[Mesa-users] Why does MESA interpret nuclear reaction rates this way?

Wed May 29 05:25:28 UTC 2024

Hello Kaili,

Very cool, thanks for sharing your interpolated rates!

> I'm quite confused about the rate floor... MESA caches end at T8 = 0.002.
The default r_n14_pg_o15 is exactly zero below T8 = 0.01 (i.e., 1 MK, not
10 MK); it is non-zero between 0.002 and 0.01 with my "refined" NAREC II
rate. So what happens below T8 = 0.002?

It is 0 below 200,000K.

> - It seems to me that jina_reaclib_min_T9 is -1, indicating "use the
standard default from rates," by default.
https://docs.mesastar.org/en/release-r22.11.1/reference/star_job.html?highlight=jina_reaclib_min_T9#jina-reaclib-min-t9
<https://urldefense.com/v3/__https://docs.mesastar.org/en/release-r22.11.1/reference/star_job.html?highlight=jina_reaclib_min_T9*jina-reaclib-min-t9__;Iw!!IKRxdwAv5BmarQ!awdjp3oKSc3tq9NkXwgBhM1J1V0MzckOyRvzNwecClRXo_u1F4aDh0f9FhAqTan_0dUfH_Qi3F-Qy7EZHKhicqBtRpVWcQ4$>
However, I don't know what "the standard default" actually means.

The default it T9 = 1d-2, i.e. 10MK. This does not apply to your situation
as you are reading the rate in directly, nor does it apply to most if not
all the networks used in the MESA test_suite, except "split_burn_big_net"
as it uses a large general network, and not for any of the core reactions
which dominate the energy generation rate of the model.

> - As for r_h2_pg_he3, it is non-zero (1.2345793441272736E-022) at 2E-3,
so MESA indeed treats some reactions differently. But again, what is the
story below T8 = 0.002? Some interpolation between (T8 = 0, rate = 0) and
this first node?

Again, I believe the rates are 0 below T8 = 0.002, as we assume no nuclear
reactions are happening at temperatures below 200,000 K. Perhaps try
running a model and plotting what the rates are in the envelope or near the
surface using the rate output provided in the profiles_columns.list. You
can output any individual reaction as a function of mass/radius in the
current version of the code. In
$MESA_DIR/star/defaults/profile_columns.list :

   !add_raw_rates      ! raw reaction rates,       reactions/second

   !add_screened_rates ! screened reaction rates reactions/second

   !add_eps_nuc_rates  ! Nuclear energy (minus neutrino losses) released
erg/s

   !add_eps_neu_rates  ! Neutrino losses             erg/s

   ! individual reactions (as many as desired)

   ! use list_net_reactions = .true. in star_job to list all reactions in
the current net

   ! reactions/second

-EbF

On Fri, May 24, 2024 at 9:23 AM Cao, Kaili <cao.1191 at buckeyemail.osu.edu>
wrote:

