A synthetic model of the gravitational wave background from evolving binary compact objects

Transcription

1 A synthetic model of the gravitational wave background from evolving binary compact objects Irina Dvorkin, Jean-Philippe Uzan, Elisabeth Vangioni, Joe Silk (Institut d Astrophysique de Paris) [arxiv: ] 11th International LISA Symposium, 8 September 2016

2 Sources of Gravitational Waves

3 Model framework

4 Model framework

5 Model framework

6 Model framework

7 BH binaries number density (simple case) If all BH are in binaries, and all merger products remain single, the number density n X of binaries in a certain mass M and orbital parameters bin is set by: [where w = (a,e)] The formation rate of BH (determined from stellar physics) R X (M,t) The initial distribution of orbital parameters P X (w) The evolution in time of the orbital parameters of the binary dw/dt

8 Evolution of the orbital parameters General case (w = (a,e)): A merger occurs when w = w merger dw dt = f(w,m)

9 Evolution of the orbital parameters General case (w = (a,e)): A merger occurs when w = w merger dw dt = f(w,m) Example: evolution due to emission of GW [Peters & Mathews (1963)] da dt = 64 5 G 3 µm 2 c 5 a 3 ( e e4) (1 e 2 ) 7/2 ( de dt = 304 G 3 µm 2 e e2) c 5 a 4 (1 e 2 ) 5/2

10 Continuity equation Hydrodynamics (matter density ρ, coordinate x, velocity u = dx/dt): dρ dt + d dx.[ρu] = 0

11 Continuity equation Hydrodynamics (matter density ρ, coordinate x, velocity u = dx/dt): dρ dt + d dx.[ρu] = 0 Binaries (number density n X, coordinate w, velocity f = dw/dt): dn X dt + d dw.[n Xf] = 0

12 Continuity equation Hydrodynamics (matter density ρ, coordinate x, velocity u = dx/dt): dρ dt + d dx.[ρu] = 0 Binaries (number density n X, coordinate w, velocity f = dw/dt): dn X dt + d dw.[n Xf] = 0 Assuming / t = 0 (stationary distribution of binaries in the galaxy) stochastic GW emission from coalescing binary NS Buitrago, Moreno-Garrido & Mediavilla (1994); Moreno-Garrido, Mediavilla & Buitrago (1995); Ignatiev et al. (2001)

13 Continuity equation Hydrodynamics (matter density ρ, coordinate x, velocity u = dx/dt): dρ dt + d dx.[ρu] = 0 Binaries (number density n X, coordinate w, velocity f = dw/dt): dn X dt + d dw.[n Xf] = R X No stationarity Source function R X is given by astrophysics

14 Continuity equation (single population) dw dt = f(w,m)

15 Continuity equation (single population) dw dt dn (1) X (M,t) dt = f(w,m) = S ( M,M,t )

16 Continuity equation (single population) dw dt dn (1) X (M,t) dt dn (2) X (M,M,w,t) dt = f(w,m) = S ( M,M,t ) = 1 2 R X(M,t)P X (w) w.[f(w,m)n(2) X (M,M,w,t)]

17 Continuity equation (single population) dw dt dn (1) X (M,t) dt dn (2) X (M,M,w,t) dt = f(w,m) = S ( M,M,t ) = 1 2 R X(M,t)P X (w) w.[f(w,m)n(2) X (M,M,w,t)] S is source term due to mergers All the merger products remain single, all objects are in binaries

18 Continuity equation (single population) dw dt dn (1) X (M,t) dt dn (2) X (M,M,w,t) dt = f(w,m) = (1 β X )S ( M,M,t ) = 1 2 R X(M,t)P X (w)+ 1 2 β XS ( M,M,t ) P X (w) w.[f(w,m)n(2) X (M,M,w,t)] S is source term due to mergers (1 β X ) of merger products remain single, all objects are in binaries

19 Continuity equation (single population) dw dt dn (1) X (M,t) dt dn (2) X (M,M,w,t) dt = f(w,m) = (1 α X )R X (M,t)+(1 β X )S ( M,M,t ) = 1 2 α XR X (M,t)P X (w)+ 1 2 β XS ( M,M,t ) P X (w) w.[f(w,m)n(2) X (M,M,w,t)] S is source term due to mergers (1 β X ) of merger products remain single, α X objects are in binaries

