theory of kilonova and afterglowyokohamagrb2019.wdfiles.com/local--files/program:files... ·...

Theory of Kilonova and

AfterglowKenta Hotokezaka

(U of Tokyo and Princeton)

With E. Nakar, O. Gottlieb (Tel Aviv), T. Piran (Hebrew), P. Beniamini, K. P. Mooley, G. Hallinan (Caltech), A. T. Deller (Swinborn), S. Nissanke (Amsterdam), K. Masuda (IAS),

M. Tanaka (Tohoku)

()

Outline

• Implications of the Kilonova in GW170817

• Implications of the Afterglow in GW170817

• Summary

1 Scientific justification

The era of gravitational-wave (GW) astronomy has begun with the announcement of the discoveryof five double black hole (BH-BH) mergers (Abbott et al. 2016a, 2017a,b,c) and one double neutronstar (NS-NS) merger (GW170817; Abbott et al. 2017d). Localized to the lenticular galaxy NGC4993 at 40Mpc (Coulter et al. 2017), GW170817 was the first GW event with an electromagnetic(EM) counterpart. It was accompanied by prompt �-rays, fast-fading UV/optical/NIR, and long-lived X-ray, optical, and radio emission (Abbott et al. 2017e and references therein; left panel ofFigure 1). GW170817 yielded a scientific bonanza in fields as wide-ranging as gravitational physics,nucleosynthesis, extreme states of nuclear matter, relativistic explosions and jets, and cosmology.The EM signatures of GW170817 were remarkably di↵erent from what prior models predicted. The

�-rays were a factor of ⇠ 103 weaker than for ordinary short �-ray bursts (SGRBs), there was an earlyblue kilonova presumably due to lanthanide-free polar ejecta (Fernandez & Metzger 2016, Kasen etal. 2017), and late onset of radio/X-ray emission (Abbott et al. 2017e and references therein). Asubsequent fainter, longer-lived, red kilonova emission was powered by lanthanide-rich tidal ejecta oran accretion disk wind. The merger likely produced a hyper-massive NS, rapidly followed by collapseto a BH on a short timescale (⇠ 100ms; Kasen et al. 2017, Pooley et al. 2018). A relativistic jet waslaunched, but became entrenched in the dynamical ejecta, driving a wide-angled, mildly relativisticoutflow, commonly referred to as a “cocoon” or “structured jet”. This cocoon was likely responsiblefor the early-time �-rays, as well as late time X-ray (Ruan et al. 2018, Margutti et al. 2018, Troja etal. 2018) and radio emission (e.g. Mooley et al. 2018, Margutti et al. 2018). It is unclear whetherthe jet eventually burrowed through the ejecta to successfully produce a SGRB (e.g. Margutti et al.2018). See Figure 1 for a depiction of the di↵erent ejecta components and EM signals.

Figure 1: Left panel: The optical/NIR “kilonova” and the X-ray, radio afterglows of GW170817.The short-lived kilonova signal is powered by the radioactive decay of r-process nuclei, while the long-lived X-ray and radio are synchrotron emission from fast-moving, wide-angle shocks. X-ray, Optical,and radio emission is expected in 30–80% of NS-NS and NS-BH mergers. Right panel: The varietyof ejecta components, labeled in black font, and resulting EM signals, labeled in colored font, fromNS-NS and NS-BH mergers (adapted from Ioka & Nakamura 2017).

Despite the smashing success of the observing campaign surrounding GW170817, many fundamen-tal questions about the NS merger process remain unanswered. What fraction of mergers producecentral engines and relativistic jets? How long do they operate, and how often are they able tosuccessfully penetrate the merger ejecta and radiate to on-axis observers as a classical SGRB? Howmuch energy is released in total? What is the maximum mass for a stable NS remnant? What will

1

Kilonova & Afterglow in GW170817

Afterglow

KilonovaKilonova: quasi-thermal Radioactive => mass & composition

Afterglow: Non-thermal Shock Acceleration => velocity, geometry

© K. Mooley

The origin of elements

site. More recent works focus on the late chemical evolution in the Milky Way. The ratio of r-processelements to Fe, [Eu/Fe], declines for [Fe/H]> �1, where [X/Y] = log

10(NX/NY)� log

10(NX/NY)�,

NX is the abundance of an element X, and � refers to the solar value. It has been questionedwhether such a behavior is consistent with the expected merger history in the Milky Way (Coteet al., 2016; Komiya & Shigeyama, 2016).

Our goal in this article is twofold. First we summarize the cumulative evidences supportingthat r-process nucleosynthesis takes place in rare events in which a significant amount of r-processelements are produced in each event. Using the rate and mass ejection per event inferred fromthese measurements, we test the neutron star merger scenario for the origin of r-process elements inthe cosmos. This evidence clearly rules out the normal cc-SNe scenario. Moreover, the rate agreeswith merger estimates from galactic binary neutron stars, from sGRBs, and from GW170817. Atthe same time the amount of matter is consistent with the kilonova/macronova, AT2017gfo, andthe candidates associated with cosmological sGRBs. Second, we turn to the Galactic chemicalevolution of r-process elements at later times [Fe/H]& �1 and discuss whether the neutron starmerger scenario can consistently explain the observed distribution of [Eu/Fe].

2 r-process production rate, sGRBs, and GW170817

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Figure 1: The solar abundance pattern of r-process elements (left) and its cumulative abundance(right). The solar r-process abundance pattern is taken from Goriely (1999); Lodders (2003).

Before discussing details, we describe here the r-process abundance pattern. Figure 1 shows thesolar abundance pattern of r-process elements taken from (Goriely, 1999; Lodders, 2003). There arethree peaks. For the solar abundance pattern, most of the mass of r-process elements (⇠ 80%) isaround the first peak. However, the abundance ratio of the first peak to the second peak of extrememetal poor stars, of which the abundance pattern likely reflects a single nucleosynthesis event, isoften di↵erent from that of the solar pattern. Some of these stars exhibit abundance patterns beyondthe second peak (heavy r-process) that are similar to the solar pattern. However, they don’t containsimilar amounts of the first peak elements as compared with expectations from the solar abundancepattern (e.g. Sneden et al. 2008 and references therein). At the same time, there are stars thatcontain a substantial amount of the first peak elements but do not show a significant enrichment ofheavy r-process elements (e.g. Honda et al. 2006). This suggests that the ratio between “heavy” and“light” r-process abundances varies among events or there may be di↵erent kinds of astrophysicalphenomena producing “light” and “heavy” r-process elements. For instance, electron capture andcc-SNe could produce a su�cient amount of “light” r-process elements (e.g. Roberts et al. 2010;Wanajo et al. 2011). Therefore, it is important to keep in mind that it is unclear what the minimalatomic mass number of elements produced by r-process events is.

Since rate estimates of r-process events are sensitive to the minimal atomic mass number as-sumed, we consider here two scenarios in which an astrophysical phenomenon predominantly pro-duces (i) all the r-process elements (Amin = 69) and (ii) only heavy r-process elements (Amin = 90).The mass fractions of the lanthanides out of the total r-process elements for these two cases are

4

KH, et al 18

Do they all come from mergers?

