We have systematically performed nucleosynthesis calculations with our new nuclear reaction networkSkyNetfor a wide range of three parameters: initial electron fraction (0.01 ≤ Ye ≤ 0.5), initial entropy 1kBbaryon−1 ≤ s ≤ 100kBbaryon−1, and the expansion timescale 0.1 ms≤ τ ≤ 500 ms during nuclear burning. We ran the full parameter space with different fission reactions, but found that there were only small quantitative and no qualitative differences between the different fission reactions.
We focused our attention on the amount of lanthanides and actinides produced and the heating rate between 0.1 and 100 days after the start of the nucleosynthesis calculation, because kilonova transients are expected to occur in this time frame.
With a spherically symmetric, gray radiation transport scheme we estimated the peak time, peak luminosity, and peak spectral temperature of the kilonova light curves.
We find that the final amount of lanthanides and actinides depends most strongly on Yeand the ejecta is lanthanide-free forYe & 0.26. However, there are some regions of the parameter space where the ejecta is lanthanide-free even for very low electron
fractions. Specifically, at high initial entropies and small expansion timescales we get a neutron-rich freeze-out, which does not produce lanthanides, but may result in a very bright, very blue transient on the timescale of an hour. At small initial entropies and very large expansion timescales, there is significant late-time heating, which causes the composition to go back to NSE and effectively restart the r-process at a much higher electron fraction, which was raised by β-decays.
Since the lanthanides and actinides can increase the opacity of the material by a factor of ∼100, we find that the peak luminosity increases by about one order of magnitude and the light curve peak timescale goes from about a week to about a day as the ejecta becomes lanthanide-free. This is consistent with previous works by Roberts et al. (2011), Kasen et al. (2013), Tanaka and Hotokezaka (2013), and Grossman et al. (2014). The heating rate at 1 day, however, remains largely unchanged and decreases by no more than one order of magnitude as the ejecta becomes lanthanide-free. Thus the increase in the kilonova luminosity is due to the decrease in the opacity when lanthanides are no longer present, which pushes the peak to earlier times when the heating is stronger. At very highYe(& 0.4), there are large variations in the heating rate because single nuclides dominate the heating. At lowerYe, the heating rate at 1 day is very uniform in entropy and expansion timescale because it is dominated by an ensemble of nuclides that average out to the same heating rate at 1 day even though the exact composition may be very different. This has already been found in Metzger et al.,2010and we are now confirming it for a larger parameter space.
Overall, we find only weak correlation between the lanthanide production and heat- ing rate. Both quantities are quite strongly correlated withYe, but not so much with one another. The heating rate at 1 day is not affected much when the lanthanide abundance suddenly drops by many order of magnitude, but it slowly declines at higherYe.
In Section 3.2.4, we provided three linear inequalities involvingYe, lns, and lnτ that can be used to determine if the ejecta with those properties is lanthanide-rich or lanthanide-free. Those inequalities give the correct answer in 98% of all cases.
We also provide parametric fits for the heating rates between 0.1 and 100 days for all cases athttp : / / stellarcollapse . org / lippunerroberts2015. The mean fractional log difference between the actual heating rate and our fit is no more than 1% in 95% of all cases. On the same website, we also provide an integrated fractional heating contribution to give an idea of which specific nuclides contribute
the most to the radioactive heating.
Our nucleosynthesis code SkyNet will be released as free and open-source code soon. In the meantime, those interested can contact the authors about getting early access to the code. Future versions ofSkyNetwill also include neutrino interactions.
Much more work needs to be done to accurately model the light curves of kilonovae and especially to calculate the line structure and hence opacity of the lanthanide and actinide elements. We hope that our heating rate fits will be useful to other researchers to calculate kilonova light curves that could aid with detecting such events.
Acknowledgments
We thank Dan Kasen for helpful discussions on light curve modeling and for gra- ciously providing us with temperature-dependent mean opacities for various mix- tures of neodymium and iron. We thank Christian Ott for numerous useful discus- sions and for a careful reading of the manuscript. We thank Brian Metzger for a number of useful comments on the manuscript. And we also thank Shri Kulkarni for discussion about computing observed magnitudes.
