Free Access
Volume 533, September 2011
Article Number A57
Number of page(s) 21
Section Extragalactic astronomy
Published online 29 August 2011

Online material

Appendix A: Large-area surveys of radio sources

A.1. Low-frequeny data: the catalogues of steep- and flat-spectrum sources

Large-area deep surveys are specially present at GHz frequencies and have allowed us to make statistical studies of the spectral behaviour of ERS for the basic classification into steep- and flat-spectrum sources.

  • By using the NRAO VLA Sky Survey (NVSS; Condon et al. 1998) at 1.4 GHz and the Green Bank survey (GB6; Gregory et al. 1996) at 4.85 GHz, we built a large and complete catalogue of steep- and flat-spectrum sources at 5 GHz. These two surveys overlap at declinations of 0° < δ <  − 75° (i.e., an area Ω ≃ 6.07 sr) and have allowed us to calculate the spectral indices of ERS in almost half of the sky. The resolution of the two surveys is quite different, being 45 arcsec in NVSS and 3.5 arcmin in GB6, whereas the flux limits are 2.5 and 18 mJy respectively. At first, we decided to consider only GB6 sources with flux density S4.85 ≥ 100 mJy and Galactic latitude |b| ≥ 10°. The 100-mJy flux limit for GB6 sources is well above the flux limit of the two surveys and guarantees that we are not losing sources with a rising spectrum, α > 0. Moreover, it minimizes the effects of flux density errors. The Galactic cut at latitude  < 10° is to avoid Galactic sources in the sample. In addition, we excluded GB6 sources flagged as “W” (not reliable source) and “C” (confused source). We cross-matched the GB6 source positions with the NVSS catalogue by taking all positive matches within a position offset of 89 arcsec. We used a slightly bigger maximum position offset with respect to Healey et al. (2007) for reducing the number of GB6 sources without NVSS counterparts. In this way, we found 8127 sources with a counterpart in NVSS and only 23 without. Finally, whenever more than one of the NVSS sources fell within the GB6 beam, as a consequence of the better NVSS angular resolution, which may lead to individually resolved multiple components, we summed their fluxes, correcting for the effect of the GB6 beam. We ended up with 2975 flat-spectrum sources (corresponding to  ~ 37% of the total number of sources in the sample) and 5152 steep-spectrum sources (~63%). Hereafter, we indicate this source catalogue with spectral information as our NVSS/GB6 sample.

  • The CRATES programme (Healey et al. 2007) has also carried out an almost all-sky sample of flat-spectrum sources brighter than 65 mJy at 5 GHz, using the existing surveys at GHz frequencies. Then they assembled the 8.4-GHz flux densities of flat-spectrum sources from observations done by CLASS (Myers et al. 2003) and from new observations by VLA and ATCA. To mantain uniformity in our analysis, we took into account only CRATES sources in the GB6 area, i.e. where spectra are computed from NVSS and GB6 measurements. In this area, the authors found  ~ 5000 flat-spectrum sources with 5-GHz flux density S ≥ 65 mJy (about a 33% of total sources).

  • A sample of flat-spectrum sources is also provided by the Parkes quarter-Jy sample (Jackson et al. 2002; see also De Zotti et al. 2005). It consists of 878 objects selected at 2.7 GHz from several complete surveys of the Parkes radio source catalogue, and having spectral index between 2.7 and 5 GHz . The flux limit of these surveys varies between 0.1 and 0.6 Jy, although it is 0.25 Jy for most of them.

A.2. Surveys at frequencies higher than 10 GHz

Recent experiments have surveyed large areas of the sky at frequencies higher than 10 GHz. They are important to test the validity of our predictions on number counts of ERS, but also to provide more direct information on the spectral shape of sources at cm/mm wavelengths.

  • The Ryle-Telescope 9C surveys (Taylor et al. 2001; Waldram et al. 2003) have provided a catalogue of sources at 15 GHz with a completeness limit of 25 mJy. These surveys cover the fields observed by the Very Small Array (VSA), corresponding to an area of  ~520   deg2. Moreover, Waldram et al. (2009) have reported on a series of deeper regions, amounting to an area of 115 deg2 complete to approximately 10 mJy, and of 29 deg2 complete to approximately 5.5 mJy. Finally, the Tenth Cambridge (10C) Survey (AMI Consortium 2010) has covered an area of  ≈ 27 deg2 at 15.7 GHz down to a completeness limit of 1 mJy (within it, some deeper areas, covering  ≈ 12 deg2, are complete down to 0.5 mJy).