Kilonova/MacronovaLi & Paczynski 1998, Kulkarni 2005, Metzger + 2010

Time

Merger Mass ejection R-process nucelosynthesis

Radioactive decay

Photons diffuse out

Optically thin

t=0 0<t<100ms ~<1s 1day > 10day 10km 10-100km < 0.1Rsun 10AU >100AU

R-process heating rate with thermalization

Radioactive power (β-decay)

Time

γ+e+ν

⇠ E(t)t / t�1.3

Days Week - month

Metzger + 10, Golierly + 11, Roberts + 11, Korobkin + 12, KH+16,17

R-process heating rate with thermalizationMetzger + 10, Golierly + 11, Roberts + 11, Korobkin + 12, KH+16,17

Radioactive power (β-decay)

Time

γ+e+ν

⇠ E(t)t / t�1.3

Days Week - month

3

Figure 1. Mean electron energy (left) and mean �-ray energy (right) released in each �-decay as a function of mean life-time. Hereelements with an atomic mass number A � 85 are included. The color of each point shows the solar abundance of r-process elements. Dataare taken from Evaluated Nuclear Data File library (ENDF/B-VII.1, Chadwick et al. 2011).

R-process nuclei with 209 < A . 250 may be disintegrated via ↵-decay and end up as 206Pb, 207Pb, 208Pb or209Bi. Each ↵-decay releases energy of ⇠ 5–10 MeV in the kinetic energy of an ↵-particle. Since the lifetimes of↵-unstable nuclides with a larger atomic mass number are typically longer, the first ↵-decay of decay chains may actas a bottleneck. Thus, the first ↵-decay is often followed immediately by several ↵ and �-decays. Wu et al. (2019)show that the ↵-decay chains of 222Rn (3.8 day, 23.8 MeV), 223Ra (11.4 day, 30.0 MeV), 224Ra (3.6 day, 30.9 MeV), and225Ra (14.9 day, 0.4 MeV) ! 225Ac (10.0 day, 30.2 MeV), where the half-life and the total energy release per decaychain are shown in the parentheses, are particularly important for the macronova heating rate. The radioactive powerof each decay chain can be approximately estimated as

Q↵(t) ⇡ 4 · 108e�t/⌧

✓Y↵

10�5

◆ ✓⌧

10 day

◆�1 ✓E↵,tot

30 MeV

◆erg/s/g, (3)

where ⌧ is the mean life, E↵,tot is the total energy release per decay chain, Y↵ is the initial number of a parent nuclideper nucleon. We take the mean-lives, Q-values, and branching ratios from ENDF/B-VII.1 to calculate the radioactivepower of decay chains.

2.3. Spontaneous fission

Finally, transuranium nuclei may be disintegrated via spontaneous fission, which releases large amounts of energy,⇠ 200 MeV, per decay. Although the abundance of such elements produced in merger ejecta is highly uncertain dueto the lack of experimental data, spontaneous fission potentially contributes to the heating rate (Wanajo et al. 2014;Hotokezaka et al. 2016; Barnes et al. 2016). The radioactive power of spontaneous fission is roughly estimated as

Qsf(t) ⇡ 3 · 108e�t/⌧

✓Ysf

10�6

◆ ✓⌧

10 day

◆�1 ✓Esf

200 MeV

◆erg/s/g, (4)

where Esf is the energy release per spontaneous fission, Ysf is the initial number of a parent nuclide per nucleon.For instance, the spontaneous fission of 254Cf is suggested as a possible energy source of macronovae at later times(Wanajo et al. 2014; Zhu et al. 2018; Wu et al. 2019). In addition, Wanajo et al. (2014) suggest that 259Fm and 262Fmsignificantly contribute to the heating rate. In later sections, we consider spontaneous fission of 254Cf, neglecting theminor contribution of �-decays of the daughter nuclei following fission.

3. THERMALIZATION

3.1. Charged Particles

Fast-moving charged particles produced by radioactive decay deposit their kinetic energy to the ejecta thermalenergy through collisional ionization and excitation, and Coulomb collision with thermal electrons. At early timesthe density of the expanding ejecta is high enough that the collisional energy loss occurs on time scales shorter thanone dynamical time. In this regime, the heating rate is practically the same to the radioactive power at any giventime. At later times, however, collisional thermalization takes longer time than one dynamical time. As a result, theheating rate deviates from the radioactive power at a given time (Barnes et al. 2016; Kasen & Barnes 2019; Waxmanet al. 2019). Our calculation is similar to the analytic methods presented by Kasen & Barnes (2019); Waxman et al.(2019), but we specify the injection energies of decay products for each decay chain, which as we show below can havea significant e↵ect on the thermalization e�ciency at late times. Note, that these energies are known rather well sincethey at the relevant times (t & 103 s), all unstable nuclides are very close to the valley of stability where there is directexperimental data.

R-process heating rate with thermalization

Heating rate (β-decay)

Time

γ+e e only e only

γ tra

nspa

rent

Elec

tron

deco

uplin

g

⇠ E(t)t / t�1.3⇠ E(t)

t / t�1.3

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Barnes+16, KH+16, Kasen & Barnes 19, Waxman+19, KH & Nakar 19

R-process heating rate with thermalizationBarnes+16, KH+16, Kasen & Barnes 19, Waxman+19, KH & Nakar 19

Heating rate (β-decay)

Time

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γ tra

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t / t�1.3

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/ t�7/3–t�2.8Heating rate ~ Ne ･σst ･ve ･ρ ~ t-3

β-decay Heating rate7

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Time since merger [days]

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Qth

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Qth : �

Figure 4. Radioactive power and heating rate of �-decay in electrons and �-rays. The solar r-process abundance pattern with aminimum atomic mass number of Amin = 85 (left) and 141 (right) is assumed. Also shown in both panels is an analytic heating rate,1010(t/day)�4/3 erg/s/g. For the thermalization processes, we assume an ejecta mass of 0.05M�, v0 = 0.1c, vmax = 0.4c and n = 4.5.

Figure 5. Same as figure 4 but for ↵-decay (left) and spontaneous fission (right). Here we assume the initial abundance of ↵-decaynuclei of (Y (222Rn), Y (223Ra), Y (224Ra), Y (225Ra)) = (4.0 · 10�5, 2.7 · 10�5, 4.1 · 10�5, 2.7 · 10�5) (Wu et al. 2019). 254Cf with an initialabundance of 2.0 · 10�6 is used. The ejecta profile same to that of figure 4 is used.

t0 (Swartz et al. 1995; Je↵ery 1999; Wygoda et al. 2019). This time scale, t0, is defined by the time at which thee↵ective optical depth for �-rays is unity, ⌧�,e↵ = 1:

⌧�,e↵ = �,e↵⌃m(t), (20)

where �,e↵ is the purely absorptive e↵ective opacity and the mass-weighted column density of the ejecta is

⌃m(t)=

Zd3x

⇢(t, ~x)

Mej

Zd⌦

4⇡

Z 1

0ds⇢(t, ~x + s~⌦), (21)

=C⌃Mejv�20 t�2, (22)

where ~⌦ is the unit solid angle vector. C⌃ is a constant that depend on the structure of the ejecta and can be foundby carrying out the integral in the equation 21. For the ejecta power-law profile that we consider (equation 12) theintegration should be carried out numerically. The analytic formula

C⌃ ⇡ 0.1w + 0.003k

w. (23)

provide a good approximation (up to a factor of order unity) for 0 < k < 5 and 0.1 < w < 0.5, which is the mostrelevant range for the merger ejecta.

