California Institute of Technology. Government sponsorship acknowledged Stephen R. Taylor New data-analysis approaches for gravitational-wave searches with pulsar-timing arrays JET PROPULSION LABORATORY, CALIFORNIA INSTITUTE OF TECHNOLOGY
1967 by Hewish, Bell, et al. ! Rapid rotation (P~1s), and strong magnetic field (~ G) ! Radio emission along magnetic field axis ! Misalignment of rotation and magnetic field axes creates lighthouse effect 1012 Image credit: Bill Saxton Pulsars
1967 by Hewish, Bell, et al. ! Rapid rotation (P~1s), and strong magnetic field (~ G) ! Radio emission along magnetic field axis ! Misalignment of rotation and magnetic field axes creates lighthouse effect 1012 Image credit: Bill Saxton Joeri van Leeuwen Pulsars
set by total observation time (1/decades) and observational cadence (1/weeks) — [ ~ 1- 100 nHz ] Primary candidate is population of supermassive black-hole binaries Searching for GWs with pulsar timing
set by total observation time (1/decades) and observational cadence (1/weeks) — [ ~ 1- 100 nHz ] Primary candidate is population of supermassive black-hole binaries Image credit: CSIRO Searching for GWs with pulsar timing
set by total observation time (1/decades) and observational cadence (1/weeks) — [ ~ 1- 100 nHz ] Primary candidate is population of supermassive black-hole binaries Image credit: CSIRO Searching for GWs with pulsar timing
set by total observation time (1/decades) and observational cadence (1/weeks) — [ ~ 1- 100 nHz ] Primary candidate is population of supermassive black-hole binaries Other sources in the nHz band may be decaying cosmic-string networks, or relic GWs from the early Universe Image credit: CSIRO Searching for GWs with pulsar timing
problem” Dynamical friction not a sufficient driving mechanism to induce merger within a Hubble time e.g., Milosavljevic & Merritt (2003) Supermassive black-hole binary evolution
problem” Dynamical friction not a sufficient driving mechanism to induce merger within a Hubble time e.g., Milosavljevic & Merritt (2003) Additional environmental couplings may extract energy and angular momentum from binary to drive it to sub-pc separations Supermassive black-hole binary evolution
final-parsec influences 12 10-9 10-8 10-7 Frequency [Hz] 10-16 10-15 10-14 10-13 10-12 Characteristic Strain [hc(f)] McWilliams et al. (2014) Model Figure 5. Probability density plots of the recovered GWB spectra for models A and B using the broken-power-law model parameterized by (Agw, fbend, and ) as discussed in the text. The thick black lines indicate the 95% credible region and median of the GWB spectrum. The dashed line shows the 95% upper limit on the amplitude of purely GW-driven spectrum using the Gaussian priors on the amplitude from models A and B, respectively. The thin black curve shows the 95% upper limit on the GWB spectrum from the spectral analysis. 16 10-9 10-8 10-7 fturn [Hz] 103 104 105 106 ⇢ [M pc-3] 0.0 0.3 0.6 0.9 1.2 Prob. [10-6] Sesana (2013) McWilliams et al. (2014) stellar scattering hc(f) = A (f/fyr) 2/3 (1 + (fbend/f))1/2 Sampson, Cornish, McWilliams (2015) Arzoumanian et al. (2016)
final-parsec influences 12 10-9 10-8 10-7 Frequency [Hz] 10-16 10-15 10-14 10-13 10-12 Characteristic Strain [hc(f)] McWilliams et al. (2014) Model Figure 5. Probability density plots of the recovered GWB spectra for models A and B using the broken-power-law model parameterized by (Agw, fbend, and ) as discussed in the text. The thick black lines indicate the 95% credible region and median of the GWB spectrum. The dashed line shows the 95% upper limit on the amplitude of purely GW-driven spectrum using the Gaussian priors on the amplitude from models A and B, respectively. The thin black curve shows the 95% upper limit on the GWB spectrum from the spectral analysis. 16 10-9 10-8 10-7 fturn [Hz] 103 104 105 106 ⇢ [M pc-3] 0.0 0.3 0.6 0.9 1.2 Prob. [10-6] Sesana (2013) McWilliams et al. (2014) stellar scattering hc(f) = A (f/fyr) 2/3 (1 + (fbend/f))1/2 Figure 2. Eccentricity population of MBHBs detectable by ELISA/NGO and PTAs, expected in stellar and gaseous environments. Left panel: The solid histograms represent the efficient models whereas the dashed histograms are for the inefficient models. Right panel: solid his- tograms include all sources producing timing residuals above 3 ns, dashed histograms include all sources producing residual above 10 ns. mechanism (gas/star) we consider two scenarios (efficient/inefficient), to give an idea of the expected eccentricity range. The models are the following (i) gas-efficient: α = 0.3, ˙ m = 1. The migration timescale is maximized for this high values of the disc parameters, and the decoupling occurs in the very late stage of the MBHB evolution; Roedig & Sesana (2012) Sampson, Cornish, McWilliams (2015) Arzoumanian et al. (2016)