> Hi Eb, and MESA users interested in NACRE II,
>
> I have used quadratic interpolation and extrapolation
> (scipy.interpolate.interp1d) in log-log space to "refine" all 32 NACRE II
> nuclear reaction rates shipped with MESA. The plots seem reasonable to me
> (an example is attached below), and I have verified that resulting MESA
> caches agree with my tables. Please feel free to grab them at:
>
> https://drive.google.com/drive/folders/1LE4NpMjauRXoGN8kVnBy2Etci-PQRQA_?usp=drive_link
> <https://urldefense.com/v3/__https://drive.google.com/drive/folders/1LE4NpMjauRXoGN8kVnBy2Etci-PQRQA_?usp=drive_link__;!!IKRxdwAv5BmarQ!awdjp3oKSc3tq9NkXwgBhM1J1V0MzckOyRvzNwecClRXo_u1F4aDh0f9FhAqTan_0dUfH_Qi3F-Qy7EZHKhicqBtU-446yY$>
> and use them in your simulations (disclaimer: at your own risk through).
>
> Continuing my discussion with Eb and Marc (others are welcome to join):
> - Thanks to Eb for pointing related issues on GitHub to me.
> - My previous statement about MESA's interpolation scheme was wrong; it is
> indeed "log T, linear rate."
>
> I'm quite confused about the rate floor.
> - MESA caches end at T8 = 0.002. The default r_n14_pg_o15 is exactly zero
> below T8 = 0.01 (i.e., 1 MK, not 10 MK); it is non-zero between 0.002 and
> 0.01 with my "refined" NAREC II rate. So what happens below T8 = 0.002?
> - It seems to me that jina_reaclib_min_T9 is -1, indicating "use the
> standard default from rates," by default.
>
> https://docs.mesastar.org/en/release-r22.11.1/reference/star_job.html?highlight=jina_reaclib_min_T9#jina-reaclib-min-t9
> <https://urldefense.com/v3/__https://docs.mesastar.org/en/release-r22.11.1/reference/star_job.html?highlight=jina_reaclib_min_T9*jina-reaclib-min-t9__;Iw!!IKRxdwAv5BmarQ!awdjp3oKSc3tq9NkXwgBhM1J1V0MzckOyRvzNwecClRXo_u1F4aDh0f9FhAqTan_0dUfH_Qi3F-Qy7EZHKhicqBtRpVWcQ4$>
> However, I don't know what "the standard default" actually means.
> - As for r_h2_pg_he3, it is non-zero (1.2345793441272736E-022) at 2E-3, so
> MESA indeed treats some reactions differently. But again, what is the story
> below T8 = 0.002? Some interpolation between (T8 = 0, rate = 0) and this
> first node?
>
> Thanks,
> Kaili
>
>
> ------------------------------
> *From:* Ebraheem Farag <ekfarag at asu.edu>
> *Sent:* Thursday, May 23, 2024 3:57 PM
> *To:* Marc Pinsonneault <mhpinsonneault at gmail.com>
> *Cc:* Cao, Kaili <cao.1191 at buckeyemail.osu.edu>; MESA Users List <
> mesa-users at lists.mesastar.org>
> *Subject:* Re: [Mesa-users] Why does MESA interpret nuclear reaction
> rates this way?
>
> Kaili, I believe you are unaffected by a rate floor when reading in an
> external rate file as you are supplying the rate in this circumstance. I
> was mistaken in initially suggesting there was a rate floor here. -EbF On
> Thu, May 23, 2024 at 11: 58
>  Kaili, I believe you are unaffected by a rate floor when reading in an
> external rate file as you are supplying the rate in this circumstance. I
> was mistaken in initially suggesting there was a rate floor here.
>
> -EbF
>
> On Thu, May 23, 2024 at 11:58 AM Ebraheem Farag <ekfarag at asu.edu> wrote:
>
> It is present, but it only affects generalized networks with reactions
> that aren't contained within the standard scope of the hardwired networks
> such as "pp_and_cno_extras.net
> <https://urldefense.com/v3/__http://pp_and_cno_extras.net__;!!KGKeukY!32AtA8uqt2-3LETjOs5yo6ou_XxokLRigiyIk2KprxjnJC_zb-6WVvTccfbtYqyKBNDqNRFZlNr_tMgVpiI_oqZ11n5K$>"
