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Constraining the neutron star equaon of state with IUCAA gravitaonal wave observaons

Sukanta Bose

Supported in part by NSF grant PHY-1506497 & IUSSTF(India). Based on LIGO-DCC-G1601432

07/13/16 Bose @ INT 1 Outline IUCAA

• Advanced LIGO detectors and ﬁrst direct GW detecons (on behalf of LIGO Scienﬁc and Virgo Collaboraons)

• Expected neutron star (NS) merger rates in advanced detectors

• Imprint of NS EoS on gravitaonal-wave signals

• How accurately can gravitaonal wave (GW) observaons constrain the NS equaon of state (EoS)?

• Eﬀects of NS-NS populaons, NS mass distribuons on EOS constraints

• Post-merger waveforms, electro-magnec counterparts, etc.

07/13/16 Bose @ INT 2 The gravitaonal-wave signal “GW150914”, extracted from noise IUCAA

Abbo et al. (LVC), Observaon of Gravitaonal Waves from a Binary Black Hole Merger," Phys. Rev. Le. 116, 061102 (2016). 07/13/16 Bose @ INT 3 The ﬁrst direct detecon of a gravitaonal-wave

event: GW150914 IUCAA

Detecon paper: B. Abbo et al., PRL 116, 061102 (2016).

07/13/16 Bose @ INT 4 Signiﬁcance of

GW150914 IUCAA

This search concluded that a noise event mimicking GW150914 would be extremely rare – less than once in about 200,000 years.

This is a value that has a detecon signiﬁcance of more than 5 ‘sigma’ , i.e., ~1 false alarm in 3.5 million trials.

Abbo et al. (LVC), Observaon of Gravitaonal Waves from a Binary Results from our binary coalescence search showing how Black Hole Merger," Phys. Rev. Le. extremely rare it would be for noise alone to produce an 116, 061102 (2016). event like GW150914. 07/13/16 Bose @ INT 5 GW151226: A second detecon! IUCAA

Abbo et al., Phys. Rev. Le., 116, 241103 (2016) 07/13/16 Bose @ INT 6 GW151226, at over 5-sigma IUCAA

Abbo et al., Phys. Rev. Le., 116, 241103 (2016)

07/13/16 Bose @ INT 7 GW151226 source parameters IUCAA

Abbo et al., Phys. Rev. Le., 116, 241103 (2016)

07/13/16 Bose @ INT 8 Characterizing the ﬁnal BH in GW150914

LVC, arXiv:1602.03840; A. Ghosh et al. (2016).

IndIGO researchers collaborated with LSC members in using ﬁng formulae from GR numerical simulaons that relate masses and spins of component BHs to the ﬁnal remnant. [Slide courtesy: K. G. Arun] 9 Did they emit anything visible? IUCAA

Source Localizaon and electromagnec counterpart follow up of GW150914:

• Javed Rana, Varun Bhalerao, & Akshat Singhal followed-up a few les of this large sky-patch for a possible opcal counterpart. We also formulated a scanning method. • No EM counterpart found ll date.

[1. J. Rana, A. Singhal, B. Gadre, V. Bhalerao, S. Bose, arXiv:1603.01689 [astro-ph.IM]; 2. Kasliwal,…,V. Bhalerao, J. Rana, A. Singhal,…, et al., arXiv:1602.08764 [astro-ph.IM]; 3. Abbo et al. (LVC), “Localizaon and broadband follow- up of the gravitaonal-wave transient GW150914," arXiv: 1602.08492 [astro-ph.HE].] [Sky at the me of the event. View is from the South Atlanc Ocean, North at the top, with the Sun rising and the Milky Way diagonally from NW to SE.]

07/13/16 Bose @ INT 10

Sky localizaon error regions IUCAA

[Courtesy: Singer et al.]

07/13/16 Bose @ INT 11 Scheduling telescope

observaons IUCAA

J. Rana, A. Singhal, B. Gadre, J. Rana, A. Singhal, B. GadreV. Bhalerao,, V. Bhalerao, S. Bose, S. Bose, arXiv:1603.01689 arXiv:1603.01689 07/13/16 Bose @ INT 12 LAXPC: Large Area UVIT: UltraViolet IUCAA Xenon Proportional Imaging Telescope Counter SXT: Soft X-ray Telescope

CZTI: CadmiumASTROSAT Zinc Telluride Imager

A Multi-Wavelength Satellite SSM: Scanning Sky Monitor

07/13/16 Bose @ INT 13 LIGO-India gets Govt. of India’s

“in principle” approval IUCAA

07/13/16 Bose @ INT 14 IUCAA

Abbo et al., arXiv:1606.04856 [gr-qc] (2016) 07/13/16 Bose @ INT 15 A broadband detector

& its noise budget IUCAA

[Credits: LIGO Lab.]

