AN OPTICAL SPECTROSCOPIC STUDY OF T TAURI STARS. I. PHOTOSPHERIC PROPERTIES

The majority of stars in our sample are M stars. At optical wavelengths, M stars are easily identified from the presence of strong TiO absorption bands. Kirkpatrick et al. (1991, 1993), hereafter Kirkpatrick, established a grid of M-dwarf spectral type standards from field stars. Reid et al. (1995), hereafter PMSU, quantified relationships between spectral type and the depth of TiO bands at 7100 Å from moderate resolution optical spectra based on the Kirkpatrick et al. (1991) sequence.

Luhman (1999); Luhman et al. (2003), hereafter Luhman (also includes, e.g., Luhman 2004, 2006), recognized that for pre-main-sequence stars, the depth of TiO features deviates from dwarf stars because of lower gravity (see also Gullbring et al. 1998). Luhman developed a spectral type sequence for young M dwarfs later than M5 based on a hybrid of field dwarf and giant stars, since TTSs are typically luminosity class IV. For stars earlier than M5, Luhman relied on the Kirkpatrick grid along with the Allen & Strom (1995) red spectroscopic survey of standards. Although the Luhman spectral sequence is well accepted and widely used, it has no standards or quantified conversions between spectral index and spectral type. As a consequence, spectral types based on the Luhman method are likely less precise when applied by authors other than Luhman himself.

Our quantified spectral type sequence is derived from the methods established in those seminal works. In the following analysis, the objects in the PMSU catalog are all assigned a spectral type based on their TiO5–SpT conversion, which is accurate to ∼0.5 subclasses between K7–M6. The TiO5 spectral index, the flux ratio of 7130–7135 to 7115–7120 Å, requires flux measurements in narrow regions and is not possible to calculate from our low resolution spectra. The Luhman sequence discussed here is from a set of 54 young stars spanning M0.5–M9.5 provided by K. L. Luhman (2008, private communication).

Four prominent TiO bands are present in our red spectra (see Figure 2 and Table 3). Figure 3 compares the spectral types and four spectral indices for the PMSU, Kirkpatrick, and Luhman samples. For stars earlier than M5, the Luhman relationship between SpT and TiO depth for young stars was intended to follow the Kirkpatrick et al. (1991) results. However, for objects from M0 to M3, the Luhman spectral types are ∼0.5 subclasses later than the median Kirkpatrick spectral type (TiO-7140 and TiO-6200 spectral indices). For the spectral types later than M5, gravity differences between field M dwarfs and pre-main-sequence M dwarfs lead to the Luhman spectral types being slightly earlier than the median Kirkpatrick object (as discussed by Luhman). For M dwarfs earlier than M4, we adopt the spectral type sequence of Kirkpatrick, which may introduce a small offset between our spectral types and Luhman spectral types. For M dwarfs later than M4, we adopt the spectral type sequence of Luhman. Several additional TiO/VO bands are detected at blue wavelengths and are not well studied (see Figure 4). While our initial approach does not consider these bands, the final spectral types are calculated from a best fit to a spectral sequence using the full optical spectrum.⁵

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M4–M8. Objects later than M4 have spectral types assessed from the TiO 7700 and 8500 Å bands, with a conversion from spectral index to spectral type calculated from the sequence of objects provided by Luhman. An uncertainty of 0.2 subclasses is assigned based on the change in feature strength versus subclass and on the standard deviation in the fits to the Luhman objects. This uncertainty is consistent with that assigned by Luhman.

M0–M4. The TiO band at 7140 Å is most reliable for early-to-mid M-dwarfs. Within the Kirkpatrick sample between M0–M4.5, the standard deviation of the index-determined SpT and adopted SpT is 0.4 subclasses. The relative accuracy of spectral typing within a single star-forming region is likely better than 0.40 subclasses because the Kirkpatrick lists SpT at only 0.5 subclass intervals and because the metallicity should be uniform in samples of nearby star forming regions but not in field dwarfs. The TiO 6200 Å band is also sensitive to early-to-mid M dwarfs, with a standard deviation of 0.22 subclasses for spectral types M0-M4 within the Kirkpatrick sample. However, few Kirkpatrick objects were observed at 6200 Å, and the PMSU sample is systematically offset from the Kirkpatrick sample in this TiO feature. As a consequence, we do not use this relationship here to derive spectral types.

Figure 4 (left panel) shows that K dwarfs are characterized by MgH and Mg b absorption at ∼5150 Å. This dip is not present in G-type stars. We define a spectral index, R(5150),

$$\begin{equation} R(5150)=\frac{F(5100)}{F(4650)}\times \frac{F_{\rm line}(4650)}{F_{\rm line}(5100)}, \end{equation} \tag{ 1 }$$

where F(λ) is the flux in a 100 Å wide band around λ, and F_line(4650)/F_line(5100) is the flux ratio expected at those same wavelengths based on the spectral slope obtained in a linear fit to the λ = 4650 and λ = 5450 Å spectral regions. Dividing by the F(5100)/F(4650) ratio calculated from the linear fit accounts for extinction.

Figure 5 shows the relationship between R(5150) versus literature spectral type for stars with little or no accretion. The spectral types earlier than M0 are obtained from the literature, usually from high-resolution spectra (Basri & Batalha 1990; White & Hillenbrand 2004; White et al. 2007), and are supplemented by some low resolution spectral types from Luhman. Spectral types later than M0 are calculated from the TiO spectral indices. Figure 5 also shows R(5150) versus SpT from the compilation of low resolution spectral atlases by Pickles (1998). The R(5150) index is similar to that of luminosity class IV subgiants and to the average index obtained by adding spectra of dwarfs and giants (luminosity class III + luminosity class V). The relationship is gravity-sensitive and should be applied only to pre-main-sequence K stars.

