6.7.1 Angular distributions of the ejected matter
Outflow detectors allows to study not only the global properties of the ejected material, but also the angular distribution of the ejected material on the detec-tor surface and hence virtually at spatial infinity. Besides having an interest in their own right, anisotropies in the distribution of the ejected matter could have important consequences on the kilonova signal of a given binary configu-ration, and impact its detectability, especially when considering the effect that the viewing angle could have on the effective observed kilonova signal in pres-ence of such anisotropies. To the best of our knowledge this is the first time that an analysis of this type has been carried out.
We consider the angular distribution of ejected mass as defined by equation (6.10), where in this case however the integration over the angular directions does not span the whole 2-sphere, but only a single patch of the outflow detec-tor. We also study the mass-averaged distribution of the electron fraction, the specific entropy and the ejecta velocity. Similarly to equation (6.10), these are defined as
hχi:=
Z Tf 0
Z
∆Ω
χ ρ∗W(αvr−βr)S dΩdt / Z Tf
0
Z
∆Ω
ρ∗W(αvr−βr)S dΩdt , (6.16)
Figure 6.13: The same as in figure 6.12 but for the electron fraction. Figure reproduced fromBovard et al.(2017).
whereχis any one ofYe,sorvej, and the same consideration as above applies to the integration over the angles.
In figure6.12we collect Mollweide projections of the fiducial outflow detec-tor relative to the time-integrated rest mass for all models. Several properties of the angular distribution of the ejected matter are apparent. Firstly the binary SFHO-M1.45, which immediately collapses to a black hole after the merger, is immediately identifiable as there is close to no ejected matter in this case. Sec-ondly it is clear that in each binary most of the mass is ejected on the orbital plane, which is consistent with expectations that the material ejected here is mostly of dynamical origin and the ejection mechanism is due to the torques in the system at merger (other types of ejecta, such as neutrino/magnetically driven winds or ejecta from viscous heating would display a more isotropic structure). Third, while concentrated at low latitudes, the ejected mass is not uniformly distributed but shows considerable anisotropies; this is simply due to the disruption of the flow produced by the tidal torques and this concen-trates the emission of matter into rather small regions on the detector surface.
The only binary that appears to evade this trend isSFHO-M1.35, which has ejected matter also at latitudes as high as ∼ 45◦ and seems to peak around
∼ 30◦.
In a similar fashion, the distribution of the electron fraction Ye is shown in figure6.13. It is apparent how the electron fraction tends to anticorrelate with the amount of ejected mass: regions in which the ejected mass fraction is higher (such as the orbital plane) tend to have very lowYe and vice-versa.
This consistent with the results of section6.5.2, where most of the ejected mass is shown to be very neutron-rich. On the other hand it can be seen that in other regions, such as the poles, the material is very neutron-poor, but has correspondingly low values of ejected mass. The evidence provided in figure 6.13that matter ejected around the poles is less neutron-rich (i.e. withYe &
0.25) suggests the possibility that material there might undergo a less robust r-process, leading to a suppressed production of lanthanides and thus to a lower opacity. This bimodal anisotropy in the distribution of the electron fraction could then lead to either a “blue” kilonova, i.e. to a kilonova signal with a comparatively strong optical component, if the line of sight is mostly along
Figure 6.14: Angular distribution of the mass fraction of lanthanides in the representative case of the binaryLS220-M1.35; the data refers to the final simulation time..Figure reproduced fromBovard et al.(2017).
the polar regions, or to a “red” kilonova,i.e. to a kilonova signal peaking in the infrared, if the line of sight is mostly along the equatorial regionsMetzger (2017a);Tanaka(2016).
To check the plausibility of such a scenario we have explicitly computed the angular distribution of the lanthanides mass fraction in the representative LS220-M1.35model,i.e. by computing the lanthanides mass fraction of ev-ery unbound tracer in the simulation and by plotting their location on the 2-sphere, as shown in figure6.14; to produce this plot the lanthanides mass frac-tion values have been averaged over patches of angular size10◦×10◦. As can be seen, even near the poles the lanthanides mass fraction is rather high,i.e.
XLa ≈10−2. This is far larger than the generally accepted limit on this value that leads to a sufficient suppression of the medium opacity for a blue kilonova to be observed,i.e. XLa ∼10−5. Very similar values have been obtained in all other BNS models. Therefore this result seems to indicate that a blue-kilonova scenario is probably unlikely to originate from the dynamical ejecta in view of GW170817 (Metzger,2017b), according to our calculations. Note however that despite the three orders of magnitude difference between the expected value of the lanthanides mass fraction and the one computed here, our conclusions may be biased by an oversimplified neutrino treatment. A proper neutrino-transfer treatment of the propagation of neutrinos in the ejected matter could in fact modify, in part at least, our results. Indeed more sophisticated neutrino treat-ments, such as the one employed inFoucart et al.(2016c), have been shown to produce higher values of the electron fraction around the polar regions. All things considered, our results suggest that while a blue kilonova component cannot be ruled out conclusively, it also seems to require an electron-fraction distribution that is considerably different from the one computed here.
