Rotation curves for the maximums obtained in the crest of maximums of previus issue.

[martinmestre]

Hello all (@Charly-Arguelles @danielcarpintero @ankrut )!

I have some good updates.
I have computed the rotation curve for 4 of the selected points in the previous issue (Crests of maximums).
They are the following:

1. beta_0 = 1.0e-5 with theta_0, d_theta = 36.5310621242485, 27.687374749498996
2. beta_0 = 1.2e-05 with theta_0, d_theta = 36.28657314629258, 27.494989979959918
3. beta_0 = 1.3e-05 with theta_0, d_theta = 36.22244488977956, 27.442885771543086
4. beta_0 =1.5e-05 with theta_0, d_theta = 36.02204408817635, 27.286573146292586

with theta_0, d_theta = 36.02204408817635, 27.286573146292586

In the plots you can see one MW model with RAR, and two other MW potentials from recent literature. There are also observationa data from 3 different origins.
I can observe that the RAR rotation curve doesn't change much. I have also computed the core mass of the central density and it
gives the following values:

1. 3.0e6
   2)3.4e6
   3)3.6e6
   4)3.9e6.

Taking in consideration that from previous works in the literature (Eduard et al.) the core mass should be around 3.5e6,
I think we have obtained the result of our work.
The model that fits GD-1 should be between cases 2 and 3. It is true that the rotation curve fit is not good for any of the observations. At least it is more or less in the middle of the three of them. In fact the rotation curve data doesn't agree between different surveys.
What do you think?
All the best,
Martín

[danielcarpintero]

Martín, Good work! A coherent model, finally. I can't see any differences between the 4 plots. Perhaps a logarithmic scale in r is a better choice (being r a radial coordinate). I see two potential issues with a future referee: 1) The curve reaches a maximum above any of the other curves/data, and with a positive slope, contrary to all the data. 2) The final slope is not near-horizontal, as observed in most disk galaxies. Maybe these are not too important, but I would point them out if I were the referee. Daniel El vie, 11 feb 2022 a las 16:47, martinmestre ***@***.***>) escribió:

…

Hello all ***@***.*** <https://github.com/Charly-Arguelles> @danielcarpintero <https://github.com/danielcarpintero> @ankrut <https://github.com/ankrut> )! I have some good updates. I have computed the rotation curve for 4 of the selected points in the previous issue (Crests of maximums). They are the following: 1. beta_0 = 1.0e-5 with theta_0, d_theta = 36.5310621242485, 27.687374749498996 2. beta_0 = 1.2e-05 with theta_0, d_theta = 36.28657314629258, 27.494989979959918 3. beta_0 = 1.3e-05 with theta_0, d_theta = 36.22244488977956, 27.442885771543086 4. beta_0 =1.5e-05 with theta_0, d_theta = 36.02204408817635, 27.286573146292586 [image: rotation_curve_beta0_1 0e-5] <https://user-images.githubusercontent.com/58749264/153658309-f0246d7a-a00b-4f70-b33e-1961287d63ed.png> with theta_0, d_theta = 36.02204408817635, 27.286573146292586 [image: rotation_curve_beta0_1 2e-5] <https://user-images.githubusercontent.com/58749264/153658319-f7e1436b-2887-4a81-817c-1449654f6315.png> [image: rotation_curve_beta0_1 3e-5] <https://user-images.githubusercontent.com/58749264/153658339-f3486717-5569-4d21-a795-213d7357776a.png> [image: rotation_curve_beta0_1 5e-5] <https://user-images.githubusercontent.com/58749264/153658352-87bc6913-042e-43eb-bcf1-a70e499bdd5a.png> In the plots you can see one MW model with RAR, and two other MW potentials from recent literature. There are also observationa data from 3 different origins. I can observe that the RAR rotation curve doesn't change much. I have also computed the core mass of the central density and it gives the following values: 1. 3.0e6 2)3.4e6 3)3.6e6 4)3.9e6. Taking in consideration that from previous works in the literature (Eduard et al.) the core mass should be around 3.5e6, I think we have obtained the result of our work. The model that fits GD-1 should be between cases 2 and 3. It is true that the rotation curve fit is not good for any of the observations. At least it is more or less in the middle of the three of them. In fact the rotation curve data doesn't agree between different surveys. What do you think? All the best, Martín — Reply to this email directly, view it on GitHub <#4>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/ATTASCZP4QHMQPFD45Z5XTDU2VRW3ANCNFSM5OFF5NKQ> . Triage notifications on the go with GitHub Mobile for iOS <https://apps.apple.com/app/apple-store/id1477376905?ct=notification-email&mt=8&pt=524675> or Android <https://play.google.com/store/apps/details?id=com.github.android&referrer=utm_campaign%3Dnotification-email%26utm_medium%3Demail%26utm_source%3Dgithub>. You are receiving this because you were mentioned.Message ID: ***@***.***>

