THE PROPER MOTIONS OF THE DOUBLE RADIO SOURCE n IN THE ORION BN/KL REGION

In the bottom panels of Figures 1 and 2 we show contour images of these two sources for epochs 1991.67 and 2012.76, where the displacement is evident. In the top panels of these figures we also show the positions of sources BN and I as a function of time. Clearly, the motions follow a straight line within the noise.

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We now discuss the proper motions of the double source n. Source n appeared as double in the north–south direction for the three observations made in the period from 1991.67 to 2000.87 (see Figure 8 of Gómez et al. 2008). We will refer to these components as nN and nS. However, by 2006.36 the double source appeared unresolved, as a single elongated object (see Figure 8 of Gómez et al. 2008). In Figure 3 we show contour images for epochs 1991.67 and 2012.76. The image for 1991.67 clearly shows the double morphology. The image for 2012.67 is complex and can be described as constituted of two components, but much more separated and of different morphology than those components seen in 1991.67. We interpret this image as follows. The northern component is taken to be the double source that remains spatially unresolved, as first observed in 2006.36. The southern component is interpreted as a cloud of ionized plasma that was ejected from one of the stars in the double system sometime after 2006.36.

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The proper motions reported in Table 1 and shown in Figure 3 are obtained from fitting the double stellar component, with the position being the average of the double source, or the centroid of a single elongated source when the double source was not resolved (which is the case for all images taken after 2006.36). This set of data contains two new observations with respect to the data used by Gómez et al. (2008). New observations over the following years are needed to test if the proper motions reported here predict the future position of the centroid of the double stellar source.

If we assume that the ejection took place after 2006.36, we can estimate lower limits to the proper motion of the ejecta from the position shown in Figure 3. If we assume that it was ejected from the northern stellar component, we obtain a lower limit for the proper motion of $\geqslant 110$ mas yr⁻¹, while if it was ejected from the southern stellar component we obtain a lower limit for the proper motion of $\geqslant 60$ mas yr⁻¹. At a distance of 414 pc (Menten et al. 2007, see however a new estimate of 388 pc by Kounkel et al. 2016), these proper motions are equivalent to velocities in the plane of the sky of 220 km s⁻¹ and 120 km s⁻¹, respectively. These velocities are comparable to those observed in the proper motions of ejecta from young, intermediate-mass stars (e.g., Rodríguez-Kamenetzky et al. 2016).

The ejecta has to be dominantly one-sided (approximately to the south), because we do not see a major distortion in the northern component. One-sided ejecta (sometimes called monopolar or asymmetric jets) from young stars are not uncommon and have been observed in sources such as OMC 1 South (Zapata et al. 2006), DG Tau (Rodríguez et al. 2012b), DG TauB (Rodríguez et al. 2012a), HH 111 (Gómez et al. 2013), NGC 1333-IRAS2A (Codella et al. 2014), and Serpens SMM1 (Hull et al. 2016).

There are two ways to test this scenario. First, if the emission observed recently to the south of the double source is produced by ejected plasma, we expect the ejecta to become fainter on a recombination timescale. From the 2012.76 observations (see Figure 3), we measure a flux density for the southern condensation of ${S}_{7.3\mathrm{GHz}}=0.45\,\mathrm{mJy}$, and an angular size ${\theta }_{s}^{2}\lt {(0\buildrel{\prime\prime}\over{.} 2)}^{2}$. Assuming optically thin free–free emission, an electron temperature ${T}_{e}={10}^{4}$ K, the emission measure is $\mathrm{EM}={n}_{e}^{2}l\gtrsim 5\times {10}^{6}{\mathrm{cm}}^{-6}\,\mathrm{pc}\left[\tfrac{{S}_{\nu }}{0.45\,\mathrm{mJy}}\right]{\left[\tfrac{{\theta }_{s}}{0\buildrel{\prime\prime}\over{.} 2}\right]}^{-2}.$ Assuming a characteristic scale $l/\mathrm{au}=({\theta }_{s}/^{\prime\prime} )(d/\mathrm{pc})\sim 83\,\mathrm{au}$, where d = 414 pc is the distance to Orion, the electron density of the plasma is ${n}_{e}\gtrsim {10}^{5}\,{\mathrm{cm}}^{-3}{\left[\tfrac{{S}_{\nu }}{0.45\mathrm{mJy}}\right]}^{1/2}{\left(\tfrac{{\theta }_{s}}{0\buildrel{\prime\prime}\over{.} 2}\right)}^{-3/2}.$ The ejected plasma will recombine in a timescale ${t}_{\mathrm{rec}}={({n}_{e}{\alpha }_{2})}^{-1}\lesssim 1\,\mathrm{year},$ where the recombination coefficient is ${\alpha }_{2}=2.6\times {10}^{-13}\,{\mathrm{cm}}^{3}\,{{\rm{s}}}^{-1}$. Assuming a proper motion of the ejecta $\mu \,\sim$ 60 mas yr⁻¹, that corresponds in Orion to 120 km s⁻¹, the crossing time is ${t}_{\mathrm{cross}}\sim l/v\sim \,3\,\mathrm{year}.$ Because ${t}_{\mathrm{cross}}\gt {t}_{\mathrm{rec}}$, one expects the plasma to recombine as it moves away from the source.⁶

