Download Extrasolar planets: where are we, and where do we want to be

Extrasolar planet detection: a view
from the trenches
Alex Wolszczan
(Penn State)
01/23/06
Collaborators:
A. Niedzielski (TCfA)
M. Konacki (Caltech)
Ways to find them…
Methods that actually work …
Radial velocity
Microlensing
Pulse timing
Transit photometry
Some examples…
Neptune-mass planet
Microlensing planet
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The transit classic: HD209458
A “super-comet” around PSR B1257+12?
Orbits from Vr measurements
• Observations are given in the form of a time series, Vr(i),
at epochs t(i), i = 1,…,n
• A transition from t(i) to (i) is accomplished in two steps:
2
E  esin E 
(t  T)
P
  1 e 1/ 2 E 
tan  
 tan 
2  1 e 
2 
Vr  K cos(   )  ecos  
Equation for
eccentric anomaly, E
K
2a1 sin i
P 1 e 2
• From the fit (least squares, etc.), one determines parameters
K, e, , T, P

…and from pulsar timing
 In phase-connected timing, one models pulse phase in terms of
spin frequency and its derivatives and tries to keep pulse count
starting at t0
 A predicted time-of-arrival (TOA) of a pulse at the Solar System
barycenter depends on a number of factors:
1
     (t  t0 )   (t  t 0 ) 2  ...
2
t    D / f 2   R sun   E sun   Ssun   R  ...
1
a1 sin i
a1 sin i
R 
sin  (cos   e) 
(1 e 2 ) 2 cos  sin 
c
c
Determining binary orbits…
Collect data: measure Vr’s, TOA’s, P’s
Estimate orbital period, Pb (see below)
Use Vr’s to estimate a1sini, e, T0, Pb, 
(use P’s to obtain an “incoherent orbital
solution”)
Use TOA’s to derive a “phase-connected”
orbital solution
Figuring out the orbital period…
 Go Lomb-Scargle! If in doubt, try this procedure
(borrowed from Joe Taylor):
 Get the best and most complete time series of your
observable (the hardest part)
 Define the shortest reasonable Pb for your data set
 Compute orbital phases, I = mod(ti/Pb,1.0)
 Sort (Pi, ti, I) in order of increasing 
 Compute s2 = ∑(Pj-Pj-1)2 ignoring terms for which jj-1> 0.1
 Increment Pb = [1/Pb-0.1/(tmax-tmin)]-1
 Repeat these steps until an “acceptable” Pb has been
reached
 Choose Pb for the smallest value of s2
The pulsar planet story…
… and the latest puzzle to play with
a
b
c
d
Timing (TOA) residuals at 430 MHz
show a 3.7-yr periodicity with a ~10
µs amplitude
At 1400 MHz, this periodicity has
become evident in late 2003, with a
~2 µs amplitude
Two-frequency timing can be used to
calculate line-of-sight electron column
density (DM) variations, using the cold
plasma dispersion law. The data show
a typical long-term, interstellar trend in
DM, with the superimposed lowamplitude variations
By definition, these variations perfectly
correlate with the timing residual
variations in (a)
Because a dispersive delay scales as
2, the observed periodic TOA
variations are most likely a
superposition of a variable propagation
delay and the effect of a Keplerian
motion of a very low-mass body
Examples of Vr time series “under
construction”
One of the promising candidates…
Periods from time
domain search: 118,
355 days
Periods from
periodogram: 120,
400 days
Periods from simplex
search: 118, 340,
also 450 days
…and the best orbital solutions
P~340 (e~0.35)
appears to be best
(lowest rms residual,
2 ~ 1)
This case will
probably be resolved
in the next 2
months, after >2
years of
observations
Summary…
 Given: a time series of your observable
 Sought: a stable orbital solution to get orbital
parameters and planet characteristics
 Question: astrophysical viability of the model (e.g.
stellar activity, neutron star seismology, fake transit
events by background stars)
 Future: new challenges with the advent of highprecision astrometry from ground and space and
planet imaging in more distant future