Gravitational-wave and multi-messenger astronomy
Koutarou Kyutoku Department of Physics, Kyoto University
2019/8/19 Strings and Fields 2019 1 Contents
1. Introduction 2. Binary black hole merger 3. Binary neutron star merger 4. Future prospect 5. Summary
2019/8/19 Strings and Fields 2019 2 1. Introduction
2019/8/19 Strings and Fields 2019 3 Gravitational-wave detector network
http://gwcenter.icrr.u-tokyo.ac.jp/wp-content/themes/lcgt/images/img_abt_lcgt.jpg KAGRA (Kamioka, Japan) under development…
Advanced LIGO (Hanford, USA) another at Livingston https://www.advancedligo.mit.edu/graphics/summary01.jpg Advanced Virgo (Pisa, Italy)
http://virgopisa.df.unipi.it/sites/virgopisa.df.unipi.it.virgopisa/files/banner/virgo.jpg 2019/8/19 Strings and Fields 2019 4 The first event: GW150914
Merger of two black holes
http://apod.nasa.gov/apod/ap160211.html 2019/8/19 Strings and Fields 2019 5 What we learned from GW150914
• Masses of individual stars are measured - even at 400Mpc (Milky way is only ~10kpc) • The luminosity distance is measured directly
1Mpc ~ 3 million light years ~ 3 x 10^24 cm Obtained from the luminosity distance using Planck cosmology … not important 2019/8/19 Strings and Fields 2019 LIGO&Virgo (2016) 6 Toward multi-messenger astronomy strong / opaque Strong interaction: (strong but short-range)
Electromagnetic interaction: electromagnetic waves Signals are strong but also hidden very easily
Weak interaction: neutrino Another interesting messenger, particle physics
Gravitational interaction: gravitational waves Signals are weak but extremely penetrating weak / transparent 2019/8/19 Strings and Fields 2019 7 Multi-messenger event: GW170817
2019/8/19 Strings and Fields 2019 8 Era of gravitational-wave astronomy
10 binary black holes, 1 binary neutron stars (2018)
2019/8/19 Strings and Fields 2019 9 Black-hole mass distribution
Light ones are dominant (detection rate ∝ ℳ2.5) Mass of the primary (=heavier member)
Mass ratio (lighter divided by heavier)
LIGO&Virgo 1811.12940
2019/8/19 Strings and Fields 2019 10 Black-hole spin distribution
휒eff = 푚1휒1,∥ + 푚2휒2,∥ / 푚1 + 푚2 (near-)extremal spins are not likely to be typical Saying more is difficult
Report of a rapid spin by non-LVC analysis [Zackey+ 2019] LIGO&Virgo 1811.12907 If true, found more soon
2019/8/19 Strings and Fields 2019 11 LIGO-Virgo Observation Run 3 (O3)
More than those found during LIGO/Virgo O1, O2 See https://gracedb.ligo.org/latest/ for the list
2019/8/19 Strings and Fields 2019 12 Example: S190412m
BBH: binary black hole BNS: binary neutron star Terrestrial ~ noise on the earth
2019/8/19 Strings and Fields 2019 13 S190814bv
The classification changed from MassGap to NSBH What is “MassGap”? What does “NSBH” mean?
Aug 14 21:31 Aug 14 22:58 Aug 15 10:16
2019/8/19 Strings and Fields 2019 14 LIGO-Virgo classification scheme https://emfollow.docs.ligo.org/userguide/_images/content-1.svg Mass-based labeling Mass of the lighter
Black hole: > 5푀⊙
Neutron star: < 3푀⊙
푀⊙: solar mass
If either star has
3푀⊙ < 푚 < 5푀⊙ -> MassGap Mass of the heavier
2019/8/19 Strings and Fields 2019 15 2. Binary black hole merger
2019/8/19 Strings and Fields 2019 16 Black hole
Object with the strongest gravity in the universe
From Wikipedia very bright in astronomy - gamma-ray burst - active galactic nuclei quantum phenomena? - evaporation? - information loss?
2019/8/19 Strings and Fields 2019 17 Observation of Galactic black holes
Black holes are invisible
Electromagnetic observations have relied on emission from black-hole activity associated w/ accretion from companions e.g., accretion disk, jet ….
2019/8/19 Strings and Fields 2019 18 Mass of (near-)Galactic black holes
We have observed up to ~20 solar-mass black holes with many objects having very weak constraints
Ozel+ (2012)
2019/8/19 Strings and Fields 2019 19 Mass gap?
