A New Look at T Tauri Star Forbidden Lines: MHD-driven Winds from the Inner Disk

Circumstellar disks form as a result of angular momentum conservation during the protostellar core collapse (Shu 1977) and play an important role in both star and planet formation. At early times, a significant fraction of the stellar mass is accreted through the disk, and what is not accreted or dispersed via other mechanisms provides the raw material to build planets. As such, it is important to understand how disks evolve and disperse.

In the current paradigm, there are three main stages of disk evolution and dispersal (e.g., Gorti et al. 2016; Ercolano & Pascucci 2017 for recent reviews). For most of the disk lifetime (Stage 1), evolution is primarily set by accretion. Beyond a fraction of the radius where the sound speed equals the local Keplerian orbital speed (∼2 au for 10⁴ K gas, and ≳10–100 au for 100–1000 K gas for a Sun-like star) gas becomes unbound, and a photoevaporative thermal wind can be established. When the disk accretion rate through this radius drops below the wind mass-loss rate, photoevaporation limits the supply of gas to the inner disk, a gap is formed (Stage 2), and the inner disk drains onto the star on the local viscous timescale—of order 100,000 yr. In the last stage (Stage 3), there is no accretion onto the star, and the disk is rapidly cleared from the inside out by stellar high-energy photons directly irradiating the outer disk.

Although photoevaporative winds are believed to play an important role in disk dispersal, large-scale jets/outflows, which contribute to significant mass loss at the earliest stages, are usually attributed to an origin in a magnetohydrodynamic (MHD) wind (e.g., Frank et al. 2014 for a recent review). Such winds can be effective in removing disk angular momentum and in facilitating accretion of disk gas onto the star (e.g., Pudritz et al. 2007; Shang et al. 2007).

Recently, significant theoretical effort has been devoted to understanding MHD disk winds and their relation to accretion and disk dispersal. It has long been realized that the inclusion of nonideal MHD effects suppresses magnetorotational instability (MRI) turbulence (e.g., Gammie 1996), and recent numerical simulations show that even a weak net vertical magnetic field, which could be, for example, leftover from the earlier stage of cloud collapse, can drive MHD winds (e.g., Suzuki & Inutsuka 2009; Fromang et al. 2013). Local box simulations (e.g., Bai & Stone 2013) and radially global, but vertically restricted, simulations (Gressel et al. 2015; Béthune et al. 2017) show that the launch of MHD winds is robust, can occur over the planet-forming region (∼1–30 au), and can drive accretion at the observed levels. However, the predicted wind mass-loss rate, and hence the accretion rate, strongly depends on the magnetic field strength and how it evolves (e.g., Armitage et al. 2013; Bai & Stone 2017), both of which are poorly constrained. Therefore, identifying diagnostics that trace disk winds and deriving wind mass-loss rates are important to understand not only how disks disperse but also how they evolve.

Low-excitation optical forbidden lines, especially from the [O i] λ6300 transition, have long been used to study jets/outflows from T Tauri stars (e.g., Edwards et al. 1987; Hartigan et al. 1995). Their line profiles typically present two distinct components: a high-velocity component (HVC), blueshifted by 30–200 km s⁻¹ from the stellar velocity, and a low-velocity component (LVC), typically blueshifted by ∼5 km s⁻¹. Spatially resolved observations have demonstrated that HVCs are formed in extended collimated jets (e.g., Bacciotti et al. 2000; Lavalley-Fouquet et al. 2000; Woitas et al. 2002), most likely linked to MHD winds (e.g., Ferreira et al. 2006).

Employing much higher spectral resolution than in previous studies (Δv ∼ 4 km s⁻¹), Rigliaco et al. (2013) found that the [O i] LVC itself can be described by the combination of a narrow component (NC) and a broad component (BC). More recently, Simon et al. (2016) confirmed this finding on a much larger sample of 33 T Tauri stars observed with Keck/HIRES (Δv ∼ 7 km s⁻¹). Using the line profiles and inclinations from resolved disk images, they inferred that most of the LVC-BC arises within ∼0.5 au while most of the LVC-NC arises outside this radius. By combining measured velocities with line widths and disk inclinations, they also found that the LVC-BC tends to be narrower and more blueshifted for closer to face-on disks, as shown in some disk wind models (e.g., Alexander 2008). Finally, since the emitting region is within the photoevaporating radius even for 10,000 K gas, they could conclude that the LVC-BC traces an MHD disk wind. The origin of the LVC-NC remains unclear, as the inferred radial extent is consistent with a thermally driven photoevaporative wind but no trend between blueshifts and disk inclinations was seen (Simon et al. 2016).

An important step in computing wind mass-loss rates is to constrain the properties of the emitting gas associated with the wind. Ratios of lines tracing the same kinematic component can be employed for this task (e.g., Dougados et al. 2010). However, so far the only lines analyzed at similarly high spectral resolution to distinguish BC and NC are the [O i] λ6300 and [O i] λ5577. Assuming that the lines are thermally excited, their ratios constrain the range of temperature–electron densities for the emitting gas and imply higher electron density in the region traced by the LVC-BC for gas at similar temperatures (Simon et al. 2016). However, far-UV photodissociation of OH molecules can produce a similar range of [O i] ratios in much cooler (∼1000 K) gas (see, e.g., Harich et al. 2000 and Gorti et al. 2011 for an application to disks). In this scenario of nonthermal emission, line ratios do not constrain the temperature and density of the gas. In order to estimate wind mass-loss rates, it is therefore necessary to first establish that the [O i] λ6300 and [O i] λ5577 emission is thermal. As first pointed out in Natta et al. (2014), the [S ii] λ4068 has a critical density very similar to the [O i] λ6300 line and is likely to be thermally excited; hence, the [S ii] and [O i] line profiles, as well as their line ratio, can be used to distinguish between thermal and nonthermal excitation.

In this work, we expand on previous high-resolution studies by analyzing the [S ii] λ4068, [O i] λ5577, and [O i] λ6300 from a sample of 48 T Tauri stars with the main goal of determining whether the [O i] emission is thermal or nonthermal. In a parallel work, we focus on the kinematic behavior of individual [O i] components to clarify the link between jets and winds (Banzatti et al. 2018). First, we describe our sample, observations, and data reduction (Section 2). Then, we present our analysis (Section 3), which includes line decomposition in HVC, LVC-BC, and LVC-NC following Simon et al. (2016). In Section 4 we show that the [S ii] λ4068, [O i] λ5577, and [O i] λ6300 line profiles are very similar within each kinematic component, strongly suggesting that the [O i] emission is thermally produced, and not the result of photodisocciation of OH in a cool gas. We use line ratios to constrain the properties of the emitting gas and compute wind mass-loss rates in Section 5. We also calculate mass accretion rates from several permitted lines and compare accretion versus mass-loss rates (Section 5). We discuss the implications of our results in Section 6 and summarize our findings in Section 7.

2.1. Sample

2.2. Observations and Data Reduction

2.3. Stellar Radial Velocity

3.1. Corrected Line Profiles and Detection Rates

To produce corrected line profiles, we first remove any telluric absorption and then subtract the photospheric features near the lines. Telluric removal is only necessary for the [O i] λ6300 line and is achieved with the procedure summarized in the HIRES Data Reduction manual¹¹ and using the telluric standards acquired in the two nights.

After telluric removal, we subtract the stellar photosphere following Hartigan et al. (1989). In short, we select a photospheric standard with a spectral type similar to the target. We then broaden (through the rotation velocity V sin i), veil (parameter r_λ), and shift in velocity its spectrum to best match the target's photospheric lines. Veiling is defined as the ratio of the excess (F_excess) to the photospheric flux (F_phot), r_λ = F_excess/F_phot, and it is used to mimic the filling in of the photospheric lines due to the excess emission from the accretion shocks. The best-fit photospheric spectrum is the one that minimizes the χ², defined as ${\chi }^{2}=\sum {({F}_{\mathrm{target}}-{F}_{\mathrm{Standard}})}^{2}$. Corrected line profiles are produced by subtracting the best-fit photospheric spectra from the target spectra. We do not apply any photospheric subtraction on extremely veiled spectra that have no photospheric features, e.g., several of the spectra in the [S ii] λ4068 setting. Figure 1 shows an example of the technique described here, including telluric removal near the [O i] λ6300 line (right panel). Table 1 lists the photospheric standards used for individual lines.

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Overall, we detect the [O i] λ6300, [O i] λ5577, and [S ii] λ4068 lines from 45, 26, and 22 sources, respectively.¹² Hence, the detection rate is 94%, 54%, and 49% in these lines.¹³ A total of 19 sources have detections in all three lines.

3.2. Line Decomposition

As recently shown in Simon et al. (2016), oxygen forbidden lines can be well reproduced by the superimposition of a few Gaussian profiles, presumably tracing different kinematic components. Figure 2 compares the [S ii] λ4068, [O i] λ5577, and [O i] λ6300 emission lines from DP Tau, one of the sources with the highest signal-to-noise ratio (S/N) spectra. Note how an NC centered at the stellar velocity is present in all lines (panel (a)). Broader, higher-velocity emission is also apparent in the three tracers (panel (b)).

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Motivated by the similarity of the profiles in the high-S/N spectrum of DP Tau and following Simon et al. (2016), we use a combination of Gaussians to decompose the [S ii] λ4068, [O i] λ5577, and [O i] λ6300 lines. To find the minimum number of Gaussians that describes the observed profile, we use an iterative approach based on the IDL procedure mpfitfun. We start by fitting each profile with one Gaussian and compute the residual spectrum by subtracting the best fit from the original profile. If the rms of the residual is higher than that of the original spectrum next to the line of interest (by more than ∼2σ), we add another Gaussian and refit the original profile simultaneously with two Gaussians. We recompute the residual spectrum and add an extra Gaussian until the rms of the residual is within 2σ of the rms of the original spectrum.

Table 2 lists the parameters resulting from the decomposition of each individual line, while Figure 3 shows examples of the best-fit Gaussian profiles for three sources. All other fits are shown in Appendix D, Figure 19. Seven sources (HN Tau A, RU Lup, EX Lup, As 205A, VV CrA, SCrA A+B, and As 353A) have [S ii] λ4068 lines highly contaminated by Fe i emission. In addition, the [O i] λ5577 line from RU Lup is also affected by Fe i emission. We decontaminate these line profiles before line decomposition as discussed in detail in Appendix E. Note that the [S ii] λ4068 profiles from EX Lup, As 205A, VV CrA, and As 353A are not well recovered at velocities more blueshifted than ∼200 km s⁻¹. Hence, the most blueshifted HVC [S ii] λ4068 component for each of these sources is marked as unreliable in Table 2 and will not be used in the following analysis.

