EVIDENCE FOR A NUCLEAR RADIO JET AND ITS STRUCTURE DOWN TO ≲100 SCHWARZSCHILD RADII IN THE CENTER OF THE SOMBRERO GALAXY (M 104, NGC 4594)

In Figure 1, we show self-calibrated images of the M 104 nucleus at all of the observed frequencies. Between 2 and 43 GHz, the images shown are made by stacking the visibility data over the two epochs. We did not find any significant structural/flux variations at each frequency over the two epochs within the calibration uncertainties.

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Thanks to the high quality of the data set, we have obtained VLBI images for the M 104 nucleus at unprecedented sensitivities and resolutions. To our knowledge, this is the first clear VLBI detection and imaging of M 104 at 15, 24, and 43 GHz. In particular at 43 GHz, where the angular resolution attains 0.35 × 0.14 mas with a uniform weighting scheme, the nuclear structure was imaged on a scale down to ∼60 R_s (Figure 2). Along with SgrA* (Shen et al. 2005; Doeleman et al. 2008; Lu et al. 2011), M 87 (Junor et al. 1999; Krichbaum et al. 2006; Ly et al. 2007; Hada et al. 2011; Doeleman et al. 2012), and Cen A (Tingay et al. 1998; Horiuchi et al. 2006; Müller et al. 2011), M 104 is the fourth source in which such a compact scale was resolved. The image parameters obtained for these maps are listed in Table 1.

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In the previous radio observations, only a single compact feature was detected for the nuclear region both on arcsecond (de Bruyn et al. 1976; Hummel et al. 1984; Bajaja et al. 1988; Krause et al. 2006) and mas scales (Graham et al. 1981; Preston et al. 1985; Shaffer & Marscher 1979). In the new experiments presented here, for the first time, we have clearly discovered the presence of the extended structure elongating from the radio core. This structure is more remarkable at lower frequencies, and appears to elongate quite symmetrically toward the northwest (P.A. ∼ −20°) and a southeast (P.A. ∼ 160°) directions. Its entire length is estimated to be ∼120 mas (4.8 pc or 5.4 × 10⁴R_s) at 1.4 and ∼30 mas (1.2 pc or 2.7 × 10⁵R_s) at 5 GHz (above 3σ level), respectively. Note that the direction of the extension is similar to that of the major axis of synthesized beams, but we are confident that this structure is not an artifact; the extension of this structure is sufficiently larger than each beam size, and a consistent structure is obtained also at 5 GHz, where the position angle of the synthesized beam is significantly different from that of the source elongation. The extended structure is quite smooth and none of the knotty features were found.

As frequency increases, the structure becomes progressively compact, and the radio core increasingly dominates the total radio emission. At 15 and 24 GHz, the northern side emission tends to be brighter than that of the southern one. We then estimated a brightness ratio R of the northern/southern emission at each frequency in the following way; using the source structure model established by a deconvolution process (i.e., a set of CLEAN components), we compared the integrated flux densities of CLEAN components in two rectangular regions, which are at the same distance from the core and have the same size (one is along P.A. = −20° and the other is along P.A. = 160°). The results are summarized in Table 2. R was derived to be ∼1.1–1.2 between 1.4 and 5 GHz, whereas it was ∼1.3–2.1 between 8.4 and 24 GHz. Note that the derived value of R at each frequency varied slightly when we changed the shape of the adopted box, but the overall trend was basically the same as the case in Table 2 and the northern side was brighter. At 43 GHz, almost all of the emission above 3σ is confined within ∼1 mas.

To quantify the structural properties of the M 104 nucleus, we performed a model fitting to the images. As a simple description, here we performed a single elliptical Gaussian model fitting to the core region using the AIPS task JMFIT, and derived deconvolved parameters of the models. Note that the actual structure is more complicated as is evident from the presence of the extended emission, but this method is still useful to examine the basic properties of the main emitting component (i.e., radio core). The obtained values for the geometrical parameters are summarized in Table 3 and shown in Figure 3 as a function of frequency.

