MODELING THE INFRARED EMISSION IN CYGNUS A

Cygnus A was observed (PI: Baum) in "mapping mode" using the low-resolution mode of IRS on board the Spitzer Space Telescope. Both the short- and long-wavelength slits were stepped across the source in increments of half the slit width. After pipeline calibration at the Spitzer Science Center, the observations were combined into a spectral data cube using the Cube Builder for IRS Spectra Maps (CUBISM; Smith et al. 2007a). From this data cube, a spectrum was extracted in a 20'' aperture (Figure 1).

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2.1.1. Removal of Mid-Infrared Emission Lines

2.1.2. Dust Features

The nucleus and hot spots were imaged using IRAC at 4.5 and 8.0 μm (see Stawarz et al. 2007, for a presentation of the data and analysis of hot spot properties). As fluxes for the core were not presented, the archival data were retrieved, re-reduced, and calibrated according to the IRAC instrument manual. The images showed strong emission at the location of both radio hot spots and the radio core in both channels. The emission was unresolved in the core component, the measured flux densities for this component are given in Table 3. Extraction apertures of 122 were used for both channels.

Shi et al. (2005) presented observation of Cygnus A using the MIPS instrument on Spitzer at 24, 70, and 160 μm. Their 24 μm flux is consistent with our IRS observations. The slope between their 70 and 160 μm points is steeper than that of the Rayleigh–Jeans tail. The 70 and 160 μm data were re-reduced from the BCD products in the Spitzer Science Center archive. Our measured flux densities are given in Table 3. The core of Cygnus A was unresolved in both the 70 and 160 μm bands. Apertures of 30'' and 48'' were used at 70 and 160 μm, respectively. Our 160 μm measurement has larger error bars, but is broadly consistent with their value.

Cygnus A's strong synchrotron emission at radio frequencies suggests that this may contribute to the infrared as well. To anchor the synchrotron spectrum we supplemented the Spitzer observations with radio measurements from the literature. Core fluxes were obtained from Eales et al. (1989), Salter et al. (1989), Alexander et al. (1984), and Wright & Birkinshaw (1984). Submillimeter nuclear fluxes were also taken from Robson et al. (1998). Based on these archival data the unresolved radio core⁹ is flat spectrum (α = 0.18, F_ν∝ν^−α), until ∼1 THz, where thermal emission from dust begins to dominate the SED. The compiled radio through mid-infrared SED is shown in Figure 2 and the flux densities taken from the literature are provided in Table 4. The resolution of the observations is also provided.

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There is some uncertainty associated with the highest frequency sub-mm observations. The 450 μm observation suggests that the synchrotron break may be occurring in this spectral regime. It is unclear if this is a genuine break or if the measurements are affected by variability. Additional observations at these frequencies may be able to clarify this issue.

A consideration of the apertures is important when assembling data across several orders of magnitude in frequency. The resolution of the data used to assemble the SED in Figure 2 varies by over a factor of 10, but in all cases the core component is unresolved. At lower frequencies the emission is due solely to synchrotron emission from the flat spectrum radio core. There is no evidence to suggest that the larger-scale steep spectrum jet will contribute emission in the infrared. Accordingly we use the unresolved VLA-scale core to anchor the synchrotron emission in the nucleus, so the difference in apertures should not affect the construction of this SED for the nucleus.

According to the unified scheme for radio-loud AGNs, the SMBH and accretion disk can be hidden from view along some lines of sight by an obscuring torus. Along these obscured lines of sight the UV/optical radiation is absorbed and re-radiated in the mid- and far-infrared. As noted above, Cygnus A shows evidence for a hidden BLR through observations of Hα in polarized light. This suggests that Cygnus A harbors a "hidden" accretion disk and a BLR which is obscured along our line of sight.

Nenkova et al. (2008) have constructed a model for an obscuring AGN torus, where the obscuration is due to the presence of multiple clouds along the line of sight to the AGN. We select this set of models because clumpy models seem to provide better fits to Sil features than smooth dust distributions (e.g., Baum et al. 2010). In order to reproduce the observed ratio of Type I/II AGNs, the obscuring clouds collectively populate a rough toroidal structure with some opening angle.

The CLUMPY torus model is specified by multiple geometrical parameters. The outer radius of the torus (R_o) is Y times the inner radius (R_d), where the inner radius is determined from a dust sublimation temperature of T = 1500 K (R_d = 0.4 × L^0.5₄₅ pc, L₄₅ is the bolometric luminosity of the AGN in units of 10⁴⁵ erg s⁻¹). The geometry of the model is shown in Figure 3. The clumps have a Gaussian angular distribution, with σ parameterizing the width of the angular distribution from the mid-plane. The radial distribution is a power law with index q: r^−q. The inclination of the torus symmetry axis to the line of sight is i and the average number of clouds along a given line of sight is N.

