Measuring cosmological parameters with GRBs

Transcription

1 Measuring cosmological parameters with GRBs Lorenzo Amati Italian National Institute for Astrophysics (INAF), Bologna with contributions by: M. Della Valle, S. Dichiara, F. Frontera, C. Guidorzi

2 Why look for more cosmological probes? q different distribution in redshift -> different sensibility to different cosmological parameters D L = { [ ] } z k k 1+ z + Ω 1+ z' dz' ( ) ( ) ( ) 1+ z c H o k S 0 M + Ω Λ

3 q Each cosmological probe is characterized by possible systematics q e.g SN Ia: Ø different explosion mechanism and progenitor systems? May depend on z? Ø light curve shape correction for the luminosity normalisation may depend on z Ø signatures of evolution in the colours Ø correction for dust extinction Ø anomalous luminosity-color relation Ø contaminations of the Hubble Diagram by no-standard SNe-Ia and/or bright SNe-Ibc (e.g. HNe)

4 If the offset from the truth is just 0.1 mag. (slide by M. della Valle)

5 Guy et al Astier et al Recent results from SNLS (231 SNe Ia at 0.15 < z < 1.1, Guy et al. 2010) compared to those of Astier et al (44 low redshift SNe along with the 71 SNe from the SNLS first year sample)

6 Are GRB standard candles? q all GRBs with measured redshift (~250, including a few short GRBs) lie at cosmological distances (z = ) (except for the peculiar GRB980425, z=0.0085) q isotropic luminosities and radiated energy are huge and span several orders of magnitude: GRB are not standard candles (unfortunately) Jakobsson, 2009 Amati, 2009

7 q jet angles, derived from break time of optical afterglow light curve by assuming standard scenario, are of the order of few degrees q the collimation-corrected radiated energy spans the range ~5x x10 52 erg-> more clustered but still not standard Ghirlanda et al., 2004

8 q GRB have huge luminosity, a redshift distribution extending far beyond SN Ia q high energy emission -> no extinction problems Ghirlanda et al, 2006

9 q GRB have huge luminosity, a redshift distribution extending far beyond SN Ia q high energy emission -> no extinction problems q potentially powerful cosmological sources but need to investigate their properties to find ways to standardize them (if possible) Ghirlanda et al, 2006

10 Ø GRB spectra typically described by the empirical Band function with parameters α= low-energy index, β= high-energy index, E 0 =break energy Ø E p = E 0 x (2 + α) = observed peak energy of the νfν spectrum Ø measured spectrum + measured redshift -> intrinsic peak enery and radiated energy E p,i = E p x (1 + z) The Ep,i Eiso correlation 190 GRB Ep Jakobsson (2009)

11 Ø ~250 GRBs with measured redshift, about 50% have measured spectra Ø both Ep, i and Eiso span several orders of magnitude and a distribution which can be described by a Gaussian plus a low energy tail ( intrinsic XRFs and sub-energetic events) 95 GRBs, sample of Amati, Frontera & Guidorzi, A&A (2009)

12 Ø Amati et al. (A&A 2002): significant correlation between Ep,i and Eiso found based on a small sample of BeppoSAX GRBs with known redshift BeppoSAX GRBs

13 Ø Ep,i Eiso correlation for GRBs with known redshift confirmed and extended by measurements of ALL other GRB detectors with spectral capabilities 120 long GRBs as of Oct BeppoSAX GRBs

14 Ø Ep,i of Swift GRBs measured by Konus-WIND, Suzaku/WAM, Fermi/GBM and BAT (only when Ep inside or close to kev and values provided by the Swift/ BAT team (GCNs or Sakamoto et al. 2008). Swift GRBs

15 Ø strong correlation but significant dispersion of the data around the best-fit powerlaw; the distribution of the residuals can be fit with a Gaussian with σ(logep,i) ~ 0.2 Ø the extra-statistical scatter of the data can be quantified by performing a fit whith a max likelihood method (D Agostini 2005) which accounts for sample variance and the uncertainties on both X and Y quantities Ø with this method Amati et al. (2008, 2009) found an extrinsic scatter σ int (logep,i) ~ 0.18 and index and normalization t ~0.5 and ~100, respectively

