1. Optical Image Analysis to detect EM-Counterparts of GW-Transients
Marica Branchesi (Università di Urbino/INFN)
&
Eric Chassande-Mottin (APC/CNRS)
Virgo Ego Scientific Forum School
(Cascina 2-6 May 2011)

2. Ground Based and Space Telescopes
ASTRONOMICAL OBSERVATIONS
Electromagnetic Spectrum
Ground Based and Space Telescopes

3. Panoramic of ASTRONOMICAL IMAGES in different wavelength bands
Optical Images
X-ray and Radio Images
Silla Observatory
Keck Observatory
VLA
Chandra-Observatory
HST

4. Electromagnetic Radiation from Astrophysical Objects
LUMINOSITY is the amount of energy an object radiates in unit time:
Units: erg/s (cgs) or watts (SI)
Intrinsic quantity for a given objects
Not dependent on the observer’s distance or viewing angle
SPECTRUM: distribution of luminosity as a function of wavelength or frequency
The shape of the spectrum depends on the radiation emission process(es)
Monochromatic Ll, Ln: relative to a given wavelength or frequency (erg s-1 Å-1 or erg s-1 Hz-1)
Bolometric L: integrated over all wavelengths or frequencies (ers s-1 )

5. What is observed and mesured of EM Radiation from Astrophysical Objects?
Types of Astronomical Spectra
FLUX is the radiative energy per unit time passing through a unit area
Monochromatic fl, fn intensity in (ergs or photons) per unit area, time, l, or n (erg cm-2 s-1 Å-1 or erg s-1 Hz-1)
Total Flux (units erg cm-2 s-1 )

6. In the “optical band” there are many bandpasses (photometric systems)
Real Detectors are sensitive over a finite range of l (or n)
In the “optical band” there are many bandpasses (photometric systems)
Some example of
optical bandpass curves
(Fukugita et al. 1995)

7. FLUX - Inverse Square Law
If d is the distance from the center of the source to the observer:
The 1/d2 fall-off of flux with distance from the source

8. Optical Wavelengths: Magnitude
For historical reason fluxes in the optical band are measured in magnitudes
The scale was defined by Pogson in 1856 using a logarithmic scale as the “logarithmic response” of the human eye:
Apparent Magnitude
an object 2.5 magnitudes brighter than another  has a 10 times larger flux
smaller magnitudes correspond to brighter objects
Absolute Magnitude: magnitude that an object would have at a distance of 10 parsec
d = source distance in parsec
measure of intrinsic luminosity
Distance Modulus
d = source distance in parsec

9. Astronomical Image Processing
1 Step) IMAGE CALIBRATION: different steps to follow and software to use on the basis of observed wavelength band
2 Step) IMAGE ANALYSIS: different analysis to perform and software to use on the basis of the project goal
IMAGE CALIBRATION: process by which astronomers convert electronic signal from the telescope into meaningful astronomical data
Raw Data
Calibrated Image
calibration

10. Optical Image Calibration Process
1) Dark Frame Subtraction to compensate for  Thermal effects that add
(taken preventing ligth entering the camera) unwanted intensity
 Readout Noise, electronics
produce noise when reading
and transmitting data
2) Flat Field Correction to overcome  image variations due to a
(taken observing a source with uniform illumination) not uniform response/
sensitivity of the detector
3) Bad Pixel Masks to exclude  “hot and cold pixels”,
pixels that saturate
prematurely or do not
produce signal
4) Fringe correction  to remove the fringe pattern
due to atmospheric OH
emission (in i- and z-band)

11. Are the images ready to be analyzed?
In order to make astrometry (evaluation of object position) and photometry (measure of the flux) two other steps are necessary:
Astrometric Calibration
Photometric Calibration
Astrometric Calibration to find mathematical transformation relating the positions of pixels in the image CCD to celestial coordinates on the sky
by using Reference Stars with well known celestial coordinate in the FOV
Star Catalogs suitable for astrometric use:
GSC, HST Guide Star Catalog
USNO, US Naval Observatory Astrometric Catalog

12. Celestial Coordinates - Right Ascension and Declination
Celestial Sphere
Ecliptic
Celestial Equator
Celestial Equatorial Coordinate System
Dec  measured from the celestial equator from 0° to +90° towards North Pole and from 0° to -90° towards South Pole.
RA  measured east from the Vernal Equinox Point in hours, 0h to 24h or in degree 0° to 360°

13. Photometric Calibration – Standard Stars
General Formula for a object’s magnitude in a filter i:
where DN = net source counts,
Exp = exposure time
ZPi (1 sec) = Zero-Point to determine
or given as ZPi (exp) = ZPi (1 sec) + 2.5log10(exp)
 mi = -2.5log10(DN) + ZPi (exp)
For a standard star mi is known and tabulated for different filters.
ZPi is determined by evaluating DN for standard stars visible in the
image FOV or for standard stars observed during the same night
Standard Star Catalogs suitable for photometric use:
BSC, Bright Star Catalog
Landolt (1992, AJ, 104, 336)
Tycho Catalog