The calculations presented here were performed on the Caltech “Zwicky” com- pute cluster (NSF MRI award No. PHY-0960291), on the NSF XSEDE network under allocation TG-PHY100033, and on NSF/NCSA Blue Waters under alloca- tion jr6 (NSF PRAC award No. ACI-1440083). Support for LR during this work was provided by NASA through an Einstein Postdoctoral Fellowship grant num- bered PF3-140114 awarded by the Chandra X-ray Center, which is operated by the Smithsonian Astrophysical Observatory for NASA under contract NAS8-03060. JL is partially supported by NSF under award Nos. TCAN AST-1333520, CAREER PHY-1151197, and AST-1205732, and by the Sherman Fairchild Foundation.
3.A Computing AB magnitude from light curve The observed AB magnitude is defined as
mAB =−5 2log10
∫ fν(ν)Tν(ν)dν 3631 Jy∫
Tν(ν)dν
!
, (3.16)
where fν(ν)is the observed spectral flux density (energy per unit time per unit area per unit frequency) at frequencyν,Tν(ν)is the filter throughput per unit frequency at frequencyν, and Jy is the unit Jansky, where 1 Jy= 10−23erg s−1cm−2Hz−1. The
HST filters are given as throughput per wavelength as a function of wavelength4, i.e.Tλ(λ). To convert fromTλ(λ)toTν(ν), we note that
Tν(ν)dν =−Tλ(λ)dλ
⇔ Tν(ν)= −Tλ(λ)dλ
dν =Tλ(c/ν) c
ν2, (3.17)
sinceλ = c/ν, wherecis the speed of light in vacuum, and the minus sign comes from the fact that the wavelength decreases as the frequency increases. The observed spectral flux density is given by
fν(ν)= Lν(ν)
4πD2, (3.18)
where Lν(ν) is the radiated spectral flux (radiated energy per unit time per unit frequency) at frequencyνandDis the distance between the source and the observer.
This assumes that the source is radiating isotropically. Our light curve model gives us the bolometric luminosity Lbol and the effective temperatureTeff as a function of time. We then assume that the radiated spectrum is a black body spectrum with total luminosityLbol, hence we get
Lν(ν)= Lbol
Bν(ν,Teff)
∫Bν(ν,Teff)dν, (3.19) whereBν(ν,Teff)is the spectral radiance given by Planck’s law.
The above is true for a source that is close to the observer compared to cosmological distances, but if the source is sufficiently far away, we need to take redshift into account. Recall that the emitted frequency is given by
νemit =(1+z)νobs, (3.20) wherez is the redshift of the source. Since (3.16) is calculated at the observer, we have fν(ν) = fνobs(νobs), and since this power per unit area per unit frequency, it follows that
fνobs(νobs)dνobs = fνemit(νemit)dνemit
⇔ fνobs(νobs)= fνemit(νemit)dνemit
dνobs =(1+z)fνemit((1+z)νobs). (3.21) Note that there are additional corrections to fν due to the photon energy and their arrival rate both being reduced by a factor of(1+z). However, we will absorb these
4http : / / svo2 . cab . inta - csic . es / svo / theory / fps3 / index . php ? mode = browse &
gname=HST
to factors of (1+ z) into the definition of the distance between the source and the observer, which is called the luminosity distanceDL. Thus we finally have
mAB =−5
2log10 (1+z)Lbol
4πD2L∫
Bν(ν,Teff)dν
∫Bν((1+z)ν,Teff)Tλ(c/ν)ν−2dν 3631 Jy∫
Tλ(c/ν)ν−2dν
!
. (3.22)
The luminosity distance as a function of redshift z can be calculated as follows (Hogg,1999). Define
E(z)=p
Ωm(1+z)3+Ωk(1+z)2+ΩΛ, (3.23) where Ωm is the total matter density, ΩΛ is the dark energy density, and Ωk = 1−Ωm−ΩΛ is the curvature. Also define the Hubble distance DH = c/H0, where H0is the Hubble parameter. Then, the comoving distanceDCis
DC(z)= DH
∫ z
0
dz0
E(z0), (3.24)
the transverse comoving distanceDM(z)is
DM(z)=
DH
√Ωk sinh√
ΩkDC(z)/DH
ifΩk > 0, DC(z) ifΩk =0,
DH
p|Ωk|sinp
|Ωk|DC(z)/DH
ifΩk < 0,
(3.25)
and finally, the luminosity distance is
DL(z)=(1+z)DM(z). (3.26) In this paper, we use the most recent Planck values (Planck Collaboration et al.,2016) for the cosmological parameters, i.e. H0 = 67.74 km s−1Mpc−1, Ωm = 0.3089, ΩΛ =0.6911, andΩk =0.
