The CIDA Variability Survey of Orion OB1. II. Demographics of the Young, Low-mass Stellar Populations^*

Our final CVSO catalog contains 1,702,231 sources located in the region α_J2000 ∼ 5^h to 6^h and ${\delta }_{{\rm{J}}2000}=\sim +6^\circ$ to $-6^\circ$. Each source has an arbitrary ID number, α_J2000 and δ_J2000 coordinates, at least one measurement in either one of the V-, R-, and I-bands (640,639 objects have photometry in all three bands), with their corresponding errors (the sum in quadrature of the photometric calibration error and the standard deviation in that magnitude bin of all stars determined to be non-variable), the number of measurements in each filter, the maximum measured amplitude of photometric variations in each filter, the standard deviation of photometric variations in each filter, the probability that the object is variable in a given photometric band based on a ${\chi }^{2}$ test, the actual value of χ in each filter, and the Stetson (1996) L_VR, L_VI, and L_RI variability indices with their corresponding weights and the number of pairs of measurements involved in the computation of each index (Mateu et al. 2012).

Though the Stetson variability indices in the CVSO catalog are a valuable new addition to our original B05 photometric variability data set, in order to be able to compare the new results presented here with our previous studies, we used the same variability selection criterion as in B05, namely, we flagged as variable (at a 99.9% confidence level) those objects for which the probability in the V-band ${\chi }^{2}$ test that the dispersion of measured magnitudes is due to random errors is very low ($\leqslant 0.001$). This criterion yielded 85,011 variable sources (5% of the 1,702,231 objects in the full CVSO catalog). With the adopted confidence level, formally only 85 of the 85,011 objects flagged as variables are expected to be false positives. But in reality, such a sample of variable objects can still potentially contain fake detections due to cosmic rays, bad pixels, or columns not properly corrected for during the data processing, or other artifacts. We dealt with this by requiring that an object have either a counterpart in more than one band, three or more measurements in a single band, or a counterpart in the 2MASS catalog (Skrutskie et al. 2006; see below). Our variability selection also sets the minimum Δmag that we can detect as a function of magnitude: 0.08 for V = 15, 0.12 for V = 17, and 0.3 for V = 19. This means that for fainter stars, we detect only those that vary the most. We cannot decrease the confidence level too much without increasing the contamination from non-variable stars to unacceptable levels, because we are dealing with such large numbers of stars.

Comparing directly the overall fraction of variable stars found in the CVSO with other similar surveys is far from straightforward. The number of variables detected will depend on, among other parameters, the criterion for declaring an object as variable, the wavelength range considered, the time sampling, the general direction on the sky, the survey brightness limits, plate scale, seeing conditions, and methods for source extraction and photometry. Nevertheless, it is useful to place the CVSO results in context with other surveys spanning a similar magnitude range. The Catalina Sky Survey found 2%–4% of variable objects on timescales spanning several years (Drake et al. 2013, 2014), and the PS1 3π survey detects 6.6% variables among $3.8\times {10}^{8}$ sources, in multi-epoch data spanning ∼3.7 yr (Hernitschek et al. 2016). In Orion, the only other significant variability survey carried out so far is that by Carpenter et al. (2001), which targeted a 084 × 6° region centered roughly on the ONC, where they found a $\sim 7 \%$ fraction of near-IR variables, similar to our result.

The availability of large-scale astronomical surveys, together with new data mining tools, has made feasible the combination and analysis of multiple data sets containing information across a wide range of wavelengths. We performed a spatial match of the full CVSO catalog against the 2MASS Point Source Catalog (PSC Skrutskie et al. 2006), which helped us weed out artifacts that may still affect the optical catalog, but more importantly, added near-IR photometry that, combined with our optical magnitudes and variability information, provided us with a longer wavelength base for a refined color selection of candidate young stars, and later enabled the determination of fundamental parameters like the stellar luminosity. We used the Tool for OPerations on Catalogs And Tables package (TOPCAT—Taylor 2005) and the Starlink Tables Infrastructure Library Tool Set (STILTS—Taylor 2006) to do a positional match, with a $2^{\prime\prime}$ search radius, between the CVSO catalog and the 2MASS PSC; the mode of the distribution of separations between our catalog positions and 2MASS is $0\buildrel{\prime\prime}\over{.} 18$ (a significant improvement over the result obtained in B05), of which $0\buildrel{\prime\prime}\over{.} 06$ comes from a systematic offset between the USNOA-2 catalog and the 2MASS PSC. The resulting combined VRIJHK catalog contained 946,934 sources; because of the reduced sensitivity of the 2MASS PSC compared to the CVSO, this match effectively set the limiting depth of our survey, such that the completeness magnitudes dropped to V_com = 18.2, R_com = 17.7, and I_com = 17.2. We could have used the much deeper YZJHK data set obtained for the VISTA telescope Galactic Science Verification (Petr-Gotzens et al. 2011), but then we would be limited to a much smaller area (∼30 deg², or ≲20% of our total photometric survey area); the VISTA observations were used by Downes et al. (2014, 2015) and Suárez et al. (2017) in their study of the 25 Ori cluster. Since our purpose was to create a spatially complete map of the low-mass young populations in Orion OB1, we opted to sacrifice depth in favor of a combined optical/near-IR catalog that spanned the full area covered by the CVSO. Even with this modestly deep completeness level, we still are sensitive to PMS stars down to $\sim 0.15{M}_{\odot }$ at 10 Myr (Siess et al. 2000), which means that we could still expect to create a rather complete map of the stellar population to very low masses. Also, from a purely observational point of view, this was a reasonable low-mass limit for a feasible spectroscopic follow-up program using existing multi-fiber spectrographs on 4–6.5 m class telescopes (see Section 2.4).