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The standard deviation between calculated and literature spectral types between K0 and M0 is 1.0 subclasses. Some of this scatter is attributable to uncertainty in literature spectral type, which typically claim an accuracy of one to two subclasses, and to studies listing integer steps in subclass. We assign an uncertainty of one subclass between K0–M0 for this relationship.

The TiO 6800 Å absorption band is detectable for spectral types K5 and later. From K5–M0, the Kirkpatrick objects are about one subclass later than the Pickles libraries. The PMSU data are also shown, though the PMSU TiO-5 index is not reliable at spectral types earlier than K7. We include a spectral type K8 as an intermediate between K7 and M0. Spectral types between K6–M0.5 are assigned an uncertainty of ∼0.5 subclasses. Most accreting stars in this spectral type range have a spectral type uncertainty of one subclass. Within this range there may be an additional systematic uncertainty of ∼0.5 subclasses between our spectral types and those of Luhman.

By design, only a few objects in our sample have a spectral type earlier than K. Spectral types for these objects are measured by visual comparison to Pickles templates. The shape of the G band helps to determine G spectral types, while the absence of the G band requires that the star be F or later (e.g., Fraunhofer 1814; Cannon 1912; Covey et al. 2007). Both G and F spectral types are also measured from the relative strengths of the 4300 Å line and the nearby Hγ line. Hotter stars have spectral types measured from the strength of Balmer lines and the Ca ii H & K lines. The strength of the Ca ii K line is particularly important for discriminating between B and early A spectral types (e.g., Mooley et al. 2013), although the absorption may be filled in with emission. More rigorous approaches to spectral typing large samples of BAF stars are described by Hernandez et al. (2004) and Alecian et al. (2013). Some uncertainty in our classification is introduced by emission and possible wind absorption in H and Ca lines.

The standard conversion from SpT to effective temperature for young stars is based on the work of Schmidt-Kaler (1982) and Straizys (1992), as compiled by Kenyon & Hartmann (1995). Luhman updated this conversion for M-dwarf TTSs, based on a scale intermediate between giants and dwarfs. Synthetic M-dwarf spectra from model atmospheres have advanced considerably since Luhman et al. (2003) established this conversion. Rajpurohit et al. (2013) recently obtained a new scaling between spectral type and temperature for M dwarfs by comparing BT-Settl synthetic spectra calculated from the Phoenix code (e.g., Allard & Hauschildt 1995; Allard et al. 2012) to observed low-resolution spectra. A similar approach by Casagrande et al. (2008) with the Cond-Gaia synthetic spectra yielded much lower temperatures than Rajpurohit et al. (2013) for the same spectral type.

An initial comparison between our standard grid and Phoenix/BT-Settl synthetic spectra with CFITSIO opacities and gravity log g = 4.0 (Allard et al. 2012; Rajpurohit et al. 2013) reveals good agreement between the observed and synthetic spectra for temperatures higher than ∼3200 K. Discrepancies between the observed and modeled depths of TiO absorption bands are problematic at cooler temperatures (Figure 7). We speculate that some of these differences may be explained with uncertainties in the strengths of TiO transitions and in the strength of continuous optical emission produced by warm dust grains in the stellar atmosphere. Details of these comparisons and fits of the synthetic spectra to observed spectra are described in Appendix B.

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An effective temperature scale for pre-main-sequence stars is derived by fitting Phoenix/BT-Settl synthetic spectra to our spectral type grid (K5–M8.5) and Pickles luminosity class IV stars (F–K3). Figure 8 and Table 5 compares our new K and M-dwarf temperature scale to other pre-main-sequence and dwarf temperature scales.⁶ Our scale matches the Luhman scale between M0–M4 and deviates at later spectral types. The differences between our scale and the Rajpurohit et al. (2013) scale are likely attributed to gravity differences between pre-main-sequence and dwarf stars. The K-dwarf temperature scale is shifted to lower temperatures relative to the scale used by Kenyon & Hartmann (1995).

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Stellar photospheric luminosities, L_phot, are calculated using the Phoenix/BT-Settl models with CFITSIO opacities (Allard et al. 2012) for effective temperatures <7000 K. Similar bolometric corrections for hotter stars are calculated from the NextGen model spectra (Hauschildt et al. 1999). The flux ratio F₇₅₁₀/L_phot is used as the bolometric correction and applied to the measured photospheric fluxes (Figure 9 and Table 6). These conversions all assume a gravity of log g = 4. Differences due to subtracting the a flat continuum in late M dwarfs (3.2) amount to ∼1% of the total stellar luminosity and are ignored here.

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At temperatures <3500 K, the opacity in a VO absorption band at 7500 Å is much larger in synthetic spectra than in the observed spectra. At these temperatures, the bolometric correction for 7510 Å flux is calculated by fitting a line between the flux at 7300 and 7580 Å, omitting the VO opacity from the fit.

Including the accretion spectrum into the spectral fit requires an estimate for veiling versus wavelength. The measureable accretion continuum is produced by H recombination to the n = 2 level (Balmer continuum, λ < 3700 Å) and to the n = 3 level (Paschen continuum λ < 8200 Å), plus an H⁻ continuum (for detailed descriptions, see Calvet & Hartmann 1992; Calvet & Gullbring 1998). The ratio of these different components depends on the temperature, density, and optical depth of the accreting gas and heated chromosphere. The size of the Balmer jump between stars is different (e.g., Herczeg et al. 2009), which forces this analysis to be restricted to the shape of the continuum either at <3700 Å or between 3700–8000 Å. Here we concentrate on the emission at >4000 Å. The spectral slope at <3700 Å is uncertain in the observed spectra due to the large wavelength dependence in the telluric correction near the atmospheric cutoff.