final-parsec influences 12 10-9 10-8 10-7 Frequency [Hz] 10-16 10-15 10-14 10-13 10-12 Characteristic Strain [hc(f)] McWilliams et al. (2014) Model Figure 5. Probability density plots of the recovered GWB spectra for models A and B using the broken-power-law model parameterized by (Agw, fbend, and ) as discussed in the text. The thick black lines indicate the 95% credible region and median of the GWB spectrum. The dashed line shows the 95% upper limit on the amplitude of purely GW-driven spectrum using the Gaussian priors on the amplitude from models A and B, respectively. The thin black curve shows the 95% upper limit on the GWB spectrum from the spectral analysis. 16 10-9 10-8 10-7 fturn [Hz] 103 104 105 106 ⇢ [M pc-3] 0.0 0.3 0.6 0.9 1.2 Prob. [10-6] Sesana (2013) McWilliams et al. (2014) stellar scattering hc(f) = A (f/fyr) 2/3 (1 + (fbend/f))1/2 Figure 2. Eccentricity population of MBHBs detectable by ELISA/NGO and PTAs, expected in stellar and gaseous environments. Left panel: The solid histograms represent the efficient models whereas the dashed histograms are for the inefficient models. Right panel: solid his- tograms include all sources producing timing residuals above 3 ns, dashed histograms include all sources producing residual above 10 ns. mechanism (gas/star) we consider two scenarios (efficient/inefficient), to give an idea of the expected eccentricity range. The models are the following (i) gas-efficient: α = 0.3, ˙ m = 1. The migration timescale is maximized for this high values of the disc parameters, and the decoupling occurs in the very late stage of the MBHB evolution; Roedig & Sesana (2012) Sampson, Cornish, McWilliams (2015) Arzoumanian et al. (2016) How do we model both eccentricity and the direct environment? Building analytic models is hard, especially if we want to continually expand the physical sophistication of the models.
emulation •Run a small number of expensive SMBHB population simulations. •Train a Gaussian process to learn the shape of the spectrum at different physical parameter values. •Learn the spectral variance due to finiteness of the SMBHB population. ! •We have a predictor for the shape of the spectrum, AND a measure of the uncertainty from the interpolation scheme. Searching for final-parsec influences
Process trained at a few stellar density values. • We can predict the spectral shape at any stellar density value! • Carry the interpolation uncertainty forward into our GW inference. 6 8 10 12 1 1 2 3 4 5 2 1 2 3 4 5 2 x = log10 ⇢ y = log10( Sh( f ) /A2 h) ln LGP = 1 2 ln det(2⇡K) 1 2 yT K 1y Kij = K ( xi, xj) Searching for final-parsec influences
0.4 0.6 0.8 1.0 p -0.4 -0.2 0.0 0.2 0.4 CDF(p)-p Model matches injected form GP model trained on 3 spectra GP model trained on 6 spectra GP model trained on 20 spectra Searching for final-parsec influences
the sky we need to dig into the spatial correlations. ! Matching GWB angular distribution to galaxy distributions builds confidence in SMBHBs as emitting source class. Mapping the nanohertz GW sky
pulsar response matrix [fixed] P = power in each pixel [parametrize] ab / (1 + ab) Z d2 ˆ ⌦P(ˆ ⌦) h F(ˆ ⌦)+ a F(ˆ ⌦)+ b + F(ˆ ⌦)⇥ a F(ˆ ⌦)⇥ b i = R · P · RT R ! [N psr ⇥ 2N pix ] P ! diag(2N pix ) ! [Npsr ⇥ Npsr] Mingarelli et al. (2013) Taylor & Gair (2013) Cornish & van Haasteren (2014) Taylor & van Haasteren (in prep.) Mapping the nanohertz GW sky
1) Spherical harmonics of power 4) Disk (multiple) 3) Point source (multiple) 2) Spherical harmonics of GW amplitude, not power Decompose amplitude with spherical harmonics, then square it. Avoids pesky “physical prior”
will detect nHz gravitational-waves within a decade. [Taylor et al., ApJL, 819, L6, (2016) ] ! The strain spectrum of nHz gravitational-waves encodes the final parsec of SMBHB evolution ! We can build physically-sophisticated spectral models by training Gaussian Processes on populations of binaries. Sometimes its easier to simulate the Universe than write down an equation. [with Laura Sampson and Joseph Simon, in prep.] ! We can map the gravitational-wave sky to infer the host galaxy angular distribution. [with Rutger van Haasteren, in prep.]
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