CHARACTERIZATION OF MOLECULAR OUTFLOWS IN THE SUBSTELLAR DOMAIN

The SMA⁶ receiver band at 230 GHz (see Ho et al. 2004) was used for the observations of GM Tau on 2010 October 26. Zenith opacities at 225 GHz were typically in the range 0.1–0.16. Both 4 GHz wide sidebands, which are separated by 8 GHz, were used. The SMA correlator was configured with a high spectral resolution of 0.2 MHz (∼0.27 km s⁻¹) per channel for ¹²CO, ¹³CO, and C¹⁸O J = 2 → 1 lines. For the remainder of each sideband, we set up a lower resolution of 3.25 MHz per channel. We used quasars 3C 111 and 3C 273 for gain and passband calibration of GM Tau, respectively. Uranus was observed for flux calibration for the target. The uncertainty in the absolute flux calibration is ∼10%.

We reduced and further analyzed the data with the MIR software package and the MIRIAD package adapted for the SMA, respectively. All eight SMA antennas were operated in the compact configuration, resulting in a synthesized beam of 305 × 282 with a position angle of 61° (natural weighting). The FWHM of the primary beam is about 50'' at the observed frequencies. The rms sensitivity was ∼1 mJy for the continuum and ∼0.15 Jy beam⁻¹ per channel for the line data (Table 1).

We observed the two BDs 2M 0414 and 2M 0438 with CARMA at 230 GHz in 2010 August. All six 10.4 m and nine 6.1 m antennas were operated in the D configuration. Zenith opacities at 227 GHz were in the range 0.21−0.3 and 0.23−0.27 for 2M 0414 and 2M 0438, respectively. All eight 500 MHz wide bands (a maximum bandwidth of 4 GHz per sideband), which may be positioned independently with the IF bandwidth, were used with different spectral resolutions for the ¹²CO J = 2 → 1 line. The eight bands were set up in the following modes with the 2-BIT level: 8 MHz, 31 MHz, and 62 MHz with 383 channels per band; 125 MHz, 250 MHz, and 500 MHz with 319, 191, and 95 channels per band, respectively. These modes give a wide range of spectral resolutions from 0.03 to 6.8 km s⁻¹ at 230 GHz. We observed quasar 3C 111 for gain calibration, 3C 84 and 3C 454.3 for passband calibration, and Uranus and 3C 84 for flux calibration. The uncertainty in the absolute flux calibration is ∼20%. We reduced the data with the MIRIAD package adapted for the CARMA. The synthesized beam sizes are about 209 × 169 and 219 × 168 using natural weighting for 2M 0414 and 2M 0438, respectively. The FWHM of the primary beam for the 10.4 × 6.1 m antennas is about 36'' at 230 GHz. The rms sensitivities of the continuum and the line data are listed in Table 1.

2M 0414 and 2M 0438 are strong accretors (see Table 3 and references therein). While the Hα emission with an obvious P Cygni profile observed in 2M 0414 (Muzerolle et al. 2005) indicates an outflow process and the presence of FELs in 2M 0438 (Luhman 2004) suggests outflow activity, our carbon monoxide (CO J = 2 → 1) maps from CARMA data do not reveal any outflows from 2M 0414 and 2M 0438. The non-detection of molecular outflows in these two BDs indicates three possible scenarios as discussed in Phan-Bao et al. (2011): (1) the outflow process has already stopped; (2) there is not much gas surrounding the sources; or (3) the outflow process in these BDs is too weak to be detectable at the millimeter wavelengths.

For the case of 2M 0414, the outflow process has clearly been indicated in its Hα emission, therefore, the first scenario should be ruled out. As the source is located in the dense region of ¹²CO and ¹³CO J = 1 → 0 of LDN 1495 (see Figure 4 in Goldsmith et al. 2008), the second scenario is thus unlikely in this case. Finally, the bolometric luminosity of 2M 0414 is 0.015 L_☉ (Luhman 2004), about three times less luminous than that of GM Tau (0.047 L_☉, Luhman 2004). If we assume that the outflow force versus bolometric luminosity correlation of proto stars (e.g., Takahashi & Ho 2012) is applicable for young BDs, this thus indicates that the outflow force of 2M 0414 would be weaker (i.e., weaker molecular outflow emission) than that of GM Tau. As a possible outflow from GM Tau is marginally detected (see Section 4.2), the third scenario would therefore be a reasonable explanation for the non-detection of outflows from 2M 0414.