07/13/16 Bose @ INT 16 Mulple observaons:

Projected improvement in GWOs IUCAA

[J. Aasi et al., LIGO Scienﬁc and Virgo Collaboraons., arXiv:1304.0670 [gr-qc] (2013).]

07/13/16 Bose @ INT 17 The GW signal IUCAA The GW strain in a detector depends at least on 9 parameters : + × h(t) = h+ (t)F + h× (t)F A t A t ( ) ( ) " i(2ϕ(t) - ϑ0 ) $ = cos 2ϕ (t) - ϑ 0 = Re e , D ( ) D # % r where the effective distance is, D ≡ , 2 F +2 (1+ cos2 ι) + 4F×2 cos2 ι

" × $ 2F cosι and the effective initial phase is, arctan' ( 2 . ϑ 0 ≡ + 2 + ϕ0 #'F (1+ cos ι)%( In the Fourier domain: h!( f ) = h!( f ) eiψ( f ), where 1/2 1/3 ! 2c ) 5Gµ , ) GM , −7/6 h( f ) = + 3 . + 2 3 . f . D * 96c - *π c - 07/13/16 Bose @ INT 18 Chirp mass & its signiﬁcance IUCAA

Chirp mass: 3/5 Mchirp = η M The leading order phase: −5/3 3 !πGMchirp f $ ψ ( f ) = 2π ftISCO + # 3 & −φISCO, 128" c % Duration of signal in detector band: −5/3 5 !πGMchirp fseismic $ Δtchirp = # & . 128" c3 %

07/13/16 Bose @ INT 19 Higher order correcons

(including spin) IUCAA

07/13/16 Bose @ INT 20 How can GWs constrain

the NS EOS? IUCAA • How sﬀ or so the NS EOS is determines how much the NS will

ﬂex (with quadrupole moment Qij) in an external dal ﬁeld, Eij . The EOS parameter to be measured is λ,

where Qij = −λEij, and 5 λ 2 " R % 2 5 = k2 $ ' ≈ 10 −10 . M 5 3 # M &

k2 is the "second Love number".

It is bigger for stiffer EOS.

• The ﬂexing of a neutron star aﬀects the GW emied by it. [Credits: J. Lamer.]

07/13/16 Bose @ INT 21 NS de in waveforms Total phase = Point-parcle phase + Tidal phase-correcon. IUCAA

Point-parcle phase has non-spinning and spinning (aligned or an-aligned) terms up to 3.5pN. We add test-parcle non-spinning correcons from 4pN to 7.5pN, in part, to bridge the gap that otherwise exists between 3.5pN terms and the terms where dal correcons come in (5pN…).

Tidal phase-correcon is: 5 ) 24 # 11η &# v & , +− %1+ (% ( . 2 [Vines, Flanagan, Hinderer, 3λ + χi $ χi '$ c ' . ψ = i , arXiv:1101.1673v1.; tidal ∑ 5 + 7 . 128ηM Damour, Nagar, Villain, i=1 + 5 2 3 # v & . − (3179 − 919χi − 2286χi + 260χi )% ( PRD85, 123007 (2012). *+ 28χi $ c ' -.

1/3 where v = (Mω) , χi = mi / M and "i" is binary component index. 2 M = m1 + m2 and η = m1m2 / M . New: We add the aforemenoned point parcle terms to improve upon waveforms used in the past 07/13/16 Bose @ INT 22 Eﬀect of EOS on GW signals Sﬀ EOS IUCAA

[Read et al. Phys.Rev. D79 (2009) 124033; Hebeler, Schwenk, Eur.Phys.J. A50 (2014) 11] So EOS 07/13/16 Bose @ INT 23 Chirp mass well determined

but not individual masses IUCAA

* If MBH= 4Msun and MNS= [1, 2]Msun, then:

Mc= [1.67, 2.43] Msun

Total mass, symmetrized mass-ratio & chirp mass: m m M = m + m , η = 1 2 , 1 2 M 2 3/5 Mc = η M .

07/13/16 Bose @ INT 24 BNS mass errors from GWs IUCAA

Errors are for SNR = 20, spinless systems in aLIGO-AdV. Rodriguez et al. ApJ 784, 114 (2014).

