Astron. Astrophys. 362, 75-96 (2000)

4. The spectral energy distributions

We report the first far-IR detection for 9 (4C 61.20, PG 1216+069, PG 1352+183, PG 1354+213, PG 1435-067, PG 1519+226, PG 1718+481, PG 2308+098, and HS 1946+7658) of the 18 sources observed with ISOPHOT. Among the remaining 9 sources, three (PKS 0135-247, PKS 0408-65, and PKS 0637-75) were not detected, and the remainings 6 were already detected by IRAS.

All the data were converted to monochromatic luminosities in the rest frame of the object ( = 75 km s^-1 Mpc^-1, =0.5) using the following equation:

where is the monochromatic flux in the observer's frame, and is the luminosity distance to the object. In the case of PKS 0408-65 we adopted a redshift value equal to 0.5, arbitrarily chosen, since no redshift measurement is available. This source will not be considered in the following analysis.

The spectral energy distributions (SEDs) as versus in the rest frame of all sources are shown in Fig. 2. Upper limits are plotted only if there is no detection at that frequency at any epoch, and in cases of multiple upper limits at the same frequency from different epochs, only the most stringent is used. A broad band spectrum of a local galaxy in its rest frame, representing the AGN host galaxy, is superposed in each panel of Fig. 2. We chose the spiral galaxy M100, modeled by Silva et al. (1998), to which we added data in the radio (Becker et al. 1991; Gregory & Condon 1991; White & Becker 1992) and in the soft X-ray energy domains (Immler et al. 1998) in the case of RQQ, and the template of a giant elliptical galaxy (Silva et al. 1998) in the case of RLQ, RIQ and RG. The reported host galaxy template was not modified by any normalization. In many cases this is orders of magnitude below the observed luminosities, and even if it is shifted towards higher luminosities to reach the quasar SED, it will remain below at most frequencies.

Fig. 2a-y. SEDs as versus in the rest frame of the objects. All sources shown on this page are FSRQ. Full circles represent literature data, stars SEST data, open diamonds ISOPHOT chopper data, triangles and filled diamonds ISOPHOT raster data at different epochs, and squares IRAS data. Arrows represent 3 upper limits. The solid line represents the sum of all single fitted components represented by dotted lines. The dotted lines represent the best fit non-thermal models of the radio component (see Sect. 4.2, and Table 7), and the parabolic fits of the IR component (see Sect. 5.2). When more than one radio component is present a symbol is reported for each spectral component: C for core and L for lobe (L1 and L2 for two lobes). A typical host galaxy template (dashed line), a spiral galaxy in the case of RQQ, and a giant elliptical galaxy in the case of RLQ, RIQ and RG, is over-plotted. The radio spectrum of PKS 0637-752 was fit in two ways, using only the simultaneous mm data corresponding to the flattest power law fit c (dash-dot line in b ) and the two corresponding to the steepest power law fit d (dash-dot-dot-dot line in b ). The radio spectrum of B2 2201+31A was also fit in two ways, taking all data from radio to mid-IR e and only data from radio to far-IR f . The flattest power law fit (dash-dot line in e ) and the steepest one (dash-dot-dot-dot in e ) measured during simultaneous mm observations of B2 2201+31A are reported. The big open circles in e correspond to simultaneous observations at mm and near-IR wavelengths.

Fig. 2a-y. (continued) SEDs for SSRQ are displayed on this page.

Fig. 2a-y. (continued) The sources shown on this page include 2 SSRQ (m, n), 2 RG (o, p), and 2 RIQ (q, r). In the case of PG 2308+098 the star represents the IRAC1 measurement.

Fig. 2a-y. (continued) All sources shown on this page are RQQ. In the case of PG 1435-067 the star represents the IRAC1 measurement.

