Steep change at Z~0.011 in the numbers of WD vs metallicity

[brettppark]

While I was looking merging CO-CO WDs, i found that there is a significant number change of CO at Z~0.011. As input binaries, I made a uniform mass distribution from 0.4M to 10M and paired them randomly. Separation is normally distributed centering ~10AU.

I think the decrease of CO-CO WDs and increase of CO-He WDs with increasing metallicity can be explained by increased mass loss. However why the significant drop happens between Z ~ 0.01 and 0.011?
Is this numerical artifact? Or is it too complex phenomenon because of the snowball effect from initial binary sets to evolution?
(Although i change my initial mass functions, there were still clear number drop at Z~0.011)

COMPAS version: v03.04.00

Configuration:
--emit-gravitational-radiation: True, --emit-gravitational-radiation: True, --evolve-unbound-systems: False, --allow-touching-at-birth: True , --include-WD-binaries-as-DCO: True, --evolve-double-white-dwarfs: True
except above options, others are set to be default.

[ilyamandel]

Hi @brettppark ,
Sorry for the delayed response.
The fitting formula for lambda, a common envelope parameter, has an abrupt change at this metallicity. Try running with --common-envelope-lambda-nanjing-interpolate-in-metallicity [and perhaps also --common-envelope-lambda-nanjing-interpolate-in-mass ] and let me know if that fixes this behaviour.

[brettppark]

Thanks for your response!

With your advice, I ran the same samples with --common-envelope-lambda-nanjing-interpolate-in-metallicity set to True. However, the results remained the same compared to when the option was not enabled.
I also ran with both options, metallicity and mass, but they showed same abrupt change at Z~0.011 (below figure).



[ilyamandel]

Hi @brettppark ,
I sincerely apologise for the very delayed response.
@themikelau explored this issue previously in the context of BBH mergers, so perhaps he has some advice.
@nrsegovia -- is there anything about WD mass transfer that is sensitive to metallicity choices?

[nrsegovia]

The figure seems to show that a fraction of CO WD secondaries at Z ~ 0.01 become He WDs instead at larger Z values. I think this makes sense under the R-Z relation for a given ZAMS mass at the tip of the RGB, assuming that this is the stage at which the secondaries are stripped of their outer layers. The sharp change is not readily explained by this... though it would be interesting to see detailed plots of a system that results in a CO-CO pair at Z~0.01 and CO-He at Z > 0.01.

Something I have noticed while running my hot subdwarf studies is that some of these systems only achieve RLOF at the very tip of the RGB, but this also depends on time-step related configuration (--mass-change-fraction and --radial-change-fraction). Using the recommended values in the documentation (different from the default) could impact the simulation, so it is also something to look at.

[themikelau]

I don't have any specific insight on the reported behaviour. The drop in CO-CO WDs at Z = 0.01 is not significantly bigger than another non-monotonic behaviour at Z = 0.005 and so it could be physical. As @brettppark showed, it is unlikely to be related to the smoothness of Nanjing lambda parameters. I can only give the general advice to plot the system formed (He-He, He-CO, CO-CO) in the space of initial parameters (e.g., initial mass ratio and period) slightly before and after Z = 0.01. This should allow you to identify the parameter space at which the difference arises, and you should then be able to isolate systems in that parameter space and compare their detailed evolution below and above Z = 0.01. I would happy to investigate more if you find a genuine bug.

[brettppark]

Hi, thanks for the responses.

I agree with @nrsegovia that this abrupt change can be explained by the mass loss although i haven't found the reason why this have to be Z~0.01 so far. I'm currently running with your suggestions (--mass-change-fraction and --radial-change-fraction), but i have very little knowledge about these options. What would be changed if i use the recommended values? If i understood the options correctly, a timestep will proceed when the particular radius or mass fraction changes. This timestep change will impact the final result of course. Then how should we choose the appropriate value of this options? Is the default value (=0.005) empirically driven? If you have any ideas or references, I’d really appreciate it if you could share....