[Charly-Arguelles]

Hi to all These are very good results Martin!. To start with, we are fitting the GD1 stream without the need to change the spherical symetry (as needed within NFW from Ibata's results), and, as was somewhat expected, you are showing that we have some degeneracy in the free parameters (very nicely shown along the crests of maximum likelihood), which include the "good" RAR solution in the sense that the central DM core can explain the S-star orbits as well (as it is for Mc = 3.5x10^6 Mo). In my opinion, one remaining point would bee to check (at least minimally) what can be gained further regarding the fitting power of the rotation curve, by varying somewhat the baryons (mainly the disk parameters). But of course, it should be re-done the analysis for GD-1, in a kind of iterative fashion (because we are not doing all the fittings in parallel as we have already agreed in the past). Martin, one question from my side (which I forgot): are we using the Miyamoto Nagai disk right?, and, what about the baryonic disks (formula and specific free parameters) used by the other authors we are comparing with in the Vrot curve?. To me, there is certainly some extra freedom about the baryons yet, in the sense that, for example the contribution of the disk could make the RAR DM tail start to decrease further in radius.. We may organize a short meeting to discuss further. Best Carlos

________________________________ De: danielcarpintero ***@***.***> Enviado: viernes, 11 de febrero de 2022 17:52 Para: martinmestre/stream-fit ***@***.***> Cc: Charly-Arguelles ***@***.***>; Mention ***@***.***> Asunto: Re: [martinmestre/stream-fit] Rotation curves for the maximums obtained in the crest of maximums of previus issue. (Issue #4) Martín, Good work! A coherent model, finally. I can't see any differences between the 4 plots. Perhaps a logarithmic scale in r is a better choice (being r a radial coordinate). I see two potential issues with a future referee: 1) The curve reaches a maximum above any of the other curves/data, and with a positive slope, contrary to all the data. 2) The final slope is not near-horizontal, as observed in most disk galaxies. Maybe these are not too important, but I would point them out if I were the referee. Daniel El vie, 11 feb 2022 a las 16:47, martinmestre ***@***.***>) escribió:

Hello all ***@***.*** <https://github.com/Charly-Arguelles> @danielcarpintero <https://github.com/danielcarpintero> @ankrut <https://github.com/ankrut> )! I have some good updates. I have computed the rotation curve for 4 of the selected points in the previous issue (Crests of maximums). They are the following: 1. beta_0 = 1.0e-5 with theta_0, d_theta = 36.5310621242485, 27.687374749498996 2. beta_0 = 1.2e-05 with theta_0, d_theta = 36.28657314629258, 27.494989979959918 3. beta_0 = 1.3e-05 with theta_0, d_theta = 36.22244488977956, 27.442885771543086 4. beta_0 =1.5e-05 with theta_0, d_theta = 36.02204408817635, 27.286573146292586 [image: rotation_curve_beta0_1 0e-5] <https://user-images.githubusercontent.com/58749264/153658309-f0246d7a-a00b-4f70-b33e-1961287d63ed.png> with theta_0, d_theta = 36.02204408817635, 27.286573146292586 [image: rotation_curve_beta0_1 2e-5] <https://user-images.githubusercontent.com/58749264/153658319-f7e1436b-2887-4a81-817c-1449654f6315.png> [image: rotation_curve_beta0_1 3e-5] <https://user-images.githubusercontent.com/58749264/153658339-f3486717-5569-4d21-a795-213d7357776a.png> [image: rotation_curve_beta0_1 5e-5] <https://user-images.githubusercontent.com/58749264/153658352-87bc6913-042e-43eb-bcf1-a70e499bdd5a.png> In the plots you can see one MW model with RAR, and two other MW potentials from recent literature. There are also observationa data from 3 different origins. I can observe that the RAR rotation curve doesn't change much. I have also computed the core mass of the central density and it gives the following values: 1. 3.0e6 2)3.4e6 3)3.6e6 4)3.9e6. Taking in consideration that from previous works in the literature (Eduard et al.) the core mass should be around 3.5e6, I think we have obtained the result of our work. The model that fits GD-1 should be between cases 2 and 3. It is true that the rotation curve fit is not good for any of the observations. At least it is more or less in the middle of the three of them. In fact the rotation curve data doesn't agree between different surveys. What do you think? All the best, Martín — Reply to this email directly, view it on GitHub <#4>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/ATTASCZP4QHMQPFD45Z5XTDU2VRW3ANCNFSM5OFF5NKQ> . Triage notifications on the go with GitHub Mobile for iOS <https://apps.apple.com/app/apple-store/id1477376905?ct=notification-email&mt=8&pt=524675> or Android <https://play.google.com/store/apps/details?id=com.github.android&referrer=utm_campaign%3Dnotification-email%26utm_medium%3Demail%26utm_source%3Dgithub>. You are receiving this because you were mentioned.Message ID: ***@***.***>