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Table 2.  Parameters for Line Decomposition of [S ii] λ4068, [O i] λ5577, and [O i] λ6300 Line Profiles

		[S ii] λ4068				[O i] λ5577				[O i] λ6300
		FWHM	vc	EW	log L4069	FWHM	vc	EW	log L5577	FWHM	vc	EW	log L6300	Preliminary	Refined
ID	Name	(km s−1)	(km s−1)	(Å)	(L⊙)	(km s−1)	(km s−1)	(Å)	(L⊙)	(km s−1)	(km s−1)	(Å)	(L⊙)	Class	Class
1	DP Tau	62.8	−91.9	1.01	−5.29	45.4	−90.6	0.08	−6.32	64.4	−89.3	0.89	−5.24	HVC-B
		115.6	31.2	5.92	−4.52	116.7	13.6	0.47	−5.54	111.8	23.5	6.03	−4.41	LVC-BC	HVC-R
		27.3	2.4	1.23	−5.20	24.4	0.4	0.60	−5.44	22.5	0.8	3.99	−4.59	LVC-NC
2	CX Tau	⋯	⋯	⋯	⋯	⋯	⋯	⋯	<−6.52	27.9	−2.6	0.05	−6.40	LVC-NC
3	FP Tau	⋯	⋯	⋯	<−5.51	84.6	1.4	0.14	−6.14	66.0	1.1	0.38	−5.68	LVC-BC
4	FN Tau	13.8	−44.1	0.09	−6.18	⋯	⋯	⋯	<−6.47	10.6	−43.0	0.03	−6.25	HVC-B
		15.3	−117.8	0.14	−5.99	⋯	⋯	⋯	<−6.36	13.7	−121.6	0.06	−6.00	HVC-B
		40.5	−79.2	0.95	−5.17	⋯	⋯	⋯	<−5.91	38.3	−77.4	0.47	−5.11	HVC-B
		30.4	−11.1	0.27	−5.72	22.8	−12.3	0.02	−6.45	26.9	−12.2	0.34	−5.26	LVC-NC
5	V409 Tau	113.3	−85.4	0.92	−5.58	⋯	⋯	⋯	<−5.81	107.6	−64.8	0.22	−5.50	HVC-B
		70.8	42.5	0.29	−6.08	⋯	⋯	⋯	<−5.95	79.3	51.5	0.10	−5.83	HVC-R
6	BP Tau	94.7	11.3	0.36	−5.22	88.3	4.0	0.17	−5.24	98.9	12.4	0.26	−5.04	LVC-BC
		37.5	−18.2	0.11	−5.73	27.5	−6.1	0.03	−6.01	26.3	−2.6	0.10	−5.44	LVC-NC
7	DK Tau A	45.1	−125.6	0.16	−5.30	⋯	⋯	⋯	<−5.69	41.0	−135.7	0.09	−5.27	HVC-B
		124.2	−18.1	0.29	−5.05	96.8	−1.4	0.16	−5.02	153.7	−27.4	0.42	−4.59	LVC-BC
		⋯	⋯	⋯	<−5.79	14.2	1.0	0.02	−5.88	24.9	−5.1	0.13	−5.09	LVC-NC
8	HN Tau A	116.2	−78.5	2.80	−4.25	183.1	−57.9	0.23	−5.19	132.4	−67.7	2.99	−4.07	HVC-B
		60.2	−9.6	1.44	−4.54	45.3	−0.0	0.10	−5.56	50.4	−6.5	1.33	−4.42	LVC-BC	HVC-B
9	UX Tau A	⋯	⋯	⋯	<−5.20	⋯	⋯	⋯	<−5.18	34.6	−1.2	0.11	−4.70	LVC-NC
10	GK Tau A	160.6	−22.4	0.36	−4.87	116.6	−35.5	0.04	−5.57	179.1	−30.7	0.38	−4.58	HVC-B
		36.0	−1.0	0.13	−5.31	51.5	3.1	0.05	−5.48	38.6	−3.3	0.17	−4.94	LVC-NC
11	GI Tau	86.3	−51.9	0.20	−4.79	38.9	−52.6	0.03	−5.73	85.9	−67.5	0.19	−4.85	HVC-B
		33.6	46.3	0.15	−4.91	54.1	40.6	0.05	−5.44	31.7	46.7	0.17	−4.90	HVC-R
		39.3	6.2	0.08	−5.20	59.0	−11.5	0.06	−5.38	44.7	1.3	0.16	−4.92	LVC-BC
12	DM Tau	⋯	⋯	⋯	<−6.17	24.8	−2.0	0.05	−6.51	26.1	0.5	0.35	−5.69	LVC-NC
13	LkCa 15	⋯	⋯	⋯	<−5.47	⋯	⋯	⋯	<−5.54	44.6	−0.6	0.14	−5.06	LVC-BC
14	DS Tau	⋯	⋯	⋯	<−4.86	⋯	⋯	⋯	<−4.93	151.1	16.3	0.19	−5.05	LVC-BC
15	SZ 65	⋯	⋯	⋯	<−4.92	⋯	⋯	⋯	<−4.87	109.9	3.6	0.25	−4.74	LVC-BC
16	SZ 68A	⋯	⋯	⋯	<−6.55	⋯	⋯	⋯	<−5.49	⋯	⋯	⋯	<−5.50	⋯	⋯
17	SZ 73	82.5	−88.4	0.70	−4.89	⋯	⋯	⋯	<−5.39	71.1	−94.4	1.67	−4.43	HVC-B
		⋯	⋯	⋯	<−5.09	⋯	⋯	⋯	<−5.27	94.2	64.2	0.25	−5.26	HVC-R
		⋯	⋯	⋯	<−5.35	41.1	−11.9	0.11	−5.66	50.8	−19.2	0.69	−4.82	LVC-BC
18	HM Lup	68.3	−119.7	0.50	−5.78	⋯	⋯	⋯	<−5.70	90.4	−116.9	0.59	−5.38	HVC-B
		⋯	⋯	⋯	<−6.41	⋯	⋯	⋯	<−6.31	22.1	−3.8	0.22	−5.81	LVC-NC
19	GW Lup	⋯	⋯	⋯	<−5.99	68.8	−7.5	0.09	−5.93	69.4	−9.7	0.29	−5.41	LVC-BC
20	GQ Lup	⋯	⋯	⋯	<−4.56	46.1	10.7	0.04	−5.04	91.4	4.0	0.28	−4.18	LVC-BC
21	SZ 76	⋯	⋯	⋯	<−5.80	69.9	31.7	0.22	−5.86	50.1	38.8	0.39	−5.66	HVC-R
		77.9	−16.0	0.48	−5.64	53.1	−26.4	0.24	−5.81	65.5	−18.3	1.21	−5.16	LVC-BC
22	RU Lup	130.0	−137.8	1.68	−3.68	⋯	⋯	⋯	<−4.67	109.9	−149.3	0.61	−4.01	HVC-B
		68.5	−38.9	0.26	−4.49	⋯	⋯	⋯	<−5.10	40.5	−32.3	0.07	−4.92	HVC-B
		150.3	−13.1	0.43	−4.28	120.5	−11.7	0.21	−4.47	176.4	−10.1	0.41	−4.18	LVC-BC
		⋯	⋯	⋯	<−5.21	⋯	⋯	⋯	<−5.57	13.9	−10.9	0.06	−5.02	LVC-NC
23	IM Lup	⋯	⋯	⋯	<−4.98	⋯	⋯	⋯	<−4.83	117.1	−10.0	0.16	−4.79	LVC-BC
24	RY Lup	⋯	⋯	⋯	<−5.18	⋯	⋯	⋯	<−5.13	30.7	2.5	0.09	−4.64	LVC-NC
25	SZ 102	206.1	−32.5	20.69	−4.54	⋯	⋯	⋯	<−5.54	209.3	−38.1	22.13	−4.63	HVC-B
		58.3	−25.8	17.62	−4.61	30.7	−16.0	0.89	−5.92	40.0	−24.5	17.99	−4.72	LVC-NC	HVC-B
		85.3	20.6	53.70	−4.13	108.9	5.9	4.45	−5.22	93.6	11.8	127.33	−3.87	LVC-BC	HVC-R
26	SZ 111	⋯	⋯	⋯	<−6.16	⋯	⋯	⋯	<−5.91	28.0	−0.4	0.41	−5.24	LVC-NC
27	SZ 98	167.4	−50.9	2.05	−4.46	108.9	−12.4	0.21	−5.13	152.5	−37.7	1.07	−4.40	HVC-B
		30.4	−8.1	0.21	−5.46	⋯	⋯	⋯	<−5.75	28.7	−6.7	0.12	−5.35	LVC-NC
28	EX Lup	⋯	⋯	⋯	⋯	⋯	⋯	⋯	<−4.98	25.1	−119.3	0.08	−4.53	HVC-B
		84.3	−181.2	0.17	−3.86	⋯	⋯	⋯	<−4.48	79.6	−179.2	0.26	−4.03	HVC-Ba
		121.9	−88.0	0.81	−3.19	⋯	⋯	⋯	<−4.69	48.9	−79.5	0.14	−4.29	HVC-B
		⋯	⋯	⋯	⋯	⋯	⋯	⋯	<−4.88	31.5	102.8	0.06	−4.64	HVC-R
		⋯	⋯	⋯	⋯	⋯	⋯	⋯	<−4.88	31.1	56.9	0.11	−4.41	HVC-R
		37.8	−15.0	0.10	−4.11	65.1	−15.8	0.07	−4.53	59.6	−17.6	0.45	−3.79	LVC-BC
29	As 205A	⋯	⋯	⋯	⋯	⋯	⋯	⋯	<−5.09	56.3	−221.9	0.11	−4.69	HVC-B
		154.2	−112.1	0.29	−4.29	⋯	⋯	⋯	<−4.49	225.5	−85.4	0.28	−4.27	HVC-Ba
		60.4	−19.0	0.12	−4.67	50.8	−0.7	0.03	−5.18	54.5	−13.5	0.16	−4.50	LVC-BC
		18.9	1.5	0.03	−5.36	12.7	1.1	0.02	−5.40	14.5	−0.7	0.11	−4.66	LVC-NC
30	DoAr 21	⋯	⋯	⋯	⋯	⋯	⋯	⋯	<−4.31	⋯	⋯	⋯	<−4.51	⋯
31	DoAr 24E	⋯	⋯	⋯	⋯	⋯	⋯	⋯	<−5.69	⋯	⋯	⋯	<−5.62	⋯
32	DoAr 44	⋯	⋯	⋯	<−5.04	35.0	3.8	0.02	−5.68	59.6	−1.1	0.15	−4.82	LVC-BC
33	SR 21A	⋯	⋯	⋯	<−3.29	⋯	⋯	⋯	<−4.45	16.3	−6.9	0.01	−4.81	LVC-NC
34	V853 Oph	30.0	−33.8	1.26	−5.27	⋯	⋯	⋯	<−6.10	28.5	−31.3	0.93	−5.00	HVC-B
		68.4	−16.0	1.19	−5.30	37.5	−12.4	0.24	−5.62	70.2	−14.4	1.31	−4.85	LVC-BC
		⋯	⋯	⋯	<−6.52	⋯	⋯	⋯	<−6.33	16.6	−1.6	0.31	−5.48	LVC-NC
35	RNO 90	⋯	⋯	⋯	<−4.14	56.1	−3.0	0.06	−4.73	57.5	−3.4	0.23	−4.17	LVC-BC
36	V2508 Oph	⋯	⋯	⋯	<−4.49	⋯	⋯	⋯	<−4.67	116.2	−38.4	0.11	−4.85	HVC-B
37	V1121 Oph	⋯	⋯	⋯	<−5.64	⋯	⋯	⋯	<−5.54	21.1	−7.2	0.03	−5.48	LVC-NC
38	J1842	36.5	−122.1	0.06	−5.60	⋯	⋯	⋯	<−5.43	45.6	−126.3	0.10	−5.18	HVC-B
		83.9	−16.4	0.28	−4.94	93.0	−3.1	0.08	−5.29	109.2	−11.5	0.35	−4.64	LVC-BC
		25.9	1.8	0.08	−5.50	23.4	−1.0	0.03	−5.71	27.3	−0.5	0.23	−4.82	LVC-NC
39	J1852	⋯	⋯	⋯	<−5.86	⋯	⋯	⋯	<−5.88	23.5	−2.4	0.09	−5.35	LVC-NC
40	VV CrA	⋯	⋯	⋯	<−3.60	85.2	−416.1	0.06	−5.06	133.2	−361.6	0.78	−3.88	HVC-B
		135.5	−209.3	1.88	−3.52	94.7	−234.8	0.30	−4.37	119.7	−205.4	1.58	−3.57	HVC-Ba
		147.8	−88.8	3.89	−3.21	101.5	−78.5	0.14	−4.71	114.2	−87.0	1.73	−3.53	HVC-B
		35.7	−22.5	0.48	−4.11	51.4	−19.8	0.18	−4.59	42.2	−22.1	0.69	−3.93	LVC-BC
		⋯	⋯	⋯	<−4.34	⋯	⋯	⋯	<−4.99	18.1	−6.7	0.29	−4.30	LVC-NC
41	SCrA A+B	44.1	−129.3	0.24	−4.67	⋯	⋯	⋯	<−5.02	45.6	−127.7	0.51	−3.91	HVC-B
		132.7	−72.3	0.60	−4.27	121.1	−40.4	0.09	−4.65	128.0	−49.5	0.66	−3.80	HVC-B
		58.5	59.1	0.07	−5.19	⋯	⋯	⋯	<−4.85	68.2	68.0	0.08	−4.70	HVC-R
42	TW Hya	15.9	−0.3	0.08	−6.29	9.6	0.1	0.08	−5.89	12.8	0.0	0.57	−5.03	LVC-NC
43	TWA 3A	⋯	⋯	⋯	<−7.03	56.0	−1.1	0.11	−6.98	61.9	1.3	0.59	−6.09	LVC-BC
44	V1057 Cyg	⋯	⋯	⋯	<−1.61	⋯	⋯	⋯	<−2.51	50.0	−154.6	0.23	−1.88	HVC-B
		⋯	⋯	⋯	<−1.55	⋯	⋯	⋯	<−2.45	58.0	−98.6	0.24	−1.86	HVC-B
		⋯	⋯	⋯	<−1.27	⋯	⋯	⋯	<−2.17	110.9	−60.0	0.25	−1.85	HVC-B
45	V1515 Cyg	⋯	⋯	⋯	<−3.05	⋯	⋯	⋯	<−3.28	32.1	−120.8	0.03	−3.45	HVC-B
		⋯	⋯	⋯	<−2.72	⋯	⋯	⋯	<−2.94	69.9	−63.2	0.18	−2.73	HVC-B
46	HD 143006	⋯	⋯	⋯	<−4.37	⋯	⋯	⋯	<−4.73	66.3	2.8	0.09	−4.45	LVC-BC
		⋯	⋯	⋯	<−4.91	⋯	⋯	⋯	<−5.27	19.1	2.1	0.02	−5.02	LVC-NC
47	DI Cep	⋯	⋯	⋯	<−4.75	⋯	⋯	⋯	<−4.69	27.3	−7.5	0.11	−4.18	LVC-NC
48	As 353A	⋯	⋯	⋯	⋯	⋯	⋯	⋯	<−4.77	48.4	−280.0	0.21	−4.25	HVC-B
		318.0	−128.6	1.96	−3.67	⋯	⋯	⋯	<−3.96	322.8	−126.6	0.94	−3.61	HVC-Ba
		95.1	−43.2	0.41	−4.35	⋯	⋯	⋯	<−4.66	62.7	−27.9	0.13	−4.47	LVC-BC	Suspicious
		⋯	⋯	⋯	⋯	⋯	⋯	⋯	<−4.99	29.1	−4.2	0.09	−4.62	LVC-NC