In selecting our photometric PMS candidates, we followed a two-step process that produced high- and low-priority targets for follow-up spectroscopy: (1) select objects located above the main sequence in optical and optical–near-IR color–magnitude diagrams (CMDs). (2) Among the PMS candidates from step one, select those identified as variable.

Following the procedure outlined in Briceño et al. (2005), of the 946,934 sources in our combined CVSO−2MASS catalog, we selected 115,071 PMS candidate stars located above the main sequence (Siess et al. 2000), set at a distance of 440 pc, in both V versus V − J and V versus V − I_c CMDs constructed using our robust mean V magnitudes; this is what we call here Candidate Sample 1 (CS1). Formally, Orion spans a range of distances, from ∼360 pc for the closer OB1a subassociation to ∼400 pc for OB1b and the molecular clouds, as shown by recent accurate distance determinations from Very Long Baseline Interferometry by Kounkel et al. (2017b) and parallaxes from the Gaia Second Data Release (DR2; Gaia Collaboration et al. 2018, see Section 3.6.1). However, assuming a slightly farther distance gave us a more relaxed selection criterion, placing the main sequence lower (fainter) in the CMD, and therefore allowing us to gather a more complete candidate sample among the more distant and in the older regions. The disadvantage of this approach is that a fainter main sequence allows more field contaminants, specially for the regions thought to be nearest to us.

Among the objects in CS1, we selected 12,928 stars (11% of the total CS1 sample) as variable objects; this is Candidate Sample 2 (CS2), which by definition is a subset of CS1. For convenience, we define here as Candidate Sample 3 (CS3) those objects in sample CS1 not flagged as variable and therefore not included in CS2; this is either because they are non-variable, or more likely have variability below our detection threshold for that magnitude. Candidates in CS2 were considered our highest priority targets for follow-up spectroscopy (see Section 2.4). In order to have a general idea of the effectiveness of our PMS candidate selection scheme, we looked up in the SIMBAD database all previously known TTSs inside our entire survey region. Though strictly this cannot be considered a quantitative test of our photometric search technique for young low-mass stars, because the PMS objects in SIMBAD constitute a very heterogeneous set, containing objects from a variety of studies with differing biases, techniques, and spatial coverage, it still provides a rough estimate of how much of the low-mass PMS population we can expect to find. Out of 275 SIMBAD objects with a "TT" or "YO" type (excluding sources in the ONC, in σ Ori, NGC 2024, NGC 2068, and those published in B05 and Briceno et al. 2007a, hereafter B07a), in the magnitude range V = 13.5–19, and located in the PMS locus in the V versus V − J CMD, we recovered 85% in CS2. The ones we did not recover were because they coincided with bad columns or fell in gaps between adjacent rows of detectors, in the master reference drift scans used to calibrate the final CVSO catalog (Section 2.2).

A total of 7796 candidates fainter than $V\sim 16$ were observed in our combined multi-fiber spectrograph campaigns. Both Hectospec and Hydra have a 1 deg diameter field of view, while M2FS has a 29.5 arcmin diameter field. Hectospec has 300 fibers, each $1\buildrel{\prime\prime}\over{.} 5$ on the sky. Hydra with the Red Channel has 90 fibers, each with a projected diameter of $2\buildrel{\prime\prime}\over{.} 0$, and M2FS offers up to 256 fibers, 128 for each of its twin Littrow spectrographs, each fiber with a projected diameter of $1\buildrel{\prime\prime}\over{.} 2$ on the sky.