16 Ø definite evidence that short GRBs DO NOT follow the Ep.i Eiso correlation: a tool to distinguish between short and long events and to get clues on their different nature (e.g., Amati 2006, Piranomonte et al. 2008, Ghirlanda et al. 2009)

17 Ø the only long GRB outlier to the correlation is the peculiar GRB (very low redshift z = , sub-energetic, inconsistent with most other GRB properties) GRB

18 Ø Up to date (March 2011) Ep,i Eiso plane: 126 long GRBs, 4 XRFs, 13 short GRBs

19 Standardizing GRB with spectrum-energy correlations q 2004: evidence that by substituting Eiso with the collimation corrected energy Eγ the logarithmic dispersion of the correlation decreases significantly and is low enough to allow its use to standardize GRB (Ghirlanda et al., Dai et al, and many)

20 q Method (e.g., Ghirlanda et al, Firmani et al., Dai et al., Zhang et al.): E p,i = E p,obs x (1 + z), tb,i = tb / /1 + z) D l = D l (z, H 0, Ω M, Ω Λ, ) Ø fit the correlation and construct an Hubble diagram for each set of cosmological parameters -> derive c.l. contours based on chi-square

21 q What can be obtained with 150 GRB with known z and Ep and complementarity with other probes (SN Ia, CMB) q complementary to SN Ia: extension to much higher z even when considering the future sample of SNAP (z < 1.7), cross check of results with different probes Ghirlanda, Ghisellini et al. 2005, 2006,2007

22 q Some problems with 3-parameters spectrum-energy correlations Ø lack of jet breaks in several Swift X-ray afterglow light curves, in some cases, evidence of achromatic break Ø challenging evidences for Jet interpretation of break in afterglow light curves or due to present inadequate sampling of optical light curves w/r to X-ray ones and to lack of satisfactory modeling of jets?

23 q the Ep-Eγ shows slightly different slope and dispersion but depends on the assumptions on the circum-burst environment density profile (ISM or wind) q in the wind case the slope is more close to 1 (-> linear correlation) and the dispersion slightly lower ISM WIND Nava et al.., A&A, 2005: ISM (left) and WIND (right)

24 q Liang & Zhang (2005) ans Xu (2005) performed a multi-variable correlation analysis between various observables of prompt and afterglow, founding a tight correlation between Epi, Eiso and tb q with respect to Ep,i Eγ correlation it has the advantage of being model independent, but it is somewhat more dispersed

25 Ø growing number of outliers to the Ep-Eiso-tb correlation GRB C GRB071010B Amati, Frontera, Guidorzi 2009 Urata et al. 2009

26 q A tight correlation between Ep,i, Lpeak,iso and time scale T 0.45 was found, also based on still small number of events and proposed for standardizing GRBs (Firmani et al and others)

27 q but Rossi et al and Schaefer et al. 2008, based on BeppoSAX and Swift GRBs, showed that the dispersion of the Lp-Ep-T 0.45 correlation is significantly higher than thought before and that the Ep,i-Lp,iso-T0.45 correlation my be equivalent to the Ep,i-Eiso correlation

28 Using the simple E p,i -E iso correlation for cosmology q Ep,i Eiso vs. other spectrum-energy correlations Ep,i Liso 04 Eiso<->Liso Ep,i Eiso Amati 02 Eiso<->Lp,iso Ep,i Lp,iso Yonetoku 04 tb,opt + jet model tb,opt T0.45 = Ep,i Eγ Ghirlanda 04 Ep,i Eiso-tb Liang-Zhang 05 Ep,i Lp,iso-T0.45 Firmani 06

29 q Eiso is the GRB brightness indicator with less systematic uncertainties q Liso is affected by the often uncertain GRB duration (e.g., long tails of Swift GRBs); q Lp,iso is affected by the lack of or poor knowledge of spectral shape of the peak emission (the time average spectrum is often used) and by the subjective choice and inhomogeneity in z of the peak time scale q addition of a third observable introduces further uncertainties (difficulties in measuring t_break, chromatic breaks, model assumptions, subjective choice of the energy band in which compute T 0.45, inhomogeneity on z of T 0.45 ) and substantially reduces the number of GRB that can be used (e.g., #E p,i E γ ~ ¼ #E p,i E iso )

