Resonant Shattering Flares: Multimessenger Probes of Neutron Star Physics

David Tsang (U. Southampton)

First release: 16 October 2017 www.sciencemag.org (Page numbers not final at time of first release) 10

Fig. 1. Localization of GW170817 and associated transient EM170817. (A) Constraints at the 90% confidence level on the sky position from gravitational-wave and γ-ray observations. The rapid LIGO localization is indicated by the green dashed contour, and the LIGO/Virgo localization by solid green. Fermi GBM (4) is shown in orange, and the Interplanetary Network triangulation from Fermi and INTEGRAL in blue (50). The shaded region is the Earth limb as seen by AstroSat which is excluded by the non-detection by the Cadmium Zinc Telluride Imager instrument. (B) 49 galaxies from the Census of the Local Universe catalog (table S3; red, with marker size proportional to the stellar mass of the galaxy) within the LIGO/Virgo three-dimensional 50% and 90% credible volumes (green). One radio-selected optically-dark galaxy whose stellar mass is unknown is marked with a +. (C) Cross-section along the X-X′ plane from panel B, showing the luminosity distances of the galaxies in comparison to the LIGO/Virgo localization. (D) False-color near-infrared image of EM170817 and its host galaxy NGC 4993, assembled from near-infrared observations with the FLAMINGOS-2 instrument on Gemini-South (10), with J, H, and Ks shown as blue, green, and red, respectively. Our Ks-band detections span 2017 Aug 18.06 to 2017 Sep 5.99 and we show 2017-08-27.97 above.

on October 30, 2017

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LETTER RESEARCH

properties of GRB 170817A (see Methods). Instead, a structured jet profile, where the outflow energetics and Lorentz factor vary with the angle from the jet axis, can explain both the GRB and afterglow prop-erties (Extended Data Fig. 3). Alternatively, the low-luminosity γ-ray transient may not trace the prompt GRB emission, but come from a broader collimated, mildly relativistic cocoon29.

Another independent constraint on the off-axis geometry comes from the spectral and temporal evolution of the kilonova light curves (Fig. 3b). The luminous and long-lived optical emission implies that the

observer intercepts a substantial contribution from the wind compo-nent along the polar axis, which would be shielded by the lanthanide- rich ejecta for an edge-on observer along the equatorial plane (Fig. 4). A comparison between the kilonova models30 and our optical- infrared photometry favours an off-axis orientation, in which the wind is partially obscured by the dynamical ejecta, with an estimated inclination angle anywhere between 20° and 60° (Extended Data Fig. 4), depending on the detailed configuration of the dynamical ejecta. Taking into account the uncertainties in the model, such as the morphologies of the ejecta and the possible different types of wind, this is in good agreement with the orientation inferred from afterglow modelling. The geometry of the binary merger GW170817 (Fig. 4), here primarily constrained through electromagnetic observations, could be further refined through a joint analysis with the gravitational- wave signal.

The discovery of GW170817 and its X-ray counterpart shows that the second generation of gravitational-wave interferometers will enable us to uncover a new population of weak and probably off-axis GRBs associated with gravitational-wave sources, thus providing an unprece-dented opportunity to investigate the properties of these cosmic explo-sions and their progenitors. This paves the way for multi-messenger (that is, electromagnetic and gravitational-wave radiation) modelling of the different aspects of these events, which may potentially help to break the degeneracies that exist in the models of neutron-star mergers when considered separately.

Online Content Methods, along with any additional Extended Data display items and Source Data, are available in the online version of the paper; references unique to these sections appear only in the online paper.

Received 12 September; accepted 21 September 2017. Published online 16 October 2017.

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

2. Kouveliotou, C. et al. Identification of two classes of gamma-ray bursts. Astrophys. J. 413, L101–L104 (1993).

3. Rezzolla, L. et al. The missing link: merging neutron stars naturally produce jet-like structures and can power short gamma-ray bursts. Astrophys. J. 732, L6 (2011).

4. Gehrels, N. et al. A short γ-ray burst apparently associated with an elliptical galaxy at redshift z = 0.225. Nature 437, 851–854 (2005).

