Update 2 On Ephemeris Uncertainty Modeling

Further updates on new advances 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 Telecon 2 (08/29/2017)
2. 2 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
3. 3 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 MARK I model
4. 4 Physical Ephemeris Uncertainty Model …where we left off last telecon MARK I model — 36 pulsars — 11 years — equally sampled w/ 500 ns precision — dataset created under DE436 — dashed = no ephemeris uncertainty modeling — solid = physical ephemeris uncertainty model …once we widened Uranus/Neptune mass priors, then added Jupiter/Saturn mass perturbations, DE430 connected with the other ephemerides Sim, Agwb = 0 —But required mass perturbations were HUGE (way beyond IAU uncertainties) Real 11yr data MARK I model However, we still could not connect the ephemeris results in the true dataset…
5. 5 Physical Ephemeris Uncertainty Model def ssephem_physical_model(x, mjd, earth, jupiter, uranus, neptune, equatorial=True): # frame rotation (only ecliptic-z drift rate can be constrained) earth = ss_framerotate(mjd, earth, x[0], offset=None, equatorial=equatorial) # jupiter mass perturbation earth = dmass(earth,uranus,x[1]) # saturn mass perturbation earth = dmass(earth,neptune,x[2]) # uranus mass perturbation earth = dmass(earth,uranus,x[3]) # neptune mass perturbation earth = dmass(earth,neptune,x[4]) # perturb jupiter’s orbital elements jup_perturb_tmp = 0.0009547918983127075 * np.einsum(‘i,ijk->jk', x[5:11], jup_orbelxyz) earth += np.array([np.interp(mjd, jup_mjd, jup_perturb_tmp[:,aa]) for aa in range(3)]).T return earth frame drift Uranus mass Neptune mass Jupiter orbit MARK II model Jupiter mass Saturn mass
6. 6 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
7. 7 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
8. 8 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
9. 9 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
10. 10 Physical Ephemeris Uncertainty Model strong GWB injection — dashed = no ephemeris uncertainty modeling — solid = physical ephemeris uncertainty model — 36 pulsars — 11 years — equally sampled w/ 500 ns precision — dataset created under DE436
11. 11 Physical Ephemeris Uncertainty Model — dashed = no ephemeris uncertainty modeling — solid = physical ephemeris uncertainty model — 36 pulsars — 11 years — equally sampled w/ 500 ns precision — dataset created under DE436 no GWB injection — DE418 and DE430 give significant signals here without ephemeris modeling — Mark I and Mark II models take care of that — But Mark II can do this with IAU mass priors
12. 12 Physical Ephemeris Uncertainty Model preliminary NANOGrav 11yr dataset analysis (only ~20k samples) PRELIMINARY — dashed = no ephemeris uncertainty modeling — solid = physical ephemeris uncertainty model
13. 13 Physical Ephemeris Uncertainty Model Next steps are to: —re-run analyses with spatial correlations switched on —quantify absorption of GWB signal by physical model