20 Continuity equation (single population) dw dt dn (1) X (M,t) dt dn (2) X (M,M,w,t) dt = f(w,m) = R (1) X (M,t)+(1 β X)S ( M,M,t ) = R (2) X (M,M,w,t)+ 1 2 β XS ( M,M,t ) P X (w) w.[f(w,m)n(2) X (M,M,w,t)] S ( M,M,t ) = fn (2) ( X M,M,w,t ).dl C m M = 2M M(M )

21 Initial distribution of orbital parameters Sana et al. (2012); de Mink & Belczynski (2015) Joint distribution: P X (w) = P(e)P(a) P(e) e 0.42 P(logT) (logt) 0.5 in T (T min,t max )

22 Initial distribution of orbital parameters Sana et al. (2012); de Mink & Belczynski (2015) Joint distribution: P X (w) = P(e)P(a) P(e) e 0.42 P(logT) (logt) 0.5 in T (T min,t max )

23 Time to coalescence a min chosen so as to fit the observed merger rate (τ merger a 4 ) Rapid mergers M =5 M =10 M =30 M =50 Eccentricity Slow mergers Log10(a/AU)

24 Initial distribution of orbital parameters Sana et al. (2012) a min = 0.2 AU T 10 days for M 10M

25 Complete model Dvorkin et al. (2016) [ ], [ ] Galaxy evolution (gas inflow/outflow, SFR, chemical evolution) [Daigne et al. (2004, 2006), Vangioni et al. (2015), Dvorkin et al.(2015)] BH formation [Fryer et al. (2012)] Distribution of masses and orbital parameters of BH binaries Evolution of the binaries due to emission of GW

26 GW background from BH binaries Dvorkin et al. [ ] 10-7 This work, a =0.2 AU min 10-8 This work, a min = AU Mergers only (D16) LIGO O elisa Ω GW Frequency [Hz]

27 Summary An exciting time for astrophysics: Gravitational wave astronomy will provide constraints on: Stellar evolution Binary interactions

28 Summary An exciting time for astrophysics: Gravitational wave astronomy will provide constraints on: Stellar evolution Binary interactions More detections to come soon: need tools to analyze them and extract astrophysical information

29 Summary An exciting time for astrophysics: Gravitational wave astronomy will provide constraints on: Stellar evolution Binary interactions More detections to come soon: need tools to analyze them and extract astrophysical information What we plan to do next: Include BH-NS mergers Explore a full merger-tree based galaxy evolution model Test different BH formation scenarios Use formalism for SMBH

30 Additional slides

31 Astrophysics with gravitational waves GW150914: The most massive stellar black holes ever observed! Masses: M and M

32 Astrophysics with gravitational waves GW150914: The most massive stellar black holes ever observed! Masses: M and M Starting to measure the BH mass distribution (LIGO Scientific, VIRGO Collaborations [ ])

33 Astrophysics with gravitational waves GW150914: The most massive stellar black holes ever observed! Masses: M and M Starting to measure the BH mass distribution (LIGO Scientific, VIRGO Collaborations [ ]) What can we learn about stellar evolution and black hole formation?

34 Stellar mass black holes - masses All previous estimates of BH masses are from X-ray binaries GW is the first direct evidence of the existence of heavy stellar mass BHs (M 20M ) Farr et al. (2007)

35 How to make a black hole BHs form at the end of the nuclear burning phase of massive stars

36 How to make a black hole BHs form at the end of the nuclear burning phase of massive stars How to relate the initial stellar mass to the BH mass?

37 From massive stars to black holes Mass prior to core collaps is determined by stellar winds Belczynski et al. (2016)

38 From massive stars to black holes Mass prior to core collapse is determined by stellar winds Vink (2008)

39 Metallicity Fryer WWp WWp + PopIII WWp + GRB-based SFR WWp + steep IMF [M/H] Redshift

40 Stochastic gravitational wave background 10-7 LIGO Fiducial (fixed mass) LIGO Fiducial + uncertainty Fryer Fiducial (mass distribution) Fryer Fiducial + uncertainty Fryer, fixed mass Fryer + Aj11 (spin = 0) Fryer + Aj11 (spin distribution) Fryer + Aj11 (spin = 0, fixed mass) 10-8 Ω GW Frequency [Hz]

41 Cosmic metallicity evolution Damped Ly-α systems data from Rafelski et al. (2012) [M/H] Redshift Dvorkin et al. (2015)

