Is the Universe More Transparent to Gamma Rays Than Previously Thought?
aa r X i v : . [ a s t r o - ph ] D ec Submitted to
The Astrophysical Journal Letters
Is the Universe More Transparent to Gamma Rays than Previously Thought?
Floyd W. Stecker
Astrophysics Science Division, NASA Goddard Space Flight CenterGreenbelt, MD 20771, [email protected]
Sean T. Scully
Department of Physics,James Madison University, Harrisonburg, VA 22807, [email protected]
ABSTRACT
The MAGIC collaboration has recently reported the detection of the strong γ -rayblazar 3C279 during a 1-2 day flare. They have used their spectral observations todraw conclusions regarding upper limits on the opacity of the Universe to high energy γ -rays and, by implication, upper limits on the extragalactic mid-infrared backgroundradiation. In this paper we examine the effect of γ -ray absorption by the extragalacticinfrared radiation on intrinsic spectra for this blazar and compare our results with theobservational data on 3C279. We find agreement with our previous results, contrary tothe recent assertion of the MAGIC group that the Universe is more transparent to γ -raysthan our calculations indicate. Our analysis indicates that in the energy range between ∼
80 and ∼
500 GeV, 3C279 has a best-fit intrinsic spectrum with a spectral index ∼ ∼ ∼ Subject headings: gamma-rays: theory, galaxies ; 3C279: cosmology: diffuse radiation
1. INTRODUCTION
It has long been recognized that by studying the spectra of strong extragalactic γ -ray sourcesone can obtain information about the density and energy spectra of intergalactic photon fields. The 2 –luminous blazar 3C279 was discovered by the EGRET detector aboard the Compton Gamma RayObservatory to be a strong flaring γ -ray source (Hartman et al. 1992). Shortly after this discovery,(Stecker, de Jager & Salamon 1992) (hereafter SDS) proposed that the study of the TeV spectraof such sources could be used to probe the intergalactic infrared radiation.SDS proposed to look for the energy dependent features indicating the mutual annihilationof very high energy γ -rays and low energy photons of galactic origin via the process of electron-positron pair production γ + γ → e + + e − . The cross section for this process is exactly determined;it can be calculated using quantum electrodynamics (Breit & Wheeler 1934). Thus, in principle, ifone knows the emission spectrum of an extragalactic source at a given redshift, one can determinethe column density of photons between the source and the Earth as a function of redshift.Since the EGRET discovery of 3C279, the infrared background at wavelengths not totallydominated by galactic or zodiacal emission has been measured by the Cosmic Background Ex-plorer (COBE). In addition, there have been extensive observations of IR emission from galaxiesthemselves, whose total emission is thought to make up the cosmic IR background (see review byHauser & Dwek 2001). The latest extensive observations have been made by the Spitzer satellite.It is thus appropriate to use a synoptic approach combining the very high energy γ -ray observa-tions with the extragalactic IR observations, in order to best explore both the γ -ray emission fromblazars and the diffuse extragalactic IR radiation. Using this approach, one must take account of both the high energy γ -ray observations and the data from the many galaxy observations presentlyavailable.The MAGIC collaboration has recently observed the spectrum of the blazar 3C279 during aflare which occurred on 22–23 February 2006 (Albert et al. 2008). The highly luminous blazar3C279 lies at a redshift of 0.536 (Marzioni et al.1996). To date, it is the most distant γ -ray sourceobserved in the sub-TeV energy range. Thus, as noted by SDS, this source is potentially highlysignificant for probing the intergalactic background radiation.Albert et al. (2008) used their observational data to draw conclusions regarding the maximumopacity of the Universe to γ -rays in the sub-TeV energy range. Their conclusions regarding theextragalactic background radiation would appear to disfavor the results of the extensive semi-empirical calculations of the extragalactic IR background spectrum given by Stecker, Malkan &Scully (2006, 2007) (hereafter SMS). In particular, the limit shown in their Figure 2 appears to beinconsistent with one of the SMS models that was based primarily on galaxy studies by the Spitzerinfrared satellite telescope.In this paper, we will reexamine both the analysis assumptions and the conclusions presentedin the paper of Albert et al. Using a different analysis technique that we show to be superior to thatof Albert et al. , we find that the observations of 3C279 are fully consistent with both diffuse IRbackground models obtained by SMS. We then discuss the implications of these results regardingboth the intrinsic energy spectrum and luminosity of the 3C279 flare and the opacity of the Universeto γ -rays. 3 –