07/13/16 Bose @ INT 25 BNS mass errors from GWs IUCAA

Errors are for SNR = 20, spinless systems in aLIGO-AdV. Rodriguez et al. ApJ 784, 114 (2014).

07/13/16 Bose @ INT 26 Double neutron star systems:

Populaons IUCAA

• Uniform distribuon of NS masses, limited to the range [1, 2] M_sun.

07/13/16 Bose @ INT 27 Double neutron star systems

Populaons IUCAA

• Gaussian distribuon of NS masses with mean = 1.35Msun, sd = 0.05Msun:

0.05 Msun

07/13/16 Bose @ INT 28 Error in determining λ

Double neutron star systems IUCAA

• Uniform distribuon of NS masses, limited to the range [1, 2] M_sun.

1σ 1σ

“Sﬀ”

“medium”

“So”

[SB et al. in preparaon; see also: Agathos et al., arXiv:1503.05405 (2015).] 07/13/16 Bose @ INT 29 Two past studies

Double Neutron Stars IUCAA

• Uniform distribuon of NS masses, • Gaussian distribuon of NS masses with limited to the range [1, 2] M_sun: mean = 1.35Msun, sd = 0.05Msun:

[del Pozzo et al., PRL 111, 071101 (2013).] [Agathos et al., arXiv:1503.05405 (2015).]

07/13/16 Bose @ INT 30 Two past studies

Double Neutron Stars IUCAA

• Spin’s eﬀect: Gaussian distribuon of • Gaussian distribuon of NS masses with NS spins: mean = 0, sd = 0.02. mean = 1.35Msun, sd = 0.05Msun:

Spin appears to improve accuracy for small lambda, and reduce systemac errors. [Agathos et al., arXiv:1503.05405 (2015).]

07/13/16 Bose @ INT 31 Error in determining λ

Double neutron star systems IUCAA

• Gaussian distribuon of NS masses, with mean = 1.35Msun, sd = 0.05Msun.

1σ 1σ

[SB et al. in preparaon]

07/13/16 Bose @ INT 32 Double neutron star systems

Populaons IUCAA

• Solar distribuon of DNS mass pairs:

[SB et al. in preparaon]

07/13/16 Bose @ INT 33 Double neutron star systems

Populaons IUCAA

• Sub-solar distribuon of DNS mass pairs:

[SB et al. in preparaon]

07/13/16 Bose @ INT 34 Error in determining λ

For four NS populaon models IUCAA

• Four diﬀerent distribuons of NS masses:

Four diﬀerent Populaon

Synthesis models

[SB et al. in preparaon]

07/13/16 Bose @ INT 35 Kilonovae can probe

nature of BNS remnants? IUCAA

07/13/16 Bose @ INT 36 Kilonovae can probe

nature of BNS remnants? IUCAA

Metzger et al. MNRAS (2014)]

07/13/16 Bose @ INT 37 Post-merger signal and NS EoS IUCAA

[Rezzolla & Takami, 2016] 07/13/16 Bose @ INT 38 Modeling the

postmerger waveforms IUCAA

Frequency (Hz)

[K. Chakravar, SB et al. (2016)]

07/13/16 Bose @ INT 39 Modeling the

postmerger waveforms IUCAA

Frequency (Hz)

[K. Chakravar, SB et al. (2016)]

07/13/16 Bose @ INT 40 IUCAA

07/13/16 Bose @ INT 41 IUCAA

07/13/16 Bose @ INT 42 EoS from

postmerger signals IUCAA

07/13/16 Bose @ INT Rezolla, Takami, arxiv (2016). 43 EoS from

postmerger signals IUCAA

and C is the compaction.

07/13/16 Bose @ INT 44 “New” physics & astronomy IUCAA • Binary black holes:

– How can massive stellar black holes form & then tango? Do super-massive black holes form hierarchically, seeded by less massive stellar / intermediate mass black holes? Hierarchical SMBH formaon. [Credits: M. – Can their mergers produce electro-magnec Volonteri.] counterparts? See, e.g., A. Loeb, “Electromagnec Counterparts to Black Hole Mergers Detected by LIGO,” ApJ Leers (2016).

– Cosmography: BBH are standard sirens that can provide distance measurements; with host galaxy idenﬁcaons, one can obtain redshis. Key to alternave measurements of the Hubble parameter & the dark energy EOS.