The exact shape of the accretion continuum likely depends on the properties of the accretion flows. Models of the accretion continuum typically assume a single shock structure. Fitting the Balmer continuum emission leads to model spectra where at >4000 Å, the flux decreases with increasing wavelength (see Figure 3 from Ingleby et al. 2013 for spectra from isothermal models at different densities). These synthetic spectra underestimate the observed veiling at red wavelengths (see, e.g., models of Calvet & Gullbring 1998 and measurements by Basri & Batalha 1990 and Fischer et al. 2011). Ingleby et al. (2013) explains this problem by invoking the presence of accretion columns with a range of densities, some of which are lower density than has been typically assumed and produces cooler accretion shocks. This physical situation may be expected if accretion occurs in several different flows or if a single flow has a range of densities, perhaps because the magnetic field connects with the disk at a range of radii. The weaker shocks yield cooler temperatures and produce redder emission, thereby recovering the measured veilings around 1 μm.

Empirical measurements of the accretion continuum flux are shown in Figure 10. The fraction of emission attributed to the accretion continuum is calculated from the optical veiling measurements of Fischer et al. (2011) and the relationship (r_λ = (F_acc/F_phot)). This fraction is then converted to the accretion continuum flux by two different methods: (a) multiplying the fraction by our flux-calibrated spectra that are corrected for extinction and (b) multiplying the veiling by the flux from the template spectrum for the relevant spectral type from Table 4. Uncertainties in the accretion continuum are estimated to be 0.05 times the flux from the calibrated spectrum and 0.05 times the total standard+accretion flux, respectively.⁷ These two methods are somewhat independent from each other but yield similar results.

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Table 7 compares the χ² from linear fits ($\chi ^2_{\rm line}$) and flat fits ($\chi ^2_{\rm flat}$) to the accretion continuum fluxes for methods (a) veil*flux and (b) veil*template described above. Most cases are consistent with a flat accretion continuum. The veiling measurements tend to be smaller at longer wavelengths because the photospheric flux is brighter in the red than in the blue. This exercise presents somewhat circular logic because the spectral type and extinction are both calculated assuming that the accretion continuum is flat. Method (b) depends less on the assumption of a flat continuum but is sensitive to gravity and spectral type uncertainties in the optical colors. However, the results from both approaches demonstrate that the assumption of a flat accretion continuum is reasonable and self-consistent.

Table 7. Slopes of the Accretion Continuum

Star	a: veil * flux			b: veil * template
	F4/F8a	$\chi ^2_{\rm line}$	$\chi ^2_{\rm flat}$	F4/F8a	$\chi ^2_{\rm line}$	$\chi ^2_{\rm flat}$
AA Tau	0.79	0.4	0.4	0.64	0.5	0.4
BP Tau	1.09	0.4	0.5	0.70	3.7	1.4
CW Taub	1.03	1.4	1.6	1.03	0.8	0.9
CW Taub	1.08	1.1	1.2	1.08	0.5	0.5
CY Tau	1.39	4.3	5.7	1.00	8.7	10
DF Tau	0.53	17	6.8	0.3	61	7.4
DO Tau	1.29	1.7	0.8	0.76	8.9	5.2
IP Tau	1.59	1.7	1.9	1.46	1.3	2.0
DG Tau	1.04	2.0	2.3	0.80	3.7	2.1
DK Tau	0.87	2.2	2.1	0.72	3.2	1.4
DL Tau	0.98	4.2	4.7	0.98	1.4	1.6
DR Tau	0.83	12.6	10	1.42	3.9	0.9
HN Tau A	1.42	3.9	0.9	1.46	5.5	1.8

Notes. Spectral slopes of the accretion continuum for two methods. of converting the veiling to flux, see also Figure 10. Flat χ² has 8 degrees of freedom, linear fit has 7. ^aF4/F8: flux ratio of accretion continuum at 4000 Å to 8000 Å. ^bFischer et al. (2011) observed CW Tau twice.

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Based on these calculations and the results of Ingleby et al. (2013), we make the simplifying approximations that the shape of the accretion continuum is (1) the same for all accretors and (2) that the accretion continuum is constant, in erg cm⁻² s⁻¹ Å⁻¹, at optical wavelengths. In contrast, Hartigan & Kenyon (2003) assumes that the accretion continuum is a line with a slope that differs from star to star. Real differences between spectra are surely missed in our approach. However, our approach is simpler and reproduces the observed spectra with fewer free parameters. A more rigorous assessment of the accretion continuum spectrum is possible from broadband high resolution spectra, which has been applied to small samples (e.g., Fischer et al. 2011; McClure et al. 2013) but is time consuming, has not yet been implemented for large data sets, and suffers from the same degeneracies and systematic trades between surface gravity, reddening, and veiling by emission from the accretion shock and the warm inner disk.

Veiling can be accurately measured from high resolution spectroscopy (e.g., Basri & Batalha 1990; Hartigan et al. 1991) or estimated from low resolution spectrophotometric fitting (e.g., Fischer et al. 2011; Ingleby et al. 2013). Here we develop an intermediate approach to measure the veiling by comparing the depth of a single, strong absorption line to its depth in a template star. While accurate veiling measurements require high resolution spectroscopy, veiling may be estimated by measuring the depth of strong photospheric lines in low resolution spectra. This section concentrates on the strong Ca i λ4227 line.

Figure 11 shows spectra of the Ca i region versus spectral type. The Ca i equivalent width depends on spectral type as

$$\begin{equation} {\rm EW({\rm Ca\,\scriptsize{I}})} = -189.218 + 7.36 x -0.072 x^2, \end{equation} \tag{ 2 }$$

where x = 50, 58, 63 for K0, M0, and M5, respectively (Figure 12). Values lower than this equivalent width indicate that the depth of the photospheric absorption is reduced because of extra emission from the accretion continuum. This difference yields the strength of the accretion continuum at 4227 Å.