Fig. 2a-y. (continued)

4.1. The nature of the IR emission: thermal or non-thermal emission?

The IR emission can have a thermal or non-thermal origin. Several investigation methods can be applied to identify the emission process:

1. The value of the slope of the sub-mm/far-IR spectral break can discriminate between optically-thick (self-absorbed) synchrotron and thermal emission from dust grains. The self-absorbed synchrotron model is characterized by a maximum value of the sub-mm/far-IR slope that is 2.5 (), if the radiation is emitted by an electron population with a simple power-law energy distribution, or somewhat larger ( 3) if a thermal electron pool or dual power-law energy distribution is invoked (de Kool & Begelman 1989; Schlickeiser et al. 1991). In either case the maximum synchrotron slope is attained only for a completely homogeneous source, otherwise it will be lower. The asymptotic thermal sub-mm/far-IR slope is expected to be 3 since the optically thin thermal spectrum derives from Rayleigh-Jeans law with an additional parameter dependent on frequency, where , the dust optical depth, is with 1-2 (see Sect. 4.3).

2. A non-thermal origin of the IR emission is indicated if relatively short time scale flux variability is observed, since a synchrotron component is expected to come from a very compact source. Most of the dust emission comes from an extended source with a long variability time scale.

3. A thermal origin can be attributed to the IR emission if a non-varying excess from any reasonable extrapolation from the radio domain in the plot versus is observed (Hughes et al. 1997).

It is possible to distinguish the origin of the IR emission based on brightness temperature (Sanders et al. 1989) and polarization measurements, but the lack of these kind of data for the sample does not allow us to apply them.

The first test will prove the thermal origin of the far-IR emission only if the coldest dust component is also the brightest one. Colder and less bright dust components will flatten the sub-mm/far-IR spectral slope. Two sources in the sample, PG 1543+489 and 3C 405, have a sub-mm/far-IR spectral index larger than 2.5. Their far-IR emission is therefore dominated by thermal radiation. The remaining sources have insufficient data at long wavelengths to constrain the sub-mm/far-IR spectral slope.

The observation of no variability is not conclusive, while if a flux variation is observed the non-thermal hypothesis will be strongly supported. This method can be applied only to those sources that were observed several times. In our sample, at least two IR observations (IRAS and ISOPHOT, or several ISOPHOT observations) at different epochs are available for ten sources (3C 47, PKS 0637-752, PG 1100+772, PG 1543+489, PG 1718+481, B2 1721+481, HS 1946+7658, 3C 405, B2 2201+31A, and PG 2214+139) (see Fig. 3). The data relative to the same observation epoch, instrument and observation mode are represented with the same symbol and connected by a line in Fig. 3. At least two measurements at the same wavelength are available for all the ten objects with the exception of PG 2214+139. Six sources (PG 1718+481, PG 1100+772, 3C 405, PG 1543+489, B2 1721+34, and PG 2214+139) show no sign of variability. Two of them also satisfy the first test. For two other sources (3C 47, and B2 2201+31A) the observed variation is only marginally 1.6, where includes the statistical and the systematic uncertainties. We consider their emission as constant in the span of our observations. In the case of PKS0637-752 we can only give a lower limit of the variation since the source was not detected by ISOPHOT. At wavelengths shorter than 60 µm ISOPHOT and IRAS give consistent results, while at longer wavelengths they differ of more than 1.9.

Fig. 3. IR data at different epochs. Symbols as in Fig. 2. Lines connect data relative to the same epoch. All objects are RLQ (2 FSRQ, 3 SSRQ, and 1 RG).

Fig. 3. (continued) (3 RQQ, and 1 RIQ).