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In addition to the geometrical parameters, the models also vary the optical depth of each clump (τ_V), using the Ossenkopf et al. (1992) dust composition and Mathis et al. (1977) grain size distribution. The overall scaling of the model flux is F_AGN, the bolometric flux of the AGN's accretion disk component (treating the synchrotron emission separately).

The clumpy nature of the obscuration implies that there is a finite probability of a direct line of sight to the BLR, even at high inclinations. However, as Cygnus A shows no evidence for directly observed broad lines, we have only fit models where the central regions are fully obscured along our line of sight.

Star formation is represented using the Siebenmorgen & Krügel (2007) models which assume spherical symmetry and an ISM with dust properties characteristic of the Milky Way. Emission is broken down into two components: an old stellar population uniformly distributed through the volume and hot, luminous O and B stars embedded in dusty hot spots. The density of OB stars is centrally peaked although the model output is the emission integrated over the entire starburst.

The free parameters for the model are: starburst radius r, total luminosity L_SB, ratio of luminosity in O and B stars to total luminosity f_OB, visual extinction from the center to the edge of the nucleus A_V, and dust density in hot spots around O and B stars n.

Owing to the spherical symmetry of this starburst model and the known ring morphology of the star formation in Cygnus A, parameters such as A_V and the radius r do not have straightforward interpretations here. The assumption of optically thick star formation does not have strong evidence (either for or against), given the absence of high-resolution far-infrared observations.

The strong radio emission in Cygnus A justifies the final model component. VLA core fluxes are consistent with power-law emission to the submillimeter where thermal emission begins to dominate. Extrapolating the power law to higher frequencies suggests that the synchrotron spectrum must either be modified or subjected to attenuation. The AGN is known to sit behind a dust lane with significant extinction (A_V = 50 ± 30; Djorgovski et al. 1991). Though some attenuation of the synchrotron flux is expected at higher frequencies, this alone is not sufficient to explain why the synchrotron power law does not continue through the mid-infrared. With extinction alone, the flux densities at 30 and 10 μm would be similar for the observed spectral index of α = 0.18. For A_V = 50, the expected flux from the extrapolated synchrotron emission would by itself exceed the measured infrared flux at 10 μm. We conclude that there must be a break in the population of emitting electrons.

One possible explanation is a simple cutoff in the population of relativistic electrons at some energy (Case I). This would manifest itself as a cutoff in the synchrotron spectrum:

$$\begin{equation} F_{\nu } \propto \nu ^{-\alpha _1} e^{-\frac{\nu }{\nu _c}}e^{-\tau _r(\nu)}, \end{equation} \tag{ 1 }$$

where ν_c is the frequency corresponding to the cutoff in the energy distribution of the particles, α₁ is the spectral index in the optically thin regime, and τ_r(ν) is the dust screen between the synchrotron emitting region and the observer. τ_r(ν) follows Draine & Lee (1984).

In Cygnus A the spectral index α₁ is measured from VLA core radio fluxes, and the amplitude of the power law fixed from the same observations. The only free parameters are the cutoff frequency ν_c and the optical depth τ_r. These parameters are partly degenerate in that in trial runs we experienced a situation where τ_r and ν_c would both increase, effectively offsetting each other. To combat this we limited τ_r such that A_V did not exceed 500 toward the radio source.

An alternative model for the synchrotron emission at higher frequencies is a broken power law behind a dust screen (Case II). Aging of the population of relativistic electrons results in a broken power law whose spectral index increases for frequencies higher than a break frequency (Kardashev 1962). The functional form adopted is

$$\begin{equation} F_{\nu } \propto e^{-\tau _r(\nu)} \times \left\lbrace \begin{array}{@{}l@{\quad }l@{}}\nu ^{-\alpha _1} & {\rm if }\; \nu < \nu _{{\rm break}} \\ \nu ^{-\alpha _2} & {\rm if }\; \nu \ge \nu _{{\rm break}}. \end{array}\right. \end{equation} \tag{ 2 }$$

For a simple aging of the electron population, the post-break spectral index in Cygnus A would be α₂ = 1.24. As with Case I, we fit a dust screen in front of the synchrotron emission (τ_r).

