Download Transit detecion on eclipsing binary systems

Transit detecion on eclipsing binary systems
Hans J. Deeg
Instituto de Astrofísica de Canarias
1. Transit observations in eclipsing binary systems, why and how
2. Transit detection algorithms for EB's
3. Considerations for computing requirements
Planet WS Berlin 12/2003
Why are EB transits of interest to be observed
The probability to detect planets around EB's with transits is higher:
Since the EB plane is aligned with the observer,
the planetary one is it likely as well
->higher probability for correct alignement
Non-aligned planetary planes would precess around EB rotation axis,
and cause periodically transits as well (Schneider, 1994)
Detection of circumbinary planets would be a very significant
extension to the variety of known planets.
Planet WS Berlin 12/2003
EB Transit
lightcurves 1
Time and duration
of transits depends
on phase of EB
during transit.
Planet WS Berlin 12/2003
For longer periodic planets
vpl << vEB : trains of several
irregularly spaced transits
per EB crossing
EB transit lightcurves 2:
after removal of binary eclipse
vpl > vEB
P=9d
vpl > vEB
vp l< vEB
P=9d
'Normal' case: planet transits
one component
vpl < vEB
P=36d
P=36d
complicated shapes:
planetary transit during
binary eclipse
A detection algorithm needs to model these curves by
considering all possible periods AND phases of EB at planet crossing
Planet WS Berlin 12/2003
EB Transit detection algorithm (TDA) development
Jenkins,Doyle & Cullers 1996: propose a matching filter TDA.The detection
statistics C is obtained from a scalar multiplication of the vectors representing
model-lc and observed data.
Jenkins et al. present this TDA in the context of the transit detection of EBs
TEP project (1994-2000; Deeg et al 1998,Doyle et al 2000.)
detection statistics is obtained from a comparison of hypotheses transit-present
vs transit-absent.
Planet WS Berlin 12/2003
EB transit detecion algorithm, general
There is nothing special about them, except for the first step:
i) removal of binary eclipses from lightcurve. Use fit obtained from
several good observations of eclipses.
ii) model signal for Planet(Ei,Pi,{Rpl,ecc})
E: Epoch [E0,..,E0+P] (or phase [0..2])
iii) compare model to data -> detection statistical value C(Ei,Pi)
within search space [E0,..,E0+P], and [Pmin..Pmax], (Rpl, ecc), repeat
steps ii) and iii) for all values of E, P that generate significantly
different model signals
Planet WS Berlin 12/2003
EB transit detecion vs single star TD
For single star transits:
Transits are strictly periodic. Transit shape, duration is invariant
against Epoch (slowly varying if eccentric)
EB transits:
Transits are semi-periodic and shapes/durations depend strongly
on planet's epoch
Difference of EB algorithms is in the generation of model transits and
in finding an efficient way to compare them to the data.
-> EB transit detection is a much larger computational problem than
single star TD on the order of the number of epoch steps needed
Planet WS Berlin 12/2003
The TEP project 1994-2000, Doyle, Deeg,
Schneider, Jenkins et al.
Observed CM Dra for 1000hrs (Deeg et al 1998, Doyle et al
2000)
TDA: searched data from 1994-98 for P=7-60 days over all
phases of CM Dra
~ 2 month computing time with Sun Ultra5 (300MHz)
a list of planet candidates was published. Follow-up
observations 1999-2001 at predicted transit times did rule
out all of them
Planet WS Berlin 12/2003
Algorithm used in TEP
Adapted for analysis of ground based data with unknown extinction slope:
Compares data to two models:
-one with transits (E,P) and extinction fits to all nights (H1)
-one without transit, only extinction fit to all nights (H0)
Detection stat. C is difference between residuals: C(E,P) =  |residH0| – |residH1|
This algorithm is NOT specific
for eclipsing binaries – but for
problematic ground-based data!
Doyle et al. 2000
Planet WS Berlin 12/2003
A transit candidate with P ≈ 11d
Doyle
et al. 2000
Planet WS Berlin 12/2003
Computational Requirements: TD stepsize
Minimum TD step sizes to not miss a transit (Jenkins et al. 1996):
If a planet (E,P) is tested by a detection test with (P±P,E) or (P,E±E), its
detection statistics is reduced 'signficantly' (to 1/2 in case of correlation).
P
td
Planet (E,P)
tobs
detc.
stat.
c=1
Model (E,P)
c=1/2
Model (E+E,P) , E=td/2
c=1/2
Model (E,P+P) , P=P td/tobs
Planet WS Berlin 12/2003
Computational Requirements 1
Number of epoch and period steps in TDA:
tobs: duration of observations
td : duration of transit ( fundamental mesh size)
P : period of planet
in Epoch: E=td/2
-> NE= P / E = 2 P /td
in Period: P=P td/tobs
-> NP= (tobs/td) ln(Pmax/Pmin)
total: Nstep ≈ 2 tobs td-2 (Pmax - Pmin)
Ignored here is a weak dependency of td ~ P1/3
Planet WS Berlin 12/2003
Computational Requirements 2
Total Number of operations of TDA:
Nop = k Nstep Npts,
= k 2 tobs td-2 (Pmax - Pmin) Npts
where k is a factor depending on the TDA used (k might
be < 1), Npts is the number of data pts.