30 q Amati et al. (2008): let s make a step backward and focus on the Ep,i Eiso correlation Ep,i Liso 04 Eiso<->Liso Ep,i Eiso Amati 02 Eiso<->Lp,iso Ep,i Lp,iso Yonetoku 04 tb,opt + jet model tb,opt T0.45 = Ep,i Eγ Ghirlanda 04 Ep,i Eiso-tb Liang-Zhang 05 Ep,i Lp,iso-T0.45 Firmani 06

31 q Amati et al. (2008): let s make a step backward and focus on the Ep,i Eiso correlation Ep,i Liso 04 Eiso<->Liso Ep,i Eiso Amati 02 Eiso<->Lp,iso Ep,i Lp,iso Yonetoku 04 tb,opt + jet model tb,opt T0.45 = Ep,i Eγ Ghirlanda 04 Ep,i Eiso-tb Liang-Zhang 05 Ep,i Lp,iso-T0.45 Firmani 06

32 q does the extrinsic scatter of the E p,i -E iso correlation vary with the cosmological parameters used to compute E iso? D l = D l (z, H 0, Ω M, Ω Λ, ) 70 GRB Amati et al. 2008

33 q a fraction of the extrinsic scatter of the E p,i -E iso correlation is indeed due to the cosmological parameters used to compute E iso q Evidence, independent on SN Ia or other cosmological probes, that, if we are in a flat ΛCDM universe, Ω M is lower than 1 Simple PL fit Amati et al Amati et al. 2008

34 q By using a maximum likelihood method the extrinsic scatter can be parametrized and quantified (e.g., D Agostini 2005) q Ω M can be constrained to (68%) and (90%) for a flat ΛCDM universe (Ω M = 1 excluded at 99.9% c.l.) q significant constraints on both Ω M and Ω Λ expected from sample enrichment Amati et al. 2008

35 q analysis of an updated sample of 109 GRBs shows significant improvements w/r to the sample of 70 GRBs of Amati et al. (2008) q this evidence supports the reliability and perspectives of the use of the Ep,i Eiso correlation for the estimate of cosmological parameters Ωm (flat universe) 68% 90% 70 GRBs (Amati 08) GRBs (Amati 10) GRBs 109 GRBs

36

37 GRB

38 But is the Ep,i Eiso correlation real? q different GRB detectors are characterized by different detection and spectroscopy sensitivity as a function of GRB intensity and spectrum q this may introduce relevant selection effects / biases in the observed Ep,i Eiso and other correlations Band 2008 Ghirlanda et al. 2008

39 q claims that a high fraction of BATSE events (without z) are inconsistent with the correlation (e.g. Nakar & Piran 2004, Band & Preece 2005, Kaneko et al. 2007, Goldstein et al. 2009) q but is it plausible that we are measuring the redshift only for the very small fraction (15-20%) of GRBs that, accordingly to these authors, follow the Ep,i Eiso correlation? This would imply unreliably huge selection effects in the sample of GRBs with known redshift q in addition: Ghirlanda et al. (2005), Bosnjak et al. (2005), Ghirlanda et al. (2008) show that most BATSE GRBs with unknown redshift are consistent with the correlation q Substantially different conclusions, but data are data, it cannot be a matter of opinions! q Explanation: Nakar & Piran, Band & Preece, Kaneko et al., Goldstein et al. are substantially underestimating the extrinsic scatter of the Ep,i Eiso correlation

40 ? OK

41 q method: unknown redshift -> convert the Ep,i Eiso correlation into an Ep,obs Fluence correlation Intrinsic (cosm. Rest-frame) plane Observer s plane 3 σ 2 σ 2 σ

42 q method: unknown redshift -> convert the Ep,i Eiso correlation into an Ep,obs Fluence correlation q the fit of the updated Ep,i Eiso GRB sample with the maximum likelihood method accounting for extrinsic variance provides a=0.53, k= 102, σ = 0.19 q for these values f(z) maximizes for z between 3 and 5

43 Intrinsic (cosm. Rest-frame) plane Observer s plane 3 σ 2 σ 2 σ

44 q Amati, Dichiara et al. (2011, in prep.): consider fluences and spectra from the Goldstein et al. (2010) BATSE complete spectral catalog (on line data) q considered long (777) and short (89) GRBs with fit with the Band-law and uncertainties on Ep and fluence < 40% LONG SHORT Ø most long GRBs are potentially consistent with the Ep.i Eiso correlation, most short GRBs are not

45 q ALL long GRBs with 20% uncertainty on Ep and fluence (525) are potentially consistent with the correlation LONG, 40% unc. LONG, 20% unc.