2. The diffuse extragalactic IR background
Various calculations of the extragalactic IR background have been made (Stecker, Puget &Fazio 1977; Malkan & Stecker (1998, 2001); Totani & Takeuchi (2002); Kneiske et al. (2004);Primack et al. (2005); SMS). Of these models, the most empirically based are those of Malkan& Stecker (1998, 2001), Totani & Takeuchi (2002) and SMS. Since the largest uncertainty inthese calculations arises from the uncertainty in the temporal evolution of the star formation ratein galaxies, SMS assumed two different evolution models, viz., a “baseline” model and a “fastevolution” model. These models produced similar wavelength dependences for the spectral energydistribution of the extragalactic IR background, but gave a difference of roughly 30-40% in overallintensity.The empirically based calculations mentioned above include the observationally based contri-butions of warm dust and emission bands from polycyclic aromatic hydrocarbon (PAH) moleculesand silicates, which have been observed to contribute significantly to galaxy emission in the mid-IR(e.g., Lagache et al. 2004). These components of galactic IR emission have the effect of partiallyfilling in the “valley” in the mid-IR spectral energy distribution between the peak from starlightemission and that from cold dust emission. The model of Primack et al. (2005), which was based onstrictly theoretical galaxy spectra, does not take the warm dust, PAH, and silicate emission com-ponents of mid-IR galaxy spectra into account and therefore exhibits a steep mid-IR valley that isin direct conflict with solid lower limits obtained from galaxy counts obtained from observationsof galaxies at mid-IR wavelengths (Altieri et al. 1999; (Elbaz et al2002). This is clearly shown inFigure 2 of the supplemental online material of Albert et al. (2008). However, since Albert et al.(2008) considered it to be a “lower limit” model, we will discuss the Primack et al. model in ouranalysis.
3. The observed spectrum of 3C279 and its derived intrinsic spectrum
According to the MAGIC analysis, the 2006 flare on 3C279 had an observed spectral indexof 4.11 ± ∼
80 and ∼
500 GeV. In their analysis, the MAGICgroup chose to multiply their data points by e τ ( E γ ) , where the optical depth, τ ( E γ )) is chosen byusing the results of various optical depth calculations. They then fit simple power-law spectra tothe resulting fluxes. Using estimated optical depths for only the fast evolution model of SMS, theygave a best-fit power-law spectral index for the intrinsic source spectrum of Γ s of 0.49 ± s ≥ . deabsorbed data points. 4 –Instead we assume an intrinsic power-law spectrum emitted by the source over the limited observedenergy range that covers less than a decade in energy. In order to compare with the observations,we multiply this power law by an absorption factor e − τ ( E γ ,z =0 . , where the optical depth, τ ,is calculated for a redshift z = 0.536. We then employ a nonlinear least squares fit of our twoparameter model to the observational data.Our method has several advantages over that chosen by the MAGIC collaboration. To beginwith, the redshift of the source and the energy range of the observations implies that even thecounts in the lowest MAGIC energy bin have been affected by at least some amount of intergalacticabsorption. As a result, multiplying the data by e τ and then fitting an arbitrary power-law as doneby Albert et al. (2008) does not allow a proper fit to the normalization of the spectrum. Both thetrue blazar luminosity and the true form of the intrinsic spectrum are masked. Furthermore, theactual intrinsic spectrum cannot be assumed to have a power-law form after multiplication by anexponential that is nonlinear in energy at this particular redshift (see, however, Stecker & Scully2006). Also, in order to properly account for the effect of the optical depth, one should directlyinclude it in the unfolding method used to produce the fluxes from the raw photon counts. Sincethe MAGIC data points represent a mean for an energy bin, it is not sufficient to simply multiplythat mean point by e τ . The function e τ ( E γ ) is a rapidly changing function of energy. This fact mustbe taken into account when computing both the spectrum and error bars. The implied weightingtowards a lower energy within a bin indicates that the appropriate value for τ ( E ) should be lowerthan that assumed for the mean energy in the bin. Thus, the values for τ used in the MAGICanalysis are too high for all of the EBL models they used.
