Solar-system Ephemeris Uncertainties & GW Constraints

Presentation given at NANOGrav Spring meeting at West Virginia University.

Transcript

1. Stephen Taylor NANOGrav Spring Meeting, WVU, 04/20/2017 © 2017 California Institute of Technology. Government sponsorship acknowledged Stephen R. Taylor Solar System Ephemeris Uncertainties & GW Constraints JET PROPULSION LABORATORY, CALIFORNIA INSTITUTE OF TECHNOLOGY (…or “How do you solve a problem like Ephemeria?”) barycenter
2. Stephen Taylor NANOGrav Spring Meeting, WVU, 04/20/2017 Overview The Solar System ephemeris. JPL ephemerides. Modeling Solar-system ephemeris uncertainties. Impact on GW constraints, including preliminary11yr dataset results. Outlook and potential avenues for future study.
3. Stephen Taylor NANOGrav Spring Meeting, WVU, 04/20/2017 The Solar System Ephemeris All TOAs are referenced to the solar-system barycenter. Roemer delay. Computing the location of the barycenter requires the masses and trajectories of all important dynamical objects in solar-system. JPL do not really care about the barycenter. They care about navigating probes to planets. The ephemeris time-series is not fit for in Tempo2. It is subtracted.
4. Stephen Taylor NANOGrav Spring Meeting, WVU, 04/20/2017 “The Problem”
5. Stephen Taylor NANOGrav Spring Meeting, WVU, 04/20/2017 “The Problem” NANOGrav DWG
6. Stephen Taylor NANOGrav Spring Meeting, WVU, 04/20/2017 JPL ephemerides DE435 Created in Jan 2016 for the Cassini project, this is primarily an incremental improvement in the orbit of Saturn. Jupiter had already been updated in DE434 for the Juno mission. DE436 is a small improvement on DE435.
7. Stephen Taylor NANOGrav Spring Meeting, WVU, 04/20/2017 Quadratic and 1-yr sinusoid removed BIG DIFFERENCES! — Need to understand how this impacts GW searches Figure by M. Vallisneri JPL ephemerides
8. Stephen Taylor NANOGrav Spring Meeting, WVU, 04/20/2017 Modeling ephemeris uncertainties Introduce an ephemeris uncertainty term in our full model. This is a perturbation to the ephemeris. Should be able to marginalize over this perturbation, regardless of which JPL version we start from. We want to “connect” the results of all the ephemerides. Isolate GW constraints from the choice of ephemeris.
9. Stephen Taylor NANOGrav Spring Meeting, WVU, 04/20/2017 Ephemeris uncertainties as a Gaussian process Lentati, Taylor, Mingarelli et al. (2015), MNRAS, 453, 2576, arXiv:1504.03692 Just like red-noise or the GWB, we marginalize over “a” with a Gaussian prior. We parametrize the power in the error vector along each direction. Power spectrum model can be power-law, free-spectral, etc.
10. Stephen Taylor NANOGrav Spring Meeting, WVU, 04/20/2017 Simulate a PTA dataset. Inject an ephemeris uncertainty at Jupiter periodicity. Nothing else in dataset. Our model correctly isolates the ephemeris uncertainty, with no leakage into a common red process. Figure by J. Ellis
11. Stephen Taylor NANOGrav Spring Meeting, WVU, 04/20/2017 14.1 13.9 13.7 13.5 13.3 log10 Agwb 3.8 4.0 4.2 4.4 4.6 4.8 5.0 5.2 gwb 14.2 14.0 13.8 13.6 13.4 13.2 13.0 log10 Aclk 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 clk 9.0 8.8 8.6 8.4 8.2 log10 (| Mjup. |/M ) 0.0 0.2 0.4 0.6 0.8 1.0 sgn( Mjup. ) Taylor et al. (2017a), PRD, 95, 042002, arXiv:1606.09180 Deterministic planet-mass perturbations Model is a Roemer delay perturbation, as in Champion et al. (2010).
12. Stephen Taylor NANOGrav Spring Meeting, WVU, 04/20/2017 Modeling uncertainties in the true ephemerides Simulate 36 pulsars (IPTA MDC), with 11.4 yr baseline (same as NANOGrav 11yr dataset). 500 ns precision. No other processes in data. Create dataset with DE436. Analyze with others. Power-law red process for {x,y,z} ephemeris time-series