Time since gravitational-wave trigger (days) Time since gravitational-wave trigger (days)

1 10 100 1 10

Flux

den

sity

(mJy

)

10–1

10–2

10–3

10–4

10–5

10–6

10–7

10–8

App

aren

t AB

mag

nitu

de

15

20

25

30

35

101

100

10–1

10–2

10–3

10–4

10–5

10–6

10–7

Flux

den

sity

(mJy

)Tv ≈ 28º, Tj ≈ 15º Tv ≈ 28º

X-ray(on-axis)

6 GHz

19 GHz

i band

X-ray

B + 7V + 6R + 5I + 4

z + 3J + 2H + 1Ks

No wind

Figure 3 | Multi-wavelength light curves for the counterpart of GW170817. a, Temporal evolution of the X-ray and radio counterparts of GW170817 compared to the model predictions (thin solid lines) for a short GRB afterglow viewed at an angle θv ≈ 28°. The thick grey line shows the X-ray light curve of the same afterglow as seen on-axis, falling in the typical range15 of short GRBs (vertical dashed line). Upper limits are 3σ. b, Temporal evolution of the optical and infrared transient AT 2017gfo compared with the theoretical predictions (solid lines) for a kilonova seen

off-axis with viewing angle θv ≈ 28°. For comparison with the ground-based photometry, Hubble Space Telescope measurements (squares) were converted to standard filters. Our model includes the contribution from a massive, high-speed wind along the polar axis (Mw ≈ 0.015M⊙, v ≈ 0.08c) and from the dynamical ejecta (Mej ≈ 0.002M⊙, v ≈ 0.2c). The presence of a wind is required to explain the bright and long-lived optical emission, which is not expected otherwise (see dashed line).

On-axisobserver

GW170817

vw ≈ 0.08c

vej ≈ 0.2c

Tj

Time

Lum

inos

ity

Time

Lum

inos

ity

Time

Lum

inos

ity Tv = 90º

Tv = 0º

Edge-onobserver

Intermediate-angleobserver

Tv

Figure 4 | Schematic diagram for the geometry of GW170817. Following the neutron-star merger, a small amount of fast-moving neutron-rich ejecta (red shells) emits an isotropic kilonova peaking in the infrared. A larger mass neutron-free wind along the polar axis (blue arrows) produces kilonova emission peaking at optical wavelengths. This emission, although isotropic, is not visible to edge-on observers because it is only visible within a range of angles and otherwise shielded by the high-opacity ejecta. A collimated jet (black solid cone) emits synchrotron radiation visible at radio, X-ray and optical wavelengths. This afterglow emission outshines all other components if the jet is seen on-axis. However, to an off-axis observer, it appears as a low-luminosity component delayed by several days or weeks.

© 2017 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.

The 90% credible intervals(Veitch et al. 2015; Abbott et al.2017e) for the component masses (in the m m1 2. convention)are m M1.36, 2.261 Î :( ) and m M0.86, 1.362 Î :( ) , with totalmass M2.82 0.09

0.47-+

:, when considering dimensionless spins with

magnitudes up to 0.89 (high-spin prior, hereafter). When thedimensionless spin prior is restricted to 0.05- (low-spin prior,hereafter), the measured component masses are m 1.36,1 Î (

M1.60 :) and m M1.17, 1.362 Î :( ) , and the total mass is

Figure 2. Joint, multi-messenger detection of GW170817 and GRB170817A. Top: the summed GBM lightcurve for sodium iodide (NaI) detectors 1, 2, and 5 forGRB170817A between 10 and 50 keV, matching the 100 ms time bins of the SPI-ACS data. The background estimate from Goldstein et al. (2016) is overlaid in red.Second: the same as the top panel but in the 50–300 keV energy range. Third: the SPI-ACS lightcurve with the energy range starting approximately at 100 keV andwith a high energy limit of least 80 MeV. Bottom: the time-frequency map of GW170817 was obtained by coherently combining LIGO-Hanford and LIGO-Livingston data. All times here are referenced to the GW170817 trigger time T0

GW.

3

The Astrophysical Journal Letters, 848:L13 (27pp), 2017 October 20 Abbott et al.