Furthermore, if the ionized plasma is expanding, the density will drop. If the expansion is isotropic, the plasma volume is $V\propto {l}^{3}$ and the electron density will decrease like ${n}_{e}\propto {l}^{-3}$. For a jet condensation expanding with a fixed solid angle Ω, at a distance r from the source, the volume is $V\propto {\rm{\Omega }}{r}^{2}{\rm{\Delta }}r$. If the size ${\rm{\Delta }}r\sim$ constant, the volume will increase as $V\sim {l}^{2}$ and the electron density will decrease like ${n}_{e}\propto {l}^{-2}$. The optically thin radio flux density is ${S}_{\nu }\propto {n}_{e}^{2}V$, and it will decrease like ${S}_{\nu }\propto {l}^{-3}$ in the isotropic case, and like ${S}_{\nu }\propto {l}^{-2}$ in the case of the jet condensation. Both types of flux density decrease were observed in the thermal radio jet HH 80–81 by Martí et al. (1998) who studied the evolution of two jet condensations. In any case, one expects that the observed radio emission of the ejection would decrease very fast both due to recombination and expansion of the ionized gas.

The assumption that we are dealing with optically thin free–free emission in the ejecta is supported by an analysis of the spectral index of source n in epoch 2012.76. Using the data of Forbrich et al. (2016) we obtain a total flux density of 1.45 ± 0.03 mJy at 7.3 GHz and of 1.68 ± 0.05 mJy at 4.7 GHz, This gives a spectral index of −0.3 ± 0.1, in agreement with Forbrich et al. (2016). For the southern component (the ejecta) we obtain flux densities of 0.45 ± 0.02 and 0.49 ± 0.03 at 7.3 and 4.7 GHz, respectively. This results in a spectral index of −0.2 ± 0.2, consistent with optically thin free–free-emission. Finally, for the northern component (proposed here to be the unresolved double stellar source) we obtain flux densities of 1.00 ± 0.02 and 1.19 ± 0.04 at 7.3 and 4.7 GHz, respectively. This gives a spectral index of −0.4 ± 0.1, suggesting a possible non-thermal component.

The total flux density of source n as a function of time (Figure 4) shows an important increment in epoch 2011.56. We believe that this increase (that has practically disappeared in more recent epochs) was the result of the ejection of the plasma cloud.

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One can also estimate the mass-loss rate of an ionized jet, ${\dot{M}}_{i}={\rm{\Omega }}{r}^{2}\mu {{\rm{m}}}_{H}{n}_{e}v\,\sim$ $3\times {10}^{-8}{\left[\tfrac{{S}_{\nu }}{0.45\mathrm{mJy}}\right]}^{1/2}{\left[\tfrac{{\theta }_{s}}{0\buildrel{\prime\prime}\over{.} 2}\right]}^{1/2}{M}_{\odot }\,{\mathrm{yr}}^{-1}.$ Assuming a jet ionization fraction ${x}_{e}\sim 0.1$, one obtains a total mass-loss rate $\dot{M}\sim {10}^{-7}\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$. This implies that source n must have an accretion disk with a healthy mass accretion rate, one order of magnitude larger, ${\dot{M}}_{\mathrm{acc}}\sim {10}^{-6}\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$ (e.g., Shu et al. 1993, p. 3).