3.B Slice plots
In this section we show all the slice plots from our runs, which have also been made available athttp://stellarcollapse.org/lippunerroberts2015.
3.B.1 High-resolutionsym0run
1 10 100
0.1 1 10 100
500 sym0,Ye= 0.01
s[kBbaryon−1]
τ[ms]
1 10 100
sym0,Ye= 0.04
s[kBbaryon−1]
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
1 10 100
0.1 1 10 100
500 sym0,Ye= 0.07
s[kBbaryon−1]
τ[ms]
1 10 100
sym0,Ye= 0.10
s[kBbaryon−1]
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
1 10 100
0.1 1 10 100
500 sym0,Ye= 0.13
s[kBbaryon−1]
τ[ms]
1 10 100
sym0,Ye= 0.16
s[kBbaryon−1]
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
1 10 100 0.1
1 10 100
500 sym0,Ye= 0.19
s[kBbaryon−1]
τ[ms]
1 10 100
sym0,Ye= 0.22
s[kBbaryon−1]
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
1 10 100
0.1 1 10 100
500 sym0,Ye= 0.25
s[kBbaryon−1]
τ[ms]
1 10 100
sym0,Ye= 0.29
s[kBbaryon−1]
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
1 10 100
0.1 1 10 100
500 sym0,Ye= 0.32
s[kBbaryon−1]
τ[ms]
1 10 100
sym0,Ye= 0.35
s[kBbaryon−1]
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
1 10 100 0.1
1 10 100
500 sym0,Ye= 0.38
s[kBbaryon−1]
τ[ms]
1 10 100
sym0,Ye= 0.41
s[kBbaryon−1]
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
1 10 100
0.1 1 10 100
500 sym0,Ye= 0.44
s[kBbaryon−1]
τ[ms]
1 10 100
sym0,Ye= 0.47
s[kBbaryon−1]
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
1 10 100
0.1 1 10 100
500 sym0,Ye= 0.50
s[kBbaryon−1]
τ[ms]
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
Figure 3.10: All theYeslices showing the final lanthanide and actinide mass fraction of the high-resolutionsym0run.
1 10 100 0.1
1 10 100
500 sym0,Ye= 0.01
s[kBbaryon−1]
τ[ms]
1 10 100
sym0,Ye= 0.04
s[kBbaryon−1]
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
1 10 100
0.1 1 10 100
500 sym0,Ye= 0.07
s[kBbaryon−1]
τ[ms]
1 10 100
sym0,Ye= 0.10
s[kBbaryon−1]
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
1 10 100
0.1 1 10 100
500 sym0,Ye= 0.13
s[kBbaryon−1]
τ[ms]
1 10 100
sym0,Ye= 0.16
s[kBbaryon−1]
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
1 10 100 0.1
1 10 100
500 sym0,Ye= 0.19
s[kBbaryon−1]
τ[ms]
1 10 100
sym0,Ye= 0.22
s[kBbaryon−1]
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
1 10 100
0.1 1 10 100
500 sym0,Ye= 0.25
s[kBbaryon−1]
τ[ms]
1 10 100
sym0,Ye= 0.29
s[kBbaryon−1]
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
1 10 100
0.1 1 10 100
500 sym0,Ye= 0.32
s[kBbaryon−1]
τ[ms]
1 10 100
sym0,Ye= 0.35
s[kBbaryon−1]
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
1 10 100 0.1
1 10 100
500 sym0,Ye= 0.38
s[kBbaryon−1]
τ[ms]
1 10 100
sym0,Ye= 0.41
s[kBbaryon−1]
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
1 10 100
0.1 1 10 100
500 sym0,Ye= 0.44
s[kBbaryon−1]
τ[ms]
1 10 100
sym0,Ye= 0.47
s[kBbaryon−1]
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
1 10 100
0.1 1 10 100
500 sym0,Ye= 0.50
s[kBbaryon−1]
τ[ms]
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
Figure 3.11: All theYeslices showing the heating rate at 1 day of the high-resolution sym0run.
