The Influence of the Galactic Bar on the Dynamics of Globular Clusters

Round 1

Reviewer 1 Report

The manuscript presents a consideration of the influence of the Galactic bar onto dynamics of globular clusters, highlighting resulting uncertainties on recent claims on GC accretion events. The MS is useful for the readers and the comments are directly on improving the clarity of the presentation. 

line 91 with with -> with

line 91 (highlighted by -> inside the

line 112 refrain this study to follow -> in this study we will refrain from 

line 166 was adopted -> we adopted

line 168 estimated less value -> estimated the value to be lower

Eq.6 specify n

Caption of Fig.2: explain better what is plotted. Introduce angle \phi instead of its numerical value. The axis of bar rotation and the sign for rotation is hard to understand. Use of \omega in the Figure 2 vs use of \Omega in the text. 

Fig.3 Add \phi to inserted box, which lists the solutions for different values of \phi

line 182: in our in -> in our

Fig.4-5 Consider using different symbols for different GC, as readers m.b. color blind (or print in grey scale)

line 222: affected by the influence of the -> affected by the

The statement contained in the lines 221-224 on significance of the influence of the MW bar. The reader is not provided with the quantitative value of a threshold above which the influence shall be considered significant and below which it shall be considered insignificant.

line 286 one take -> one takes

line 287:positions of clusters on ... diagram is not -> positions of clusters on ... diagram are not

line 292 together in tandem : use either one (together OR in tandem)

Fig.9 to back up authors statement about "impossible to discriminate between different parent merger events" it would be great to have a mark of typical size of the zones considered to the "different" for such an analysis.

 

 

 

 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

 

     Referee's report on the manuscript galaxies - 2139037,

 

      'The influence of the Galactic bar on the dynamics of globular

      clusters'

 

       By: Tkachenko et al.

 

------------------

 

This is a concise paper convincingly showing that the varying potential

produce by the rotation of the MW bar significantly modifies the position

of its globular clusters (GC) in the Lz - E plane. This fact, together with

the observational errors, makes it imposible to use the position in this

plane for assigning individual GCs to particular merger events.  Thus,

I do not hesitate to recommend the publication of the manuscript

once a few clarifications are included, and a large number of typos

and language difficulties are fixed. The main issues are in items

# 22, 27, 28, 31, 36, and 43.

 

   1.- Introduction, first sentence.

 

       '... and small galaxies [1,2].' -->

       '... and small galaxies [1,2],  as well as gas accretion events

       [e.g., Dekel+09, Nat., 457, 451].' 

 

   2.- Introduction, 2nd paragraph, line 28.

 

      '(GSE) accretion event [3]. A comprehensive study' -->

      '(GSE) accretion event. A comprehensive study'

 

   3.- Introduction, 3rd paragraph, line 31.

 

       'Gaia mission' --> 'The Gaia mission'

 

   4.- Introduction, 6th paragraph, lines 70 - 71.

 

       'because calculation of JR and Jz values in the

       non-axisymmetric and time-dependent potential

       with elongated bar/bulge component is not possible.'

 

       I think you should explain why. 

 

   5.- Introduction, last paragraph, line 75.

 

       'different accretion events Malhan et al. [25]'

       --> 'different accretion events [25]'

 

   6.- Introduction, last paragraph, line 77.

 

       'Hattori et al. [29], Hunt and Bovy [30]' -->

       'Hattori et al. [29], and Hunt and Bovy [30]'

 

   7.- Sect. 2, 1st paragraph, lines 91 - 92'

 

       'together with ...  taken from' -->

       'together with their observational errors (in parentheses)

       taken from'

 

   8.- Sect. 3, 2nd paragraph,  lines 94 - 96.

 

       'adopt for Sun’s Galactocentric distance'  -->

       'adopt for the solar galactocentric distance'

 

       'GRAVITY Collaboration ... Galactocentric' -->

       'the GRAVITY Collaboration et al. [34], for the velocity components of the

       Sun in the galactocentric'

 

       It may be a good idea to split this long sentence

       into several smaller, to facilitate reading. 