– Can BBH mergers be so many that they actually form a confusion noise / stochasc background in our data? . – Observe quasinormal modes and orbital precession.

Abbo et al. (LVC), Phys. Rev. Le. 116, 131102 (2016) 07/13/16 Bose @ INT 45 “New” physics & astronomy Tanvir et al., Nature (2013). IUCAA

• Involve neutron stars:

– Do kilonovae/macronovae and short GRBs share a common origin?

– What is the equaon of state of a neutron star? [Deaton et al. 2013; Foucart et al. 2014] – What are the host galaxies of binary NS systems like?

– Can GWs help track how BNS formaon rate evolved with redshi?

07/13/16 Bose @ INT [Credits: Wikipedia.] 46 “New” physics & astronomy LSST [Credits: LSST Project Oﬃce.] IUCAA

• Future missions / surveys / experiments:

– LSST: Rate of EM-GW coincidences & the SGRB beaming angle

– SKA: NS mergers with radio counterparts can inform us about the circum-merger environments.

– GW missions (proposed): Combine informaon about the same system from mulple missions, e.g., Einstein’s Telescope, eLISA, DECIGO, etc.

– ASTROSAT: Is following up GW triggers (beginning with GW151226).

• More exoc inquiries: – Are (stellar or heavier) primordial black holes a signiﬁcant component of dark maer?

07/13/16 Bose @ INT eLISA [Credits: eLISA consorum.] 47 In conclusion IUCAA • Indian sciensts collaborated with their LSC colleagues to detect and characterize GW150914 and GW151226.

• Searching for an EM counterpart was diﬃcult owing to a large sky-error region. KAGRA, LIGO-India & Virgo can help by reducing that error region.

• The LIGO-India project is moving ahead.

• Coincident GW-EM observaons hold out promise for interesng new discoveries, including those of unimagined phenomena

07/13/16 Bose @ INT 48 Non-linear coupling in neutron star mergers IUCAA

[Rezzolla & Takami, 2016] 07/13/16 Bose @ INT 49 IUCAA

07/13/16 Bose @ INT 50 IUCAA

07/13/16 Bose @ INT 51 Find “cheaper” coordinates IUCAA

• Possible to ﬁnd coordinates (chirp mes) in which the metric is slowly varying (sll, not constant).

Color shows log(det(metric))

“physical coordinates” (large “chirp-time coordinates” (small variation in template density) variation in template density)

52 07/13/16 Bose @ INT The spin challenge IUCAA

07/13/16 Bose @ INT 53 The spin challenge:

A proliferaon of parameters IUCAA

The wave phase is determined by the orbital phase:

07/13/16 Bose @ INT 54 The spin challenge:

Beer coordinates IUCAA

+…

07/13/16 Bose @ INT 55 The spin challenge:

Find beer coordinates IUCAA

07/13/16 Bose @ INT 56 The source orientation & location… IUCAA

…in the detector frame.

07/13/16 Bose @ INT [D. Brown, PhD Thesis ’04] 57 The GW strain in a detector IUCAA

In the transverse, trace - free (TT) gauge, the space-space components of the wave tensor, h, are : + × hij (t) = h+ (t) eij + h× (t) eij . The GW strain in a detector is: δL 1 1 h = = nx ⋅ h ⋅ nx − ny ⋅ h⋅ ny L 2 2 [See, e.g., B. Schutz, GR, ’85] and can be re- expressed as, + ij × ij h(t) = h⋅d = h+ (t) [eij d (t)] + h× (t) [eij (t)d (t)] + × = h+ (t) F (t;θ,ϕ,ψ ) + h× (t) F (t;θ,ϕ,ψ ) .

07/13/16 Bose @ INT 58 Inspiral searches: The waveforms IUCAA

The two polarization components of a (restricted) waveform are : 2/3 Gµ ⎛ 2πGMf ⎞ 2 h+ (t) = 2 ⎜ 3 ⎟ (1+ cos ι)cos(2φ(t) - 2φ0 ), 2c r ⎝ c ⎠ 2/3 Gµ ⎛ 2πGMf ⎞ h× (t) = 2 ⎜ 3 ⎟ (2cosι)sin(2φ(t) - 2φ0 ), 2c r ⎝ c ⎠ Here, M = total mass, µ = reduced mass, f = wave- frequency = twice the orbital frequency, ι = orbital inclination angle, t PN orbital phase f t dt, 2 initial phase. φ( )= = π ∫ ( ) φ0 = 07/13/16 Bose @ INT 59 Chirp mass Chirp mass: IUCAA 3/5 Mchirp = η M The leading order phase: −5/3 3 !πGMchirp f $ π ψ ( f ) = 2π ftISCO + # 3 & −φISCO − , 128" c % 4 Duration of signal in detector band: 2/3 Gµ ! 2πGMf $ Δtchirph× (t) = 2 # 3 & (2cosι)sin 2ϕ (t) - 2ϕ0 , 2c r " c % ( ) Here, M = total mass, µ = reduced mass, f = wave-frequency = twice the orbital frequency, ι = orbital inclination angle, 07/13/16 Bose @ INT 60 ϕ (t) = PN orbital phase = π ∫ f (t)dt, 2ϕ0 = initial phase. Signal parameters IUCAA