For the case of 2M 0438, the source is also located in the dense region (see Figure 4 in Goldsmith et al. 2008) and it is close to GM Tau (at a distance of only ∼28), the second scenario is thus very unlikely. The FELs may be associated with outflow or accretion activities, the first scenario is thus still possible. One should note that the bolometric luminosity of 2M 0438 is very low (0.0018 L_☉, Luhman 2004), therefore, the outflow force is expected to be much less powerful than that of any class II BDs with molecular outflows detected so far. So, the first and the third scenarios are both possible for 2M 0438.

One should also note that we did not detect the dust continuum emission from 2M 0414 and 2M 0438 with an upper limit of about 1σ (1σ = 1.4 mJy for 2M 0438 and 1.1 mJy for 2M 0414). Our measurements are comparable within error bars to those reported in Scholz et al. (2006), 0.91 ± 0.65 mJy for 2M 0414 and 2.29 ± 0.75 mJy for 2M 0438.

GM Tau is also a strong accretor with a mass accretion rate stronger than that of 2M 0414 and 2M 0438 (Table 3). Its obvious P Cygni profile of Hα emission strongly indicates the outflow process occurring in the BD.

The systemic velocity of GM Tau has not been available in the literature so far. To measure the systemic velocity of the BD, we extract a ¹³CO J = 1 → 0 spectrum toward GM Tau with the reprocessed FCRAO Taurus survey data from Qian et al. (2012). The FWHM of the ¹³CO line is about 2.2 km s⁻¹ (Figure 1), which is better described by two Gaussian components with peak velocities of 5.5 ± 0.3 km s⁻¹ and 6.5 ± 0.3 km s⁻¹, respectively. The large-scale velocity gradient of ¹³CO seems to roughly follow a Larson's law-type power-law with respect to spatial scales (see Figure 18 in Qian et al. 2012). The FWHM of the FCRAO primary beam is about 50''. Within 50'', it is thus normal in Taurus to have gas components moving at 0.5−1 km s⁻¹ with respect to each other. The FCRAO data therefore suggests the systemic velocity of GM Tau to be in the range from 5.5 to 6.5 km s⁻¹. We thus take an average value of 6.0 km s⁻¹ for the systemic velocity of the BD. Figure 2 presents the integrated intensity in the CO J = 2 → 1 emission toward GM Tau. Our map reveals only a redshifted (∼6.6−7.2 km s⁻¹) CO gas lobe around the BD position. No blueshifted emission is detected. It is therefore difficult to confirm that the redshifted lobe is outflow emission from GM Tau. However, the gas lobe is elongated in the northeast direction of the BD position, with a position angle of about 36°. This suggests that the redshifted emission is possibly outflow emission from GM Tau. One should note that the redshifted component is marginally detected at only 4σ. Therefore, if it really comes from an outflow of the BD, the detection of the CO outflow from GM Tau should be considered as a tentative detection. Our previous detections (Phan-Bao et al. 2008, 2011) have shown that the molecular outflow in the VLM objects is bipolar as seen in low-mass stars and the intensity of the outflow emission differs significantly between the redshifted and blueshifted components. Therefore, the non-detection of blueshifted outflow emission from GM Tau is probably due to the emission being too weak to be detected with SMA. The redshifted emission being brighter than the blueshifted emission implies that the redshifted jet propagates into denser gas than the blueshifted jet, leading to a larger swept up mass of CO gas (i.e., stronger molecular outflow emission). Deeper observations are needed to confirm this scenario.

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If the detected redshifted gas lobe is a component of outflows from GM Tau, we then follow the standard manner (Cabrit & Bertout 1990; André et al. 1990) as used in previous papers (Phan-Bao et al. 2008, 2011) to calculate the outflow properties. The size of the redshifted CO gas lobe is about 5'' corresponding to ∼700 AU in length (see Figure 2). We assume a value of 20 K for the excitation temperature, and then derive a lower limit to the outflow mass M_out ∼ 1.9 × 10⁻⁶M_☉. The correction factors due to optical depth and missing flux for the outflow mass of GM Tau are uncertain. However, the typical values of optical depths for class II objects in Taurus are from 1 to 5 (Levreault 1988a). As GM Tau lies in the densest part of HCL 2 (see Figure 4 of Goldsmith et al. 2008), it is therefore reasonable to assume an optical depth of five for the case of GM Tau. If a missing flux factor of three for SMA (Bourke et al. 2005) is applicable here, then we obtain an upper limit to the outflow mass of ∼2.9 × 10⁻⁵M_☉.

