# Constraining blazars distances with combined GeV and TeV data

###### Abstract

Recently, a new method to constrain the distances of blazars with unknown redshift using combined observations in the GeV and TeV regimes has been developed. The underlying assumption is that the Very High Energy (VHE, E 100 GeV) spectrum corrected for the absorption of TeV photons by the Extragalactic Background Light (EBL) via photon-photon interaction should still be softer than the gamma-ray spectrum observed by Fermi/LAT. The constraints found are related to the real redshifts by a simple linear relation, that has been used to infer the unknown or uncertain distance of blazars. The sample is revised with the up-to-date spectra in both TeV and GeV bands and the method applied to the unknown distance blazar PKS 1424+240 detected at VHE.

## I Introduction

### i.1 TeV Blazars

The large majority of extragalactic TeV photons emitters belongs to the class of blazars: radio-loud Active Galactic Nuclei (AGN) with a relativistic jet closely oriented towards the Earth urry ().

The typical spectrum emitted by a blazar is non thermal and covers the entire electromagnetic spectrum, as sketched in Fig 1. It is composed by two bumps: at low energies the emission is synchrotron radiation by relativistic electrons, while at higher energies the origin of the radiation is more uncertain. The most credited models, referred as leptonic models, involve the inverse Compton scattering mechanism to explain the high energy emission. However, alternative models taking into account the presence of a hadronic component in the emission are not ruled out.

At GeV and TeV regimes, the photon energy flux emitted by a blazar
is usually well approximated with a power
law^{1}^{1}1Indeed, this is true at a reasonable distance from the
peak maximum. of the form
.

### i.2 EBL absorption

An important effect involving VHE photons emitted by blazars is the production of electron-positron pairs (), caused by the interaction with the EBL stecker92 (). EBL is composed of stellar light emitted and partially reprocessed by dust throughout the entire history of cosmic evolution.

Due to the lack of direct EBL knowledge, many models have been elaborated in the last years dominguez10 (); franceschini08 (); kneiske10 (); stecker06 (), but the uncertainties remains quite large.

Quantitatively, the effect of the interaction of VHE photons with EBL is an exponential attenuation of the flux by a factor , where is the optical depth, function of both photon energy and source redshift. This is represented in Fig. 1, where, due to the absorption, the observed TeV spectrum (continuous line) differs significantly from the emitted spectrum (dashed line). The observed differential energy spectrum from a blazar is related to the emitted one according to .

In principle it is possible to derive the emitted (or intrinsic) spectrum by deabsorbing the observed spectrum. This procedure depends on the absorption coefficient and the redshift of the source. Vice versa, if the intrinsic source spectrum is known, given the absorption coefficient , the redshift can be estimated comparing the absorbed spectrum with the observed one. Here, we use the second approach.

Source Name | ||||
---|---|---|---|---|

Mkn 421 | 0.030 | 1.81 0.02 | 0.07 0.02 | 0.02 0.05 |

Mkn 501 | 0.034 | 1.85 0.04 | 0.08 0.02 | 0.03 0.05 |

1ES 2344514 | 0.044 | 1.57 0.17 | 0.19 0.03 | 0.09 0.05 |

Mkn 180 | 0.045 | 1.86 0.11 | 0.21 0.11 | 0.11 0.05 |

1ES 1959650 | 0.047 | 2.09 0.05 | 0.07 0.03 | 0.02 0.05 |

BL Lacertae | 0.069 | 2.37 0.04 | 0.27 0.14 | 0.14 0.05 |

PKS 2005489 | 0.071 | 1.90 0.06 | 0.18 0.03 | 0.09 0.05 |

W Comae | 0.102 | 2.06 0.04 | 0.24 0.05 | 0.13 0.05 |

PKS 2155304 | 0.116 | 1.91 0.02 | 0.22 0.01 | 0.11 0.05 |

RGB J0710591 | 0.125 | 1.28 0.21 | 0.21 0.06 | 0.11 0.05 |

1ES 0806524 | 0.138 | 2.09 0.10 | 0.23 0.15 | 0.12 0.05 |

H 2356309 | 0.165 | 2.10 0.17 | 0.16 0.07 | 0.08 0.05 |

1ES 1218304 | 0.182 | 1.70 0.08 | 0.21 0.08 | 0.11 0.05 |

1ES 1101232 | 0.186 | 1.36 0.58 | 0.23 0.11 | 0.12 0.05 |

1ES 1011496 | 0.212 | 1.93 0.04 | 0.60 0.18 | 0.35 0.05 |

S5 0716714 | 0.310 | 2.15 0.03 | 0.23 0.10 | 0.12 0.05 |

PG 1553+113 | 0.400 | 1.66 0.03 | 0.75 0.07 | 0.45 0.05 |

3C 66A | 0.444 | 1.92 0.02 | 0.39 0.05 | 0.22 0.05 |

## Ii The Method

In a recent paper, we have proposed a method to derive an estimate on the distance of a blazar prandini10 (). The method is based on the comparison between the spectral index at GeV energies as measured by LAT after 5.5 months of data taking, basically unaffected by the cosmological absorption, and the TeV spectrum corrected for the absorption. In that work, it is shown that according to present observations, the spectral slope measured by LAT, , in the energy range 0.2 – 300 GeV, can be considered as a limiting slope for the emitted spectrum at TeV energies (i.e. corrected for EBL absorption). This maximum hardness hypothesis was successfully tested on a sample of 14 well–known distance sources. Consequently, the redshift, , at which the deabsorbed TeV slope equals , can be used as an upper limit on the source distance.