In Table 2, we show the full log of all the multi-fiber spectrograph observations for Hydra, Hectospec, and the Michigan/Magellan Fiber System (M2FS), including those discussed in B05;

WIYN+Hydra—In B05, we reported on 320 targets observed with Hydra in five fields (six fiber configurations) on 2000 November 26 and 27 (W02, W03, W04, W05, W07, and W09 in Table 2). Here we consider an additional 932 objects for which we obtained WIYN-Hydra spectra during the nights of 2000 November 26–28 and February 2, and 2002 November 13–15. These candidates were distributed in 15 fields (see Figure 6), spanning an area of $\sim 11\,{\deg }^{2};$ 138 (15%) objects listed in CS2 were selected as priority 1 targets. We used the Red Channel fibers ($2^{\prime\prime}$ diameter), the Bench Camera with the T2KC CCD, and the 600@10.1 grating, yielding a wavelength range ∼4700–7500 Å with a resolution of 3.4 Å. The left panels in Figure 8 show TTS spectra obtained with Hydra. All fields were observed with airmasses = 1.0–1.5, and integration times for individual exposures were 1800 s. When weather allowed, we obtained two or three exposures per field. Comparison CuAr lamps were obtained between each target field. In each Hydra field, we assigned fibers to all candidates from CS2 with V = 16–18.5, then to candidates from CS3, and with the lowest priority to objects from the 2MASS near-IR CMD. Typically, we assigned 10–12 fibers to empty sky positions and five to six fibers to guide stars. We used standard IRAF routines to remove the bias level from the two-dimensional Hydra images. Then, the dohydra package was used to extract individual spectra, derive the wavelength calibration, and do the sky background subtraction. Since the majority of our fields are located in regions with little nebulosity, background subtraction was in general easily accomplished.

MMT+Hectospec—With Hectospec, we observed 6110 targets distributed in 28 fields (34 fiber configurations), covering 23 deg², during the period 2004 November–2010 February (Table 2 and Figure 6). We excluded the 124 members of 25 Ori from B07a and the 77 very low-mass PMS members in that same cluster already reported by us in Downes et al. (2008, 2014). We assigned the highest priority in the fiber configuration software to the 813 candidates flagged as PMS variables (CS2). The spectrograph setup used the 270 groove mm⁻¹ grating, yielding spectra in the range $\lambda 3700\mbox{--}9000$ Å, with a resolution of 6.2 Å. Sample TTS spectra obtained with Hectospec are shown in the right panels in Figure 8. As for Hydra, objects in CS2 had the highest priority, followed by objects from CS3, and the remaining fibers were filled with 2MASS JH-selected PMS candidates. On average, we assigned 50 fibers per field to empty sky positions; the majority of our fields are located in regions with little or no extinction, so nebulosity was not an issue for sky subtraction. All of the Hectospec spectra were processed, extracted, corrected for sky lines, and wavelength-calibrated by S. Tokarz at the CfA Telescope Data Center, using customized IRAF routines and scripts developed by the Hectospec team (see Fabricant et al. 2005).

Magellan+M2FS—We used the M2FS instrument to obtain spectra of 434 targets distributed in five fields, spanning a total area of $1\,{\deg }^{2}$, during several runs between 2013 November and 2015 February (Table 2 and Figure 6). As we did for Hectospec, we assigned the highest priority to candidates flagged as PMS variables (CS2). The spectrograph setup used the 600 lines mm⁻¹ grating and 125 μm slit, yielding spectra in the range 5670–7330 Å, with a resolution of 1.3 Å. Two representative M2FS TTS spectra are shown in Figure 9. Sky fibers were assigned as for Hydra and Hectospec. The raw data were processed using custom Python scripts developed by John Bailey, which apply a bias correction, merge the four files per image produced by each of the four amplifiers, and correct cosmic rays (see Bailey et al. 2016 for a more detailed description of the software). Extraction of spectra, wavelength calibration, and correction for sky lines were done using the routines in the twodspec and onedspec packages in IRAF.

FLWO 1.5 m+FAST—We obtained spectra for a total of 3383 bright candidates ($V\lt 16$) in queue mode at the FAST spectrograph. Out of these 3383 FAST targets, 1235 (37%) objects from subset CS2 were observed as highest priority. We then continued with the remaining 2148 objects from set CS3.

In B05, we presented results for the first 1083 FAST candidates observed from 1999 January through 2002 January. Here we discuss the additional 2300 candidates for which we obtained FAST spectra up to 2013 April. In Figure 7, we show the spatial distribution of the Orion TTS members confirmed with FAST. We obtained a relatively uniform spatial coverage across the entire survey area, except for the decl. band $+4\deg \lesssim \delta \lesssim +6\deg$. The FAST Spectrograph was equipped with the Loral 512 × 2688 CCD, in the standard configuration used for "FAST COMBO" projects: a 300 groove mm⁻¹ grating and a 3'' wide slit, producing spectra spanning the range from 4000 to 7400 Å with a resolution of 6 Å. In Figure 10, we show FAST spectra of two new TTSs. The spectra were reduced at the CfA using software developed specifically for FAST COMBO observations. All individual spectra were wavelength-calibrated using standard IRAF routines. The effective exposure times ranged from 60 s for the $V\sim 13$ stars to ∼1500 s for objects with $V\sim 16$.