The e↵ective opacity �,e↵ accounts for the fraction of the energy that �-rays deposit when they propagate through

tth

KH & Nakar 19, https://github.com/hotokezaka/HeatingRate

https://github.com/hotokezaka/HeatingRate

An example for GW170817KH & Nakar 19, https://github.com/hotokezaka/HeatingRate

Lbol

Qtot

1D ejecta model

Low κ

High κ

An example for GW170817KH & Nakar 19, https://github.com/hotokezaka/HeatingRate

tdiff>t

tdiff<tτ<1

• Bolometric light curve follows the r-process heating rate. • The steep decline around a week can be interpreted as the diffusion

wave crossing the entire ejecta.

Lbol

Qtot

Composition and light curve11

Figure 9. Bolometric light curves for di↵erent nuclear compositions. The ejecta mass is chosen to be 0.1M� for 141 A 209 and0.05M� for the others. The values of the opacity are the followings: 0.3 cm2/g (v > 0.18c) and 3 cm2/g (v 0.18c) for Amin = 72,0.5 cm2/g (v > 0.2c) and 3 cm2/g (v 0.2c) for Amin = 85, and 0.1 cm2/g (v > 0.18c) 3 cm2/g (v 0.18c) for Amin = 141.

for this di↵erence is, at least in part, due to the fact that Waxman et al. (2018, 2019) assume that the energy of thedeposited electrons is 1MeV, while experimental data show that at the relevant time it is typically lower (see figure1), which corresponds to a larger value of tth,� .

An interesting point that we find in the attempt to fit the data with di↵erent compositions is that including a�-decay chain, 88Kr!88Rb!88Sr, enhances the peak luminosity, where 88Kr and 88Rb have a half-life of 2.83 hr and17.8 min, respectively. This decay chain releases ⇠ 5 MeV in electrons and �-rays. For example, the peak luminositywith Amin = 85 is higher by a factor of ⇠ 2 than that with Amin = 90. The high peak luminosity of the macronovaGW170817 may indicate that this decay chain significantly contributes to the heat around the peak.

The dependence of the heating rate on the composition may provide some clues about the ejecta. Figure 9 showsthe bolometric light curves powered by �-decay with di↵erent atomic mass ranges (assuming a solar abundance ratio).The light curve model with 85 A 140, where there are no elements beyond the second peak, is similar to theone with 85 A 209. The reason is that the contribution of elements with A > 140 to the heating is minor.Thus, at least for heating, these elements are not required, although the late time spectrum and color evolution of themacronova GW170817 suggest that the ejecta contains elements beyond the second peak (e.g., Chornock et al. 2017).In the case that only the first peak elements are included (72 A 85), the luminosity is too low to reproduce thelate-time Spitzer data (see Kasliwal et al. 2019 for details). The reason is that during the first week the heat depositionis dominated by a single chain of the elements with A = 72 and there are no element with a significant contributionat late times. When heavier elements are added, 72 A 209, the emission at late time is brighter and marginallyconsistent with the strict Spitzer lower limits. The reason for the rather low late-time heating (compared to the casewith 85 A 209) is that also here the large mass carried by first peak elements that do not contribute to the latetime emission is coming on the expense of the heavier elements that contribute to the late-time heating. Given thatthe Spitzer lower limits account only for the emission seen within the Spitzer band, it is most likely that the actualbolometric luminosity is at least a factor of a few brighter than these lower limits and therefore it is most likely thatthe ejecta did not contain a significant fraction of first peak elements. Finally, when only elements beyond the secondpeak are included (140 A 209), the luminosity at early times is lower by a factor of ⇠ 5 than the observed data.This suggests that while elements above the second peak are probably present in the ejecta (based on their opacitysignature), the total ejecta mass is dominated by elements with atomic mass 85 A 140.

Figure 10 depicts the bolometric light curve and temperature in the case that ↵-decay heating is included assumingthe abundances of ↵-decaying nuclei used for figure 5. Because the heating rate at later times is significantly enhancedby the ↵-decay contribution, the total ejecta mass required to fit the data is reduced to ⇡ 0.023M�. Here, we usethe density profile same to the above and the opacity of 0.5 cm2/g for v > 0.14c and 3 cm2/g for v 0.14c. In thismodel, the light curve at 1 . t . 10 days declines with / t�1 resulting from that the ↵-decay heating kicks in around2 days. Then the model light curve turns to declines as / t�2.8 due to the thermalization ine�ciency. However, theobserved light curve falls more quickly than the model light curve, although this may be a result of underestimate ofthe observed bolometric luminosity at t & 7 days.

5. EJECTA MASS ESTIMATE BASED ON THE KATZ INTEGRAL

Estimate of the ejecta mass that uses light curve modeling are degenerated with the opacity, heating rate, densityprofile, as well as the outflow geometry and the viewing angle. Katz et al. (2013) suggest a powerful method to obtainthe total mass of radioactive elements, Mrad, from observed bolometric light curve data, Lbol(t), as long as the heatdeposition rate is known. The following relation between the heating rate and the bolometric light curve should be


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Beyond 2nd peak

Including the 2nd r-process peak seems necessary.

Sr lines in the kilonova spectrum

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Figure 4 | Spectral series of AT2017gfo 1.5–4.5 days after the merger. Dataare shown in grey and have been smoothed slightly. A model (solid red lines)consisting of a blackbody (blue dotted lines) with P Cygni profiles (red transparentfill) for the Sr lines is shown. The rest (black) and observed (blue) positions of themodel’s Sr lines are shown, with the blueshift indicated by arrows. Green dottedlines show the Gaussian emission profiles added to ensure the overall continuumis not biased. A vertical offset has been applied to each spectrum for clarity, withzero flux indicated by the dashed horizontal line segment. Bottom panels show theresiduals between model and data.

from Sr is also 1,050 nm. This adds to our confidence in the line iden-tification based on the simple thermal r-process absorption model.

We further confirm our results using TARDIS, extending the code’satomic database to include elements up to 92U with the latest Ku-rucz linelists24 with its 2.31 million lines. Our TARDIS models pro-duce results very similar to our static-code models, reproducing thespectra well (Extended Data Fig. 6). In particular, the P Cygni emis-sion/absorption structure is well-reproduced as expected, confirmingour LTE and MOOG modelling, and showing Sr dominating the fea-tures around 1µm.