 

   9.- Caption of Fig1, 1st sentence.

 

       'on (Lz,E)-plane' --> 'in the (Lz,E)-plane'

 

  10.- Caption of Fig. 1, last sentence starting 'Dots show ..'.

 

       It is a bit confusing. Please, reword. Something in the line of 

 

       'Dots show ...' -->

       'The dots show one hundred randomly chosen globular cluster

       locations consistent with the errors in Table 1. We have assumed

       a normal distribution with the standard distribution set by the

       errors.'

 

       The same comment applies to the reference made in the text

       in line 102.

 

  11.- Sect. 2, last paragraph, lines 110 - 119.

 

       'the authors Malhan et al.' --> 'Malhan et al.'

 

       'We will refrain this study to follow this procedure, since'

       -->

       'We will refrain to follow this procedure in our study, since'

 

       'in the non-axisymmetric' --> 'in an axisymmetric'

 

       'that accreted almost' --> 'that were accreted almost'

 

  12.- Sect. 3, 1st paragraph.

 

       'using astrophysical package' -->

       'using the astrophysical package' 

 

  13.- Sect. 3.1, lines 127 - 128.

 

       'First model has an axisymmetric ... axisymmetric' -->

       'The first model has an axisymmetric and time-independent potential,

       whereas the second one has a non-axisymmetric'

 

       'with elongated bar/bulge' --> 'with an elongated bar/bulge'

 

  14.- Sect. 3.1.1, 1st sentence.

 

       'Modeling the axisymmetric Milky Way ...' -->  

       'Following Malhan et al. [25], first we model the Milky Way using the axisymmetric

       potential described by McMillan [39] (McMillan17). The model includes the bulge,

       the thick and thin stellar disks, two gaseous disks (H I and H2), and the

       dark matter halo.'

 

  15.- Sect. 3.1.1, sentences after Eq. (1).

 

       'where r′ = ... ; the' --> 'where r′ = ... , the'

 

       '0.075 kpc correspondingly, rcut = 2.1 kpc and'

       -->

       '0.075 kpc, respectively, rcut = 2.1 kpc, and'

 

       'gives the total bulge mass' -->

       'gives a total bulge mass' 

 

  16.- Sect. 3.1.1 and throughout the text.

 

       Use 'disc' or 'disk', but not both.

 

  17.- Sect. 3.1.1, 3rd paragraph starting after line 139.

 

      'subsystems, - the thin' --> 'subsystems, the thin'

 

      'disks described by the density profile:' -->

      'disks both described by density profiles with the form,'

 

      'density respectively. Vertical scale' -->

      'density, respectively. The vertical scale'

 

      'are accepted to be equal to 2.5 kpc and 3.02 kpc

      respectively.' -->

      'are assumed to be 2.5 kpc and 3.02 kpc, respectively.'

 

      'of the thin and of the thick disks Σ0,d,thin = 896'

      -->

      'of the thin and of the thick disks taken to be

      Σ0,d,thin = 896'

 

      '(can be estimated as' --> '('

 

      'M_\odot respectively. The possible' -->

      'M_\odot, respectively. A possible'

 

  18.- Eqs. (2) and (3). Replace the final comma with a full stop.

 

  19.- Sect. 3.1.1, 3rd paragraph starting in line 148.

 

       'includes also two gaseous disks, - the atomic H I and

       molecular H2.' -->

       'also includes two gaseous disks; the atomic (H I) one and

       molecular (H2) one.'

 

       'by equation:' --> 'by the equation,'

 

       'For HI disk' --> 'For the HI disk'

 

       'For H2 gaseous disk accepted values' -->

       'For the H2 gaseous disk the accepted values'

 

  20.- Sentences after Eq. (4).

 

       rho_0,h is not the 'central volume density' since

       the central density goes to infinity in a NFW profile.

 

       'the central volumen density' -->

       'a characteristic scaling density'

 

  21.- Sentences after Eq. (4).

 

      Give the DM halo mass of the model.