> or "co_burn.net
> <https://urldefense.com/v3/__http://co_burn.net__;!!KGKeukY!32AtA8uqt2-3LETjOs5yo6ou_XxokLRigiyIk2KprxjnJC_zb-6WVvTccfbtYqyKBNDqNRFZlNr_tMgVpiI_oufCkAfz$>"
> etc.. I believe all the core pp and cno reactions (not including be9
> burning) are unaffected and are evaluated separately without a rate floor.
> This includes 'r_h2_pg_he3'. The floor exists because certain reactions
> coming out of the JINA reaclib database result in numerical issues in the
> cold regions of post-main sequence stars with very large general reaction
> networks. Hence, a rate floor was implemented for reactions which do not
> normally dominate the energy budget of the model. We're working to remove
> this, but you're always welcome to lower the floor to capture the other
> reactions if your model is unaffected. : &starjob 'jina_reaclib_min_T9 = '
>
> If you're curious which reactions are hardcoded, see
> $MESA_DIR/rates/raw_rates.f90.
>
> -EbF
>
> On Thu, May 23, 2024 at 11:16 AM Marc Pinsonneault <
> mhpinsonneault at gmail.com> wrote:
>
> Is this reaction floor present for all reactions, or only for late stage
> burning? We have seen reports on this list of Be9 burning being set to zero
> below 10^7 K; how is p+d (critical for the pre-MS) treated?
>
> cheers
>
> marc
>
> On Wed, May 22, 2024 at 3:36 PM Ebraheem Farag via Mesa-users <
> mesa-users at lists.mesastar.org> wrote:
>
> Hi Kaili,
>
> Thanks for raising this issue! As far as I'm aware, the rates are not
> interpolated in log-log space as you've identified. This is the same case
> for  the latest MESA release version. You can look into
> $MESA_DIR/rates/private/rates_support.f90 to see how the rates are
> tabulated. The only course of action I can see at the moment is to rewrite
> this portion of the rates module which appears to interpolate over the rate
> in linear-log space, i.e. the raw/screened rate vs logT.
>
> I don't have any immediate solution for you, but this is a great issue for
> the MESAhub github
> <https://urldefense.com/v3/__https://github.com/MESAHub/mesa/issues__;!!IKRxdwAv5BmarQ!cwA7vnByCpKUIQ8GCMc_uq6jZysiv3RDUzCW-mYeOE4w5aSA9WolZvYDpG3zY3ixf0Gjr6WPUYamTDYpDt0-Mn1fV_Ys$>,
> if you'd like to open an issue there, we can take a closer look and see
> what can be done to address this in the near term and ultimately in a
> future MESA releases.
>
> As for "C12(a,g)O16", this is a helium burning nuclear reaction rate
> which only dominates near the end of Helium burning to set the C/O ratio
> for later phases of evolution. This is to say the rate floor being at T8 =
> 0.6 should be a non-issue, although not ideal.
>
> -EbF
>
> On Tue, May 21, 2024 at 8:43 AM Cao, Kaili via Mesa-users <
> mesa-users at lists.mesastar.org> wrote:
>
> Dear MESA developers and users,
>
> Thanks again to Mathieu (Renzo) for teaching me how to check nuclear
> reaction rates in MESA.
>
> Employing $MESA_DIR/rates/test/show_rates, I managed to visualize how MESA
> interprets NACRE II rates. Using h2_he3_to_h1_he4 as an example, the plot
> below compares MESA's interpretation (black curve; I have been using
> release/r22.11.1) with its underlying NACRE II data (red crosses) shipped
> with MESA ($MESA_DIR/data/rates_data/rate_tables/r_*_nacreII.dat).
>