14. Zero-point is dependent on airmass
Due to Earth’s Atmospheric Extinction (absorption and scattering of light ) a source appears bigther observed at the zenith and fainter close to the horizon
Airmass = 1/cos(z) , z=zenith distance
(ratio between the thickness of the Earth’s atmosphere at the observing altitude and at the zenith)
Select STANDARD STARS whose airmass is
the same as the target airmass

15. “not calibrated magnitude” xxxxxxxxxxxxxxxxxxxxxx )
Photometric Calibration – “Clear Filter” Wide Field Telescope
There are telescopes , likeTAROT, that observe with a “Clear filter”
The conversion of “Clear filter observed flux (DN)” into
“standard reference magnitude system” can be done
estimating the Zero-Point (ZP)
by using a linear least squares fit between:
“not calibrated magnitude” xxxxxxxxxxxxxxxxxxxxxx )
and
“reference-catalog magnitude” for common stars in the FOV

16. musno = mimage+ ZP Example for TAROT images
Reference Star Catalog USNO-A2.0 that lists magnitudes in a
standard red filter: POSSI-R1
POSS-I 103aE
1.0
0.8
0.6
0.4
0.2
The POSSI red magnitude is
chosen as reference
Trasmission(%)
Wavelength (Angstroms)
-2.5log10 (DN(ADU counts))+ZP
Linear Least Squares Fit
musno = mimage+ ZP
using USNO stars brigther than mag=16
R1 magnitude USNOA-2

17. IMAGE ANALYSIS: DS9-Saoimage
File Name
Pixel Count in ADU
DS9 - Astronomical imaging and data visualization application
Celestial Coordinates (RA,Dec)
Image Pixel Coordinates (X,Y)
Astronomical Image and Table Format FITS - Flexible Image Transport System

18. Simple Aperture Photometry
m = log (Source_counts) + ZP
Source_counts =Total_counts – Bkg_counts
Sum counts in all pixels aperture
Sky background counts in annulus or separate region
Star Brightness Profile
Define the correct size of aperture
Size  comprimise between including all the light from the star and excluding excessive amount of noisy background
FWHM
good choice  1.5 or 2.0 X FWHM

19. Larger aperture telescope
Image Resolution
In the absence of aberrations and atmospheric turbulence, the
Point-Spread Function (the response to a point-source) is the Airy pattern
Diffraction-Limited PSF
The IMAGE RESOLUTION:
minimum angular separation at which two equally bright stars would just be distinguished
Larger aperture telescope
Higher Resolution
D =aperture diameter
l = wavelength of light
First Diffraction Ring
Airy Disk

20. The resolution of ground-based telescope is limited by the atmosphere
Lens or mirror aberrations and atmospheric turbulence cause the width of the PSF to broaden and its shape to become distorted
Central maxima of PSF expanded by atmospheric turbulence is called “seeing”
The “seeing” is estimated by measuring the
FWHM (full width at half maximum) of
the star brightness radial profile
The FWHM is estimated by fitting with a Gaussian model the brightness profile of a sample of not saturated stars (e.g. IRAF)
The observation “seeing” gives the measure of IMAGE RESOLUTION

21. Signal To Noise Ratio
For a counting process (e.g photons) the error is the “Poisson noise”:
Since the source is seen over a background:
where Bsky are the sky background counts
and Bother are readout and dark noise
in the same area occupied by the source.

22. SExtractor for large field photometry
SExtractor is an astronomical software to extract and build catalogs of objects from optical images
Steps:
1) Estimate Background and its RMS noise
2) Detect objects (thresholding)
3) Deblend merged objects
4) Measure shapes and position
5) Perform Photometry
6) Classify objects: star-like/galaxy
7) Output catalog
star
galaxy
Detection  SExtractor consider a “minimum number” of adjacent pixel above a “certain threshold” an object detection
Deblending  use a multiple pass thresholding to separate neighbour objects detected as single source
Photometry  isophotal, isophotal-corrected, automatic, best-estimate and fixed circular aperture approaches

23. ISOPHOTAL  the user defines the threshold above which SExtractor does photometry: pixels above this threshold constitute an isophotal area
ISOPHOT-CORRECTED  objects rarely have all their flux within neat boundaries, some of the flux is in the “wings” of the profile. Sextractor do a correction for that, assuming a symmetric Gaussian profile for the object
AUTOMATIC  SExtractor uses an adaptive elliptical aperture around every detected object by analyzing the objet’s light ditribution and using the Kron (1980) approach: the ellipical sizes are defined in order to capture most (> 90%) of the objetc flux
BEST  is usually equal to AUTO photometry,
but if the contribution of other nearby sources
exceeds 10%, it is ISOPHOT-CORRECTED
FIXED CIRCULAR APERTURES  the user
specified fixed circular aperture where
the flux is estimated

