The gravitational wave radiation from Galactic double compact binaries

Shenghua YuBinary Star Conference In University of Cambridge

28.07.2016

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Collaborator: C. Simon Jeffery, Zhanwen Han, …

Outline• Chapter 1 – Why Gravitational Wave (GW) radiation from binaries

• Chapter 2 – Methodology and a sample of double compact binaries : theory vs observation

• Chapter 3 – GW strain amplitude, energy flux– frequency relations • Chapter 4 – Conclusions

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• Chapter 1 – Why Gravitational Wave (GW) radiation from binaries

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Gravitational waves & Electromagnetic waves

Gravitational waves Electromagnetic waves

Generation mechanism

Acceleration of mass (wave equations)

Acceleration of charged particles(wave equations)

Meaning Oscillations of space (time)

Oscillations of Electromagnetic field

Frequency (Hz) ~10^-18 --- ~10^6 ~10^3 --- ~10^21

Background emission

Binaries motion, Cosmic

Thermal, Nonthermal

… … …

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Existence of GW Hulse-Taylor binary pulsar :

PSR 1913-16 orbital decay Taylor+1982, ApJ

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aLIGO bianry black holes: GW150914, GW151226 Abbott+2016, PRL, 116, 241103 Abbott+2016, PRL, 116, 061102

Existence of GW background ?

• Background: – induced by a number of binaries – & their harmonics

• Theory indicate that the background may exist

• Aim to investigate the background & related events

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Evans+1987; Hils+1990,2000; Webbink&Han1998; Hiscock2000; Nelemans+2001; Farmer+2003; Liu+2009;Yu&Jeffery 2010,2013; Ruiter+2009,2010; Nissanke+2012Belczynski+2008, 2010; Rosado 2012; Zhu+2013; Yu&Jeffery 2015; … …

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• Chapter 2 – Methodology & a sample of double compact binaries: theory vs observation

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Method: Binary Population Synthesis

Initial parameters Stellar evolution

Parametric CE ejection

Galactic structure

GW from single binary

A sample of DCOs

GW strain - frequency relation

Compare with observationsNot fit well Fit well

Energy flux - frequency relation

superposition

CE: Common EnvelopeDCOs:Double Compact Objects

Galactic structure

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e.g. Klypin+2002, Robin+2003 Nelemans+2001,Yu&Jeffery2010,…

• Total mass of the Galaxy: ~6x10^11 Msun• Mass of stars: ~ 1.25x10^11 Msun

• Bulge: ~2x10^10 Msun (size: ~3.5 kpc)• Disc, thin+thick : ~5.5x10^10 Msun(size: ~25 kpc)• Halo: 5x10^10 Msun +dark matter (size: ~50 kpc) (consistent with e.g. Klypin+2002; Robin+2003)

• Mass of dark matter: ~85% of the total mass • Mass of gas (H & He …): ~2x10^10 Msun• Mass of interstellar dust: ~10^8-9 Msun

Initial Parameters and stellar evolution

• Initial conditions – 1. Star formation history– 2. metallicity – 3. Initial mass function – 4. Mass ratio – 5. orbital period – 6. eccentricity

• Stellar evolution model (e.g. Han1998; Hurley+2002,2003)

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(constant, exponential, instantaneous)

Z=0.001, 0.02 for the halo, disc & bulge

-1.5

Parametric CE ejection (initial-final orbit separation)

• Energy model (alpha-mechanism)

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• Angular moment model (gamma-mechanism)

GW radiation from one binary system (Landau 1975)

=• Wave equations :

Associated with energy-momentum tensor

Presence of matter

GW radiation from point mass binary system in general (Peters&Mathews1963, Yu&Jeffery2015)

• G: gravity constant• c: speed of light• Rb : distance • e: eccentricity• a: semi-major axis• M:total mass, reduced

mass • : orbit phase

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GW radiation from one binary system (e.g. Peters+1963, Landau+1975,Nelemans+2001,Yu+2015)

After Fourier analysis of Kepler motion

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Normalized Energy flux:

Critical density

GW radiation from one binary system strain amplitude vs time

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GW radiation from one binary system strain amplitude vs frequency

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m1=2Msunm2=2MsunPorb=1000s

Observations vs. simulations: white dwarf binaries

• ~ 22 observed detached double white dwarfs (including sdB), and ~12 AM CVn

Nelemans+2001a,2001b,2013,Amaro-Seoane2012 & references therein

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Observations vs. simulations: NS-WD binaries

• 64 NS-WD in the disc (Lorimer2008)• 39 NS-WD in globular clusters (camilo+2005)

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NS: neutron starWD: white dwarf

Observations of NS-NS (Lorimer2008)

Observations vs. simulations: black holes

• X-ray (gamma-ray) emission (4,20Msun), Centered at 8 Msun

• 4 Microlensing events: (3,45Msun)

• aLIGO observations: 36, 29 & 14.2, 7.5 Msun

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Ziolkowski2010, Postnov&Yungelson2014, references therein

• Simulations: (2,41Msun)

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Birth, merger rates & numbers

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NS-NS

NS-WD

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BH-WD

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BH-BH

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• Chapter 3 – GW strain amplitude, energy flux– frequency relations

Strain – frequency

• Strain: h = dL/L

• f=n/P

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WD-WD

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NS-WD

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NS-NS

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BH-WD

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BH-NS

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BH-BH

Energy flux – frequency

• ~1 10^-27 kg m^-3

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• 0.027 erg s^-1 m^-2

• How many 0.027 erg s^-1 m^-2 per Hz

NS-WD

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NS-NS (Yu&Jeffery2015)

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BH-WD

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BH-NS

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BH-BH

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Energy flux – frequency relation

Conclusions

• WD-WDs and NS-WDs significantly contributes to the eLISA signal.

• BH-WDs may have some contribution.

• WD-WDs & NS-WDs: the disc and bulge population may be important

• BH-BHs: the halo population becomes important.

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• Energy flux – frequency relation may obey

NOT t

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How to observe?

eLISA, pulsar timing (BH-BH?), sitellite signal … …

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•Thank you！

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