 

  22.- (I) Sect. 3.1.1.

 

       Where are all the numerical values describing the

       MW potential coming from? If they come from

       MacMillan [39], say it explicitly. Otherwise, cite

       the appropriate reference(s). 

 

  23.- Sect. 3.1.2, sentences before Eq. (5), lines 160 - 161.

 

       'Following to ...  Ferrers model [44]:' -->

       'Following Chemel et al. [28] and Yeh et al. [43], we

       approximate the bar/bulge by a rotating ellipsoid with

       a density distribution given by a Ferrers model [44],'

 

  24.- Sect. 3.1.2, line 162.

 

       Take out the indentation of the sentence after Eq. (5).

 

  25.- Sect. 3.1.2, sentences after Eq. (5).

 

       'We choose the values for bar semi-axes' -->

       'For the bar semi-axes, we choose the values'

 

       'which gives good approximation for elongated

       bar/bulge' -->

       'which gives a good approximation for the

       elongated bar/bulge' 

 

       '(see, for example Model M85' -->

       '(see, for example, Model M85'

 

       'of the bar equal' -->

       'of the bar taken to be equal'

 

       'estimated less value' -->

       'estimated a smaller value of'

 

  26.- Sect. 3.1.2, sentence right before Eq. (6).

 

       'The potential satisfying equation 5 can be'

       -->

       'The gravitational potential produced by the

       density in equation (5) can be'

 

  27.- (I) Eq. (6).

 

       The symbols 'm^2' is misleading since it was

       already used in Eq. (4) with another meaning.

       Please, change it.

 

  28.- (I) Sect. 3.1.2 and Eq. (6).

 

       Could you please give explicitly the time variation

       of the potential, i.e., once the time variation

       induced by the rotation of the bar is taken into

       account.

       

  29.- Fig. 2, caption.

 

       'of Milky Way bar' --> 'of the Milky Way bar'

 

  30.- Sect. 3.1.2, paragraph starting in line 174.

 

       'Debattista et al. [52] was the first who estimated'

       -->

       'Debattista et al. [52] were the first to estimate'

 

       'using VVV Infrared' --> 'using the VVV Infrared'

 

       'DR2 proper motion' --> 'DR2 proper motions'  

 

       ',  Clarke et al. [53]' --> '. Clarke et al. [53]'

 

       ' model for the bar angular velocity the'

       --> ' model the'

 

       'Portail et al. [7,8], Bovy et al. [56]' -->

       'Portail et al. [7,8] and Bovy et al. [56]'

 

  31.- (I) Sect. 3.2 and Fig. 3.

 

       Explain how rotation curves were derived.

 

  32.- Sect. 3.2, starting in line 189.

 

        'with elongated ... the mass' --> 

'with an elongated bar/bulge whose mass is

about two times larger than the mass'

 

  33.- Sect. 4, first two paragraphs starting in line 185.

 

       'the dynamics of halo globular clusters' -->

       'the dynamics of the halo globular clusters'

 

       'Figure 4 ... galactic models' --> 

       'Figure 4 shows the (Lz, E)-positions of the globular clusters

       calculated using data taken from Table 1 for barred and

       non-barred galactic potential models' 

 

       'Figure 4 ... observational errors' --> 

       'Figure 4 also shows one hundred alternative positions

       of each cluster considering observational errors'

 

       ' non-axisymmetric (left panel) models.' --> 

       ' non-axisymmetric (right panel) models.'

       (Although see the next item.)

       

  34.- Fig. 4.

 

       Change the layout so that the two panels lie on

       top of each other rather than side by side.

 

  35.- Fig. 4, caption.

 

       'clusters on (Lz,E)-plane' --> 'clusters on the (Lz,E)-plane'

 

       'and non-axisymmetric mode' -->

       'and a non-axisymmetric mode'

 

  36.- (I) Sect. 4.

 

       Please, explain how do you integrate the orbits given the mass

       distributions. A few references should suffice.

 

       Do you integrate the orbits backwards of forward in time?