Starlight can potentially contribute to the mid-infrared flux, especially in a large aperture. Using the flux of the stellar component from Jackson et al. (1998) and their brightness profile, we determined the contribution due to starlight in a 20'' aperture. The relative fluxes were consistent with an elliptical galaxy template from Silva et al. (1998). Expected flux densities at 2.2, 5, and 10 μm were computed using the same template spectrum. After subtracting a nuclear point source, the K-band flux density in starlight is consistent with the flux in a 20'' aperture as measured using Two Micron All Sky Survey (2MASS) data products (Skrutskie et al. 2006). At 5 and 10 μm, the starlight contributes roughly 14% and 2%, respectively, of the flux measured by IRS. Therefore, we do not include any contribution to the mid-infrared flux from an old stellar population in our modeling.

Warm dust in the NLR directly illuminated by the AGN can also contribute to the mid- and far-infrared emission (e.g., Groves et al. 2006). Ramos Almeida et al. (2009) find that a significant contribution to the mid-infrared flux can come from sources other than the AGN torus, particularly additional hot dust. In Cygnus A Radomski et al. (2002) find an extended component to the mid-infrared emission which is consistent with T ∼ 150 K dust. Some of this extended emission is cospatial with sites of possible star formation. Dust of this temperature is well reproduced with our choice of starburst models (with the implicit assumption that this dust is heated by star formation).

Higher temperature dust is also present in the inner regions of Cygnus A. However the resolved mid-infrared images of the nuclear regions by Radomski et al. (2002) are unable to distinguish between dust in the "torus" and dust in the NLR heated by the AGN. Without strong observational motivation for an additional dust component we opt not to include one. As will be shown in the next section we are able to reproduce the observed emission without this additional component.

Prior to fitting the models, the available parameter space was constrained using results from previous studies of Cygnus A. The opening angle and covering fraction of the CLUMPY torus are determined from the σ and N parameters (see Equations (3) and (4) in Mor et al. 2009). We define the half opening angle of the torus as the angle at which the escape probability of a photon drops below e⁻¹:

$$\begin{equation} \theta _{{\rm half}}=90-\sigma \sqrt{\ln {N_0}}. \end{equation} \tag{ 3 }$$

Tadhunter et al. (1999) measured the opening angle of the ionization cone in Cygnus A using near-infrared HST data, finding θ_half = (58 ± 4)°. We use this value as the torus opening angle and limit the parameter range of σ and N according to Equation (3).

The inclination range of the torus i was limited by VLBI observations and modeling of the inner pc-scale jet (50° ⩽ i ⩽ 85°; Sorathia et al. 1996). Additionally, the available VLA core radio fluxes were used to fix the synchrotron spectrum at radio frequencies (α₁ and the amplitude).

The best-fit combination of parameters for Case I has χ²/DOF = 1.35. The range of acceptable matches for the 1641 model combinations is shown in Figure 4 (left). Histograms of the best-fit parameters are given in Figures 5 (left) and 6, where f is the fraction of models within the 95.4% confidence interval in a given bin. Parameters for the best-fit model are marked with a small blue horizontal bar.

4.1.1. AGN/Torus Properties and Contribution

4.1.2. Starburst

The median value of the starburst luminosity for Case I is log (L_SB/L_☉) ∼ 10.8, with a tail up to ∼11.6 containing approximately 40% of the fits (Figure 5). This covers a range of star formation rates from 10 to 70 M_☉ yr⁻¹, as determined by the L_IR calibration from Kennicutt (1998b) (for a review of SFR estimates, see Kennicutt 1998a):

$$\begin{equation} \frac{{\rm SFR}}{(M_{\odot } {\rm \,yr}^{-1})} = 4.5\times 10^{-44} \frac{L_{{\rm FIR}}}{{\rm \,erg \,s}^{-1}}=1.72\times 10^{-10} \frac{L_{{\rm FIR}}}{L_{\odot }}. \end{equation} \tag{ 4 }$$

Roughly half the fits within this confidence interval have 40% of the starburst luminosity in the form of OB stars. The distribution of size parameters is relatively flat, although even the largest sizes would be unresolved by our Spitzer observations. The distribution of dust density n peaks around 10³ cm⁻³. The extinction through this starburst is relatively unconstrained.

The strengths of dust features in starburst models falling within the 95.4% confidence interval were also measured using PAHFIT to compare with the intensities of observed dust feature. Figure 8 shows histograms of the predicted intensities from our models divided by the measured intensity from the IRS spectrum. Only dust features which are detected in the IRS spectrum have been plotted. In general the agreement is good with most models matching the measured line intensities. However for some dust features a significant number of the models within the confidence interval predict emission in excess of what is observed. While a detailed comparison of the relative strengths of dust features is beyond the scope of the paper, we suggest the models are able to generally reproduce the dust features seen in the spectrum. The dust features which show the greatest discrepancy between observed fluxes and those predicted from the modeling (6.2, 7.8, and 11.3 μm) comprise three of the five lowest signal-to-noise dust feature fits in the spectrum. The discrepancy may then be due to the difficulty of fitting low equivalent width dust features.