The maximum mass of neutron stars ∼ 2 − 3푀⊙? - determined by the high-density equation of state
The minimum mass of
black holes ∼ 5 − 7푀⊙? Kreidberg+ (2012) - relying on observations - matter of vigorous debate
Nothing in between?
2019/8/19 Strings and Fields 2019 20 Supernova: birth of a compact object
When the massive star dies, a supernova explosion could occur and leave a black hole or a neutron star
(Two outcomes may be distinguishable w/ neutrinos for nearby [Galactic] supernovae)
2019/8/19 Strings and Fields 2019 21 Mass after supernovae?
Massive stars do not necessarily end in black holes due to complexity associated with stellar evolution (but supernova simulations are not mature enough) Ugliano+ (2012)
Red: explode -> neutron star Gray: not explode -> black hole
= initial stellar mass 2019/8/19 Strings and Fields 2019 22 Compact object before GW150914 mass (Primordial black hole?)
~1푀⊙: neutron-star minimum mass Neutron star
∼ 2 − 3푀⊙: neutron-star maximum mass Absence of compact objects - Mass gap?
∼ 5 − 7푀⊙: astro. black-hole minimum mass Stellar-mass black hole
~15 − 20푀⊙: astro. black-hole maximum mass (some researchers have predicted heavier: e.g., Kinugawa+ 2014)
2019/8/19 Strings and Fields 2019 23 GW150914
Observed data Agreement at two location!
Theoretical model
Residual
LIGO&Virgo (2016), filtered to 35-350Hz 2019/8/19 Strings and Fields 2019 24 Mass of observed binary black holes
Massive black holes are ubiquitous in the universe
LIGO&Virgo 1811.12907
2019/8/19 Strings and Fields 2019 25 Metallicity as the key to the mass
Metallicity: fraction of elements other than H/He
Stellar winds should have reduced the mass during the stellar lifetime… LIGO&Virgo (2016) Massive BHs challenge Upper limit of formed BH mass the stellar evolution (unit: solar mass)
Low-metallicity + weak stellar wind
high metal (normal) low metal Abundances of metal compared to solar values 2019/8/19 Strings and Fields 2019 26 Question about black holes
What is the origin of these massive black holes? Metal-deficient, old stars must be important • Born as a binary and evolve via a suitable path? • Assembled into a binary in dense environments? Other possibilities (somehow popular in Japan) • First stars(=BBN composition) in the universe? • Primordial black hole? The mass/spin distribution will be important
2019/8/19 Strings and Fields 2019 27 Remark on classification
We have not yet understood the minimum mass of the stellar-mass, astrophysical black holes (as well as the maximum mass … another topic)
Whether a 2.5푀⊙ object (say) is a black hole or a neutron star cannot be answered with confidence unless we observe electromagnetic counterparts
But it is treated as an “NS” in the LVC classification, e.g., “NSBH” at least formally … be careful!
2019/8/19 Strings and Fields 2019 28 Test of general relativity
This event probes the strong and dynamical gravity
Small curvature scale (quantum somewhere) 퐺 = 푐 = 1 assumed
Yunes+ (2016) Yunes+ (2016)
Weak gravity Strong gravity Dynamical Static Large curvature scale (classical)
2019/8/19 Strings and Fields 2019 29 Basic strategy
Compute post-Newtonian correction terms, say
푑푓 푑푓 2 3 = 1 + 푎2푣 + 푎3푣 + ⋯ 푑푡 푑푡 quadrupole Usually, an expansion parameter is taken to be 2/3 푣 2 퐺휋푓푀 푥 = ≡ 푐 푐3 A term at 푣2푛 or 푓2푛/3 relative to the leading term is called the 푛-th post-Newtonian correction
2019/8/19 Strings and Fields 2019 30 Post-Newtonian coefficient
Combination of all events improves the constraint - every terms are consistent with general relativity - these constraints will keep becoming tighter (may not kill general relativity in the near future)
LIGO&Virgo 1903.04467 Merger-part obtained by numerical-relativity sims. Note: The 0PN term = quadrupolar emission is much strongly constrained by binary pulsars
2019/8/19 Strings and Fields 2019 31 Did we constrain modified gravity?
Not very severely constrained model parameters regarding wave generation mechanisms… One reason is simply that merger simulations have not been performed for many of such theories!