Similar observations as for theYemorphology hold true for the distribution of the specific entropy, as shown in figure6.15: the entropy anticorrelates with the ejected matter, as regions close to the orbital plane tend to have small en-tropies, while around the poles values of the entropy can be very high. These
Figure 6.15: The same as in figure6.12but for the specific entropy.
Figure 6.16: The same as in figure6.12but for the ejecta velocity.
corresponds to the tails shown in figure6.5, extending to specific entropies of 200 kB/baryonand above. The case of theSFHO-M1.45model is particularly striking, with most of the ejected material at extremely high entropy. As ob-served in the previous discussion, however, this model also ejects an almost negligible amount of mass, which enhances the shock-heating efficiency.
The velocity distribution, shown in figure 6.16, is instead rather peculiar.
For many models, especially the lower mass ones, including the unequal-mass models in the rightmost column of the figure, the material appears to be ex-panding at the same velocity in most directions, save for a few “hot” or “’cold”
spots of limited angular size. In the three higher mass models, shown in the third column of figure6.16, some large-scale structure could be present, but there is no evidence of the correlation observed for the electron fraction or en-tropy.
6.7.2 Kilonova light curves and observability
We use the simple gray opacity model of kilonovae developed inGrossman et al.(2014) to assess the observability of the infrared transients associated to the decay of r-process elements. The comparatively small ejected masses re-sulting from our simulations preclude the use of more sophisticated radiative
transfer treatments (left for future work) when these ejecta could be a signifi-cant source of opacity (the “lanthanide curtain”) for potential secondary out-flows, such as magneticallySiegel et al.(2014) and viscously driven wind from an accretion disk, or neutrino-driven wind from the hypermassive neutron star Perego et al.(2014).
In the model ofGrossman et al. (2014) the background dynamical ejecta are approximated by a homologously expanding spherically symmetric shell of density ρ(r, t) = ρ0(t0/t)3(1−v2/v2max)3 (also described in detail in Wol-laeger et al.(2017)), andvmax = 2hv∞i, taken from table6.2. The luminosity output is computed by integrating the nuclear heating rate from the nuclear network over the layer of matter from which photons can diffuse out. A sim-ilar model is used in (Perego et al.,2014;Martin et al.,2015b;Rosswog et al., 2017). We employ an effective gray opacityκ = 10 cm2 g−1, which was re-cently demonstrated to reproduce the infrared luminosity of lanthanide- and actinide-contaminated ejecta reasonably well (Wollaeger et al.,2017). Note that the same study shows the flux in the optical bands to be strongly suppressed when detailed opacities of lanthanides are used; for this reason, we consider here only the infrared magnitudesJ,H andK-bands in the Two Micron All Sky Survey (2MASS)Skrutskie et al.(2006).
The nuclear heating which powers the kilonova for each model is calcu-lated with the nuclear network codeWinNet(Winteler et al.,2012;Korobkin et al.,2012) (cf. section6.2.4) using the average electron fractionhYei, specific entropyhsiand expansion velocity hv∞ias given in table 6.2. We compute the nucleosynthesis yields with reaction rates based on the finite-range droplet model (FRDM) (Möller et al.,2012) only. This is motivated by the fact that nu-clear mass models show little discrepancy in the heating rates at epochs around t ' 1day (Rosswog et al.,2017), where the peak magnitudes for our models are expected.
Figure 6.17: Synthetic light curves in the infrared 2MASSJ, HandK-bands for all of the binaries considered.Figure reproduced fromBovard et al.(2017).
The resulting peak bolometric luminosities, peak magnitudes in the in-frared bands, and the peak epochs in theH-band are presented in table6.2, while the light curves in the three infrared bands (indicated by different line colors) are shown in figure6.17, with different line types referring to the differ-ent binaries.
Clearly all of our models show a very similar behaviour, peaking around half a day in theH-band and rapidly decreasing in luminosity after one day, reaching a maximum magnitude of−13. We note that these luminosities are smaller than those normally expected (seee.g. (Tanaka,2016) for a recent
re-view), which peak around magnitude of∼ −15; this difference is not surprising and is mostly due to the amounts of ejected mass, which is normally assumed to be∼ 10−2Mand hence at least one order of magnitude larger than what measured here. With 3-minuteJ-band exposure on the VISTA telescope (Emer-son et al.,2004), these magnitudes result in a detection horizon of∼100 Mpc, which, in combination with a very short time around the peak, makes these light curves extremely difficult to detect in a follow-up survey. As observed in the follow-ups to GW170817, light curves were observed that originate from a kilonova (The LIGO Scientific Collaboration and The Virgo Collaboration, 2017;Cowperthwaite et al.,2017;Metzger,2017b) which suggests that a signi-ificant amount of material, on the order of10−2M, became unbound. As this amount of ejecta is above the amount we have seen in dynamical merger sim-ulations, this suggests that the source of the radioactive decay powering the kilonova is not in the dynamical ejecta, but in other sources such as neutrino drive winds or viscous ejecta (Metzger,2017b).