Update On Ephemeris Uncertainty Modeling

Update to colleagues on the development of new methods to construct a Bayesian solar-system ephemeris model.

Transcript

1. UPDATE ON EPHEMERIS UNCERTAINTY MODELING Stephen Taylor & Michele Vallisneri JET PROPULSION LABORATORY, CALIFORNIA INSTITUTE OF TECHNOLOGY © 2017 California Institute of Technology. Government sponsorship acknowledged 1
2. 2 Physical Ephemeris Uncertainty Model def ssephem_physical_model(x, mjd, earth, jupiter, uranus, neptune, equatorial=True): # it's a twelve parameter model (with argument x, see below for priors). # Feed it the TOA vector (size n) and Earth-to-SSB, Jupiter-to-SSB, etc. # (n,3) arrays. Set equatorial=True or False depending on the tempo2 # coordinate frame, which matches the par-file coordinates. # frame rotation (three angles, a rate, and an absolute offset) earth = ss_framerotate(mjd, earth, x[0], x[1], x[2], x[3], offset=x[4:7], equatorial=equatorial) # uranus mass perturbation earth = dmass(earth,uranus,x[7]) # neptune mass perturbation earth = dmass(earth,neptune,x[8]) # rotate jupiter earth = dorbit(mjd, earth, jupiter, x[9], x[10], x[11], 0.0, 0.0009547918983127075) return earth frame rotation Uranus mass Neptune mass Jupiter orbit
3. 3 Physical Ephemeris Uncertainty Model Model is 12-D 3 frame rotation angles 1 frame-rotation rate about ecliptic “z” 3 Earth absolute-offset parameters 1 Uranus mass perturbation 1 Neptune mass perturbation 3 Jupiter orbit rotation angles
4. 4 1 2 3 4 remove tempo2 geocenter to barycenter correction construct new roemer (geo. to bary.) from physical model add to residuals Physical Ephemeris Uncertainty Model still use tempo2 geocenter to observatory correction 5 search over physical ephemeris parameters along with pulsar noise & GWB
5. 5 Physical Ephemeris Uncertainty Model original priors wider jupiter-orbit priors wider planet-mass priors same wider priors, fixed 1713 sky position
6. 6 4 2 0 2 4 earth-yang ⇥10 9 4 2 0 2 4 earth-zang ⇥10 7 0 2 4 6 8 earth-zang-rotate ⇥10 11 0.8 0.4 0.0 0.4 0.8 earth-xoffset ⇥10 8 4 2 0 2 4 earth-yoffset ⇥10 9 8 4 0 4 8 earth-zoffset ⇥10 11 3.0 1.5 0.0 1.5 3.0 uranus-dmass ⇥10 10 4 2 0 2 4 neptune-dmass ⇥10 10 6 4 2 0 jupiter-xang ⇥10 8 0.3 0.0 0.3 0.6 0.9 jupiter-yang ⇥10 7 0.8 0.4 0.0 0.4 0.8 earth-xang ⇥10 9 1.5 0.0 1.5 