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)

ASTRONOMICAL OBSERVATIONS

Electromagnetic Spectrum

Ground Based and Space Telescopes

Panoramic of ASTRONOMICAL IMAGES in different wavelength bands

X-ray and Radio ImagesOptical Images

Chandra-Observatory

VLA

HST

Keck Observatory

Silla Observatory

Electromagnetic Radiation from Astrophysical Objects

LUMINOSITY is the amount of energy an object radiates in unit time:

Intrinsic quantity for a given objects Not dependent on the observer’s distance or viewing angle

Units: erg/s (cgs) or watts (SI)

dtdE

L

SPECTRUM: distribution of luminosity as a function of wavelength or frequency

The shape of the spectrum depends on the radiation emission process(es)

Monochromatic L ,l 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 )

dLdLL

00

What is observed and mesured of EM Radiation from Astrophysical Objects?

FLUX is the radiative energy per unit time passing through a unit area

dtdAdE

dAdL

f

dfdff

00

Monochromatic f ,l 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 )

Types of Astronomical Spectra

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)

FLUX - Inverse Square Law

The 1/d2 fall-off of flux with distance from the source

If d is the distance from the center of the source to the observer:

24 d

Lf

fddAfL 24

Optical Wavelengths: Magnitude

For historical reason fluxes in the optical band are measured in magnitudesThe scale was defined by Pogson in 1856 using a logarithmic scale as the “logarithmic response” of the human eye:

)/(log5.2 211021 ffmm an object 2.5 magnitudes brighter than another has a 10 times larger flux smaller magnitudes correspond to brighter objects

5log5 10 dmM

measure of intrinsic luminosity

Apparent Magnitude

Absolute Magnitude: magnitude that an object would have at a distance of 10 parsec

5log5 10 dMmDistance Modulus

d = source distance in parsec

d = source distance in parsec

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

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)

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

Celestial Coordinates - Right Ascension and Declination

Celestial Sphere

Celestial Equator

Ecliptic

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°

Photometric Calibration – Standard Stars

General Formula for a object’s magnitude in a filter i:

ii ZPDNm exp)/(log5.2 10

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

Zero-point is dependent on airmass

Airmass = 1/cos(z) , z=zenith distance(ratio between the thickness of the Earth’s atmosphere at the observing altitude and at the zenith)

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

Select STANDARD STARS whose airmass is the same as the target airmass

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

There are telescopes , likeTAROT, that observe

with a “Clear filter”

))((log5.2 10 ADUcountsDN

Photometric Calibration – “Clear Filter” Wide Field Telescope

Reference Star Catalog USNO-A2.0 that lists magnitudes in a standard red filter: POSSI-R1

The POSSI red magnitude is chosen as reference

Example for TAROT images

1.0

0.8

0.6

0.4

0.2

0

Tra

sm

iss

ion

(%)

POSS-I 103aE

Wavelength (Angstroms)

6000 6400 6800

R1 magnitude USNOA-2-2.5

log

10 (

DN

(AD

U c

ou

nts

))+Z

P

Linear Least Squares Fit

musno = mimage+ ZPusing USNO stars brigther than mag=16

IMAGE ANALYSIS: DS9-Saoimage

DS9 - Astronomical imaging and data visualization application

Astronomical Image and Table Format FITS - Flexible Image Transport System

Celestial Coordinates (RA,Dec)Image Pixel Coordinates (X,Y)

File Name Pixel Count in ADU

Simple Aperture Photometry

Sum counts in all pixels aperture

Sky background counts in annulus or separate region

m = - 2.5 log (Source_counts) + ZP

Source_counts =Total_counts – Bkg_counts

Define the correct size of aperture Star Brightness Profile

Size comprimise between including all the light from the star and excluding excessive amount of noisy background

good choice 1.5 or 2.0 X FWHM

FWHM

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

Airy DiskFirst Diffraction Ring

Dsen

22.1

D =aperture diameter

l = wavelength of light

Larger aperture telescope

Higher Resolution

The “seeing” is estimated by measuring the FWHM (full width at half maximum) of

the star brightness radial profile

The observation “seeing” gives the measure of IMAGE RESOLUTION

The FWHM is estimated by fitting with a Gaussian model the brightness profile of a sample of not saturated stars (e.g. IRAF)

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 resolution of ground-based telescope is limited by the atmosphere

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:

SSS

NS

SScountsource

S

S

2/

_

22

222

/

other

othersky

BskyT

BBST

BS

SSNS

where Bsky are the sky background counts

and Bother are readout and dark noise

in the same area occupied by the source.

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

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

star

galaxy

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

Limiting Magnitude: point where Differential/Integral Source Counts distribution (vs magnitude) bends and moves away from the power law of the reference USNOA

Differential Source Counts Integral Source Counts

R magnitudeR magnitude

Co

un

ts(0

.5 m

ag b

in)/

sq d

egre

e

Co

un

ts(<

mag

)/sq

deg

ree+

x x+

Limiting magnitudeLimiting magnitude

USNOA countsUSNOA counts

TAROT image countsTAROT image counts

Image Sensitivity – Limiting Magnitude

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

Analysis Procedure for Optical Images taken with Wide Field Telescopes

Searching for Electromagnetic Counterparts

of Gravitational-Wave Transients

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

Limit regions to observe to Globular Clusters and Galaxies within 50 Mpc

(GWGC catalog White et al. 2011)

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

The expected EM counterpart are transient objects whose brightness changes with time: Optical Afterglows

Metzger et al.(2010), MNRAS, 406..265

Kann et al. 2010, ApJ, 720.1513

Kann et arXiv:0804.1959

KILONOVASRadioactively Powered Object

LONG/SOFT GRBMassive star Progenitor

SHORT/HARD GRB Compact Object

mergers

R m

agn

itu

de

assu

min

g z

=1

R m

agn

itu

de

assu

min

g z

=1

Time (days after burst in the observer frame)Time (days after burst in the observer frame)Time (Days)

Lu

min

osi

ty (

erg

s s-1

)

Metzger et al.(2010), MNRAS, 406..265

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

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”

detect sources in each image

select“unknown objects”

(not in USNO2A)

Catalog-based Detection Pipeline

SExtractor to build catalog of all the objects visible in each image

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)

select centralpart of

the image

FOV restricted to region with radius = 0.8 deg for TAROT

avoid problemsat image edges

Magnitude consistency

to recover possible transients that

overlap with known galaxies/stars

Recover from the list of “known objects”: |USNO_mag – TAROT_mag| > 4σ

Octave Code

11

search for objects in common to

several images

Spatial cross-positional check with match-radius of 10 arcsec for TAROT chosen on the basis of position uncertainties

reject cosmic rays, noise, asteroids...

select objects in “on-source”

(nearby galaxies)

“On-source region” = regions occupied by Globular Clusters and Galaxies up to 50 Mpc (GWGC catalog, White et al 2011)

reject backgroundevents

“Light curve” analysis

reject “contaminatingobjects” (galaxy, variable stars, false transients..)

Possible Optical counterparts

…..Catalog-based Detection Pipeline

“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

Coloured points = Optical LGRB TransientsBlack squares = contaminating objects

Contaminating objects that could pass the cut are only variable AGN or Cepheid stars

Dis

tan

ce in

Mp

c

Initial Red magnitude

Slo

pe

Ind

ex

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)