       Even though it is not mentioned explicitly in the paper,

       it seems that you integrate them forward in time, however,

       you reach conclusions on the past arrival of the globular

       clusters to the MW. Explain why you use a forward

       integration in the analysis.

 

       Why do you integrate for 4 Gyr? What is setting this

       timescale? Please, explain.

 

  37.- Sect. 4, 4th paragraph starting in line 209.

 

       'includes rotating bar/bulge.' -->

       'includes the rotating bar/bulge.'

 

       'along the straight line' -->

       'along a straight line'

 

       'This is due to ... z-component ' -->

       'This is due to the fact that in the non-axisymmetric

       time-dependent potential, the z-component '

 

  38.- Sect. 3.1.2, line 218.

 

       Take out the indentation of the sentence after Eq. (9).

 

  39.- Fig. 5, caption.

 

       'Evolution of globular clusters' -->

       'Evolution of the globular clusters'

 

       'of the clusters in Lz on E-plane (' -->

       'of the clusters ('

 

       What is the frequency at which the GCs oscillate?

       Period of the oscillation? You may want to

       mention it explicitly. 

 

  40.- Sect. 4, sentence in line 223.

 

       ' It should also be noted, ...  GSE group.' -->

       ' It should also be noted that some Pontus objects

       reach energy values of the GSE group.'

 

  41.- Sect. 4, sentence in line 227 - 229.

 

       'To do this, ... calculate' -->

       'To do this, we randomly generated one hundred sets

       of the coordinates in the 6D phase space for each globular

       cluster. They are drawn assuming gaussian errors in the

       measured coordinates and velocities, and then we

       calculate'

 

  42.- Sect. 4, paragraph starting in line 230.

 

       'and the total energy E of the ... conditions,' -->

       'and the total energy E for the mean values of the

       initial conditions,'

 

       'to the equation 9' -->

       'to equation (9)'

 

       'Already  ... range of values.' -->

       'Already after 1-2 Gyr of evolution, the range of values

       consistent the observational error is quite large.'

 

  43.- (I) Fig. 6.

 

      Why do the time variation show this stepwise

      pattern? This issue should mentioned explicitly

      in the text, and an explanation should be given.

 

  44.- Fig. 6, caption.

 

       What is t=0 in this plot. Please, mention it

       explicitly.

 

       'bar. Red line shows the orbit evolution' -->

       'bar. The red line shows the evolution'

 

       'the orbits by taking' --> 'the orbits taking'

 

       'of the orbits ... proper motions.' -->

       'of the orbits taking into account the observational

       errors in coordinates and proper motions.'

 

       'the black dotted line' -->

       'the black dashed line'

 

       'constant values for angular' -->

       'constant angular'

       

  45.- Sect. 4, paragraph starting in line 244.

 

       'Figure 7 demonstrates the three' -->

       'Figure 7 shows the three'

 

       'Figure 8 shows the orbit of' -->

       'Figure 8 shows the orbits of'

 

       'Both figures  ... of the cluster.' -->

       'The mean orbits are shown in red line, whereas

       one hundred alternative orbits consistent with

       the observational errors of these initial

       conditions are shown in black.'

 

       'bar significantly chaotizes orbits' -->

       'bar significantly randomizes the orbits'

 

       What do you mean by 'destroys orbital boxes'?

       Please, clarify.

 

       'R vs z in the Figure 8)' -->

       'R vs z in Figure 8)'

 

       'Chemel 251 et al. [28], Hattori et al. [29]' -->

       'Chemel 251 et al. [28] and Hattori et al. [29]'

 

       'NGC 288 has small pericentric' -->

       'NGC 288 has a small pericentric'

 

       'of the bar ... distance the' -->

       'of the bar will obviously decrease due to the increase

       of the distance the'

 

  46.- Fig. 7, caption.

 

       'McMillan17(left) and ... of the cluster.' -->

       'McMillan17 (left panel) and in the non-axisymmetric

       rotating bar/bulge potential (right panel). The red lines

       show the orbits for the mean initial conditions. The  gray

       lines show one hundred orbits consistent with the

       observational errors in these initial conditions.'  