Yunes+ (2016)
2019/8/19 Strings and Fields 2019 32 Graviton Compton wavelength/mass
Massive gravitons travel slower than the light 2 2 4 2 2 푣푔 푚푔푐 ℎ 푐 2 ≃ 1 − 2 = 1 − 2 2 푐 퐸 휆푔퐸 Gravitational waveforms are distorted
13 The Compton wavelength 휆푔 > 1.6 × 10 km −23 Then the graviton mass 푚푔 < 7.7 × 10 eV - nearly strongest model-independent bounds Note: “graviton mass” is a highly nontrivial quantity
2019/8/19 Strings and Fields 2019 33 3. Binary neutron star merger
2019/8/19 Strings and Fields 2019 34 Neutron star
Remnant of massive stars (mass range is uncertain)
Mostly consists of neutrons 1.4 solar mass, ~10km The density is higher than
nuclear saturation values Lattimer (2014) “a huge nucleous” Interior is not understood
2019/8/19 Strings and Fields 2019 35 Diversity of neutron stars Radio pulsar (rotation powered)
X-ray binary ©NASA (gravitation powered) ©NASA Central compact object (heat powered)
Magnetar ©NASA (magnetic-field powered) ©NASA 2019/8/19 Strings and Fields 2019 36 Neutron star binary coalescence
• Gravitational waves - test of the theory of gravitation in a non-vacuum - high-density matter signature: equation of state • Formation of a hot massive remnant (star/disk) - central engine of short gamma-ray bursts • Mass ejection of neutron-rich material - r-process nucleosynthesis - radioactively-driven “kilonova/macronova”
2019/8/19 Strings and Fields 2019 37 GW170817
LIGO twins observed clear “chirp” signals, i.e., gravitational waves with increasing frequency and amplitude in time
But Virgo did not see… -> the source should be at Virgo’s blind spot!
2019/8/19 Strings and Fields 2019 LIGO&Virgo (2017) 38 Sky map and localization accuracy
Improved with Virgo!
Improved with Virgo! http://www.ligo.org/detections/GW170817/images-GW170817/O1-O2-skymaps-white.jpg 2019/8/19 Strings and Fields 2019 39 Short gamma-ray burst
About 1051erg/s explosions - the sun is ~4 × 1033erg/s Long-soft GRB: ≥ 2s deaths of massive stars
Short-hard: ≤ 2s neutron star binary merger? rigorous confirmation needs gravitational waves
http://www.daviddarling.info/images/gamma-ray_bursts.jpg 2019/8/19 Strings and Fields 2019 40 Gamma rays at 1.7s after merger
© LIGO/Virgo; Fermi; INTEGRAL; NASA/DOE; NSF; EGO; ESA.
2019/8/19 Strings and Fields 2019 41 Electromagnetic counterpart
EM radiation will accompany neutron star mergers
localization - host identification - cosmological redshift
ejecta properties - ejection mechanism - r-process element
Berger (2014) 2019/8/19 Strings and Fields 2019 42 r-process nucleosynthesis
Synthesize heavy, neutron-rich elements (Au, Pt…) r = rapid: neutron capture faster than beta decay
need very dense and neutron-rich matter
supernova explosions now seem to fail to achieve r-process Sneden+ (2008)
2019/8/19 Strings and Fields 2019 43 Transient and host galaxy r-process-powered transient “kilonova/macronova”
Utsumi+ (2017)
2019/8/19 Strings and Fields 2019 44 Topic: gravitational waves
−3 The chirp mass is determined to 10 푀⊙ precision Tidal deformability is measured for the first time, rendering large neutron stars with >14km unlikely LIGO&Virgo (2018)
2019/8/19 Strings and Fields 2019 45 Neutron star equation of state Note: not need to observe the radius, and other quantities may be fine We want to know the realistic equation of state, that uniquely determines the mass-radius relation Equation of state: Nuclear physics Mass-Radius relation: Astrophysics Özel-Freire (2016)
Özel-Freire (2016)
2019/8/19 Strings and Fields 2019 46 Quadrupolar tidal deformability
Leading-order finite-size effect on orbital evolution (strongly correlated with the neutron-star radius) 5 5 푐2 2 푐2푅 Λ = 퐺휆 = 푘 ∝ 푅5 퐺푀 3 퐺푀 푘~0.1: (second/electric) tidal Love number
External deformed 풬푖푗 = −휆ℰ푖푗 field
1 2 2 3 휕 Φext 풬푖푗 ≡ න 휌 푥푖푥푗 − 푥 훿푖푗 푑 푥 ℰ ≡ 3 푖푗 휕푥푖휕푥푗 2019/8/19 Strings and Fields 2019 47 푀 − Λ relation and equations of state 푅 1.35푀⊙ , Λ 1.35푀⊙ 13.7km, 1211 13.0km, 863 12.3km, 607 11.6km, 422 11.0km, 289
2019/8/19 Strings and Fields 2019 48 Constraint from GW170817
100 < Λ෨ < 800, roughly 10.5-13.5km in the radius depending on waveforms, assumption (prior etc.)