4. Analysis
We begin our analysis program by calculating the optical depths in the energy range of theobservations for z = 0.536 for both the SMS fast evolution model and baseline model. For compar-ison, we also consider the optical depths taken from Primack et al. (2005) and two of the modelsof Kneiske et al. (2004) , viz., their best-fit model and their low-IR model. We find that all five ofthe optical depth models considered are well fit by third order polynomials in the energy range ofinterest of the form shown in equation (1).log τ = a log E γ + a log E γ + a log E γ + a (1)Table 1 summarizes the fit parameters to the five models considered here. Figure 1 shows theexcellent agreement of the third order polynomial fits to optical depths for the five models.Because of the nonlinear nature of the energy dependence of the optical depth, we do not expectthat the observed spectrum will have a power-law form. Thus, we fit to spectra that are assumedto be power-law intrinsic source spectra ( KE γ − Γ ) multiplied by e − τ as prescribed by equation(1) using the various optical depth models indicated in Table 1 to take account of intergalactic 5 – Ÿ Ÿ Ÿ Ÿ Ÿ Ÿ Ÿ Ÿ Ÿ Ÿ Ÿ ò ò ò ò ò ò ò ò ò ò òè è è è è è è è è è è è è è è è è è è è ì ì ì ì ì ì ì ì ì ì ì ì ì ì ì ì ì ì ì ø ø ø ø - - E Γ @ GeV D L og Τ Fig. 1.— Polynomial fits to the five optical depth models discussed in the text. The solid lineand dotted line are fits to the SMS fast evolution (triangles) and baseline (filled boxes) modelsrespectively. The short-dashed and long-dashed lines are polynomial fits to the best-fit Kneiske etal. model (filled circles) and low-IR Kneiske et al. model (diamonds) respectively. The dot-dashedline is the polynomial fit to the Primack et al. optical depth model (stars).absorption. We then employ the Levenberg-Marquardt nonlinear least squares method to fit theresulting nonlinear spectra to the observed data. We choose to fit to the data using only statisticalerrors.We first do a χ a fit with two free parameters, viz., the normalization coefficient, K and theintrinsic spectral index of the source Γ s . The best-fit spectral curves for the various EBL modelsconsidered are shown in Figure 2. The corresponding best-fit values K and Γ s are given in Table2. In this table, in the first column, the K values are given for E in GeV. The second column givesthe best-fit spectral indeces for all of the models. The third column gives the χ values for theTable 1. Parameters Used in Equation (1) for Opacity ModelsModel a a a a Fast Evolution 0.0999257 -1.26786 5.36642 -6.21713Baseline 0.103179 -1.28947 5.41409 -6.36993Kneiske Best Fit -0.477755 2.84965 -3.77753 -0.353419Kneiske Low IR -0.334462 1.75885 -1.19612 -2.30134Primack -0.549224 3.43815 -5.63807 1.57098 6 – - - - - - - - - E Γ @ GeV D L ogd N (cid:144) d E @ c m - s - T e V - D Fig. 2.— Plot of the best-fit curves with Γ s and K as free parameters for the SMS fast evolution(solid), SMS baseline (dotted), Kneiske et al. best-fit (short-dashed), Kneiske et al. low-IR (long-dashed), and Primack et al. (dash-dotted) models shown along with the observational data fromAlbert et al. (2008). The shaded region represents the combined systematic and statistical error forthe observational data. The gray curve shows the EGRET flare power-law fit extended to higherenergies multiplied by e − τ ( E ) . The respective χ values are given in the third number column inTable 2.two-parameter best fit. It can be seen from this column that although the best-fit spectral indecesare significantly different for the various EBL models, the best fit χ values are comparable for allof the models.The Levenberg-Marquardt method yields substantially different best-fit spectral indices forour modeled optical depths and those of Kneiske et al. (2004) and Primack et al. (2005). However,these fits are not particularly unique in their goodness of fit. We performed a χ analysis on all ofthe models, allowing both Γ s and K to be free parameters in the fit. As can be seen from Table 2, the form of the intrinsic spectrum of the 3C279 flare is undetermined by the five data bins obtainedby the MAGIC collaboration, even when one only considers the large statistical errors involved andneglects the significant systematic errors. This is because the lower energy points with the smallererror bars are weighted more highly than the highest energy point.Since the minimum χ is almost independent of choice of spectral index, the two-parameterfitting routine mainly tries to move the curve up and down ( i.e. adjusts the normalization) to bestfit the observational data. This feature is lacking in the MAGIC analysis of the spectrum of 3C279since they have factored in the absorption effect prior to making their fits.To further illustrate this point of ambiguity in the spectral index of the source, Figure 3 shows 7 – - - - - - - E Γ @ GeV D L ogd N (cid:144) d E @ c m - s - T e V - D Fig. 3.