The First Bayesian Solar-System Ephemeris

Description of a new Bayesian modeling scheme of the Solar System ephemeris to mitigate uncertainties propagating into nanohertz gravitational-wave searches.

Transcript

1. THE FIRST BAYESIAN 
 SOLAR SYSTEM EPHEMERIS Stephen Taylor CALIFORNIA INSTITUTE OF TECHNOLOGY, JET PROPULSION LABORATORY © 2017 California Institute of Technology. Government sponsorship acknowledged 1
2. 2 1 2 3 4 the solar-system ephemeris JPL ephemerides modeling ephemeris uncertainties impact on GW constraints Overview
3. 3 THE SOLAR-SYSTEM EPHEMERIS
4. 4 Tracing a TOA back from an observatory to the emission time at the pulsar involves a chain of corrections The Solar-System Ephemeris tpsr e = tobs a IS B tpsr e tobs a IS B
5. 5 1 2 3 4 all TOAs are referenced to the frame of the SSB (need Roemer delay) Roemer delay dependent on masses & orbits of all important dynamical objects don’t need SSB to navigate probes to planets (accurate SSB is not a big priority) the Roemer is not fit for in Tempo2, it is subtracted based on pre-fit JPL solutions The Solar-System Ephemeris
6. 6 The Solar-System Ephemeris = ~ robs · ~ RBB c Barycenter position dependent on masses & orbits of all important dynamical objects ~ r obs = ~ r SSB EB + ~ r EB obs = ~ e(t) · ~ RBB c Roemer delay Observatory position Small error in barycenter position
7. 7 JPL EPHEMERIDES
8. 8 JPL Ephemerides Credit: M. Vallisneri J1713+0747 (quadratic subtracted)
9. 8 JPL Ephemerides Credit: M. Vallisneri J1713+0747 (quadratic subtracted) GWB amplitude of ~1e-15 translates to a post-fit RMS of ~75 ns in an 11yr dataset — van Haasteren & Levin (2013)
10. 9 upper limits and detection statistics are sensitive to our choice of ephemeris model 1 2 not obvious that most recent is “best” 3 what are the big differences between all of these DE- versions?
11. 10 MODELING EPHEMERIS UNCERTAINTIES
12. 11 Modeling Ephemeris Uncertainties timing model white noise intrinsic red noise common red noise (or GWB) Current Bayesian Model ephemeris uncertainty term Expanded Model marginalize over ephemeris differences to isolate GW signal from choice of DE— GOAL
13. 12 Modeling Ephemeris Uncertainties ephemeris uncertainty term physically motivated • Fourier expansion of barycenter error vector [Lentati, Taylor, Mingarelli et al. (2015)] • planet mass perturbation [Champion et al. (2010)] • dipolar spatially-correlated red process phenomenological • Roemer mixture model • PCA of Roemer delays from DE421, DE430, etc. to construct empirical basis • [maybe] PCA of Roemer delays from many, many perturbed ephemerides
14. 12 Modeling Ephemeris Uncertainties ephemeris uncertainty term physically motivated • Fourier expansion of barycenter error vector [Lentati, Taylor, Mingarelli et al. (2015)] • planet mass perturbation [Champion et al. (2010)] • dipolar spatially-correlated red process phenomenological • Roemer mixture model • PCA of Roemer delays from DE421, DE430, etc. to construct empirical basis • [maybe] PCA of Roemer delays from many, many perturbed ephemerides
15. 12 Modeling Ephemeris Uncertainties ephemeris uncertainty term physically motivated • Fourier expansion of barycenter error vector [Lentati, Taylor, Mingarelli et al. (2015)] • planet mass perturbation [Champion et al. (2010)] • dipolar spatially-correlated red process phenomenological • Roemer mixture model • PCA of Roemer delays from DE421, DE430, etc. to construct empirical basis • [maybe] PCA of Roemer delays from many, many perturbed ephemerides
16. 13 Physical Ephemeris Uncertainty Model Model is 11-D 1 frame drift-rate about ecliptic “z” 1 Uranus mass perturbation (constrained by IAU prior) 1 Neptune mass perturbation (constrained by IAU prior) 6 Jupiter orbital element perturbations 1 Saturn mass perturbation (constrained by IAU prior) 1 Jupiter mass perturbation (constrained by IAU prior) (1) semi-major axis (2) eccentricity (3) inclination (4) longitude of the ascending node (5) longitude of perihelion (6) mean longitude
17. 14 IMPACT ON GW CONSTRAINTS
18. 15 Physical Ephemeris Uncertainty Model Upper limit (for all connected) ~ 1.34e-15 Uninformative Jupiter orbit priors 11-year
19. 16 Physical Ephemeris Uncertainty Model Highly-informative Jupiter orbit priors (from JPL) Upper limit (DE435, DE436) ~ 1.53e-15 11-year
20. 17 Physical Ephemeris Uncertainty Model purple = prior distribution blue = DE435 (uninformative prior) orange = DE436 (uninformative prior) green = DE435 (JPL prior) red = DE436 (JPL prior) 11-year
21. 17 Physical Ephemeris Uncertainty Model purple = prior distribution blue = DE435 (uninformative prior) orange = DE436 (uninformative prior) green = DE435 (JPL prior) red = DE436 (JPL prior) 11-year l0 + r [⇥10 6] p [⇥10 6] q [⇥10 7] e r [⇥10 7] a/a [⇥10 7] e [⇥10 7] Set III celestial mechanics coordinates
22. 18 Physical Ephemeris Uncertainty Model Uninformative Jupiter orbit priors Upper limit (for all connected) ~ 2.7e-15 9-year
23. 19 Physical Ephemeris Uncertainty Model weak GWB injection — 36 pulsars — 11 years — equally sampled w/ 500 ns precision — dataset created under DE436 — dashed = no ephemeris uncertainty modeling — solid = physical ephemeris uncertainty model
24. 20 Physical Ephemeris Uncertainty Model moderate GWB injection — 36 pulsars — 11 years — equally sampled w/ 500 ns precision — dataset created under DE436 — dashed = no ephemeris uncertainty modeling — solid = physical ephemeris uncertainty model
25. 21 Physical Ephemeris Uncertainty Model 11-year dataset simulations Uninformative Jupiter orbit priors (created with exactly the same pulsars, noise properties, and sensitivity as the real dataset)
26. 22 1 2 3 4 choice of solar-system ephemeris affects GW upper limits and detection statistics our physical model perturbs gas-giant masses, and Jupiter’s orbit to bridge all ephemerides with this new model (BayesEphem) the upper- limit is 1.34e-15 (1.46e-15) for a common red process (GW background) Summary & Outlook these are the first robust nHz GW constraints