The maximum outflow velocity v_max can be computed from the observed maximum outflow velocity and the outflow inclination. The observed maximum outflow velocity is about 1.2 km s⁻¹. Based on optical, near-infrared, and infrared data, Riaz et al. (2012) performed disk modeling for GM Tau with a circumstellar geometry consisting of a rotationally flattened infalling envelope, bipolar cavities, and a flared accretion disk in hydrostatic equilibrium. Their best-fitting model spectral energy distribution was obtained with the disk's inclination angle between 70° and 80°. We therefore use an average value of 75° for the outflow inclination (the angle between the outflow axis and the line of sight). From the observed maximum outflow velocity of 1.2 km s⁻¹ and the outflow inclination angle i = 75°, we derive the maximum outflow velocity v_max = 4.6 km s⁻¹. We then use this value to compute upper limit values for the kinematic and dynamic parameters. We find that the momentum is P = 8.7 × 10⁻⁶ M_☉ km s⁻¹ and the energy is E = 2.0 × 10⁻⁵ M_☉ km² s⁻². From the outflow size of ∼700 AU and the observed maximum outflow velocity of 1.2 km s⁻¹, we derive a dynamical time t_dyn for GM Tau of about 700 yr (with a correction for the outflow inclination). With this dynamical time value, we then find the force F = 1.2 × 10⁻⁸ M_☉ km s⁻¹ yr⁻¹ and the mechanical luminosity L = 4.7 × 10⁻⁶ L_☉, where L_☉ is the solar luminosity. If we apply a correction for the optical depth factor of five and the missing flux factor of three for SMA, these upper limit values will increase by a factor of fifteen. Lower limits to these parameters could be estimated by using the outflow mass in each velocity channel and the space velocity of the outflow, which is assumed to be equal to the radial velocity of that channel, as if the gas was moving along the line of sight (Cabrit & Bertout 1990). This could be done for observations with good signal-to-noise ratio. However, as our detection levels of outflows in each velocity channel are rather low, we do not estimate these lower limits.

The mass-loss rate of molecular outflows can be computed by dividing the outflow mass by the dynamical time of the outflow. However, the estimated dynamical time t_dyn ∼ 700 yr for the outflow from GM Tau is over two orders of magnitude smaller than the age of VLM objects in Taurus, expected to be from a few 10⁵ yr to a few Myr (Muzerolle et al. 2003; White & Basri 2003). Therefore, the correction factor of about 10 for the outflow dynamical time of young low-mass stars (Parker et al. 1991) may be not valid here. This value for VLM objects should be over 100 (see further discussion in Section 5.1). Without correction applied for the outflow dynamical time and using the lower and upper values of the outflow mass, we directly derive the lower and upper limits to the mass-loss rate of molecular outflows $\dot{M}_{\rm mol} = M_{\rm out}/t_{\rm dyn}$ to be 2.7 × 10⁻⁹M_☉ yr⁻¹ and 4.1 × 10⁻⁸M_☉ yr⁻¹, respectively.

We now consider the possibility that the detected redshifted emission might be due to gravitationally bound motion and not outflow emission. For gravitationally bound motion, an outflow size l = 700 AU with a velocity v = 4.6 km s⁻¹ would require an enclosed mass of ⩾8.4 M_☉ (M ⩾ v²l/2G; see Lada 1985). If we assume that the densest cores in Taurus have been detected by Onishi et al. (2002, see their Table 2), then we derive a possible largest mass of ∼0.003 M_☉ for a core 700 AU in diameter. In addition, we also estimate an upper limit to the mass of a core of 700 AU using the gas density around the GM Tau position, which is estimated from the FCRAO observations (Qian et al. 2012). The line intensity ratio between ¹²CO J = 1 → 0 and ¹³CO J = 1 → 0 is much smaller than the corresponding isotopic ratio, thus it is safe to assume that the ¹²CO line is optically thick. We then derive the gas excitation temperature of about 10 K based on the peak antenna temperature of ¹²CO. The ¹³CO opacity, and in turn the gas column density, can then be derived by assuming a [¹³CO]/[H₂] abundance ratio of 1.7 × 10⁻⁶ (Frerking et al. 1982). The resulting H₂ column density is 6.0 × 10²¹ cm⁻², which is consistent with 2MASS extinction measurement on arcminute spatial scale (Qian et al. 2012). Using the measured H₂ column density and the FWHM of the FCRAO primary beam, we finally obtain an upper limit of ∼0.13 M_☉ for a core of 700 AU within 25'' from the GM Tau position. Both the estimated masses from the Onishi et al. (2002) observations and FCRAO are well below the enclosed mass of 8.4 M_☉ required for gravitational bound motion. We therefore conclude that the detected emission is from the outflow.