0.01 0.1 0.2 0.3 0.4 0.5 0.1
1 10 100
500 sym0,s= 1.0kBbaryon−1
Ye
τ[ms]
0.01 0.1 0.2 0.3 0.4 0.5 sym0,s= 1.3kBbaryon−1
Ye
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
0.01 0.1 0.2 0.3 0.4 0.5 0.1
1 10 100
500 sym0,s= 1.8kBbaryon−1
Ye
τ[ms]
0.01 0.1 0.2 0.3 0.4 0.5 sym0,s= 2.4kBbaryon−1
Ye
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
0.01 0.1 0.2 0.3 0.4 0.5 0.1
1 10 100
500 sym0,s= 3.2kBbaryon−1
Ye
τ[ms]
0.01 0.1 0.2 0.3 0.4 0.5 sym0,s= 4.2kBbaryon−1
Ye
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
0.01 0.1 0.2 0.3 0.4 0.5 0.1
1 10 100
500 sym0,s= 5.6kBbaryon−1
Ye
τ[ms]
0.01 0.1 0.2 0.3 0.4 0.5 sym0,s= 7.5kBbaryon−1
Ye
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
0.01 0.1 0.2 0.3 0.4 0.5 0.1
1 10 100
500 sym0,s= 10kBbaryon−1
Ye
τ[ms]
0.01 0.1 0.2 0.3 0.4 0.5 sym0,s= 13kBbaryon−1
Ye
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
0.01 0.1 0.2 0.3 0.4 0.5 0.1
1 10 100
500 sym0,s= 18kBbaryon−1
Ye
τ[ms]
0.01 0.1 0.2 0.3 0.4 0.5 sym0,s= 24kBbaryon−1
Ye
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
0.01 0.1 0.2 0.3 0.4 0.5 0.1
1 10 100
500 sym0,s= 32kBbaryon−1
Ye
τ[ms]
0.01 0.1 0.2 0.3 0.4 0.5 sym0,s= 42kBbaryon−1
Ye
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
0.01 0.1 0.2 0.3 0.4 0.5 0.1
1 10 100
500 sym0,s= 56kBbaryon−1
Ye
τ[ms]
0.01 0.1 0.2 0.3 0.4 0.5 sym0,s= 75kBbaryon−1
Ye
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
0.01 0.1 0.2 0.3 0.4 0.5 0.1
1 10 100
500 sym0,s= 100kBbaryon−1
Ye
τ[ms]
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
Figure 3.12: All thesslices showing the final lanthanide and actinide mass fraction of the high-resolutionsym0run.
0.01 0.1 0.2 0.3 0.4 0.5 0.1
1 10 100
500 sym0,s= 1.0kBbaryon−1
Ye
τ[ms]
0.01 0.1 0.2 0.3 0.4 0.5 sym0,s= 1.3kBbaryon−1
Ye
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 0.1
1 10 100
500 sym0,s= 1.8kBbaryon−1
Ye
τ[ms]
0.01 0.1 0.2 0.3 0.4 0.5 sym0,s= 2.4kBbaryon−1
Ye
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 0.1
1 10 100
500 sym0,s= 3.2kBbaryon−1
Ye
τ[ms]
0.01 0.1 0.2 0.3 0.4 0.5 sym0,s= 4.2kBbaryon−1
Ye
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 0.1
1 10 100
500 sym0,s= 5.6kBbaryon−1
Ye
τ[ms]
0.01 0.1 0.2 0.3 0.4 0.5 sym0,s= 7.5kBbaryon−1
Ye
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 0.1
1 10 100
500 sym0,s= 10kBbaryon−1
Ye
τ[ms]
0.01 0.1 0.2 0.3 0.4 0.5 sym0,s= 13kBbaryon−1
Ye
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 0.1
1 10 100
500 sym0,s= 18kBbaryon−1
Ye
τ[ms]
0.01 0.1 0.2 0.3 0.4 0.5 sym0,s= 24kBbaryon−1
Ye
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 0.1
1 10 100
500 sym0,s= 32kBbaryon−1
Ye
τ[ms]
0.01 0.1 0.2 0.3 0.4 0.5 sym0,s= 42kBbaryon−1
Ye
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 0.1
1 10 100
500 sym0,s= 56kBbaryon−1
Ye
τ[ms]
0.01 0.1 0.2 0.3 0.4 0.5 sym0,s= 75kBbaryon−1
Ye
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 0.1
1 10 100
500 sym0,s= 100kBbaryon−1
Ye
τ[ms]
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
Figure 3.13: All thesslices showing the heating rate at 1 day of the high-resolution sym0run.