SOAR+Goodman—We used the GHTS, installed on the SOAR 4.1 m telescope on Cerro Pachón, Chile, to obtain slit spectra of 23 candidate TTSs that needed confirmation and had not been observed with any other spectrograph. We used available time slots during the engineering nights of 2014 March 19, 2017 September 6, and 2017 December 5. The GTHS is a highly configurable imaging spectrograph that employs all-transmissive optics and Volume Phase Holographic Gratings, which result in high throughput for low- to moderate-resolution spectroscopy over the 320–850 nm wavelength range. The 2014 March 3 and 2017 September 6 observations both used the 400 lines mm⁻¹ grating in its 400M2 preset mode combined with the GG 455 order-sorting filter. This configuration provides a wavelength range $\sim 5000\lesssim \,\lambda \,\lesssim 9000$ Å, which combined with the $1^{\prime\prime}$ wide slit results in an FWHM resolution of 6.7 Å (equivalent to $R\sim 800$). Examples of Goodman-SOAR spectra are shown in the two right panels of Figure 10. The 2017 December 5 observations were done with the 600 lines mm⁻¹ grating in the "mid" setup, with the GG385 order-blocking filter and the $1^{\prime\prime}$ slit. This setup results in an FWHM spectral resolution of 4.4 Å (equivalent to R ∼ 1300) in the wavelength range of $\sim 4450\lesssim \,\lambda \lesssim \,7050$ Å. In all cases, we used 1 × 1 binning, keeping the native pixel scale of $0\buildrel{\prime\prime}\over{.} 15$ pixel⁻¹. For each object, we obtained three integrations, which were median-combined after correcting for bias and spatially registering the second and third exposures to the first one, which we used as reference. Integration times ranged from 300 s for the brightest targets (V ∼ 15) to 900 s for the fainter ones (V ∼ 18). The basic image reduction was performed using standard IRAF packages: CCDPROC and IMSHIFT. The one-dimensional spectrum was extracted using routines in the IRAF TWODSPEC and ONEDSPEC packages. For wavelength calibration, we used a HgArNe lamp.

We did not perform flux calibration in any of our spectra, since the main purpose of our follow-up spectroscopy is membership identification and SpT classification. We measured Hα and Li i equivalent widths in all our low-resolution spectra from the various instruments, using the splot routine in IRAF and the SPTCLASS tool (Hernandez et al. 2017), an IRAF/IDL code based on the methods described in Hernández et al. (2004). Lines in the far red region of the spectrum were only available for TTSs confirmed in Hectospec and SOAR spectra. The signal-to-noise ratio (S/N) of our spectra was typically $\gtrsim 25$ at Hα λ6563, sufficient for detecting equivalent widths down to a few 0.1 Å at our spectral resolution of ∼6–7 Å FWHM. In Figures 8–10, we show sample spectra of Orion OB1 WTTSs and CTTSs observed with the Hydra and Hectospec, M2FS, and FAST and SOAR spectrographs, respectively.

We establish membership based on our low-resolution spectra from FAST, Hydra, Hectospec, M2FS, and SOAR (Figures 8–10). Our criteria to identify PMS low-mass stars are the following:

(1) SpT between K and M type, which corresponds to the range of colors and magnitudes expected from our photometric survey candidate selection.

(2) Presence of the Balmer hydrogen lines in emission, in particular Hα λ6563, which are characteristic of active late SpT young ($\lesssim 1$ Gyr) dwarfs (e.g., Stauffer & Hartmann 1986; Stauffer et al. 1997).

(3) Presence of the Li i (6707 Å) line strongly in absorption (Briceno et al. 1997; Briceño et al. 1998). Li i is our main youth criterion for late-type stars. Since lithium is depleted during the PMS stage in the deep convective interiors of K- and M-type stars, we regarded a candidate object to be a TTS if it had Hα λ6563 in emission and Li i λ6707 in absorption with equivalent width larger than the upper value for a Pleiades star of the same SpT (Soderblom et al. 1993; Garcia Lopez et al. 1994), which represents the young main sequence for late-type stars (Figure 11). With an S/N $\gtrsim 25$ in our spectra, we could detect Li i λ6707 absorption down to W(Li i) ∼ 0.1 Å. There are some cases in which Li i could not be reliably measured, but we still classified the star as a TTS. The decision to include the star as a TTS was based on the presence of Hα λ6563 clearly in emission, in addition to other lines like Hβ λ4861, Ca H & K $\lambda \lambda 3934,3969$, He i $\lambda \lambda 5876,6678$, and in some cases also [O iii] $\lambda \lambda 6300,6364$, [N ii] $\lambda \lambda 6548,6583$, [S ii] $\lambda \lambda 6716,6732$, and Ca ii $\lambda \lambda \lambda 8498,8542,8662$. This generally only applied to strongly accreting CTTSs. Reasons for Li i not being measured could be due to a noisy spectrum, or because the spectrum is heavily veiled by the excess continuum emission from an accretion shock, created by material infalling from the circumstellar disk onto the star. In this latter case, a TTS would exhibit weak Li i absorption, below the Pleiades distribution upper envelope, thus failing our Li i TTS classification criterion, but otherwise fulfilling all other spectroscopic indicators of it being a very active, accreting young star (see (4) below).