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Figure 13 shows an example of how the veiling at 4227 Å is estimated for each source. A flat accretion spectrum is added to the template photospheric spectrum so that the combination matches the observed line depth. The Ca i absorption line is sometimes filled in by emission from nearby Fe lines, thereby affecting the veiling estimate (Gahm et al. 2008; Petrov et al. 2011; Dodin & Lamzin 2012). Although this particular line is also sensitive to surface gravity, the use of temperature matched WTTS as templates should mitigate gravity-dependent line depth systematics. For cooler stars, calculating the accretion continuum flux at 4227 Å maximizes the sensitivity to accretion for cool stars because the ratio of accretion flux to photospheric flux is higher at short wavelengths.

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UScoCTIO 33 was originally identified as a possible member of the Upper Scorpius OB Association in a photometric survey by Ardila et al. (2000). A spectroscopic survey by Preibisch et al. (2002) confirmed membership, classified the star as M3, and found strong Hα emission indicative of accretion.

Figure 15 shows our Keck spectrum of UScoCTIO 33 compared with M3 and M4.5 stars with a veiling r₇₅₂₅ = 0.0 and 0.25. If the veiling is 0, the red spectrum is best classified as an M3 spectral type, with only small inconsistencies between the template and the spectrum. However, the M3 template spectrum is much weaker than the observed blue emission. The veiling r₇₅₂₅ = 0.25 is calculated from the depth of the Ca i λ4227 line. Subtracting this accretion continuum off of the observed spectrum yields photospheric lines that are deeper than the uncorrected observation. The consequent M4.5 spectral type with veiling improves the fit to the red and blue spectra.

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The M4.5 SpT leads to a mass of 0.11 M_☉ and an age of 5 Myr. The M3 SpT and no veiling yields a mass of 0.32 M_☉ and an age of 35 Myr, assuming no change in A_V.

The literature spectral type of M1 for DM Tau traces back to Cohen & Kuhi (1979). Despite significant interest as the host of a transition disk (e.g., Calvet et al. 2005), its spectral type has not been reassessed using modern techniques.

Figure 16 shows the veiling-corrected DM Tau spectrum 2008 December 29, compared with M2, M3, and M4 spectra. The veiling is calculated from the depth of the Ca i 4227 Å line. The veiling r₇₅₁₀ = 0.17 leads to SpT of M3 and A_V = 0.08. If the composite photospheric+accretion spectrum is not constrained by a good fit to the Ca i λ4227 line, then r₇₅₁₀ could range from 0.09, with SpT M2.7 and A_V = −0.20, to 0.31, with SpT M3.4 and A_V = 0.50. In this case, the extinction increases with later spectral type because the veiling has increased (see also the case of DP Tau). If the blue side is ignored entirely, then a veiling of r₇₅₁₀ = 0 would yield M2.5 and A_V = 0.06 while an upper limit on veiling of r₇₅₁₀ = 0.39 would yield M4.1 and A_V = −0.06. In these latter cases, the resulting red spectrum looks reasonable. The uncertainties in SpT and veiling are about half the size of these ranges when using the blue and red spectra together. Even with the blue+red spectrum, differences between M2 and M4 are subtle and are likely undetectable with a cruder method, such as photometry.

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The change from M1 to M3 for DM Tau leads to a younger age (17 versus 4.9 Myr) and a lower mass (0.62 versus 0.35 M_☉), assuming no change in A_V. The luminosity does not change significantly because the bolometric correction from the red photospheric flux is similar for an M1 and an M3 star.

Despite being the closest and possibly the most studied CTTS, the spectral type of TW Hya has been the subject of some controversy. The original spectral type of K7 was obtained from low resolution spectroscopy by de la Reza et al. (1989). Yang et al. (2005) used high-resolution optical spectra to measure an effective temperature of 4126 ± 24 K, equivalent to K6.5. They caution that the uncertainty in effective temperature likely underestimates systematic uncertainties. This spectral type is consistent with the K7 SpT derived by Alencar & Batalha (2002), also from high-resolution spectra. In contrast, Vacca & Sandell (2011) relied on low resolution spectra from 1–2.4 μm to obtain a new spectral type of M2.5. McClure et al. (2013) found that TW Hya is consistent with roughly M0 spectral type at 1.1 μm. Debes et al. (2013) argued that the 5500–10200 Å spectrum is a composite K7+M2 in the near-IR, with the warmer component related to accretion. Debes et al. (2013) did not consider veiling by the accretion continuum, which would preferentially cause the measured SpT at short wavelengths to be earlier than the actual spectral type.

Figure 16 shows that the optical spectrum is consistent with an M0.5 spectral type, which corresponds to ∼3810 K, with A_V = 0.0 mag. and veilings that range r = 0.09–0.21. This spectral type is consistent with all of our TW Hya spectra, obtained on seven different nights in 2008 January, May, and December. The effective temperature is significantly lower than that from Alencar & Batalha (2002) and Yang et al. (2005). While spectral fits to high resolution spectra may suffer from emission lines filling in photospheric absorption for strong accretors (e.g., Gahm et al. 2008; Dodin & Lamzin 2012), this problem is not expected to be significant for a weakly accreting star like TW Hya. However, the high veiling during the Yang et al. (2005) observation, three times higher than the median veiling measured here and by Alencar & Batalha (2002), may have complicated their temperature measurements.