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At all of the observed frequencies, the derived Gaussian models show highly elongated shapes in a mean position angle of P.A. ∼ −25° (or 155°), which smoothly connects to the direction of the larger scale extension. In terms of the core size, the length of the major axis (θ_maj) is clearly frequency dependent, becoming smaller as frequency increases. We examined an averaged frequency dependence of the major axis size by fitting a power-law function to the data between 1.4 and 43 GHz, and obtained the best-fit solution as θ_maj∝ν^{−1.20 ± 0.08}. On the other hand, the structure along the minor axis tends to be largely unresolved; the derived lengths result in typically ∼1/5 of the beam size or smaller at each frequency. At 43 GHz, the size of the radio core is derived as 0.22 (mas) × 0.08 (mas) in P.A. = −20° with a flux density of 91 mJy, corresponding to 0.009 × 0.003 pc (1900 × 600 AU) or 100 × 36R_s. With this parameter set at 43 GHz, the brightness temperature of the most compact region is estimated to be ∼3 × 10⁹ K. If the obtained size of the minor axis is treated as an upper limit, this brightness temperature would be regarded as a lower limit.

We note that a frequency-dependent size of the radio core is also seen in the M 81 nucleus with a slightly shallower profile (∝ν^−0.8; Bietenholz et al. 1996, 2004; Ros & Pérez-Torres 2012). We also remark that no signs of the scatter-broadening law, which is obviously seen toward SgrA* as θ∝ν⁻² (Lo et al. 1993), was found in the case of M 104, despite a comparable physical scale being observed in the gravitational unit.

Multi-frequency images of M 104 show the nuclear radio structure to be clearly frequency dependent, indicating that the spectral property is spatially varying. We then investigated the spectral properties and the their spatial distributions. Quasi-simultaneous observations with a wide frequency coverage at good image qualities allow us to examine these in detail.

In Figure 4, we first show a spectral index distribution map between 2 and 5 GHz and its slice along P.A. = −20° in order to qualitatively describe the overall spectral characteristics. The two images at 2 and 5 GHz are aligned by the respective phase centers. While a careful alignment is necessary if one seeks a more accurate distribution, the frequency-dependent position shift of the radio core between these frequencies is small compared with the structural extension (see the next section). Thus Figure 4 gives a reasonable approximation for the true spectral distribution. As seen in this map, the M 104 nucleus clearly shows a spatially varying spectral property. The spatial gradient of the spectral index distribution is apparent along the source elongation; the spectrum is slightly inverted near the core and progressively becomes steeper as it recedes from the core toward both the northern and southern directions.

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Then, we combined all of the multi-frequency data to clarify more detailed spectral properties. In Figure 5 and Table 4, we show combined radio spectra between 1.4 and 43 GHz. Here we plot the spectra for three different regions: (1) the total CLEANed VLBI flux, (2) the radio core flux derived by the model fitting in the previous section, and (3) the integrated CLEANed flux for the extended region. For (3), we defined such a region as the outside of 4 mas diameter circle centered on the core, which corresponds to the exterior part of the model-fitted core at >2 GHz. We stress that these spectra are quasi-simultaneously obtained between 2 and 43 GHz, which is essential for correctly understanding the spectral properties.

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Over the observed frequency range, the total emission shows a quite flat spectrum with an averaged spectral index of α = 0.08 ± 0.03. However, our high-resolution observations revealed that such a total spectrum consists of distinct spectral components. The radio core shows a slightly inverted spectrum with an averaged spectral index α = 0.14 ± 0.02, whereas the extended part shows a steep spectrum with α = −1.11 ± 0.04.