(4) Presence of additional youth signatures, in particular gravity-sensitive features like the Na i 8173/8195 Å doublet weakly in absorption (e.g., Martin et al. 1996; Luhman et al. 2003; Martín et al. 2004, 2010; Slesnick et al. 2006; Downes et al. 2008; Lodieu et al. 2011; Schlieder et al. 2012). In strongly accreting young stars, other spectral features like He i $\lambda \lambda 5876,6678$, [O i] $\lambda \lambda 6300,6346$, [S ii] $\lambda \lambda 6716,6732$, and the Ca ii triplet $\lambda \lambda \lambda 8500,8544,8665$ can also be seen in emission (Edwards et al. 1987; Hamann & Persson 1990, 1992; Hamann 1994), and we take these as features that confirm and reinforce the PMS nature of a star.

In Figure 12, we show our classification procedure.

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Following this approach, we classified 2062 candidates as confirmed low-mass, PMS stars of K- and M-type, based on our low-resolution spectra (passed Hα, Li i criterion). The properties of each TTS are provided in Table 3: ID, designation in Hernández et al. (2007b, hereafter H07) and in SIMBAD (when available), coordinates on the sky, SpT, equivalent width of Hα, equivalent width of Li i 6707 Å, total equivalent width of Na i 8183 Å+8195 Å, type (WTTS, CTTS, or C/W—see Section 3.3), CVSO photometry and variability information, 2MASS JHKs photometry, T_eff, A_V, location within the Orion association, and luminosity. There are a few very active CTTSs that show many emission lines in their spectra, but we provide here measurements only for Hα, Li i, and the Na i 8183, 8195 Å doublet (this last spectral feature only for the 1025 objects observed with Hectospec).

Table 3.  T Tauri Stars in the CVSO

Column Number	Column Name	Description
1	CVSO	CVSO number
2	H07	ID from Hernández et al. (2007a)
3	Other ID	Other designation, from SIMBAD
4	R.A.(J2000)	R.A. J2000.0 (hh:mm:ss.ss)
5	Decl.(J2000)	Decl. J2000.0 (dd:mm:ss.s)
6	SpT	Spectral type
7	WHa	Equivalent width of Hα 6563 (Å)
8	WLi	Equivalent width of Li i 6707 (Å)
9	WNaI	Total equivalent width of the Na i 8183, 8195 doublet (Å)
10	Type	C = CTTS, CW = C/W, W = WTTS (Section 3.3)
11	$\bar{V}$	V-filter robust mean (mag; Stetson 1996)
12	err(V)	1σ error of $\bar{V}$, computed from err versus mag diagram (mag)
13	N(V)	Number of non-null V-band observations
14	$\bar{R}$	R-filter robust mean (mag; Stetson 1996)
15	err(R)	1σ error of $\bar{R}$, computed from err versus mag diagram (mag)
16	N(R)	Number of non-null R-band observations
17	$\bar{{I}_{C}}$	I-filter robust mean (mag; Stetson 1996)
18	err(IC)	1σ error of $\bar{I}$, computed from err versus mag diagram (mag)
19	$N({I}_{C})$	Number of non-null I-band observations
20	${\rm{\Delta }}(V)$	V-band peak-to-peak amplitude (mag)
21	${\rm{\Delta }}(R)$	R-band peak-to-peak amplitude (mag)
22	${\rm{\Delta }}({I}_{C})$	I-band peak-to-peak amplitude (mag)
23	$\sigma (V)$	V-band standard deviation (mag)
24	$\sigma (R)$	V-band standard deviation (mag)
25	$\sigma ({I}_{C})$	V-band standard deviation (mag)
26	Vprob	${\chi }^{2}$ probability of variability in V
27	Rprob	${\chi }^{2}$ probability of variability in R
28	Iprob	${\chi }^{2}$ probability of variability in I
29	LVR	Stetson (1996) variability index for V and R magnitudes
30	LVI	Stetson (1996) variability index for V and I magnitudes
31	LRI	Stetson (1996) variability index for R and I magnitudes
32	J	2MASS J magnitude (mag)
33	err(J)	2MASS J 1σ combined error (mag)
34	H	2MASS H magnitude (mag)
35	err(H)	2MASS H 1σ combined error (mag)
36	K	2MASS Ks magnitude (mag)
37	err(K)	2MASS Ks 1σ combined error (mag)
38	Teff	Effective temperature (K) (1)
39	AV	Extinction in the V-band (mag) (2)
40	Loc	Location within Orion OB1: 1a, 1b, 25 Ori, HR 1833, A_cloud, B_cloud

Notes.

