Trends and noise removal using a Wavelet based ...icc.ub.edu/webs/ICCUB_Winter_Meeting/sites/icc.ub...surveying purposes. • The project is a joint collaboration between the Reial

TRENDS AND NOISE REMOVAL USING A WAVELET BASED

MODIFICATION OF THE TREND FILTERING ALGORITHM:

APPLICATION TO WIDE-FIELD ASTRONOMICAL SURVEYS

DANIEL DEL SER BADIA

ICCUB WINTER MEETING

FEBRUARY 7, 2017

OUTLINE

• Trend Filtering Algorithm (TFA): basics and formulation • Introduction to Wavelets

• What is a Wavelet?

• Discrete Wavelet Transform (DWT) vs Stationary Wavelet Transform (SWT)

• Modified TFA (TFAW): application of the SWT • TFAW application to simulated data • TFAW application to ground-based wide-field surveys

• Telescope Fabra-ROA at Montsec (TFRM)

• The Evryscope

• TFAW application to space-based exoplanet surveys • CoRoT

• Kepler

• Conclusions

TREND FILTERING ALGORITHM (TFA): BASICS AND FORMULATION

• Many stars within a photometric survey suffer from the same systematic effects.

• Build an optimum filter from a template of reference stars:

• A(i) represents the noise- and trend-free signal to be found.

• TFA frequency analysis step:

• A(i) = <Y(i)>

• Most trends and systematics are removed Increased period detection probability.

• Signal distorted as we have assumed that the signal is constant.

TFA: Kovács, G., Bakos, G. & Noyes, R. W. 2005, MNRAS, 356, 557-567

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TREND FILTERING ALGORITHM (TFA): BASICS AND FORMULATION

• Many stars within a photometric survey suffer from the same systematic effects.

• Build an optimum filter from a template of reference stars:


• TFA signal reconstruction step:

• Iterative approximation of A(i).

• Can only be applied to periodic signals.

• A(i) computed through bin averaging the phase folded light curve. Although more complex methods are recommended.

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TFA: Kovács, G., Bakos, G. & Noyes, R. W. 2005, MNRAS, 356, 557-567

WHAT IS A WAVELET?

• Highly localized impulses obtained from shifting and scaling the ‘mother wavelet’.

• Scaling and shifting allow to calculate the wavelet coefficients Correlation between the wavelet and a localized section of the signal.

Introduction to Wavelets

Biorthogonal 3.9 wavelet function

• Signal decomposed in dyadic blocks (i.e. shifting and scaling is based on a power 2).

• DWT calculated applying high and low pass filters to the signal Detail and Approximation coefficients.

• Signal can be iteratively decomposed into components of lower scale (higher resolution) Filter Bank.

• Maximum number of decomposition levels depends on the length of the data:

• Data length = 2N max_level == N

Discrete Wavelet Transform (DWT) vs Stationary Wavelet Transform (SWT)



• DWT is not a time-invariant transform very sensitive to the alignment of the signal in time.

• SWT is designed to overcome the lack of translation-invariance of the DWT.

• Same low and high pass filters are applied.

• NO subsampling Filters are upsampled versions of the previous ones (padded with zeroes) new sequences at each level have the same length as the original time series.




Noise

High-frequency sinusoidal

Low-frequency sinusoidal Original signal

MODIFIED TFA (TFAW): APPLICATION OF THE SWT


• Frequency analysis step is the same as with TFA (A(i) = <Y(i)>).

• Search for any significant period Light curve is phase folded.

• SWT of the phase folded light curve is computed.

• Noise and signal levels are selected.

• A(i) computed with those decomposition levels below signal level.

• New filter becomes:

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TFAW APPLICATION TO SIMULATED DATA

High SNR sinusoidal Low SNR sinusoidal

TFAW APPLICATION TO SIMULATED DATA

High SNR transit Low SNR transit

TFAW APPLICATION TO GROUND-BASED SURVEYS

THE TELESCOPE FABRA-ROA AT MONTSEC (TFRM)

• The Telescope Fabra-ROA at Montsec (TFRM) is a refurbished f/0.96 0.50m Baker-Nunn Camera for robotic CCD wide-FoV surveying purposes.

• The project is a joint collaboration between the Reial Acadèmia de Ciències i Arts de Barcelona - Observatori Fabra and the Real Instituto y Observatorio de la Armada (ROA).

• Installed at the summit of the Montsec d'Ares as part of the Observatori Astronòmic del Montsec.

TFAW application to ground-based surveys

TFRM: Fors, O. et al. 2013, PASP, 125, (927), 522


• TFRM is surveying a selected list of M-dwarfs for exoplanetary transits (TFRM-PSES) since its deployment at the end of 2011.

