The Highly Collimated Radio Jet of HH 80–81: Structure and Nonthermal Emission

In order to study the structure of the radio jet with our new high angular resolution images, we compare images at different wavelengths and different resolutions. Low-frequency images are more sensitive to extended structures, while high-frequency images tend to filter extended emission and detect only compact emission. Therefore, by observing in different spectral bands, we are able to study different structures in the jet.

In Figure 2, we can see that the structure emanating in opposite directions from the central region is detected with a full extension of $\simeq 1\,\mathrm{pc}$ at all bands (L, S, and C) and angular resolutions. However, a change in the morphology is observed when going from low to higher frequencies: at low frequencies and low angular resolution (L band; Figure 2) very extended lobes are observed to the northeast and southwest of the central region, while for increasing frequencies and higher angular resolution (S and C bands; Figure 2), a very well-collimated jet and several high-intensity spots on the lobes are revealed. These changes in morphology seem to be real when comparing the extent of the emission with the beam size of each image. In Figure 2, we labeled the two brightest compact knots in the northern lobe (knot 1 and knot 2) that are interpreted as strong shocks of the jet with the ambient medium (see Section 4). Both knots are detected with intensities up to nine times the rms noise level.

Zoom In Zoom Out Reset image size

In this subsection, we study the different emission mechanisms in the radio jet by comparing spectral index maps made at different frequency ranges and angular resolutions. We combined data from the L and S bands to obtain a low-frequency map with a relatively low angular resolution, which allows us to study the emission mechanism of the extended emission (left panel in Figure 3). Similarly, the combination of the S and C bands yields a higher angular resolution map that enables the study of the emission mechanisms in the more compact structures (central and right panels in Figure 3). Finally, we combined the L, S, and C bands to obtain the highest angular resolution map (∼2''), covering a wider frequency range (Figure 4).

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

In all of the spectral index maps, we measured a positive spectral index $\alpha =0.33\pm 0.02$ for the central region of the jet, suggesting partially optically thick free–free emission, in good agreement with what is expected for a thermal radio jet (Anglada 1996). In contrast, emission from the collimated jet and the northeastern lobe show peculiar variations with frequency and angular resolution.

Figure 3(a) shows that negative spectral indices dominate the extended emission at the L+S bands, suggesting a nonthermal nature. An index of $\alpha =-0.5\pm 0.4$ is found in high-intensity spots of the northeastern lobe (knot 1 and 2), while even more negative values ($\sim -0.8$) are computed in surrounding regions and in the collimated jet ($\sim -0.7$), with typical errors of 0.2. Since synchrotron radiation dominates at low frequencies, it is expected that its contribution is smaller at the S+C bands. Indeed, thermal emission seems to be dominant in the S+C bands (Figure 3(b)), where a zone with positive spectral indices can be clearly identified in the northeastern lobe, aligned with the collimated jet. Nevertheless, the high-intensity spots, knot 1 and knot 2, present a mixture of flat (α ≃ 0) and negative spectral indices ($\alpha \simeq -0.5$), indicating contribution of both optically thin free–free and nonthermal emission, respectively. When improving the angular resolution in the same frequency range (S+C bands, robust = 0; Figure 3(c)), the emission contribution from the extended component is practically absent and knots 1 and 2 reveal their nonthermal origin ($\alpha =-0.6\pm 0.2$). In the same image (Figure 3(c)), a knotty distribution of spectral indices is found in the collimated jet: regions with negative and positive spectral indices alternate.

In Figure 4 (L+S+C bands), due to the wide frequency range, the observed emission is expected to be a combination of thermal and nonthermal components. In this image, nonthermal emission dominates in both the northeastern lobe and the jet, with spectral indices −1 ≤ α ≤ 0, and errors of ∼0.4. Knots 1 and 2 present spectral indices of −0.5 ± 0.4. It is worth noting that spectral indices of −0.6 ± 0.1 are measured very near the thermal source associated with the central massive protostar, in the region where the jet seems to collimate. Close to this area, positive and negative spectral indices alternate, and a high-intensity knot with $\alpha =-0.8\pm 0.4$ is detected. Errors in the most collimated region of the jet (8–23 arcsec from the central region) are of the order of 0.3. Aligned with the jet, the thermal structure in the northeastern lobe is also present in this range of frequencies.