From the detection of Sr, it is clearly important to consider lighterr-process elements in addition to the lanthanide elements in shapingthe kilonova emission spectrum. Observations of abundances in starsin dwarf galaxies6 suggest that large amounts of Sr are produced to-gether with Ba (Z=56) in infrequent events, implying the existence of asite that produces both light and heavy r-process elements together inquantity, as found in some models25, 26. This is consistent with our spec-tral analysis of AT2017gfo and analyses of its lightcurve27, 28. Togetherwith the differences observed in the relative abundances of r-processBa and Sr in stellar spectra29, this suggests that the relative efficienciesof light and heavy r-process production could vary substantially frommerger to merger.

Extreme-density stars composed of neutrons were proposed shortlyafter the discovery of the neutron13, and identified with pulsars three

decades later30. However, no spectroscopic confirmation of the com-position of neutron stars has ever been made. The identification here ofan element that could only have been synthesised so quickly under anextreme neutron flux, provides the first direct spectroscopic evidencethat neutron stars comprise neutron-rich matter.

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2. Siegel, D. M., Barnes, J. & Metzger, B. D. Collapsars as a major sourceof r-process elements. Nature 569, 241–244 (2019).

3. Lattimer, J. M., Mackie, F., Ravenhall, D. G. & Schramm, D. N. Thedecompression of cold neutron star matter. Astrophys. J. 213, 225–233(1977).

4. Eichler, D., Livio, M., Piran, T. & Schramm, D. N. Nucleosynthesis, neu-trino bursts and gamma-rays from coalescing neutron stars. Nature 340,126–128 (1989).

5. Freiburghaus, C., Rosswog, S. & Thielemann, F.-K. R-Process in NeutronStar Mergers. Astrophys. J. Lett. 525, L121–L124 (1999).

6. Ji, A. P., Frebel, A., Simon, J. D. & Chiti, A. Complete Element Abun-dances of Nine Stars in the r-process Galaxy Reticulum II. Astrophys. J.830, 93 (2016).

7. Metzger, B. D. et al. Electromagnetic counterparts of compact objectmergers powered by the radioactive decay of r-process nuclei. Mon. Not.R. Astron. Soc. 406, 2650–2662 (2010).

8. Barnes, J. & Kasen, D. Effect of a High Opacity on the Light Curves ofRadioactively Powered Transients from Compact Object Mergers. Astro-phys. J. 775, 18 (2013).

9. Tanvir, N. R. et al. A ‘kilonova’ associated with the short-duration �-rayburst GRB 130603B. Nature 500, 547–549 (2013).

10. Abbott, B. P., Abbott, R. & et al. GW170817: Observation of GravitationalWaves from a Binary Neutron Star Inspiral. Physical Review Letters 119,161101 (2017).

11. Pian, E. et al. Spectroscopic identification of r-process nucleosynthesisin a double neutron-star merger. Nature 551, 67–70 (2017).

12. Smartt, S. J. et al. A kilonova as the electromagnetic counterpart to agravitational-wave source. Nature 551, 75–79 (2017).

13. Baade, W. & Zwicky, F. Cosmic Rays from Super-novae. Proceedings ofthe National Academy of Science 20, 259–263 (1934).

14. Tanaka, M. & Hotokezaka, K. Radiative Transfer Simulations of NeutronStar Merger Ejecta. Astrophys. J. 775, 113 (2013).

15. Kasen, D., Metzger, B., Barnes, J., Quataert, E. & Ramirez-Ruiz, E.Origin of the heavy elements in binary neutron-star mergers from agravitational-wave event. Nature 551, 80–84 (2017).

16. Sneden, C., Bean, J., Ivans, I., Lucatello, S. & Sobeck, J. MOOG: LTEline analysis and spectrum synthesis. Astrophysics Source Code Library(2012).

17. Kerzendorf, W. E. & Sim, S. A. A spectral synthesis code for rapid mod-elling of supernovae. Mon. Not. R. Astron. Soc. 440, 387–404 (2014).

18. Lodders, K., Palme, H. & Gail, H.-P. Abundances of the Ele-ments in the Solar System. Landolt Bornstein (2009). 2011 updatearxiv:0901.1149v2.

19. Bisterzo, S., Travaglio, C., Gallino, R., Wiescher, M. & Kappeler, F. Galac-tic Chemical Evolution and Solar s-process Abundances: Dependenceon the 13C-pocket Structure. Astrophys. J. 787, 10 (2014).

20. Honda, S., Aoki, W., Ishimaru, Y. & Wanajo, S. Neutron-Capture El-ements in the Very Metal-poor Star HD 88609: Another Star with Ex-cesses of Light Neutron-Capture Elements. Astrophys. J. 666, 1189–1197 (2007).

21. Sneden, C. et al. Evidence of Multiple R-Process Sites in the EarlyGalaxy: New Observations of CS 22892-052. Astrophys. J. Lett. 533,L139–L142 (2000).

22. Kasen, D., Badnell, N. R. & Barnes, J. Opacities and spectra of the r-process ejecta from neutron star mergers. Astrophys. J. 774, 25 (2013).

23. Jeffery, D. J. & Branch, D. Analysis of Supernova Spectra. In Wheeler,J. C., Piran, T. & Weinberg, S. (eds.) Supernovae, Jerusalem WinterSchool for Theoretical Physics, 149 (1990).

24. Kurucz, R. L. Including all the lines: data releases for spectra and opaci-ties. Canadian Journal of Physics 95, 825–827 (2017).

25. Wanajo, S. et al. Production of All the r-process Nuclides in the Dynami-cal Ejecta of Neutron Star Mergers. Astrophys. J. Lett. 789, L39 (2014).

26. Just, O., Bauswein, A., Pulpillo, R. A., Goriely, S. & Janka, H.-T. Compre-hensive nucleosynthesis analysis for ejecta of compact binary mergers.Mon. Not. R. Astron. Soc. 448, 541–567 (2015).

27. Drout, M. R. et al. Light curves of the neutron star mergerGW170817/SSS17a: Implications for r-process nucleosynthesis. Sci-ence 358, 1570–1574 (2017).

3

Watson et al 19

X-shooter spectra are explained by blackbody + Sr II lines.

Sr lines in the kilonova spectrum

10

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from Sr is also 1,050 nm. This adds to our confidence in the line iden-tification based on the simple thermal r-process absorption model.

We further confirm our results using TARDIS, extending the code’satomic database to include elements up to 92U with the latest Ku-rucz linelists24 with its 2.31 million lines. Our TARDIS models pro-duce results very similar to our static-code models, reproducing thespectra well (Extended Data Fig. 6). In particular, the P Cygni emis-sion/absorption structure is well-reproduced as expected, confirmingour LTE and MOOG modelling, and showing Sr dominating the fea-tures around 1µm.

From the detection of Sr, it is clearly important to consider lighterr-process elements in addition to the lanthanide elements in shapingthe kilonova emission spectrum. Observations of abundances in starsin dwarf galaxies6 suggest that large amounts of Sr are produced to-gether with Ba (Z=56) in infrequent events, implying the existence of asite that produces both light and heavy r-process elements together inquantity, as found in some models25, 26. This is consistent with our spec-tral analysis of AT2017gfo and analyses of its lightcurve27, 28. Togetherwith the differences observed in the relative abundances of r-processBa and Sr in stellar spectra29, this suggests that the relative efficienciesof light and heavy r-process production could vary substantially frommerger to merger.