0.01 0.1 0.2 0.3 0.4 0.5 1
10
100 sym0,τ= 0.10 ms
Ye
s[kBbaryon−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 sym0,τ = 0.17 ms
Ye
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
0.01 0.1 0.2 0.3 0.4 0.5 1
10
100 sym0,τ= 0.29 ms
Ye
s[kBbaryon−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 sym0,τ = 0.49 ms
Ye
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
0.01 0.1 0.2 0.3 0.4 0.5 1
10
100 sym0,τ= 0.84 ms
Ye
s[kBbaryon−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 sym0,τ= 1.4 ms
Ye
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
0.01 0.1 0.2 0.3 0.4 0.5 1
10
100 sym0,τ= 2.4 ms
Ye
s[kBbaryon−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 sym0,τ= 4.2 ms
Ye
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
0.01 0.1 0.2 0.3 0.4 0.5 1
10
100 sym0,τ= 7.1 ms
Ye
s[kBbaryon−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 sym0,τ= 12 ms
Ye
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
0.01 0.1 0.2 0.3 0.4 0.5 1
10
100 sym0,τ= 21 ms
Ye
s[kBbaryon−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 sym0,τ= 35 ms
Ye
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
0.01 0.1 0.2 0.3 0.4 0.5 1
10
100 sym0,τ= 59 ms
Ye
s[kBbaryon−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 sym0,τ = 100 ms
Ye
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
0.01 0.1 0.2 0.3 0.4 0.5 1
10
100 sym0,τ= 170 ms
Ye
s[kBbaryon−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 sym0,τ = 290 ms
Ye
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
0.01 0.1 0.2 0.3 0.4 0.5 1
10
100 sym0,τ = 500 ms
Ye
s[kBbaryon−1 ]
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
Figure 3.14: All theτslices showing the final lanthanide and actinide mass fraction of the high-resolutionsym0run.
0.01 0.1 0.2 0.3 0.4 0.5 1
10
100 sym0,τ= 0.10 ms
Ye
s[kBbaryon−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 sym0,τ = 0.17 ms
Ye
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 1
10
100 sym0,τ= 0.29 ms
Ye
s[kBbaryon−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 sym0,τ = 0.49 ms
Ye
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 1
10
100 sym0,τ= 0.84 ms
Ye
s[kBbaryon−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 sym0,τ= 1.4 ms
Ye
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 1
10
100 sym0,τ= 2.4 ms
Ye
s[kBbaryon−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 sym0,τ= 4.2 ms
Ye
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 1
10
100 sym0,τ= 7.1 ms
Ye
s[kBbaryon−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 sym0,τ= 12 ms
Ye
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 1
10
100 sym0,τ= 21 ms
Ye
s[kBbaryon−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 sym0,τ= 35 ms
Ye
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 1
10
100 sym0,τ= 59 ms
Ye
s[kBbaryon−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 sym0,τ = 100 ms
Ye
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 1
10
100 sym0,τ= 170 ms
Ye
s[kBbaryon−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 sym0,τ = 290 ms
Ye
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 1
10
100 sym0,τ = 500 ms
Ye
s[kBbaryon−1 ]
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
Figure 3.15: All theτslices showing the heating rate at 1 day of the high-resolution sym0run.