> I find the results quite unsettling, principally for two reasons:
> - For temperatures below the first node or above the last one, it seems
> that MESA uses a nearest-neighbor extrapolator. For some reactions, e.g.,
> C12(a,g)O16, for which NACRE II starts at T8 = 0.6, this indicates that
> MESA assumes the rate at solar surface is identical to that at solar center.
> - As can be seen on http://www.astro.ulb.ac.be/nacreii/index.html
> <https://urldefense.com/v3/__http://www.astro.ulb.ac.be/nacreii/index.html__;!!IKRxdwAv5BmarQ!c4bjDS3MpzcYVlEzXF7wJX2bZDe29vLOaOhgvrkOWW5Wzf3oXksUkagITelOKylEOSB-tKTF-DhiqX-uzktLbt5ZPrySVg$>,
> NACRE II nuclear reaction rates are smooth functions of the temperature in
> log-log space. However, MESA's interpolation scheme seems to be "wavy"
> (best shown in the interval between first two NACRE II nodes).
>
> Are there scientifical justifications for the above choices? If not, have
> these issues been addressed in r23.05.1, r24.03.1, or the development
> version? Or do you have suggestions to make the results closer to what one
> would expect from published tables and figures? Thank you.
>
> Cheers,
> Kaili
>
>
> ------------------------------
> *From:* Mesa-users <mesa-users-bounces at lists.mesastar.org> on behalf of
> Cao, Kaili via Mesa-users <mesa-users at lists.mesastar.org>
> *Sent:* Saturday, May 18, 2024 9:43 AM
> *To:* Ebraheem Farag <ekfarag at asu.edu>
> *Cc:* mesa-users at lists.mesastar.org <mesa-users at lists.mesastar.org>
> *Subject:* Re: [Mesa-users] [EXT] How to check a nuclear reaction rate?
>
> This Message Is From an External Sender
> This message came from outside your organization.
> Report Suspicious
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>
> Hello Eb,
>
> Thanks. I removed reactions not in pp_and_cno_extras and it worked. The
> test rates (r1 to r9) and those for al26 isomers are also not included, so
> I thought redundant rates were fine, but I was wrong.
>
> Cheers,
> Kaili
> ------------------------------
> *From:* Ebraheem Farag <ekfarag at asu.edu>
> *Sent:* Saturday, May 18, 2024 4:16 AM
> *To:* Cao, Kaili <cao.1191 at buckeyemail.osu.edu>
> *Cc:* mesa-users at lists.mesastar.org <mesa-users at lists.mesastar.org>
> *Subject:* Re: [Mesa-users] [EXT] How to check a nuclear reaction rate?
>
> Hello Kaili,
>
> The isotope li6 is not contained in the 'pp_and_cno_extras.net
> <https://urldefense.com/v3/__http://pp_and_cno_extras.net__;!!KGKeukY!wRpNUs2FYL9xM-l5TQ68oEWuZPWUU2fsjtBKO3aUGUFGOn32_m3SRislwndYL2tTCECDplkDSyamxc4P899l8CxNO3dG$>',
> let alone that reaction rate. You'll have to decide whether this is a
> reaction you need for your science or not. If so, you can make your own
> network to include it.
>
> -EbF
>
> On Fri, May 17, 2024 at 7:15 AM Cao, Kaili <cao.1191 at buckeyemail.osu.edu>
> wrote:
>
> Hello Eb,
>
> Thank you for your previous help regarding nuclear reaction rates and
> local cache directories.
>
> Following your instructions, specifically your method 3, I made a local
> copy of rate_tables/, and added lines like:
> r_h1_h1_ag_li6         'r_h1_h1_ag_li6_nacreII.dat'
> into rate_list.txt therein.
>
> However, when I tried to ./rn the model, I got:
> add_reaction_for_handle failed in reaclib_parse_handle r_h1_h1_ag_li6
>  invalid rate file r_h1_h1_ag_li6
>  rates_init failed in init_raw_rates_records
>  read_raw_rates_records failed in net_setup_tables