3.0 4.5 jupiter-zang ⇥10 8 4 2 0 2 4 earth-yang ⇥10 9 4 2 0 2 4 earth-zang ⇥10 7 0 2 4 6 8 earth-zang-rotate ⇥10 11 0.8 0.4 0.0 0.4 0.8 earth-xoffset ⇥10 8 4 2 0 2 4 earth-yoffset ⇥10 9 8 4 0 4 8 earth-zoffset ⇥10 11 3.0 1.5 0.0 1.5 3.0 uranus-dmass ⇥10 10 4 2 0 2 4 neptune-dmass ⇥10 10 6 4 2 0 jupiter-xang ⇥10 8 0.3 0.0 0.3 0.6 0.9 jupiter-yang ⇥10 7 1.5 0.0 1.5 3.0 4.5 jupiter-zang ⇥10 8 Physical Ephemeris Uncertainty Model DE421 —wide mass priors, —wide jupiter orbit priors, — p u l s a r l o c a t i o n s marginalized over
7. 7 4 2 0 2 4 earth-yang ⇥10 9 4 2 0 2 4 earth-zang ⇥10 7 3.0 1.5 0.0 1.5 3.0 earth-zang-rotate ⇥10 11 0.8 0.4 0.0 0.4 0.8 earth-xoffset ⇥10 8 4 2 0 2 4 earth-yoffset ⇥10 9 8 4 0 4 8 earth-zoffset ⇥10 11 3.0 1.5 0.0 1.5 3.0 uranus-dmass ⇥10 10 4 2 0 2 4 neptune-dmass ⇥10 10 5.0 2.5 0.0 2.5 jupiter-xang ⇥10 8 8 4 0 4 jupiter-yang ⇥10 8 0.8 0.4 0.0 0.4 0.8 earth-xang ⇥10 9 2 0 2 4 6 jupiter-zang ⇥10 8 4 2 0 2 4 earth-yang ⇥10 9 4 2 0 2 4 earth-zang ⇥10 7 3.0 1.5 0.0 1.5 3.0 earth-zang-rotate ⇥10 11 0.8 0.4 0.0 0.4 0.8 earth-xoffset ⇥10 8 4 2 0 2 4 earth-yoffset ⇥10 9 8 4 0 4 8 earth-zoffset ⇥10 11 3.0 1.5 0.0 1.5 3.0 uranus-dmass ⇥10 10 4 2 0 2 4 neptune-dmass ⇥10 10 5.0 2.5 0.0 2.5 jupiter-xang ⇥10 8 8 4 0 4 jupiter-yang ⇥10 8 2 0 2 4 6 jupiter-zang ⇥10 8 Physical Ephemeris Uncertainty Model DE430 —wide mass priors, —wide jupiter orbit priors, — p u l s a r l o c a t i o n s marginalized over
8. 8 4 2 0 2 4 earth-yang ⇥10 9 4 2 0 2 4 earth-zang ⇥10 7 2 0 2 4 earth-zang-rotate ⇥10 11 0.8 0.4 0.0 0.4 0.8 earth-xoffset ⇥10 8 4 2 0 2 4 earth-yoffset ⇥10 9 8 4 0 4 8 earth-zoffset ⇥10 11 3.0 1.5 0.0 1.5 3.0 uranus-dmass ⇥10 10 4 2 0 2 4 neptune-dmass ⇥10 10 2 0 2 4 6 jupiter-xang ⇥10 8 3 0 3 6 jupiter-yang ⇥10 8 0.8 0.4 0.0 0.4 0.8 earth-xang ⇥10 9 0 2 4 jupiter-zang ⇥10 8 4 2 0 2 4 earth-yang ⇥10 9 4 2 0 2 4 earth-zang ⇥10 7 2 0 2 4 earth-zang-rotate ⇥10 11 0.8 0.4 0.0 0.4 0.8 earth-xoffset ⇥10 8 4 2 0 2 4 earth-yoffset ⇥10 9 8 4 0 4 8 earth-zoffset ⇥10 11 3.0 1.5 0.0 1.5 3.0 uranus-dmass ⇥10 10 4 2 0 2 4 neptune-dmass ⇥10 10 2 0 2 4 6 jupiter-xang ⇥10 8 3 0 3 6 jupiter-yang ⇥10 8 0 2 4 jupiter-zang ⇥10 8 Physical Ephemeris Uncertainty Model DE435 —wide mass priors, —wide jupiter orbit priors, — p u l s a r l o c a t i o n s marginalized over