^aCorresponding to the spectral type interpolated in Table A5 of Kenyon & Hartmann (1995). ^bFor 86% of the sample, A_V was derived from the V − I_c color. For an additional 8% of stars which lacked an I-band measurement, we used the V − J color. For the remainder of the stars, we used either the R − I, R − J or I − J colors. We adopted the Cardelli et al. (1989) extinction law, and intrinsic colors from Kenyon & Hartmann (1995).

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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Of the 2062 TTS, 245 were identified in Hydra spectra, 1025 in Hectospec spectra, 49 in the M2FS spectra, 722 in FAST spectra, and 21 in SOAR GHTS spectra. About 50% of the CS2 candidates were confirmed as TTSs, compared to a ∼9% success rate for the TTSs confirmed from the CS3 + 2MASS J − H color-selected sample. This result highlights the importance of optical variability as a tool for tracing young, low-mass populations of young stars in regions devoid of molecular gas. Since our variability detection rate is highest for the bright ($V\lesssim 16$) sample (because of the smaller measurement errors), we can look at the success rate of the FAST follow-up spectroscopy as an indicator of the best-case efficiency we can expect from our variability selection technique. Of the 1235 variable candidates observed with FAST, 650 (∼53%) were classified as TTSs. By contrast, only ∼21% of the stars in the entire FAST sample were labeled as a TTS, a number we would expect from a conventional single-epoch color–magnitude selection. In the combined Hydra and Hectospec sample, 428 of 951 PMS candidate variables (45%) were classified as TTSs, a slightly lower success rate compared to the FAST sample, but consistent with the fact that as we go to fainter magnitudes, we can detect only those variables that have increasingly larger amplitudes.

The usefulness of the Na i lines as surface gravity indicators has been known since Luyten (1923) first showed that the sodium D doublet (5890, 5895 Å) was stronger in dwarfs than in giants. The low ionization potential of alkali atoms like sodium, which have a single valence electron, means that they are easily pressure-broadened, and therefore the absorption line strength increases as the gas density gets larger. However, Na i (5890, 5895 Å) is strongly affected by TiO absorption bands in stars later than ∼M2, and absorption by the interstellar medium may also affect the line strength. On the other hand, the Na i subordinate doublet at 8183 Å and 8195 Å is located in a region of high S/N in our Hectospec spectra and not significantly affected by telluric absorption, or by TiO bands up to SpTs as late as M9. This feature has been used many times to discriminate between field dwarfs and younger, late-type objects (Martin et al. 1996; Martín et al. 2004, 2010; Lawson et al. 2009; Lodieu et al. 2011; Hillenbrand et al. 2013; Hernández et al. 2014; Suárez et al. 2017), though with samples of limited sizes. With our spectroscopic follow-up with Hectospec, we have amassed a large number of spectra going out to ∼9000 Å. Armed with such a large sample of TTSs and field stars, all identified and measured with the same instrumental setup and uniform criteria, we can now explore the behavior of the Na i (8183, 8195 Å) doublet as a youth indicator across the K to M SpT range in a consistent way.

In Figure 13, we show the total equivalent width of the Na i (8183, 8195 Å) doublet as a function of the observed V − J color¹⁴ for 3441 stars: 1025 TTSs (dark green dots) and 2416 field stars (light blue dots). For every object, the equivalent widths of each of the Na i lines were measured both with SPTCLASS (Hernandez et al. 2017) and interactively with the splot utility in IRAF, which allowed us to obtain an estimate of the measurement uncertainty, indicated by the error bar in the figure. It is important to point out that the TTSs were identified based solely on the presence of Hα in emission and Li i 6707 Å strongly in absorption, above the Pleiades level, as described in Section 3.1.1. Stars lacking Li i were classified as field stars. A least-squares fit to the distribution of field stars is shown as a blue straight line.

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As expected from the V ∼ 13 saturation limit of the photometry, our color selection, the relatively low extinction, and the nature of the stellar mass function in the thin disk of the Galaxy (Robin et al. 2003), the majority (65%) of the field stars in our sample are K- and M-type dwarfs (see Section 3.2 below, and also Downes et al. 2014), with a median SpT of M0 and median A_V = 0.64 mag. Among the late-type field stars, 23% were classified as active K- and M-type dwarfs with Hα in emission (dKe and dMe stars); this subset is characterized by a later median SpT of M3.

Despite the large scatter of Na i equivalent widths at any given V − J, it is readily apparent that the bulk of the TTSs lie distinctly below the distribution of field stars. To quantify this effect, we show in Figure 13 isochrones calculated by Schlieder et al. (2012), using the Siess et al. (2000) evolutionary tracks and the PHOENIX model atmospheres (Hauschildt et al. 1999; Rice et al. 2010). The mean value for the field stars in Figure 13 matches very well the 100 Myr isochrone, and 99.9% of the TTSs fall below this line. Most of the spread seen in the field stars for SpTs later than ∼M0 is encompassed within the 50 Myr and 1 Gyr isochrones. It is also noticeable that the TTSs and field stars tend to separate in the W(Na i) versus T_eff plane, only for V − J ≳ 3, corresponding to SpTs later than ∼M1.5.