>  set_net failed in net_tables
>  failed in set_net
>
> I have been using MESA release/r22.11.1, and
>       change_net = .true.
>       new_net_name = 'pp_and_cno_extras.net
> <https://urldefense.com/v3/__http://pp_and_cno_extras.net__;!!KGKeukY!wRpNUs2FYL9xM-l5TQ68oEWuZPWUU2fsjtBKO3aUGUFGOn32_m3SRislwndYL2tTCECDplkDSyamxc4P899l8CxNO3dG$>
> '
>
> Is there anything else I need to do if I want to use NACRE II rates?
> Please let me know if you need additional information. Thanks.
>
> Cheers,
> Kaili
> ------------------------------
> *From:* Mesa-users <mesa-users-bounces at lists.mesastar.org> on behalf of
> Cao, Kaili via Mesa-users <mesa-users at lists.mesastar.org>
> *Sent:* Thursday, March 28, 2024 9:32 AM
> *To:* Ebraheem Farag <ekfarag at asu.edu>
> *Cc:* mesa-users at lists.mesastar.org <mesa-users at lists.mesastar.org>
> *Subject:* Re: [Mesa-users] [EXT] How to check a nuclear reaction rate?
>
> Hello Eb,
>
> Thank you for sharing these approaches, and sorry for the delay. I think
> your method 3 is especially good for running models in parallel.
>
> Cheers,
> Kaili
> ------------------------------
> *From:* Ebraheem Farag <ekfarag at asu.edu>
> *Sent:* Tuesday, March 26, 2024 9:08 PM
> *To:* Cao, Kaili <cao.1191 at buckeyemail.osu.edu>
> *Cc:* Mathieu Renzo <mrenzo at arizona.edu>; mesa-users at lists.mesastar.org <
> mesa-users at lists.mesastar.org>
> *Subject:* Re: [Mesa-users] [EXT] How to check a nuclear reaction rate?
>
> Hello Kaili,
>
> Yes, it's probably wise to always clear the cache if you are going to
> regenerate new rates, just in case.
>
> 1- Setting those controls in the inlists is one approach, especially if
> you want to provide a special rate factor.
> 2- Another approach is to change the global default in MESA by navigating
> to $MESA_DIR/star/data/rate_tables/rate_list.txt and adding a line that
> says 'r_n14_pg_o15     r_n14_pg_o15_nacreII.dat'.
> 3- One more approach (that I personally opt for in most cases) is to
> repeat 2 but with a local copy of /rate_tables in your MESA model folder.
> MESA should by default use this local rate_tables directory over the main
> default.
>
> In fact, in most of my inlists, I place the following in star_job so that
> my rate_tables and rates_cache are stored locally with some other caches
> and not bound to MESA's default rates or other data folders. (useful for
> running on a cluster)
>
> ! local directories data
>       mesa_dir =''
>       eosDT_cache_dir      = './eosDT_cache'
>       kap_cache_dir        = './kap_cache'
>       rate_tables_dir      = './rate_tables'
>       rates_cache_dir      = './rates_cache'
>
> > Would this be due to different forms of fitting functions?
> Possibly, MESA constructs its own piecewise monotonic cubic spline
> functions to interpolate and tabulate the rate. You can find the calls that
> do this in the same raw_rates.f90 file I referred to previously.
>
> -EbF
>
> On Tue, Mar 26, 2024 at 5:44 PM Cao, Kaili <cao.1191 at buckeyemail.osu.edu>
> wrote:
>
> Hello Eb,
>
>
> Thanks a lot for this information.
>
>
> Following the changelog, I suppose if I want to replace the default 14N
> proton capture rate with the NACRE II value shipped with MESA, I should
> write:
>
> num_special_rate_factors = 1
>
> reaction_for_special_factor(1) = 'r_n14_pg_o15'
>
> special_rate_factor(1) = 1
>