PAHFIT also attempted to fit eight other dust features in the IRS spectrum. The upper limits for three (5.7, 14.0, and 15.9 μm) are consistent with expectations from the starburst models. One dust feature (16.4 μm) has a measured limit below that expected from the best-fitting starburst model, and so is discrepant. The other four features (7.6, 10, 7, 11.2, and 12.7 μm) also have upper limits from PAHFIT which are lower than the expected value from the starburst models. However, these are coincident with or near other spectral features (e.g., narrow emission lines or the Sil absorption). Thus an accurate measurement of these dust features in the IRS spectrum would rely more heavily on fitting the wings, which could prove difficult in a continuum dominated source such as Cygnus A.

4.1.3. Synchrotron Radiation

The synchrotron emission amplitude was fixed using the non-thermal emission from the radio core, assuming it to be a point source at all frequencies observed. The synchrotron model, therefore, has only two parameters: cutoff frequency (ν_c) and extinction due to dust (τ_r).

The distribution of cutoff frequencies is somewhat broad, covering the range of ν ≈ 10–60 THz (5–30 μm) (Figure 9). The fits show a range of acceptable extinction for the dust screen, peaking in the range of A_V ≈ 60–80, slightly lower than the predicted line of sight A_V from the torus models. The integrated luminosity of the "core" synchrotron flux is log (L_sync/L_☉) ∼ 11.2.

This break in the synchrotron spectrum is consistent with other powerful FR II radio sources, where an extrapolation of the radio synchrotron emission significantly exceeds the observed optical flux (e.g., Schwartz et al. 2000; Sambruna et al. 2004; Mehta et al. 2009). In these cases, the similarity of the radio and X-ray spectral indices suggests that the X-rays may be produced by inverse Compton (IC) scattering.

With the modeled synchrotron spectrum, a magnetic field strength, and the assumption that each electron emits at a single frequency, the energy distribution of relativistic electrons can be determined:

$$\begin{equation} \gamma (\nu)= \sqrt{\frac{4\pi m_e c \nu }{3eB}}, \end{equation} \tag{ 5 }$$

where all constants and values are in the cgs system of units.

The magnetic field strength has been estimated from VLBI observations to be roughly 17 mG (100 mG) in the jet (core) (Roland et al. 1988; Kellermann et al. 1981). Using ν ≈ 30 THz and Equation (5) we find γ ∼ 2 × 10⁴ (8 × 10³) for the jet (core).

In addition to radiating energy via synchrotron emission, relativistic electrons can also lose energy via IC scattering. The ratio of the energy lost through synchrotron to the energy lost to IC is simply given by the ratio of the magnetic and radiation energy densities, with the cosmic microwave background (CMB) setting a minimum value for the radiation energy density. Using the magnetic field strength assumed above (17 mG), and T_CMB = 2.73 K, synchrotron losses are dominant by a factor >10⁸. A larger magnetic field would further enhance this ratio, so IC losses from scattering of CMB photons have a negligible effect on the population of relativistic particles.

The range of best-fit models for Case II is shown in Figure 4 (right). The best-fit model had χ²/DOF = 1.03. Figure 4 (right) shows the range of the 1580 model fits within the 95.4% confidence interval. Histograms of the best-fit parameters are given in Figures 5 (left) and 6. A red horizontal bar marks the parameter for the parameters with the lowest χ² value.

4.2.1. AGN/Torus

4.2.2. Starburst

4.2.3. Synchrotron Properties and Contribution

Our best estimate of the bolometric AGN luminosity in Cygnus A (log(L/L_☉) ∼12, including the synchrotron component and X-ray emission) is above the Whysong & Antonucci (2004) estimate using Keck mid-infrared observations and a PG-quasar spectrum (3.9 × 10¹¹ L_☉), but is somewhat below the estimates of Tadhunter et al. (2003) who find L_bol = (12–55) × 10¹¹ L_☉ (although consistent with the low end of their range). The bolometric AGN luminosity is the best constrained parameter and is insensitive to the synchrotron model adopted.