LIGO&Virgo (2018) tidal deformability equal mass (푚2 ≤ 푚1)
Chirp mass ℳ푐 variation Mass ratio variation
mass
See also De+ (2018) 2019/8/19 Strings and Fields 2019 49 Role of theoretical templates
Parameters of binaries are estimated by measuring the match between data and theoretical waveforms Accurate theoretical models are indispensable! LIGO&Virgo (2016)
2019/8/19 Strings and Fields 2019 50 Uncertainty in the waveform model
1 radian difference usually makes the difference Current systematic errors are larger than 1 radian We need accurate waveforms for better estimation
Λ෩ = 400
LIGO&Virgo (2018)
2019/8/19 Strings and Fields 2019 51 Necessity of numerical simulations
The amplitude maximum comes after the contact Nonlinearities of both gravity and hydrodynamics are crucial - numerical relativity simulations
Kiuchi+KK+ (2017)
2019/8/19 Strings and Fields 2019 52 Waveform library https://www2.yukawa.kyoto-u.ac.jp/~nr_kyoto/SACRA_PUB/catalog.html
2019/8/19 Strings and Fields 2019 53 Numerical waveform
Binaries merge earlier for stiffer equations of state Accurate to <1rad but the #models is still limited
13.7km, Λ = 1211
11.0km, Λ = 289
Kiuchi+KK+ 1907.03790
2019/8/19 Strings and Fields 2019 54 Kyoto model
TaylorF2: analytic, Post-Newton phase 푥 ∝ 푓2/3
+ correction terms associated w/ mass asymmetry We introduce a nonlinear-in-Λ෨ term (empirically)
This Λ෨2/3 term well reproduces numerical relativity
2019/8/19 Strings and Fields 2019 55 Accuracy of our waveform model
<0.1 radian errors for validation models up to 1kHz
Kawaguchi+KK+ (2018)
Color: EOS Line type: mass ratio
2019/8/19 Strings and Fields 2019 56 Independent analysis by KAGRA group
Systematic bias of ~100, currently negligible, but may become problematic in the foreseeable future Kyoto: our NR-based model Dietrich: another NR-based model used in LVC analysis LAL/PNtidal: post Newton
Narikawa, Uchikata+KK+ (in prep.)
2019/8/19 Strings and Fields 2019 57 Gravitational-wave cosmology
Hubble’s constant is determined in a novel manner CMB Supernova
푐푧 = 푣 = 퐻0퐷 z: redshift from the host galaxy D: distance from gravitational waves +12 −1 −1 퐻0 = 70−8 km s Mpc
See also Seto-Kyutoku (2018)
LIGO&Virgo+ (2017) 2019/8/19 Strings and Fields 2019 58 Hubble tension?
New physics beyond standard ΛCDM?
Error in measurements?