Extreme-density stars composed of neutrons were proposed shortlyafter the discovery of the neutron13, and identified with pulsars three

decades later30. However, no spectroscopic confirmation of the com-position of neutron stars has ever been made. The identification here ofan element that could only have been synthesised so quickly under anextreme neutron flux, provides the first direct spectroscopic evidencethat neutron stars comprise neutron-rich matter.

1. Burbidge, E. M., Burbidge, G. R., Fowler, W. A. & Hoyle, F. Synthesis ofthe Elements in Stars. Rev. Mod. Phys. 29, 547–650 (1957).

2. Siegel, D. M., Barnes, J. & Metzger, B. D. Collapsars as a major sourceof r-process elements. Nature 569, 241–244 (2019).

3. Lattimer, J. M., Mackie, F., Ravenhall, D. G. & Schramm, D. N. Thedecompression of cold neutron star matter. Astrophys. J. 213, 225–233(1977).

4. Eichler, D., Livio, M., Piran, T. & Schramm, D. N. Nucleosynthesis, neu-trino bursts and gamma-rays from coalescing neutron stars. Nature 340,126–128 (1989).

5. Freiburghaus, C., Rosswog, S. & Thielemann, F.-K. R-Process in NeutronStar Mergers. Astrophys. J. Lett. 525, L121–L124 (1999).

6. Ji, A. P., Frebel, A., Simon, J. D. & Chiti, A. Complete Element Abun-dances of Nine Stars in the r-process Galaxy Reticulum II. Astrophys. J.830, 93 (2016).

7. Metzger, B. D. et al. Electromagnetic counterparts of compact objectmergers powered by the radioactive decay of r-process nuclei. Mon. Not.R. Astron. Soc. 406, 2650–2662 (2010).

8. Barnes, J. & Kasen, D. Effect of a High Opacity on the Light Curves ofRadioactively Powered Transients from Compact Object Mergers. Astro-phys. J. 775, 18 (2013).

9. Tanvir, N. R. et al. A ‘kilonova’ associated with the short-duration �-rayburst GRB 130603B. Nature 500, 547–549 (2013).

10. Abbott, B. P., Abbott, R. & et al. GW170817: Observation of GravitationalWaves from a Binary Neutron Star Inspiral. Physical Review Letters 119,161101 (2017).

11. Pian, E. et al. Spectroscopic identification of r-process nucleosynthesisin a double neutron-star merger. Nature 551, 67–70 (2017).

12. Smartt, S. J. et al. A kilonova as the electromagnetic counterpart to agravitational-wave source. Nature 551, 75–79 (2017).

13. Baade, W. & Zwicky, F. Cosmic Rays from Super-novae. Proceedings ofthe National Academy of Science 20, 259–263 (1934).

14. Tanaka, M. & Hotokezaka, K. Radiative Transfer Simulations of NeutronStar Merger Ejecta. Astrophys. J. 775, 113 (2013).

15. Kasen, D., Metzger, B., Barnes, J., Quataert, E. & Ramirez-Ruiz, E.Origin of the heavy elements in binary neutron-star mergers from agravitational-wave event. Nature 551, 80–84 (2017).

16. Sneden, C., Bean, J., Ivans, I., Lucatello, S. & Sobeck, J. MOOG: LTEline analysis and spectrum synthesis. Astrophysics Source Code Library(2012).

17. Kerzendorf, W. E. & Sim, S. A. A spectral synthesis code for rapid mod-elling of supernovae. Mon. Not. R. Astron. Soc. 440, 387–404 (2014).

18. Lodders, K., Palme, H. & Gail, H.-P. Abundances of the Ele-ments in the Solar System. Landolt Bornstein (2009). 2011 updatearxiv:0901.1149v2.

19. Bisterzo, S., Travaglio, C., Gallino, R., Wiescher, M. & Kappeler, F. Galac-tic Chemical Evolution and Solar s-process Abundances: Dependenceon the 13C-pocket Structure. Astrophys. J. 787, 10 (2014).

20. Honda, S., Aoki, W., Ishimaru, Y. & Wanajo, S. Neutron-Capture El-ements in the Very Metal-poor Star HD 88609: Another Star with Ex-cesses of Light Neutron-Capture Elements. Astrophys. J. 666, 1189–1197 (2007).

21. Sneden, C. et al. Evidence of Multiple R-Process Sites in the EarlyGalaxy: New Observations of CS 22892-052. Astrophys. J. Lett. 533,L139–L142 (2000).

22. Kasen, D., Badnell, N. R. & Barnes, J. Opacities and spectra of the r-process ejecta from neutron star mergers. Astrophys. J. 774, 25 (2013).

23. Jeffery, D. J. & Branch, D. Analysis of Supernova Spectra. In Wheeler,J. C., Piran, T. & Weinberg, S. (eds.) Supernovae, Jerusalem WinterSchool for Theoretical Physics, 149 (1990).

24. Kurucz, R. L. Including all the lines: data releases for spectra and opaci-ties. Canadian Journal of Physics 95, 825–827 (2017).

25. Wanajo, S. et al. Production of All the r-process Nuclides in the Dynami-cal Ejecta of Neutron Star Mergers. Astrophys. J. Lett. 789, L39 (2014).

26. Just, O., Bauswein, A., Pulpillo, R. A., Goriely, S. & Janka, H.-T. Compre-hensive nucleosynthesis analysis for ejecta of compact binary mergers.Mon. Not. R. Astron. Soc. 448, 541–567 (2015).

27. Drout, M. R. et al. Light curves of the neutron star mergerGW170817/SSS17a: Implications for r-process nucleosynthesis. Sci-ence 358, 1570–1574 (2017).

3

Watson et al 19

X-shooter spectra are explained by blackbody + Sr II lines.

8 Tanaka & Hotokezaka

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Fig. 6.— UVOIR spectra of model NSM-all at t = 1.5, 5.0, and 10.0 days after the merger. The spectra are almost featureless. At NIRwavelengths, there are possible absorption troughs, which result from Y i, Y ii, and Lu i in our simulations. However, the features couldbe result from the incompleteness of the line list in the NIR wavelengths.