42 Galaxy evolution model Daigne et al. (2006)

43 Model summary Baryon flow: Ṁ struct = a b (t)+e(t) ψ(t) o(t) Ṁ = ψ(t) e(t)

44 Model summary Baryon flow: Ṁ struct = a b (t)+e(t) ψ(t) o(t) Ṁ = ψ(t) e(t) Chemical evolution (X i is the mass fraction of element i): Ẋi ISM = 1 { M ISM (t) ei (t) e(t)xi ISM +a b (t) [ Xi IGM Ẋ IGM i = 1 M IGM (t) o(t){ Xi ISM (t) X IGM i (t) } X ISM i ]}

45 Self-consistent model of BBH birth rate: overview Input Galaxy growth (inflow and outflow) prescriptions Cosmic star formation rate Stellar initial mass function Stellar yields Black hole mass as a function of initial stellar mass and metallicity Dvorkin et al. [ ]

46 BH masses Fryer et al. (2012)

47 BH masses Kinugawa et al. (2014)

48 Star formation rate 10 0 Fiducial SFR Fiducial SFR+PopIII GRB-based SFR 10-1 M sun Mpc -3 yr Redshift

49 Optical depth to reionization Planck 2015 Fiducial SFR Fiducial SFR+PopIII GRB-based SFR 0.09 Optical depth Redshift

50 Optical depth to reionization Planck 2016 Fiducial SFR Fiducial SFR+PopIII GRB-based SFR 0.09 Optical depth Redshift

51 Self-consistent model of BBH birth rate: overview Dvorkin et al. (2015) [ ] Input Galaxy growth (inflow and outflow) prescriptions Cosmic star formation rate Stellar initial mass function Stellar yields Black hole mass as a function of initial stellar mass and metallicity

52 Self-consistent model of BBH birth rate: overview Dvorkin et al. (2015) [ ] Input Galaxy growth (inflow and outflow) prescriptions Cosmic star formation rate Stellar initial mass function Stellar yields Black hole mass as a function of initial stellar mass and metallicity Constraints Cosmic chemical evolution Optical depth to reionization

53 Self-consistent model of BBH birth rate: overview Dvorkin et al. (2015) [ ] Input Galaxy growth (inflow and outflow) prescriptions Cosmic star formation rate Stellar initial mass function Stellar yields Black hole mass as a function of initial stellar mass and metallicity Constraints Cosmic chemical evolution Optical depth to reionization Output Birth rate of black holes per unit mass

54 Merger rates vs. mass Normalized to the observed merger rate: Dvorkin et al. (2016) [ ] 10-8 Fryer WWp WWp + K + PopIII WWp + GRB-based SFR WWp + steep IMF 10-9 Mpc -3 yr -1 M sun BH Mass

55 Total merger rates Normalized to the observed merger rate: R = 10 7 Mpc 3 yr Fryer WWp WWp + PopIII WWp + GRB-based SFR WWp + steep IMF 10-7 Mpc -3 yr Redshift

56 Merger rates vs. redshift Normalized to the observed merger rate: R = 10 7 Mpc 3 yr Mass=3,WWp Mass=10,WWp Mass=20,WWp Mass=30,WWp 10-8 Mass=30,Fryer Mpc -3 yr -1 Msun Redshift

57 Stochastic gravitational wave background The background due to unresolved mergers of binary BHs Emission of gravitational waves during SN collapse

58 Stochastic gravitational wave background The background due to unresolved mergers of binary BHs Emission of gravitational waves during SN collapse Dimensionless density parameter (energy density in units of ρ c per unit logarithmic frequency) Ω gw (f o ) = 8πG 3c 2 H0 3 f o dm bh dz R source(z,m bh ) de gw (m bh ) (1+z)E V (z) df R source (z,m bh ) is the merger rate, de gw /df is the emitted spectrum

59 Stochastic gravitational wave background 10-7 LIGO Fiducial LIGO Fiducial + uncertainty Dvorkin et al. (2016) Dvorkin et al. (2016) + uncertainty O1: O2: O5: Ω GW Frequency [Hz]

60 Stochastic gravitational wave background Ω GW Fryer, mergers WWp, mergers Fryer, single WWp, single Frequency [Hz]

61 Initial distribution of orbital parameters Sana et al. (2012); de Mink & Belczynski (2015) P(logT) (logt) 0.5 in a (a min,a max )