GW-EM can examine this discrepancy in an independent manner Riess+ (2019)
2019/8/19 Strings and Fields 2019 59 But caution! Calibration accuracy
Amplitude measurements by LIGO/Virgo have ~5% systematic errors … equally for the distance
Cahillane+ (2017)
Livingston, similar for Hanford
2019/8/19 Strings and Fields 2019 60 Topic: short-hard gamma-ray burst
Is this really caused by neutron star mergers? http://www.icrr.u-tokyo.ac.jp/~cta/images/GRB.jpg
2019/8/19 Strings and Fields 2019 61 GRB 170817A
Fermi and INTEGRAL agree each other though relatively weak The 1.7s delay from GWs - jet launch - jet propagation in the ejected material LIGO&Virgo, Fermi, - onset of transparency INTEGRAL (2017)
2019/8/19 Strings and Fields 2019 62 Underluminous…
(isotropic-equivalent) luminosity of gamma-ray emission
Detection threshold vs redshift
Because this event was quite nearby, the normal apparent luminosity means the intrinsically low luminosity
LIGO&Virgo, Fermi, INTEGRAL (2017)
2019/8/19 Strings and Fields 2019 63 Superluminal motion
Radio VLBI resolved material motion with Γ ≈ 4 Evidence of a jet! But Γ > 30 is not yet confirmed
Apparently Mooley+ (2018) 푣 ≈ 4푐
2019/8/19 Strings and Fields 2019 64 Structured jet
The jet of gamma-ray bursts is not very simple but is associated with a non-trivial angular structure
Lazzati+ (2018)
2019/8/19 Strings and Fields 2019 65 Implication to fundamental physics
The timing difference of 1.7s for GW-GRB (gamma) - 40Mpc approximately corresponds to 4e15s Assumptions on GRB models “gamma rays are emitted 0-10s after the merger” - 1000s delay is not necessarily rejected Modified gravity predicting 푣GW ≠ 푐 is disfavored “propagation reduced a long delay to 1.7s” will be rejected by another event at other than 40Mpc
2019/8/19 Strings and Fields 2019 66 The difference of speeds in GW/EM
Timing difference Δ푡 = 퐷/푣GW − 퐷/푣EM renders the velocity difference Δ푣 ≔ 푣GW − 푣EM Δ푣 −3 × 10−15 ≤ ≤ 7 × 10−16 푣EM if the difference at the source is [0:10]s (model!) • Lower limit: gravitational delay 10s ->1.7s • Upper limit: electromagnetic delay 0s -> 1.7s Multiple events will alleviate model dependence
2019/8/19 Strings and Fields 2019 67 Dispersion relation
Propagation of electromagnetic waves (in a suitable gauge) is governed by the spacetime metric as 휇휈 휂 휕휇휕휈퐴훼 = 0
Gravitational waves ℎ훼훽 must obey the same causal structure, so that 휇휈 푔ො 휕휇휕휈ℎ훼훽 = 0 with 푔ො휇휈 = Ω2휂휇휈, no correction such as ∇휇휙∇휈휙 This is not usually assuring for modified theory of gravity with higher derivatives of scalar fields
2019/8/19 Strings and Fields 2019 68 Constraint on modified gravity
Various theories are now regarded as rejected
Ezquiaga-Zumalacarregui (2017)
2019/8/19 Strings and Fields 2019 69 Topic: r-process element https://en.wikipedia.org/wiki/Gold#/media/File:Gold-crystals.jpg Gold a half of nuclides heavier than the iron - the other half for “s”
Platinum
Where in the Universe are they produced?
https://en.wikipedia.org/wiki/Platinum#/media/File:Platinum_crystals.jpg 2019/8/19 Strings and Fields 2019 70 Periodic table
Bigger picture: where are the elements produced?
From Wikipedia
2019/8/19 Strings and Fields 2019 71 Cosmic nucleosynthesis
H, He, Li: big bang nucleosynthesis Be, B: cosmic-ray spallation C, N, O … Fe, Co, Ni: stellar evolution
But the iron is the most stable element, and thus nuclear fusion cannot go substantially beyond it
How elements heavier than the iron group formed? - gold, platinum, uranium, rare-earth element…
2019/8/19 Strings and Fields 2019 72 R-process in neutron star mergers
Successful at least for certain binary models How can we confirm this idea? Sekiguchi+KK+ (2015)
Wanajo+KK+ (2014)
2019/8/19 Strings and Fields 2019 73 Kilonova/macronova
Ejected material contain radioactive r-elements Their decay heat the ejecta Thermal photons try to diffuse from the ejecta But r-elements efficiently traps the photon inside Characteristic “kilonova”!