46 q measure only the harder portion of the event: overestimate of Ep and underestimate of the fluence

47 q Amati, Dichiara et al. (2011, in prep.): MC simulations assuming the existence and the measured parameters of the Ep,i Eiso correlation and accounting for the observed distributions (Eiso, z, Eiso vs. z) and BATSE instrumental sensitivity as a function of Ep (Band ) q When accounting for spectral evolution, i.e. Ep = f(flux), the small fraction of outliers in the Ep,obs Fluence plane is reproduced

48 q Amati, Frontera & Guidorzi (2009): the normalization of the correlation varies only marginally using GRBs measured by individual instruments with different sensitivities and energy bands Amati, Frontera & Guidorzi 2009

49 q selection effects in the process leading to the redshift estimate are also likely to play a relevant role (e.g., Coward 2008) q Swift: reduction of selection effects in redshift -> Swift GRBs expected to provide a robust test of the Ep,i Eiso correlation

50 Ø Ep,i of Swift GRBs measured by Konus-WIND, Suzaku/WAM, Fermi/GBM and BAT (only when Ep inside or close to kev and values provided by the Swift/ BAT team (GCNs or Sakamoto et al. 2008):Swift GRBs are consistent with the Ep,i Eiso correlation Red points = Swift GRBs Slope ~ 0.5 σ (logep,i) ~ 0.2 Gaussian distribution of data scatter

51 Ø the Ep,i Liso correlation holds also within a good fraction of GRBs (Liang et al. 2004, Firmani et al. 2008, Frontera et al. 2009, Ghirlanda et al. 2009): robust evidence for a physical origin and clues to explanation Liang et al., ApJ, 2004 Frontera et al (in prep.)

52 Combining spectrum-energy correlations with other (less tight) GRB correlations (e.g., Schaefer 2007, Mosquera Cuesta et al. 2008) Luminosity-Variability correlation (Reichart et al., Guidorzi et al., Rizzuto et al.) Luminosity-time lag correlation (Norris et al.)

53 Ø pseudo redshift estimates and GRB Hubble diagram Ø cosmological parameters consistent with standard cosmology with no dark energy evolution Ø drawbacks: no substantial improvements in estimation accuracy with respect to spectrum-energy correlations alone; adding other more dispersed correlations and new observables adds more systematics and uncertainties (and some correlations are not independent)

54 Calibrating spectrum-energy correlations with SN Ia Ø Very recently, several authors (e.g., Kodama et al., 2008; Liang et al., 2008, Li et al. 2008, Demianski et al ) calibrated GRB spectrum energy correlation at z < 1.7 by using the luminosity distance redshift relation derived for SN Ia Ø The aim is to extend the SN Ia Hubble diagram up to redshift where the luminosity distance is more sensitive to dark energy properties and evolution Ø Obtained significant constraints on both Ω M and Ω Λ but with this method GRB are no more an indipendent cosmological probe

55 Investigating other correlations: the Lx Ta correlation Ø A tight correlation between the time, Ta, and the luminosity, Lx, of the end of the plateau phase in GRB X-ray afterglows was recently reported (Dainotti et al. 2008,2010)

56 Using E p,i E iso correlation for z estimates Ø redshift estimates available only for a small fraction of GRBs occurred in the last 10 years based on optical spectroscopy Ø pseudo-redshift estimates for the large amount of GRB without measured redshift -> GRB luminosity function, star formation rate evolution up to z > 6, etc. Ø use of the Ep,i Eiso correlation for pseudo-redshift: most simple method is to study the track in the Ep,i - Eiso plane ad a function of z Ø not precise z estimates and possible degeneracy for z > 1.4 Ø anyway useful for low z GRB and in general when combined with optical