One of the key approaches for specifying the origin of nuclear radio emission is to examine the position shift of the radio core as a function of frequency. This "core shift" is expected to be a natural consequence of the nuclear opacity effect if the radio emitting region is dominated by a radio jet (Königl 1981; Lobanov 1998; Falcke & Biermann 1999; Hada et al. 2011). Our quasi-simultaneous, multi-frequency, phase-referencing observations relative to the calibrator J1239–1023 allow us to examine this.

In Figure 6, we show the astrometry results of the M 104 core positions. Here we plot a weighted mean position over the two epochs at each frequency to better constrain the position. While the jet base structure of J1239–1023 is relatively complex, we detected a well-isolated, optically thin feature, A1, in the downstream side of this jet (see the Appendix for the structure of J1239–1023). Therefore, we measured the relative position of the M 104 core at each frequency with respect to the intensity centroid of this feature, which is supposed to be stationary on the sky in terms of frequency (Kovalev et al. 2008; Sokolovsky et al. 2011). For both of the M 104 core and the reference feature in J1239–1023, their positions were registered using a Gaussian model fitting on each image. The quoted position uncertainties in Figure 6 refer to statistical terms, which are purely caused by image qualities (phase-referenced images were used for the M 104 core, whereas self-calibrated images were used for the reference feature in J1239–1023), by calculating the beam size divided by the peak-to-noise ratio of each component.

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The derived result indicates that the observed core positions tend to move toward a northern direction as frequency decreases, although the position uncertainties are rather large because M 104 is a low-declination source. An overall position angle of the shift is roughly −10° ∼ −30°, which is similar to the direction of the larger-scale northern extension. Mean values of the observed position shifts are measured to be ∼0.2 mas, ∼0.3 mas, and ∼0.4 mas for 2–5 GHz, 2–24 GHz, and 2–43 GHz pairs, respectively.

We should note that, while non-dispersive tropospheric residuals produce a common systematic position shift at different frequencies (thus such shifts can be canceled out among frequencies in our quasi-simultaneous observations), dispersive ionospheric residuals can cause an unwanted frequency-dependent position shift. We then checked a possible impact of the ionospheric effect by comparing the astrometry results made with and without the ionospheric correction (AIPS task TECOR). Phase-referenced images without the correction produced position shifts of M 104 as large as ∼3 mas toward a similar (P.A. ∼ 0°) northern direction between 2 and 43 GHz with degrading of the image quality (∼30% decrease of the peak-to-noise ratio was seen at 2 GHz). Therefore, one cannot completely exclude the possibility that the observed northward shifts are related to the ionospheric effect. However, we confirmed that the amount of position differences between the two methods was well fitted by an inverse-square law with frequency ν^{−2.19 ± 0.20}, indicating that the ionospheric correction is indeed working effectively. Using the equation provided in Hada et al. (2011), we estimate a potential remaining uncertainty due to the ionospheric residuals after the correction to be ∼0.2 mas at 2 GHz, under the observed condition of δZ = 123, Z ∼ 50°, and δI ∼ 3 × 10¹⁶ m⁻² where δZ, Z, and δI represent the source separation, source zenith angle, and residual total electron content, respectively. Hence, if the position measurements are still affected by the ionospheric residuals, the observed ∼0.2 mas shift for 2–5 GHz pair would be regarded as an upper limit, and for the pair of 2–24 GHz or 2–43 GHz, a level of ∼0.1–0.2 mas is eventually left for the intrinsic core shift.

Previous arcsecond-scale observations report that the M 104 nucleus is variable at radio frequencies at some of the different time scales and amplitudes. De Bruyn et al. (1976) report a 10∼20% level variability at 5 and 8 GHz during a period of a few months, whereas Bajaja et al. (1988) found a ∼70% level flux increase at 1.7 GHz between 1971 and 1986. We searched for any possible variability by comparing the data on March 23 and 30 separately. However, no significant variability was found for any component within the amplitude calibration accuracy (∼10%).