The 150 µm flux values for the high redshift source HS 1946+7658 differ by at least a factor of 6 between two epochs separated by less than a year (see Table 5 and Table 6). Such extreme FIR variability is unlikely in a RQQ. The larger flux resulted from a chopped measurement, which is more susceptible at longer wavelengths to both background fluctuations and instrumental effects (e.g., a number of inadequately corrected cosmic ray strikes, unusually high detector drift, etc...) than the raster maps. Fig. 4 shows a 1.11.1 degree region around HS 1946+7658 at 100 µm from IRAS, with the position of the source and the ISOPHOT chopper direction indicated. Bright cirrus structures are nearby, and the background ranges from 0.21-0.38 MJy/sr within 90" of the source (equivalent to 0.16-0.28 Jy on the C200 covered area) (IRSKY ⁵ version 2.5). A strong gradient in the direction SE-NW in the background emission is clearly shown, which coincides with the ISOPHOT chopper direction. These variations may be greater at longer wavelengths and with the better spatial resolution of ISOPHOT. As a consequence of the uncertainties for this source, chopped data at 100 µm for HS 1946+7658 will not be included in subsequent analysis.

Fig. 4. IRAS observation at 100 µm of a sky region of 1.11.1 degrees around the source HS 1946+7658, whose position is indicated by S. The sky region where the background was measured is indicated by B. The white polygon represents approximatively the region observed by the C200 camera. The solid line indicates the chopper direction 41o to the West of North.

The result of this method suggests that for all the selected objects, with the exception of PKS 0637-752, the IR emission is thermal in origin. The result is not very strong since a non-thermal process may also produce a constant flux. However, it is unlikely to measure the same flux from a non-thermal source during three different observations performed in a range of 14 years (from 1983 to 1997) as observed in six objects (see Fig. 3).

The third test is the simplest, and it can be applied to the whole sample since a broad spectral coverage from radio to the IR is available for all the sources. Before applying this test we need to estimate the contribution from the non-thermal component in the IR and subtract it from the observed IR spectrum. The non-thermal contribution can be estimated by fitting the radio data with a reasonable model and then extrapolating it to higher frequencies (see next section).

4.2. Contribution of the radio non-thermal component in the infrared

In order to estimate the contribution of the radio non-thermal component in the IR domain, the radio continuum was fitted with some plausible models, and extrapolated to higher frequencies. In the following we will distinguish two components in the radio spectra of RLQ, the extended component (radio lobes), and the core component (unresolved core, jet, etc...).

The radiation emitted by compact sources, like the cores and the hot-spots of radio loud objects, can be modeled by a self-absorbed synchrotron emission spectrum. In the case of a homogeneous plasma with isotropic pitch angle distribution and power law energy distribution of the form , this can be expressed as:

where is the frequency at which the optical depth of the plasma is equal to unity, and is the frequency corresponding to the cut off energy of the plasma energy distribution, at which the energy gains and losses of the electrons are equal. The optically thick and optically thin spectral indices are denoted by , and . In the case of a homogeneous source, is expected to be 2.5, and is related to the exponent s of the plasma energy distribution by the relationship: . The superposition of several self-absorbed components can produce a flatter power law. In this case the spectral model of Eq. (2) will remain valid, but will not have the same meaning. If the source is optically thin, as in extended sources (radio lobes), the emitted spectrum can be expressed more simply as:

In many cases the contribution of the synchrotron component at high frequencies is negligible compared to the observed emission, therefore a high energy cut off was not included in the model. The model is then represented by a broken power law of slopes and , or by a simple power law of slope , according to the presence/absence of self absorption.

The synchrotron model describes well the observed radio spectra of most of the sources in the sample. However, while in the case of SSRQ it is quite easy to separate the different components and hence apply a model for each of them, the spectral modeling is more difficult for FSRQ. For these sources we parameterize the emitted spectrum with an empirical equation that is valid if the resulting spectrum is produced by self-absorbed synchrotron emission or by optically thin synchrotron emission due to a hard electron spectrum produced through the acceleration processes in turbulent plasma (Wang et al. 1997). The observed flat radio spectra are described by the following equation:

where is the frequency at which the spectrum flattens, is the spectral index observed at low frequencies (), and the other model parameters have the same meaning as in Eq. (2).