Kisaka+ (2015)
2019/8/19 Strings and Fields 2019 74 AT 2017gfo
In general agreement with theoretical models particularly in NIR Tanaka+ (2017) Compared to SNe many other obs. - small mass - high velocity - high opacity - no time scale of the heating
2019/8/19 Strings and Fields 2019 75 No indication of ultraheavy elements
A moderate amount of lanthanide is required but gold, platinum, etc. are not concretely detected - it is simply hard to confirm their presence, though
Pt, Au lanthanide actinide
Tanaka+ (2017) 2019/8/19 Strings and Fields 2019 76 Too many lines of lanthanides
A bunch of energy levels -> complex line structures -> very frequent interaction -> very high opacity But modeling is incomplete (quantum many-body)
Kasen+ (2013) 2019/8/19 Strings and Fields 2019 77 Heating-source consideration
Some people claim that heavy elements such as gold and platinum better explain late-time emission Kasliwal+ (2018) but - the prediction is not very robust - late bolometric luminosity is not very accurate
2019/8/19 Strings and Fields 2019 78 4. Future prospect
2019/8/19 Strings and Fields 2019 79 Future observation
KAGRA would also join the observation this year
Observable range of binary neutron stars: 100Mpc=300M light years
KAGRA (2019)
2019/8/19 Strings and Fields 2019 80 Polarization as a test of gravity
KAGRA will be important to investigate whether gravitational waves are really transverse as GR predicts
The number of available detectors determines the number of constraints
Will (2014) 2019/8/19 Strings and Fields 2019 81 Further gravitational-wave sources
Transient Persistent inspiral: compact binaries continuous: BH-BH, BH-NS, NS-NS … deformed neutron stars Known waveform
Kyutoku+ (2015) ©NASA.Goddard SFC burst: stochastic: superposition supernova Takiwaki+ (2014) of weak sources, inflation, Unknown cosmic string phase transition… waveform …
unknown unknown? BICEP2 (2014) 2019/8/19 Strings and Fields 2019 82 Black hole-neutron star binaries
Alternative central engines of short GRBs? Likely to synthesize heaviest r-process elements (extremely neutron rich)
Kyutoku+ (2015) Kyutoku+ (2018)
2019/8/19 Strings and Fields 2019 83 Clue to ultraheavy elements
Late-time kilonova emission may be enhanced by fission and/or alpha-decay of ultraheavy nuclei - one interesting direction of nuclear astrophysics
Wu+ (2019)
Zhu+ (2018) see also Wanajo+KK+ (2014)
2019/8/19 Strings and Fields 2019 84 Multi-wavelength GW astronomy
May not be near, but the foreseeable future
http://rhcole.com/apps/GWplotter/
Current observation
2019/8/19 Strings and Fields 2019 85 LISA
Space-borne gravitational-wave detector operated by ESA/NASA, sensitive at ~mHz bands Amaro-Seoane+ (2017)
2019/8/19 Strings and Fields 2019 86 Supermassive black hole
6 9 Galaxies often host black holes with 10 − 10 푀⊙ at their centers: how are they formed and evolved? How did they affect evolution of galaxies/universe? https://www.nature.com/news/galaxy-formation-the-new-milky-way-1.11517
From Wikipedia 2019/8/19 Strings and Fields 2019 87 B-DECIGO/DECIGO (Japan)
Aiming at ~0.1Hz at very high sensitivity [Seto+ 2001]
Nakamura+ (2016)
Yagi+ (2011)
2019/8/19 Strings and Fields 2019 88 Black holes in the very old universe
Even z>30 can be detected as far binaries exist
Nakamura+ (2016)
2019/8/19 Strings and Fields 2019 89 Toward all-messenger astronomy
Coincident neutrino and gamma-ray detections from a supermassive black hole were reported GW + neutrino + electromagnetic?
IceCube collaboration et al. (2018) 2019/8/19 Strings and Fields 2019 90 5. Summary
2019/8/19 Strings and Fields 2019 91 Summary
• Gravitational-wave and multi-messenger astronomy have started. • The black-hole mass can be large, but we still do not know the smallest/largest-possible value. • The neutron-star tidal deformability (and radius) cannot be very large, but precise estimation requires further theoretical improvement. • We begin to understand short gamma-ray bursts and r-process nucleosynthesis.