Our spectral type is inconsistent with the late spectral type of Vacca & Sandell (2011). An M2 spectral type could only be recovered for our TW Hya spectra if the accretion continuum were three times larger in the red than that measured in the blue, which is inconsistent with both models and previous measurements of the accretion continuum. The spectral templates of Vacca & Sandell (2011) were dwarf stars, which may differ in certain near-IR features from TTSs. Visual inspection of these templates do not reveal significant differences between TW Hya and an M0.5 dwarf star, except in the H₂O band at 1.35 μm. McClure et al. (2013) also found that all K7–M0 CTTSs appear as M2 dwarf stars in one of their most prominent line ratios, which demonstrates the need to use WTTSs as templates. A composite spectrum of photospheres with different temperatures is not needed to explain the optical spectrum at <10,000 Å, although magnetic spots are expected to affect effective temperature measurements.

FM Tau is our most extreme example of a change in spectral type. The most commonly used spectral type of M0 can be traced back to Cohen & Kuhi (1979). However, the Cohen & Kuhi (1979) spectra cover 4500–6600 Å, where FM Tau looks like an M0 star because of high veiling. Hartigan et al. (1994) twice obtained FM Tau spectra from 5700–7000 Å and classified FM Tau as M0 and M2. The prominent TiO absorption bands are readily detected at >7000 Å, where the red photosphere is stronger than the accretion continuum.

FM Tau is classified here as an M4.5 ± 0.4. The large uncertainty in spectral type is caused by the high level of veiling. The measured extinction of A_V = 0.35 ± 0.2 is mostly constrained by fitting to the accretion continuum rather than the photosphere. The systematic uncertainty in A_V is caused by the uncertain shape of the accretion continuum. An M0 star is a reasonable approximation for the FM Tau colors, so our extinction is similar to literature values (e.g., Kenyon & Hartmann 1995; White & Ghez 2001).

DG Tau is the source of a famous and well-studied jet (e.g., Eislöffel & Mundt 1998; Bacciotti et al. 2000). Literature spectral types range from K3–M0 (Basri & Batalha 1990; Kenyon & Hartmann 1995; White & Hillenbrand 2004), including what should be a reliable spectral type of K3 from high-resolution optical spectra (White & Hillenbrand 2004). The discrepancies are caused by the high veiling. Gullbring et al. (2000) called DG Tau a continuum star, implying that no photosphere is detectable.

At low resolution, the spectrum shows the 5200 feature, which is typical of K stars, and TiO bands, which are seen only in stars with SpT K5 and later (Figure 17). The SpT is K7$^{+1}_{-1}$, with A_V = 1.6 ± 0.15 mag. The extinction depends mostly on the shape of the accretion continuum and does not significantly change with a small change in SpT. The SpT is limited to earlier than or equal to M0 by the shallow depth of the TiO bands.

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CW Tau is a heavily veiled TTS with a jet (e.g., Coffey et al. 2008). Cohen & Kuhi (1979) classify CW Tau as a K3 star, which is consistent with our measurement. Horne et al. (2012) and Brown et al. (2013) found absorption in CO v = 1–0 transitions, indicating that our line-of-sight passes through the surface layers of the circumstellar disk. The spectral analysis presented here is based on the 2008 January 18 spectrum. The three spectra obtained in 2008 December are ∼eight times fainter because of a change in extinction. This variability will be discussed further in a future paper.

Unlike DG Tau and DL Tau, the CW Tau spectrum does not show any TiO absorption, which restricts the SpT to earlier than K5. The presence of the 5200 Å bump suggests that CW Tau is later than K0. Our best fit is a K3 star with A_V = 1.74. The acceptable SpT range is from K1–K4 with corresponding A_V of 1.9 and 1.6, respectively. As with other heavily veiled stars, the methodological uncertainty in A_V is smaller than would be expected for this range in SpT because of high veiling. However, the systematic uncertainty in extinction may be higher because the extinction relies on the assumption that the accretion continuum is flat.

The observed spectrum is weaker than the model spectrum at >8000 Å, a difference which is also detected in some other accreting stars. The weaker flux indicates a smaller veiling, which could be attributed to the Paschen jump.

DP Tau is a 15 AU binary system (Kraus et al. 2011) that appears as a heavily veiled star. The spectral type assigned here of M0.8 is based on the depth of the TiO bands for accretion continuum veilings of r₇₅₁₀ = 0.36, 0.38, and 0.40 for our three spectra. The uncertainty in spectral type is ∼0.5 subclasses and is dominated by the uncertainty in the accretion continuum. The extinction of A_V = 0.78 mag is calculated by comparing the observed spectrum to a combined accretion plus photospheric spectrum.

DP Tau is highlighted here as an example of a counterintuitive parameter space, like DM Tau but with higher veiling, where a later spectral type leads to a higher extinction. This behavior for heavily veiled stars is the opposite of expectations for stars without accretion. For DP Tau, if the accretion continuum is increased so that r₇₅₁₀ = 0.55, then the increased depth of the TiO features leads to a SpT of M1.9. However, the combined spectrum of accretion plus photospheric template is bluer than the M0.8+accretion spectrum, so the A_V = 0.98 mag. Similarly, a low veiling of r₇₅₁₀ = 0.28 leads to M0.6 and A_V = 0.56 mag. These fits are the limiting cases for reasonable fits to the observed spectrum. The extinction measurements are similar because they are based largely on the shape of the blue accretion continuum, which is assumed to be flat.

The spectral type sequence described here is based largely on that established by Luhman. Table 8 compares 29 stars with spectral types and extinctions measured here, in a survey of the MBM 12 Association by Luhman (2001), and in a survey of Spitzer IRAC/X-ray excess sources by Luhman et al. (2009).

The median absolute difference between our and Luhman M-dwarf spectral types is 0.25 subclasses. The standard deviation is 0.37 subclasses. Six objects (20% of the sample) differ by more than 0.5 subclasses. Three of those six objects have spectral types in the K7–M1 range, as expected given the possible differences in our SpT scales (see Section 3.1).