The observed VLBI flux densities of ≲ 100 mJy are 20%–40% lower than those measured in previous VLBI experiments at 2 and 5 GHz (∼120–140 mJy; Graham et al. 1981; Shaffer & Marscher 1979). This implies the presence of a long-term variability on an mas scale.

Because of its highly sub-Eddington luminosity and the absence of Fe Kα lines, it is suggested that the standard thin accretion disk is not present in the nuclear accretion of M 104 (Pellegrini et al. 2003). Similar to other LLAGNs, its accretion state is preferably modeled by RIAF (Di Matteo et al. 2001; Yuan et al. 2009). However, a predicted amount of RIAF emission with its Bondi accretion rate ($\dot{M}_{\rm Bondi}$) overestimates the observed radio luminosity by a factor of ∼10 (Di Matteo et al. 2001); to reconcile the RIAF model, they point out the necessity of reducing the accretion rate down to a few percent of $\dot{M}_{\rm Bondi}$ near the inner edge of the accretion flow. Such an inward decrease of the accretion rate can be realized via outflow/winds (adiabatic inflow–outflow solution; Blandford & Begelman 1999) or convection (convection-dominated accretion flow; Narayan et al. 2000), although recent studies tend to disfavor the latter scenario because the real accretion flow is convectively stable (Yuan et al. 2012; Narayan et al. 2012). On the other hand, RIAF with such a strong mass loss leads to a significant reduction of the radio-to-X-ray luminosity ratio (L_radio/L_X) from the original (non-mass loss) RIAF (Quataert & Narayan 1999). This situation then leads to a significant "underestimate" of the expected radio emission once the model attempts to match the observed X-ray luminosity. In the end, these theoretical studies conclude that the presence/dominance of a nuclear radio jet is a natural solution in order to consistently explain the observed luminosities in the radio/X-ray and the requirement of mass loss (Di Matteo et al. 2001; Yuan et al. 2009). Nonetheless, previous radio observations of M 104 have not found such a jet-like signature; only a point-like structure was seen both on subarcsecond (de Bruyn et al. 1976; Hummel et al. 1984; Bajaja et al. 1988; Krause et al. 2006) and mas (Graham et al. 1981; Preston et al. 1985; Shaffer & Marscher 1979) scales, resulting in a major puzzle for the nuclear structure of M 104.

In this work, our deep VLBA observations have finally obtained compelling evidence for the nuclear radio jets in the center of M 104. In terms of its morphology, the parsec to sub-parsec scale structure is never point-like, but clearly has an extended component. This extended structure is narrow and collimated with a two-sided shape, and both sides show steep radio spectra at the observed frequency range. At the base of the extended structure, the central radio core shows a high-brightness temperature with a flat ∼slightly inverted spectrum. The model fitting shows the radio core to be highly elongated in the same direction of the outer extended structure with a clear frequency-dependent size. Moreover, the astrometric measurement shows a tendency of the core position to shift with frequency. While these characteristics cannot be explained by thermal synchrotron from RIAF, all of the observed radio properties share the well-known characteristics in more luminous AGNs such as FR I or FR II radio galaxies; the radio emission is created by nonthermal synchrotron emission from relativistic jets with spatially varying nuclear opacities. Note that creating higher brightness temperatures and flatter spectra of radio cores are still possible with RIAF if one introduces a nonthermal electron population in the accretion flow (Yuan et al. 2003; Liu & Wu 2013). However, such a scenario by RIAF would still have difficulty in explaining the observed geometrical properties of the radio core; the emission region of such a hot accretion flow is nearly spherically symmetric (Narayan & Yi 1994); thus one does not expect a significant elongation of the emitting region and a core shift toward a specific direction. Based on a number of these new pieces of evidence, therefore, we argue that the radio emission of the M 104 nucleus is dominated by the nuclear radio jets emanating from its central engine over the observed frequencies.