Of our list of 2062 spectroscopically confirmed TTSs, 1484 (72%) are characterized here for the first time, as newly identified members of the Orion OB1 association; 787 have a match within 3 arcsec in the SIMBAD database (the average separation is $0\buildrel{\prime\prime}\over{.} 31\pm 0\buildrel{\prime\prime}\over{.} 33$) and are classified as a star. However, only 433 of the matches (55%) have a SIMBAD type "TT" (TTS), "YO" (young stellar object), "pr" (PMS star), "Or" (variable star of Orion type), "iC" (star in cluster), or "iA" (star in association), and an SpT. We adopt these objects as previously known, confirmed young members of Orion OB1. In Table 3, we provide the SIMBAD identification and type for matching objects.

Among the 433 TTSs in SIMBAD, 225 were published by us in B05, B07a, and Biazzo et al. (2011); another 77 in Downes et al. (2014); and 53 in Suárez et al. (2017). The other 78 are from various other studies (see Section 3.4.3). The remaining 354 SIMBAD objects are stars that lacked SpT determination and Li i or Na i measurement. They are either candidate PMS stars from other studies such as Hernández et al. (2007a; 212 objects) and Megeath et al. (2012; 82 objects) or objects classified as an emission-line star, X-ray source, variable star, flare star, irregular variable, star in cluster, or star in association, but lacking membership information. For these, we provide here, for the first time, spectroscopic confirmation of their youth.

Combined with our previous works (B05, B07a), this constitutes the largest sample of low-mass PMS stars with both multiband photometry and optical spectra, obtained in a consistent and systematic way in all of Orion, even when compared to the intensively studied ONC (H97; Carpenter et al. 2001; Slesnick et al. 2004; Tobin et al. 2009; Hillenbrand et al. 2013).

The Orion region has been studied extensively since it was recognized as an OB association by Blaauw (1964). However, few studies have undertaken the task of mapping in detail the young stellar population across the entire complex. In the 1990s, Wiramihardja et al. (1989), Kogure et al. (1989), and Wiramihardja et al. (1991) searched ∼100 square degrees for Hα emission-line stars using photographic plates on the 1 m Kiso Schmidt telescope equipped with an objective prism. They published 759 candidate young stars, but without membership confirmation; 102 are confirmed as members here. Newer objective prism studies like that of Szegedi-Elek et al. (2013) have focused on the ONC, finding 587 candidate young stars, of which 35 are in our CVSO catalog.

Recent work has revealed large numbers of PMS stars in Orion, but concentrating on the youngest populations on the A and B molecular clouds. Such is the case of the Spitzer study by Megeath et al. (2012), which covered the entire Orion A cloud and most of the B cloud. They identified nearly 3500 young stars based on their spectral energy distributions and infrared variability; 82 of these sources match our CVSO catalog, of which 80% are classified by us as CTTSs, a result consistent with a search for objects with IR-excess emission. Alves & Bouy (2012) presented a photometric study of the region surrounding the ONC, but their proposed population is based on photometric candidates only; 118 of their sources are in our TTS list. Da Rio et al. (2012) carried out a deep photometric survey of 0.25 deg² in the ONC region, proposing 1750 objects as candidate young members; 26 match our CVSO catalog, of which 20 are CTTSs. Pillitteri et al. (2013) conducted an X-ray study of the L1641 cloud; they found 716 candidate young stars, of which 16 have a counterpart in our CVSO TTS list, with 12 being WTTSs, 3 CTTSs, and 1 C/W. Sanchez et al. (2014) carried out a UV-based selection of candidate young stellar objects across ∼400 deg² encompassing all of Orion, using data from the Galaxy Evolution Explorer (GALEX). They identified 111 candidate PMS objects, of which 11 are found in our list. As expected from the UV-excess selection, all but one are CTTS. Spezzi et al. (2015) used the VISTA Orion Mini Survey to identify 186 candidate young objects in the B cloud, including the embedded clusters NGC 2068 and 2071. Ten of their targets match our CVSO catalog, and all but one are CTTSs, as would be expected from a selection biased toward IR-excess sources. In the Orion OB1b subassociation, Kubiak et al. (2017) identified 789 candidate young members, based on optical/infrared photometry, with no spectroscopic confirmation. Unfortunately, their target table is not yet available in either SIMBAD, Vizier, or the CDS data services, so we could not cross-match their list with our CVSO sample. For all of the objects in these studies in common with our CVSO catalog, we provide here spectroscopic membership confirmation and characterization of SpT, among other stellar parameters.

Among the few studies targeting the older populations, Van Eyken et al. (2011) used the Palomar Transient Factory survey to look for eclipsing binaries in the 25 Ori cluster. They presented 16 candidate young stars, of which 6 have a counterpart in the CVSO. One is CVSO-35, already known from B05, and the other five are confirmed here as TTSs.