3.B.2 sym0run
1 10 100
0.1 1 10 100
500 sym0,Ye= 0.01
s[kBbaryon−1]
τ[ms]
1 10 100
sym0,Ye= 0.07
s[kBbaryon−1]
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
1 10 100
0.1 1 10 100
500 sym0,Ye= 0.13
s[kBbaryon−1]
τ[ms]
1 10 100
sym0,Ye= 0.19
s[kBbaryon−1]
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
1 10 100
0.1 1 10 100
500 sym0,Ye= 0.25
s[kBbaryon−1]
τ[ms]
1 10 100
sym0,Ye= 0.32
s[kBbaryon−1]
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
1 10 100 0.1
1 10 100
500 sym0,Ye= 0.38
s[kBbaryon−1]
τ[ms]
1 10 100
sym0,Ye= 0.44
s[kBbaryon−1]
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
1 10 100
0.1 1 10 100
500 sym0,Ye= 0.50
s[kBbaryon−1]
τ[ms]
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
Figure 3.16: All theYeslices showing the final lanthanide and actinide mass fraction of thesym0run.
1 10 100
0.1 1 10 100
500 sym0,Ye= 0.01
s[kBbaryon−1]
τ[ms]
1 10 100
sym0,Ye= 0.07
s[kBbaryon−1]
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
1 10 100 0.1
1 10 100
500 sym0,Ye= 0.13
s[kBbaryon−1]
τ[ms]
1 10 100
sym0,Ye= 0.19
s[kBbaryon−1]
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
1 10 100
0.1 1 10 100
500 sym0,Ye= 0.25
s[kBbaryon−1]
τ[ms]
1 10 100
sym0,Ye= 0.32
s[kBbaryon−1]
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
1 10 100
0.1 1 10 100
500 sym0,Ye= 0.38
s[kBbaryon−1]
τ[ms]
1 10 100
sym0,Ye= 0.44
s[kBbaryon−1]
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
1 10 100 0.1
1 10 100
500 sym0,Ye= 0.50
s[kBbaryon−1]
τ[ms]
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
Figure 3.17: All theYe slices showing the heating rate at 1 day of thesym0run.
0.01 0.1 0.2 0.3 0.4 0.5 0.1
1 10 100
500 sym0,s= 1.0kBbaryon−1
Ye
τ[ms]
0.01 0.1 0.2 0.3 0.4 0.5 sym0,s= 1.8kBbaryon−1
Ye
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
0.01 0.1 0.2 0.3 0.4 0.5 0.1
1 10 100
500 sym0,s= 3.2kBbaryon−1
Ye
τ[ms]
0.01 0.1 0.2 0.3 0.4 0.5 sym0,s= 5.6kBbaryon−1
Ye
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
0.01 0.1 0.2 0.3 0.4 0.5 0.1
1 10 100
500 sym0,s= 10kBbaryon−1
Ye
τ[ms]
0.01 0.1 0.2 0.3 0.4 0.5 sym0,s= 18kBbaryon−1
Ye
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
0.01 0.1 0.2 0.3 0.4 0.5 0.1
1 10 100
500 sym0,s= 32kBbaryon−1
Ye
τ[ms]
0.01 0.1 0.2 0.3 0.4 0.5 sym0,s= 56kBbaryon−1
Ye
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
0.01 0.1 0.2 0.3 0.4 0.5 0.1
1 10 100
500 sym0,s= 100kBbaryon−1
Ye
τ[ms]
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
Figure 3.18: All thesslices showing the final lanthanide and actinide mass fraction of thesym0run.
0.01 0.1 0.2 0.3 0.4 0.5 0.1
1 10 100
500 sym0,s= 1.0kBbaryon−1
Ye
τ[ms]
0.01 0.1 0.2 0.3 0.4 0.5 sym0,s= 1.8kBbaryon−1
Ye
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 0.1
1 10 100
500 sym0,s= 3.2kBbaryon−1
Ye
τ[ms]
0.01 0.1 0.2 0.3 0.4 0.5 sym0,s= 5.6kBbaryon−1
Ye
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 0.1
1 10 100
500 sym0,s= 10kBbaryon−1
Ye
τ[ms]
0.01 0.1 0.2 0.3 0.4 0.5 sym0,s= 18kBbaryon−1
Ye
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 0.1
1 10 100
500 sym0,s= 32kBbaryon−1
Ye
τ[ms]
0.01 0.1 0.2 0.3 0.4 0.5 sym0,s= 56kBbaryon−1
Ye
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 0.1
1 10 100
500 sym0,s= 100kBbaryon−1
Ye
τ[ms]
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
Figure 3.19: All the sslices showing the heating rate at 1 day of thesym0run.