Finally, Anglada et al. (2015) proposed a correlation between the radio luminosity of the jet, ${S}_{3.6\mathrm{cm}}{d}^{2}$, and the bolometric luminosity of the source, L_bol (their Equation (3)). Assuming a flat spectrum, this relation gives a luminosity $L\sim 44\,{L}_{\odot }$. From the observed IR fluxes from $5\mbox{--}10\,\mu {\rm{m}}$ (Gezari et al. 1998), one obtains a lower limit to the luminosity of source n, $L\gt 4\,{L}_{\odot }$.

The second way of testing the scenario is to verify that the proper motions derived for source n excluding the southern ejecta are consistent with the epoch of cluster disintegration, as determined from the well-behaved proper motions of sources BN and I. To pursue this test, in Table 2 we give the proper motions corrected for the mean proper motions of the Trapezium-BN/KL region (${\mu }_{\alpha }\cos \delta =1.07\pm 0.09$ mas yr⁻¹; μ_δ= −0.84 ± 0.16 mas yr⁻¹), as determined by Dzib et al. (2017). This relatively small correction is required to present the proper motions in the rest frame of Orion. In Figure 5 we present the position of the sources BN, I, and n as a function of time, as extrapolated from the proper motions in Table 2. The angle associated with each source represents the 2-σ error in the proper motions. We can see that the past positions of BN, I, and n overlap in the past both in right ascension as in declination. The data are consistent with a disintegration epoch during the 15th century with an initial position of $\alpha (J2000)={05}^{{\rm{h}}}{35}^{{\rm{m}}}14\buildrel{\rm{s}}\over{.} 41;$ $\delta (J2000)=-05^\circ 22^{\prime} 28\buildrel{\prime\prime}\over{.} 2$. The more accurate determination using only the relative positions of BN and I gives a disintegration epoch of 1490 ± 11 (Gómez et al. 2008) and, with additional data points, of 1453 ± 9 (Goddi et al. 2011). With more data available, we will repeat below this determination.

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Table 2.  Proper Motions Corrected to the Orion Frame and Deconvolved Dimensions of the Radio Sources

	Proper Motionsa		Total Proper Motionb	Deconvolved Dimensionsc
Name	${\mu }_{\alpha }{\cos }\delta$	${\mu }_{\delta }$	Magnitude; PA	(${\theta }_{\mathrm{maj}}\times {\theta }_{\min };\mathrm{PA}$)
BN	–8.1 ± 0.4	+10.8 ± 0.4	13.5 ± 0.4; –37 ± 2	$0\buildrel{\prime\prime}\over{.} 19\pm 0\buildrel{\prime\prime}\over{.} 01\times 0\buildrel{\prime\prime}\over{.} 07\pm 0\buildrel{\prime\prime}\over{.} 01;+58^\circ \pm 1^\circ$
n	+0.0 ± 0.9	–7.8 ± 0.6	7.8 ± 0.6; +180 ± 4	$0\buildrel{\prime\prime}\over{.} 43\pm 0\buildrel{\prime\prime}\over{.} 01\times 0\buildrel{\prime\prime}\over{.} 17\pm 0\buildrel{\prime\prime}\over{.} 01;+16^\circ \pm 1^\circ$
I	+1.8 ± 0.4	–4.6 ± 0.4	4.9 ± 0.4; +159 ± 5	$0\buildrel{\prime\prime}\over{.} 13\pm 0\buildrel{\prime\prime}\over{.} 01\times \leqslant 0\buildrel{\prime\prime}\over{.} 03\pm 0\buildrel{\prime\prime}\over{.} 01;+58^\circ \pm 3^\circ$

Notes.

^aIn mas yr⁻¹. ^bMagnitude in mas yr⁻¹, PA in degrees. ^cFrom the data of the Jansky VLA project SD0630 observed in epoch 2012.76 at the frequency of 7.3 GHz.

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In Figure 6 we show the location of the three sources and, with arrows, the proper motions in the frame of Orion for a period of 200 years.

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