9. 9 4 2 0 2 4 earth-yang ⇥10 9 4 2 0 2 4 earth-zang ⇥10 7 3.0 1.5 0.0 1.5 3.0 earth-zang-rotate ⇥10 11 0.8 0.4 0.0 0.4 0.8 earth-xoffset ⇥10 8 4 2 0 2 4 earth-yoffset ⇥10 9 8 4 0 4 8 earth-zoffset ⇥10 11 3.0 1.5 0.0 1.5 3.0 uranus-dmass ⇥10 10 4 2 0 2 4 neptune-dmass ⇥10 10 2 0 2 4 jupiter-xang ⇥10 8 6 3 0 3 6 jupiter-yang ⇥10 8 0.8 0.4 0.0 0.4 0.8 earth-xang ⇥10 9 3.0 1.5 0.0 1.5 3.0 jupiter-zang ⇥10 8 4 2 0 2 4 earth-yang ⇥10 9 4 2 0 2 4 earth-zang ⇥10 7 3.0 1.5 0.0 1.5 3.0 earth-zang-rotate ⇥10 11 0.8 0.4 0.0 0.4 0.8 earth-xoffset ⇥10 8 4 2 0 2 4 earth-yoffset ⇥10 9 8 4 0 4 8 earth-zoffset ⇥10 11 3.0 1.5 0.0 1.5 3.0 uranus-dmass ⇥10 10 4 2 0 2 4 neptune-dmass ⇥10 10 2 0 2 4 jupiter-xang ⇥10 8 6 3 0 3 6 jupiter-yang ⇥10 8 3.0 1.5 0.0 1.5 3.0 jupiter-zang ⇥10 8 Physical Ephemeris Uncertainty Model DE436 —wide mass priors, —wide jupiter orbit priors, — p u l s a r l o c a t i o n s marginalized over
10. 10 1.2 1.3 1.4 1.5 1.6 earth-yang ⇥10 9 2 4 6 8 earth-zang ⇥10 10 6 3 0 3 6 earth-zang-rotate ⇥10 11 0.8 0.4 0.0 0.4 0.8 earth-xoffset ⇥10 8 4 2 0 2 4 earth-yoffset ⇥10 9 8 4 0 4 8 earth-zoffset ⇥10 11 3.0 1.5 0.0 1.5 3.0 uranus-dmass ⇥10 10 4 2 0 2 4 neptune-dmass ⇥10 10 6 4 2 0 jupiter-xang ⇥10 8 3 0 3 6 jupiter-yang ⇥10 8 3.0 1.5 0.0 1.5 earth-xang ⇥10 10 1.5 0.0 1.5 3.0 4.5 jupiter-zang ⇥10 8 1.2 1.3 1.4 1.5 1.6 earth-yang ⇥10 9 2 4 6 8 earth-zang ⇥10 10 6 3 0 3 6 earth-zang-rotate ⇥10 11 0.8 0.4 0.0 0.4 0.8 earth-xoffset ⇥10 8 4 2 0 2 4 earth-yoffset ⇥10 9 8 4 0 4 8 earth-zoffset ⇥10 11 3.0 1.5 0.0 1.5 3.0 uranus-dmass ⇥10 10 4 2 0 2 4 neptune-dmass ⇥10 10 6 4 2 0 jupiter-xang ⇥10 8 3 0 3 6 jupiter-yang ⇥10 8 1.5 0.0 1.5 3.0 4.5 jupiter-zang ⇥10 8 Physical Ephemeris Uncertainty Model DE421 —wide mass priors, —wide jupiter orbit priors, —all pulsar locations fixed
11. 11 Physical Ephemeris Uncertainty Model 2.4 1.8 1.2 0.6 0.0 earth-yang ⇥10 10 5.5 5.0 4.5 4.0 earth-zang ⇥10 10 1 0 1 2 earth-zang-rotate ⇥10 11 0.8 0.4 0.0 0.4 0.8 earth-xoffset ⇥10 8 4 2 0 2 4 earth-yoffset ⇥10 9 8 4 0 4 8 earth-zoffset ⇥10 11 3.0 1.5 0.0 1.5 3.0 uranus-dmass ⇥10 10 4 2 0 2 4 neptune-dmass ⇥10 10 6 4 2 0 2 jupiter-xang ⇥10 8 0.8 0.4 0.0 0.4 0.8 jupiter-yang ⇥10 7 2.4 3.2 4.0 4.8 earth-xang ⇥10 10 2 0 2 4 jupiter-zang ⇥10 8 2.4 1.8 1.2 0.6 0.0 earth-yang ⇥10 10 5.5 5.0 4.5 4.0 earth-zang ⇥10 10 1 0 1 2 