets.”
• Line 307: It would be useful for the reader to present more details of this comparison including values.
  • We modified the text in Section 4: "This sample included 59 YSOs, 19 Asymptotic giant branch (AGB) stars, and 15 other radio stars (for example, low-mass stars, cataclysmic binaries, high-mass X-ray binaries and long-period variable stars). The AGB and YSO subclasses were further divided into binaries and non-binaries. The authors calculated the slope and intercept of each subclass and combined samples, for the sample including binaries and without. For each stellar subclass and also for their full dataset \cite{Xu:2019} found that VLBI and {\em Gaia} DR2 parallaxes have slopes of unity within $2\sigma$. Per subclass they measured the following slopes: AGBs: $1.008 \pm 0.080$ and $1.069 \pm 0.078$ when removing binaries; YSOs: $0.999 \pm 0.010$ and $0.985 \pm 0.012$ when removing binaries; other radio stars: $1.004 \pm 0.003$. Clearly, AGB stars have larger uncertainties with respect to the other classes. The intercepts have all a small, negative value (all below $-$0.103\,mas, the value for other radio stars) for all subclasses and the full sample. These results imply that the VLBI and Gaia results are in good agreement on average, but that AGB stars are more prone to discrepant astrometry."
• Line 314-317: I suggest including the zero-point values of the cited references.
  • The zero-point values for the faint quasars and bright stars have been added (and references of the latter updated). The text was changed to: “This is a bit larger than the value presented for faint quasars of $-$29\,$\mu$as by \cite{Lindegren:2018} and more similar to the values presented for the (optically) brighter stars of about $-$50\,$\mu$as \cite[see][for references]{Riess:2018, Zinn:2019, schoenrich:2019}.”
• Line 323-326: I was a little confused because of this statement. I had understood that O-type stars did indeed trace the spiral arms similar to the masers. Couldn't the greater scattering of the spiral pattern be due to age scattering? This can be clearly seen when using samples of objects with different ages.
  • O-type stars do trace the spiral arms but just not as well as the maser-bearing SFRs.
  • We rewrote the text and it reads now: “From figure 2 in \cite{Xu:2021a}, it is clear that O-stars trace the spiral arms but not as precisely as maser-bearing SFRs as the O-star distribution is more scattered and a number of O-stars appear to be present in the inter-arm regions.”
  • Indeed, B-type stars (which are longer lived than O-stars) do not trace the spiral arms as well as the O-type stars so age scattering might have an effect. However, it is beyond the scope of this review to investigate this further.
• Line 327-328: Regarding migration, I had understood that typically the O-type stars should not have moved more than 0.2 kpc from their birthplaces and should still be in their birth spiral arms. See the simple calculation presented in Section 3 of Xu et al. 2018 A&A 616, L15. In the paper published by Xu et al. 2021 the same numerical argument is given considering B-type stars, although in the conclusions the authors said: "In short, the O-type stars tend to clump together and some of them are frequently found between the major spiral arms, indicating that recent star formation does occur in the inter arm regions and/or some of them have migrated far away from their birthplaces." I was confused. What I missed
  • We rewrote the text and it reads now: “ \cite{Xu:2021a} interpret this finding as an indication for some high-mass star formation occurring possibly in the inter-arm regions or potential migration of O-type stars from their birth sites in the spiral arms. However, the latter would require unusually high peculiar motions for these objects \citep[][]{Xu:2018b}.”
• Line 332-334: I think it is interesting to present to the reader the future projects of Southern Hemisphere VLBI and LBA arrays.
  • We have included the LBA in the Section “Observations and data calibration”. The Southern Hemisphere VLBI is mentioned in the Outlook of the paper, as the only AuScope publication at this moment is a calibration technique paper by Hyland et al. 2022.
  • We added the following sentence in Section 8: “\cite{Green:2015} summarizes the upcoming opportunities for maser astrometry when including the SKA in existing VLBI arrays.”
• Line 339: It was not clear how figure 1 shows this.
  • We changed the text to: “These, together with the radial velocity of the maser star, taken from typical high-density tracing molecules such as NH$_{3}$, CS or CO, can be used to obtain 3D positions (X, Y, Z) and 3D motions (U; motion toward the Galactic Centre, V; motion in direction of Galactic rotation, W; motion toward the north Galactic pole). Fig.~\ref{fig:UVW-plane} shows the orientation of these motion components.”
• Line 354: The first line in the paragraph is not clear.
  • We changed the text to: “After the assignment of the maser sources to spiral arms, the spiral arm structure becomes evident when the maser sources are plotted in a plan view of the Milky Way (see Fig.~\ref{fig:planview_mw}).”
