Extrasolar planet detection: a view from the

trenches

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…Ways to find them…

Methods that actually work …Methods that actually work …

Pulse timing

Microlensing Transit photometry

Radial velocity

Some examples…Some examples…

Neptune-mass planet

A “super-comet” around PSR B1257+12?

The transit classic: HD209458

QuickTime™ and aYUV420 codec decompressor

are needed to see this picture.

QuickTime™ and aYUV420 codec decompressor

are needed to see this picture.

Microlensing planet

Orbits from Vr measurementsOrbits 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:

€

E − esinE =2π

P(t −T)

tanθ

2

⎛

⎝ ⎜

⎞

⎠ ⎟=

1+ e

1− e

⎛

⎝ ⎜

⎞

⎠ ⎟

1/ 2

tanE

2

⎛

⎝ ⎜

⎞

⎠ ⎟

Vr =K cos(θ +ω) + ecosω( )

Equation foreccentric anomaly, E

€

K =2πa1 sini

P 1− e2

• From the fit (least squares, etc.), one determines parameters K, e, , T, P

…and from pulsar timing…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:

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:

€

φ=φ+ν(t − t0) +1

2ν•

(t − t0)2 + ...

t = τ −D / f 2 + ΔRsun− ΔEsun

+ ΔSsun+ ΔR + ...

ΔR =a1 sini

csinω(cosθ − e) +

a1 sin i

c(1− e2)

1

2 cosω sinθ

Determining binary orbits…

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

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…

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

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…The pulsar planet story…

… and the latest puzzle to play with

… and the latest puzzle to play with

a Timing (TOA) residuals at 430 MHz show a 3.7-yr periodicity with a ~10 µs amplitude

b At 1400 MHz, this periodicity has become evident in late 2003, with a ~2 µs amplitude

c 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 low-amplitude variations

d 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

a Timing (TOA) residuals at 430 MHz show a 3.7-yr periodicity with a ~10 µs amplitude

b At 1400 MHz, this periodicity has become evident in late 2003, with a ~2 µs amplitude

c 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 low-amplitude variations

d 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”

Examples of Vr time series “under construction”

One of the promising candidates…

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

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

…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

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…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 high-precision astrometry from ground and space and planet imaging in more distant future

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 high-precision astrometry from ground and space and planet imaging in more distant future