In summary, the central part of the jet is consistent with a thermal radio jet, while nonthermal emission seems to be present in different spots in the collimated part of the radio jet, in the high-intensity spots that trace the termination shocks of the radio jet, and in an extended emission surrounding the whole radio jet.

Our new images revealed an interesting behavior of the spectral index in the most collimated part of the radio jet. We noted several changes in the spectral index from positive to negative and then to positive again. This is the first time that images of a radio jet with high enough quality are available to detect these changes. Therefore, in this subsection, we deepen the analysis of the most collimated region of the jet by studying how the spectral index, the jet width, and the position of the jet central axis vary along the distance z from the protostar. For this, we analyze the highest signal-to-noise ratio images, combining the L, S, and C bands. We defined a slice along the jet, from the central region of the jet to the farthest point in the northeastern lobe (α(J2000) = 18^h19^m13227, δ(J2000) = −20°46'48271), with a total length of ∼45 arcsec. Centered on each pixel of this line, we took a 3 arcsec cross-section for computing intensity and spectral index values. For each transversal section, we estimated the jet width as the FWHM of a Gaussian fit to the intensity profile. Values of the spectral indices and their errors were measured in the pixels where the Gaussian fit center is located, while variations in the position of the jet central axis were computed with respect to the slice. The northeastern lobe region is much more complex than the most collimated one; the brightest points are not aligned with the collimated jet, and the brightness profiles significantly differ from Gaussian fits. For this reason, we restricted our analysis to the region up to ∼23 arcsec from the phase center of the observations. Figure 5 shows the intensity and spectral index images of the studied region, and the variations of the spectral index, jet width, and jet central axis, with distance z.

Zoom In Zoom Out Reset image size

Figure 5 shows that, initially, the jet widens, and its emission presents a positive spectral index, consistent with thermal free–free emission. At a distance of ∼2 arcsec from the center, the jet continues widening and the spectral index starts to decrease, reaching its most negative value (∼−0.5) at ∼5 arcsec, roughly matching with the jet width relative maximum. Then, the jet starts to get narrower while the spectral index increases, again reaching positive values at ∼7 arcsec. Between ∼7 and ∼9 arcsec, the spectral index decreases to negative values at the point where the jet width increases. At a distance of ∼16 arcsec, a relative maximum in the index is observed once more, coincident with a decreasing jet width.

Except for the thermal central region of the jet (see Section 3.2), the spectral index seems to decrease in widening regions and increase when the jet becomes narrower. We speculate that pressure differences between the jet and the ambient medium might give rise to expansion and recollimation of the jet. In this case, increasing spectral indices in narrow regions could be due to (1) an increment in the opacity and (2) a local increase in thermal emission, through the conversion of kinetic into internal energy in shocks. We also observe that the jet is suffering lateral displacements, consistent with a precessing jet as observed by Martí et al. (1993). These displacements might also produce an increase in the spectral index, e.g., in regions where the jet approaches our line of sight, becoming apparently thicker, and therefore, enlarging the integration depth of the radiation (and also the opacity if we assume a constant density). It is worth noting that these behaviors resemble those observed in recollimation shocks in AGN jets (e.g., Mimica et al. 2009; Fromm et al. 2013; Perucho 2013). Supersonic flows that are not in pressure equilibrium with their environment generate such shocks naturally: (1) the overpressured jet expands in the ambient medium, (2) once the jet pressure in the outer (radial) regions becomes smaller than the external pressure, recollimation starts from the jet boundary toward the axis, but (3) with the flow being supersonic, the information crosses the jet as a shock. This process is natural to any supersonic jet flow, including YSO jets, and may trigger the observed structure. The interaction between shells of gas propagating at different speeds can trigger internal shocks in a jet. However, this would not imply changes in the jet width as significant as those given by jet overpressure (Fromm et al. 2016). Numerical simulations show that travelling shocks, if strong enough, can trigger local pressure enhancements and an increase of the jet cross-section, which could be the source of the features known as trailing components (Agudo et al. 2001). However, there are a number of differences between travelling shocks (and trailing components) and standing, recollimation shocks: (1) the brightest spot would coincide with the presence of the travelling shock, i.e., with an expanded region, and not with the minimum in the jet radius (as observed in Figure 5), (2) the trailing features show a shorter wavelength than the distance between recollimation shocks, and (3) the travelling shocks and the trailing features propagate downstream. The observed evolution of the jet radius with distance is favored in this case, which implies strong changes in the jet radius, our interpretation in terms of recollimation shocks. Nevertheless, in order to get a better understanding of the emission nature and structure of this highly collimated jet, new observations with higher angular resolution and higher sensitivity in small frequency intervals are needed.