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Fig. 7.— Bolometric light curves for realistic models (Table 1).The expected emission of models with a soft EOS APR4 (red) isbrighter than that with a stiff EOS H4 (blue). For the soft EOSAPR4, the light curve does not depend on the mass ratio, while fora stiff EOS H4, a higher mass ratio (1.2M⊙ + 1.5M⊙, solid line)results in a large ejecta mass, and thus, brighter emission than alower mass ratio (1.3M⊙ + 1.4M⊙, dashed line).

fiducial model NSM-all (black) is similar to that of modelAPR4-1215 and APR4-1314 because these models havea similar mass and a characteristic velocity (Table 1).For the soft EOS APR4, the brightness does not de-

pend strongly on the mass ratio of the binary NSs (redsolid and dashed lines in Figure 7). This is because fora soft EOS, such as APR4, the mass ejection by shockheating is efficient. By contrast, for the stiff EOS H4, themass ejection occurs primarily by tidal effects (the effectof shock heating is weak, Hotokezaka et al. 2013). Thus,the mass ejection is more efficient for a higher mass ra-tio. As a result, model H4-1215 (mass ratio of 1.25) isbrighter than model H4-1314 (mass ratio of 1.08).These results open a new window to study the nature

of the NS merger and EOSs. By adding the information

of EM radiation to the analysis of GW signals, we may beable to pin down the masses of two NSs and/or stiffnessof the EOSs more accurately. Note that, in the currentsimulations, the heating rate per mass is fixed. To fullyunderstand the connection between the initial conditionof the NS merger and expected emission, detailed nucle-osynthesis calculations are necessary.

6. IMPLICATIONS FOR OBSERVATIONS

6.1. Follow-up Observations of EM Counterparts

In this section, we discuss the detectability of UVOIRemission from NS merger ejecta. Figure 8 shows expectedobserved light curves for a NS merger event at 200 Mpc.Model NSM-all (black) and 4 realistic models (red andblue) are shown. Note that all the magnitudes in Figure8 are given in AB magnitude for the ease of comparisonwith different survey projects. Horizontal lines show 5σlimiting magnitudes for different sizes of telescopes with10 min exposure time.After the detection of GW signal, EM follow up ob-

servations should discover a new transient object froma ∼ 10-100 deg2 area. Thus, the use of wide-field tele-scope/camera is a natural choice (e.g., Nissanke et al.2013). For optical wavelengths, there are several projectsusing 1 m-class telescopes that can cover ∼

> 4 deg2 area,such as Palomar transient factory (PTF, Law et al. 2009;Rau et al. 2009), La Silla-QUEST Variability Survey(Hadjiyska et al. 2012), and Catalina Real-Time Tran-sient Survey (Drake et al. 2009). In Figure 8, we showthe limiting magnitudes deduced from Law et al. (2009).Because of the red color, the detection in blue wave-lengths (ug bands) seems difficult. Even for the brightcases, deep observations with > 10 min exposure in redwavelengths (i or z bands) are needed. The faint modelsare far below the limit of 1m-class telescopes.For larger optical telescopes, the field of view tends to

be smaller. Among 4m-class telescopes, Canada-France-Hawaii Telescope (CFHT)/Megacam and the Blanco4m telescope/DECAM for the Dark Energy Survey 8

have 3.6 deg2 and 4.0 deg2 field of view, respectively.

8 https://www.darkenergysurvey.org

Tanaka & KH 13

Sr II

• Sr lines are expected to be very strong. • The early blackbody is surprising. • Heavy elements may be absent in the

outer part of the ejecta.



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Bolometric light curve indicates the second peak elements

Late spectrum and light curve indicate lanthanides

Kilonova Emission Line Nebula (Pure Nd)

Nebular Emission of Neutron Star Merger 11

Figure 8. Same as figure 3 but those with and without the radiation trapping e↵ect (left) and those at di↵erent densities(right).

Figure 9. .

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JWST will be able to see emission lines of heavy elements.

R-process mass budgetKH, Beniamini, Piran 18

Neutron star mergers seem to be sufficient to provide all of r-process elements in the Galaxy.

⇡ 0.025 and 0.1, respectively. In the following, we test the neutron star merger scenario for theorigin of (heavy) r-process elements. It is worth noting that numerical simulations of merger ejectashow that heavy r-process elements are robustly synthesized (Goriely et al., 2011; Korobkin et al.,2012; Perego et al., 2014; Wanajo et al., 2014; Eichler et al., 2015; Just et al., 2015; Wu et al.,2016; Siegel & Metzger, 2017). The first peak elements are not necessarily synthesized and theirabundances depend on the ejection mechanism and on the nature of the remnant of mergers (e.g.Wanajo et al. 2014; Lippuner & Roberts 2015; Wu et al. 2016; Lippuner et al. 2017) so that mergerswith di↵erent masses may produce di↵erent abundance patterns. Note that there are metal poorstars in which the abundance ratio of Th to Eu is larger than that of the sun, the so-called “actinideboost stars” (e.g. Hill et al. 2002; Roederer et al. 2009). The variation in elemental abundancesbeyond the third r-process peak elements does not a↵ect the mass estimates but they suggest thatthere are r-process events that produce larger amounts of very heavy elements.

2.1 Production rate inferred from r-process measurements

Astrophysical observations and geological measurements provide evidence that r-process elementsare produced in rare events in each one of those a significant amount of r-process elements (a fewpercent of solar masses) are produced. These observations support the merger scenario. In thissection, we briefly summarize the observations and demonstrate their compatibility with each otherand with the merger scenario. The results are summarized in Figs. 2 and 3.

0.1

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Figure 2: The rate of r-process production events in the Milky Way and the mass produced perevent inferred from various measurements (see the text for details and also Hotokezaka et al. 2015).Here, we assume r-process elements with the solar abundance pattern for A � 69 (including the firstpeak r-process elements) are produced in each event. For GW170817, we take the rate estimatedwith the 90% confidence interval (Abbott et al., 2017b) and the mass estimate of ⇡ 0.05M� withan uncertainty of a factor of 2. To convert the volumetric event rate Gpc�3 yr�1 to the galacticevent rate, we use the number density of Milky-Way like galaxies of ⇡ 0.01Mpc�3.

(i) The total mass of r-process elements in the Milky Way: The total mass of r-process elementsin the Milky Way gives a rough estimate for the product of the event rate RMW and the averagemass produced by each event mr: Mtot, r ⇠ tMW · RMW · mr, where tMW ⇡ 10 Gyr is the age ofthe Milky Way (e.g. Eichler et al. 1989; Bauswein et al. 2014; Hotokezaka et al. 2015; Rosswog

5

1 Scientific justification

The era of gravitational-wave (GW) astronomy has begun with the announcement of the discoveryof five double black hole (BH-BH) mergers (Abbott et al. 2016a, 2017a,b,c) and one double neutronstar (NS-NS) merger (GW170817; Abbott et al. 2017d). Localized to the lenticular galaxy NGC4993 at 40Mpc (Coulter et al. 2017), GW170817 was the first GW event with an electromagnetic(EM) counterpart. It was accompanied by prompt �-rays, fast-fading UV/optical/NIR, and long-lived X-ray, optical, and radio emission (Abbott et al. 2017e and references therein; left panel ofFigure 1). GW170817 yielded a scientific bonanza in fields as wide-ranging as gravitational physics,nucleosynthesis, extreme states of nuclear matter, relativistic explosions and jets, and cosmology.The EM signatures of GW170817 were remarkably di↵erent from what prior models predicted. The