0.01 0.1 0.2 0.3 0.4 0.5 1
10
100 sym0,τ= 0.10 ms
Ye
s[kBbaryon−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 sym0,τ = 0.29 ms
Ye
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
0.01 0.1 0.2 0.3 0.4 0.5 1
10
100 sym0,τ= 0.84 ms
Ye
s[kBbaryon−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 sym0,τ= 2.4 ms
Ye
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
0.01 0.1 0.2 0.3 0.4 0.5 1
10
100 sym0,τ= 7.1 ms
Ye
s[kBbaryon−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 sym0,τ= 21 ms
Ye
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
0.01 0.1 0.2 0.3 0.4 0.5 1
10
100 sym0,τ= 59 ms
Ye
s[kBbaryon−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 sym0,τ = 170 ms
Ye
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
0.01 0.1 0.2 0.3 0.4 0.5 1
10
100 sym0,τ = 500 ms
Ye
s[kBbaryon−1 ]
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
Figure 3.20: All theτslices showing the final lanthanide and actinide mass fraction of thesym0run.
0.01 0.1 0.2 0.3 0.4 0.5 1
10
100 sym0,τ= 0.10 ms
Ye
s[kBbaryon−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 sym0,τ = 0.29 ms
Ye
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 1
10
100 sym0,τ= 0.84 ms
Ye
s[kBbaryon−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 sym0,τ= 2.4 ms
Ye
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 1
10
100 sym0,τ= 7.1 ms
Ye
s[kBbaryon−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 sym0,τ= 21 ms
Ye
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 1
10
100 sym0,τ= 59 ms
Ye
s[kBbaryon−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 sym0,τ = 170 ms
Ye
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 1
10
100 sym0,τ = 500 ms
Ye
s[kBbaryon−1 ]
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
Figure 3.21: All the τslices showing the heating rate at 1 day of thesym0run.
3.B.3 sym2run
1 10 100
0.1 1 10 100
500 sym2,Ye= 0.01
s[kBbaryon−1]
τ[ms]
1 10 100
sym2,Ye= 0.07
s[kBbaryon−1]
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
1 10 100
0.1 1 10 100
500 sym2,Ye= 0.13
s[kBbaryon−1]
τ[ms]
1 10 100
sym2,Ye= 0.19
s[kBbaryon−1]
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
1 10 100
0.1 1 10 100
500 sym2,Ye= 0.25
s[kBbaryon−1]
τ[ms]
1 10 100
sym2,Ye= 0.32
s[kBbaryon−1]
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
1 10 100 0.1
1 10 100
500 sym2,Ye= 0.38
s[kBbaryon−1]
τ[ms]
1 10 100
sym2,Ye= 0.44
s[kBbaryon−1]
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
1 10 100
0.1 1 10 100
500 sym2,Ye= 0.50
s[kBbaryon−1]
τ[ms]
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
Figure 3.22: All theYeslices showing the final lanthanide and actinide mass fraction of thesym2run.
1 10 100
0.1 1 10 100
500 sym2,Ye= 0.01
s[kBbaryon−1]
τ[ms]
1 10 100
sym2,Ye= 0.07
s[kBbaryon−1]
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
1 10 100 0.1
1 10 100
500 sym2,Ye= 0.13
s[kBbaryon−1]
τ[ms]
1 10 100
sym2,Ye= 0.19
s[kBbaryon−1]
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
1 10 100
0.1 1 10 100
500 sym2,Ye= 0.25
s[kBbaryon−1]
τ[ms]
1 10 100
sym2,Ye= 0.32
s[kBbaryon−1]
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
1 10 100
0.1 1 10 100
500 sym2,Ye= 0.38
s[kBbaryon−1]
τ[ms]
1 10 100
sym2,Ye= 0.44
s[kBbaryon−1]
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
1 10 100 0.1
1 10 100
500 sym2,Ye= 0.50
s[kBbaryon−1]
τ[ms]
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
Figure 3.23: All theYe slices showing the heating rate at 1 day of thesym2run.