57 q The case of GRB B at a photometric redshift of ~9.4! (Cucchiara et al. 2011, ApJ, in press + press releases of May 25)

58 The future: what is needed? q increase the number of z estimates, reduce selection effects and optimize coverage of the fluence-ep plane in the sample of GRBs with known redshift q more accurate estimates of Ep,i by means of sensitive spectroscopy of GRB prompt emission from a few kev (or even below) and up to at least ~1 MeV NARROW BAND BROAD BAND q Swift is doing greatly the first job but cannot provide a high number of firm Ep estimates, due to BAT narrow energy band (sensitive spectral analysis only from 15 up to ~200 kev) q in last years, Ep estimates for some Swift GRBs from Konus (from 15 kev to several MeV) and, to minor extent, RHESSI and SUZAKU

59 q present and near future: main contribution expected from joint Fermi + Swift measurements Ø Up to 2009: ~290 Fermi/GBM GRBs, Ep estimates for ~90%, ~35 simultaneously detected by Swift (~13%), 13 with Ep and z estimates (~10% of Swift sample) Ø 2008 pre-fermi : 61 Swift detections, 5 BAT Ep (8%), 15 BAT + KONUS + SUZAKU Ep estimates (25%), 20 redshift (33%), 11 with Ep and z estimates (~15% of Swift sample) Ø Fermi provides a dramatic increase in Ep estimates (as expected), but a only small fraction of Fermi GRBs is detected / localized by Swift (~15%) -> low number of Fermi GRBs with Ep and z (~5%). Ø It is difficult to improve this number: BAT FOV much narrower than Fermi/GBM; similar orbits, each satellite limited by Earth occultation but at different times, ) Ø Summary: GRB/year in the Ep,i Eiso plane

60 q In the > 2014 time frame a significant step forward expected from SVOM: Ø spectral study of prompt emission in kev -> accurate estimates of Ep and reduction of systematics (through optimal continuum shape determination and measurement of the spectral evolution down to X-rays) Ø fast and accurate localization of optical counterpart and prompt dissemination to optical telescopes -> increase in number of z estimates and reduction of selection effects Ø optimized for detection of XRFs, short GRB, subenergetic GRB, high-z GRB Ø substantial increase of the number of GRB with known z and Ep -> test of correlations and calibration for their cosmological use

61 Conclusions and perspectives Ø Given their huge radiated energies and redshift distribution extending from ~ 0.1 up to > 9, GRBs are potentially a very powerful cosmological probe, complementary to other probes (e.g., SN Ia, clusters, BAO) Ø The Ep,i Eiso correlation is one of the most robust (no firm evidence of significant selection / instrumental effects) and intriguing properties of GRBs and a promising tool for cosmological parameters Ø Analysis in the last years (>2008) provide already evidence, independent on, e.g., SN Ia, that if we live in a flat ΛCDM universe, Ωm is < 1 at >99.9% c.l. (χ 2 minimizes at Ωm ~ 0.25, consistent with standard cosmology) Ø the simulatenous operation of Swift, Fermi/GBM, Konus-WIND is allowing an increase of the useful sample (z + Ep) at a rate of GRB/year, providing an increasing accuracy in the estimate of cosmological parameters Ø future GRB experiments (e.g., SVOM) and more investigations (statistical tools, simulations, calibration) will improve the significance and reliability of the results

62 END OF THE TALK

63 q estimating cosmological parameters with the Ep,i Eiso correlation by using symmetric statistical methods Symmetric likelihood by Reichart Chi-square with systematic

64 Likelihood by Reichart Likelihood by D Agostini

65 q the quest for high-z GRB Ø for both cosmological parameters and SFR evolution studies it is of fundamental importance to increase the detection rate of high-z GRBs Ø Swift recently changed the BAT trigger threshold to this purpouse Ø the detection rate can be increased by lowering the low energy bound of the GRB detector trigger energy band adapted from Salvaterra et al. 2008

66 q debate on Swift outliers to the Ep-Eγ correlation (including both GRB with no break and a few GRB with achromatic break) q recent Fermi observations confirm the Ep,i Eiso correlation and that the dispersion of the Ep Eγ correlation is likely significantly larger than claimed in Campana et al McBreen et al. 2010