• Figure 2: Especially in Q1 I see dots of one color on arms of another color. For example, at 5<x<10 and -5<Y<0 I see Perseus's points on the outer arm. There are also points with Sagittarius's colors on arms of other colors. I don't understand how it is possible since first the maser is associated with the arm and then the fits are made. What I missed?
  • The association of sources to the spiral arm is indeed done before the fits to the spiral arms are made. The association is primarily based on the VLSR of the maser source (in a molecular line that traces dense gas). In some cases if it was difficult to obtain a good match through VLSR, also the proper motion and parallax values were used to determine the spiral arm association using the parallax-based distance estimator. It is thus entirely possible that for a few objects with a velocity profile of one arm the parallax (and proper motion) places them rather far from that arm. These objects are by far in the minority. In addition, all the parallax measurements have error bars that are not drawn in this figure but are represented by the size of the dot (the bigger the dot, the larger the uncertainty of the parallax measurement).
  • We adjusted the text in Section 5.1 “Arm assignment” to “Maser sources in high-mass star-forming regions can be assigned to spiral arms by associating them with molecular clouds. This requires a good agreement of the position and line-of-sight velocity of the maser with the ($l$-$v$) locus of the arm \citep[see][their figure 3]{Reid:2019}. For objects with uncertain spiral arm assignment based on their line-of-sight velocities alone, additionally their proper motion and parallax are used in the updated version\footnote{The updated version can be found here \url{http://bessel.vlbi-astrometry.org/node/378}.} of the parallax-based distance estimator \citep{Reid:2016,Reid:2019} for their localisation in the Milky Way.”
• Line 365: Table1: A few words about the cause of such a large discrepancy in values would be interesting. Are the methods and data used similar?What does that mean? I think the spiral structures is still difficult to trace with precision. Is that correct?
  • The methods are the same and the datasets are mostly maser parallax observations (except the results from Boblev et al. 2014 who augmented the relatively small maser dataset with young stellar clusters). However, the sample size and the covered azimuth ranges can have a large effect on the fitted pitch angle. The spiral arms in Q1, 2 and 3 are relatively well traced now (except for the far side of the Milky Way where there are not that many measurements yet). Larger sample sizes allow splitting up the spiral arms into smaller sections and do a more detailed analysis on these sections which can result in different fitted pitch angle values. Increasing the azimuth range of the arms in the future, especially into Q4, will yield a more detailed picture of the structure of each arm.
  • We added the following text: “The size of the fitted maser sample as well as the covered azimuth range can have a large effect on the pitch angle. Within overlapping azimuth ranges, the pitch angles of the global fits for each of the arms agree within their joint uncertainties. However, larger sample sizes and azimuth ranges allow to split up the spiral arm into smaller sections or fit the arm with a kink which can result in different pitch angles compared to the global fit. Increasing the azimuth coverage of the maser sample for each of the arms in the future, especially into Quadrant 4, will contribute to uncovering a more detailed picture of the spiral arms.”
• Other authors find different values for the pitch angle, also using the same tracers. I think it is important for the reader to say a few words about that.
  • This is mostly due to different sample sizes and covered azimuth ranges. See comment above.
• Line 373: It is not easy to see it in the plots. For example, there is no clear difference if compared to Perseus.
  • This connection is inferred from an extrapolation of the Norma and Outer arms. The plan view of the Milky Way in Figure 2 shows that the two arms connect relatively well between Q4 and Q1. Of course, since there are no parallax measurements yet towards the Norma arm in Q4 and the far side of the Outer arm in Q1, this is still a theory. Hopefully, future maser parallax observations from the Southern Hemisphere will corroborate this theory.
• Line 385-387: I couldn't see it in the Figure 2.
  • Again, this is an extrapolation of the spiral arm fit to the maser data in Q1, 2 and 3. We added “fourth and” to the text to correct that the Perseus arm starts already in quadrant 4. Hopefully, future maser observations from the Southern Hemisphere will pinpoint this part of the arm.
• lines 396-413: I’m thinking about the role of the corotation. The explanation given by Monteiro et al. 2021 (see their Figure 4) can't be an option too?
  • We are not quite sure how corotation would explain the peculiarities of the Perseus arm and thus we do not discuss this reference here.
• Line 422: suggestion: at separations of 1.5 and 2.0 kpc, respectively.
  • We changed the text accordingly.
• Line 447: Wouldn't it be easier to see in the figure 2? Where is the bar in figure 7?
  • We agree! The text was modified accordingly.
• line 565: Missing space before 36
  • When multiple references are given in one \cite command they don’t have spaces after the comma in this style format. We will enquire with the Editor.
• line 596: suggestion: The two distances to the Galactic Centre obtained…
  • This reads much better, thank you! We changed the text accordingly.
• line 598 - 600: These results were not redetermined with Gaia data?