0.01 0.1 0.2 0.3 0.4 0.5 0.1
1 10 100
500 sym2,s= 1.0kBbaryon−1
Ye
τ[ms]
0.01 0.1 0.2 0.3 0.4 0.5 sym2,s= 1.8kBbaryon−1
Ye
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
0.01 0.1 0.2 0.3 0.4 0.5 0.1
1 10 100
500 sym2,s= 3.2kBbaryon−1
Ye
τ[ms]
0.01 0.1 0.2 0.3 0.4 0.5 sym2,s= 5.6kBbaryon−1
Ye
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
0.01 0.1 0.2 0.3 0.4 0.5 0.1
1 10 100
500 sym2,s= 10kBbaryon−1
Ye
τ[ms]
0.01 0.1 0.2 0.3 0.4 0.5 sym2,s= 18kBbaryon−1
Ye
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
0.01 0.1 0.2 0.3 0.4 0.5 0.1
1 10 100
500 sym2,s= 32kBbaryon−1
Ye
τ[ms]
0.01 0.1 0.2 0.3 0.4 0.5 sym2,s= 56kBbaryon−1
Ye
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
0.01 0.1 0.2 0.3 0.4 0.5 0.1
1 10 100
500 sym2,s= 100kBbaryon−1
Ye
τ[ms]
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
Figure 3.24: All thesslices showing the final lanthanide and actinide mass fraction of thesym2run.
0.01 0.1 0.2 0.3 0.4 0.5 0.1
1 10 100
500 sym2,s= 1.0kBbaryon−1
Ye
τ[ms]
0.01 0.1 0.2 0.3 0.4 0.5 sym2,s= 1.8kBbaryon−1
Ye
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 0.1
1 10 100
500 sym2,s= 3.2kBbaryon−1
Ye
τ[ms]
0.01 0.1 0.2 0.3 0.4 0.5 sym2,s= 5.6kBbaryon−1
Ye
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 0.1
1 10 100
500 sym2,s= 10kBbaryon−1
Ye
τ[ms]
0.01 0.1 0.2 0.3 0.4 0.5 sym2,s= 18kBbaryon−1
Ye
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 0.1
1 10 100
500 sym2,s= 32kBbaryon−1
Ye
τ[ms]
0.01 0.1 0.2 0.3 0.4 0.5 sym2,s= 56kBbaryon−1
Ye
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 0.1
1 10 100
500 sym2,s= 100kBbaryon−1
Ye
τ[ms]
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
Figure 3.25: All the sslices showing the heating rate at 1 day of thesym2run.
0.01 0.1 0.2 0.3 0.4 0.5 1
10
100 sym2,τ= 0.10 ms
Ye
s[kBbaryon−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 sym2,τ = 0.29 ms
Ye
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
0.01 0.1 0.2 0.3 0.4 0.5 1
10
100 sym2,τ= 0.84 ms
Ye
s[kBbaryon−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 sym2,τ= 2.4 ms
Ye
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
0.01 0.1 0.2 0.3 0.4 0.5 1
10
100 sym2,τ= 7.1 ms
Ye
s[kBbaryon−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 sym2,τ= 21 ms
Ye
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
0.01 0.1 0.2 0.3 0.4 0.5 1
10
100 sym2,τ= 59 ms
Ye
s[kBbaryon−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 sym2,τ = 170 ms
Ye
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
0.01 0.1 0.2 0.3 0.4 0.5 1
10
100 sym2,τ = 500 ms
Ye
s[kBbaryon−1 ]
10−5 10−4 10−3 10−2 10−1 0.3
finalXLa+Ac
Figure 3.26: All theτslices showing the final lanthanide and actinide mass fraction of thesym2run.
0.01 0.1 0.2 0.3 0.4 0.5 1
10
100 sym2,τ= 0.10 ms
Ye
s[kBbaryon−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 sym2,τ = 0.29 ms
Ye
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 1
10
100 sym2,τ= 0.84 ms
Ye
s[kBbaryon−1 ]
0.01 0.1 0.2 0.3 0.4 0.5 sym2,τ= 2.4 ms
Ye
1037 1038 1039 1040 1041 1042
Mǫat1day[ergs−1 ]