2019/8/19 Strings and Fields 2019 92 2019/8/19 Strings and Fields 2019 93 Appendix
2019/8/19 Strings and Fields 2019 94 Redshift from the host galaxy
The redshift has to be extracted from host galaxies by electromagnetic observations… How can we determine the host galaxy? [Schutz 1986] - Accurate localization by gravitational waves This may be possible with space-borne detectors! - Detect electromagnetic counterparts short GRB, kilonova/macronova … for neutron stars not applicable to stellar-mass binary black holes
2019/8/19 Strings and Fields 2019 95 Radiation-driven stellar wind
Photons emitted from the central region interact with the surrounding envelope via line structures For heavier elements, the stellar wind is stronger because more lines give more frequent interaction Thus, metal-poor stars tend to stay massive
photon hot momentum transfer core -> ejected as a wind envelope element
2019/8/19 Strings and Fields 2019 96 GW distance determination
Observed gravitational-waves are (schematically) ℳ5/3푓2/3 ℎ 푡 = 퐹 휃, 휑, 횤, 휓 cos Φ 푡 퐷 Φ 푡 ≃ 2휋 푓푡 + 푓ሶ푡2/2 + ⋯ 푓ሶ = 96/5 휋8/3ℳ5/3푓11/3 The phase tells us binary parameters, e.g., the mass The amplitude can be predicted, and the distance 퐷 is found (degenerated w/ the direction, inclination)
2019/8/19 Strings and Fields 2019 97 Problem: degeneracy with the redshift
Signal frequency from 푧 decreases to 푓/ 1 + 푧
General relativity does not have a scale, and thus 푡 → 푡 1 + 푧 , ℳ → ℳ 1 + 푧 , 퐷 → 퐷(1 + 푧) makes both the amplitude and phase invariant
distant high-mass = near low-mass - we can determine the luminosity distance - but no cosmological redshift, in principle [note: neutron stars could resolve this degeneracy]
2019/8/19 Strings and Fields 2019 98 2019/8/19 Strings and Fields 2019 99 Neutrinos from SN 1987A
The first event of multi-messenger astronomy (… if we do not consider the Sun as astronomical) Basically confirmed supernova theory
http://nu.phys.laurentian.ca/~fleurot/supernova/nu1987a.png Kamiokande
2019/8/19 Strings and Fields 2019 100 Neutron-star matter
Cold, high-density, highly neutron-rich matter also could be magnetized up to ~1017G 1013T
Fukushima-Hatsuda (2011)
~density 2019/8/19 Strings and Fields 2019 101 One-to-one correspondence
Via Tolman-Oppenheimer-Volkoff equation of GR 푑푃 푒 + 푃 푚 + 4휋푃푟3 휌푚 = − → − 푑푟 푟 푟 − 2푚 푟2
Equation of state M-R relation
−1 휓OV
Lindblom (1992) 2019/8/19 Strings and Fields 2019 102 Maximum mass of neutron stars
Put a robust constraint on equation-of-state models
Generally, emergence of observed maximum exotic particles tend to reduce the maximum mass … not so preferred Demorest+ (2010), see also Antoniadis+ (2013)
2019/8/19 Strings and Fields 2019 103 Two-body problem in general relativity
Neglecting spins, eccentricity, finite-size effects…
Distant Buonanno-Sathyaprakash (2014) (Newtonian)
Orbital separation
Close (relativistic)
Comparable Mass ratio Extreme 2019/8/19 Strings and Fields 2019 104 Numerical relativity
The Einstein equation 퐺휇휈 = 8휋푇휇휈 (퐺 = 푐 = 1) Local energy-momentum conservation equation 휇휈 훻휈푇 = 0 Rest-mass (or particle number) continuity equation 휇 훻휇 휌푢 = 0
+ equation of state, e.g., 푃 = 푃 휌 , 푃 휌, 푇, 푌푒 … We have developed our own waveform models
2019/8/19 Strings and Fields 2019 105 Triangulation by a detector network
Determine the sky position from timing difference need multiple detectors d~O(1000km) 푑 cos 휃 푡 = 푑 푐
휃 푑
LIGO&Virgo (2016) 2019/8/19 Strings and Fields 2019 106 Shape of mass constraints
Gravitational waves tightly constrain the chirp mass 3/5 3/5 푚1 푚2 3/5 2/5 ℳ = 1/5 = 휇 푀 푚1 + 푚2 But the mass ratio (e.g., 푞 = 푚2/푚1 < 1) tends to be degenerated with the spin of components, 푐푆푖 휒푖 = 2 𝑖 = 1,2 퐺푚푖 The error in 푞 appears large particularly for nearly equal-mass systems like binary neutron stars
2019/8/19 Strings and Fields 2019 107 Definition of parameters
Total mass 푀 = 푚1 + 푚2 Reduced mass 휇 = 푚1푚2/푀 3/5 2/5 Chirp mass ℳ푐 = 휇 푀 Symmetric mass ratio 휂 = 휇/푀