�-rays were a factor of ⇠ 103 weaker than for ordinary short �-ray bursts (SGRBs), there was an earlyblue kilonova presumably due to lanthanide-free polar ejecta (Fernandez & Metzger 2016, Kasen etal. 2017), and late onset of radio/X-ray emission (Abbott et al. 2017e and references therein). Asubsequent fainter, longer-lived, red kilonova emission was powered by lanthanide-rich tidal ejecta oran accretion disk wind. The merger likely produced a hyper-massive NS, rapidly followed by collapseto a BH on a short timescale (⇠ 100ms; Kasen et al. 2017, Pooley et al. 2018). A relativistic jet waslaunched, but became entrenched in the dynamical ejecta, driving a wide-angled, mildly relativisticoutflow, commonly referred to as a “cocoon” or “structured jet”. This cocoon was likely responsiblefor the early-time �-rays, as well as late time X-ray (Ruan et al. 2018, Margutti et al. 2018, Troja etal. 2018) and radio emission (e.g. Mooley et al. 2018, Margutti et al. 2018). It is unclear whetherthe jet eventually burrowed through the ejecta to successfully produce a SGRB (e.g. Margutti et al.2018). See Figure 1 for a depiction of the di↵erent ejecta components and EM signals.

Figure 1: Left panel: The optical/NIR “kilonova” and the X-ray, radio afterglows of GW170817.The short-lived kilonova signal is powered by the radioactive decay of r-process nuclei, while the long-lived X-ray and radio are synchrotron emission from fast-moving, wide-angle shocks. X-ray, Optical,and radio emission is expected in 30–80% of NS-NS and NS-BH mergers. Right panel: The varietyof ejecta components, labeled in black font, and resulting EM signals, labeled in colored font, fromNS-NS and NS-BH mergers (adapted from Ioka & Nakamura 2017).

Despite the smashing success of the observing campaign surrounding GW170817, many fundamen-tal questions about the NS merger process remain unanswered. What fraction of mergers producecentral engines and relativistic jets? How long do they operate, and how often are they able tosuccessfully penetrate the merger ejecta and radiate to on-axis observers as a classical SGRB? Howmuch energy is released in total? What is the maximum mass for a stable NS remnant? What will

1

Kilonova & Afterglow in GW170817

Afterglow

KilonovaKilonova: quasi-thermal Radioactive => mass & composition

Afterglow: Non-thermal Shock Acceleration => velocity, geometry

© K. Mooley

GW170817 HST 5

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Figure 2. Top: HST/F606W light curve of the afterglow ofGW170817 spanning ⇡ 110.5 - 584.1 days (green points; observerframe); downwards triangles denote 3� upper limits. The upperlimit at ⇡ 584.1 d is measured from the median-subtracted image,while all other data points are measured from HOTPANTS residualimages. Also shown are a structured jet model and the range oflight curves describing the top 5% of models (black solid and dot-dashed lines), and a quasi-spherical outflow model (dotted line; Wu& MacFadyen 2018). Bottom: Magnitude difference, �m, betweenpublished values in previous works (Alexander et al. 2018; Marguttiet al. 2018; Lyman et al. 2018; Lamb et al. 2019a; Piro et al. 2019)and the new values measured in this work. Upward triangles denoteepochs which were previously reported as upper limits, and are nowdetected in this work.

the radio band, there are available data for all epochs exceptat �t ⇡ 137, 337 days, and 362 days. The data are takenwith the Karl G. Jansky Very Large Array (VLA) and theAustralia Telescope Compact Array (ATCA), spanning 2.5-17 GHz (Alexander et al. 2018; Dobie et al. 2018; Marguttiet al. 2018; Mooley et al. 2018a,b,c; Troja et al. 2018c). Wealso use a 6 GHz VLA observation at �t ⇡ 585 days, pre-sented in Hajela et al. (in prep.).

In the X-ray band, we find relevant comparison Chan-dra X-ray Observatory observations at five epochs. Previousanalyses of these observations have appeared in Nynka et al.(2018); Margutti et al. (2018); Troja et al. (2018a); Pooleyet al. (2018); Ruan et al. (2018); Troja et al. (2018c); Linet al. (2019). Here, we use the fluxes and spectral parame-ters calculated in Hajela et al. (in prep.), which serves as auniform analysis of all available Chandra data of the X-rayafterglow of GW170817 to ⇡ 583.1 days. To enable compar-ison of the X-ray observations to the optical and radio data,we convert the 0.3 - 10 keV X-ray fluxes to flux densities,F⌫,X , at a fiducial energy of 1 keV, using the derived photonindex, � at each epoch, where F⌫,X / ⌫�X and �X ⌘ 1 -�.The radio and X-ray data, along with our HST photometry,are displayed in Figure 3.

108 1010 1012 1014 1016 1018

Frequency (Hz)

10-4

10-2

100

102

104

106

108

1010

Flu

x D

en

sity

(Jy

)

x10 8

110 d

x10 7

165 d

x10 6

172 d

x10 5

209 d

x10 4

218 d

x10 3

297 d

x10 2

328 d

x10

362 d

584 d

Figure 3. Broad-band SED of the afterglow of GW170817 at nineepochs of our HST observations, spanning ⇡ 110 - 584 days; fluxesare scaled for clarity. The HST photometry in this paper (greencircles), radio afterglow (red squares; Margutti et al. (2018); Mooleyet al. (2018c); Dobie et al. (2018); Mooley et al. (2018b); Alexanderet al. (2018); Troja et al. (2018c), Hajela et al. in prep.), and X-rayafterglow (blue diamonds; Hajela et al. in prep.) are shown. Thegray lines are best-fit power laws to the data at each epoch. 1�uncertainties are plotted but the large majority are smaller than thesize of the symbols.

We use �2-minimization to fit the broad-band spectrum ateach epoch to a single power law model in the form F⌫ / ⌫� ,characterized by spectral index � and a flux normalizationparameter. We fit all of the available data at each epoch sep-arately. The resulting fits have �2

⌫ ⇡ 0.6 - 1.3, demonstrat-ing that the single power law model is adequate to fit thedata over all epochs (Figure 3). The values for � and 1�uncertainties are given in Table 2 and the temporal evolu-tion is displayed in Figure 4. We calculate a weighted aver-age of the spectral index across all epochs considered here ofh�i = -0.583±0.013.

4. DISCUSSION

4.1. Off-Axis Afterglow Properties

We present a revised light curve of the optical afterglowof GW170817, relative to previous studies which have usedsubsets of HST observations to derive measurements and up-per limits of the afterglow in the F606W filter (Alexanderet al. 2018; Margutti et al. 2018; Lyman et al. 2018; Lambet al. 2019a; Piro et al. 2019). We calculate the difference�m between the published values and the values presentedin this work (Figure 2). Overall, we find that the afterglowin most epochs is systematically brighter than previously re-ported, with differences of �m ⇡ -0.1-1 mag between pub-lished values and the values presented in this work (Figure 2),

GW170817: Afterglow spectrum

Fong+19, also Margutti+18

Hallinan+17, Margutti+17,18, Troja+17,19, Haggard+17, Ruan+17,Lyman+18,Mooley+18

Radi

o

Opt

ical

X-ra

y

Spectrum• A single power law: ~ν-0.6 => synchrotron radiation (optically thin)

• Electron distribution:

~5 orders of magnitude in γe

• Fermi acceleration works well

dNd�e

/ ��2.2e

Kinetic energy powers the afterglow.