@themikelau -- For the initial parameters, each metallicity has exactly same configurations (e.g., primary mass, secondary mass, mass ratio, and period). Only just metallicity values are different. I think that some metallicity dependent things at Z=0.01 are affecting WD masses while the binaries are evolving, although i've found nothing from the source codes related with Z=0.01.

These figures are mass distributions of CO-CO/He systems.

For both figures, left column is the distribution of ZAMS masses of DCOs. Right column is the distribution of WD masses when they became DCOs. Upper row is for primaries (M1) and lower row is for secondaries (M2). Legends show metallicity(Z) and total number(#) of binaries that are involved in the system.

As we can see in the right column of CO–CO systems, as metallicity increases, the numbers of both primary and secondary CO WDs decrease noticeably at Z~0.01. Maybe this decrease in number contributes the increase in the number of DCOs in CO-He systems at Z>0.01 since the combined numbers (CO-CO + CO-He ~ 650) are similar across all metallicities.

It is quite obvious that it is related with the mass loss, but i couldn't figure out why this abrupt change happens at Z=0.01.

[ilyamandel]

Also see #1171

[brettppark]

Hi, from your advices, @nrsegovia, I have simulated using two options (--mass-change-fraction and --radial-change-fraction) as a default value. Here's the results for merging WDs.
However, it seems like nothing has changed so far....
From this figure (also previous figures), we also found non monotonic change in numbers at Z~0.002.

For this metallicity range (Z~0.002), they have completely different secondary WD mass distribution in the CO-CO system (see below figure). Why this phenomenon happens in the middle of the low metallicity range?

[nrsegovia]

Hi @brettppark, I agree that the overall trend has not been greatly impacted by the change on the time step configuration, but the numbers have changed a tiny bit. Anyway, I'm not sure I can draw any conclusions without further looking into the data... are you using a grid file as input? if so, would you be able to share it? I tried to reproduce your results but I haven't been successful.

About your other question: you would have to check what the typical evolutionary path for those secondaries is. It seems they are low-mass CO WDs (0.3-0.4), possibly product of progenitors that have a mass around the transition between helium ignition in a flash and quiescent ignition. This again hints at mass transfer playing a big role, which is why I suggest you take a look at the detailed evolution of some of these systems at different metallicity regimes.

[brettppark]

Thanks @nrsegovia , I’ll review the detailed evolution as you suggested. If I discover anything noteworthy, I’ll share it here for further discussion. In the meantime, I’ve attached the grid files and the configuration file used in my analysis.

grid_files_brett.zip

[nrsegovia]

@brettppark Thanks for sharing the grid files. I was able to run some tests and I noted the following:

• There are some odd episodes of mass transfer (perhaps mergers?) when both GW radiation and DWD evolution are enabled. This should not affect your merger numbers, but it would impact the time at which this happens (I will take a look soon). I am not sure this configuration has been properly tested before.
• I'm pretty confident about the reason for the jump at Z ~ 0.01. One of the "limits" used during the computation of lambda under the LAMBDA_NANJING prescription is LAMBDA_NANJING_ZLIMIT, set to 0.0105 (constants.h). I have not dealt with the interpolation routines, but enabling them does not change the results that much (in the scenarios I tested, similar to one of the plots you shared). The differences seem to be pretty big, lambda ~7 at z = 0.01 but ~130 at 0.011 in one of my test cases, while the mass being lost and the COWD core mass are almost the same (and alpha is set to 1 by default). You could try taking a look at the lambda values in your simulations (storing LAMBDA_AT_COMMON_ENVELOPE or LAMBDA_NANJING) to further explore this idea. If you want to take a look at related code, check CalculateLambdaNanjingStarTrack.

