radiation transport modeling for the kilonova...

Jennifer Barnes NASA Einstein Fellow Columbia University

Radiation transport modeling for the kilonova enthusiast

Abbott+2017, PRL 119

KITP December 6, 2017

Radiation transport in context

image adapted from LSC

stellar binary evolution: component stars & masses

GR(M)HD: dynamics

NS EOS

nuclear physics mass model &

Radiation transport

{Ye, sB, ⌧}

Radiation transport in a nutshell

Radioactivity

Erad / ⇢⇥ t�↵,↵ ⇠ 1.1� 1.4

Thermalization

fth = Erad/Edep

Temperature T (�!v )

Excitation/ ionization Atomic

data

opacity (�) emissivity

/ (�)B�(T )

j�

Adiabatic losses

W =

ZPdV


Radioactivity

Erad / ⇢⇥ t�↵,↵ ⇠ 1.1� 1.4

Thermalization

fth = Erad/Edep



data


/ (�)B�(T )

j�

The radiation field

Adiabatic losses

W =

ZPdV


Radioactivity

Erad / ⇢⇥ t�↵,↵ ⇠ 1.1� 1.4

Thermalization

fth = Erad/Edep



data


/ (�)B�(T )

j�

The radiation fieldThe obstacles

Adiabatic losses

W =

ZPdV

Radiation transport: heating

Lipp

un

er &

Ro

be

rts 2015

Heating • ~power law, due to many

decay chains; • -decay, -decay, fission↵�

Thermalization • not perfectly efficient • depends on time, decay

mode, decay spectrum

JB+2016

Radiation transport: opacity

test case 1: Iron (Z=26)

ab. m

ag +

offs

et

-26

-24

-22

-20

-18

-16 time

K-6R-2

V

B+1

SN Ia broadbands: Autostructure ( — ) Kurucz CD23 ( - - )

Kasen, Badnel, & JB 2013

Part 1: the ingredients

• Bound-bound opacity dominates • Energy levels and transition oscillator

strengths for r-process elements


• Bound-bound opacity dominates • Energy levels and transition oscillator

strengths for r-process elements

charge state

Nlevels (KBB13)

Nlevels (F+17)

Nlines (KBB13)

Nlines (F+17)

I II III IV

18,104 6,888 1,650 241

~2.52e7 ~3.95e6 ~2.33e5 ~5.78e4

18,104 6,888 1,650 241

~2.46e7 ~3.87e6 ~2.33e5 5.78e4

test case 1: Neodymium (Z=60)

Part 1: the ingredients


Kasen, Badnel, & JB 2013

lanthanides sustain a

high opacity at lower T

NdII NdI at ~0.2 eV more densely-spaced levels

more at high �

Part 1(b): the implications


challenge: an expanding medium enhances the effective opacity

cros

s se

ctio

n

wavelength

photon

�

exp

=1

⇢ctexp

X

i

�i

��c

�1� e�⌧i

�

⌧ =⇡e2

me

cfosc

nl

tej

�0

Expansion Opacity

Sobolev ⌧

Part 2: the method

Radiation transport: opacityPart 3: the results

open d-shell

open f-shell

Kasen, Badnell, & JB 2013

boun

d-bo

und

expa

nsio

n op

acity

(cm

2 g-1

)

102

101

10-5

10-4

10-3

10-2

10-1

100

5,000 10,000 15,000 20,000 25,000angstroms

FeII (Z = 26)CeII (Z = 58)NdII (Z = 60)OsII (Z = 76)

atomic complexity

Pan-lanthanide opacitiesComplexity arguments Gd catastrophy?!


Nd

Pan-lanthanide opacitiesComplexity arguments Gd catastrophy?!


Nd

Leve

l exc

itatio

n e

ne

rgy

(eV

)

Atomic number

log

10 n

um

be

r of l

eve

ls

auto-ionizing

credit: D. Kasen

0 2 4 6 8 10 12 14

Days

1039

1040

1041

1042

Lum

inos

ity

(erg

ss�

1)

Fe r-processIron opacities

lanthanide opacities

Bolometric Luminosity

0 2 4 6 8 10 12 14 days

1042

1041

1040

1039

ergs

s-1

6

4

2

0

8

rela

tive

flux

Spectra

0 500 1000 1500 2000 3000 nanometers

The Astrophysical Journal, 774:25 (13pp), 2013 September 1 Kasen, Badnell, & Barnes

Figure 11. Synthetic spectra (2.5 days after mass ejection) of the r-process SNmodel described in the text, calculated using either Kurucz iron group opacities(black line) or our Autostructure-derived r-process opacities (red line). Forcomparison, we overplot blackbody curves of temperature T = 6000 K (blackdashed) and T = 2500 K (red dashed). The inset shows the correspondingbolometric light curves assuming iron (black) or r-process (red) opacities.For comparison, we also plot a light curve calculated with a gray opacity ofκ = 10 cm2 g−1 (blue dashed line).(A color version of this figure is available in the online journal.)

