示例#1
0
def hfpc(f,
         Mc,
         eta,
         chi1z,
         chi2z,
         DL,
         tc,
         phic,
         iota,
         lam_t,
         delta_lam_t,
         is_lam12=0):
    '''
    Mc ... in solar mass
    DL ... in mega parsec
    '''
    # convert to sec
    Mc = Mc * time_fac
    DL = DL * time_fac / strain_fac

    # get sym and asym chi combinations
    chi_s = brs.chi_s(chi1z, chi2z)
    chi_a = brs.chi_a(chi1z, chi2z)

    if is_lam12:
        # in this case: lam_t = lam1, delta_lam_t = lam2
        lam1 = lam_t
        lam2 = delta_lam_t
        delta = sqrt(1 - 4 * eta)
        lam_t = 8. / 13. * ((1. + 7. * eta - 31. * eta**2) *
                            (lam1 + lam2) + delta *
                            (1. + 9. * eta - 11. * eta**2) * (lam1 - lam2))
        delta_lam_t = 0.5 * (
            delta * (1319. - 13272. * eta + 8944. * eta**2) / 1319. *
            (lam1 + lam2) +
            (1319. - 15910. * eta + 32850. * eta**2 + 3380. * eta**3) / 1319. *
            (lam1 - lam2))
    '''
    Mc is in sec, e.g., Mc = 10*MTSUN_SI (for 10 solar mass)
    DL is in sec, e.g., DL = 100*1e6*PC_SI/C_SI (for 100 Mpc)
    '''
    M = Mc / eta**(3. / 5.)
    delta = (1. - 4. * eta)**0.5
    v = (PI * M * f)**(1. / 3.)
    flso = brs.f_isco(M)
    vlso = (PI * M * flso)**(1. / 3.)
    A = ((5. / 24.)**0.5 / PI**(2. / 3.)) * (Mc**(5. / 6.) / DL)

    # 3.5PN phasing (point particle limit)
    p0 = 1.

    p1 = 0

    p2 = (3715. / 756. + (55. * eta) / 9.)

    p3 = (-16. * PI + (113. * delta * chi_a) / 3. + (113. / 3. -
                                                     (76. * eta) / 3.) * chi_s)

    p4 = (15293365. / 508032. + (27145. * eta) / 504. +
          (3085. * eta**2) / 72. + (-405. / 8. + 200. * eta) * chi_a**2 -
          (405. * delta * chi_a * chi_s) / 4. + (-405. / 8. +
                                                 (5. * eta) / 2.) * chi_s**2)

    gamma = (732985. / 2268. - 24260. * eta / 81. - 340. * eta**2 /
             9.) * chi_s + (732985. / 2268. + 140. * eta / 9.) * delta * chi_a

    p5 = (38645. * PI / 756. - 65. * PI * eta / 9. - gamma)

    p5L = (38645. * PI / 756. - 65. * PI * eta / 9. - gamma) * 3 * log(
        v / vlso)

    p6 = (11583231236531./4694215680. - 640./3.*PI**2 - 6848./21.*GammaE + eta*(-15737765635./3048192. + 2255./12.*PI**2) + eta*eta*76055./1728. - eta*eta*eta*127825./1296. \
         - (6848./21.)*log(4.) + PI*(2270.*delta*chi_a/3. + (2270./3. - 520.*eta)*chi_s) + (75515./144. - 8225.*eta/18.)*delta*chi_a*chi_s \
         + (75515./288. - 263245.*eta/252. - 480.*eta**2)*chi_a**2 + (75515./288. - 232415.*eta/504. + 1255.*eta**2/9.)*chi_s**2)

    p6L = -(6848. / 21.) * log(v)

    p7 = (((77096675. * PI) / 254016. + (378515. * PI * eta) / 1512. -
           (74045. * PI * eta**2) / 756. +
           (-25150083775. / 3048192. + (10566655595. * eta) / 762048. -
            (1042165. * eta**2) / 3024. + (5345. * eta**3) / 36. +
            (14585. / 8. - 7270. * eta + 80. * eta**2) * chi_a**2) * chi_s +
           (14585. / 24. - (475. * eta) / 6. +
            (100. * eta**2) / 3.) * chi_s**3 + delta *
           ((-25150083775. / 3048192. + (26804935. * eta) / 6048. -
             (1985. * eta**2) / 48.) * chi_a +
            (14585. / 24. - 2380. * eta) * chi_a**3 +
            (14585. / 8. - (215. * eta) / 2.) * chi_a * chi_s**2)))

    phase = 2 * f * PI * tc - phic - PI / 4. + (3. / (128. * v**5 * eta)) * (
        p0 + v * p1 + v**2 * p2 + v**3 * p3 + v**4 * p4 + v**5 *
        (p5 + p5L) + v**6 * (p6 + p6L) + v**7 * p7)

    # From Lesli Wade's paper ... adding the tidal deformability phase
    pT = (3. / 128. / eta /
          v**5.) * (-39. * lam_t * v**10 / 2. +
                    (-3115. * lam_t / 64. + 6595. *
                     (1 - 4 * eta)**0.5 * delta_lam_t / 364.) * v**12)
    phase += pT

    hp = 0.5 * (1 + (cos(iota))**2) * A * f**(-7. / 6.) * (cos(phase) -
                                                           1j * sin(phase))
    hc = -1j * cos(iota) * A * f**(-7. / 6.) * (cos(phase) - 1j * sin(phase))

    return hp, hc
示例#2
0
def hfpc(f, Mc, eta, chi1z, chi2z, DL, tc, phic, iota, Heff5, Heff8, e0):
    '''
    Mc ... in solar mass
    DL ... in mega parsec
    '''
    # convert to sec
    Mc = Mc * time_fac
    DL = DL * time_fac / strain_fac

