Blazars distance indications from Fermi and TeV data
Elisa Prandini, Giacomo Bonnoli, Laura Maraschi, Mose' Mariotti, Fabrizio Tavecchio
aa r X i v : . [ a s t r o - ph . C O ] J a n Blazars distance indications from
Fermi and TeV data
E.Prandini ( )( ∗ ) , G. Bonnoli ( ) , L. Maraschi ( ) , M. Mariotti ( )and F. Tavecchio ( ) ( ) Dipartimento di Fisica & INFN Padova, via Marzolo 8, 35134, Padova ( ) Osservatorio Astronomico di Merate, via E. Bianchi 46, 23807, Merate (Lc) ( ) Osservatorio Astronomico di Brera, via Brera 28, 20121, Milano
Summary. — A new method to constrain the distance of blazars with unknownredshift using combined observations in the GeV and TeV regimes will be presented.The underlying assumption is that the Very High Energy (VHE) spectrum correctedfor the absorption of TeV photons by the Extragalactic Background Light (EBL)via photon-photon interaction should still be softer than the extrapolation of thegamma-ray spectrum observed by Fermi/LAT. Starting from the observed spectraldata at VHE, the EBL-corrected spectra are derived as a function of the redshift zand fitted with power laws. Comparing the redshift dependent VHE slopes with thepower law fits to the LAT data an upper limit to the source redshift can be derived.The method is applied to all TeV blazars detected by LAT with known distanceand an empirical law describing the relation between the upper limits and the trueredshifts is derived. This law can be used to estimate the distance of unknownredshift blazars: as an example, the distance of PKS 1424+240 is inferred.PACS – X and γ -ray telescopes and instrumentation.PACS – Active and peculiar galaxies and related systems.PACS – Background radiations.
1. – Introduction
The extragalactic TeV sky catalogue (
E >
100 GeV), counts nowadays 45 objects( ).Many of these sources have been recently detected also at GeV energies by the Fermi satellite [1], allowing for the first time a quasi-continuous coverage of the spectral shapeof extragalactic VHE emitters over more than 4 decades of energy. The large majorityof extragalactic TeV emitting objects are blazars, radio-loud active galactic nuclei with ( ∗ ) e-mail: [email protected]( ∼ rwagner/sources/ 1 E.PRANDINI ETC.
Source Name z [real] Fermi /LAT slope TeV slope z ∗ Mkn 421 0.030 1.78 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± −
489 0.071 1.91 ± ± ± ± ± ± −
304 0.116 1.87 ± ± ± ± ± ± ± ± ± ± ± ± a,b ± ± ± c ± ± ± a ± ± ± ± ± ± Table
I. –
TeV blazars used in this study. The sources used in this study are listed in the firstcolumn, their redshift (second column), their Fermi/LAT slope (third column), the VHE slopeof the observed differential energy spectrum fit (fourth column) and the value z ∗ (last column). a Uncertain; b from [5]; c from [6]. Detailed references can be found in [3]. a relativistic jet closely oriented toward the Earth, as described in [2]. Here, we discussa method, recently published in [3], to derive an upper limit on the redshift of a blazar,based on the comparison between the spectral index at GeV energies as measured by LAT(unaffected by the cosmological absorption up to redshifts far beyond those of interesthere) and the TeV spectrum corrected for the absorption. Starting from the derivedlimits, we find a simple law relating these values to real redshift, which can be used toguess the distance of unknown redshift blazars. We assume a cosmological scenario with h = 0 .
72, Ω M = 0 . Λ = 0 .
2. – Results
The photon flux emitted by a blazar in both GeV and TeV regimes can be well approxi-mated by power laws, of the form dN/dE = f ( E/E ) − Γ , where Γ is the power-law index.At VHE, the photons of the spectrum interact with the extragalactic background light(EBL), via electron-positron pair creation. Quantitatively, the effect is an exponentialattenuation of the flux by a factor τ ( E, z ), where τ is the optical depth, a function of bothphoton energy and source redshift. Thus, the observed differential energy spectrum froma blazar, F obs , is related to the emitted one, F em , according to F obs ( E ) = e − τ ( E ) F em ( E ).In order to estimate a safe upper limit to the source distance, we can reasonablyassume that the intrinsic spectrum at TeV energies cannot be harder than that in theadjacent GeV band. Indeed, from the brightest objects studied at both GeV and TeVenergies it appears that the SED is continuous, with a broad peak not requiring ad-ditional spectral components [4]. Hence, a natural assumption is to require that theslope measured in the GeV energy range is a limit value for the power-law index of thede-absorbed TeV spectrum.For the study, we consider the blazar sample listed in table I and containing all the LAZARS DISTANCE INDICATIONS FROM
FERMI
AND TEV DATA z[true] -1 z * -1 / ndf χ ± ± χ ± ± Fig. 1. – z ∗ versus true redshift derived with the procedure described in the text. The openpoints are the two uncertain redshift sources, namely 3C 66A and S5 0716+714, not used in thefit calculation (continuous line). The dashed line is the bisector. extragalactic TeV emitters located at redshift larger than z = 0 .