Binary tidal deformability (푚1 ≤ 푚2) 8 Λ෨ = [ 1 + 7휂 − 31휂2 Λ + Λ 13 1 2 2 − 1 − 4휂 1 + 9휂 − 11휂 Λ1 − Λ2 ]
2019/8/19 Strings and Fields 2019 108 Measurable quantities ℳ푐 − Λ෩
GW mainly measure specific combinations Mass ratio of two neutron stars, variation
called ℳ푐 and Λ෨ Strongly correlated GW170817: 1/5 ℳ푐 = 1.186푀⊙ Λ 푀 = 2 ℳ푐 is primarily constrained
Kawaguchi+KK+ (2018) 2019/8/19 Strings and Fields 2019 109 Maximum mass from GW170817
Upper limits are proposed based on assumptions • Optical emission rejects magnetar models
Margalit-Metzger: ≤ 2.17푀⊙
Shibata+KK+: 2.15 − 2.25푀⊙ • A GRB jet launch calls for gravitational collapse
Rezzolla+, Ruiz+: ≤ 2.16푀⊙ I do not think any argument is strongly convincing, but similar values are inferred anyway
2019/8/19 Strings and Fields 2019 110 2019/8/19 Strings and Fields 2019 111 Other high-energy emission
Mostly upper limit for >MeV gamma and neutrinos, and Fermi/LAT put an upper limit only at late times
Abdalla+ (2017)
2019/8/19 Strings and Fields 2019 112 South Atlantic Anomaly
Sensitivity is not good, LAT was not available
Fermi-LAT (2017)
2019/8/19 Strings and Fields 2019 113 Off-axis? early X/radio afterglow
Earliest observations disfavored on-axis short GRBs and an off-axis jet offered a natural interpretation previous SGRB Troja+ (2017) likely on-axis
GRB 170817A
Multiband Murguia-Berthier+ (2017) explanation
2019/8/19 Strings and Fields 2019 114 Late rise due to relativistic beaming
Emission from relativistically moving material is concentrated (beamed) within an angle of 휃 ∼ 1/Γ
Jet w/ Γ Usual GRB observer Observable throughout Emission mechanism: 휃 ∼ 1/Γ nonthermal synchrotron Off-axis observer Observable only after the jet is decelerated to Γ < 1/휃obs
2019/8/19 Strings and Fields 2019 115 But … 100-day radio observation
An ultra-relativistic top-hat jet is rejected (for any angle), because the afterglow keeps brightening
A top-hat jet must evolve rapidly
Mooley+ (2018)
2019/8/19 Strings and Fields 2019 116 Peak and decline of the luminosity
Decline after the peak is not very slow: jet-like This does not fit with quasispherical cocoon models
Troja+ (2018)
2019/8/19 Strings and Fields 2019 117 (weak) Equivalence principle violation
Comparable Shapiro time delays for gravitational and electromagnetic radiation imply −7 −6 −2.6 × 10 ≤ 훾GW − 훾EM ≤ 1.2 × 10 훾 indicates “how the gravitational potential curves the space” and is unity in general relativity Constrains violation of weak equivalence principle
Cassini has constrained the violation in EM channels −5 훾EM − 1 ≤ 2.1 ± 2.3 × 10
2019/8/19 Strings and Fields 2019 118 Shapiro time delay
The parametrized post-Newtonian metric 푔푡푡 = − 1 − 2푈 푔푖푗 = 1 + 2훾푈 푓푖푗 U: sign-inverted gravitational potential ∼ 퐺푀/푟 (useful when higher-order effects are considered) The Shapiro time delay is given by 1 + 훾 훿푡 = − න푈(풓)푑푙 푐3 훾 = 1 for all the particles in general relativity
2019/8/19 Strings and Fields 2019 119 Lorentz invariance violation (direction)
If the Lorentz invariance is violated differently in gravity/EM, the dispersion depends on the direction 1 Δ푣 = −Σ 푌 푛ො −1 1+푙푠ҧ 4 − 푐ҧ 4 푙푚,푙≤2 푙푚 2 푙푚 퐼 푙푚 s and c are violation in gravity and EM, respectively
set to c=0
2019/8/19 Strings and Fields 2019 120 2019/8/19 Strings and Fields 2019 121 Uniqueness as an optical transient
Consistent w/ kilonova/macronova
Black (SSS17a=AT 2017gfo): this event Colored: other known transients featureless red spectrum rapid dimming and reddening red
bright
blue dim blue red
2019/8/19 Strings and Fields 2019 Siebert+ (2017) 122 Kilonova/macronova characteristics
For spherical ejecta (Li-Paczynski 1998, also Arnett 1982) −1/2 1/2 1/2 The peak luminosity: 퐿peak ∝ 푓휅 푀 푣 1/2 1/2 −1/2 The peak time : 푡peak ∝ 휅 푀 푣 Heating efficiency 푓 and opacity 휅 – microphysics particularly, r-process elements have high opacity Ejecta mass 푀 and ejecta velocity 푣 – macrophysics small mass and high velocity (vs supernovae)
2019/8/19 Strings and Fields 2019 123