— Reply to this email directly, view it on GitHub<#4 (comment)>, or unsubscribe<https://github.com/notifications/unsubscribe-auth/AMVDHKVBF5QEZUCKOABERETU2VZIJANCNFSM5OFF5NKQ>. Triage notifications on the go with GitHub Mobile for iOS<https://apps.apple.com/app/apple-store/id1477376905?ct=notification-email&mt=8&pt=524675> or Android<https://play.google.com/store/apps/details?id=com.github.android&referrer=utm_campaign%3Dnotification-email%26utm_medium%3Demail%26utm_source%3Dgithub>. You are receiving this because you were mentioned.Message ID: ***@***.***>

[martinmestre]

Hi @danielcarpintero @Charly-Arguelles

Good work! A coherent model, finally. I can't see any differences between the 4 plots.

The difference in the models is in the region of the central core. For slightly different beta_0 values, the other two parameters
compensate in order to have the same rotation curve for r> 1kpc at least.

Perhaps a logarithmic scale in r is a better choice (being r a radial coordinate).

Yes, if we would be interested in fitting rotation curve deep inside r< 5kpc. Are we ?

I see two potential issues with a future referee: 1) The curve reaches a maximum above any of the other curves/data, and with a positive slope, contrary to all the data. 2) The final slope is not near-horizontal, as observed in most disk galaxies.

1. I do not exactly get what is meant by positive slope.
2. Yes, its true. Our rotation curve falls faster, because the dark matter ball has finite radius around 30 kpc.

[danielcarpintero]

positive slope = increasing = derivative > 0 El lun, 14 feb 2022 a las 17:57, martinmestre ***@***.***>) escribió:

…

Hi @danielcarpintero <https://github.com/danielcarpintero> @Charly-Arguelles <https://github.com/Charly-Arguelles> Good work! A coherent model, finally. I can't see any differences between the 4 plots. The difference in the models is in the region of the central core. For slightly different beta_0 values, the other two parameters compensate in order to have the same rotation curve for r> 1kpc at least. Perhaps a logarithmic scale in r is a better choice (being r a radial coordinate). Yes, if we would be interested in fitting rotation curve deep inside r< 5kpc. Are we ? I see two potential issues with a future referee: 1) The curve reaches a maximum above any of the other curves/data, and with a positive slope, contrary to all the data. 2) The final slope is not near-horizontal, as observed in most disk galaxies. 1. I do not exactly get what is meant by positive slope. 2. Yes, its true. Our rotation curve falls faster, because the dark matter ball has finite radius around 30 kpc. — Reply to this email directly, view it on GitHub <#4 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/ATTASCY7YIFJHJNL3INXTFTU3FUBXANCNFSM5OFF5NKQ> . Triage notifications on the go with GitHub Mobile for iOS <https://apps.apple.com/app/apple-store/id1477376905?ct=notification-email&mt=8&pt=524675> or Android <https://play.google.com/store/apps/details?id=com.github.android&referrer=utm_campaign%3Dnotification-email%26utm_medium%3Demail%26utm_source%3Dgithub>. You are receiving this because you were mentioned.Message ID: ***@***.***>

[martinmestre]

In my opinion, one remaining point would bee to check (at least minimally) what can be gained further regarding the fitting power of the rotation curve, by varying somewhat the baryons (mainly the disk parameters). But of course, it should be re-done the analysis for GD-1, in a kind of iterative fashion (because we are not doing all the fittings in parallel as we have already agreed in the past). Martin, one question from my side (which I forgot): are we using the Miyamoto Nagai disk right?, and, what about the baryonic disks (formula and specific free parameters) used by the other authors we are comparing with in the Vrot curve?. To me, there is certainly some extra freedom about the baryons yet, in the sense that, for example the contribution of the disk could make the RAR DM tail start to decrease further in radius..

I will do some fits varying the barions as follows:
15% for central values of the masses and 10% for characteristic scales, according to the first paragraph of section 3.1.2 of this paper