The observed SEDs from the radio to the mm energy domains were fitted with one or a combination of these models (see best fit parameters in Table 7). In some cases near-IR data have also been used in the fits, in particular when no data in between mm and near-IR frequencies constrained the spectrum to lie below the near-IR flux (PKS 0135-247, PKS 0637-752, 4C 61.20, PG 1004+130, PG 1216+069, PG 1718+481, 3C 405, and B2 2201+31A). In a few cases we fixed some model parameters, as indicated in a footnote of Table 7, since the available data could not constrain them. The fixed values were chosen in the range of values that provided reasonable spectra with properties similar to those observed in other sources. Model a in Table 7 corresponds to Eq. (2). It was applied for modeling core spectra of PG 1216+069, and 3C 405. The same model without the cut off (b) was applied for modeling weak core spectra for which the high energy cut off was not constrained (3C 47, PG 1004+130, 4C 61.20, PG 1048-090, PG 1100+772, PG 1103-006, and PG 1718+481). A simple power law model (c) was used to fit the radio emission from the lobes of SSRQ and RG (3C 47, PKS 0408-65, PG 1004+130, 4C 61.20, PG 1048-090, PG 1100+772, PG 1103-006, B2 1721+34, 3C 405 and PG 2308+098) and the radio emission of RQQ (PG 1543+489, and PG 2214+139). Simultaneous observations available in the literature generally do not provide wide or well-sampled wavelength coverage, so all available data were used in the fits to the SEDs. The data and analysis are adequate for the central purpose of estimating the contribution of the non-thermal component to the IR emission. The model d, corresponding to Eq. (4), was applied to fit the radio emission of FSRQ (PKS 0135-247, PKS 0637-752, and B2 2201+31A). The value of the break frequency was arbitrarily fixed to 2.75 GHz, since it provides a good fit to the emitted spectrum of the three objects. In the case of PKS 0637-752 (Low) (see Sect. 4.2.1) the cut off was not included in the model (e) since the high frequency part of the spectrum is very steep.

Table 7. Best fit parameters of non-thermal models.
Notes:
) Model a corresponds to Eq. (2), and model b to the same equation without cut off; model c corresponds to a simple power law; model d to Eq. (4), and model e to the same equation without cut off. (F) indicates a fixed value.

4.2.1. Uncertainties in the radio contribution estimate

The location of the high energy cut off is difficult to establish. Every power law relative to the optically thin emission was extended at higher frequencies until the spectrum turned down, and hence a cut off was required by the data. A spectral cut off was thus required only in five objects (PKS 0135-247, PKS 0637-75, PG 1216+069, 3C 405, and B2 2201+31A), but it could have been located at lower frequencies and present in other objects, too. In most of the cases this parameter does not affect the presence and the strength of the remaining IR flux, but its energy value may be important in FSRQ (PKS 0135-247, PKS 0637-75, and B2 2201+31A), since these objects have flat radio spectra for which extrapolation up to IR frequencies is comparable to the IR fluxes. For these sources a more accurate analysis of their radio spectra is needed. Since PKS 0135-247 was not detected in the IR, no further analysis can be performed. We concentrate only on PKS 0637-75 and B2 2201+31A. In order to better constrain the non-thermal radio spectrum, i.e. to find some evidence of a spectral cut off at sub-mm/far-IR frequencies, we searched in the literature for simultaneous observations at these wavelengths, and we selected those that showed the flattest and the steepest spectrum. For PKS 0637-75 the flattest mm power law, chosen among several simultaneous observations (Tornikoski et al. 1996), was measured on February 15th, 1990 ((3.0-1.3 mm) = -0.77), and the steepest one was measured on April 4th, 1991 ((3.0-1.3 mm) = -1.47). The two power laws are reported in Fig. 2b with a dashed, and a dashed-dotted line, respectively, plus displayed separately with flattest (Fig. 2c) and steepest (Fig 2d) spectral fits. The flattest spectrum overlaps the observed IR spectrum, leaving no additional IR component. On the contrary, the extrapolation of the steepest spectrum to IR frequencies is clearly below the observed IR spectrum, but the IR observations were not simultaneous to the mm observations. The source was observed by IRAS in 1983, and by ISO at different wavelengths in 1997. During the elapsed time the source became fainter in the far-IR, while shorter wavelength data from the two diferent epochs are consistent. In the following we will suppose that a thermal IR component is present, but dominating only at 60 µm, and we will analyze its properties and compare them with those observed in other sources.