In addition to the central radio continuum source and the inner jet, we detected four new point-like sources in the field (Figure 1). The positions of these sources were measured in the highest-resolution image (209 × 126 at the C band), and whenever possible, fluxes at different frequencies were measured to compute their spectral indices. The main parameters of these radio sources are given in Table 2. Source RC-1 presents ${\alpha }_{(18.4-10)\mathrm{cm}}\gt 0$ and ${\alpha }_{(10-5.5)\mathrm{cm}}\lt 0$, suggesting it could be an H ii region (emitting free–free radiation), optically thick at $\lambda \gt 10\,\mathrm{cm}$ and optically thin at $\lambda \lt 10\,\mathrm{cm}$. For source RC-4, we obtain ${\alpha }_{(10-5.5)\mathrm{cm}}\lt 0$, suggesting nonthermal emission, although within errors, optically thin free–free radiation is also possible. Sources RC-2 and RC-3 were reliably detected only at the C band.

Table 2.  Parameters of New Sources

	Position		Flux (μJy)			Spectral Index
Source	α(J2000)	δ(J2000)	18.4 cm	10 cm	5.5 cm	${\alpha }_{(18.4-10)\mathrm{cm}}$	${\alpha }_{(10-5.5)\mathrm{cm}}$
RC-1a	18h19m1099	−20°48' 2959	444 ± 56	662 ± 78	481 ± 48	+0.7 ± 0.3	−0.5 ± 0.2
RC-2b	18 19 12.48	−20 47 27.30	⋯	⋯	61 ± 8	⋯	⋯
RC-3b	18 19 12.58	−20 47 30.45	⋯	⋯	100 ± 8	⋯	⋯
RC-4c	18 19 12.93	−20 47 37.77	⋯	81 ± 6	60 ± 8	⋯	−0.5 ± 0.3

Notes. All positions are measured from a Gaussian fit to the C-band image, with the highest resolution (209 × 126, PA = 5°).

^aFlux densities are obtained from Gaussian fits to the L, S, and C images convolved to the same beam size (73 × 44, PA = 7°). ^bFlux densities are obtained from Gaussian fits to the C-band image. ^cFlux densities are obtained from Gaussian fits to the Sand C images convolved to the same beam size (42 × 23, PA = 0°).

Download table as:  ASCIITypeset image

No proper motions for the identified knots are available at present, since no previous observations were able to resolve the structure of the radio jet. Therefore, the bow-shock propagation velocity (${v}_{\mathrm{bs}}$) needs to be indirectly estimated. Following Blondin et al. (1990), ${v}_{\mathrm{bs}}$ can be approximated by equating the momentum flux of the beam (the collimated supersonic flow) at the working surface with the momentum flux of the bow shock:

$$\begin{eqnarray}&&{v}_{\mathrm{bs}}\approx \displaystyle \frac{{v}_{\mathrm{jet}}}{1+{\eta }^{-1/2}},\,\,\eta \equiv \displaystyle \frac{{n}_{\mathrm{jet}}}{{n}_{\mathrm{amb}}}.\end{eqnarray} \tag{ 3 }$$

For the ambient density, we adopt the average value measured by Torrelles et al. (1986), ${n}_{\mathrm{amb}}=5\times {10}^{3}\,{\mathrm{cm}}^{-3}$, and for the jet velocity, we set ${v}_{\mathrm{jet}}=1000\,\mathrm{km}\,{{\rm{s}}}^{-1}$ (Martí et al. 1995). For the jet density at a distance z from the protostar, we estimated a value $n({z}_{\mathrm{knot}})=40$ cm⁻³ (see the Appendix). Therefore, from Equation (3), we find a bow-shock velocity ${v}_{\mathrm{bs}}=80\,\mathrm{km}\,{{\rm{s}}}^{-1}$. Using this value, we calculate the cooling distance from Equation (1). This gives a ${d}_{\mathrm{cool}}/{r}_{\mathrm{jet}}$ ratio smaller than unity (4 × 10⁻⁵), which implies that the bow shock is radiative. In a radiative shock, Alfvén waves are mostly suppressed and DSA is inefficient.