01, detected by LATafter taking 5.5 months of data [1]. In order to estimate the redshift z ∗ for which theTeV spectral slope equals to the GeV one, the measured spectral points of each sourcehave been corrected for the corresponding absorption factor [7], starting from redshift z = 0 .
01, and the resulting spectrum fitted with a power law. The procedure, appliedin fine steps of redshift, is iterated until the slope of the de-absorbed spectrum equalsto the one measured by LAT. The corresponding redshift, z ∗ , reported in table I, is thelimit value on the source distance.Among the 16 sources considered in this study, 14 blazars have well-known red-shift and are used to test the method, while the remaining two blazars (3C 66A andS5 0716+714) have uncertain redshift, and are considered separately. The errors on z ∗ are estimated taking into account both errors on the TeV and LAT slopes. Fig. 1 showsthe comparison between the known redshift, x -axis, and z ∗ . All the z ∗ lie above thebisector (dashed line) meaning that their values are larger than those of the the real red-shift z [ true ]. This is expected since we are not considering the presence of the intrinsicbreak in the blazar spectra, and confirms that the method can be used to set safe upperlimits on blazars distance. The only exceptions are the two sources with uncertain dis-tance, S 0716+714 and 3C 66A (open circles). This could be either due to some intrinsicproperties of the sources or to a wrong estimate of their distances. In the latter case,our method would constrain, at two sigma level, the redshift of S5 0716+714 below 0 . . z ∗ is related to this steepening, it isnatural to assume that also z ∗ and z [true] are related by a linear function, of the form z ∗ = A + Bz [true]. The meaning of the coefficients is rather transparent: basically A is ameasure of the intrinsic spectral break of the sources, while, following [8], B is a measure(increasing values for decreasing EBL level) of the optical depth of the EBL model used.We interpolate with this linear function the data with well-known distance of figure 1.The linear fit (continuous line) has a probability of 62%. Once derived this empiricalrelation, one can use it to determine the redshift of sources with uncertain distance. For E.PRANDINI ETC.
Energy [GeV] ] - T e V - s - d N / d E [ c m -12 -11 -10 PKS 1424+240 observed spectrumPKS 1424+240 deabsorbed spectrum (z = 0.382)Power law fit
Fig. 2. – Measured (open points) and deabsorbed (filled points) spectrum of PKS 1424+240 atredshift z = 0.382. S5 0716+714 the reconstructed redshift is z [ rec ] = 0.11 ± z [ rec ] = 0.21 ±
3. – The redshift of PKS 1424+240
As a final example of application, we use our procedure on PKS 1424+240, a blazar ofunknown redshift recently observed in the VHE regime by Veritas [9]. The slope spectrummeasured by
Fermi /LAT between 0 . . ± .
05. The corresponding z ∗ redshift at which the de-absorbed TeV spectrum slope becomes equal to it, is 0 . ± . . ± .
1, reported in [9], calculated applying the same procedure but only simultaneous
Fermi data. Our estimate on the most probable distance for PKS 1424+240, obtainedby inverting the z ∗ formula, is z [rec]= 0 . ± .
05, where, as before, the error quoted isestimated in [3]. ∗ ∗ ∗
GB, LM and FT acknowledge a 2007 Prin-MIUR grant for financial support.
REFERENCES[1]
Abdo A. A. et al. , ApJ , (2009) 1310.[2] Urry, C. M. and
Padovani, P. , PASP , (1995) 803[3] Prandini, E., Bonnoli, G., Maraschi, L., Mariotti, M. and
Tavecchio, F. , MNRAS , (2010) L76[4] Aharonian F. et al. , ApJ , (2009) L150[5] Nilsson K., Pursimo T., Sillanp¨a¨a A., Takalo L. O. and
Lindfors E. , A&A , (2008) L29[6] Danforth, C. W., Keeney, B. A., Stocke, J. T., Shull, J. M. and
Yao, Y. , submittedto ApJ[7]
Franceschini A., Rodighiero G. and
Vaccari M. , A&A , (2008) 837[8] Stecker F. W. and
Scully S. T. , ApJ , (2010) L124[9] Acciari V. A. et al. , ApJ ,708