basic concepts to understand Gamma Ray Bursts

basic concepts to understand Gamma Ray Bursts

The waves

Direction of propagation

perturbation

ELETTROMAGNETIC WAVE

Continuum series of pulses originated from a variation of the electromagnetic field.

It is a perturbation of the electromagnetic field.

The redshift and the distance Measurementredshift:

The light frequency is lower than the frequency was emitted.This happens when the source is receding in the

observer

SUN GALAXY

We look at the spectrum of an electromagnetic light emission of an object and we compare it

with another nearer

EMITTED

OBSERVEDz

1

1EMITTED

OBSERVEDz

Gamma-Ray Bursts: The story begins

Klebesadel R.W., Strong I.B., Olson R., 1973, Astrophysical Journal, 182, L85

`Observations of Gamma-Ray Bursts of Cosmic Origin’

Brief, intense flashes of g-rays

The Vela are American satellites that try to see if the URSS respects theTreats banning nuclear tests between USA and URSS in the early 60s

They were too much long to be nuclear explosions and too much short to be a known phenomenon!

GRBs phenomenology

Basic phenomenology– Flashes of high energy photons in the sky (typical duration is few seconds).– Isotropic distribution in the sky – Cosmological origin accepted (furthest GRBs observed z ~ 7 – billions of light-years).– Extremely energetic and short: the greatest amount of energy released in a short time (not considering the Big Bang).– Sometimes x-rays and optical radiation observed after days/months (afterglows), distinct from the main γ-ray events

(the prompt emission).– Observed non thermal spectrum

The energetics of GRBs

An individual GRB can release in a matter of seconds the same amount of energy that our Sun will radiate over its 10-billion-year lifetime

Isotropical distribution in the sky

12

Short vs Long GRBs

Kouveliotou et al., 1996, AIP Conf. Proc., 384, 42.Paciesas et al., 1999, ApJS, 122, 465.Donaghy et al., 2006, astro-ph/0605570.

Short (hard) Long (soft)

Short GRBs -> T90<2 s Long GRBs -> T90>2 sShort GRBs -> T90<5 s Long GRBs -> T90>5 s Norris et Bonnell 2006

What is the T90

• Time interval in which the instrument reveal the 5% of the total counts and the 90%.

• To the duration of this event it is associated the 90% of the emission

Progenitors for traditional model core collapse of massive stars (M > 30 Msun)

long GRBs Collapsar or Hypernova (MacFadyen & Woosley 1999 Hjorth et al. 2003; Della Valle et al. 2003, Malesani et al. 2004, Pian et al. 2006) GRB simultaneous with SN

Discriminants: host galaxies, location within host, duration, environment, redshift distribution, ...

compact object mergers (NS-NS, NS-BH) short GRBs

Collapsar model

• Very massive star that collapses in a rapidly spinning BH. • Identification with SN explosion.

Woosley (1993)

prompt emission FRED (Fast Rise, Exponential Decay)

Pre-Swift vs Swift for the afterglows

Typical lightcurve for BeppoSAX Typical lightcurve for Swift

Swift zmedio = 2.5!!!

Pre-Swift zmedio = 1.2

Definition of the Flux and Energy• The flux F is the energy carried by all rays passing

through a given area dA .• dA normal to the direction of the given ray • all rays passing through dA whose direction is within a

solid angle dΩ of the given ray

• E=Iν *dA*dt*dΩ*dν• Iv= is the brightness or specific intensity• dFν =E/(dA*dt*dν)

• dF= dIF cos For some arbitrary orientation n

Gamma-ray Burst Real-time Sky Map http://grb.sonoma.edu/

• Burst List• Burst ID GRB 090301A• Date 2009/03/01• Time 06:55:55• Mission Swift• RA 22:32• Dec 26:38• brief Burst Description

This burst had a complex multipeak structure and a duration of ~50 seconds. Due to observing constraints Swift cannot slew to this position until after April 15. No XRT or UVOT was available as a result.

SpectraNon thermal spectra

α ~-1β ~ -2 Ebreak ~ 100 keV - MeV

Epeak =(α +2) Ebreak

E

N(E) Eα

Eβ

Ebreak

The phenomenological Band law hold in a wide energy interval 2keV-100MeV

Time [sec]

cts/sec

GRB spectrum evolves with time within single bursts

Hard to soft evolution

featureless continuum power-laws - peak in F F ~ Ea F ~ Eb

Epeak

Jet half opening

angle

Jet effect , S

urf.

