Dear All,
Quick follow-up on Ken's remark during the meeting: I was saying
that I find excellent agreement between (1) my calculation based
on the VOS model and only assuming GW emission from cusps and (2)
Ken's numerical data. I just had another look at my code and can
now quantify a bit better what I mean by "excellent" agreement.
Have a look at the attached file "comparison_1png", which shows the GW spectrum from stable cosmic strings for Gmu = 10^-14, 10^-12, 10^-10, 10^-8. The vertical axis is log10(h^2 Omega_GW) and the horizontal axis is log10(f/Hz). The black lines correspond to Ken's data, the red lines to my data. My statement on the agreement between our data sets was based on plots like this one.
Now, however, look at the file "comparison_2.png", which zooms in on the GW spectrum for Gmu = 10^-10. So, if we look a bit closer, we actually see that both spectra do no agree *exactly* with each other. At frequencies around f ~ 1 / year, the difference between the black and red curves is around
\Delta log10 h^2 Omega_GW ~ 0.04
which translates into a difference in the characteristic strain amplitude of around
\Delta log10 A ~ 0.02
This is perfectly consistent with the results in Fig. 1 of https://arxiv.org/abs/2102.08194, where, at Gmu ~ 10^-10, the BOS curve is also located at A values around \Delta log10 A ~ 0.02 larger than the curve for the cusp-only model.
In addition, keep in my mind that my calculation is based on the VOS model, which is not exactly the same as the cusp-only model in 2102.08194. So, in this situation, I would say agreement is as good as we can expect it to be and everything is consistent and under good control.
TL;DR: There actually is a tiny difference between Ken's and my data of the order of \Delta log10 h^2 Omega_GW ~ 0.04. Initially, I had not noticed this difference because I had plotted my results on a vertical axis spanning 20 orders of magnitude. But the difference is there; it is physical; it is expected; and we know where it comes from.
Please let me know what you think.
Best regards, Kai.
Attachment:
comparison_1.png
Description: PNG image
Attachment:
comparison_2.png
Description: PNG image