The GW strain (2PN) in a detector depends at least on 9 parameters :

+ × A(t) A(t) i(2φ (t ) - ϑ0 ) h(t) = h (t)F + h (t)F = cos(2φ(t) - ϑ0 ) = Re e , + × D D [ ] where

2Gµ 2/3 A(t) = (2πGMf (t)) , c2 r r the effective distance is, D ≡ ∝ , F + (1+ cos2 ι)+ i2F × cosι E ⎡ 2F × cosι ⎤ and the effective initial phase is, arctan 2 . ϑ0 ≡ ⎢ + 2 ⎥ + φ0 ⎣ F (1+ cos ι)⎦ Grouping the time - dependent terms together gives :

−iϑ0 2/3 1 h(t) = a Re E(θ,ϕ,ψ ,ι) H (t;m1,m2 ,t0 ) e , where H (t)∝ f (t) and a ∝ . [ ] r

07/13/16 Bose @ INT 61 Signal parameters IUCAA

The GW strain in a detector depends on 9 parameters :

+ × −iϑ0 h(t) = h+ (t)F + h× (t)F = ARe[E(θ,ϕ,ψ ,ι) S(t;m1,m2 ,t0 ) e ],

m1m2 3/5 1 where M = m1 + m2 , η = 2 , M c =η M , and A ∝ . M deff (dL )

dL dL The effective distance is, deff ≡ = . F + (1+ cos2 ι)+ i2F × cosι E

The red factors are amplitude-like parameters whose accuracies improve as 1/SNR.

The green parameters are frequency-like factors whose accuracies improve as 1 / [SNR * (Number of wave cycles)k ].

2 2 2 2 ⎛ Δd ⎞ 25 ΔM 1 ⎛ Δη ⎞ 5 ΔM Δη 5 ΔM ΔA Δη ΔA ΔA ⎜ eff ⎟ ⎛ ⎞ C C C ⎛ ⎞ . ⎜ ⎟ = ⎜ ⎟ + ⎜ ⎟ + Mη − MA − ηA + ⎜ ⎟ ⎝ deff ⎠ 36 ⎝ M ⎠ 4 ⎝ η ⎠ 6 M η 3 M A η A ⎝ A ⎠

07/13/16 Bose @ INT [P. Ajith, SB, PRD79, 084032 (2009)] 62 Consistency of the signal in LIGO-Hanford & LIGO-Livingston IUCAA posters. See Haris & Sumit’s

Interferometry with interferometers: Abbo et al. (LVC), Observaon of Gravitaonal Waves from a A. Pai, S. Dhurandhar, SB, IJMPD (2000); Binary Black Hole Merger," Phys. Rev. Le. 116, 061102 (2016). PRD (2001). 07/13/16 Bose @ INT 63 NS de in waveforms Total phase = Point-parcle phase + Tidal phase-correcon. IUCAA

Point-parcle phase has non-spinning and spinning (aligned or an-aligned) terms up to 3.5pN. We add test-parcle non-spinning correcons from 4pN to 7.5pN, in part, to bridge the gap that otherwise exists between 3.5pN terms and the terms where dal correcons come in (5pN…).

Tidal phase-correcon is: 5 ) 24 # 11η &# v & , +− %1+ (% ( . 2 [Vines, Flanagan, Hinderer, 3λ + χi $ χi '$ c ' . ψ = i , arXiv:1101.1673v1.; tidal ∑ 5 + 7 . 128ηM Damour, Nagar, Villain, i=1 + 5 2 3 # v & . − (3179 − 919χi − 2286χi + 260χi )% ( PRD85, 123007 (2012). *+ 28χi $ c ' -.