An empirical relation between the upper limit, , and the true redshift of a blazar was then found. A simple linear relation fits well the – distribution, for three different EBL models. The relation is associated to the linear expression, found in stecker10 (), for the steepening of the observed TeV slopes due to EBL absorption. Hence, and are related by a linear function of the form . This relation can be used to give an estimate on the source distance.

In this paper we present an update of that work, based on a more recent LAT catalogue abdo10 (). We test the validity of the maximum hardness hypothesis and that of the linear relation between and . A cosmological scenario with , and is assumed.

## Iii Analysis and results

The sample presented in this study is composed by all the extragalactic TeV emitters located at redshift larger than and detected by LAT after the first year of data taking abdo10 (). In total, there are 16 sources with well known redshift and two additional sources with uncertain redshift, namely 3C 66A and S5 0716+714. In the first column of Table 1 we list the sources used in the study. The second column represents the slope measured by LAT after the first year of data taking, in the energy range 0.1 –100 GeV. Three new sources are added to the sample considered in the original study, namely: RGB J0710591, H 2356309 and 1ES 1101232, located at redshifts 0.125, 0.165 and 0.186, respectively. The last two sources were not detected by LAT in the first 5.5 months, while the spectrum of RGB J0710591 has only recently been published by the VERITAS collaboration acciari10b (). With respect to the 5.5 months catalogue, the new LAT determination of the spectral slopes is characterized by smaller errors, due to the increased statistics.

With this enlarged data set, we estimate the quantity
, redshift at which the deabsorbed
TeV spectrum exhibits the same slope measured by LAT at lower energies.
We adopt the energy density EBL model franceschini08 (),
hereafter Franceschini model^{2}^{2}2The absorption values
used here are taken directly from the WEB site http://www.astro.unipd.it/background,
and differ slightly from those used in prandini10 (), where an
extrapolation method was used..
The values obtained are listed in the fourth
column of Table 1.

Figure 2 represents the distribution obtained. All the values distribute above or on the bisector. This confirms that can be considered an upper limit on the source redshift, hence the maximum hardness hypothesis is confirmed also in this study. The linear curve drawn represents the fit of the data. The linear trend of the distribution is less evident here than in the previous study. The probability of the fit is, in fact, 6%, well below the previous value (58%). The reason for this behaviour can be related to the new sources introduced, but also to the new LAT determination of the slopes. In order to investigate such alternatives, we have fitted the distribution excluding the three new sources. The new fit returns a probability of 9%, close to the value obtained with the full sample. This result suggests that the low probability found is mainly due to the smaller error bars characterizing the determination of the new slopes in the GeV band with respect to previous estimates. The parameters obtained are listed in Table 2.

0.036 0.014 | 1.60 0.14 |

Following the first study, we investigate the distribution , difference between the values , listed in the last column of Table 1, obtained by inverting the linear formula = (, and the true redshifts, . The histogram obtained, Figure 3, is well fitted by a Gaussian of , which can be assumed as the error on the reconstructed redshift, , estimated with this method. In the histogram, the two sources with uncertain redshift, not used for the Gaussian fit, lie outside the expected interval. This result confirms that the behaviour of S5 0716+714 and 3C 66A is different from that found for other sources and suggests that or these sources are peculiar, or their redshift is incorrect.

In conclusion, we can say that with an enlarged data set the results previously found are confirmed. However, the linearity of the – relation has a smaller probability, due to the reduced errors of the new determinations.

## Iv The redshift of PKS 1424+240

As a final application, we use our method on PKS 1424+240, a blazar of unknown redshift recently observed in the VHE regime by VERITAS acciari10 (). The slope measured by Fermi/LAT in the energy range 0.1 – 100 GeV is .

The corresponding at which the slope of the deabsorbed TeV spectrum becomes equal to it is , filled circles in Fig. 4. This result is in agreement with the value of , reported in acciari10 (), calculated by applying the same procedure but using only simultaneous LAT data.

Our estimate on the most probable distance for PKS 1424+240 is 0.26 0.05, where the error is the of the Gaussian fitting the z distribution. The deabsorbed spectrum of PKS 1424+240 assuming this distance is drawn in Fig 4, filled squares.

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