It should be noted that the nuclear radio jets are similarly resolved in the other nearest cases M 81 (3.6 Mpc) and NGC 4258 (7.2 Mpc) together with an obvious offset of the radio cores from their putative black hole positions (Bietenholz et al. 2000, 2004; Herrnstein et al. 1997; Doi et al. 2013). Since the radio powers of these sources (P_5 G ∼ 10^20.9, 10^20.4, and 10^19.3 W Hz⁻¹ for M 104, M 81, and NGC 4258) fall on a roughly intermediate level among the LLAGN population (Nagar et al. 2005), this implies that the production of jets is a common ability of LLAGN central engines. Regarding more distant sources, Ulvestad & Ho (2001) and Anderson et al. (2004) have shown in six prototypical LLAGNs (at distances between 15∼40 Mpc with their radio powers ranging from P_5 G ∼ 10^19.5–21 W Hz⁻¹, comparable to those of the above three sources) that their nuclear radio structures are unresolved on an mas scale, but too bright to be explained by RIAF. This situation would naturally be expected if their jets were highly compact similar to those seen in M 104, M 81, and NGC 4258. We also note that recent high-sensitivity VLBI studies suggest the dominance of jet emission in some of the faintest ends of LLAGNs (down to around 10¹⁹ W Hz⁻¹; Giroletti & Panessa 2009; Bontempi et al. 2012).

We attempt to estimate fundamental parameters of the M 104 jet based on the obtained radio results.

First, since the M 104 nucleus shows a two-sided structure, it is important to determine which is the approaching jet and which is the receding side. Assuming that the two-sided jet is intrinsically symmetric and any apparent asymmetry is caused by Doppler-beaming/de-beaming effects, here we claim that the northern part is the approaching jet. This is because, while the observed structures at 1.4 and 2.3 GHz are relatively symmetric, at higher frequencies the northern part tends to become brighter than the southern part with a brightness ratio R = 1.3 ∼ 2.1. This argument is also supported by a tendency of the core to shift toward the northern direction as frequency decreases.

Next, by using the brightness ratio of the jet/counterjet, we estimate an allowed range of the inclination angle i and the intrinsic velocity β_int = v_int/c. In general, these two parameters are derived simultaneously by measuring a brightness ratio and an apparent jet velocity. However, the data used here are not enough to measure the jet motion reliably. Instead, here we attempt to constrain i by comparing the observed core shift with a theoretical expectation assuming that the observed radio core at each frequency marks a synchrotron-self-absorption surface of the approaching jet.

According to the compact jet model proposed by FB99, the amount of the core shift in LLAGN jets is mainly dependent on observing frequency, characteristic electron Lorentz factor γ_e, and inclination angle of the jet. This model has been applied to several LLAGNs such as SgrA*, M 81, and NGC 4258 as well as some galactic sources, and successfully explains many observational aspects of these sources. In Figure 7, we show a comparison of the observed core shift (relative to the 43 GHz core position) with model predictions for several different inclination angles. We calculated these expected values by combining Equations (8) and (16) in FB99 under the assumption of γ_e = 300, which is suggested to be a typical value for LLAGN (similar discussion is presented in Anderson et al. 2004).

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Because the observed core shift is relatively small, matched models suggest small inclination angles around i ∼3–15°. For larger i, e.g., i = 25°, the model still matches the observed core shift between 43 GHz and 15/24 GHz within the uncertainties, but tends to overestimate the values at lower frequencies. We also checked the impact of γ_e by changing its value between 250 and 630, the range of which is implied by the modeling of M 81 and NGC 4258 (FB99). We confirmed that this uncertainty of γ_e eases the allowed range of i to be about 1°–25° in order to reproduce the 0.1–0.7 mas separation between 2 and 43 GHz. In fact, this range of i creates integrated jet luminosities with flat ∼ only mildly inverted radio spectra α ∼ 0–0.10 in their model ($S_{\nu }\propto \nu ^{0.20\xi _2}$ where ξ₂ ≡ −0.155 + 1.79i − 0.634i²; Equation (8) in FB99), which is consistent with the observed integrated spectrum for M 104 (α ∼ 0.08 ± 0.03). Thus, a range of 1° < i < 25° would be a reasonable constraint on the inclination angle of the M 104 jet.