Afterglow light curve Light CurveHallinan..KH+17, Margutti+17,18, Mooley..KH+18a, Mooley+18b, Troja+19, Hajela+19

Jet core

Structure

• The power-law rise => Angular and/or radial structure. • The steep decline => A jet core dominates later.

Figure 1: Proper motion of the radio counterpart of GW170817. The centroid offset posi-

tions (shown by 1� errorbars) and 3�-12� contours of the radio source detected 75 d (black)

and 230 d (red) post-merger with Very Long Baseline Interferometry (VLBI) at 4.5 GHz. The

two VLBI epochs have image RMS noise of 5.0 µJy beam�1 and 5.6 µJy beam�1 (natural-

weighting) respectively, and the peak flux densities of GW170817 are 58 µJy beam�1 and 48 µJy

beam�1 respectively. The radio source is consistent with being unresolved at both epochs. The

shape of the synthesized beam for the images from both epochs are shown as dotted ellipses to the

lower right corner. The proper motion vector of the radio source has a magnitude of 2.7± 0.3 mas

and a position angle of 86o ± 18o, over 155 d.

Superluminal Jet in GW170817VLBI resolve the motion of the radio source Mooley…KH, 2018,

Ghirlanda+2018

Day 75Day 240

1, The source moved 2.7 mas in 155 day.

=> 2.7 mas ~ 0.5 pc (at 40Mpc)

�app = 4.1± 0.4 at 41Mpc

2, The source size is unresolved.

A narrowly collimated relativistic jet!!

Jet Parameters

≤5o

15o–25o

n ≈ 10-4 – 5x10-3 cm-3

E ≈ 1049 – 1050 erg

θjet

θobs

Mooley+KH,18

Ejet and θjet imply Liso ~ 1052 erg/s

(typical SGRB: 1049 erg/s)

SGRB Rate (Liso>1052) ~ 0.1 Gpc-3yr-1

After the beaming correction: Rate (Liso>1052) ~ 100 Gpc-3yr-1

3 - 30% of LIGO’s merger rate.

Jet Parameters

≤5o

15o–25o

n ≈ 10-4 – 5x10-3 cm-3

E ≈ 1049 – 1050 erg

θjet

θobs

Mooley+KH,18

Superluminal motion allows us to measure the viewing angle.

0

1

2

3

4

5

6

7

8

9

10

0 0.2 0.4 0.6 0.8 1 1.2 1.4

βapp

θ [rad]

γ=10γ=5γ=3

Figure 3: Apparent velocity as a function of viewing angle.

The same relation is valid also for the source function S⌫ .The optical depth, ⌧ , is a Lorentz invariant because e�⌧ gives the fraction of photons after

passing through some object, which involves only counting the photon number. Imagine materialAbsorption coe�cient, ↵⌫ , is defined as ⌧ = ↵⌫ l/(sin ✓)

The above relations are useful when calculating observed quantities of relativistic emission.

3 Gamma-ray bursts

Gamma-ray bursts (GRBs) are extremely powerful emission and considered to be produced byrelativistic jets (Figure 4). Emission is highly collimated to the direction of the jet motion due tothe relativistic beaming e↵ect. The isotropic equivalent energy of ⇠ 1051–1053 erg is radiated on atime scale of 1 s and the peak spectral energy is ⇠ 0.1–10 MeV. GRBs are far luminous comparedto the Eddington luminosity of stellar mass objects. Here we will first discuss briefly the emissionfrom relativistically expanding objects and the condition in order that such objects release a largeamount of high energy photons. Then we will discuss the properties of GRBs when we observe themfrom o↵-axis.

3.1 Fireball model

One of the leading models to explain the emission of GRBs is the fireball model, in which anexpanding material radiates photons. In order to radiate high energy photons at GRB luminosities,the expansion must be relativistic otherwise the material is optically thick to high energy photonsdue to the pair production process.

3.2 On-axis: GRB 170817A

First, we consider the outflow’s properties that required from the observation of GRB 170817A.

6

GW170817

θ=1/Γ

Γ~4 => θobs - θjet ~ 0.25 radPo

int s

ourc

e ap

prox

.

GW + light curve + VLBI => H0

3-4% of a systematic uncertainty due to jet modeling

the information about the host galaxy NGC4993 (see Methods)15. Figure 2 depicts the poste-84

rior distribution for H0 for a PLJ model and that of the GW-only analysis15, 27. The constraint85

is improved from the GW-only analysis, 74+16�8 km/s/Mpc, to 68.1+4.5

�4.3 km/s/Mpc (median and86

symmetric 68% credible interval). Also depicted in Figure 2 are the regions determined by the87

Planck CMB3 and SH0ES Cepheid-supernova distance ladder surveys4 respectively. Figure 388

shows the posterior distributions for H0 with the different jet models: hydrodynamics simula-89

tion jet (0.25 < ✓obs

⇣d

41 Mpc

⌘< 0.5 rad), PLJ, and GJ models. The medians and 68% credible90

intervals are 70.3+5.3�5.0, 68.1+4.5

�4.3, and 68.3+4.4�4.3 km/s/Mpc, respectively, corresponding to a precision91

of 6–7% at 1-� level. These are consistent with that estimated by using the surface brightness92

fluctuation technique applied to NGC 499328. The sources of errors in our analysis are the GW93

data, the shape of the light curve, the centroid motion, and the peculiar velocity of the host galaxy.94

While the constraint on ✓obs is slightly different between the three models, the systematic error95

in H0 due to this difference is much smaller than 7%. This is because the uncertainty in H0 of96

our analysis is dominated by both the GW data and the peculiar motion of NGC 4993 (contrary97

to the GW-only analysis, where the uncertainty in the observing angle is a major source of error).98

Finally, it is important to bear in mind that our result does not depend on the spin prior in the GW99

analysis27 (see Methods).100

Our new analysis, which is based on this single event, improves the H0 measurement to101

a precision of ⇠ 7% but it does not resolve the discrepancy between Planck and SH0ES yet. We102

expect that the precision of the measurement will improve by observing more merger events similar103

to GW170817, i.e, mergers with detectable jet afterglows. In the coming years, several to tens of104

5

KH+19

Summary• Open kilonova heating & ight curve code is available.

• Observed light curve of GW170817 is reproduced and a break at ~7day is interpreted as a diffusion break.

• Sr II lines seem to be strongly imprinted in the spectra.

• The 2nd peak elements are necessary for GW170817.

• The ejecta mass is 0.05 Msun.

• Afterglow light curve suggests a jet core.

• VLBI resolves superluminal motion confirms a strong and narrowly collimated jet.

• The Gw Hubble constant measurement can be improved with the superluminal motion.

https://github.com/hotokezaka/HeatingRate

theory of kilonova and afterglowyokohamagrb2019.wdfiles.com/local--files/program:files... ·...

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