13. Stephen Taylor NANOGrav Spring Meeting, WVU, 04/20/2017 Perturbing the planet masses in Roemer delay correction. Modeling uncertainties in the true ephemerides
14. Stephen Taylor NANOGrav Spring Meeting, WVU, 04/20/2017 Creating a weighted mixture of Roemer delays from DE421, DE430, DE435, DE436 -> let the data figure out what it wants… Modeling uncertainties in the true ephemerides
15. Stephen Taylor NANOGrav Spring Meeting, WVU, 04/20/2017 Preliminary NANOGrav 11yr Results 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 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
16. Stephen Taylor NANOGrav Spring Meeting, WVU, 04/20/2017 Preliminary NANOGrav 11yr Results PRELIMINARY
17. Stephen Taylor NANOGrav Spring Meeting, WVU, 04/20/2017 Summary & Outlook
18. Stephen Taylor NANOGrav Spring Meeting, WVU, 04/20/2017 Summary & Outlook Ephemerides affect upper limits and detection statistics. Our models perturb the Roemer delay to attempt to account for offsets in the ephemerides. These are not yet good enough to “connect” the results of the different JPL ephemerides (DE421, DE430, DE435, …).
19. Stephen Taylor NANOGrav Spring Meeting, WVU, 04/20/2017 Summary & Outlook Ephemerides affect upper limits and detection statistics. Our models perturb the Roemer delay to attempt to account for offsets in the ephemerides. These are not yet good enough to “connect” the results of the different JPL ephemerides (DE421, DE430, DE435, …). Options being developed: Perturb planet trajectory. Use dense low-frequency spectral coefficients to mitigate potential ephemeris spectral leakage from low frequencies. Work with ephemeris team at JPL to construct a search basis out of “perturbed" ephemerides. Are there pulsars in advantageous positions to minimize ephemeris uncertainties?
20. Stephen Taylor NANOGrav Spring Meeting, WVU, 04/20/2017 Provocative Question
21. Stephen Taylor NANOGrav Spring Meeting, WVU, 04/20/2017 Provocative Question Do we want to “connect” the different ephemerides to get the same GWB amplitude posterior?
22. Stephen Taylor NANOGrav Spring Meeting, WVU, 04/20/2017 Provocative Question Do we want to “connect” the different ephemerides to get the same GWB amplitude posterior?
23. Stephen Taylor NANOGrav Spring Meeting, WVU, 04/20/2017 Provocative Question Do we want to “connect” the different ephemerides to get the same GWB amplitude posterior? If one ephemeris is closer to being “right”, then the size of any uncertainty term in our Bayesian analysis will be smaller.
24. Stephen Taylor NANOGrav Spring Meeting, WVU, 04/20/2017 Provocative Question Do we want to “connect” the different ephemerides to get the same GWB amplitude posterior? If one ephemeris is closer to being “right”, then the size of any uncertainty term in our Bayesian analysis will be smaller. e.g. DE430 DE421 DE436 DE435 TRUTH
25. Stephen Taylor NANOGrav Spring Meeting, WVU, 04/20/2017 Provocative Question Do we want to “connect” the different ephemerides to get the same GWB amplitude posterior? If one ephemeris is closer to being “right”, then the size of any uncertainty term in our Bayesian analysis will be smaller. e.g. DE430 DE421 DE436 DE435 TRUTH Maybe test for ephemeris version with least evidence for an ephemeris uncertainty. That one is the closest to being “right”.
26. Stephen Taylor NANOGrav Spring Meeting, WVU, 04/20/2017 Even More Provocative Question How do we move forward?
27. Stephen Taylor NANOGrav Spring Meeting, WVU, 04/20/2017 Even More Provocative Question How do we move forward?