Then, we can now infer the intrinsic velocity β_int by combining the observed brightness ratio and the core shift. Figure 8 shows an allowed range of the β_int − i plane for the M 104 jet. In this plot, we adopt the continuous jet model to relate R to (β_int − i), i.e., R = [(1 + β_intcos θ)/(1 − β_intcos θ)]^{2 − α} (e.g., Ghisellini et al. 1993). Here, we adopt α = −1.1 based on the optically thin part of the observed jet. We found that the allowed range of the jet velocity results in 0.02 < β_int < 0.2 (1.00 < Γ < 1.02) under the ranges of inclination angle 1° < i < 25° and the brightness ratio 1.1 < R < 2.1, implying that the M 104 jet is highly sub-relativistic. Interestingly, this jet speed of M 104 seems to be quite slower than that suggested for M 81/NGC 4258 based on their VLBI-scale properties (roughly β_int ≳ 0.9 or Γ ≳ 2–3; Doi et al. 2013; Falcke & Biermann 1999). Since VLBI observations of M 104 are looking at the very first stage of jet formation (100R_s scale from the black hole) compared to those for M 81/NGC 4258 (10^3–4R_s or a more downstream region), this discrepancy could be related to some acceleration processes along the jet. Note that the suggested tendency of a smaller i with a slower β_int would become even stronger if the observed core shift is affected by the ionospheric residuals.

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The derived inclination angle of the M 104 jet has an intriguing implication for the AGN unification paradigm (Urry & Padovani 1995). The M 104 nucleus is known to be one of the representative sources belonging to the "true type II AGN"; only narrow optical emission-line components are detected (e.g., Nicholson et al. 1998), but the amount of obscuring materials along our line-of-sight is only moderate, as indicated by X-ray studies (e.g., N_H = 1.8 × 10²¹ m⁻²; Pellegrini et al. 2003) and also by optical studies (Ho et al. 1997a). If the plane of the circumnuclear torus is perpendicular to the radio jets (such a condition seems to be actually realized for nearby AGNs; Matsushita 2012), the observed weak obscuration can be a natural consequence of less intervening material along our line-of-sight (i.e., a nearly face-on-view torus). In this case, the M 104 nucleus would actually belong to the type I AGN instead of the type II, and thus the apparent absence/weakness of the broad line components indicates the intrinsic disappearance/weakness of the broad line region (BLR). Indeed, some theoretical studies predict the intrinsic disappearance of BLR under certain bolometric luminosities (e.g., L_bol < 10^41.8(M_BH/10⁸ M_☉)² erg s⁻¹; Laor 2003), and M 104's low luminosity satisfies this criteria well. A face-on view of the M 104 circumnuclear torus is also suggested by the detection of a silicate emission feature in the IR spectra (Shi et al. 2010).

Finally, we briefly remark on a potential importance of the comparison between M 104 and M 87. While these two sources harbor the central black holes with similar masses, the power of the radio jets is remarkably different. Such a distinction may be regulated by the other fundamental parameters of black holes such as spin and/or accretion rate (Sikora et al. 2007), or physical properties of the inner part of the accretion flow. In any case, the direct vicinity of the black hole is relevant. M 104 and M 87 are a unique pair for testing this issue because the black hole vicinity is actually accessible at a similar horizon-scale resolution. In particular, the use of ALMA or VLBI in the millimeter-to-submillimeter regime (Doeleman et al. 2012) will be key because at such frequencies the synchrotron emission becomes more transparent to the jet base and most of the emission comes from the closest part of the central black hole.