  • A 20-GHz survey of the whole southern sky has been carried out by the Australian Telescope Compact Array (ATCA) from 2004 to 2008. The full source catalogue (AT20G) is presented in Murphy et al. (2010) and in Massardi et al. (2011a), and it includes 5890 sources above a flux-density limit of 40 mJy. The completeness of the AT20G catalogue is 93 percent above 100 mJy and 78 percent above 50 mJy in regions south of declination  − 15°. Most of sources with declination δ <  −15° were also followed-up at 5 and 8 GHz by near-simultaneous observations. In our analysis we made an extensive use of this survey but we limited ourselves to the almost-complete sample of the AT20G catalogue at declinations δ <  −15°. It consists of 2195 sources with flux density S ≥ 100 mJy and of 1612 with 50 ≤ S < 100   mJy. We called these two sub-samples AT20G-d15S100 and AT20G-d15S50, if the flux limit is 100 mJy and 50 mJy respectively. For these sources, we were able to determine the spectral index at low frequencies by exploiting ATCA 5-GHz measurements and low-frequency surveys in the southern sky: the NVSS at 1.4 GHz for δ >  −40°; the Sydney University Molonglo Sky Survey (SUMSS Mauch at al. 2003) and the Molonglo Galactic Plane Survey (MGPS Murphy et al. 2007) at 843 MHz for δ ≤  −40°. Whereas 5-GHz ATCA measurements were not available, we searched for the source counterparts in the Southern Parkes-MIT-NRAO (PMN) survey (Wright et al. 1994, 1996). In AT20G-d15S100 we obtained the spectral index for 2158 sources, more than 98% of the sub-sample: there were 395 sources with steep spectrum and 1763 with flat spectrum (~82%), of which 471 with inverted spectrum α ≥ 0.3. In Table A.1 we report the number of sources with 5-GHz measurements and the number of steep- and flat-spectrum sources in the two sub-samples of the AT20G. The percentages of flat- and steep-spectrum sources agree with the ones given by Massardi et al. (2011a) over a slightly different and smaller area of AT20G (see their Fig. 1), where they found  ~82% and  ~74% of flat-spectrum sources with flux density  ≥ 100 and 50 mJy respectively.

    Table A.1

    Spectral information in the two almost-complete sub-samples of AT20G.

  • At ν ≃ 30 GHz various CMB experiments have provided samples of extragalactic radio sources, giving estimates of the number counts at different ranges of flux densities: the Cosmic Background Imager (CBI; Mason et al. 2003) in the range 5–50 mJy; the Degree Angular Scale Interferometer (DASI; Kovac et al. 2002) for S ≳ 100   mJy; the Very Small Array (VSA; Cleary et al. 2005) in the range 20–114 mJy; the Sunyaev-Zel’dovich Array (SZA; Muchovej et al. 2010) in the range 0.7–15 mJy.

  • The Wilkinson Microwave Anisotropy Probe (WMAP) carried out all-sky surveys at 23, 33, 41, 61, and 94 GHz and provided a catalogue of ERS at a completeness levels of  ≳ 1   Jy. Analyses from the WMAP team have yielded 390 point sources in the five-year data (Wright et al. 2009), whereas 62 new point sources are found in the seven-year data (Gold et al. 2011). WMAP five-year maps has been also analyzed by Massardi et al. (2009) that detected 516 point sources, 457 of which were previously identified as extragalactic sources.

  • Data on ERS are also present for frequencies ν ≳ 100 GHz: the South Pole Telescope (SPT; Vieira et al. 2010) carried out a survey of ERS at 1.4 and 2.0 mm wavelengths with arcmin resolution and mJy depth over an area of 87 deg2; the Atacama Cosmology Telescope (ACT; Marriage et al. 2011) provided a catalog of 157 sources with flux density between 15 and 1500 mJy detected at 148 GHz in an area of 455 deg2.