For equidistant points: Npts = tobs/tinc and then:
Nop = k 2 td-2 (Pmax-Pmin) tobs2 tinc-1
(1)
Examples: (k =1, Pmin=7d, Pmax=60d, td =0.0139d = 20min)
TEP: Nop ≈ 2 .1013
(tobs = 1526d, Npts=24 874)
COROT: Nop ≈ 1.1 .1012
(tobs=150d, Npts=13 500, tinc=16min)
Kepler/Eddi: Nop ≈ 1.0 .1014 (tobs=1100d, Npts= 158 000, tinc=10min)
Planet WS Berlin 12/2003
Slicing the lightcurve: saving computing steps
Principle: running a TDA on shorter sections of a lightcurve, and
co-adding detection statistics from individual sections.
If a lightcurve of Npts points is divided into ns sections of Npts,s
points, of length tobs,s, the computing requirement Nop,s for each
section is:
Nop,s = k 2 td-2 (Pmax-Pmin) tobs,s Npts,s.
The total number of operations is then given by:
Nop = ns Nop,s = k 2 td-2 (Pmax-Pmin) tobs,s Npts
i.e. Nop is reduced by tobs/tobs,s against (1)
(2)
This scheme was used by TEP project, dividing the observations of
tobs=1529d into 5 sections corresponding to the yearly (1994-1998)
observing seasons, using tobs = 200d for each of them (mid-march to
october). Savings: 1526/200 ≈ 7.6
Only this made the computation feasable with a CPU time of 2 months
Planet WS Berlin 12/2003
Slicing: Adding of detection statistics
maps C(E,P) of small region around a candidate with P ≈ 36d, using td = 20min, tobs=200d
1994 (186h)
36,7d
1995 (185h)
1996 (246h)
1997 (250h)
Once maxima in C(Ei,Ti) map are found, TDA needs to be rerun with a finer
mesh (td,fine ≈ 1/4 td) in small area in E,P around all maximum to find best
value of C in (E,P) space.
In TEP, this fine-mesh search was performed around the 5000 highest
maxima -> final list of planet candidates, subject to follow-up observations
P
36,1d
JD0+0
E
JD0+3
dominant
lines are
caused by
individual
features in
lightcurve
epoch E is an offset {0 ..P}
from reference Epoch
JD0=2450000 (9 Oct 1995)
Bright: high C(E,P)
coadded C(E,P) arrays: 94-96
94-97
Planet WS Berlin 12/2003
Slicing for equidistant data
starting from (2) :
Nop = k 2 td-2 (Pmax-Pmin) tobs,s Npts
with Npts = tobs/tinc the total number of computations is:
Nop = k 2 td-2 (Pmax-Pmin) tobs,s tobs tinc-1 (3)
now, Nop  tobs , instead of Nop  tobs2 without 'slicing'.
Savings from slicing is  ns..
Drawbacks: added complexity.
Slicing allows running the TDA on shorter sections of data, with
the possiblitity to add matrizes C of later data at any time (useful
for missions with long tobs)
Planet WS Berlin 12/2003
Analysis of COROT EB data vs TEP
-data span only 150 days, not 5 years as in TEP
-homogenous noise characteristics in data set
-no atmosphere with ‘unkown’ extinction
-computers became faster
With O(100) EB's to analyze in COROT fields, no serious
computing obstacles are expected.
Selection of best TDA-kernel (matched filter, BLS,..) is
TBD and requires lightcurves with realistic noise
simulations.
Planet WS Berlin 12/2003
Summary
1. algorithms to analyze EB lightcurves: fundamentally similar to
single stars; need to model more complex transits; more 'tricky'
to obtain efficient transit detection, as there are fewer invariants
in transit lightcurves.
2. Slicing the data into smaller sections improves computational
efficiency of TDA, adding complexity. Also, allows efficient
adding of additional data.
¿How useful may this method be to single star TD? - TBD
3. COROT EB analysis is not expected to cause serious
difficulties. Selection of best TDA is TBD
Planet WS Berlin 12/2003
References
Deeg, H.J., et al.1998, A&A 338, 479
Doyle, L.R., et al. 2000, ApJ, 535, 338
Jenkins, J. M.; Doyle, L. R.; Cullers, D. K. 1996, Icarus 119, 244
Schneider, J. 1994, Planet Space Sci. 42, 539
Planet WS Berlin 12/2003