  • We found a recent R0 determination from Gaia ED3 + APOGEE by Leung et al. 2020.
  • We added the result to Table 2 and in Section 7.1.1: “\cite{Leung:2022} found $8.23\pm0.12$\,\kpc though the combination of {\em Gaia} EDR3 \citep{Gaia:2021} and Apache Point Observatory galactic evolution experiment (APOGEE) DR17 \citep{Abdurrouf:2022} astrometry of Galactic bar stars augmented spectro-photometric distances from the neural network method {\tt astroNN}.”
  • We also added the Gaia value for the rotation speed of the Sun (Mroz et al. 2019 - thank you for pointing out this paper - and Ablimit et al. 2020).
• Line 604: Missing the unity
  • Added. Thank you for spotting this!
• Line 605: Missing the unity
  • Added. Thank you for spotting this!
• line 606-607: But previously you said that similar values were in agreement.
  • The sentence was rewritten to make it clear that the two maser distances are in agreement with both the values from stellar orbits, but that the two stellar orbit distances have a slight tension. “While the two distances derived from stellar orbits are in slight tension with each other, the maser-parallax derived distances, which have larger uncertainties, are in agreement with both these values” We hope this makes it more clear.
• line 620: What is the value of the uncertainty?
  • We added the formal uncertainty in the text.
• Figure 8: rotation curve: Are the error bars in R (x-axis) included in the error bars presented in y-axis?
  • The error bars in the y axis are the uncertainties in the V component of the peculiar motion. This uncertainty depends mainly on the uncertainties in the proper motions and the radial velocity but also on the parallax uncertainty (which is directly related to the uncertainty in galactocentric distance).
• Comparing the curves on an enlarged scale I don't see them as quite similar as commented in the line 666. I notice important differences that do not appear on the scale used. For example, the universal curve is systematically higher (+~10km/s) than the other curves between 5 and 10kpc. After 12 kpc the RG and 2nd-order polynomial curves fall while the other two are flat.
  • Thank you for this excellent comment. We have modifed the text accordingly: “Figure~\ref{fig:galrot} shows the three rotation curves based on maser parallaxes and the two rotation curves based on RGB stars and Classical Cepheid stars. Between 5 and 12 kpc, the rotation curves have a similar slope; they are nearly flat. The two evolved star rotation curves appear to match the maser data points well. Looking at the rotation curves in more detail, however, one can note that the Universal Rotation Curve by \cite{Reid:2019} has a slightly different shape than the linear curves, and that it has, on average, higher rotational velocities in this galactocentric distance range. Beyond 10-12\,kpc, the rotation curves start to diverge more: while the Universal Rotation Curve of \cite{Reid:2019}, the power-law fit of \cite{VERA:2020} and the Cepheid-based linear rotation curve of \cite{Mroz:2019} are around 224\,\kms\ and remain flat at these large galactocentric distances, the second order polynomial fit of \cite{VERA:2020} and the RSG-based linear rotation curve of \cite{Eilers:2019} are dropping with distance from the Galactic Centre. The maser data appear to prefer the rotation curves that are close to flat at distances of 12-15\,kpc. However, more maser stars with precise astrometry, and, in particular, maser stars at large Galactocentric distances, are needed to better constrain the type and thus the shape of the Galactic rotation curve. Finding high-mass star-forming regions with maser emission at large galactocentric distances is not simple: the star-forming activity in the Outer arm is rather low and decreases further at distances beyond the Outer arm.”
• There are authors who fit to the same data a gap in about 9 kpc. The gap in this region, which has smaller errors, can be seen in the maser data and even more clearly in the data from the Gaia DR2 catalog by Crosta et al. 2019.
  • Thank you for this reference. We think that discussing the gap at about 9 kpc is too much detail for what we had in mind for this section. The maser data in the Outer Galaxy is rather sparse, as high-mass star-forming regions are sparser and those with bright enough methanol masers even more. A non-uniform maser coverage on galactocentric radii in the Outer Galaxy is therefore not peculiar, and other gaps are seen as well. We did not include a discussion of any of the gaps in the review.
• I think it is important a mention about different tracers show different rotation curves and maybe important some comment about how it is difficult to measure.
  • This comment has been included in the reply above.
• Moreover, the text gives the impression that we know the rotation curve well, but different authors using different objects obtain different results and from what I can see in the literature this subject is in debate. As an example, Mróz 2019 claims that gives using cepheids the most accurate Galactic rotation curve at distances R>12 kpc constructed so far.
  • We thank the referee for the Mroz 2019 reference which we used in the review and included in Figure 8.
• Line 673 - 674: I don't see so clearly that the curves from maser and stellar astrometry give similar results.
  • This comment has been included in the reply above.
• Line 718: suggestion: parameters instead numbers
  • We replaced “numbers” with “results”.