1/3 where v = (Mω) , χi = mi / M and "i" is binary component index. 2 M = m1 + m2 and η = m1m2 / M . New: We add the aforemenoned point parcle terms to improve upon waveforms used in the past 07/13/16 Bose @ INT 64 Details of the

piecewise polytropic NS EOS IUCAA

' α β * ' α β * ! ρ $ ! ρ $ 2 ! ρ $ ! ρ $ ε = ρ)a# & + b# & + mN c ,, P = ρ)aα# & + bβ # & ,, () " ρ0 % " ρ0 % +, () " ρ0 % " ρ0 % +, −3 mN = nucleon mass, ρ0 = 0.16 fm is the saturation density. Also, a ~ 12.71 - 13.3 MeV, α ~ 0.48 - 0.52, and b = 2 − 5 MeV, β~ 2.1 - 2.5.

This form was found to accurately fit QMC calculaons of the EOS using nuclear Hamiltonians with realisc two- and three-body forces. [Gandolfi:2009, Gandolfi:2010b, Gandolfi:2012]

It is also consistent with recent QMC results based on chiral EFT interacons. [Wlazlowski:2014a, Gandolfi:2014, Gandolfi:2014a, Gandolfi:2015, Lynn:2015]

07/13/16 Bose @ INT 65 Results IUCAA

' α β * ' α β * ! ρ $ ! ρ $ 2 ! ρ $ ! ρ $ ε = ρ)a# & + b# & + mN c ,, P = ρ)aα# & + bβ # & ,, () " ρ0 % " ρ0 % +, () " ρ0 % " ρ0 % +, −3 mN = nucleon mass, ρ0 = 0.16 fm is the saturation density. Also, a ~ 12.71 - 13.3 MeV, α ~ 0.48 - 0.52, and b = 2 − 5 MeV, β~ 2.1 - 2.5.

• If none of the four EOS parameters (a, α, b, β) are known from theory, then the observaonal errors (1σ) in them are larger than 100%.

• If (a, α) are known from theory, then the observaonal errors (1σ) in (b, β) reduce to several percent in a simulaon where one assumes observaons of 121 binary NS systems, all (unrealiscally) at 100Mpc.

07/13/16 Bose @ INT [SB et al. in preparaon] 66 Results IUCAA

' α β * ' α β * ! ρ $ ! ρ $ 2 ! ρ $ ! ρ $ ε = ρ)a# & + b# & + mN c ,, P = ρ)aα# & + bβ # & ,, () " ρ0 % " ρ0 % +, () " ρ0 % " ρ0 % +, −3 mN = nucleon mass, ρ0 = 0.16 fm is the saturation density. Also, a ~ 12.71 - 13.3 MeV, α ~ 0.48 - 0.52, and b = 2 − 5 MeV, β~ 2.1 - 2.5.

• Upcoming neutron skin experiments expect to constrain the slope of the density dependence of the symmetry energy to within an error of ΔL=41 MeV, with possible reducon to 15 MeV.

• For our EOS, L =3(aα + bβ); hence these constraints from gravitaonal wave observaons could have an impact at the level of 5 MeV.

07/13/16 Bose @ INT [SB et al. in preparaon] 67 Fisher informaon IUCAA s(t;ϑ k ) = h(t;ϑ k )+n(t), where ϑ k are signal parameters. Or s!( f ;ϑ k ) = h!( f ;ϑ k ) + n!( f ) in the Fourier domain. The cross-correlation of the data with a template is:

* k k $ f2 s! f ;ϑ h! f ;ϑ ' ' C Δϑ k = s ϑ k h ϑ 'k ∝ Re& ( ) ( ) df ), ( ) ( ) ( ) & ∫ P f ) % f1 ( ) ( where P( f ) is the noise power-spectral density. The probability distribution of the parameter error(s) is related to that of noise, which is taken to be Gaussian:

$ n0 n0 ' $ s − h' s − h' ' $ s h' ' p(n = n0 ) ∝ exp&− )∝ exp&− )∝ exp&− ) % 2 ( % 2 ( % 2 (

$ 1 k l ' ∂h ∂h p n n exp , where . Fisher informaon ( = 0 ) ∝ &− ΓklΔϑ Δϑ ) Γkl = k l % 2 ( ∂ϑ ∂ϑ matrix For large signal-to-noise ratio, parameter error variance-covariance is: kl {Δϑ kΔϑ l } = (Γ−1) .

07/13/16 Bose @ INT 68 Details of the parameter

esmaon method IUCAA

• Let the signal parameters, θ k , be the NS EOS parameters (a, α, b, β), with k=1-4, respecvely.