 

  47.- Fig. 8, caption.

 

       'for axisymmetric potential ' -->

       'for the axisymmetric potential'

 

       'for non-axisymmetric potential' -->

       'for the non-axisymmetric potential'

 

       'Red lines show  ... of the cluster.' -->

       'The red lines show the orbit for the mean initial

       conditions whereas the gray lines show one

       hundred orbits consistent with the observational

       errors in these initial conditions.'  

 

  48.- Sect. 4, paragraph starting in line 256.

 

       'on evolution of the clusters (Lz, E)-plane.' -->

       'on the evolution of the clusters in the (Lz, E)-plane.'

 

       'orbits using ... cluster listed in' -->

       'orbits using the errors in' 

 

  49.- Fig. 9, caption.

 

       'after beginning ...  cluster’s parameters.' -->

       'after the beginning of simulations, taking into account

       the non-axisymmetric potential of the rotating bar and

       the observational errors of the initial conditions.'

 

  50.- Sect. 4, paragraph starting in line 260.

 

       'in Figure 9, with ...  non-stationary' -->

       'in Figure 9, which shows the evolution of the clusters

       in the non-stationary'

 

       'It appears impossible to conclude' -->

       'It becomes difficult to conclude'

 

       'belong to any specific accretion events,' -->

       'belong to two different accretion events,'

 

       Use GSE for Gaia-Sausage/Enceladus,

       here and throughout the text.

 

       'intersects with ... it cannot' -->

       'overlaps with both groups. Thus, it cannot 

 

       'belong to the ... progenitor galaxies' -->

       'belong to different accretion events and so to

       different progenitor galaxies'

 

       'object NGC 6864 belongs.' -->

       'object NGC 6864 belongs to.'

 

  51.- Sect. 4, paragraph starting in line 270.

 

       'We can conclude therefore that' -->

       'In more general terms, we conclude that'

 

       'close enough passages' -->

       'close passages'

 

       'dwarf galaxy dynamical friction' -->

       'dwarf galaxy, dynamical friction'

 

       'of the former accretion events' -->

       'of the original accretion events'

 

  52.- Sect. 4, paragraph starting in line 275.

 

       'clusters on Lz, E-diagram' -->

       'clusters on the (Lz, E)-diagram'

 

       'accretion and evolution' -->

       'accretion and secular evolution'

 

  53.- Sect. 5.

 

       'we got to the conclusion' -->

       'we conclude'

 

       'We find that bar potential render the orbits'

       -->

       'We find that the bar potential renders

       the orbits'

       

       'of the clusters simultaneously, it is' -->

       'of the clusters, it is' 

 

       'event or progenitor galaxies.' -->

       'event or progenitor galaxy.' -->

 

       'we provided strong evidences in this work'

       -->

       'in this work we provide strong evidence'

 

       'together in tandem observational errors'

       -->

       'together with the observational errors'

 

       'and showed that it is clearly' -->

       'and clearly showed that it is' 

 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

I apologize with the authors for the delay in providing my report. The paper reads well apart few minor comments ( see below) and both problem and results are well stated and clear. Please address the following major comments in the next revision.

1.Major comment: The adopted galpy and symplectic integrators should be better described in order to understandmethod assumptions and results as well as their limits. Please do not assune all readers know the method assumptions and just summarize/comment on features and limits ( i.e. pro/cons) of the adopted tools.

2. This work has a dynamical approach to the problem, which is appropriate for stellar dynamics. Can you comment in the results section  what is the possible impact of missing a full hydrodynamical approach when considering the interaction of globular clusters with bar and spiral arms?  What correction or further confusion in the results do you expect?

MInor comments:

Page 2 line 39: that objects that ->that these objects have?

Page 2 line 42. "the our Galaxy" -> our Galaxy

All figures: asterisks -> stars?

Page 10 line 249: that bar -> that the bar

Author Response

Please see the attachment.

Author Response File: Author Response.pdf