Relativistc beaming:

emitting surface

1/

1/

Log(t)

Log(F) Jet

break

>> 1/

X-ray Flashes and X-ray Rich Bursts

• XRFs prompt emission spectrum peaks at energies tipically one order of magnitude lower than those of GRBs.

XRFs empirically defined by a greater fluence in the X-ray band (2-30keV) than in the γ-ray band (30-400keV).

• XRR are an intermediate class between XRFs and GRBs

Why GRBs are so studied for the correlations?

GRBs are extremely energetic events and are expected to be visible out to z ~ 15-20 (Lamb & Reichart, 2000, ApJ, 536, 1), which is further than that obtainable by quasars (zmax ~ 6). GRB z ~ 6.7 (Tagliaferri et al. 2005)

Potential use of GRBs to derive an extended z Hubble-diagram.

Amat

i et

al. 2

002

9+2 BeppoSAX GRBs

E peak

E iso

0.5

Peak energy – Isotropic energy Correlation

E pe a

k(1+

z)

+ 21 GRBs (Batse, Hete-II, Integral)

Ghi

rlan

da, G

hise

llini

, Laz

zati

200

4Am

ati 2

006

(mos

t re

cent

upd

ate)

E peak

E iso

0.5

X2=35

7/28

E pe a

k(1+

z)

Eiso

Nav

a et

al.

2006

; Ghi

rlan

da e

t al

. 200

7

“Amati

” (62

)

“Ghi

rland

a”

(25)

1- cos jet

Why is the Ghirlanda relation, Eg (Epeak) 1.5, different from the Amati relation, Eiso Epeak 0.5 ? Because of the correction of

the beaming angle

Model dependent: uniform jet + homogeneous density

Model dependent: uniform jet + wind density

Through simple algebra it can be verified that the

model dependent correlations are

consistent with the empirical correlation!

(Nava et al. 2006)

A completely empirical correlation between prompt (Ep, Eiso) and afterglow properties (tbreak)

(Liang & Zhang 2005)

… still not convinced ? …

Good fitConsistentwith other

corr

Firmani et al. 2006

ONLY PROMPT EMISSION

PROPERTIES

A new correlation between Liso, Ep, T0.45

Piro

ast

ro-p

h/00

0143

6 A lot of kinetic energy should remain to power the afterglow

SAX X-ray afterglow light curve

Prompt

The study of prompt vs afterglow

A further step to build LX –Ta relation

Eafterglow < Eprompt

E afterglow

~ 0.1 E prompt

Flux vs observed time

s=0.48

Nar

dini

et

al. 2

006

Luminosity vs rest frame time

s=0.28

Nar

dini

et

al. 2

006

Clustering of the optical luminosities

GRB – Afterglow – Temporal PropertiesGRB multiwavelength

emission

Panaitescu & Kumar

No corr.

LX-Eg correlate in optical and in X?

The X-ray luminosities are more widely used for testing correlations

We also choosed X-ray luminosity for our analysis

• to find a relation involving an observable property to standardize GRBs

• in the same way as the Phillips law with SNeIa

Why we are searching a new correlation?

• GRBs possible cosmological distance estimators since they are observed up z = 8.26, much larger than SNeIa (z = 1.77)

• but GRBs seem to be everything but the standard candles

• with their energetics spanning over seven orders of magnitude

• as an attempt to solve this problem we have probed the relation L-Ta that tries to standardize GRBs:

Dainotti, Cardone and Capozziello, Mon. Not. R. Astron. Soc. 391, L79–L83 (2008)

• the presentation describes a new analysis of the extended GRB afterglow sample

Why we study the L-Ta correlation?

INAF, Bologna, Italy 10 January 2011

Focusing on L2

• L2=

Linearization provides a visual evidence of the claimed model and it gives the quantities as logarithms ready to compute the distance moduli

Linear fits are used to find parameters also of other models which can be linearized

through a suitable transformation of the variables.

Non-linear least-squares (NLLS) Marquardt-Levenberg algorithm, .a and b computed by the fit.

Values for -1.17 < b < -1.91

bat tbaL logloglog

yy

xx

Time rescaled to restframe

The tbreak of the lightcurve is highly variable 103<tstart<104s

btLb

starttL The Spearman coefficient of correlation is 0.75

How can we improve it?