— Plot of the best fit curves obtained using the SMS baseline model for fixed spectral indicesof 1.5, 2.0, 2.5, and 3.0. The shaded region represents the combined systematic and statistical errorfor the observational data.the best fit obtained for the SMS baseline model to the observational data for the range of spectralindices indicated. Spectra with the higher values of Γ s provide a good fit to the three lower energydata points which have the smallest error bars. However, they miss the higher energy data points.Those with lower values of Γ s miss the lower energy data point but pass through the four higherenergy data points. all of these fits have almost identical reduced χ values of ∼ s between 1.5 and 3 as shown in Figure 3, and varying the normalization constant, K tofind the best fit in each case, it is found that all of these spectral fits have almost identical reduced χ values of ∼ χ over a range of spectral indeces.Table 2. Best-fit Spectral Parameters for EBL Models with χ ValuesModel K Γ s χ χ for Γ s = 2 .
5. Hypothetical Consideration of the Luminosity of the 3C279 Flare Observed byMAGIC
As discussed above, our statistical analysis shows that the spectral index of the flare is notwell determined by the MAGIC data. Given this uncertainty, we can conditionally compare theluminosity of the MAGIC flare with that of an earlier flare observed by EGRET by assuming thesame intrinsic spectral index as the EGRET flare. The 1991 EGRET flare had an observed spectralindex of Γ s = 2 .
02 at energies between 50 MeV and 10 GeV (Hartman et al. 1992) where EBLabsorption is negligible.We note that this choice of spectral index gives good χ fits for all the EBL models consideredhere. Assuming the value for Γ s of 2.02, we obtain the best fits to the MAGIC data using theLevenberg-Marquardt method for the single free parameter, K . The χ values obtained for thesebest fits are shown in the last column of Table 2. The resulting curves for the fits of all five modelsare illustrated in figure 2.If we then choose the form of τ ( E ) given by the SMS fast evolution model as input to equation(1), by extending the Γ s = 2 .
02 power-law fit from Hartman et al. to an energy of ∼
500 GeV,we find a value for K that is ∼
6. Conclusions and Discussion
We conclude that the observational data of 3C279 from the MAGIC collaboration do notsignificantly constrain the intergalactic low energy photon spectra, nor do they indicate that theUniverse is more transparent to high energy γ -rays than previously thought or obtained by theSMS models. Including the effects of the systematic errors, which only significantly affect the twohighest energy data points, would only strengthen our conclusions.We show here, as well as in our analysis of 1ES0229 (Stecker & Scully 2008), that the SMSmodels produce reasonable fits to the observational data. We further demonstrate that othermodels in the literature that give lower transparencies do not fit the 3C279 data better than theSMS models do. This is because the magnitude and shape of the intrinsic spectrum of the flare arenot well determined by the MAGIC data, as we have shown.The spectral energy distribution of the intergalactic IR radiation is well constrained by astro-nomical data, as discussed in detail in SMS. However, the form of the intrinsic source spectrum ofthe γ -ray flare is not well constrained. If one should wish to speculate on producing a fit to theMAGIC data to go through all of the points, one would require an intrinsic flare spectrum whichflattens at higher energies. Such a spectrum may arise either from relativistic shock acceleration(Stecker, Baring & Summerlin 2007; Resmi & Bhattacharya 2008) or from intrinsic source absorp- 9 – - - - - - - - - E Γ @ GeV D L ogd N (cid:144) d E @ c m - s - T e V - D Fig. 4.— Plot of the best fit curves with Γ s = 2 .