earth-zang-rotate ⇥10 11 0.8 0.4 0.0 0.4 0.8 earth-xoffset ⇥10 8 4 2 0 2 4 earth-yoffset ⇥10 9 8 4 0 4 8 earth-zoffset ⇥10 11 3.0 1.5 0.0 1.5 3.0 uranus-dmass ⇥10 10 4 2 0 2 4 neptune-dmass ⇥10 10 6 4 2 0 2 jupiter-xang ⇥10 8 0.8 0.4 0.0 0.4 0.8 jupiter-yang ⇥10 7 2 0 2 4 jupiter-zang ⇥10 8 DE430 —wide mass priors, —wide jupiter orbit priors, —all pulsar locations fixed
12. 12 1.6 0.8 0.0 0.8 earth-yang ⇥10 10 1.0 0.5 0.0 0.5 earth-zang ⇥10 10 1.5 0.0 1.5 earth-zang-rotate ⇥10 11 0.8 0.4 0.0 0.4 0.8 earth-xoffset ⇥10 8 4 2 0 2 4 earth-yoffset ⇥10 9 8 4 0 4 8 earth-zoffset ⇥10 11 3.0 1.5 0.0 1.5 3.0 uranus-dmass ⇥10 10 4 2 0 2 4 neptune-dmass ⇥10 10 2 0 2 4 6 jupiter-xang ⇥10 8 3 0 3 6 jupiter-yang ⇥10 8 1.6 0.8 0.0 0.8 earth-xang ⇥10 10 0 2 4 jupiter-zang ⇥10 8 1.6 0.8 0.0 0.8 earth-yang ⇥10 10 1.0 0.5 0.0 0.5 earth-zang ⇥10 10 1.5 0.0 1.5 earth-zang-rotate ⇥10 11 0.8 0.4 0.0 0.4 0.8 earth-xoffset ⇥10 8 4 2 0 2 4 earth-yoffset ⇥10 9 8 4 0 4 8 earth-zoffset ⇥10 11 3.0 1.5 0.0 1.5 3.0 uranus-dmass ⇥10 10 4 2 0 2 4 neptune-dmass ⇥10 10 2 0 2 4 6 jupiter-xang ⇥10 8 3 0 3 6 jupiter-yang ⇥10 8 0 2 4 jupiter-zang ⇥10 8 Physical Ephemeris Uncertainty Model DE435 —wide mass priors, —wide jupiter orbit priors, —all pulsar locations fixed
13. 13 1.2 0.6 0.0 0.6 earth-yang ⇥10 10 1.2 0.8 0.4 0.0 0.4 earth-zang ⇥10 10 2 1 0 1 earth-zang-rotate ⇥10 11 0.8 0.4 0.0 0.4 0.8 earth-xoffset ⇥10 8 4 2 0 2 4 earth-yoffset ⇥10 9 8 4 0 4 8 earth-zoffset ⇥10 11 3.0 1.5 0.0 1.5 3.0 uranus-dmass ⇥10 10 4 2 0 2 4 neptune-dmass ⇥10 10 1.5 0.0 1.5 3.0 4.5 jupiter-xang ⇥10 8 5.0 2.5 0.0 2.5 jupiter-yang ⇥10 8 1.2 0.6 0.0 0.6 earth-xang ⇥10 10 1.5 0.0 1.5 3.0 jupiter-zang ⇥10 8 1.2 0.6 0.0 0.6 earth-yang ⇥10 10 1.2 0.8 0.4 0.0 0.4 earth-zang ⇥10 10 2 1 0 1 earth-zang-rotate ⇥10 11 0.8 0.4 0.0 0.4 0.8 earth-xoffset ⇥10 8 4 2 0 2 4 earth-yoffset ⇥10 9 8 4 0 4 8 earth-zoffset ⇥10 11 3.0 1.5 0.0 1.5 3.0 uranus-dmass ⇥10 10 4 2 0 2 4 neptune-dmass ⇥10 10 1.5 0.0 1.5 3.0 4.5 jupiter-xang ⇥10 8 5.0 2.5 0.0 2.5 jupiter-yang ⇥10 8 1.5 0.0 1.5 3.0 jupiter-zang ⇥10 8 Physical Ephemeris Uncertainty Model DE436 —wide mass priors, —wide jupiter orbit priors, —all pulsar locations fixed
14. 14 Physical Ephemeris Uncertainty Model Next steps are to — widen Uranus and Neptune mass perturbation priors — add a Jupiter mass perturbation