To study whether particle acceleration can be efficient in the reverse shock, we first estimate its velocity ${v}_{\mathrm{rs}}$. From conservation arguments in fluid equations and assuming pressure equilibrium in shocked regions, the reverse-shock velocity can be expressed as

$$\begin{eqnarray}&&{v}_{\mathrm{rs}}={v}_{\mathrm{jet}}-3{v}_{\mathrm{bs}}/4.\end{eqnarray} \tag{ 4 }$$

Considering the values adopted in the previous section for ${v}_{\mathrm{bs}}$ and ${v}_{\mathrm{jet}}$, we found the reverse-shock velocity to be ${v}_{\mathrm{rs}}\sim 940\,\mathrm{km}\,{{\rm{s}}}^{-1}$. Therefore, the thermal cooling distance estimated from Equation (2) with $n={n}_{\mathrm{jet}}$ gives ${d}_{\mathrm{cool}}/{r}_{\mathrm{jet}}\,=432$, implying an adiabatic reverse shock, which, in principle, might produce efficient particle acceleration up to relativistic energies.

We will now explicitly show that the source can produce the relativistic electrons required to generate the observed synchrotron radiation, and we will discuss the efficiency of the process.

The acceleration timescale for electrons in the reverse shock is

$$\begin{eqnarray}&&{t}_{\mathrm{acc}}=\eta \displaystyle \frac{E}{{eBc}},\end{eqnarray} \tag{ 5 }$$

$$\begin{eqnarray}&&\mathrm{with}\,\eta \sim 20\displaystyle \frac{D}{{r}_{{\rm{g}}}c}{\left(\displaystyle \frac{c}{{v}_{\mathrm{rs}}}\right)}^{2}.\end{eqnarray} \tag{ 6 }$$

In these expressions, B is the magnetic field strength, E is the energy of the particles, ${v}_{\mathrm{rs}}$ is given by Equation (4) above, and D is the diffusion coefficient. In the Bohm limit, $D\,\sim {D}_{{\rm{B}}}={r}_{{\rm{g}}}\tfrac{c}{3}$, with ${r}_{{\rm{g}}}$ the gyroradius of the particles being accelerated. Thus,

$$\begin{eqnarray}&&\eta \sim \displaystyle \frac{20}{3}{\left(\displaystyle \frac{c}{{v}_{\mathrm{rs}}}\right)}^{2}.\end{eqnarray} \tag{ 7 }$$

If the synchrotron losses dominate, the maximum energy of electrons—${E}_{\max }$—is determined by the condition ${t}_{\mathrm{acc}}={t}_{\mathrm{synch}}$, where ${t}_{\mathrm{synch}}$ is the timescale of synchrotron losses. In suitable units,

$$\begin{eqnarray}&&{t}_{\mathrm{synch}}\sim 4\times {10}^{11}{\left(\displaystyle \frac{B}{\mathrm{mG}}\right)}^{-2}{\left(\displaystyle \frac{E}{\mathrm{GeV}}\right)}^{-1}\,\,{\rm{s}}.\end{eqnarray} \tag{ 8 }$$

Thus,

$$\begin{eqnarray}&&{E}_{\max }\sim 2.4\times {10}^{3}\left(\displaystyle \frac{{v}_{\mathrm{rs}}}{{10}^{8}\,\mathrm{cm}\,{{\rm{s}}}^{-1}}\right){\left(\displaystyle \frac{B}{\mathrm{mG}}\right)}^{-\tfrac{1}{2}}\,\,\mathrm{GeV}.\end{eqnarray} \tag{ 9 }$$

The strength of the magnetic field and the diffusion regime are unknown. We consider a magnetic field strength of the order of 1 mG (Carrasco-González et al. 2010), and Bohm diffusion. Thus, the maximum energy of the electrons results in ${E}_{\max }\sim 2$ TeV. This means Lorentz factors of $\gamma \sim 4\times {10}^{6}$ for electrons. This value should be considered as an upper limit, since other losses, such as relativistic Bremsstrahlung, are present. In any case, the energies necessary to produce the observed nonthermal radio emission by synchrotron mechanism (of the order of ∼GeV) are easily achieved in this source. This does not seem to be the case in other YSOs with slower jets and denser media. In particular, if the particle density of not-fully ionized atoms is large, ionization losses can quench the acceleration (Bosch-Ramon et al. 2010; Padovani et al. 2015, 2016). The crucial point is that if the shock is radiative, instead of adiabatic, a lot of heat will be generated in the shocked region, and this will dramatically increase the entropy. This means that all order will be destroyed, in particular the inhomogeneities in the magnetic field that make the diffusive particle acceleration possible. Since the condition of adiabaticity is that the thermal timescale ${t}_{\mathrm{therm}}\propto {n}^{-2}$ be longer than the shock timescale ${t}_{\mathrm{sh}}$ (or equivalently, ${d}_{\mathrm{cool}}\gt {r}_{\mathrm{jet}}$), the DSA will be halted by either a slow shock or a dense medium. In this sense, the conditions in HH 80–81 seem to be quite special, making it an almost unique laboratory for particle acceleration in YSO jets.