• The goal is to ﬁnd how much any variaon in the EOS parameters changes the waveform. That informaon is obtained from the Fisher matrix. ∂h ∂h Γ = . kl ∂ϑ k ∂ϑ l # & ∂h ∂h ∂k ∂h ∂mp ∂h ∂Rp 2 , i = i + ∑ % i + i ( ∂ϑ ∂k 2 ∂ϑ p=1,2$%∂mp ∂ϑ ∂Rp ∂ϑ '( ∂h where is obtained by keeping mp and Rp fixed. ∂k 2

Similary for the mp and Rp derivatives of h. Next find parameter error variance-covariance (for large SNR): kl {Δϑ kΔϑ l } = Γ−1 . 07/13/16 ( ) Bose @ INT 69 NS-BH systems IUCAA

• Gaussian distribuon of NS and BH masses:

0.05 Msun

07/13/16 Bose @ INT 70 Where is more than half of

the heavy elements produced? IUCAA

Stephane Goriely, Andreas Bauswein and Hans-Thomas Janka, "r-process nucleosynthesis in dynamically ejected maer of neutron star mergers", 2011 ApJ 738 L32

07/13/16 Bose @ INT 71 The spin problem

Double neutron star systems IUCAA • Gaussian distribuon of NS masses, with mean = 1.35Msun, sd = 0.2Msun. • Aligned spin, J/m2 = 0.1.

1σ

07/13/16 Bose @ INT 72 Einstein Telescope

Double neutron star systems IUCAA

• Non-spinning DNS systems in Einstein Telescope (ET):

1σ

07/13/16 Bose @ INT 73 Populaons

Double neutron star systems IUCAA

• Gaussian distribuon of NS masses, with mean = 1.35Msun, sd = 0.2Msun.

1σ 1σ

Reference: aLIGO

07/13/16 Bose @ INT 74 Real nuclear maer & neutrinos IUCAA • Need “real” NSE equaon of state for composion, phase change, neutrino interacon info

• Use Lamer-Swesty (K0=220MeV, Sv=37MeV) EoS – Includes free neutrons, protons, electrons, photons, 1 species of heavy nucleus, and alpha parcles

– R=11.5km for MNS=1.4M! • Neutrino cooling/deleptonizaon through leakage scheme: linear combinaon of Local emission rate = • Free emission rate from nucleon capture, pair annihilaon, etc. • Diﬀusive emission rate, depends on opcal depth

07/13/16 Bose @ INT 75 Summary of ﬁrst part IUCAA

• NS mass distribuon: Uniform distribuon will help esmaon of λ. GW observaons will provide some insight into what this distribuon is.

• NS spin helps or hurts λ esmaon? We ﬁnd that it hurts but only negligibly.

• How can waveform modeling systemacs aﬀect λ esmaon? We have the tools to answer it (future work).

• In light of the prospect of LOFT, it is interesng to compare how well ET will perform.

07/13/16 Bose @ INT 76 Take-away messages IUCAA

• Knowing certain EOS parameters from theory helps constrain, observaonally, the other EOS parameters beer.

• The measurement accuracy improves with the number of observed double neutron star systems.

• The eﬀects of NS mass distribuon, DNS formaon scenarios, and waveform modeling on measurement accuracy can be quanﬁed.

07/13/16 Bose @ INT 77 IUCAA

Tables for NS-BH ﬁng factors phenomc.

07/13/16 Bose @ INT 78 IUCAA

Tables for NS-BH ﬁng factors phenomc.

07/13/16 Bose @ INT 79 Is that a neutron star? (Is GRB 130603B the ﬁrst ever kilonova detecon?) IUCAA • Late-type galaxy at z ~ 0.35 • No late-me opcal counterpart (rules out Ni-decay emission as in a supernova) • Single late-me near-infrared emission.

• N-IR emission consistent with kilonova models of CBC-NS with ejected mass ~ 10-2 – 10-1 Msun.

[Tanvir et al., , Nature doi:10.1038/nature12505 (2013). 07/13/16 Bose @ INT 80 What are the alternaves to GWs?