Kasliwal+ 2017

LVC + Fermi, 2017Troja+, 2017

GW/EM170817 - A Golden Binary

Metzger & Berger (2011)

GWs can provide tidal constraints

But, kNe & SGRBs don’t tell us much about NS structure

Only (messy) post merger physics

r-process

Mejecta

GWs can provide tidal constraints

But, kNe & SGRBs don’t tell us much about NS structure

Only (messy) post merger physics

r-process

Mejecta

Mad Max: Fury Road (2015)

GWs can provide tidal constraints

But, kNe & SGRBs don’t tell us much about NS structure

Only (messy) post merger physics

r-process

Mejecta

Mad Max: Fury Road (2015)

RSFs are bright, isotropic EM counterparts that can provide detailed asteroseismic constraints on NS physics

• Tidal Resonance can transfer huge amounts of energy from orbit to modes

• Need a mode that:

• strains the crust

• couples to the tidal field (l=2, spheroidal)

• hits a resonance well before merger (f < 1 kHz)

Tidal Resonance

• Tidal Resonance can transfer huge amounts of energy from orbit to modes

• Need a mode that:

• strains the crust

• couples to the tidal field (l=2, spheroidal)

• hits a resonance well before merger (f < 1 kHz)

Tidal Resonance

2i2

2 4 6 8 10

2

4

6

8

0-1 1 2

0.20.40.60.8

0.94

0.96

0.98

1.00

Cor

eC

rust

U(r)

displacement km

fract

iona

l rad

ius r

/R

10

V(r)10

l = 2 crust-core interface mode

DT+, PRL, 108, 011102 (2012)

The i-mode exists because of the solid-fluid transition. The frequency depends on the core-crust transition radius and shear speed…

Orbit

Mode

Seismic

Seismic (shattered)

Magnetic Field

Cracking

ResonanceEb ' 1047erg

Ecrack ' ✏2bµ�r3crust

' 1043erg

Etidal ' 1050erg s�1

Eelastic =I

dV ✏2bµ ⇠ 1046erg

Resonant Shattering Flares

DT+, PRL, 108, 011102 (2012)DT, ApJ, 777, 103 (2013)

Pair-Fireball

Lmax

⇠ 1049erg s�1(v/c)

⇥ (Bsurf

/1014G)2(R/10 km)2

1047-1049 ergs

• RSF model can be easily tested with EM/GW coincident timing

• Predicts weak GRB-like emission seconds before the chirp coalescence

• The timing of the RSF provides precision asteroseismology of the NS i-mode

• i-mode frequency dependent on EOS, NS bulk properties and shear velocity at base of the crust

• Constrains unknown nuclear physics (Symmetry energy, EOS…)

Resonant Shattering Flares

timefrom

merger0

~10 -100 ms

~1-10 s

• ERSF ~ 1047 - 1049 erg, ΔtRSF ~ 0.1s

• RSF model can be easily tested with EM/GW coincident timing

• Predicts weak GRB-like emission seconds before the chirp coalescence

• The timing of the RSF provides precision asteroseismology of the NS i-mode

• i-mode frequency dependent on EOS, NS bulk properties and shear velocity at base of the crust

• Constrains unknown nuclear physics (Symmetry energy, EOS…)

Resonant Shattering Flares

timefrom

merger0

~10 -100 ms

~1-10 s

• ERSF ~ 1047 - 1049 erg, ΔtRSF ~ 0.1s

DT+, PRL, 108, 011102 (2012)

DT+, PRL, 108, 011102 (2012)

�t

DT+, PRL, 108, 011102 (2012)

�t

DT+, PRL, 108, 011102 (2012)

Resonant Shattering Flares• RSF model can be easily tested

with EM/GW coincident timing

• Predicts weak GRB-like emission seconds before the chirp coalescence

• The timing of the RSF provides precision asteroseismology of the NS i-mode

• i-mode frequency dependent on EOS, NS bulk properties and shear velocity at base of the crust

• Constrains nuclear physics?(Symmetry energy, EOS…)

• ERSF ~ 1047 - 1049 erg, ΔtRSF ~ 0.1s

timefrom

merger0

~10 -100 ms

~1-10 s

Resonant Shattering Flares• RSF model can be easily tested

with EM/GW coincident timing

• Predicts weak GRB-like emission seconds before the chirp coalescence

• The timing of the RSF provides precision asteroseismology of the NS i-mode

• i-mode frequency dependent on EOS, NS bulk properties and shear velocity at base of the crust

• Constrains nuclear physics?(Symmetry energy, EOS…)

• ERSF ~ 1047 - 1049 erg, ΔtRSF ~ 0.1s

timefrom

merger0

~10 -100 ms

~1-10 s

Magnetic Field

Pair-Fireball

Lmax

⇠ 1049erg s�1(v/c)

