Institute of Technology. Government sponsorship acknowledged Stephen R. Taylor Probing The Nanohertz GW Landscape With Pulsar Timing Arrays: A Status Report JET PROPULSION LABORATORY, CALIFORNIA INSTITUTE OF TECHNOLOGY
Searching for gravitational waves Supermassive black-hole binaries as sources of nanohertz gravitational waves Impact of binary environments on GW signals. The Solar-system Ephemeris: our new noise floor.
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
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
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
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 Other sources in the nHz band may be decaying cosmic-string networks, or relic GWs from the early Universe
How do we build a stochastic signal from these binaries, and how do the different physical processes affect the spectrum? h2 c (f) = Z 1 0 dz Z 1 0 dM1 Z 1 0 dq d4N dzdM1dqdtr dtr d ln fK,r ⇥h2(fK,r) 1 X n=1 g[n, e(fK,r)] (n/2)2 f nfK,r (1 + z) e.g. Phinney (2001), Sesana (2013)
How do we build a stochastic signal from these binaries, and how do the different physical processes affect the spectrum? h2 c (f) = Z 1 0 dz Z 1 0 dM1 Z 1 0 dq d4N dzdM1dqdtr dtr d ln fK,r ⇥h2(fK,r) 1 X n=1 g[n, e(fK,r)] (n/2)2 f nfK,r (1 + z) e.g. Phinney (2001), Sesana (2013) (a) (b) (c) (a) Comoving merger rate — affects overall signal level (b)Binary evolution — affects shape of spectrum through time binaries spend emitting at each frequency (binary environmental influences enter here) (c) Eccentricity — affects shape of spectrum through binary orbital evolution
the characteristic strain amplitude at a GW frequency of 1/yr (~32 nHz) . 3.0 ⇥ 10 15 Environmental Coupling • Stellar hardening • Gas-driven inspiral • Eccentricity Galaxy Population Uncertainties • Merger timescale • SMBH - host relations • Pair fraction • Redshift evolution Diminished GW Signal • BSMBH stalling • GW absorption Characteristic strain, hc 1E-17 1E-16 1E-15 1E-14 1E-13 1E-12 Gravitational Wave Frequency, f (Hz) 1E-10 1E-09 1E-08 1E-07 1E-06 hc f 10.— A conceptual view of how various uncertainties in the BSMBH population and the GWs we can Burke-Spolaor (2015) Sources & Spectrum
the characteristic strain amplitude at a GW frequency of 1/yr (~32 nHz) . 3.0 ⇥ 10 15 Environmental Coupling • Stellar hardening • Gas-driven inspiral • Eccentricity Galaxy Population Uncertainties • Merger timescale • SMBH - host relations • Pair fraction • Redshift evolution Diminished GW Signal • BSMBH stalling • GW absorption Characteristic strain, hc 1E-17 1E-16 1E-15 1E-14 1E-13 1E-12 Gravitational Wave Frequency, f (Hz) 1E-10 1E-09 1E-08 1E-07 1E-06 hc f 10.— A conceptual view of how various uncertainties in the BSMBH population and the GWs we can Final- parsec physics Merger rate, BH-galaxy relationships Burke-Spolaor (2015) Sources & Spectrum
Dynamical friction not a sufficient driving mechanism to induce merger within a Hubble time e.g., Milosavljevic & Merritt (2003) Supermassive black-hole binary evolution
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
t/d ln f term) of this equation (see Colpi 2014, for a w of SMBHB coalescence). Following Sampson et al. 5) we can generalize the frequency dependence of the n spectrum to dt d ln f = f ✓ d f dt ◆-1 = f X i ✓ d f dt ◆ i !-1 , (23) e i ranges over many physical processes that are driv- he binary to coalescence. If we restrict this sum to GW- n evolution and an unspecified physical process then the n spectrum is now hc (f) = A (f/fyr )↵ 1+(fbend/f) 1/2 , (24) Binary evolution will be dominated by environment at low frequencies, and radiation reaction at high frequencies dt d ln f = f " X i df dt i # Following Sampson & Cornish (2015), NANOGrav [Arzoumanian et al. (2016)] modeled the GW strain spectrum with a low- frequency turnover