> filename_of_special_rate(1) = 'r_n14_pg_o15_nacreII.dat'
>
> in my inlists, and run $MESA_DIR/empty_caches before running my models;
> and if I want to replace multiple rates, I set num_special_rate_factors to
> the number I want and define other entries in a similar way. Please tell me
> if this is wrong, thank you.
>
>
> I have not changed nuclear reaction rates before, so I should have been
> using the defaults. I used `show_rates` to convert r_n14_pg_o15_1.bin, and
> the txt file tells me that:
>
> when T8 = 1.0000690699539715E-01, rate = 2.0247671654597788E-022.
>
> However, this is slightly (about 3.3%) below the NACRE rate provided by
> REACLIB Database
>
> https://reaclib.jinaweb.org/n14(p,g)o15/nacr/
> <https://urldefense.com/v3/__https://reaclib.jinaweb.org/n14(p,g)o15/nacr/__;!!IKRxdwAv5BmarQ!Z-CvDte8VjT4Inevmze_uCwVFvUjK3D6-CqjkxLALmrWBnmcVoiN3LIAbdO7AujD4bq5F0RgnDTghEqcs_gG6NChnPveJPM$>
>
> which claims: when T9 = 1.0000690699539715E-02, rate = 2.09489965936E-22.
>
> Could this be due to different forms of fitting functions? Thanks.
>
>
> Cheers,
>
> Kaili
> ------------------------------
> *From:* Ebraheem Farag <ekfarag at asu.edu>
> *Sent:* Tuesday, March 26, 2024 6:58 PM
> *To:* Cao, Kaili <cao.1191 at buckeyemail.osu.edu>
> *Cc:* Mathieu Renzo <mrenzo at arizona.edu>; mesa-users at lists.mesastar.org <
> mesa-users at lists.mesastar.org>
> *Subject:* Re: [Mesa-users] [EXT] How to check a nuclear reaction rate?
>
> Hello Kaili and thanks Mathieu,
>
> Be careful that you are sure which rate you are reading in. The default
> n14pg rate in MESA is from NACRE1, and is set in
> $MESA_DIR/rates/private/raw_rates.f90
> <https://urldefense.com/v3/__https://github.com/MESAHub/mesa/blob/5992b8ed6c3033a560ee4361f4cc86335c2bb6f4/rates/private/raw_rates.f90*L239__;Iw!!KGKeukY!zVv5mOzul0tRIDw0i-sHh034ARffwLjtJr6Dx4ry-uN7hRx4Tqorb_93tx9KO1RmpSUQcSGJSwue5kueu_2eyYbXs7cD$>
> :
> 239            case(ir_n14_pg_o15)
> 240               call do1(rate_n14pg_nacre)
>
> The controls for changing which n14_pg rate you adopt have been removed,
> but you can still adopt the rate by placing it in your local ./rate_tables
> directory or the global one that lives in
> $MESA_DIR/data/rates_data/rate_tables. See the changelog for rates in
> version r22.05.1
> <https://urldefense.com/v3/__https://docs.mesastar.org/en/release-r24.03.1/changelog.html*id10__;Iw!!KGKeukY!zVv5mOzul0tRIDw0i-sHh034ARffwLjtJr6Dx4ry-uN7hRx4Tqorb_93tx9KO1RmpSUQcSGJSwue5kueu_2eyZmYtvWT$>
> which describes all of this in detail.
>
> The default $MESA_DIR/data/rates_data/rate_tables directory also provides
> the n14_pg rate from cf88 as well as NACREII if you want to give those a
> try.
>
> Cheers,
> EbF
>
> On Tue, Mar 26, 2024 at 2:25 PM Cao, Kaili via Mesa-users <
> mesa-users at lists.mesastar.org> wrote:
>
> Dear Mathieu,
>
> Thank you very much for your quick reply! The `show_rates` script is very
> handy.
>
> For those who are interested, I checked several values and found a slight
> disagreement between MESA and JINALAB. I will think more about this.
>
> Cheers,
> Kaili
>
> ------------------------------
> *From:* Mathieu Renzo <mrenzo at arizona.edu>
> *Sent:* Tuesday, March 26, 2024 4:47 PM
> *To:* mesa-users at lists.mesastar.org <mesa-users at lists.mesastar.org>
> *Cc:* Cao, Kaili <cao.1191 at buckeyemail.osu.edu>