Many of the most famous objects in Taurus have spectral types that date back to Cohen & Kuhi (1979), as listed in the compilations of Herbig & Bell (1988) and Kenyon & Hartmann (1995). The Cohen & Kuhi (1979) spectral coverage was optimal for early spectral types but insufficient for M stars. Table 9 lists the most significant changes in Taurus spectral types, relative to the compilation of spectral types by Luhman et al. (2010). Our new spectral types are often two to three subclasses later than those from Cohen & Kuhi (1979), particularly when veiling affected the spectral typing at short wavelengths. In cases of overlap with D'Orazi et al. (2011), our spectral types are consistent to within 0.5 subclasses of the measured effective temperature.

Several Taurus stars with spectral types earlier than K0 are challenging for spectral type measurements because accretion produces emission in the same lines (e.g., Ca ii infrared triplet, H Balmer lines) that are used for spectral typing. For example, Hα appears in emission from V892 Tau and RY Tau despite early spectral types. While RY Tau has had numerous spectral types between F7–G1 (Mora et al. 2001; Calvet et al. 2004; Hernandez et al. 2004), the Cohen & Kuhi (1979) spectral type of K1 has been adopted in several recent computations. Our spectral type of G0 for RY Tau agrees with other recent spectral types.

Our spectral types for the TWA are uniformly later than the spectral types obtained from Webb et al. (1999; see Table 10). Our spectral types for TWA 8A, TWA 8B, TWA 9A, and TWA 9B are consistent with those obtained from high-resolution spectra by White & Hillenbrand (2004). Our spectral types are also mostly consistent with the recent spectral types measured from X-Shooter spectra by Stelzer et al. (2013), with the exception of TWA 14 (M1.9 here versus M0.5 in Stelzer et al.). The outdated spectral types from Webb et al. (1999) have led to some confusion regarding membership. Weinberger et al. (2013) discuss that space motions may suggest that TWA 9A and 9B are not members of the TWA, which they support with ages of 63 and 150 Myr, respectively. The later SpT measured here lead to younger age estimates that are consistent with the ∼10 Myr age of the TWA.

In some cases, the age of a star as measured from an H-R diagram may differ from the dynamical or global age of a cluster. For example, with their later spectral type, Vacca & Sandell (2011) argue that the age of TW Hya is ∼3 Myr. Our age is now consistent with the global age of the TWA. However, even if the estimated age of a single star were younger, the dynamical age and cluster age are both consistent with 7–10 Myr (e.g., Mamajek 2005; Ducourant et al. 2014). Any deviations from this age for confirmed members are likely due to real scatter in observed photospheric luminosities and temperatures rather than the actual age of the star. These uncertainties are discussed in more detail in Section 5.

Veiling of the photospheric emission by the accretion continuum and any disk emission increases the observed flux. If the accretion continuum flux is not subtracted, then the measured flux will overestimate the photospheric flux. In this work, the photospheric luminosity is always corrected for veiling and as a result are usually lower than previous estimates. Uncertainties of ∼20% in the strength of the accretion continuum typically lead to ∼5% uncertainties in the final luminosity, with larger uncertainties for higher veiling. This error can be assessed for each target by comparing the veiling to the 7510 Å photospheric flux (see Appendix C and Table 14). Failure to subtract the accretion continuum off from the measured flux will lead to systematically overestimating the stellar luminosity in a way that correlates with veiling and accretion.

We assess internal SpT uncertainties of 0.2 subclasses for M dwarfs, 0.5 subclasses between K8–M0.5, and 1 subclass for stars between G0 and K8. The spectral types are repeatable to those levels of precision for stars with multiple spectra. These spectral types are optimized with a quantified inclusion of both the accretion continuum flux and reddening and should have smaller uncertainties than spectral types obtained by eyeball comparisons of spectra to a grid of standard spectra. The uncertainty for M-dwarfs relative to literature estimates is ∼0.5 subclasses.

Veiling affects spectral type measurements. Our largest change in spectral type is 4.4 subclasses (for FM Tau), though errors larger than two subclasses would be surprising for the type of red spectra that have been obtained in most studies over the past decade. However, differences of one to two subclasses for veiled spectra can be subtle, as demonstrated for UScoCTIO 33 and DM Tau above.

For an error in spectral type, the bolometric correction and therefore the estimated luminosity of the star does not change significantly, unless the photospheric flux is measured in the Wien tail for the relevant temperature. However, the stellar luminosity at a given age is sensitive to the effective temperature. The comparison between the expected and estimated luminosity thereby introduces a luminosity spread. Figure 19 shows that 3500 K stars with temperatures overestimated by 300 K and 75 K (∼1.5 and 0.2 SpT, respectively) would appear underluminous by a factor of ∼2.8 and ∼1.3, respectively. This uncertainty may lead to veiled stars, such as UScoCTIO 33, systematically appearing underluminous and old if veiling is not accounted for in the SpT. Some of this underluminosity may be balanced if veiling is also mistakenly unaccounted when converting a band flux to the luminosity.

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An error in the spectral type introduces a mismatch between the template and object spectra, thereby causing an error in the extinction. Figure 20 shows the uncertainty in A_V introduced by the average spectral typing error. In optical spectra or photometry, the uncertainty in spectral type dominates extinction uncertainties beyond ∼M5 because the spectral slope changes sharply in the Wien tail. In terms of the luminosity spread, some of the uncertainty introduced by a spectral type error may be partially balanced by the extinction error, which pushes the expected luminosity in the other direction (e.g., da Rio et al. 2010).

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The gravity of the spectral template can also introduce significant errors, even when non-accreting TTSs are used as photospheric templates. Low mass stars with ages of 1–10 Myr have log g ∼ 3.4–4.2, depending on the age and mass (see Figure 1). The gravity difference between log g ∼ 3.4–4.2 (1–10 Myr for 0.7 M_☉ star) leads to maximum errors of A_V = 1.1 mag in F_red = F(8330)/F(6448) for M stars (Figure 21).