Note.

^aThe fitted parameters for the components from [S ii] λ4068 are unreliable.

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Table 2 also lists upper limits for undetected lines. For sources with detections in the [O i] λ6300 line, the upper limits on the other lines are computed assuming that they share the [O i] λ6300 profile and have peaks of 3× rms, where the rms is calculated from the standard deviation of the continuum near the line. For sources with nondetections in all the lines, the upper limits are calculated assuming a Gaussian profile with the FWHM of an unresolved line (∼6.3 km s⁻¹) and a peak of 3× rms.

3.3. Preliminary Classification

3.4. Refined Classification

Ratios of lines that trace the same kinematic component can be used to constrain the properties of the emitting gas. Simon et al. (2016) have already shown that the [O i] λ6300 and [O i] λ5577 lines have very similar LVC profiles (e.g., their Figure 15 and best-fit parameters in Table 5). Section 4.1 will illustrate that, within a specific kinematic component, the similarity extends to the [S ii] λ4068 line. Hence, here we use the ratios of these three forbidden lines to test whether different kinematic components separate out and, if so, further refine our preliminary classification.

Figure 4 shows line ratios (left panel) or upper limits (right panel) for all 45 sources that are detected in the [O i] λ6300, the brightest of our forbidden lines. HVCs (green circles) have a combination of higher [S ii] λ4068/[O i] λ6300 (hereafter SII40/OI63) and lower [O i] λ5577/[O i] λ6300 (hereafter OI55/63) ratios than LVCs. This is best illustrated by the mean and standard deviation of different component line ratios, which are shown as dotted ellipses in both panels. Note that these values are computed from our preliminary classification and only from sources with at least two detected forbidden lines that are used to calculate line ratios.

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The left panel of Figure 4 reveals four possible LVCs with line ratios more compatible with HVCs (circles surrounded by green squares: one LVC-BC from DP Tau (ID 1) and HN Tau A (ID 8), and one LVC-NC and one LVC-BC from SZ 102 (ID 25). Interestingly, HN Tau A and SZ 102 have close to edge-on disks (i > 70°). Thus, it is very likely that, owing to projection effects, their HVCs have centroids <30 km s⁻¹ and have been erroneously categorized as LVCs by our preliminary classification scheme. Although the disk inclination of DP Tau is not known, the star is about an order of magnitude underluminous compared to other Taurus members of the same spectral type (Herczeg & Hillenbrand 2014), pointing to obscuration from a highly inclined disk (see discussions on such underluminous young stars in Fang et al. 2009, 2013b). In addition, the [O i] λ6300 and [S ii] λ4068 LVC-BC centroids are close to our 30 km s⁻¹ HVC/LVC boundary. Thus, we reclassify all four LVCs as HVCs; see the last column of Table 2.

Figure 4 also shows the expected SII40/OI63 and OI55/63 ratios for gas at 10⁴ K, where collisions with electrons (densities 10^5.8–10^8.5 cm⁻³) excite the upper level of the transitions (e.g., Natta et al. 2014; see also Section 4.2.1). Most HVCs have SII40/OI63 ratios higher than the model-predicted ones, while most LVCs have lower ratios. We also note that one LVC-BC from As 353A (ID 48; right panel) shows higher SII40/OI63 ratios than the model-predicted ones, similar to HVCs. This, combined with possible Fe i contamination in the [S ii] λ4068 transition (see Appendix E), leads us to mark the LVC-BC as suspicious; see the last column of Table 2.

Following this refined classification, we find that 51% (23/45) of the sources with [O i] λ6300 detection have an HVC, while 84% (38/45) show an LVC. Furthermore, 31% (14/45) of the sample presents an LVC-BC, while 33% (15/45) has an LVC-NC. Finally, only 20% (9/45) of our sources have both LVC-BC and LVC-NC components.

4.1. The Similarity of [S ii] and [O i] Profiles of Individual Kinematic Components

Figure 5 shows a comparison of HVC, LVC-NC, and LVC-BC profiles for the sources that are detected in both [S ii] λ4068 and [O i] λ6300. Whenever detected, [O i] λ5577 lines are also superimposed. To test how similar are the profiles of individual kinematic components, we remove from the observed profile the other components using our best-fit parameters reported in Table 2.

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Regardless of kinematic component (HVC, LVC-BC, or LVC-NC), most profiles are similar in the [O i] and [S ii] lines. Only BP Tau has an LVC-NC that is clearly more blueshifted in the [S ii] λ4068 than in the [O i] lines, although the line widths are actually similar. This similarity is strengthened when comparing the centroids and FWHMs of individual components (see Figures 21 and 22 in Appendix F). Thus, we conclude that, within a kinematic component, the three lines trace a similar region. This means that their line ratios can be used to constrain the properties of the emitting gas, in particular temperature and density.

4.2. Gas Properties Constrained by Line Ratios

The difference in the HVC and LVC forbidden-line ratios was already noted in Section 3.4 and used to improve on our preliminary kinematic classification. Here, we search for and quantify any difference in line ratios between LVC-NC, LVC-BC, and HVC. Table 3 lists the mean and standard deviation of log OI55/63 and log SII40/OI63 for three types of components when considering only detections. LVC-BCs have the largest mean log OI55/63 ratio, while HVCs have the lowest one. HVCs have the highest mean log SII40/OI63 ratio, while LVC-NCs the lowest one.

Table 3.  Mean Line Ratios and Standard Deviations after HVC Reclassification

Line Ratios	LVC-NC	LVC-BC	HVC
log OI55/63	−0.81 ± 0.19	−0.62 ± 0.20	−0.97 ± 0.31
log SII40/OI63	−0.56 ± 0.35	−0.25 ± 0.18	−0.08 ± 0.36

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Next, we include upper limits and use Gehan's generalized Wilcoxon test in the ASURV code (Feigelson & Nelson 1985) to quantify any statistically significant difference between pairs of kinematic components. The test finds a low probability that the HVC log OI55/63 and log SII40/OI63 are the same as those of the LVC-BC. HVC and LVC-NC also have statistically different log SII40/OI63, but indistinguishable log OI55/63. Finally, the LVC-BC and LVC-NC differ in both log OI55/63 and log SII40/OI63; see Table 4. These findings suggest that the combination of these three forbidden lines is sufficient to separate the kinematic components discussed in this paper.

Table 4.  Results fro Gehan's Generalized Wilcoxon Test

log OI55/63		log SII40/OI63
Pairs	Probability	Paris	Probability
LVC-NC/LVC-BC	p = 6 × 10−3	LVC-NC/LVC-BC	p = 1 × 10−2
LVC-NC/HVC	p = 1 × 10−1	LVC-NC/HVC	p < 5 × 10−5
LVC-BC/HVC	p < 5 × 10−5	LVC-BC/HVC	p = 4 × 10−4

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4.2.1. Thermally Excited Gas Explains Most LVC Line Ratios

Figure 6(a) shows the relation between the SII40/OI63 and the OI55/63 ratios for the LVC components. In the same figure we also plot predicted ratios for homogeneous and isothermal gas that is thermally excited by collisions with electrons (gray lines). When computing these ratios, we take the solar sulfur abundance, α(S) = 1.4 × 10⁻⁵ (Asplund et al. 2005), and a depleted oxygen abundance as in the interstellar medium, α(O) = 3.2 × 10⁻⁴ (Savage & Sembach 1996). Following Natta et al. (2014), we also assume that all oxygen is neutral while all sulfur is singly ionized. Gas at higher temperature and electron density is predicted to have higher SII40/OI63 and OI55/63 line ratios.

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Most of the observed LVC ratios correspond to thermally excited gas with temperatures between 5000 and 10,000 K and electron densities of ∼10⁷–10⁸ cm⁻³. In As 353A, its LVC-BC has an SII40/OI63 ratio higher than expected from this simple model, with a value seen in some of the HVC. As discussed in Section 3.4, the [S ii] λ4068 line in this very high accretion rate star is blended with Fe i emission and classified as suspicious in Table 2, after our attempt at deblending. Turning to the LVC-NC, three of the transition disk sources, TW Hya, TWA 3A, and SZ 111, have much lower SII40/OI63 ratios than those expected for gas at ∼5000 K. Gehan's generalized Wilcoxon test finds a low probability (p = 6 × 10⁻²) that the SII40/OI63 ratios of LVC-BCs of full disks and TDs are drawn from the same parent population, while their OI53/63 ratios are indistinguishable (p = 0.3 for both the LVC-NC and the LVC-BC). This can be explained if TDs have a decreased S II/O i abundance ratio, as could happen if sulfur is sequestered in large grains in the disk midplane.

4.2.2. Shock-heated Gas Explains Most HVC Line Ratios

Jets generate shock waves in the surrounding medium, where part of their kinetic energy is converted into thermal motion, thereby producing bright forbidden-line emission (e.g., Giannini et al. 2015). To further investigate the origin of the HVCs detected in our sample, we compare their [S ii] and [O i] line ratios to those expected from the shock models of Hartigan & Wright (2015); see Figure 6(b). The model line ratios were calculated for a range of input parameters: log n₀(cm⁻³) = 2–11 with an increment of unity in log scale, X_e = 0.1 and 0.6, V_s = 30–80 km s⁻¹, M_A = 1.5, 4.6, and 10. Here, n₀ is the pre-shock number density of nucleons, X_e is the pre-shock ionization fraction, V_S is the shock velocity, and M_A is the Alfvénic Mach number. We have also scaled the ratios to the atomic abundances used in Section  4.2.1, α(O) = 3.2 × 10⁻⁴ and α(S) = 1.4 × 10⁻⁵, from the original solar abundances in Hartigan & Wright (2015).

Shock models with a pre-shock number density of log n₀(cm⁻³) ∼ 6–7 can reproduce most of the observed SII40/OI63 and OI55/63 HVC line ratios. As forbidden-line emission occurs in the post-shock cooling zone, the specific transition critical density and excitation temperature dictate how close to the front the emitting material is located. For instance, the [O i] λ6300 line probes gas slightly closer to the front than the [S ii] λ6731 line (see, e.g., Figure 3 in Hartigan & Wright 2015), which has a similar excitation temperature but a critical density about 100 times lower. The [S ii] λ4068 line investigated in this work has similar temperature and density to the [O i] λ6300 line and hence should also trace denser/hotter gas closer to the front than the [S ii] λ6731 line.