> *Subject:* Re: [EXT][Mesa-users] How to check a nuclear reaction rate?
>
> Dear Kaili,
>
> there is a way to have MESA print out in a txt file the value of the rate
> used for a specific reaction as a function of T. This requires using a
> small script called `show_rates` to convert rates cached in binary format
> into a human-readable format. The script is available in
> $MESA_DIR/rates/test, see also the relevant section in the documentation
> <https://urldefense.com/v3/__https://docs.mesastar.org/en/latest/net/nets.html*inspect-the-temperature-dependence-of-used-rates__;Iw!!KGKeukY!0QlmTdnJvC0E1CaZrSUz7TvYvpiV-rjmVoz9yx6tnS8Bq_rNHy-Qb3j8dCKZJbXvYMrjHylRUXvL-uRn3JfLrjyeo4yp7N0$>
> .
>
> Hope this helps!
> Mathieu (with many thanks to Rob Farmer who taught me how to do this)
>
>
> On 3/26/24 13:41, Cao, Kaili via Mesa-users wrote:
>
> *External Email*
>
> Dear MESA Users,
>
>
>
> Thank you for reading this email.
>
>
>
> I would like to ask about how to check a nuclear reaction rate used in
> MESA, specifically the proton capture rate of 14N, which was halved in
> 2006 and is important for my purposes.
>
>
>
> I understand that the jina_reaclib_filename control is default to "current
> standard version," but I find the corresponding file
> (jina_reaclib_results_20171020_default) hard to decipher, and I wish to
> make a direct comparison to:
>
> https://reaclib.jinaweb.org/n14(p,g)o15/im05/
> <https://urldefense.com/v3/__https://reaclib.jinaweb.org/n14(p,g)o15/im05/__;!!KGKeukY!0QlmTdnJvC0E1CaZrSUz7TvYvpiV-rjmVoz9yx6tnS8Bq_rNHy-Qb3j8dCKZJbXvYMrjHylRUXvL-uRn3JfLrjyefN_wm2c$>
>
>
>
> Can someone please confirm that this rate is up to date, or instruct me
> how to check it? Thanks a lot.
>
>
>
> Best regards,
>
> Kaili Cao
>
> _______________________________________________mesa-users at lists.mesastar.orghttps://lists.mesastar.org/mailman/listinfo/mesa-users <https://urldefense.com/v3/__https://lists.mesastar.org/mailman/listinfo/mesa-users__;!!KGKeukY!0QlmTdnJvC0E1CaZrSUz7TvYvpiV-rjmVoz9yx6tnS8Bq_rNHy-Qb3j8dCKZJbXvYMrjHylRUXvL-uRn3JfLrjye3_SwXpY$>
>
>
> --
> Mathieu Renzo
> <https://urldefense.com/v3/__https://users.flatironinstitute.org/*mrenzo/__;fg!!KGKeukY!0QlmTdnJvC0E1CaZrSUz7TvYvpiV-rjmVoz9yx6tnS8Bq_rNHy-Qb3j8dCKZJbXvYMrjHylRUXvL-uRn3JfLrjyeqnLyNwI$>
> Assistant Professor
> University of Arizona & Steward Observatory
> _______________________________________________
> mesa-users at lists.mesastar.org
>
> https://urldefense.com/v3/__https://lists.mesastar.org/mailman/listinfo/mesa-users__;!!IKRxdwAv5BmarQ!foyQi1VBFivv-y4at5IxR0HkoxALt1Rstta9UwJqBMM8kJ_UfaXxwO9Qrm5MyeMiMleRNa7811_iIG1mJbHjW5zrweVEBw$
>
> _______________________________________________
> mesa-users at lists.mesastar.org
>
> https://urldefense.com/v3/__https://lists.mesastar.org/mailman/listinfo/mesa-users__;!!IKRxdwAv5BmarQ!c4bjDS3MpzcYVlEzXF7wJX2bZDe29vLOaOhgvrkOWW5Wzf3oXksUkagITelOKylEOSB-tKTF-DhiqX-uzktLbt4SVH-O2A$
>
> _______________________________________________
> mesa-users at lists.mesastar.org
> https://lists.mesastar.org/mailman/listinfo/mesa-users
> <https://urldefense.com/v3/__https://lists.mesastar.org/mailman/listinfo/mesa-users__;!!IKRxdwAv5BmarQ!cwA7vnByCpKUIQ8GCMc_uq6jZysiv3RDUzCW-mYeOE4w5aSA9WolZvYDpG3zY3ixf0Gjr6WPUYamTDYpDt0-MrfF8QWm$>
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>
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