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The extinction law is assumed to be that of median interstellar grains, with a total-to-selective extinction of R_V = 3.1. Most spectra in our sample can be well fit with R_V = 3.1 and have A_V < 3 mag, where the mean interstellar extinction law should apply. The differences in the relative flux attenuation between extinction laws is particularly significant at <5000 Å. Grain growth in high extinction regions makes the extinction curve much more gray, with R_V as high as 5.5 (Indebetouw et al. 2005). The few stars in our sample that are heavily extincted (A_V > 5) are only well fit with R_V ⩾ 4.

In our optical spectra, for a star with a measured A_V = 1.0 mag, applying extinction laws with R_V = 5 from Cardelli et al. (1989) or R_V = 5.1 from Weingartner & Draine (2001) would lead to A_V = 1.2 and 1.15 mag, respectively. The difference in luminosity is minimal for low extinctions. However, an extinction A_V = 10 mag and R_V = 5 will be measured (in red-optical spectra or colors) as A_V = 8.3 mag if R_V = 3.1 is assumed, yielding a factor of 5.6 difference in luminosity if assessed at 7510 Å.

Our analysis relies on an assumption that the accretion continuum flux is constant in erg cm⁻² s⁻¹ Å⁻¹ versus wavelength. While this assumption is reasonable, it may not apply to some sources (see Figure 10). A negative slope (stronger emission at 4000 Å than 8000 Å) would lead to the inference of an earlier spectral types because the veiling would be weaker, so the photospheric TiO features would not be as deep. For sources with moderate or strong veiling, the extinction would be underestimated in our paper.

DM Tau is used here as an example of the effect of the shape of the veiling continuum for a moderately veiled star. If the accretion continuum is two times weaker at 8000 Å than at 4000 Å, then the best-fit model is M2.7 with A_V = −0.02 mag. If instead the accretion continuum is two times stronger at 8000 Å than at 4000 Å, then the best-fit model is M3.6 and A_V = 0.2 mag. The different spectral types are caused by different TiO absorption depths. The extinction does not change significantly because the color change in the accretion continuum is offset by a color change in spectral type.

Table 11 describes a similar analysis for a few stars with a range of veilings. The synthetic spectra with an accretion continuum that get brighter to longer wavelengths are typically bad fits to the observed spectra. For heavily veiled stars, the change in extinction could be as large as A_V = 0.9 mag. Spectral types of heavily veiled stars around K7 are especially dependent on the shape of the veiling continuum. The real uncertainty in SpT and A_V are likely smaller than the differences described in this paragraph because the accretion continuum is likely much closer to a flat spectrum at optical wavelengths.

The temperature scale for pre-main-sequence likely has an uncertainty of ∼50 K for early M dwarfs and ∼100 K for late M dwarfs based on the comparisons between different temperature scales described in Section 3.2. In addition to these uncertainties, the models themselves have some uncertainty. Any error in the temperature scale will apply systematically throughout the entire sample and does not introduce a luminosity spread for stars with similar spectral types. The conversion from spectral type to temperature applied here is measured from our spectral type scale.

Our bolometric corrections are calculated from the BT-Settl model spectra (Allard et al. 2012). The mismatch between models and real spectra may introduce small systematic errors into our luminosity calculations. As with the conversion from spectral type to temperature, this error should not introduce a significant luminosity spread for stars with similar spectral types.

The age of a pre-main-sequence star is calculated from the contraction timescale and the effective temperature. In most comparisons between data and model spectra, the photospheric luminosity is used as a proxy for the radius. This surface area does not include the fraction of the star covered by the spot. In the shock models of Gullbring et al. (1998), corrections are less than ∼20% and are not significant. However, the shock models of Ingleby et al. (2013) include components at lower density than Gullbring et al. in order to explain veiling at red wavelengths, in excess of previous models. In three cases—RW Aur A, DR Tau, and CV Cha—the accretion shock covers 20%–40% of the stellar surface. In extreme cases, especially for outbursts or Class I objects, some estimate of this covering fraction would need to be combined with the photospheric surface area to calculate a stellar radius. This uncertainty is ignored in this work.

Hillenbrand et al. (2012) found TiO in emission from two Class I sources and one CTTS undergoing an outburst (see also Covey et al. 2011). In our sample, VV CrA and the 2008 January GV Tau¹⁰ spectrum show TiO in emission (Figure 22). Emission lines blanket the optical spectra of VV CrA, GV Tau, and three objects described by Hillenbrand et al. (2012). All objects with TiO emission have evidence from their SEDs that an envelope is present.

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The TiO emission must be related in some way to strong accretion. The warm TiO gas is likely located in a warm disk surface, which may be viscously heated by the accretion flow. TiO emission has only been detected in clear cases. Presumably other CTTSs have weak TiO emission that would require a dedicated search to detect. The possible complications of TiO emission filling in absorption bands has not been considered here or in other work but would severely complicate spectral typing. Most likely, these complications arise for only Class I stars.

The nearby TWA is a loose association of ∼30 stars with an age of ∼10 Myr (Webb et al. 1999). The members are especially meaningful for age estimates because of proximity, prevalence of parallax measurements, negligible extinction, and near-complete accounting of binarity.

Since the association is not near any molecular cloud, extinction is assumed to be zero for most members. Two stars, TWA 30A and 30B, have disks that are nearly edge-on and may attenuate photospheric emission (Looper et al. 2010a, 2010b) and are therefore ignored in this analysis. Although Ducourant et al. (2014) calculate and apply extinction corrections to several TWA members, the color corrections may be introduced by small errors in spectral type and at present are not accurate enough to use anything other than A_V = 0 mag for members of this association.