The kinetic power in the expansion of the radio lobes in Cygnus A can be inferred from X-ray observations of the cluster environment (Wilson et al. 2006). From this analysis of Chandra observations Cygnus A has a kinetic power of L_kin = 1.2 × 10⁴⁶ erg s⁻¹ (log (L_kin/L_☉) = 12.5), a factor of three larger than the bolometric AGN luminosity inferred from the modeling. Given the uncertainties in the determinations of both the kinetic and bolometric power, it is unclear if the kinetic power dominates significantly over the power emitted as radiation.

The probable torus sizes from the SED modeling give outer radii of R_o = 130 pc (≈02 at the distance of Cygnus A). Generally, the torus parameters provide reasonable estimates of the properties of the obscuring structure. This predicted outer radius is significantly larger than what is generally assumed to be reasonable for the obscuring torus. A torus with an angular diameter of ≈02 is well within the range of multiple mid- and near-infrared instruments. At large radii, the distinction between torus clouds and NLR clouds may be somewhat arbitrary. The observations by Canalizo et al. (2003) show extended emission on scales including and larger than our fit torus sizes. The degree of contamination by emission lines is unclear, and it would be interesting to attempt to obtain a line-free continuum image to ascertain the true size and shape of the continuum emitting region.

The torus size parameters are consistent with those found from modeling of the 9.7 μm Sil feature by Imanishi & Ueno (2000). Their radiative transfer modeling suggested some torus properties similar to those presented here, namely, a small inner radius (<10 pc) and an inner-to-outer radius of 80–500. In contrast they find a steeper radial dependence for the dust distribution q ∼ 2–2.5, possibly due to the use of a smooth dust distribution.

The preferred parameters for the obscuring torus; low q, high A_V, and large Y suggest the model is being driven toward a cooler spectrum. This could influence the starburst component, leading to a lower inferred star formation rate. In order to combat this it would be beneficial to place tighter constraints on the far-infrared SED to enable better modeling of the star formation in Cygnus A.

A comparison of our IRS data with mid-infrared observations by Radomski et al. (2002) is consistent with the suggestion of our model that at 10 and 18 μm, the emission is dominated by the torus + synchrotron component. Tadhunter et al. (1999) measure a K-band nuclear point source with F_ν = (49 ± 10) μJy. This flux limit is broadly consistent with some model fits for the torus + synchrotron component.

For the estimated bolometric luminosity 10¹² L_☉ and a black hole mass of 2.5 × 10⁹ M_☉, the Eddington ratio (L/L_edd) is ∼1.3 × 10⁻². This is similar to, but slightly lower than, previous estimates from Tadhunter et al. (2003), likely due to the fact that our model attributes some of the IR luminosity to the heating of dust from star formation. This starburst luminosity is relatively well constrained, with consistent values across the bulk of fits. The AGN (torus plus jet) contributes ∼90% of the infrared luminosity and star formation produces the remaining 10%.

The results of our modeling can be tested and improved with the help of future observations in various wavelength regimes.

Around 1 THz (∼300 μm) the synchrotron and starburst model components are of similar flux density, with the synchrotron contribution decreasing and the thermal contribution from star formation beginning to dominate. Unfortunately, data at this location are limited in resolution, sensitivity, and wavelength coverage. Disentangling the emission from the starburst and emission from the AGN at this frequency will be possible with the Atacama Large Millimeter Array (ALMA; e.g., Carilli 2005), particularly with the availability of Band 10 and full science capabilities.

The far-infrared suffers from poor sampling of the SED. In this regime the Herschel Space Observatory (Pilbratt et al. 2010) provides an opportunity to improve on the understanding of the continuum emission. SPIRE and PACS cover wavelength ranges of interest: the region of the possible jet-break and the long wavelength side of the infrared bump. Observations here can provide improved constraints for the synchrotron and starburst models. González-Alfonso et al. (2010) demonstrate decomposition of far-infrared emission for Mrk 231, with the Herschel SPIRE observations providing important constraints. Similar observations of Cygnus A will provide important data on this sparsely observed portion of the SED. PACS observations would contribute measurements of far-infrared fine structure lines which could be used in concert with the mid-infrared lines to provide an alternative method of determining the relative contribution of star formation and AGN activity to the infrared luminosity (e.g., Fischer et al. 2010, for Mrk 231).

Although the synchrotron spectrum breaks in our fits, it may still dominate the flux between 5 and 10 μm. This result can be tested by future mid-infrared polarimetry or variability studies. Synchrotron emission from a compact source such as the radio core or jet knots should be subject to flaring. If the emission in this wavelength range is instead of a thermal origin (e.g., hot dust in the host galaxy), the 10 μm flux will remain relatively stable.