The spectrum at 2.5 days after the merger is much redder, withmost of the flux emitted in the near infrared (∼1 µm). Due to theextreme line blanketing at bluer wavelengths, the photons areeventually redistributed (through lines) to the infrared, wherethe opacities are lower and radiation can escape more readily.As shown in Figure 11, the bolometric light curve from the fullmulti-wavelength calculation resembles one calculated with aneffective gray opacity of κ = 10 cm2 g−1, which is two ordersof magnitude greater than values used in previous gray transportmodels.

Other than the unusually red color, the r-process spectragenerally resemble those of ordinary SNe, and in particularthose with high expansion velocities (e.g., the hyper-energeticType Ic event, SN 1998bw; Galama et al. 1998). The continuumflux, which is produced by emission in the Doppler-broadenedforest of lines, resembles a blackbody with a few broad (∼200 Å)spectral features. It is not easy to associate these features witheither absorption or emission from a single line; instead theyarise from blends of many lines. Because our atomic structuremodels do not accurately predict line wavelengths (and we onlyinclude lines of Nd and Fe), the location of the features in oursynthetic spectra are not to be trusted. Nevertheless, the modelspectra are likely qualitatively correct. One can anticipate wherefeatures are most likely to appear by examining the energyspacing of the low lying levels of the lanthanides.

Figure 12 shows the time evolution of the synthetic spectra.At the earliest times (!0.25 days after ejection) some fluxemerges at optical wavelengths, but this phase is short lived.By day 0.5, the optical emission has faded, and the spectraevolve relatively slowly thereafter, with effective blackbodytemperatures steady in the range T ≈ 2000–3000 K. Thetemporal evolution can be understood by considering the meanopacity curves (e.g., Figure 6). At early times, the ejecta isrelatively hot ("4000 K) throughout, and the opacity is roughlyconstant with radius. By day ∼0.3, however, the outermostlayers have cooled below !3000 K, and the r-process opacities

Figure 12. Synthetic spectra time series of the r-process SN model describedin the text. The times since mass ejection are marked on the figure.

drop sharply due to lanthanide recombination. The ejectaphotosphere forms near the recombination front (as overlyingneutral layers are essentially transparent) which regulates theeffective temperature to be near the recombination temperature.This behavior is similar to the plateau phase of the (hydrogen-rich) Type IIP SNe, although in this case the opacity is due toline blanketing, not electron-scattering. More importantly, thetemperature at the recombination front (TI ∼ 2500 K) is a factorof ∼2 lower for r-process ejecta, as the ionization potentialsof the lanthanides (∼6 eV) are lower than that of hydrogen(∼13.6 eV).

Our calculated SEDs are somewhat sensitive to the atomicstructure model used to generate the line data. Figure 13compares calculations using line data from the differentAutostructure optimization runs (opt1, opt2, and opt3). Theobserved differences can be taken as some measure of the un-certainty resulting from inaccuracies in our atomic structurecalculations. Notably, the spectrum calculated using the opt2linelist has significantly higher flux in the optical (∼6000 Å).This is presumably due to the lower overall opacity of the opt 2model (Figure 8). Given the superior match of the opt3 model tothe experimental level data, we consider the spectral predictionsusing this line data to be the most realistic; however, it is clearthat some significant uncertainties remain.

Another concern for the spectrum predictions is the potentialbreakdown of the Sobolev approximation. At bluer wavelengths,the mean spacing of strong lines can become less than theintrinsic (presumed thermal) width of the lines, which violatesthe assumptions used to derive an expansion opacity. It is not

11

r-process (lanth)

T ~ 2500K

Iron T ~ 6000K

Kasen, Badnell & JB 2013

JB & Kasen 2013

Effect of opacity

sidebar: how red are they?

(Back to the algorithm)

Use of expansion opacity requires narrow, non-overlapping lines. Otherwise, Sobolev Breakdown

expansion opacity v. line-broadened opacity

v.

sidebar: how red are they?BUT: while line-broadening gives much higher opacities, the light curves it predicts are not so different.

e.g., Wollaeger+2017

(also: we now have observations to work with)

Lippuner & Roberts 2015

more free n per seedfewer free n per seed

opacities and nucleosynthesis



I.G.E.s

light r-process

heavy r-process




I.G.E.s

light r-process

heavy r-process

more -irradiation ⌫ less -irradiation ⌫


light curves and spectra

18

20

22

24

26 Cowperthwaite+2017

AB m

ag

broadband light curves

Time (days) 0 2 4 6 8 10 12 14 16 18

light curves and spectra

18

20

22

24

26 Cowperthwaite+2017

AB m

ag

broadband light curves

Time (days) 0 2 4 6 8 10 12 14 16 18

Nicholl+2017

NIR

4000 5000 6000 7000 8000 9000Rest wavelength ( )

F�

A

UV/optical

F�

Nicholl+2017

Cho

rnoc

k+20

17

spectral features + diagnostics

Kasen, Metzger, JB+17

1. Is there a case to be made for a single component kilonova model?

* fine-tuned Ye? * mixing of r-processed ejecta?

2. How important are 2-D effects? * viewing angle effects * windows/curtains * reprocessing of radiation?

3. How can we improve spectral diagnostics?

lingering questions

radiation transport modeling for the kilonova...

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