Increasing the statistic of GRBs observed by the same instruments to see if there is a selection effect depending on the instruments and improving the statistical method

We used Ta and Fa values computed through Willingale et al. 2007 of the afterglow and the D’Agostini method as statistical method.

The correlation is new because it involves only the afterglow quantities

Will

inga

le e

t al

. 20

07

SWIFT

aac

cctTta

a

(Tc, Fc) is the transition between the exponential and the power law

αc the time constant of the exponential decay, Tc/αc

•tc marks the initial time rise and the time of maximum flux occurring atc

cctTta

In most cases ta=Tp.

No case in which the two componets were sufficiently separated such that this time could be fitted as a free parameter. We are unable to see the rise of the afterglow component because the promptcomponent always dominates at early times and ta could be much less than Tp formost GRBs.

The phenomenological formula

)exp(tt

TtF a

aa

a

a

)/()/( ttTtp

pppp eeF aa

• 1)f_c(t) = f_p(t) + f_a(t)

• 2)f_p(t)=

• fa(t)=

Willingale at al. 2007

For t<Ta

aTt

Negligible if ta=0 and in that case we return to the simple case of power law decay

General treatment

3) Lbol = 4 πDL2 (z) P bol

max

min

)(

)(1/10000

1/1E

E

zkeV

zkeVbolo

dEEE

dEEEPP

Pbolo is the bolometric flux, while P is the peak flux, Emin-Emax is the energy range in which P occurs

f(t)=f (Ta)=fa(Ta)

3) LX(Ta) = 4 πDL 2(z) FX(Ta)=aTab

We compute the X-ray luminosities at the time Ta so that we have to set

Since the contribution on the prompt component is typically smaller than the 5%,Much lower than the statistical uncertainty on Fa(Ta).Neglecting Fp(Ta) we reduce the error on Fx(Ta) without introducing any bias.

E_min, E_max = (0.3, 10) keV set by theinstrument bandpass

max

min

)(

)()(

1max/

1min/E

E

zE

zEX

dEEE

dEEEtfF

• Due to the limited energy range, the GRB spectrum may be described by a simple

• power law

• β(t)• βp for the prompt phase

• βpd for the prompt decay

• βa for the plateau observed at the time Ta

• βad for the afterglow at t > Ta

We estimate βa because we compute Fx(Ta)

bEE )(

Afterglow LT correlation

- canonical vs irregular light curves

Dainotti et al. ApJL, 722, L 215 (2010)

= the source rest frame isotropic X-ray luminosity

= the transition time separating the afterglow plateau phase and the power-law decay phase

baaXLaX TaTFDTL *)(4)( 2

)( aX TL

z

MM

Lz

dzzHcD

03

0 )1()'1(

')1(

aaX TTL )(

aT

(E min, E max) = (0.3, 10) keV - the instrument energy band

max

min

)(

)(

)(

)1max/(

)1min/(E

E

zE

zEX

dEEE

dEEE

tfF

INAF, Bologna, Italy 10 January 2011

Data and methodologySample : afterglows detected by Swift from January 2005 up to March 2009

Redshifts : from the Greiner's web page http://www.mpe.mpg.de/jcg/grb.html.

Spectrum for each GRB was computed using the Evan's web page http://www.swift.ac.uk/xrt curves in the filter time Ta ± σTa

For some GRBs in the sample the error bars are so large that determination of the observables (Lx, Ta ) is not reliable. We therefore study effects of excluding such cases from the analysis (for details see Dainotti et al. 2011 to appear in ApJ ).

To study the low error subsamples we use the respective logarithmic errors bars to formally define the error parameter

2/122 )( TaLxu ss INAF, Bologna, Italy 10 January 2011

INAF, Bologna, Italy 10 January 2011

aX TL **

L*x(Ta) vs T*a distribution for the sample of 62 long afterglows

D’Agostini method (D’Agostini 2005 )

errors measurements on both x and y

The computations errors

• the parameters of interest are given with their 90%confidence ranges.

• Following Willingale (priv. comm.), we have assumed independent Gaussian

• errors and obtained 1 sigma uncertainties by roughly dividing by 1.65 the 90% errors.