One should note that we did not detect the dust continuum emission with an upper limit of 1 mJy (=1σ) measured at the GM Tau position.

So far, we have observed eight VLM objects and detected three of them with CO molecular outflows: ISO-Oph 102 in ρ Ophiuchi (Phan-Bao et al. 2008), MHO 5 (Phan-Bao et al. 2011), and GM Tau (this paper) in Taurus. The molecular outflows from these three sources show similar molecular outflow properties: a small scale of 600–1000 AU, a low velocity of <5 km s⁻¹ (with a correction of outflow inclination), a tiny outflow mass of 10⁻⁶–10⁻⁴ M_☉, and a low mass-loss rate of 10⁻⁹–10⁻⁷ M_☉ yr⁻¹. Table 2 lists these properties for each source. Our molecular outflow mass estimates in VLM objects are smaller than the typical values 0.01−0.7 M_☉ of class II low-mass stars (G and K spectral types; see Levreault 1988b and references therein) by over an order of magnitude.

Table 2. Molecular Outflow Properties of Class II VLM Objects in ρ Ophiuchi and Taurus

Target	Array	Mass	Region	Size (length)	vmax	log Mouta	log $\dot{M}_{\rm mol}$a	log Moutb	log $\dot{M}_{\rm mol}$b	tdyn	Reference
		(MJ)		(AU)	(km s−1)	(M☉)	(M☉ yr−1)	(M☉)	(M☉ yr−1)	(yr)
ISO-Oph 32	SMA	40	ρ Oph	...	...	...	...	...	...	...	1, 2
ISO-Oph 102	SMA	60	ρ Oph	1000	4.7	−4.5	−7.5	−3.3	−6.3	1100	1, 3
2M 0441+2534	CARMA	35	Taurus	...	...	...	...	...	...	...	4, 2
2M 0439+2544	CARMA	50	Taurus	...	...	...	...	...	...	...	4, 2
2M 0438+2611	CARMA	70	Taurus	...	...	...	...	...	...	...	4, 5
GM Tau	SMA	73	Taurus	700	4.6	−5.7	−8.6	−4.5	−7.4	700	6, 5
2M 0414+2811	CARMA	75	Taurus	...	...	...	...	...	...	...	4, 5
MHO 5	SMA	90	Taurus	600	2.1	−4.9	−8.3	−3.7	−7.1	2700	7, 2

Notes. ^aLower limits of outflow mass and mass-loss rate without mass corrections. ^bUpper limits of outflow mass and mass-loss rate with mass corrections: a factor of three for SMA missing flux (Bourke et al. 2005) and five for optical depth (Levreault 1988a). References. References for mass estimate, outflow mass and mass-loss rate: (1) Natta et al. (2004); (2) Phan-Bao et al. (2011); (3) Phan-Bao et al. (2008); (4) Muzerolle et al. (2005); (5) this paper; (6) White & Basri (2003); (7) Muzerolle et al. (2003).

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To estimate the mass-loss rate of the stellar wind that drives the molecular outflow in the VLM objects, we can assume that the stellar wind-molecular gas interaction is momentum-conserving (e.g., Levreault 1988b; André et al. 1990). We thus equate the momentum P = M_outv_max of the molecular outflow with that supplied by the wind over the outflow's lifetime ($\dot{M}_{\rm wind}t_{\rm dyn}v_{\rm wind}$). This yields the expression $\dot{M}_{\rm wind} = M_{\rm out}v_{\rm max}/(t_{\rm dyn}v_{\rm wind})$, where v_wind is the wind velocity. For ISO-Oph 102, the wind velocity is ∼107 km s⁻¹, which is estimated from v_jet = 45 km s⁻¹ (Whelan et al. 2005) with a correction of outflow inclination of ∼65° to the line of sight (Phan-Bao et al. 2008). For the cases of MHO 5 and GM Tau, as no measurements of wind velocities have been reported so far, so we assume a wind velocity of about 100 km s⁻¹ for these two objects. Using the upper and lower limit values of outflow mass (see Table 2), we derive the upper and lower limits (Table 3) to the wind mass-loss rates of the VLM objects, respectively.