  • The Planck ERCSC (Planck Collaboration 2011b) reported data on compact sources detected in the nine Planck frequency channels between 30 and 857 GHz during the first 1.6 full-sky surveys. The analysis of the Planck ERCSC data presented in Planck Collaboration (2011c) is limited to a primary sample of 533 compact extragalactic sources at |b| > 5°, selected at 30 GHz. More than the 97% of these compact objects have been identified in external, published catalogues of ERS at GHz frequencies (see the Planck ERCSC Explanatory Supplement, for more details). Moreover, this 30-GHz sample is found to be statistically complete down to a flux density of  ≈ 0.9–1.0 Jy and 290 ERS are found at above this flux density limit. The Planck Collaboration has been able to measure the number counts at the Planck LFI (30, 44 and 70 GHz) and at the HFI frequencies of 100, 143 and 217 GHz, with an estimated completeness limits of 1.0, 1.5, 1.1, 0.9, 0.5, 0.4 Jy respectively (Planck Collaboration 2011c).

Appendix B: Estimate of the break frequency in blazars

Spectra for the synchrotron emission from a spherical and homogeneous source have a peak due to the self-absorption of their own radiation. The observed frequency at which the peak of the self-absorption occurs depends on the magnetic field and the depth of the source, and it can be computed by (Pacholczyk 1970) (B.1)where θ is the observed angular dimension of the source and νsyn,   abs is measured in GHz. The parameter p depends on the emission model and gives the enhancement of the observed flux due to the beaming (Sobs = δ   p − α   S). It is equal to 3 for a moving isotropic source and 2 for a continuous jet (see Ghisellini et al. 1993; and Urry & Padovani 1995, for detailed discussion). In the analysis we used as reference value p = 3. We also assumed that emitting electrons have a power-law energy distribution N(γ) = Kγ − (1 − 2α), where α is the spectral index of the optically thin synchrotron emission. The term Cα in Eq. (B.1) depends on α by (B.2)with c1 = 3e/4πm3c5 and τm the optical depth of the source at νm. The functions c5(α) and c6(α) are provided in Pacholczyk (1970).

As discussed in the text, the break frequency (νM) in a flat-spectrum source is approximately the synchrotron self-absorption frequency νsyn,   abs for the innermost part of the jet whose emission is observed at cm/mm wavelengths. If this region is assumed to be homogeneous and spherical (with diameter d), νM can be obtained from Eq. (B.1). For a conical jet geometry, the diameter is related to the distance from the AGN core rM by d = 2rMtan(φ/2) ≃ φrM, where φ is the semiangle of the conical jet.

If the flux density for a flat-spectrum source is known at the observational frequency νo, the observed flux density at νM (SM) can be extrapolated from νo using a power law spectrum (we are assuming that SM ≃ Ssyn,   abs, i.e. the contributions from other jet regions are negligible at the frequency νM): (B.3)Moreover, we have seen from Eq. (5), (6) that the magnetic field in equipartition condition is (B.4)The total luminosity of the source L can be calculated by the integral of the observed flux density: (B.5)where DL is the luminosity distance in Mpc, νmin and νcut give the frequency range where the source emission is concentrated (we take νmin = 10 MHz and νcut = 105 GHz, in agreement with standard assumptions on synchtrotron emission in blazar sources). We used the relation between the luminosity emitted at a given frequency and the observed flux density, which takes into account the K-correction and the relativistic beaming effects on the flux. The integral on the flux density is now expressed as a function of SM and νM: (B.6)for α ≠  − 1 (if α =  −1 the integral is equal to SMνMln(νcut/νmin). Below we assume this condition is verified; it is easy to extend the calculation for α =  −1). Using Eq. (B.3) the total luminosity becomes (B.7)where (B.8)By assuming for simplicity that the source is spherical with diameter d ≃ 0.1rM (Königl 1981; Ghisellini & Tavecchio 2009), we obtain the expression for the magnetic field: (B.9)where (B.10)The observed angular dimension of the source in Eq. (B.1) is (B.11)with Cθ ≃ 2.1 × 107.

Finally, including Eqs. (B.3)–(B.11) in Eq. (B.1), the break frequency becomes (B.12)where , and , , , , .