02 for the SMS fast evolution (solid), SMSbaseline (dotted), Kneiske et al. best-fit (short-dashed), Kneiske et al. low-IR (long-dashed), andPrimack et al. (dash-dotted) models for a fixed spectral index of Γ s = 2 .
02 shown along with theobservational data from Albert et al. (2008). The shaded region represents the combined systematicand statistical error for the observational data. The gray curve shows the EGRET flare power-lawfit extended to higher energies multiplied by e − τ ( E ) . The respective χ values are given in the lastcolumn of Table 2.tion (Liu & Bai 2006; Liu, Bai & Ma 2008; Sitarek & Bednarek 2008). However, given both thestatistical and the systematic errors of the MAGIC data, particularly those for the highest energybin, the invocation of such processes is unnecessary.If we apply our analysis technique to the MAGIC data and assume an intrinsic power-lawspectrum with index 2.02 as observed for the earlier EGRET flare at lower energies where absorptionis negligible, we find that the luminosity of the MAGIC flare was similar to that of the earlierEGRET flare. In fact, the MAGIC flare was ∼ all of the data points thatthey started from were affected by intergalactic absorption.One would need to have additional information concerning the intrinsic source spectrum suchas additional observations at lower γ -ray energies that are unaffected by pair-production absorptionin order to better constrain the intergalactic IR radiation through an analysis of the resulting opticaldepth at the higher energies where absorption is more significant. We note that the ideal situationfor exploring the exact amount of intergalactic absorption would be to have simultaneously andwith overlapping observational energy ranges (1) observations of a strong flare with large photoncounts at lower energies unaffected by intergalactic absorption, as can be obtained by FGST (Fermi 10 –Gamma-ray Space Telescope, nee GLAST), and (2) ground based sub-TeV observations of such astrong flare with larger photon counts.We wish to thank Rudolf Bock for sending us a list of data on the spectrum of 3C279 observedby MAGIC. STS gratefully acknowledges partial support from the Thomas F. & Kate Miller JeffressMemorial Trust grant no. J-805. REFERENCES
Albert, J. et al. 2008, Science 320, 1752Altieri, B. et al. 1999, A&A 343, L65Breit, G. & Wheeler, J. A. 1934, Phys. Rev. 46, 1087Elbaz, D. et al. 2002, A&A 384, 848Hartman, R. C. et al. 1992, ApJ 385, L1Hauser, M.G. & Dwek, E. 2001 ARA&A 39, 249Katarzy´nsky, K., Ghisellini, G., Svensson, R., Gracia, J. & Maraschi, L. 2006, MNRAS 368, L52Kneiske, T. M. et al. 2004, A&A 413, 807Lagache,G. et al. 2004, ApJS 154, 112Liu, H. T. and Bai, J. M. 2006, ApJ 653, 1089Liu, H. T., Bai, J. M. & Ma, L. 2008, arXiv:0807.3133Malkan, M. A. & Stecker, F. W. 1998, ApJ 496, 13Malkan, M. A. & Stecker, F. W. 2001, ApJ 555, 641Marziani, P. et al. 1996, ApJS 104, 37Primack, J. R., Bullock, J. S. & Somerville, R. S. 2005, AIP Conf. Proc. 745, 23Resmi, L. & Bhattacharya, D. 2008, MNRAS 388, 144Sitarek, J & Bednarek, W. 2008, arXiv:0807.4228Stecker, F. W., Baring, M.G., & Summerlin, E.J. 2007, ApJ 667, L29Stecker, F. W., de Jager, O. C. & Salamon, M. H. 1992, ApJ 390, L49Stecker, F. W., Malkan, M.A., & Scully S.T. 2006, ApJ 648, 774 11 –Stecker, F. W., Malkan, M. A. & Scully, S. T. 2007, ApJ 658, 1392Stecker, F. W., Puget, J.-L. & Fazio, G. G. 1977, ApJ 214, L51Stecker, F. W. & Scully, S. T. 2006, ApJ 652, L9Stecker, F. W. & Scully, S. T. 2008, A&A 478, L1Totani, T. & Takeuchi, T. T. 2002, ApJ 570, 470