⇥ (Bsurf

/1014G)2(R/10 km)2

1047-1049 ergs

Magnetic Field

Pair-Fireball

Lmax

⇠ 1049erg s�1(v/c)

⇥ (Bsurf

/1014G)2(R/10 km)2

1047-1049 ergs• NS Surface B-field determines max

luminosity

• Surface B-field depends on initial conditions, age, toroidal field, accretion history, core flux vs crust only (see e.g. Ho, Andersson, & Graber [2017])

• Do not expect bright RSFs for all NS

• e.g. RSF not seen in GW170817

7

Figure 5. Magnetic field structure for models A50-4 (top left), A90-4 (top right), A99-4 (bottom left) and B99-4 (bottom right), at the time when their crossingthe Death Line (t

d

). The magnetic field lines are plotted in red, the color-scale corresponds to (B/1014G)2 on the surface of the star. The initial location of themagnetic dipole axis is indicated with a black spot.

reflects the decay of the magnetic field due to Ohmic dissi-pation, and the inevitable loss of magnetic energy. However,there are some temporary increases of the dipole strength, inthe form of a superimposed oscillatory term which are evi-dent in A99 and B99-4 runs. The e↵ect of this variation canprovide an up to 10% increase of the magnetic dipole strengthbetween a consecutive local minimum and maximum. In theA50 and A90 runs while some fluctuation is still present, thedipole component monotonically decreases.

4.4. Evolution on P � P diagram

Assuming that a pulsar spins down entirely due to its mag-netic field, and using canonical values for its radius and themoment of inertia (Lorimer & Kramer 2012), we can relateits dipole magnetic field its period and period derivative

B

d

= 3.2 ⇥ 1019G⇣PP/s

⌘1/2. (2)

We then calculate its trajectory on the P � P diagram by inte-grating in time

dP

2

dt

= 2✓

B

d

3.2 ⇥ 1019G

◆2s . (3)

Assuming an initial spin period of 50ms we deduce the tra-jectories shown in Figure 8 for the models simulated. We findthat all pulsars follow straight line trajectories, parallel to thelines of constant magnetic field PP =const. for their first 10kyr. Later on, as the dipole magnetic field decays they devi-ate from these trajectories, and eventually follow vertical linesmoving towards lower P’s, without any significant change onP. We notice large discrepancies between characteristic ageof the pulsar ⌧ = P/(2P), and the real age, especially once thereal age exceeds 500kyrs. In all cases the circles drawn onthe trajectory denote the position at which the age of the pul-sar is 500 kyrs, and lie well beyond the 1Myr line, Figure 8.We continue our integration until the pulsar crosses the DeathLine described by the equation (Bhattacharya et al. 1992)

log B

d

� 2 log P = 25.86 , (4)

where their radio emission mechanism is expected to turn o↵.We notice in a few runs with strong toroidal fields (A99-2,

A99-4, B99-4) that the trajectories move temporarily towardshigher P. This occurs because of the temporary increase inthe dipole component of the magnetic field and the faster spin-down rate.

Gourgouliatos & Hollerbach (2018)

BH

/NS H

oriz

on ~

930M

pc

NS/N

S H

oriz

on ~

440M

pc

kNe

(Red)

kNe (Blue)

kNe (Bright) (DT et al. in prep)

How detectable are EMcounterparts?

(kNe detectability from Kalsiwal & Nissanke, 2014)

BH

/NS H

oriz

on ~

930M

pc

NS/N

S H

oriz

on ~

440M

pc

sGRB1-2% of mergers(beaming)

kNe

(Red)

kNe (Blue)

kNe (Bright) (DT et al. in prep)

How detectable are EMcounterparts?

(kNe detectability from Kalsiwal & Nissanke, 2014)

BH/NS Horizon ~930Mpc

NS/NS Horizon ~440Mpc

sGRB1-2% of mergers(beaming)

kNe(Red)

kNe (Blue)

RSF(Pessimistic Fraction

of Mergers ~1/10)

RSF(Optimistic)

kNe (Bright)

Detectable out to z~0.9

Triggering (~1100 Mpc)

(DT et al. in prep)

How detectable are EMcounterparts?

(kNe detectability from Kalsiwal & Nissanke, 2014)

Troja et al. ApJ, 723, 1711 (2010)

SGRB Precursors Potential Orphan RSFs?