Appendix C: Physical quantities relevant for the estimate of the break frequency in blazars spectra

C.1. Redshift distribution of blazars

In Massardi et al. (2010) the redshift distribution of radio sources at low frequencies is widely discussed, and we followed this paper to derive the redshift distribution of flat-spectrum sources. Most of the samples with redshift information do not distinguish between steep- and flat-spectrum sources. Spectral information are present in the Kühr et al. (1981) catalogue, however: this sample comprises 518 ERS to a 5-GHz flux density limit of 1 Jy, over an area of 9.811 sr. Based on the catalogued spectral indices, 299 sources are classified as flat-spectrum; 212 of which are FSRQs (200 with measured redshift), 26 are BL Lacs (20 with measured redshift) and 61 are classified as galaxies or with missing classification. Moreover, in the Parkes quarter-Jy sample of flat-spectrum ERS (Jackson et al. 2002), redshifts are available for the 58% of sources. From this sample, De Zotti et al. (2005) have defined a complete sub-sample of 514 objects with flux limit of 0.25 Jy, aiming at maximizing the fraction (~75%) of ERS with known redshift. This sub-sample includes 370 FSRQs (93% with known redshift) and 47 BL Lacs, of which only 21% with known redshift.

In Fig. C.1 we plot the redshift distributions of FSRQs and of BL Lacs, and the fits we used for our predictions. For FSRQs only, it has been possible to calculate them from both the samples: in this case, the redshift distribution is observed to shift to higher redshifts as the flux limit of the sample is lowered down, with the peak of the distribution moving from z ≃ 1.2 to z ≃ 1.5. Moreover, Fig. C.1 shows that the relative number of low-redshift FSRQs is strongly reduced, if a fainter flux detection limit is adopted. As for BL Lacs, the redshift distribution can be obtained from the Kühr et al. catalogue, and for only 20 very bright objects. Because of the lack of information at faint fluxes, this redshift distribution will be considered representative also for BL Lac sources with flux density lower than the sample limit. Owing to this, our predictions on number counts of ERS discussed in Sect. 7 are, therefore, more uncertain when applied to sources at S < 0.1 Jy.

thumbnail Fig. C.1

Upper panels: redshift distributions of BL Lacs (left panel) and of FSRQs (right panel) from the samples by Kühr et al. (1981) (solid points) and Jackson et al. (2002) (empty points), and the corresponding fits (solid and dashed lines, respectively). Lower panels: histograms of the Doppler factor as obtained by Ghisellini et al. (1993) (dashed lines) and Gu et al. (2009) (dotted lines) for BL Lacs (left panel) and core-dominated quasars (right panel). The solid line in the right panel is the fit of the two δ distributions for core-dominated quasars.

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C.2. The Doppler factor in AGNs

The estimate of the Doppler factor δ in AGNs is something complex and model-dependent. In the framework of the synchrotron self-Compton model (Marscher 1987), Ghisellini et al. (1993) calculated the Doppler factor for a sample of 105 radio sources using VLBI measurements of the core angular dimensions and radio fluxes. The value of δ is calculated comparing the observed X-ray fluxes with the ones predicted on the based of a homogeneous spherical emitting model. In Fig. C.1 we show the δ distribution for the 53 core-dominated quasars and the 33 BL Lacs present in the sample. These distributions can be compared with results from Gu et al. (2009) where the Doppler factor is computed using the Königl inhomogeneous jet model instead of the homogeneous spherical model. Their sample consists of 128 sources, with 80 core-dominated quasars and 26 BL Lacs (37 quasars and 19 BL Lacs are in common with the sample used by Ghisellini et al.). The δ distributions are similar in the case of core-dominated quasars, with most of sources having δ between 1 and 30, as expected for objects where the relativistic beamed emission is dominant. For BL Lacs the results from Ghisellini et al. (1993) and Gu et al. (2009) do not agree: the former find very low δ values, extending from 10-2 to 10; in the latter the δ distribution is similar to the core-dominated quasars one. The inhomogeneous model, in general, provides a better description of AGN jet properties, but has the disavantage to involve more free parameters than the homogeneous model. Note, however, that in the case of the homogeneous model it is assumed that all the observed X-ray flux is

produced through inverse Compton scattering by the core component dominanting at the radio frequency. If part of the X-ray flux is produced in other components or by some other mechanism, then the computed δ is a lower limit. For these reasons and for greater simplicity, we assumed the same δ distribution for BL Lacs and core-dominated quasars (in general for all the flat-spectrum sources), described by the fit in Fig. C.1.

© ESO, 2011

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