    # get sym and asym chi combinations
    chi_s = brs.chi_s(chi1z, chi2z)
    chi_a = brs.chi_a(chi1z, chi2z)
    '''
    Mc is in sec, e.g., Mc = 10*MTSUN_SI (for 10 solar mass)
    DL is in sec, e.g., DL = 100*1e6*PC_SI/C_SI (for 100 Mpc)
    '''

    M = Mc / eta**(3. / 5.)
    delta = (1. - 4. * eta)**0.5
    v = (PI * M * f)**(1. / 3.)
    flso = brs.f_isco(M)
    vlso = (PI * M * flso)**(1. / 3.)
    f0 = 10.
    fbyf0 = f / f0
    A = ((5. / 24.)**0.5 / PI**(2. / 3.)) * (Mc**(5. / 6.) / DL)

    # 3.5PN phasing (point particle limit)
    p0 = 1. - (2355. / 1462.) * e0**2. * fbyf0**(-19. / 9.)

    p1 = 0

    p2 = (3715. / 756. + (55. * eta) / 9.)

    p3 = (-16. * PI + (113. * delta * chi_a) / 3. + (113. / 3. -
                                                     (76. * eta) / 3.) * chi_s)

    p4 = (15293365. / 508032. + (27145. * eta) / 504. +
          (3085. * eta**2) / 72. + (-405. / 8. + 200. * eta) * chi_a**2 -
          (405. * delta * chi_a * chi_s) / 4. + (-405. / 8. +
                                                 (5. * eta) / 2.) * chi_s**2)

    gamma = (732985. / 2268. - 24260. * eta / 81. - 340. * eta**2 /
             9.) * chi_s + (732985. / 2268. + 140. * eta / 9.) * delta * chi_a

    p5 = (38645. * PI / 756. - 65. * PI * eta / 9. - gamma)

    p5L = (38645. * PI / 756. - 65. * PI * eta / 9. - gamma) * 3 * log(
        v / vlso)

    p6 = (11583231236531./4694215680. - 640./3.*PI**2 - 6848./21.*GammaE + eta*(-15737765635./3048192. + 2255./12.*PI**2) + eta*eta*76055./1728. - eta*eta*eta*127825./1296. \
         - (6848./21.)*log(4.) + PI*(2270.*delta*chi_a/3. + (2270./3. - 520.*eta)*chi_s) + (75515./144. - 8225.*eta/18.)*delta*chi_a*chi_s \
         + (75515./288. - 263245.*eta/252. - 480.*eta**2)*chi_a**2 + (75515./288. - 232415.*eta/504. + 1255.*eta**2/9.)*chi_s**2)

    p6L = -(6848. / 21.) * log(v)

    p7 = (((77096675. * PI) / 254016. + (378515. * PI * eta) / 1512. -
           (74045. * PI * eta**2) / 756. +
           (-25150083775. / 3048192. + (10566655595. * eta) / 762048. -
            (1042165. * eta**2) / 3024. + (5345. * eta**3) / 36. +
            (14585. / 8. - 7270. * eta + 80. * eta**2) * chi_a**2) * chi_s +
           (14585. / 24. - (475. * eta) / 6. +
            (100. * eta**2) / 3.) * chi_s**3 + delta *
           ((-25150083775. / 3048192. + (26804935. * eta) / 6048. -
             (1985. * eta**2) / 48.) * chi_a +
            (14585. / 24. - 2380. * eta) * chi_a**3 +
            (14585. / 8. - (215. * eta) / 2.) * chi_a * chi_s**2)))

    phase = 2 * f * PI * tc - phic - PI / 4. + (3. / (128. * v**5 * eta)) * (
        p0 + v * p1 + v**2 * p2 + v**3 * p3 + v**4 * p4 + v**5 *
        (p5 + p5L) + v**6 * (p6 + p6L) + v**7 * p7)

    #phase due to tidal heating
    #--------------------------------------------------------------------------------
    psi_so1 = (1 / 6.) * (-56 * eta - 73 * np.sqrt(1 - 4 * eta) + 73) * chi1z
    psi_so2 = (1 / 6.) * (-56 * eta - 73 * np.sqrt(1 - 4 * eta) + 73) * chi2z
    psi_so = psi_so1 + psi_so2
    con = (3. / 128. * eta) / v**5
    term1 = -(10 / 9.) * (v**5) * Heff5 * (3 * np.log(v) + 1)
    term2 = -(5 / 168.) * (v**7) * Heff5 * (952 * eta + 995)
    term3 = (5 / 9.) * (v**8) * (3 * np.log(v) - 1) * (-4 * Heff8 +
                                                       Heff5 * psi_so)

    heated_phase = con * (term1 + term2 + term3)
    phase += heated_phase

    hp = 0.5 * (1 + (cos(iota))**2) * A * f**(-7. / 6.) * (cos(phase) -
                                                           1j * sin(phase))
    hc = -1j * cos(iota) * A * f**(-7. / 6.) * (cos(phase) - 1j * sin(phase))

    return hp, hc