Table 3. Wind Mass-loss Rate of Young VLM Objects in ρ Ophiuchi and Taurus

Target	log $\dot{M}_{\rm acc}$	log $\dot{M}_{\rm wind}$a	log $\dot{M}_{\rm wind}$b	$\dot{M}_{\rm wind}$/$\dot{M}_{\rm acc}$c	Reference
	(M☉ yr−1)	(M☉ yr−1)	(M☉ yr−1)
ISO-Oph 102	−9.0	−8.9	−7.7	1.3–20.0	1
GM Tau	−8.6	−9.9	−8.7	0.05–0.8	2
MHO 5	−10.8	−10.0	−8.8	6.3–100.0	3

Notes. ^aLower limit of wind mass-loss rate. ^bUpper limit of wind mass-loss rate. ^cThe range of the ratio of wind mass-loss rate to the accretion rate. References. References for accretion rate: (1) Natta et al. (2004); (2) White & Basri (2003); (3) Muzerolle et al. (2003).

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There is a possibility that our values of wind mass-loss rates are underestimated if the momentum from the wind might not be transferred all to the molecular gas. This happens when there is less molecular gas surrounding the source at late stages (class II) than early stages (class 0, I). However, the wind mass-loss rates of VLM objects (e.g., ISO-Oph 102) estimated from molecular outflows (see Table 2) are comparable to those derived from optical jets using the spectro-astrometric method (see Table 6 in Whelan et al. 2009, Whelan et al. 2014). This implies that our values are not significantly underestimated. All these values of wind mass-loss rates of VLM objects are smaller than a typical value of ∼10⁻⁷M_☉ yr⁻¹ for class-II low-mass stars of 0.5–5.0 M_☉ (Levreault 1988a) by over about an order of magnitude (see Figure 3). Our results have shown that the outflow process occuring in VLM objects is a scaled-down version of that in low-mass stars.

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We should note here that the ratios of wind mass-loss rate to mass accretion rate $\dot{M}_{\rm wind}/\dot{M}_{\rm acc}$ in ISO-Oph 102 and MHO 5 (see Table 3) are significantly higher than that in T Tauri stars (∼0.0003–0.4; Hartigan et al. 1995). These high ratio values imply three possible scenarios.

• 1.  
  First, we might underestimate the accretion rates as the accretion rates measured in the VLM objects at different epochs may vary over an order of magnitude on timescales of months to years (e.g., Stelzer et al. 2007). Therefore, the rates measured at particular epochs do not reflect the long-term accretion rates that are more appropriate for comparison with the outflow rates in the two VLM objects. However, the accretion rate in MHO 5 measured at different epochs has suggested that the accretion rate is stable, ∼10^−10.8M_☉ yr⁻¹ (Muzerolle et al. 2003; Herczeg & Hillenbrand 2008). In the case of ISO-Oph 102, the accretion rate of ∼10^−9.0M_☉ yr⁻¹ was measured at epoch 2003.411 (Natta et al. 2004), and an increase of the accretion rate by a factor of five within a week was also observed (Natta et al. 2004). However, the accretion rate of 10^−9.17M_☉ yr⁻¹ (Gatti et al. 2006) measured at epoch 2005.384 agrees with Natta et al.'s measurement, suggesting a long-term accretion rate in ISO-Oph 012 of ∼10^−9.0M_☉ yr⁻¹. Therefore, this scenario is unlikely the case here.
• 2.  
  Second, we might overestimate the wind mass-loss rate. This is due to the fact that we did not apply a correction factor for the dynamical time (see Table 3). If the estimated dynamical time is a lower limit to the real dynamical time, then we need to apply a correction factor of about 100 for the case of ISO-Oph 102 and 1000 for MHO 5 as well as GM Tau (see Section 5.2 for further discussion), instead of 10 as estimated for low-mass stars (Parker et al. 1991), for the outflow dynamical time of VLM objects. The wind mass-loss rates, and hence the ratios $\dot{M}_{\rm wind}/\dot{M}_{\rm acc}$, will decrease by the same factors and they are thus comparable to those in T Tauri stars.
• 3.  
  Third, this ratio in VLM objects is really higher than that in low-mass stars. This is possibly due to a sudden drop of the mass accretion rate during the formation process of brown dwarfs as proposed by Machida et al. (2009). Further observations and theoretical works are needed to confirm these possible scenarios.