IUCAA

Constraints on NS EOS can be obtained from observaons of x ray pulsars

07/13/16 Bose @ INT 81 What do X-ray observaons

say about NS radii? IUCAA

System Mass (M_sun) Radius (km) 4U 1608-248, 1.3 – 1.95 8 - 12 EXO 1745-248, 4U 1820-30 KS 1731-260 <= 2.1 <= 12.5 4U 1820-30 1.58+/-0.06 9.11+/-0.4 4U 0614+09 <= 1.9 <= 15.2 the list goes on…. X-ray observaons of LMXB systems => for NS masses in the range M ~ 1.3 – 1.95 Msun the NS radii are measured in the range R ~ 8-12km. Allowing for other systemacs for this mass range can increase the radius upper limit to 15km. Radius error typically of the order of > 10%

07/13/16 Bose @ INT 82 NS ellipcity from a stochasc

GW background from gravitars IUCAA

Two simulated SGWBs, one with origin conﬁned to the Galacc disk (le) and another with origin in the Virgo Cluster (right).

About 40,000 millisecond pulsars esmated. Further the the total number of NSs in our Galaxy ≈ 108 for spin frequency f < 50Hz and 40,000 for f > 50 Hz. [D. Talukder, E. Thrane, SB, T. Regimbau, PRD 89, 123008 (2014).] 07/13/16 Bose @ INT 83 NS ellipcity IUCAA . Units) arbit Spectral proﬁle (

To model the spectrum, we simulate the NS spin frequency distribuon assuming various populaon distribuons, including a “power law”.

2 GIε 2 We consider the populaon synthesis model, where the populaon of (millisecond) h( f ) = 4π β 4 f . pulsars has ages uniformly distributed between 0-12 Gyr, inial magnec ﬁelds drawn rc from a uniform distribuon in [108, 1012] Gauss (with no magnec ﬁeld decay), and for which the actual period is calculated assuming magnec (dipole) braking only.

07/13/16 Bose @ INT 84 Number of gravitars

in the galaxy? IUCAA • Esmated upper limits average ellipcity ε of a neutron star in our galaxy achievable with 1 yr of integraon… ˆ • …presented as funcons of the number of ε Galacc NSs eming GWs with frequency in the range 600 – 1000 Hz.

• (Here, H and L denote the LIGO detectors in Hanford and Livingston with 4km long arms.)

• For the Advanced LIGO detectors in Hanford and Livingston, that upper-limit is -7 ancipated to be 1.3×10 for Ntotal = 1/ 2 Ntotal 19 ⎛ 2 ⎞ 1/ 2 40,000. 3×10 ⎜ r 10 kpc⎟ 2 ⎝ ⎠ ⎛ 3H 0 δf −7 ⎞ ˆ f ⎜ f f ⎟ . ε ( ) ≈ 1/ 2 45 2 ⎜ 2 Ω( )⎟ N ( f )(I 1.1×10 gm ⋅cm )⎝ 10π ⎠ 07/13/16 Bose @ INT 85 Neutron star – black hole binaries IUCAA • Massive ejecta from neutron star dal disrupon • r-process nucleosynthesis in ejecta – An important site for the creaon of these elements? 2 10 SkyNet result 3 • Kilonova signal 10 Observation

4 10

5 10

6 10

7 10

8

Amount of each element 10 Gold Silver Caesium Selenium Holmium

9 Uranium-235 10

10 10 0 50 100 150 200 250 300 Atomic number (number of neutrons + protons) of the element Tidal tail in a SpEC Final abundances in oulow NS/BH calculaon From nuclear reacon network calculaon 07/13/16 Bose @ INT 86 using SpEC NS/BH oulow (Lippuner et al, in prep) Complemenng

LMXB observaons with GWs IUCAA

A. Mukherjee, SB, in preparaon.

07/13/16 Bose @ INT 87 Complemenng

LMXB observaons with GWs IUCAA

2 G[Iε] 2 h( f ) = 4π β 4 f , rc A. Mukherjee, SB, in preparaon. 32G"I 2 $ − # ε % 5 f! = f 07/13/16 Bose @ INT 5c5 88 IUCAA

07/13/16 Bose @ INT 89 IUCAA

07/13/16 Bose @ INT 90 BNS mass errors from GWs IUCAA

07/13/16 Bose @ INT 91 “New” physics & astronomy Tanvir et al., Nature (2013). IUCAA

• Involve neutron stars:

– Do kilonovae/macronovae and short GRBs share a common origin?

– What is the equaon of state of a neutron star? [Deaton et al. 2013; Foucart et al. 2014] – What are the host galaxies of binary NS systems like?

– Can GWs help track how BNS formaon rate evolved with redshi?

07/13/16 Bose @ INT [Credits: Wikipedia.] 92

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