5.1. Mass Accretion Rates

After flux-calibrating our spectra (see Appendix B), we estimate the accretion luminosity using 12 emission lines covered by the HIRES spectra, including five Balmer lines (Hζ, Hδ, Hγ, Hβ, and Hα), four He i lines (4026, 4471, 5876, and 6678 Å), the He ii line at 4686 Å, and the Ca ii lines at 3934 and 3968 Å. These lines are chosen because their luminosities are known to correlate tightly with accretion luminosities (e.g., Herczeg & Hillenbrand 2008; Fang et al. 2009; Rigliaco et al. 2012; Alcalá et al. 2014, 2017). After computing line luminosities, we convert them into accretion luminosities via the empirical relations listed in Appendix G. Table 5 lists the accretion luminosities derived from the transitions discussed above, as well as the 3σ-clipping mean of the accretion luminosities for each source. Mean accretion luminosities are converted into mass accretion rates using the following relation:

$$\begin{eqnarray}&&{\dot{M}}_{\mathrm{acc}}=\displaystyle \frac{{L}_{\mathrm{acc}}{R}_{\star }}{{\rm{G}}{M}_{\star }\left(1-\tfrac{{R}_{\star }}{{R}_{\mathrm{in}}}\right)},\end{eqnarray} \tag{ 1 }$$

where R_in denotes the truncation radius of the disk, which is taken to be 5R_⋆ (Gullbring et al. 1998), G is the gravitational constant, M_⋆ is the stellar mass, and R_⋆ is the stellar radius. Mass accretion rates are also listed in Table 5. Our sample covers a large range in accretion luminosities and mass accretion rates, from log(L_acc/L_⊙) = −3.48 to 0.72 and from $\mathrm{log}({\dot{M}}_{\mathrm{acc}}/{M}_{\odot }\,{\mathrm{yr}}^{-1})=-10.15$ to −6.12, estimated from the accretion-related emission lines.

Table 5.  Accretion Luminosity and Accretion Rates of the Sources in This Work

		log Lacc
		(Hζ)	(Hδ)	(Hγ)	(Hβ)	(Hα)	(He i λ4026)	(He i λ4471)	(He i λ5876)	(He i λ6678)	(He ii λ4686)	(Ca ii λ3934)	(Ca ii λ3968)	$\mathrm{log}\,\overline{{L}_{\mathrm{acc}}}$	$\mathrm{log}\,{\dot{M}}_{\mathrm{acc}}$
ID	Name	(L⊙)	(L⊙)	(L⊙)	(L⊙)	(L⊙)	(L⊙)	(L⊙)	(L⊙)	(L⊙)	(L⊙)	(L⊙)	(L⊙)	(L⊙)	(M⊙ yr−1)
1	DP Tau	...	−1.74	−1.73	−1.69	−2.17	−1.74	−1.55	−1.91	−1.95	−1.87	−1.35	−1.46	−1.69	−9.07
2	CX Tau	...	...	−2.44	−2.32	−2.62	...	−2.66	−3.12	n	n	...	...	−2.56	−9.37
3	FP Tau	...	−2.32	−2.32	−2.15	−2.16	...	−2.24	−2.53	−2.23	−2.31	...	...	−2.27	−9.17
4	FN Tau	...	−1.50	−1.47	−1.48	−1.87	−1.58	−1.44	−1.33	−1.12	−1.92	...	...	−1.53	−7.97
5	V409 Tau	...	n	n	n	a	n	n	n	n	n	−1.53	−1.79	−1.64	−8.44
6	BP Tau	−0.99	−1.16	−1.19	−1.16	−1.24	−1.25	−1.24	−1.22	−1.18	−1.14	−1.13	−1.02	−1.17	−8.14
7	DK Tau A	−0.67	−0.89	−0.87	−0.76	−1.18	−0.79	−0.98	−0.74	−0.72	−0.74	−0.76	−0.64	−0.79	−7.86
8	HN Tau A	...	−1.10	−1.26	−1.00	−1.92	−0.54	−0.78	−1.46	−0.85	−1.10	−0.89	−0.67	−0.93	−8.37
9	UX Tau A	...	n	n	n	−1.56	n	n	n	n	n	−1.16	−1.46	−1.51	−8.81
10	GK Tau A	...	−1.31	−1.56	−1.34	−1.64	−1.41	−1.47	−1.16	n	−1.30	−0.76	−0.88	−1.38	−8.35
11	GI Tau	...	−0.55	−0.59	−0.89	−1.46	−0.71	−0.68	−0.78	−0.75	−0.64	...	...	−0.69	−7.61
12	DM Tau	...	−1.92	−1.94	−1.89	−1.92	−2.43	−1.91	−1.91	−2.33	−1.93	...	...	−1.92	−8.79
13	LkCa 15	...	−1.70	−1.88	−1.84	−1.65	−1.66	−1.78	−1.51	n	−1.22	...	...	−1.70	−8.75
14	DS Tau	...	−1.30	−1.20	−1.45	−1.67	−1.28	−1.39	−1.12	−0.93	−1.13	−1.76	−1.51	−1.28	−8.42
15	SZ 65	−1.92	−1.87	−2.21	a	...	n	n	−2.76	...	n	−1.66	−1.88	−1.94	−8.90
16	SZ 68A	n	n	n	n	...	n	n	n	...	n	−1.16	−1.20	−1.18	−8.13
17	SZ 73	−1.14	−1.21	−1.29	−1.33	...	−1.22	−1.30	−1.41	...	−1.27	−1.16	−1.05	−1.22	−8.54
18	HM Lup	−1.54	−1.62	−1.64	−1.43	...	−1.69	−1.66	−1.52	...	−1.98	−1.23	−1.29	−1.61	−8.45
19	GW Lup	−1.61	−1.74	−1.80	−1.87	...	−1.84	−1.99	−1.91	...	−1.94	−1.89	−1.96	−1.87	−8.71
20	GQ Lup	−0.32	−0.49	−0.66	−0.40	...	−0.53	−0.61	−0.26	...	−0.51	−0.10	−0.11	−0.36	−7.39
21	SZ 76	−1.92	−2.12	−2.16	−2.52	...	−2.82	−2.82	−3.46	...	n	−1.85	−2.22	−2.23	−8.96
22	RU Lup	−0.34	−0.16	0.03	−0.01	...	b	b	0.11	...	−0.32	0.18	0.13	−0.01	−6.76
23	IM Lup	−1.68	−1.92	a	a	...	n	n	−2.41	...	n	−1.49	−1.72	−1.75	−8.68
24	RY Lup	n	n	n	n	...	n	n	n	...	n	−1.39	−1.40	−1.40	−8.59
25	SZ 102	−2.00	−1.92	−1.91	−1.71	...	−1.81	−1.55	−2.26	...	−1.91	−1.80	−1.57	−1.89
26	SZ 111	−1.49	−1.65	−1.70	−1.86	...	−1.67	−1.82	−1.87	...	−1.69	−1.99	−1.89	−1.74	−8.79
27	SZ 98	−1.39	−1.66	−1.66	−1.53	...	−1.56	−1.80	−1.65	...	−1.50	−1.42	−1.36	−1.53	−8.58
28	EX Lup	0.39	0.53	0.79	0.62	...	b	0.89	0.39	...	0.19	0.99	0.99	0.72	−6.12
29	As 205A	−0.44	−0.26	−0.20	−0.10	...	−0.05	−0.39	0.02	...	−0.30	0.23	0.20	−0.07	−6.58
30	DoAr 21	...	...	...	n	...	...	n	n	...	n	...	...
31	DoAr 24E	...	...	...	n	...	...	n	n	...	n	...	...
32	DoAr 44	−0.64	−0.87	−0.91	−0.66	...	−1.04	−1.30	−0.70	...	−1.20	−0.42	−0.41	−0.73	−8.05
33	SR 21A	n	n	n	n	...	n	n	n	...	n	n	n
34	V853 Oph	−1.21	−1.43	−1.50	−1.48	...	−1.41	−1.39	−1.38	...	−1.43	−1.65	−1.54	−1.46	−8.08
35	RNO 90	−0.01	0.13	−0.01	0.02	...	0.32	0.12	0.05	...	n	...	...	0.06	−7.26
36	V2508 Oph	−0.56	−0.63	−0.70	−0.61	...	−0.76	−0.89	−0.74	...	−0.86	−0.56	−0.50	−0.66	−7.35
37	V1121 Oph	−1.01	−1.39	−1.47	−1.06	...	−1.35	−1.56	−1.10	...	−1.00	−0.90	−0.95	−1.12	−8.30
38	J1842	−1.09	−1.34	−1.42	−1.11	...	−1.33	−1.69	−1.08	...	−1.18	−0.91	−1.11	−1.18	−8.52
39	J1852	−1.62	−1.83	−1.94	−1.61	...	−1.82	n	−1.69	...	−1.49	−1.66	−1.75	−1.69	−9.03
40	VV CrA	−0.22	0.24	0.25	0.12	...	b?	−0.12	−0.65	...	n	1.07	0.70	0.21	−6.43
41	SCrA A + B	a	a	a	a	...	b	−0.75	0.14	...	−0.59	a	a	−0.66	−7.43
42	TW Hya	−1.43	−1.48	−1.42	−1.25	...	−1.68	−1.64	−1.49	...	−1.64	−1.83	−1.79	−1.53	−8.67
43	TWA 3A	−3.51	−3.70	−3.54	−3.58	...	−3.87	−3.84	−3.47	...	n	−3.18	−3.18	−3.48	−10.15
44	V1057 Cygc	n	n	n	n	...	n	n	n	...	n	a	n		∼−4.3
45	V1515 Cygc	n	n	n	n	...	n	n	n	...	n	1.09	a		∼−4.5
46	HD 143006	n	n	n	−0.68	...	n	n	n	...	n	−0.65	b	−0.66	−7.99
47	DI Cep	−0.05	−0.04	0.19	0.53	...	n	0.04	0.27	...	−0.24	0.54	0.45	0.26	−6.97
48	As 353A	n	a	a	a	...	n	0.08	−0.22	...	n	−0.35	a	−0.13	−6.81

Note. In the table, "..." marks the lines that are not covered or fully covered by the extracted spectra, "a" is for the ones that appear as emission but are strongly affected by the absorption due to the winds, "n" is for those that do not clearly appear as emission lines, and "b" is for the ones that are seriously contaminated by other nearby emission lines.

^cFor the two FU Ori objects, their accretion rates are obtained from Green et al. (2006) by fitting the SEDs, assuming a central stellar mass of 1 M_⊙.

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We do not detect any accretion-related emission lines from DoAr 21 (λ = 4420–6300 Å), DoAr 24E (λ = 4420–6300 Å), SR 21A (λ = 3650–6300 Å), and V1057 Cyg (λ = 3650–6300 Å); hence, we do not list their accretion luminosities in Table 5. Note that V1057 Cyg and V1515 Cyg are well-known FU Ori objects. For this class of objects accretion luminosities are best derived from the emission of their self-luminous disks (e.g., Kenyon et al. 1998), and we use the more recent estimates from Green et al. (2006) in our paper. Interestingly, the spectra of DoAr 21 and DoAr 24E do not show any [O i] λ6300 emission, while those of SR 21A show only a marginal detection; see Appendix C for more details. To clarify which sources are truly accreting, we also compare the derived accretion luminosities with typical chromospheric values (see Manara et al. 2017). Only TWA 3A has an accretion luminosity below the chromospheric emission, suggesting that chromospheric activity dominates the line emission.

Figure 7(a) compares the distribution of accretion rates for full disks (gray-filled histogram) and TDs (hatch-filled histogram). The K-S test returns a low probability (P ∼ 1.8 × 10⁻⁵) for the full disks and TDs to be drawn from the same parent population. The accretion rates of TDs are systematically lower than those of full disks with a median value of 1.6 × 10⁻⁹ M_⊙ yr⁻¹, about seven times lower than that of the full disks in our sample. A similar result is reported in Najita et al. (2015) when comparing full and transition disks in Ophiuchus and Taurus. Figure 7(b) compares the distribution of stellar masses. The K-S test gives a 55% probability that the two samples are drawn from the same stellar mass distribution; hence, the difference in accretion rates most likely relates to their different evolutionary stage.