GRB T90(s) zBAT

Fluence(10-7 erg

cm-2)

EBAT ISO (erg) Notes

150101B 0.018 0.13 0.23 2.6 x 1048High Ekin; Fong+ (2016)

050509B 0.073 0.225 0.09 1.1x1048Gehrels+

(2005)

060502B 0.131 0.287 0.4 7.9x1048 Bloom+ (2006)

050906 0.128 0.031* 0.07 1.5 x 1046Levan & Tanvir (2008)

ERSF ~ 1047 - 1049 erg, tRSF ~ 0.1s

Q: Is there a local orphan RSF component in SGRB population? (see e.g. Tanvir [2005])

*no afterglow; host galaxy within BAT error box

NS NS NS BH BHBH

BH BHNS BH

NS + Disk/Ejecta BH + Disk/Ejecta No Tidal Disruption No Matter

Post-

Merg

er

Progenit

or

kilo/macronovae kilo/macronovae

SGRB(prompt + afterglow)

SGRB(prompt + afterglow)

EM C

ount

erpa

rt

Cocoon emission Cocoon emission

(DT et al. in prep)

NS NS NS BH BHBH

BH BHNS BH

NS + Disk/Ejecta BH + Disk/Ejecta No Tidal Disruption No Matter

Post-

Merg

er

Progenit

or

kilo/macronovae kilo/macronovae

SGRB(prompt + afterglow)

SGRB(prompt + afterglow)

EM C

ount

erpa

rt

Cocoon emission Cocoon emission

RSF(prompt precursor + afterglow)

RSF(prompt precursor + afterglow)

RSF(prompt precursor + afterglow)

(DT et al. in prep)

Black Hole - Neutron Star Mergers

DT et al. (in prep)

• RSFs caused by resonant tidal excitation of i-mode injecting energy into pair-fireball, seconds before merger

• RSFs are:

• Isotropic

• Bright: should be easily detectable within the LIGO horizon

• ERSF ~ 1047 - 1049 ergs

• tRSF ~ 0.1s

• Can appear as SGRB precursors or orphan RSFs (underluminous, very short GRBs)

Summary

• Weak X-ray/Optical/Radio afterglow

• Coincident EM/GW timing will confirm RSF model and determine mode freq.

• Shear speed/nuclear physics constraints; Complementary to M, R, λ

• Does not need tidal disruption - larger fraction of NS-BH mergers

BH/NS Horizon ~930Mpc

NS/NS Horizon ~440Mpc

sGRB1-2% of mergers(beaming)

kNe(Red)

kNe (Blue)

RSF(Pessimistic Fraction

of Mergers ~1/10)

RSF(Optimistic)

kNe (Bright)

Detectable out to z~0.9

Triggering (~1100 Mpc)

BH/NS Horizon ~930Mpc

NS/NS Horizon ~440Mpc

sGRB1-2% of mergers(beaming)

kNe(Red)

kNe (Blue)

RSF(Pessimistic Fraction

of Mergers ~1/10)

RSF(Optimistic)

kNe (Bright)

Detectable out to z~0.9

Triggering (~1100 Mpc)

• Surface B-field - core vs crust evolution?

• NRSF/Nmerger?

• Excess of nearby orphan RSFs? Injection tests for burst pipelines?

• How do the core-crust transition density and (effective) shear modulus/speed depend on nuclear physics parameters? (model dependence?) Pasta layer thickness?

• What constraints on NS EOS and dense matter can we obtain with i-mode frequency from coincident timing?

Questions

BH/NS Horizon ~930Mpc

NS/NS Horizon ~440Mpc

sGRB1-2% of mergers(beaming)

kNe(Red)

kNe (Blue)

RSF(Pessimistic Fraction

of Mergers ~1/10)

RSF(Optimistic)

kNe (Bright)

Detectable out to z~0.9

Triggering (~1100 Mpc)

• Surface B-field - core vs crust evolution?

• NRSF/Nmerger?

• Excess of nearby orphan RSFs? Injection tests for burst pipelines?

• How do the core-crust transition density and (effective) shear modulus/speed depend on nuclear physics parameters? (model dependence?) Pasta layer thickness?

• What constraints on NS EOS and dense matter can we obtain with i-mode frequency from coincident timing?

Questions

Steiner & Watts, (2009), PRL, 103, 181101