The outflow dynamical times estimated for the three class-II VLM objects, ISO-Oph 102 (Phan-Bao et al. 2008), MHO 5 (Phan-Bao et al. 2011), and GM Tau (this paper) are from 7.0 × 10² yr to 2.7 × 10³ yr (see Table 2). These values are still about two or three orders of magnitude smaller than the ages of ISO-Oph 102, GM Tau, and MHO 5 expected to be from a few 10⁵ yr (ISO-Oph 102; Natta et al. 2004) to a few Myr (GM Tau and MHO 5, see Muzerolle et al. 2003 and references therein).

The extreme discrepancy between the outflow dynamical time and the age of the VLM objects indicates two possibilities.

• 1.  
  The extent of outflows is not completely revealed because of the coverage and the sensitivity of our observations. For example, an outflow with velocity of 5 km s⁻¹ and a dynamical time of 10⁵ yr will have a length of about 0.5 pc, or 12' at the distance of Taurus. This is more than an order of magnitude larger than the SMA primary beam size. Therefore, any molecular outflow emission that lies more than half a primary beam from the source would be impossible to detect. In addition, the full extent of outflows to the edge of the primary beam has not been detected (e.g., ISO-Oph 102; see Figure 1 in Phan-Bao et al. 2008), which is possibly due to the sensitivity limit of SMA. The estimated outflow dynamical time is thus a lower limit to the true outflow duration as discussed in Parker et al. (1991) for the case of low-mass stars.
• 2.  
  The outflow process in the VLM objects is episodic, occurring in class II with duration of a few 10³ yr. An episodic outflow will have a discrete blob morphology. In this case, other blobs of the molecular outflows from our VLM objects that lie outside the primary beam would not be detected. The outflows detected by SMA are thus from the last active episodes. If the episodicity of these outflows is confirmed, the outflow process in VLM objects will include quiescent and active episodes. One can then expect that the accretion associated with the outflow is also episodic. This is consistent with evolutionary models as proposed by Baraffe et al. (2009) that the accretion process in BDs at early stages could be episodic, including long quiescent phases of accretion interrupted by short episodes (a few 10³ to 10⁴ yr) of high accretion. Their evolutionary models taking into account episodic phases of accretion successfully explain the significant luminosity spread observed in H-R diagrams of star-forming regions.

More extended and deeper observations are therefore needed to explore the morphology of the outflows from these VLM objects in order to confirm the scenarios.

The outflow masses and the mass-loss rates of the molecular outflows from ISO-Oph 102, GM Tau, and MHO 5, which are class II objects, are comparable to those of L1014-IRS (Bourke et al. 2005), a proto BD candidate at a younger age (class 0/I) that has an outflow with a mass and mass-loss rate of ∼10⁻⁵ M_☉ and ∼10⁻⁹ M_☉ yr⁻¹, respectively. In the case of the class I proto BD candidate L1148-IRS (Kauffmann et al. 2011), the outflow mass (∼10⁻³ M_☉) and the mass-loss rate (∼10⁻⁷ M_☉ yr⁻¹) are slightly larger than that from our VLM objects but still comparable to the range of our lower and upper limits (see Table 2). This similarity implies that the mass-loss rate, hence the associated wind mass-loss and accretion rates in VLM objects do not significantly change in different formation stages (from class 0/I to class II).

As discussed in Section 5.1, the ratio of wind mass-loss rate to accretion rate $\dot{M}_{\rm wind}/\dot{M}_{\rm acc}$ in VLM objects is possibly higher than that in low-mass stars (Table 3). If the wind mass-loss rate does not significantly change for different classes of VLM object formation, 10⁻¹¹–10⁻⁸ M_☉ yr⁻¹ (see Table 3), then one may expect that this ratio also holds in earlier classes, such as classes 0, I. This suggests that the accretion rate in VLM objects may also be expected to be in the range 10⁻¹¹–10⁻⁹ M_☉ yr⁻¹ at earlier stages. The starlike models for BD formation predict that VLM cores produced by fragmentation (Padoan & Nordlund 2004; Bonnell et al. 2008) are dense enough to be gravitationally unstable. The detection of such a VLM core (André et al. 2012) supports these models. Our observations suggest that these VLM cores may undergo some active episodes of outflow and associated accretion with duration of a few 10³ yr. The accretion rates, however, are very low, in the range 10⁻¹¹–10⁻⁹ M_☉ yr⁻¹ or lower, and they are comparable or smaller than the mass-loss rate. This may therefore prevent the VLM cores from accreting enough material to become a star.