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5.2. Correlation between [O i] and Accretion Luminosity

Previous work has shown that the [O i] λ6300 line luminosity correlates with stellar properties like stellar and accretion luminosity but not with X-ray luminosity (e.g., Rigliaco et al. 2013; Nisini et al. 2018). Here, we repeat the analysis by combining our sample with that of Nisini et al. (2018), as they cover a large range in stellar properties, and by implementing the new Gaia distances (Bailer-Jones et al. 2018) for all samples. Our goal is to clarify which correlations are present and provide the most up-to-date relations with accurate distances for individual sources.

Figures 8(a) and (b) show the relationship between the LVC (NC+BC) and HVC [O i] λ6300 line luminosity versus the accretion luminosity. The Spearman's rank correlation coefficients for the LVCs and HVCs are 0.79 and 0.55, respectively, with a probability lower than 5 × 10⁻⁵ that the data are uncorrelated. We perform outlier-resistant two-variable linear regressions including only the detections¹⁴ and obtain the following relationships:

$$\begin{eqnarray}&&\mathrm{log}\,{L}_{\mathrm{OI}63,\mathrm{LVC}}=(0.60\pm 0.03)\mathrm{log}\,{L}_{\mathrm{acc}}-(4.07\pm 0.06)\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&\mathrm{log}\,{L}_{\mathrm{OI}63,\mathrm{HVC}}=(0.72\pm 0.07)\mathrm{log}\,{L}_{\mathrm{acc}}-(3.90\pm 0.11).\end{eqnarray} \tag{ 3 }$$

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The slope for the L_OI63,LVC versus L_acc in this work is similar to those (0.52 ± 0.07, 0.59 ± 0.04) in Rigliaco et al. (2013) and Nisini et al. (2018), but much flatter than the one (0.81 ± 0.09) in Natta et al. (2014), which could be due to their smaller sample size. Our L_OI63,HVC versus L_acc slope is also similar to the one (0.75 ± 0.08) in Nisini et al. (2018), but slightly flatter than the one (∼0.9) in Rigliaco et al. (2013). The L_OI63,HVC versus L_acc slope is steeper than the L_OI63,LVC versus L_acc slope with a 2σ confidence, consistent with the findings in Rigliaco et al. (2013). Note that, using only our sources, we find the same slopes as those reported in Equations (2) and (3) within the (now larger) uncertainties (0.60 ± 0.06 and 0.62 ± 0.16).

For our sources we can further correlate the line luminosity of individual LVC components with L_acc; see Figure 9. The Pearson correlation coefficients for the LVC-NC and LVC-BC are 0.71 and 0.92 with two-sided p-values of 1.4 × 10⁻⁴ and 7.6 × 10⁻¹⁰, respectively. This means that their luminosities are correlated with the accretion luminosity, with the LVC-BC displaying a higher correlation than the NC and the total LVC (see Figure 8(a)). The outlier-resistant two-variable linear regression gives the following relations:

$$\begin{eqnarray}&&\mathrm{log}\,{L}_{\mathrm{OI}63,\mathrm{LVC}\mbox{--}\mathrm{BC}}=(0.51\pm 0.05)\mathrm{log}\,{L}_{\mathrm{acc}}-(4.22\pm 0.07)\end{eqnarray} \tag{ 4 }$$

$$\begin{eqnarray}&&\mathrm{log}\,{L}_{\mathrm{OI}63,\mathrm{LVC}\mbox{--}\mathrm{NC}}=(0.49\pm 0.10)\mathrm{log}\,{L}_{\mathrm{acc}}-(4.53\pm 0.14).\end{eqnarray} \tag{ 5 }$$

The L_{OI63,LVC–BC} and the L_{OI63,LVC–NC} versus L_acc slopes are the same within the uncertainties.

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5.3. Inner Disk Evolution Traced by the [O i] Emission

The evolutionary stage of a star+disk system is often assessed from its SED. However, optical forbidden lines can aid in understanding the evolutionary stage of a system by probing the evolution of the gas content (see, e.g., Figure 5 in Ercolano & Pascucci 2017).

The frequency of different [O i] λ6300 line components differs for full and TDs; see Table 6, where we provide statistics¹⁵ for our sample. Full disks more frequently than TDs show an HVC in their [O i] λ6300 profiles,¹⁶ as well as a BC accompanied by an NC. In contrast, TDs more frequently than full disks present only an LVC-NC or LVC-BC. In addition, TDs have simpler line profiles: ∼81% (13/16) of our TDs only show one LVC-NC or one LVC-BC without any other LVC or HVCs components, while this fraction is down to 24% (7/29) for the full disks;¹⁷ see also Figures 16 and 17 in Appendix A. With a larger sample of 65 T Tauri stars, Banzatti et al. (2018) also find that those surrounded by a TD tend to show only a single component in their [O i] λ6300 line profile (see their Section 5.5 for details). The much lower fraction of TDs with an HVC and a BC+NC with respect to full disks might indicate an evolution in disk winds (see also Ercolano & Pascucci 2017). The TDs in our sample have lower mass accretion rates than full disks, and hence lower HVC and LVC luminosities (Figure 8), and likely a more depleted inner gas disk. As also suggested in Banzatti et al. (2018), winds in TDs might be launched from larger radii, have a larger opening angle, and not recollimate into jets.

Table 6.  Statistics on the Line Profiles

	Only NC	Only BC	NC+BC	HVC
Full disks	28% (8/29)	24% (7/29)	24% (7/29)	72% (21/29)
TDs	44% (7/16)	44% (7/16)	13% (2/16)	13% (2/16)

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Furthermore, the [O i] λ6300 line profiles can be used to distinguish the evolutionary stage of systems with similar SEDs. An example is shown in Figure 10 for LkCa 15 and J1842, both classified as TDs. The central stars have similar spectral types (K5.5 vs. K3) and accretion rates (1.8 × 10⁻⁹ vs. 3.0 × 10⁻⁹ M_⊙ yr⁻¹), and their disks present very similar SEDs. However, their forbidden-line profiles are clearly different: LkCa 15 only presents an LVC-BC (with an FWHM, 44.6 km s⁻¹, near the boundary to separate the LVC-NCs and LVC-BCs) in the [O i] λ6300, while J1842 shows an LVC-NC, an LVC-BC, and an HVC in both the [S ii] λ4068 and [O i] λ6300 lines and an LVC-NC and an LVC-BC in the [O i] λ5577 line. Thus, while both sources would appear to be in the same evolutionary stage based on their SED, the forbidden-line profiles demonstrate that the inner gaseous disk of LkCa 15 is in a more evolved stage than that of J1842.

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5.4. Mass Outflow Rates

Previous analysis of [O i] λ6300 high-resolution spectra has demonstrated that a significant number of LVC-BC and LVC-NC peak centroids are blueshifted with respect to the stellar velocity (Simon et al. 2016; Banzatti et al. 2018; McGinnis et al. 2018). With the largest blueshifts found in sources surrounded by lower-inclination disks and an emitting region within ∼0.5 au from the star, Simon et al. (2016) attributed the LVC-BC to the base of an MHD-driven wind. Although the focus of our paper is on forbidden-line luminosities and line ratios, here we show that the kinematics of the LVC-BC and LVC-NC of our sample are consistent with previous findings.

The top panel of Figure 11 shows the distribution of the NC and BC centroids. About 63% (15/24) of NCs and 57% (13/23) of BCs have blueshifts larger than 1.5 km s⁻¹, while only 8% (2/24) of NCs and 22% (5/23) of BCs are redshifted by more than 1.5 km s⁻¹. The larger proportion of blueshifts when compared to no shift or redshifts is consistent with a wind origin for both components. The bottom panel of Figure 11 shows the relation between disk inclination and the BC and NC FWHMs, corrected for instrumental broadening and normalized by stellar mass.

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If we attribute the line width primarily to Keplerian broadening as in previous studies (Simon et al. 2016; McGinnis et al. 2018), most BCs trace radii within 0.5 au, while NCs probe gas farther out but mostly within ∼5 au. A few sources appear as outliers in this plot and are worth discussing. First, the FWHMs from DK Tau A and RU Lup are much larger than those expected from pure Keplerian rotation using the disk inclinations given in Table 1. The disk inclination of DK Tau A is not well constrained: the 20° value we adopted here comes from the analysis of millimeter CO lines, but the continuum emission points to a much higher inclination of 65° (Simon et al. 2017). In the case of RU Lup the outer disk inclination of 3° derived from ALMA millimeter imagery may not apply to the forbidden lines studied here. Indeed, spectroastrometry in the CO rovibrational band suggests a higher inclination of 35° for the inner disk (Pontoppidan et al. 2011), and an even higher inclination is implied by MIDI visibilities (see Varga et al. 2018 and Banzatti et al. 2018 for further details). If we use these alternative/higher disk inclinations, the BC FWHM of DK Tau A falls in the same region as the other BCs, and that of RU Lup becomes much closer to that region. Finally, the BCs from LkCa 15, SZ 73, RNO 90, and VV CrA fall within the domain of LVC-NC; they could have been misclassified using our stringent cut in FWHM that does not take into account disk inclination.

Having established that our sample supports the scenario in which LVC-BC and LVC-NC trace a wind and their FWHMs are consistent with being broadened by Keplerian rotation, we use the [O i] λ6300 luminosity and our constraints on the gas temperature, velocity, and emitting radii to compute wind mass-loss rates. Figure 6(a) shows that electron densities n_e ≥ 3 × 10⁶ cm⁻³ are needed to reproduce the measured LVC line ratios. As these densities are larger than the [O i] λ6300 critical density, which is 1.8 × 10⁶ cm⁻³, the LVC emitting gas is most likely in LTE. In addition, very high densities are required to make the [O i] λ6300 line optically thick (see Table 9 in Hollenbach & McKee 1989). Hence, we will use equations for optically thin LTE gas to relate the LVC [O i] λ6300 luminosity to a gas mass. As a shock origin is more likely for the HVC emission and this lower-density gas may not be in LTE (see Section 4.2.2 and Figure 6(b)), we will use equations derived for radiative shocks to estimate the mass-loss rate from this HVC.

5.4.1. Mass-Loss Rates from the LVC

As the [O i] λ6300 line is optically thin, its luminosity (L₆₃₀₀) can be written as

$$\begin{eqnarray}&&{L}_{6300}={N}_{{\rm{u}}}\,A\,h\nu ,\end{eqnarray} \tag{ 6 }$$

where N_u is the total number of O atoms in the upper ${}^{1}{D}_{2}$ level, A is the transition probability (6.503 × 10⁻³ s⁻¹), and hν is the associated energy they emit (Dere et al. 1997). In addition, for gas in LTE the total number of O atoms (N) is related to N_u as

$$\begin{eqnarray}&&{N}_{{\rm{u}}}=N\,\displaystyle \frac{{g}_{u}\,{e}^{-h\nu /{kT}}}{Z(T)},\end{eqnarray} \tag{ 7 }$$

where g_u is the upper-level statistical weight, k is the Boltzmann constant, T is the gas temperature, and Z(T) is the partition function at temperature T. We calculate Z(T) assuming a five-level oxygen atom. Considering that in disks the abundance of neutral oxygen is reduced because half of the cosmic O is in silicate grains (Jenkins 2009) and the wind is launched from outside the dust sublimation radius (Figure 11 lower panel), we take α(O) = 3.2 × 10⁻⁴ to calculate the total mass of gas M from the total number of O i atoms. Finally, the mass-loss rate ${\dot{M}}_{\mathrm{wind}}$ can be written as

$$\begin{eqnarray}&&{\dot{M}}_{\mathrm{wind}}=M\displaystyle \frac{{V}_{\mathrm{wind}}}{{l}_{\mathrm{wind}}},\end{eqnarray} \tag{ 8 }$$

where V_wind and l_wind are the velocity and wind height, respectively. We further write the unconstrained wind height as l_wind = f × r_base, i.e., the wind vertical extent is f times the emitting radius at the base of the wind. Combining Equations (6) through (8), we have

$$\begin{eqnarray}\begin{array}{rcl}{\dot{M}}_{\mathrm{wind}} & = & \displaystyle \frac{{V}_{\mathrm{wind}}}{{l}_{\mathrm{wind}}}\displaystyle \frac{\eta {m}_{{\rm{H}}}}{\alpha ({\rm{O}})}\,{e}^{h\nu /{kT}}Z(T)\displaystyle \frac{{L}_{6300}}{{g}_{{\rm{u}}}\,A\,h\nu }\\ & = & {\rm{C}}({\rm{T}})\left(\displaystyle \frac{{V}_{\mathrm{wind}}}{10\,\mathrm{km}\,{{\rm{s}}}^{-1}}\right){\left(\displaystyle \frac{{l}_{\mathrm{wind}}}{1\mathrm{au}}\right)}^{-1}\left(\displaystyle \frac{{L}_{6300}}{{L}_{\odot }}\right){M}_{\odot }\,{\mathrm{yr}}^{-1},\end{array}\end{eqnarray} \tag{ 9 }$$

where η = 1.34 is the ratio of total gas mass to hydrogen mass. From this equation it is clear that the estimated mass-loss rate has a strong dependence on the gas temperature T and scales linearly with V_wind and l_wind. LVC gas temperatures range from 5000 to 10,000 K (Section 4.2.1), and within this range C(T) varies by an order of magnitude: from 2.4 × 10⁻⁴ for T = 5000 K down to 2.6 × 10⁻⁵ for T = 10,000 K.