For B2 2201+31A the flattest mm power law ((1.0-0.87 mm) = -0.09) was measured on February 1989 (Chini et al. 1989a), and the steepest one was measured on September 14th, 1993 ((2.0-1.3-1.1 mm) = -0.72). The two power laws are reported in Fig. 2e with a dashed, and a dashed-dotted line, respectively. The spectrum is in both cases quite flat, however the extrapolation of the 1993 spectrum lies below the IR spectrum. More than the sub-mm data, the analysis of the emission at shorter wavelengths gives important indications on the origin of the IR emission. B2 2201+31A was observed on September 15th, 1993 also in the near-IR (simultaneous sub-mm and near-IR data are indicated by large open circles in Fig. 2e). The near-IR data are above the extrapolation of the sub-mm data, suggesting the presence of two different spectral components in these two wavelength ranges (see the analogous case of 3C 273 in Robson et al. (1986)). This hypothesis is also suggested by the constant emission observed up to 60 µm. A non-thermal source is expected to vary more at higher frequencies, due to greater energy losses. All these considerations suggest the short wavelength continuum is dominated by a thermal component. As in the case of PKS 0637-75 we will suppose that an additional IR thermal component is present at 60 µm.

These two sources (PKS 0637-752, and B2 2201+31A) are good examples of how variability can create an artificial IR spectral turnover, or hide a real one. An IR spectral turnover may be due to different luminosity states of the source at different epochs, instead of to the presence of a separate IR component. The weakness of the radio emission in RQQ precludes that its extrapolation could account for the IR emission for all reasonable assumptions on the radio variability. In SSRQ the extrapolation of the radio component in the IR is usually too faint to explain the IR emission, even if we take into account variability. The variability factors observed in two SSRQ in our sample, 3C 47 and PG 1004+130, are too small to explain the much higher IR fluxes, and this is probably true for the SSRQ in general. In the mm domain we measured a flux variation from the core of the SSRQ 3C 47 of a factor of 2 in almost three years (the emitted flux density at 100 GHz was equal to 16.30.9 mJy on September 1995 (van Bemmel et al. 1998), and equal to 30.80.6 mJy on July 1998 (this work)). The SSRQ PG 1004+130 was observed twice at 6 cm, in 1982 and in 1984, with a flux variation of a factor 2.5, from 12 mJy to 30 mJy (Lister et al. 1994).

In conclusion, the radio models shown in Fig. 2 indicate the presence of an additional IR component in almost the whole sample. According to the third test, this result indicates that the observed IR emission is of thermal origin. The properties of the IR emission in quasars will be derived and analyzed in Sect. 4.3, after subtraction of the non-thermal contribution extrapolated from the radio domain.

4.3. Modeling of the IR component

The IR emission can be accounted for by reradiation of the central luminosity by gas and dust in warped discs in the host galaxies of the quasars (Sanders et al. 1989), in the outer edge of the accretion disc and in a torus of molecular gas within a few parsecs of the central energy source (Niemeyer & Biermann 1993; Granato & Danese 1994; Granato et al. 1997; Pier & Krolik 1992, 1993), and/or by starburst emission (Rowan-Robinson 1995). The host galaxy starlight contribution is probably negligible in the far/mid-IR since the host galaxy spectrum largely differs in shape and luminosity from the SED of the selected objects (see Fig. 2). We describe here the main observational properties of the different objects of each class and compare them using a very simple model of thermal emission: the grey body model. This model does not take into account the source geometry (toroidal, warped disc, etc). An isothermal grey body at the temperature T emits at frequency a luminosity density given by the following Eq. (Gear 1988, Weedman 1986):

where r is the radius of the projected source, B(,T) is the Planck function for a blackbody of temperature T, and is the optical depth of the dust. The optical depth can be approximated by a power law of type = , where is the frequency at which the dust becomes optically thin, and is the dust emissivity index. A non-linear least squares fit was used in the fitting procedure, leaving the radius r, the temperature T, and the frequency free to vary, while the emissivity exponent was fixed equal to 1.87 (Polletta & Courvoisier 1999).