• TFRM-PSES benefits from the combination of its wide FoV (19.4 sq. deg.) for a 16 MPix camera, and from the 0.1% -precision 20-second-cadence light curves for every object brighter than V~16th magnitude.



• TFRM is surveying a selected list of M-dwarfs for exoplanetary transits (TFRM-PSES) since its deployment at the end of 2011.

• TFRM-PSES benefits from the combination of its wide FoV (19.4 sq. deg.) for a 16 MPix camera, and from the 0.1% -precision 20-second-cadence light curves for every object brighter than V~16th magnitude.


4.4 degrees aprox. 8.5 full Moons


• TFRM-PSES survey data used for the TFAW performance assessment comprises 2048 data points 11 SWT decomposition levels.


New Discovery!!!

2MASS10144313+5018191 NSVS 4921994

• The Evryscope is a University of North Carolina at Chapel Hill project.

• It is a telescope which covers the entire accessible sky above an airmass of 2. It consists of a single hemisphere containing twenty-three 61mm-aperture telescopes imaging a 691 MPix instantaneous 8000 sq. deg. FoV every 2 minutes.


Evryscope: Law, N. M. et al. 2015, PASP, 127, (949), 234

THE EVRYSCOPE

THE EVRYSCOPE


36K x 36K pixels, 100º x 100º FoV every 2 minutes down to g=16mag. 2 million objects detected per exposure.

• The Evryscope is located at Cerro Tololo Inter-American Observatory (CTIO), covering declinations between -90º and +10º.

• Currently delivering multi-year 1%-precision 2-minute-cadence light curves for every object brighter than g ~16, and millimagnitude-precision 16-minute-cadence light curves for every object brighter than g~12.

• BigData production: 230 TB/year (all archived in drives).

• Coadding allows deeper detections: glim~17.5(1hr) ; glim~19 (1 night)


THE EVRYSCOPE

2MASS13190996-8347115 1RXS J031713.9-853231

THE EVRYSCOPE • Evryscope data used for the TFAW performance assessment comprises 2048

data points.


New Discovery!!!

TFAW APPLICATION TO SPACE EXOPLANET SURVEYS

CoRoT

• Space observatory mission led by the French Space Agency (CNES) in conjunction with the European Space Agency (ESA).

• Launched 27 December 2006

• Mission objectives:

• Search for extrasolar planets with short orbital periods, particularly those of large terrestrial size.

• Perform asterosysmology by measuring oscillations in stars.

• 29 confirmed exoplanets, hundreds of candidates.

• De-orbited 17 June 2014.

• Systematics due to high energetic proton flux near the South Atlantic Anomaly (SAA), residuals at the CoRoT orbital period, spacecraft jitter, CCD long-term aging…

TFAW application to space exoplanet surveys

CoRoT • Data comprises 4096 points from light curves observed during the IRa0 run

of the CoRoT mission.


2MASS J06441118-0117536

KEPLER

• Kepler is a space mission led by NASA to discover Earth-size planets orbiting other stars.

• Launched on March 7, 2009 and still running.

• Designed to survey a portion of our region of the Milky Way to discover Earth-size exoplanets in or near habitable zones and estimate how many of the billions of stars in the Milky Way have such planets.

• 2331 confirmed planets (plus 144 from K2 mission) and over 5000 candidates.

• Systematics due to thermal effects, jitter, pixel sensitivity dropouts…


KEPLER • Data comprises 16384 points observed with the short cadence mode.


Kepler-19 b

CONCLUSIONS • TFA can remove trends and systematics but does not decouple noise from

signal.

• SWT allows to recover the noise-free signal without need of binning or fitting a model.

• TFAW is an algorithm that combines TFA trend and systematic removal with the SWT noise decoupling and filtering capabilities.

• TFAW is able to increase the SNR of periodic signals affected by systematics, trends and noise whithout modifying their shape, amplitude and phase.

• Also TFAW does not introduce any “fake” signatures in the data and improves the characterization of the frequency power spectra of the signals.

• TFAW is a totally generic algorithm that can be applied to ground- and space-based surveys provided that a sample of reference stars is available.

THANKS FOR YOUR ATTENTION

APPENDIX I

2MASS J06441118-0117536


APPENDIX I • Data comprises 4096 points from light curves observed during the IRa0 run

of the CoRoT mission.

CoRoT 102712679

APPENDIX I

CoRoT 102712679

APPENDIX I

Kepler-19 b


KEPLER • Data comprises 16384 points observed with the short cadence mode.

kplr003114661

APPENDIX I

kplr003114661

APENDIX II: MULTIPERIODIC SIGNAL

APENDIX III

Documents

Trends and noise removal using a Wavelet based ...icc.ub.edu/webs/ICCUB_Winter_Meeting/sites/icc.ub...surveying purposes. • The project is a joint collaboration between the Reial