Figure 23 shows the H-R diagram and luminosity spread of the TWA. Table 12 lists the stellar parameters of TWA members, including an age from the Baraffe et al. (2003) pre-main-sequence evolutionary tracks and a ratio L/L10 of the measured luminosity to L10, the 10 Myr luminosity for the relevant temperature. Most of the luminosities are calculated from our optical spectra. The luminosities of several close binaries are obtained from HST narrowband imaging at 1.64 μm Weintraub et al. (2000), while others are obtained from the J-band magnitude measured in 2MASS. All total fluxes are calculated using bolometric corrections calculated from the BT-Settl spectra. The binary systems TWA 3Aab, TWA 5Aab, TWA 16AB, TWA 23 AB, and TWA 32AB are roughly equal mass (Muzerolle et al. 2000; Zuckerman et al. 2001; Shkolnik et al. 2011; Weinberger et al. 2013), so the luminosities used for this analysis are divided by 2. For HD 98800 Aa, Ba, and Bb, we used the temperatures calculated by Laskar et al. (2009). The luminosities of HD 98800 Bab are calculated from the absolute K-band magnitudes of Boden et al. (2005), adjusted for distance. The luminosity of HD 98800 Aa is calculated from the K-band flux in Prato et al. (2001).

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The combined TWA 2AB spectrum is classified here as an M2.2 object. The color difference suggests a 1.5–2 subclass difference between the pair. To determine the spectral type of the primary, we added scaled template spectra together and subsequently calculated a new spectral type and extinction. As the secondary-to-primary mass ratio decreases, the secondary reduces the inferred temperature of the total system, thereby also decreasing the expected luminosity. With complete optical wavelength coverage, the resulting spectral type is typically 0.5 subclasses later than the primary SpT and the extinction is within 0.1 mag. TWA 2A is assigned a spectral type of M1.7 and used in the analysis below. TWA 2B is tentatively assigned a spectral type of M3.5 and is not used in the analysis.

Between K5–M3.5, the average scatter in luminosity is 0.39 dex relative to a 9 Myr isochrone. This scatter is dominated by TWA 9A and 9B and TWA 14 (see Table 12). Weinberger et al. (2013) suggest that TWA 9A and 9B are too old to be TWA cluster members. Ducourant et al. (2014) also note that the kinematic distance for TWA 9A is highly discrepant with the parallax distance. However, Malo et al. (2013) assign a dynamical membership probability of 99%. Hα emission, Li absorption strength, and gravity indicators show that both stars are young. Our ages of TWA 9A and 9B are younger than the Weinberger et al. (2013) estimate because of later spectral types measured here, though the pair is still underluminous. Between M4–M7, most stars become significantly overluminous for a 10 Myr age, according to these isochrones. Some of this overluminosity could be reduced if the objects are hotter than the SpT-effective temperature conversion (Section 3.2). The brown dwarfs at ∼M8 are near the predicted H-R diagram location for the 10 Myr isochrone.

A more empirical approach suggests that the slope of luminosity versus temperature is much flatter between K0–M5 than the isochrone. A best fit line to the K0–M5 objects yields a luminosity spread of only 0.13 dex and is able to recover the objects down to 3000 K (compared with 3300 K for the 10 Myr isochrone). Only one object, TWA 9B, is severely underluminous relative to the line. Such a fit would suggest that the contraction timescale for very low mass stars is longer than predicted, relative to the contraction timescales of solar mass stars and brown dwarfs. Empirical isochrones crossing theoretical isochrones in this manner is not uncommon (e.g., Hillenbrand et al. 2008).

Of the resolved stars in multiple systems, the four closest in spectral type are co-eval to within a luminosity of 20%. The exceptions, such as TWA 8A/8B and TWA 5Aab/5B, have large differences in spectral type, often with one in the problematic M4–M6 spectral type range. The discrepancy points to an error in either effective temperature measurements or in pre-main-sequence tracks rather than a real luminosity spread.

The MBM 12 cloud was initially found by Magnani et al. (1985). A census of MBM 12 revealed a total of 12 stellar systems (Luhman 2001). The approximate distance of 275 pc was calculated by comparing the luminosities to other nearby star forming regions. The age (∼1–5) Myr and the distance are degenerate parameters. Seven of the 12 objects retain a disk (Meeus et al. 2009), which is consistent with a <5 Myr age.

A binary census of the eight brightest targets revealed seven multiple star systems (Chauvin et al. 2002; Brandeker et al. 2003). Based on near-IR photometry of these multiple systems, four (MBM12 1, 3, 5, and 10) are roughly equal mass stars, so their measured fluxes here are divided by two to estimate the luminosity of a single star. MBM12 12 (S018) is a triple system where the primary is a single star while the secondary is a resolved binary. Based on the near-IR colors, we divide the optical flux by a factor of 1.6 and shift the primary spectral type to M2.1 (from M2.6). Two other binaries, MBM12 4 (LkHα 264) and MBM12 2 (LkHα 262) are widely separated are not affected by possible companions.

The resulting H-R diagram (Figure 23) is roughly consistent with a ∼3 Myr age, if the 275 pc distance is accurate. As with the TWA, stars hotter than 4000 K are fainter than expected from the 3 Myr isochrone. Brown dwarfs cooler than 3000 K are brighter than the 3 Myr isochrone and may be affected by unaccounted binarity. For stars warmer than 3000 K, the luminosity spread about a best fit line is 26%. The slope of the line is 5.8 × 10⁻⁴ log L K⁻¹, almost exactly the same as the slope of 6.6 × 10⁻⁴ log L K⁻¹ for the TWA. The most underluminous star, MBM 2 (LkHα 262), is an accretor with an anomalously large extinction (A_V = 1.75) relative to other stars in the association. Some obscuration by the central star or a gray extinction law could lead to this underluminosity.