t/d ln f term) of this equation (see Colpi 2014, for a w of SMBHB coalescence). Following Sampson et al. 5) we can generalize the frequency dependence of the n spectrum to dt d ln f = f ✓ d f dt ◆-1 = f X i ✓ d f dt ◆ i !-1 , (23) e i ranges over many physical processes that are driv- he binary to coalescence. If we restrict this sum to GW- n evolution and an unspecified physical process then the n spectrum is now hc (f) = A (f/fyr )↵ 1+(fbend/f) 1/2 , (24) Binary evolution will be dominated by environment at low frequencies, and radiation reaction at high frequencies dt d ln f = f " X i df dt i # 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 10-9 10-8 10-7 Frequency [Hz] 10-16 10-15 10-14 10-13 10-12 Characteristic Strain [hc( f)] Sesana et al. (2013) Model Following Sampson & Cornish (2015), NANOGrav [Arzoumanian et al. (2016)] modeled the GW strain spectrum with a low- frequency turnover B = 22 B = 2.2
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 10-9 10-8 10-7 fturn [Hz] 10-2 10-1 100 101 102 ˙ M1 [M yr-1] 0.0000 0.0025 0.0050 0.0075 0.0100 Prob. Sesana (2013) McWilliams et al. (2014) circumbinary disk Probing Final-parsec Processes eft) and ˙ M1 (right). (bottom): Posterior distributions for the mass density of stars in the galactic core m a circumbinary disk (right). These distributions are constructed by first converting the marginalized ), and then using the empirical mapping described in the text to convert from fturn to the astrophysical rresponding in- quency is main- n of black holes mponent or red- of lower mass o smaller stellar 10. Varying the relation such pact on the envi- n eccentricity nt of SMBH bi- stic strain spec- t GWs at a spec- The cumulative o a depletion of al. 2007; Sesana and a turnover trized spectrum an use our fturn ver all to de- 10-9 10-8 10-7 fturn [Hz] 0.3 0.4 0.5 0.6 0.7 0.8 0.9 e0 0 2 4 6 8 Prob. Sesana (2013) McWilliams et al. (2014) Figure 11. Same as Figure 10 except now we display the empirical map- binary eccentricity
a bank of spectral shapes from population simulations (including all physics). Train a Gaussian Process to learn the spectral properties. Provides a fast physically-trained model. Can be trivially expanded. Build a semi-analytic model to probe loss- cone scattering. Also expand merger-rate density with simplified prescription. Taylor et al., PRL 118, 181102 (2017) Chen et al., arXiv:1612.02826
Ephemeris All TOAs referenced to the SSB. Location of SSB requires the masses and trajectories of all objects in solar-system. JPL do not really care about the position of the SSB. They care about navigating probes to planets. The ephemeris time-series has not usually been fit for in our PTA analysis. It has been subtracted.
Results Bayes factor for a common red process (i.e. leaving out H&D correlations) versus noise range from ~1 (DE435) to ~10 (DE430). It is crucial to marginalize over the difference in the ephemeris uncertainties for robust GW statistics. 18 17 16 15 log10 AGWB 10 3 10 2 10 1 100 Deterministic object-mass perturbation model 9 objects (Mercury to Pluto) DE421 DE430 DE435 DE436 18 17 16 15 log10 AGWB 10 3 10 2 10 1 100 Power-law ephemeris model 30 linear-spaced frequencies (1/T to 30/T) DE421 DE430 DE435 DE436 PRELIMINARY
Results Bayes factor for a common red process (i.e. leaving out H&D correlations) versus noise range from ~1 (DE435) to ~10 (DE430). It is crucial to marginalize over the difference in the ephemeris uncertainties for robust GW statistics. PRELIMINARY
expected to make a GW detection within ~5-10 years. The GW strain spectrum encodes information about SMBHB dynamical evolution. Constraining the spectral shape can tell us about disc accretion, and loss-scone scattering. PTAs are now sensitive to the solar-system ephemeris. A huge milestone for us!
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