The observed IR SEDs are smooth and indicate a wide and probably continuous range of dust temperatures, describable by several grey body components. The best fit grey body models of the observed IR SEDs are shown in Fig. 5. The thick solid line represents the sum of non-thermal and grey body components. Each individual component is represented by a dotted line. The temperature (T) and the size (r) of each grey body component are listed in columns 5-10 of Table 8. It is worth noting that we could fit the observed IR spectra using a different optical depth function (different , and values). The optical depth value is important in a discussion of the source geometry in terms of an extended or compact heating source. In our models the optical depth values derived by the fits are low (1) in the far/mid-IR, and 1 in the near-IR ( 3 µm). If the dust becomes optically thin at longer wavelengths, the real source sizes will be smaller than our estimates, and vice versa. Using our optical depth values, the estimated sizes of the observed dust components range between 0.06 pc and 9.0 kpc, and the temperatures between 43 K and 1900 K. The minimum temperature may be due to an absence of dust at large distances (few kpcs) or at low temperature, and/or to starlight heating to the orders of the inferred minima. The maximal temperature is generally explained as a drop in opacity caused by the sublimation of the most refractory grains at temperatures T 2000 K (Sanders et al. 1989). The total luminosities observed in the IR, obtained by integrating the grey body components (see column 1 in Table 8), vary over a wide range, from 2.010¹¹ to 7.610¹³ . No significant difference in the distribution of sizes, temperatures, and luminosities are observed among different types of quasars. We also derive the mass of each dust component at the measured temperature, using the following Eq. (Hughes et al. 1997):

where , = 1.87, is the rest-frequency dust absorption coefficient. The normalization is at 250 µm (Hildebrand 1983), giving = 1.14 cm² g^-1 at 800 µm. The range of assumed values of at 800 µm in the literature is 0.4-3.0 cm² g^-1 (Draine & Lee 1984; Mathis & Whiffen 1989). Our dust mass estimates can thus differ by, at most, a factor 2.7. The derived values of dust masses are reported in column 4 of Table 8, and, separately for each class, in Fig. 6. Since the largest dust masses are located in the outer, less illuminated, lower temperature regions of the dust distribution, is mainly constrained by far-IR data. Therefore, when sub-mm and far-IR data are not available, the real dust mass cannot be well measured. For this reason we did not report the dust and gas masses when the low temperature component was not constrained. The absence of data in the near-IR has a negligible effect on the dust mass estimate. As for the other parameters (T, L(IR), r), the dust mass distribution does not differ significantly among different types of quasars (see Fig. 6).

Fig. 5a. SEDs as versus in the rest frame of the objects (2 FSRQ, 2 RIQ, 1 RG, 1 RQQ). Symbols as in Fig. 2. Dotted lines represent the best fit non-thermal models of the radio component and the best fit grey body models of the IR component. The temperature of each grey body component is reported. The sum of all single fitted models is shown by a solid line.

Fig. 5b. (continued) (6 SSRQ).

Fig. 5c. (continued) (6 RQQ).

Fig. 6. Histogram of the dust masses for the different classes: RQQ, SSRQ, FSRQ, and RIQ.

Table 7. Best fit parameters of non-thermal models.
Notes:
) Model a corresponds to Eq. (2), and model b to the same equation without cut off; model c corresponds to a simple power law; model d to Eq. (4), and model e to the same equation without cut off. (F) indicates a fixed value.

© European Southern Observatory (ESO) 2000

Online publication: October 30, 19100
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