The synchrotron luminosity that we can expect from the electrons will depend on the efficiency for transforming shock power to nonthermal particles and the fraction that goes to electrons. Currently, it is not clear how efficient particle acceleration is in the case of shocks in protostellar jets. However, we can obtain some information about cosmic rays received at the Earth and compare with the better understood case of shocks in Galactic supernovae in order to arrive at some preliminary estimates.

The energy density of Galactic cosmic rays (CRs) around the Earth is explained if 1%–10% of the explosion energy of Galactic supernovae is used for CR acceleration (Ginzburg & Syrovatskii 1964). Detailed studies of particular supernova remnants (SNRs) such as those of the northeast region of the young SNR RCW 86 (Helder et al. 2009) suggest extremely efficient CR acceleration with $\eta \approx 87$% for shocks with velocities of ∼6000 km s⁻¹. Even if the shock velocity is as low as 1200 km ${{\rm{s}}}^{-1}$, the efficiency would be 18%. Recent investigations using three-dimensional magnetohydrodynamics simulations of supernova shock waves propagating into a realistic, diffuse medium by Shimoda et al. (2015) show that the above values might be overestimated by 10%–40% because a rippled shock does not immediately dissipate all of the upstream kinetic energy. On this basis, efficiencies of ∼10% for shocks of ∼1000 km s⁻¹ moving through a complex medium, as it is in the case of the HH 80–81 jet, seem to be reasonable, i.e., in accordance with both observational inferences in a variety of circumstances and theoretical expectations (see, for instance, Bell 2013; Blasi 2013; Morlino et al. 2013, 2014).

The composition of CRs in the solar neighborhood indicates that about 1% of them are electrons. The luminosity ratio of electrons to protons as it is produced in stochastic acceleration processes in different sources is an important quantity relevant for several aspects of the modeling of the sources. The mentioned ratio of 1% is usually assumed to be valid for the case of Galactic sources. Different types of observations show that the average ratios should be close to this value (although fluctuations will occur depending on specific conditions of the source; see Merten et al. 2017).

In order to obtain an estimation of the expected synchrotron luminosity in HH 80–81, we first derive the synchrotron bolometric luminosity of the shock, following Bosch-Ramon et al. (2010):

$$\begin{eqnarray}&&\displaystyle \frac{{L}_{\mathrm{shock}}}{\mathrm{erg}\,{{\rm{s}}}^{-1}}\sim {10}^{35}{\left(\displaystyle \frac{R}{3\times {10}^{16}\mathrm{cm}}\right)}^{2}{\left(\displaystyle \frac{{v}_{\mathrm{rs}}}{1000\mathrm{km}{{\rm{s}}}^{-1}}\right)}^{3}\left(\displaystyle \frac{{n}_{{\rm{j}}}}{40\,{\mathrm{cm}}^{-3}}\right).\end{eqnarray} \tag{ 10 }$$

In accordance with the above considerations, we adopt an efficiency of 10% for the particle acceleration in the shocks of HH 80–81, and we assume that ∼1% of them are electrons. Thus, we get a bolometric luminosity ${L}_{\mathrm{synch}}\sim {10}^{32}\ \mathrm{erg}\,{{\rm{s}}}^{-1}$, which is well above the vaule inferred from the radio observations (${L}_{(1\mbox{--}6)\mathrm{GHz}}\sim \,9\,\times \,{10}^{27}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$, synchrotron luminosity integrated in the 1–6 GHz spectral range). Therefore, the observed synchrotron emission seems to be easily explained with particle acceleration in strong shocks of the jet against the ambient medium, assuming reasonable parameters.