24. Image Sensitivity – Limiting Magnitude Example for TAROT images
For large FOV images the survey sensitivity can be estimated by comparing “image Source Counts” with a “Reference-Catalog Source Counts”
in the same region of the sky
Example for TAROT images
Differential Source Counts
Integral Source Counts x
TAROT image counts x
TAROT image counts +
USNOA counts +
USNOA counts
Limiting magnitude
Limiting magnitude
Counts(0.5 mag bin)/sq degree
Counts(<mag)/sq degree
R magnitude
R magnitude
Limiting Magnitude:
point where Differential/Integral Source Counts distribution (vs magnitude) bends and moves away from the power law of the reference USNOA

25. Analysis Procedure for Optical Images taken with Wide Field Telescopes
Searching for Electromagnetic Counterparts of Gravitational-Wave Transients
Analysis Procedure for Optical Images taken with Wide Field Telescopes

26. (GWGC catalog White et al. 2011)
A goal of LIGO and Virgo interferometers is the first direct detection of gravitational waves from ENERGETIC ASTROPHYSICAL events:
Mergers of NeutronStars and/or BlackHoles SHORT GRB
Kilonovas
Core Collapse of Massive Stars Supernovae
LONG GRB
GW Source Sky Localization: signals near threshold localized to regions of
tens of square degrees possibly in
several disconnected patches
Necessity of wide field of view telescopes
LIGO/Virgo horizon: a stellarmass BH/NS binary inspiral detected out to 50 Mpc
distance that includes thousands of galaxies
GW observable sources are likely to be extragalactic
Limit regions to observe to Globular Clusters and Galaxies within 50 Mpc
(GWGC catalog White et al. 2011)

27. Compact Object mergers Massive star Progenitor
The expected EM counterpart are transient objects whose brightness changes with time: Optical Afterglows
SHORT/HARD GRB
Compact Object mergers
LONG/SOFT GRB
Massive star Progenitor
KILONOVAS
Radioactively Powered Object
R magnitude assuming z=1
R magnitude assuming z=1
Luminosity (ergs s-1)
Metzger et al.(2010), MNRAS,
Kann et arXiv:
Time (Days)
Time (days after burst in the observer frame)
Time (days after burst in the observer frame)
Metzger et al.(2010), MNRAS,
Kann et al. 2010, ApJ,
The study of transient objects requires the analysis of images taken over several nights to sample flux variation as a function of time - light curve study

28. Analysis Procedure for Wide Field Optical Images
Limited Sky localization of GW interferometers
Wide field of view optical images
Requires to develop specific methods to detect
the Optical Transient Counterpart of the GW trigger
Main steps for a EM-counterpart Detection Pipeline:
Find all “Transient Objects” visible in the images
Select the EM-counterpart from the “Contaminating Transients”

29. Catalog-based Detection Pipeline
Octave Code
detect sources in each image
SExtractor to build catalog of all the objects visible in each image
select central
part of
the image
FOV restricted to region with
radius = 0.8 deg for TAROT
avoid problems
at image edges
select
“unknown objects”
(not in USNO2A)
Match Algorithm (Valdes et al 1995; Droege et al 2006)
to identify “known stars” in USNO2A
(catalog of 5 billion stars down to R ≈ 19 mag)
Magnitude consistency
to recover possible transients that overlap with known galaxies/stars
Recover from the list of “known objects”:
|USNO_mag – TAROT_mag| > 4σ 11

30. …..Catalog-based Detection Pipeline
Spatial cross-positional check
with match-radius of 10 arcsec for TAROT chosen on the basis of position uncertainties
reject cosmic rays, noise, asteroids...
search for objects in common to several images
“On-source region” = regions occupied by Globular Clusters
and Galaxies up to 50 Mpc
(GWGC catalog, White et al 2011)
reject background
events
select objects in “on-source”
(nearby galaxies)
reject “contaminating
objects” (galaxy, variable stars, false transients..)
“Light curve” analysis
Possible Optical counterparts

31. to discriminate expected light curve from “contaminating events”
“Light curve” analysis - cut based on the expected luminosity dimming
of the EM counterparts
recall magnitude α [-2.5 log10 (Luminosity)]
expect Luminosity α [time- β] magnitude α [2.5 β log10(time)]
slope index = measurement of (2.5 β)
to discriminate expected light curve from “contaminating events”
The expected slope index for SHORT/LONG GRB is around 2.7 and kilonova is around 3
Optical counterparts the ones with slope index > 0.5
Slope Index
Distance in Mpc
Contaminating objects that could pass the cut are only variable AGN or Cepheid stars
Initial Red magnitude
Coloured points = Optical LGRB Transients
Black squares = contaminating objects

32. Thank you for your attention!!
Ready to start the practical section....
You are provided with a set of 10 images taken by TAROT telescope observing the same region of the sky during three consecutive nights
after a fictitious GW trigger
Some optical transients have been injected in the images by using
LONG and SHORT GRB and kilonova models
The transients were injected in nearby galaxies (within the LIGO/Virgo horizon of 50 Mpc) with an offset from the galaxy center in the range of the observed ones for GRBs (within 100 Kpc)