For each source with an [O i] λ6300 detection we calculate its own ${\dot{M}}_{\mathrm{wind}}$ by taking as V_wind the median of projected peak velocities and as r_base the Keplerian radius from half of the line FWHM, corrected for the instrumental broadening and projected (see Figure 11, bottom panel). For the BC these values correspond to −15 km s⁻¹ and 0.15 au, while for the NC they are −6 km s⁻¹ and 1.7 au.¹⁸ We then divide ${\dot{M}}_{\mathrm{wind}}$ by each source ${\dot{M}}_{\mathrm{acc}}$ and show in Figure 12 how the median and upper- and lower-quartile ratios depend on T and l_wind. As expected from Equation (9), ${\dot{M}}_{\mathrm{wind}}$, and hence ${\dot{M}}_{\mathrm{wind}}/{\dot{M}}_{\mathrm{acc}}$ ratios, increase with decreasing gas temperature and wind height. Since the extent of the [O i] λ6300 emitting region is unknown, we vary the factor f within a range of plausible values for which l_wind is similar in the LVC-BC and LVC-NC.

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For the BC, f = 1 produces unreasonably large ${\dot{M}}_{\mathrm{wind}}/{\dot{M}}_{\mathrm{acc}}$ ratios for most temperatures, except for 10,000 K. However, such a high temperature is unlikely; otherwise, emission lines from ionized oxygen would have been also easily detected (see Section 5.7 in Simon et al. 2016). Heating processes not driven by photons (e.g., ambipolar drift heating; see Safier 1993) could result in higher gas temperatures without affecting the ionization state, but their efficiency has not been sufficiently explored in this context. We will further discuss the implications of Figure 12 in Section 6. However, it is already worth noting that, for likely wind extents, the mass-loss rates implied by the BC are much higher than those implied by the NC. This results from the fact that [O i] λ6300 luminosities, as well as the median peak centroid, are larger for the LVC-BC than for the LVC-NC (see Figures 9 and 11), and the wind heights of the NC are likely higher than for the BC.

This last point is important; hence, we summarize here additional arguments supporting a large vertical extent of the LVC-NC. First, it is highly unlikely that the wind height of the LVC-NC is small (f < 1) compared to the Keplerian radius because with our high-resolution (Δv ∼ 6 km s⁻¹) spectra we would see double-peaked NC profiles. Next, as we will discuss, it is very likely that the extent of the NC is larger than that of the BC. The LVC-BC traces an MHD wind because of its small Keplerian radius (0.05–0.5 au) and blueshifted centroids; thermal pressure is insufficient to launch the gas flow, and MHD forces are required. The NC may similarly also trace an MHD wind and being further out than the BC is likely to be more vertically extended. If the LVC-NC is partly supported by a photoevaporative (thermal) wind, it should be even more extended vertically given the gas temperature (5000–10,000 K) inferred from the line ratios (see Figure 6). As an example, in the X-ray-driven photoevaporative wind model (Ercolano & Owen 2016), the winds can extend to about 35 au above the disk. While the wind height cannot be determined without spatially resolved observations, our finding that the mass-loss rates implied by the BC are higher than those implied by the NC should be reliable.

5.4.2. Mass-loss Rates from the HVC

As discussed in Section 4.2.2, shock models reproduce most of the [O i] and [S ii] HVC line ratios. In fast shocks, most of the mechanical energy of the pre-shock gas is converted into heat (e.g., Hollenbach & McKee 1979; Shull & McKee 1979). The mass-loss rate can then be estimated assuming that a certain fraction of the kinetic energy is radiated away in the [O i] λ6300 line. Hence, we use the equations for radiative shocks as presented, e.g., in Hollenbach & Gorti (2009). If the hydrogen density is high (n_H ∼ 10⁶ cm⁻³), the line luminosity can be computed as

$$\begin{eqnarray}&&{L}_{6300}=\displaystyle \frac{{y}_{0}}{2}{\dot{M}}_{\mathrm{loss}}{V}_{{\rm{s}}}^{2},\end{eqnarray} \tag{ 10 }$$

with y₀ being the fraction of cooling that goes into the [O i] λ6300 line and V_s being the shock velocity. The mass-loss rate is then

$$\begin{eqnarray}&&{\dot{M}}_{\mathrm{jet}}={L}_{6300}\displaystyle \frac{2}{{y}_{0}}{V}_{{\rm{s}}}^{-2}.\end{eqnarray} \tag{ 11 }$$

At a density n_H ∼ 10⁶ cm⁻³, y₀ is around 0.1–0.3; hence, we take here y₀ = 0.2. As for the LVC, we first compute individual ${\dot{M}}_{\mathrm{jet}}$, divide them by each source ${\dot{M}}_{\mathrm{acc}}$, and show the behavior of median and upper- and lower-quartile ratios for a range of shock velocities compatible with observations (e.g., Hartigan et al. 1987). The faster the shock velocity, the lower the ${\dot{M}}_{\mathrm{jet}}/{\dot{M}}_{\mathrm{acc}}$ ratio. For a typical shock velocity of 30 km s⁻¹ (Hartigan et al. 1994), the median ${\dot{M}}_{\mathrm{jet}}/{\dot{M}}_{\mathrm{acc}}$ ratio is around 0.1.

The approach we have taken above differs from the one typically used in the literature, where it is assumed that the jet has uniform properties within the slit width and the line luminosity is calculated from a collisional excitation model akin to that described in Section 4.2.1 for the LVC (see also Figure 6, left panel). More specifically, and following Hartigan et al. (1995) and Nisini et al. (2018), the mass-loss rate from the jet can be written as

$$\begin{eqnarray}&&{\dot{M}}_{\mathrm{jet}}=C(T,{n}_{{\rm{e}}})\left(\displaystyle \frac{{V}_{\perp }}{100\,\mathrm{km}\,{{\rm{s}}}^{-1}}\right){\left(\displaystyle \frac{{l}_{\perp }}{100\mathrm{au}}\right)}^{-1}\left(\displaystyle \frac{{L}_{6300}}{{L}_{\odot }}\right){M}_{\odot }\,{\mathrm{yr}}^{-1},\end{eqnarray} \tag{ 12 }$$

where V_⊥ is the component of the jet velocity in the plane of the sky (we assume 100 km s⁻¹ as Nisini et al. 2018) and l_⊥ is the projected size of the slit aperture (0861) on the plane of the sky. C(T, n_e) depends on the gas temperature and electron density and is calculated assuming a five-level oxygen atom as in Section 4.2.1. For T = 10,000 K, C(T, n_e) are 9.0 × 10⁻⁵, 6.1 × 10⁻⁵, and 4.6 × 10⁻⁵ for n_e = 5.0 × 10⁴, 7.5 × 10⁴, and 1.0 × 10⁵ cm⁻³, respectively. Taking the same temperature (10,000 K) and electron density (5.0 × 10⁴ cm⁻³) as Nisini et al. (2018), we find a median ${\dot{M}}_{\mathrm{jet}}/{\dot{M}}_{\mathrm{acc}}$ ratio of ∼0.1. The right panel of Figure 13 also shows the ${\dot{M}}_{\mathrm{jet}}/{\dot{M}}_{\mathrm{acc}}$ for the [O i] λ6300 detected HVCs in Nisini et al. (2018) after implementing the new Gaia distances (Bailer-Jones et al. 2018) and assuming α(O) = 3.2 × 10⁻⁴, T = 10,000 K, and n_e = 5.0 × 10⁴ cm⁻³. The median ${\dot{M}}_{\mathrm{jet}}/{\dot{M}}_{\mathrm{acc}}$ ratio is ∼0.18 for this sample.¹⁹ Furthermore, the same panel shows the dependence of ${\dot{M}}_{\mathrm{jet}}/{\dot{M}}_{\mathrm{acc}}$ on T and n_e: the ratio decreases with increasing gas temperature and electron density. For values of T ∼ 7000–15,000 K and n_e = (2–6) × 10⁴ cm⁻³ that are appropriate for the base of the T Tauri jets (Hartigan & Morse 2007; Agra-Amboage et al. 2011; Giannini et al. 2013; Maurri et al. 2014), the median ${\dot{M}}_{\mathrm{jet}}/{\dot{M}}_{\mathrm{acc}}$ ratios vary from 0.8 to 0.04.

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It is already well established that the HVC and the LVC of forbidden lines trace different physical environments, where the HVC is more spatially extended and formed in shock-excited collimated jets, and the LVC, with a higher density than the HVC, is confined to scales of less than 5 au (e.g., Hartigan et al. 1995; Hirth et al. 1997; Simon et al. 2016). Our study expands on the literature by combining the [S ii] λ4068 transition with the well-studied [O i] λ6300 and [O i] λ5577 lines, demonstrating that the same kinematic components appear in all three lines, thus enabling the use of component line ratios to constrain the properties of the emitting gas (Section 4.1 and Figure 5). By including detections and upper limits, we found that the HVC SII40/OI63 ratios are statistically higher than the LVC (both BC and NC) and that there is a low probability that the BC OI55/63 ratios are drawn from the same parent population as the NC and HVC (Table 4). These differences and the mean line ratios of the three components corroborate previous suggestions, mostly based on kinematics (e.g., Simon et al. 2016; Banzatti et al. 2018; McGinnis et al. 2018), that the LVC-BC traces a higher density/hotter region than the LVC-NC, probably the base of an MHD disk wind. Finally, we could show that thermally excited gas with temperatures of 5000–10,000 K and electron densities of ∼10⁷–10⁸ cm⁻³ can explain most of the LVC-BC and LVC-NC line ratios, while the HVC ratios are best reproduced by radiative shock models where forbidden lines arise in the hot (∼7000–10,000 K) but less dense (total H density ∼10⁶ cm⁻³) post-shock cooling zone (Sections 4.2.1 and 4.2.2).

Armed with the physical properties of the emitting gas in each component, we computed mass-loss rates for the LVC-BC, LVC-NC, and HVC (Section 5.4). To evaluate the efficiency of winds in removing disk mass, we also computed mass accretion rates by converting the luminosity of several permitted lines covered in our spectra to the accretion luminosity (Section 5.1). For the HVC, we relied on radiative shock models that convert a fraction of the mechanical energy of the pre-shock gas into the [O i] λ6300 luminosity. We found relatively low ${\dot{M}}_{\mathrm{jet}}/{\dot{M}}_{\mathrm{acc}}$ with a median value of ∼0.1 for typical shock velocities of 30 km s⁻¹, but this ratio could be as low as 0.01 for a high shock velocity of 100 km s⁻¹ or as high as 0.3 for a low shock velocity of 20 km s⁻¹. These values are similar to those previously reported in the literature, which were instead calculated assuming a collisional excitation model, and hence sensitive to several not well-constrained quantities such as gas temperature and electron density in addition to jet velocity (e.g., Hartigan et al. 1995; Nisini et al. 2018; see also Section 5.4.2).