[ilyamandel]

@nrsegovia rightly points out something I forgot to mention: Interpolation in metallicity and mass are only relevant if using Enhanced Nanjing lambdas; see the help output:

--common-envelope-lambda-nanjing-interpolate-in-mass
  Use Nanjing lambda's with mass interpolation (only used when using enhanced Nanjing lambda's) (default = FALSE)
--common-envelope-lambda-nanjing-interpolate-in-metallicity
  Use Nanjing lambda's with metallicity interpolation (only used when using enhanced Nanjing lambda's) (default = FALSE) 

So you'll need to also run with --common-envelope-lambda-nanjing-enhanced if you haven't done that already.

I didn't quite understand the point @nrsegovia made about the drastic jump in lambdas: are you saying that lambda goes from 7 at Z=0.01 to 130 at Z=0.011 for the same star (mass, radius), even after interpolation in metallicity was turned on?

[nrsegovia]

@brettppark please enable --common-envelope-lambda-nanjing-enhanced in your runs, I believe this should help with the jump in merger numbers at Z ~ 0.01. Take for example the detailed run of one of the "odd" binaries I found in the grids you shared:

COMPAS --allow-touching-at-birth TRUE --detailed-output TRUE -n 1 (-z 0.01) --initial-mass-1 4.771790958963 --initial-mass-2 3.686370704892 --semi-major-axis 6.375201842038 --emit-gravitational-radiation True --evolve-double-white-dwarfs True (--common-envelope-lambda-nanjing-interpolate-in-metallicity TRUE --common-envelope-lambda-nanjing-interpolate-in-mass TRUE --common-envelope-lambda-nanjing-enhanced TRUE)

In this command I have added parentheses to properties that I have modified between different runs. Some important results are shown in the following plots (apologies for the low quality plots, I made them in a rush with TOPCAT):


The first plot shows you the evolution of lambda around the time the primary star overflows its Roche Lobe and becomes a WD, when no interpolation is used. I would think that since metallicities are quire similar in both cases, the radii and core should also be similar and lead to similar final separations, which is not the case (second plot). This is due to the noticeably different lambda values. Instead, if you enable interpolation, the plots become the following:

If you apply this to the entire population, the total number of mergers does not show the jump anymore. I only tested z = 0.01 and z = 0.011, which yields 670 and 663 COCO WDs, respectively. COHe WD merger numbers also yield a smoother change, 275 at z = 0.01 to 278 at z = 0.011. Not using lambda interpolation yields differences similar to the ones you found.

[ilyamandel]

Thanks, @nrsegovia !
BTW, we should probably switch to Enhanced Nanjing Lambda's and interpolation as a default...

[brettppark]

Thanks so much @nrsegovia , @ilyamandel !!! After turning on the --common-envelope-lambda-nanjing-enhanced, abrupt change at Z=0.0105 disappeared like you said. However, with the changed options, there’s still a noticeable dip at Z=0.005, where the count drops and rises again. What could be causing this behavior in this case? Below figure is a result of the 10% of the original samples to reduce computation.

[nrsegovia]

Well, I would follow a similar procedure to the one I used before. Take a few systems that seem interesting around the metallicity values where you find the dip, then analyze their detailed evolution. For example, Binary A becomes a COCO WD system at Z = 0.005, but it does not become one at Z = 0.004 or 0.006. Why? That would give you some hints. It could be anything from metallicity effects on single stellar evolution to mass transfer related physics, or the time (or conditions) it takes for a merger to happen.

[themikelau]

@nrsegovia Just a comment that the --common-envelope-lambda-nanjing-enhanced flag does a flat extrapolation of lambda beyond their radius limits. It is not simply a flag that allows turning on mass and metallicity interpolation. Startrack also tried to extrapolate lambdas in radius, but their implementation was inaccurate and contained a lot of discontinuities.

[ilyamandel]

Just a heads up for everyone in this thread that following the discussion here and in our Slack, I made --common-envelope-lambda-nanjing-enhanced as well as interpolation of Nanjing lambdas in mass and metallicity the default in the latest version of the code, see
#1379 . That means if you run with the latest code version and don't want them on, you have to actively set these options to False.

[nrsegovia]

@brettppark I think you will find the discussion in #1384 interesting/relevant, too.