Important remark

• The presence of the luminosity distance in the equation 1) DL(z) = (c/H0) dL(z)

dL(z)= (1+z)*

constrain us to adopt a cosmological model to compute Lx(Ta)

• with (ΩM,h)=(0.291, 0.697)

(ΛCDM)

z

MM z

dz

03 )1()'1(

'

The program to compute dl• ΩM=0.291• h0=0.697*100• c=300000• Mpc=3.08*10^(24)

DLz : 1 z NIntegrate1 Sqrt 1 t ^3 1 , t, 0, z name ReadList"directorynamegrbname.txt", TableString, 1 name Partname, All, 1z ReadList"directorynamegrbz.txt", Table Number, 1 z Partz, All, 1Fori 1, i 107, i , Printnamei , " z", z i , " DL", Mpc^2 c h0 DLz i ^2

• L and Ta • measurement errors :σL, σTa

• statistical uncertainties on log(L), log(Ta) : • (σL)/L *(1/ln(10) , (σTa)/Ta *(1/ln(10) respectively. • These errors may be comparable so that it is not possible to decide what is

the independent variable to be used in the usual χ2 fitting analysis.• Moreover, the relation L = a Tab may be affected by an intrinsic• scatter σint of unknown nature that has to be taken into• account. • to determine the parameters (a, b, σint)• a Bayesian approach D’agostini 05 thus maximizing the likelihood function• L(a, b, σint) = exp (-L(a, b, σint).

The error computationsThe D’Agostini Method

Error on Lx(Ta)

• error[L_X(T_a)] = L_X(Ta) * {(DeltaF/F)^2 + [log(1+z)]^2 * DeltaBetaa}^{1/2}

• (DeltaF/F)^2 = (TpErr/Tp)^2 + (TaErr * Tp/Ta^2)^2 + (FaErr/Fa)^2

(FaErr/Fa)^2 = [ln(10)]^2 * [(logTaErr/logTa)^2 + (logFaTaErr/logFata)^2]

The likelihood

• whose maximization is performed in the two parameter space (b, σint) since a may be estimated analytically

• so that we will not consider it anymore as a fit parameter.

• (a, b, σint) = (48.54, -0.74, 0.43)

The goodness of the fit

Defining the best fit residuals as

δ = yobs – yfit, < δ>=-0.08

δ does not correlate with the other parameters of the fitted fluxSperman correlation coefficient r =-0.23 between and δ and z favours no significative evolution of the Lx - Ta relation with the redshift ( in the exercise you will do the same but simply beetwen Lx-z and Ta-z)

δ rms = 0.52

The comparison between the statistical methods

• the best fit obtained through a Levemberg Marquardt algorithm with 1.5 σ outliers rejection

• (a, b) = (48.58, -0.79) in good agreement with the below maximum likelihood estimator results are

independent on the fitting method (a, b, σint) = (48.54, -0.74, 0.43).

• since the Bayesian approach is better motivated and also allows for an intrinsic scatter, we hereafter elige this as our preferred technique.

• (but you will use in the excercise for semplicity the Levemberg Marquardt algorithm)

solid lines D’Agostini method

dashed lines Levemberg-Marquardt estimator

Best fit curves

• Two parameters correlation• A small scatter compared to the other correlation• Well defined quantities involved Lx(Ta) and Ta• A good sample • No evolution with redshift

• Lx(Ta) is not an observable!

Disavantage

Advantages

HOW TO FIND THE LIGHTCURVES AND SPECTRA

http://www.swift.ac.uk/xrt_spectra/00100585/

http://www.swift.ac.uk/xrt_curves/00100585/

The temporal decays parameters corresponding to a certain time region and the spectral decay ones are in the following papers

arXiv.org > astro-ph > arXiv:0812.3662v1

arXiv.org > astro-ph > arXiv:0812.4780v1

arXiv.org > astro-ph > arXiv:0704.0128v2

http://www.swift.ac.uk/burst_analyser/00148225/#BAT

Exercise• 1) dowload the name of the GRBs with firm redshifts From http://www.oa.uj.edu.pl/M.Dainotti/GRB2010/

GRBupdate_selescted_z.xls 2) Download all the lightcurves indicated in the file with firm

redshift go to http://www.swift.ac.uk/burst_analyser/• In the all range XRT and BAT lightcurve• 3)Install the EDA package on the PC• 4)take off from the lightcurves the flares • 5)find the parameters Tp,to,Fp, from the BAT • 6)find using Tp the parameters Ta,Fa, necessary to compute

Lx(Ta)• 7) compute the spectral index beta_afterlow• 8) compute Lx(Ta) for the GRBs in the table