A first estimate for mass-loss rates for the LVC, assuming a spherical outflow geometry, comes from Natta et al. (2014), who find ${\dot{M}}_{\mathrm{wind}}/{\dot{M}}_{\mathrm{acc}}$ between 0.1 and 1 for their sample of T Tauri stars in Lupus and σ Ori. These values are on the high end of the HVC ${\dot{M}}_{\mathrm{jet}}/{\dot{M}}_{\mathrm{acc}}$ ratios, suggesting that the LVC may have a higher mass-loss rate than the jet. Our work is the first to provide ${\dot{M}}_{\mathrm{wind}}/{\dot{M}}_{\mathrm{acc}}$ separately for the BC and NC. One important finding is that the mass-loss rate from the BC exceeds that from the NC by at least a factor of 5. A comparison of the mass-loss rates between the BC and HVC is more uncertain. To this end we explored the sensitivity of wind mass-loss rates in thermally excited gas to the parameters that are the least constrained and most affect the estimates, namely, the gas temperature and l_wind (Section 5.4.1). For the BC, a wind extent equal to the radial extent inferred from Keplerian broadening of the [O i] λ6300 lines (f = 1, Figure 12, left panel) provides unreasonably large ${\dot{M}}_{\mathrm{wind}}/{\dot{M}}_{\mathrm{acc}}$, i.e., larger than 1, for most sources. Most likely the vertical extent of the BC, which remains unconstrained from our data, is larger than the Keplerian radius inferred from the BC FWHM. If we assume a vertical extent comparable to the NC radius inferred from Keplerian broadening (f = 1, Figure 12, right panel; and f = 10, Figure 12, left panel), the median ${\dot{M}}_{\mathrm{wind}}/{\dot{M}}_{\mathrm{acc}}$ from the BC ranges from ∼0.05 for gas as hot as 10,000 K up to ∼0.4 for gas at 5000 K. As already discussed in Section 5.4.1, a temperature of 10,000 K is unlikely for the LVC gas; hence, higher mass-loss rates are more realistic. However, given the sensitivity of ${\dot{M}}_{\mathrm{wind}}/{\dot{M}}_{\mathrm{acc}}$ on l_wind, we cannot conclusively state that the LVC-BC is carrying away more mass than the HVC. What is more certain is that the NC ${\dot{M}}_{\mathrm{wind}}/{\dot{M}}_{\mathrm{acc}}$ is lower than the BC for reasonable l_winds by at least a factor of 5. Thus, most of the disk mass appears to be lost close to the central star in the region traced by the BC.

How do our results compare with theoretical models of winds? Both photoevaporative and MHD winds have been proposed to explain forbidden-line emission. However, as already pointed out by Simon et al. (2016) and confirmed by McGinnis et al. (2018) and Banzatti et al. (2018), the only component that may be tracing a thermal photoevaporative wind is the LVC-NC, as the BC is formed well inside the gravitational potential well of the star. Our findings that most NC ratios can be reproduced by thermally excited gas and that the line luminosity correlates with accretion luminosity agree with the most recent predictions from X-ray-driven photoevaporative winds (Ercolano & Owen 2016). In these models, stellar EUV photons heat the forbidden-line-emitting region and, due to their low penetration depth, constrain it to a thin vertically extended (up to ∼35 au) zone above the inner disk (see, e.g., their Figure 4). In addition, Ercolano & Owen (2016) claim that most of the EUV luminosity comes from accretion and that would lead to a correlation between the [O i] luminosity and L_acc. The vertical extent of the emitting region results in a wide range of wind velocities that can broaden the [O i] lines up to ∼30 km s⁻¹ for close to edge-on disks while keeping moderate blueshifts of up to ∼7 km s⁻¹ for disks inclined by ∼50° with respect to the observer.²⁰ While the predicted FWHM and peak centroids are consistent with most of the LVC-NC values we report here, more detailed kinematic comparisons disfavor a thermal outflow origin because several [O i] λ6300 widths are still larger than predicted (Banzatti et al. 2018; McGinnis et al. 2018), the largest observed blueshifts occur for a lower disk inclination than predicted, and the centroids of the BC and NC are correlated (see Banzatti et al. 2018 for further details). For these reasons we favor a similar origin for both the BC and the NC in an MHD wind.

MHD wind models come in two broad categories: (1) winds arising close to the corotation radius (≤0.1 au), such as X-winds (e.g., Shang et al. 2007), conical winds (e.g., Romanova et al. 2009), magnetospheric ejections (e.g., Zanni & Ferreira 2009), or accretion-powered stellar winds (e.g., Matt & Pudritz 2005), and (2) winds arising over a broad range of radii in the disk, from 0.1 to 10 au, sometimes called D-winds (e.g., Pudritz et al. 2007). A key difference between these two genres of models is that the former are important in removing angular momentum from the accreting star, enabling it to spin down, and the latter in removing angular momentum from the disk itself, enabling accretion to occur through the disk rather than relying on some kind of magnetic viscosity (e.g., MRI). Note that these types of winds are not mutually exclusive. All of these scenarios can reproduce the terminal velocity of the fast (∼100 km s⁻¹) outflowing gas traced by the HVC. However, only D-winds can account for the high angular resolution observations showing a decrease in outflow velocity with increasing jet radius, implying an "onion-like" layering of a faster flow engirdled by a slower flow (e.g., Bacciotti et al. 2000, 2002; Pyo et al. 2002, 2003; Takami et al. 2004; Beck et al. 2010; Agra-Amboage et al. 2011). Also, D-winds provide a natural explanation for possible rotation signatures in jets, implying wind footpoints spanning a large range of disk radii, from ∼0.1 to 5 au (e.g., Ferreira et al. 2006; Cabrit 2009).

Our results provide strong support for the presence of D-winds, although they do not help in determining whether D-winds are the dominant contributor to the jet traced by the HVC, or whether the jet is primarily fed by an MHD wind from near the corotation radius. However, the Keplerian radii for the BC inferred from their FWHM are larger than the corotation radii (∼0.05 au), and the ones for NCs are well beyond the corotation radii, implying a large range of wind radii (from ∼0.05 out to 5 au), similar to those expected in D-winds and inferred from jet rotation signatures. The observed correlation between the [O i] line and accretion luminosity might indicate that the wind truly drives accretion: as the [O i] λ6300 line is optically thin, a higher luminosity implies more mass removed in the wind, and hence more angular momentum promoting mass accretion from the disk onto the central star.

Another prediction from some D-wind models is that most of the mass is lost within a few au from the central star (e.g., Pelletier & Pudritz 1992), in agreement with our finding that the BC has larger ${\dot{M}}_{\mathrm{wind}}/{\dot{M}}_{\mathrm{acc}}$ than the NC. This last result also places interesting constraints on more recent disk simulations that include nonideal MHD effects (e.g., Bai 2014; Gressel et al. 2015; Béthune et al. 2017 ). These simulations show that disk winds are launched from radii extending out to ∼10–20 au with vigorous mass-loss rates out to these radii (see also Bai 2017). However, even for gas at 5000 K we obtain an ${\dot{M}}_{\mathrm{wind}}/{\dot{M}}_{\mathrm{acc}}$ of 0.4 from the upper quartile of the f = 1 LVC-NC curve (Figure 12, right panel), suggesting that the mass-loss rate is not as large as predicted out to the ∼5 au radii we can trace with the NC. If the theoretically predicted winds exist, most of the gas must be cooler (<5000 K) than what can be traced with the forbidden lines analyzed here. Other wind diagnostics that can probe cooler neutral hydrogen in the flow would be valuable in determining the presence of more extended disk winds.

We analyzed optical high-resolution spectra, covering the [S ii] λ4068, [O i] λ5577, and [O i] λ6300 forbidden lines, from a sample of 48 T Tauri stars, 31 of which are surrounded by full disks and 17 by TDs. We detected the [O i] λ6300 from 45 sources, the [O i] λ5577 from 26 sources, and the [S ii] λ4068 from 22 sources. Following Simon et al. (2016), we decomposed the line profiles into HVC, LVC-NC, and LVC-BC. As in previous studies, we attribute the line width primarily to Keplerian broadening, with forbidden emission arising in both the inner (BC within 0.5 au) and outer (NC within 1–5 au) disk. Many components show peak centroids blueshifted by more than 1.5 km s⁻¹ with respect to the stellar velocity. Thus, the LVC is most likely tracing unbound slow wind gas. After flux-calibrating our spectra, we derived line luminosity and line ratios for individual kinematic components to assess the properties of the emitting gas and with the goal of measuring mass-loss rates. We also estimated mass accretion rates using 12 accretion-related permitted lines to then evaluate the mass loss over mass accretion rate. Our main results can be summarized as follows:

• 1.  
  About 72% of full disks present an HVC, while this number is down to 13% for TDs. Furthermore, TDs more frequently than full disks show only an LVC-NC (44% for TDs vs. 28% for the full disks), while full disks tend to show line profiles with multiple components. These findings point to a depletion of gas in the inner disk of TDs, in agreement with their lower average mass accretion rate.
• 2.  
  The HVC and LVC [O i] λ6300 luminosity is confirmed to correlate with the accretion luminosity. When the [O i] λ6300 LVC is decomposed into LVC-BC and NC, we see that the LVC-BC luminosity is more tightly correlated with accretion luminosity than the NC.
• 3.  
  The profiles of individual kinematic components are similar in the [S ii] λ4068, [O i] λ5577, and [O i] λ6300 lines, when detected. This indicates that they trace a similar region; hence, their line ratios can be used to infer the physical properties of the emitting gas.
• 4.  
  The HVC has statistically different SII40/OI63 ratios than the LVC-BC and NC. Its OI55/63 ratios are also statistically different from the LVC-BC, while they are not distinguishable from the LVC-NC. These differences and the mean line ratios corroborate previous suggestions that the BC traces hot/dense gas close to the base of an MHD wind.
• 5.  
  Most LVC-BC and NC ratios can be explained by thermally excited gas with electron densities of ∼10⁷–10⁸ cm⁻³ and temperatures of 5000−10,000 K. HVC line ratios are better explained by shock models with a pre-shock number density of nucleons of ∼10⁶–10⁷ cm⁻³.
• 6.  
  Building on the [O i] λ6300 HVC luminosity, converting a fraction of the shock mechanical energy into radiant energy, and adopting a typical shock velocity of 30 km s⁻¹, we find a median ${\dot{M}}_{\mathrm{jet}}/{\dot{M}}_{\mathrm{acc}}$ ratio of 0.1. This value is comparable to previous results from the literature that were calculated with a very different approach. The agreement between these different approaches to convert HVC luminosity into a mass outflow rate suggests that this ratio may be robust. An ${\dot{M}}_{\mathrm{jet}}/{\dot{M}}_{\mathrm{acc}}$ of 0.1 reflects a minimal impact on disk mass removal by outflowing material seen in the jet.
• 7.  
  Building on our finding that the [O i] LVC emission is most likely thermal, gas is in LTE, and the [O i] λ6300 line is optically thin, we estimate for the first time ${\dot{M}}_{\mathrm{wind}}/{\dot{M}}_{\mathrm{acc}}$ ratios separately for the BC and NC. We show that ${\dot{M}}_{\mathrm{wind}}$ is a factor of 5 higher in the BC (inner disk) than the NC (outer disk). However, absolute ${\dot{M}}_{\mathrm{wind}}$ values are sensitive to the gas temperature and wind height, making direct comparisons between outflow rates in the LVC and the HVC uncertain. However, for plausible wind heights, we find that the mass flowing out in the BC is likely at least as large as in the HVC and may be considerably higher. If so, then the inner disk wind traced by the BC may play an important role in the evolution of the disk mass.

Taken together, our results favor D-wind models. In particular, we find that winds are launched from a range of disk radii beyond the gas corotation radius even in the LVC-BC alone. In addition, most of the mass is lost close to the star, within a few au. For plausible wind heights, LVC-NC ${\dot{M}}_{\mathrm{wind}}/{\dot{M}}_{\mathrm{acc}}$ ratios are lower than ∼0.4, and thus lower than the ratios predicted by recent nonideal MHD simulations for radii of ∼1–20 au (e.g., Bai 2017). Additional wind diagnostics tracing cooler gas would be helpful to test whether indeed radially extended winds could drive accretion.

We thank Kelle Cruz and Scott Dahm for doing the observations with Keck/HIRES. I.P., U.G., and S.E. acknowledge support from a Collaborative NSF Astronomy & Astrophysics Research Grant (ID:1715022, ID:1713780, and ID:1714229). This material is based on work supported by the National Aeronautics and Space Administration under agreement no. NNX15AD94G for the program "Earths in Other Solar Systems." The results reported herein benefited from collaborations and/or information exchange within the NASA Nexus for Exoplanet System Science (NExSS) research coordination network sponsored by NASA's Science Mission Directorate. The data presented here were obtained at the W. M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California, and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation. The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Maunakea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain. This research has made use of the Keck Observatory Archive (KOA), which is operated by the W. M. Keck Observatory and the NASA Exoplanet Science Institute (NExScI), under contract with the National Aeronautics and Space Administration.

Facility: Keck:I (HIRES). -

Figures 14 and 15 show the SEDs of our sources. SEDs are constructed using the Two Micron All Sky Survey (2MASS; Skrutskie et al. 2006), the Spitzer and Herschel photometric data, the Spitzer IRS spectra, and the Wide-field Infrared Survey Explorer (WISE; Wright et al. 2010). For the sources in Taurus, their Spitzer data are collected from Luhman et al. (2010) and Rebull et al. (2010), and the Herschel data are from Howard et al. (2013). For the sources in Lupus and ρ Oph, the Spitzer data are from the c2d catalog (Evans et al. 2003), and the Herschel data are from Bustamante et al. (2015) and Rebollido et al. (2015). For the sources in Corona Australis, the Spitzer data are collected from Hillenbrand et al. (2008) and Dunham et al. (2015), and the Herschel data are from Sicilia-Aguilar et al. (2013). For the two sources in the TW Hya association, their Spitzer data are collected from Luhman et al. (2010), and their Herschel data are from Riviere-Marichalar et al. (2013).

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For each source in our sample, we construct a median SED from CTTSs with similar spectral type in Lynds 1641 (Fang et al. 2009, 2013a). The age of Lynds 1641 is around 1–2 Myr (Fang et al. 2013a), which is similar to most of the sources in this work, besides the TW Hya association. In each panel of Figures 14 and 15, we show in gray the upper and lower quartiles of the median SEDs. We classify a disk as TD if its SED is below the lower quartile of the Lynds 1641 median SED at more than two bands, and otherwise as a full disk. As Lynds 1641 lacks G- and F-type stars (Fang et al. 2013a), we cannot use our approach to classify SR 21A, HD 143006, V1057 Cyg, V1515 Cyg, and DI Cep. In this case we adopt the TD classification for SR 21A and HD 143006, found in the literature (Najita et al. 2015; van der Marel et al. 2016), and consider the other three ones as full disks.

Figures 16 and 17 show the [O i] λ6300 line profiles for the TDs and full disks. It is clear that the TDs have simpler forbidden-line profiles than the full disks.

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We use three spectrophotometric standards each night to flux-calibrate the spectra of our scientific targets. First, we obtain the BT-settl model atmosphere (Allard et al. 2011) corresponding to each telluric standard spectral type in the night of 2008 January 23 and the white dwarf model atmosphere (Koester 2010) for the white dwarf telluric standards in the night of 2008 May 23. Next, we fit its broadband photometry using the aforementioned model with two free parameters, extinction and stellar angular radius, as in Fang et al. (2009, 2013a). Then, we shift and rotationally broaden the best-fit model atmosphere and degrade it to the Keck spectral resolution. In each order, the ratio between the observed and model spectrum is fitted with a fourth-order polynomial function, from which we obtain the conversion from counts to absolute flux. The spectrophotometric standard that is observed closest in time to each of our targets is chosen as its flux calibration. As our slit width is narrow (0861), we also correct for the missing flux due to the difference in point spread functions between the target and the spectrophotometric standard. Atmospheric absorption due to the different air mass between the spectrophotometric standards and the scientific objects is also corrected using optical extinction coefficients proper for Maunakea.²¹ The flux calibration did not account for atmospheric dispersion in the observations of DK Tau A, where the slit position angle was offset from the parallactic angle. For SCrA A + B, the MAKEE pipeline cannot resolve the SCrA A and B components, and thus the flux calibration overcorrects the flux for the slit loss by ∼20%.

We use two methods to estimate the uncertainty on the flux calibration. The first one is to flux-calibrate one spectrophotometric standard using another close-in-time spectrophotometric standard and compare the calibrated flux with the expected one. We found differences of ∼14% for the night on 2008 January 23 and only ∼3% for the night on 2008 May 23. To evaluate the uncertainty on line ratios close to the forbidden lines analyzed here, we also calculate the F_cont,4068/F_cont,6300 and the F_cont,5577/F_cont,6300, basically continuum fluxes near the [S ii] λ4068, [O i] λ5577, and [O i] λ6300 transitions, from the flux-calibrated spectra of one spectrophotometric standard using another one close in time. When comparing them with the expected values, we find differences of ∼5% and 3% on 2008 January 23 and ∼5% and 1% on 2008 May 23 for the F_cont,4068/F_cont,6300 and F_cont,5577/F_cont,6300 ratios, respectively.

The data acquired on 2008 January 23 cover wavelengths near 7510 Å. Hence, we can further estimate the uncertainty on our flux calibration by comparing our calibrated 7510 Å fluxes with those reported in Herczeg & Hillenbrand (2014). Unfortunately, the 7510 Å wavelength is located in the gap between two HIRES orders. So, we did not measure the 7510 Å flux directly, but instead interpolate the flux using wavelengths near 7510 Å. Figure 18 shows our flux values compared to those from Herczeg & Hillenbrand (2014). The mean difference between the two works is about 0.07 dex. Four sources, DS Tau, HN Tau A, GI Tau, and V409 Tau, show larger differences (0.10–0.37 dex), which may be due to their brightness variability (see Rodriguez et al. 2015 for V409 Tau and Guo et al. 2018 for GI Tau). V409 Tau, which sports the largest difference (0.37 dex), has been also observed with the Sloan Digital Sky Survey (SDSS; Ahn et al. 2012) and is 11.934 mag in SDSS − i band. We convert the i-band photometry to flux and correct for the extinction A_V = 1 from Herczeg & Hillenbrand (2014), which gives a flux of 5.76 × 10⁻¹⁴ erg s⁻¹ cm⁻² Å⁻¹ at 7625 Å (the center of SDSS − i band). The difference between our 7510 Å flux and the SDSS 7625 Å flux is ∼0.09 dex, much lower than that with Herczeg & Hillenbrand (2014), which supports the hypothesis of variability driving a larger difference. If we exclude the four outliers in Figure 18, the mean difference between our 7510 Å fluxes and those from Herczeg & Hillenbrand (2014) is reduced to ∼0.03 dex. In summary, two different methods suggest that the uncertainty on our absolute flux calibration is likely better than 10%.

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Our sample includes three sources (SZ 68A, DoAr 21, and DoAr 24E) with no [O i] λ6300 detection. Neither DoAr 21 nor DoAr 24E shows emission lines in our spectra that can be used to derive accretion luminosities; thus, they are inferred to have weak or absent disk accretion. In the following, we provide additional information on these sources.

SZ 68A is a a triple system with a close binary (separation 0126) and a third faint companion (M6) with a separation of 2808 (Correia et al. 2006). Our spectroscopic observation targeted the close binary. We detect the Ca  ii lines at 3934 and 3968 Å but only weak Hα emission (EW ∼ −2.8 Å). This star has been classified as a weak-line T Tauri star, a young nonaccreting star, by Cieza et al. (2007) and Alcalá et al. (2017). The [O i] λ6300 emission is not detected in our HIRES spectra, and it is also absent in the X-Shooter spectra by Nisini et al. (2018). Ansdell et al. (2016) reported cold CO gas emission around the binary and no gas or dust cavity at a resolution of 50 × 40 au. The SED of SZ 68A is compatible with that of a full disk.

DoAr 21 is a close binary with a separation of 1.2–1.8 au (Loinard et al. 2008). The HIRES spectrum of DoAr 21, which covers from 4420 to 6310 Å, does not show any accretion-related emission lines. Salyk et al. (2013) detected Pfβ emission from DoAr 21 and estimated a mass accretion rate of 1.7 × 10⁻⁸ M_⊙ yr⁻¹. DoAr 21 is detected at far-infrared wavelengths (Rebollido et al. 2015) and has reduced mid-infrared emission as TDs (see Figure 14 from our paper). However, based on high spatial resolution mid-infrared imagery, Jensen et al. (2009) find very weak, almost absent, excess emission from this source at 9–18 μm and argue that low-resolution data could be contaminated by an extended infrared source. Thus, they suggested that either the disk is in the final stage of clearing or there is no disk around DoAr 21. The recent ALMA imaging of DoAr 21 at 870 μm shows no detection at a spatial resolution of 02 and a sensitivity of 0.02 mJy (Cox et al. 2017). Therefore, even if there is a disk around DoAr 21, its disk mass should be very low.

DoAr 24E has a faint companion at a separation of 203 (Ratzka et al. 2005). Our HIRES spectrum covering from 4420 to 6310 Å does not show any accretion-related emission lines. Natta et al. (2006) detected Paβ emission from its near-infrared spectrum and estimated a mass accretion rate of 6.2 × 10⁻⁹ M_⊙ yr⁻¹. The source SED is compatible with that of full disks. The continuum emission from the disk has been detected at far-infrared, submillimeter, and millimeter wavelengths (Mohanty et al. 2013; Rebollido et al. 2015). No [O i] and o-H₂O emission is detected around 63 μm (Riviere-Marichalar et al. 2016).

The rationale for decomposing corrected line profiles with Gaussians is discussed in Section 3.2, while the best-fit parameters are summarized in Table 2. Figure 19 provides the best-fit Gaussian profiles color-coded by kinematic component and superimposed on the corrected [S ii] λ4068, [O i] λ5577, and [O i] λ6300 profiles for all the sources in our sample.

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View extended figure (8 panels)

Seven sources present [S ii] λ4068 line profiles that are highly contaminated by Fe i emission at 4063.6 and 4071.7 Å. In addition, the [O i] λ5577 line from RU Lup is also contaminated by Fe i emission at 5572.8 Å. Figure 20 shows the contaminated line profiles. We fit the wings of the Fe i emission with linear functions and tentatively decontaminate the profiles by subtracting the fitted function from the observed spectra. The corrected [S ii] λ4068 and [O i] λ5577 line profiles are also shown in Figure 20. Due to the strong contamination from the Fe i line at 4063.6 Å, any [S ii] λ4068 flux more blueshifted than ∼200 km s⁻¹ cannot be recovered. A comparison of [S ii] λ4068 and [O i] λ6300 profiles suggests that we achieve a good correction for less blueshifted emission (see Figure 5 in the main text).

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As discussed in the main text (Section 4.1), individual kinematic components present similar [S ii] λ4068, [O i] λ5577, and [O i] λ6300 profiles, indicating that they trace the same physical region. Here, we provide further evidence to this finding by showing a comparison of centroids and FWHMs of individual [S ii] λ4068 and [O i] λ5577 components versus the [O i] λ6300 components (see Figures 21 and 22). Note the similarity in centroids and FWHMs for individual kinematic components.

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In view of the Gaia DR2 release (Bailer-Jones et al. 2018), we revisit the relations between the luminosity of permitted lines (L_line) and the accretion luminosity (L_acc). We collect L_line and L_acc from Alcalá et al. (2017) and scale them to the new Gaia DR2 distance of each source.²² We carry out a linear regression to fit log L_acc = a × log L_line + b. We have excluded weak (or dubious) accretors and subluminous objects from the fit. The best-fit a and b coefficients and their uncertainties are listed in Table 7. Within 1σ, most of them are the same as those reported in Alcalá et al. (2017).