Work based on optical low-resolution spectroscopic membership confirmation has largely focused on the ONC region and its surroundings in the A cloud. H97 carried the first landmark study of the ONC, producing spectral classification for 675 stars. Then, Hillenbrand et al. (2013) added 254 new stars and reclassified many of the H97 stars; 27 of their sources are found in our TTS list. Hsu et al. (2012) surveyed ∼3.25 deg² in the L1641 dark cloud, located within the Orion A cloud, south of the ONC. They confirmed 864 low-mass PMS members, 723 of them in common with the Megeath et al. (2012) survey. A total of 22 objects have a match in our CVSO catalog.

After the ONC, the σ Orionis cluster is probably the most studied stellar aggregate in Orion. Among the most recent comprehensive spectroscopic studies is that of Hernández et al. (2014). In our CVSO catalog, we have 16 sources in common with their list of 340 confirmed members. Another cluster that has been the subject of several spectroscopic studies is 25 Ori. Downes et al. (2014) used deep, coadded I_C-band photometry from the CVSO, combined with VISTA data and follow-up spectroscopy, to search for very low-mass TTSs and young brown dwarfs; 65 of their 77 new members are in our catalog. More recently, Suárez et al. (2017) combined optical photometry from the CVSO with spectroscopy from SDSS-III/BOSS to identify 53 new members in an area of ∼7 deg² roughly centered on the cluster. We find 25 TTSs in common with their study.

The proposed foreground population of NGC 1980 has been studied spectroscopically by Kounkel et al. (2017a), who obtained spectra for 148 young stars. Nine objects are in common with our work; SpTs determined in both studies compare well. Fang et al. (2017) also investigated the "foreground" population to NGC 1980 proposed by Alves & Bouy (2012) and Bouy et al. (2014). They obtained spectra and stellar properties for 691 young stars within ∼12 square degrees in this region. We found 24 stars in common with our list. In general, few objects in our CVSO catalog match these various studies in the ONC and the A cloud. The main reason is that our south survey limit is close to δ = 0°–6°, and we avoided the central region of the ONC, so there is little spatial overlap with these various studies.

After we take into account repeats between the aforementioned studies, there are only 78 objects with existing spectroscopic membership confirmation among the 2062 CVSO TTS (∼4%), excluding the 356 sources already published in our previous works (B05, B07a; Biazzo et al. 2011; Downes et al. 2014) and in Suárez et al. (2017). Aside from the stars in 25 Ori and σ Ori, all of the other sources are located south of δ = −6°. Therefore, our survey provides the basis for a consistent and comprehensive characterization of the young stellar population across the Orion OB1 association, north of δ = −6° and south of +6°.

With such a large number of confirmed TTS members, we have the means to derive, for the first time, robust demographics of the populations of low-mass PMS stars in this star-forming complex, across a range of ages and differing environments, with an emphasis on the largely unknown off-cloud component.

As is the case for 25 Ori (B07a), we expect these other groupings of TTSs in 1a to be likely younger than ∼20 Myr. Because of this, we also expect the more massive B- and A-type stars to be located on, or very close to, the zero-age main sequence (ZAMS) in an extinction-corrected CMD. This provides us with the opportunity to derive a photometric parallax for each group by applying the main-sequence fitting technique instead of simply assuming a common distance for all groups.

A practical advantage of these particular groups is that they are located in an area of very low extinction, well removed from the Orion molecular clouds (A_V ≲ 0.3 for the 25 Ori group; Briceño et al. 2007; Downes et al. 2014; Suárez et al. 2017); therefore, reddening is not an issue when correcting the observed photometry. Within each circular region, we looked up the SIMBAD database and the Kharchenko et al. (2005) catalog of 109 new open clusters for B- and A-type stars. We then cross-referenced these lists with Hernández et al. (2005), using their SpTs whenever available, matched to the Spitzer Orion OB1 observations of early-type stars by Hernández et al. (2006) and to the WISE catalog (Wright et al. 2010). In each group, we determined which B- and A-type stars showed IR-excess emission typical of circumstellar dusty disks. In the 25 Ori cluster and the HR 1833 groups, where we have Spitzer 24 μm data, we followed the criterion shown in Figure 4 of Hernández et al. (2006): we used the J − H versus Ks − [24] color–color diagram to select objects with Ks − [24] ≥ 0.5 as disk systems; this selection includes those classified as debris disk systems (0.5 < Ks − [24] < 5), and those in the Herbig Ae/Be locus (Ks − [24] > 5). In the HD 35762 group, we used the WISE W4 band (22 μm), using only measurements with S/N $\gtrsim 5$ and that had an actual source visible in the W4 image. We further assumed that the disk-bearing B- and A-type stars located within the circular area defined for each group are high-probability early-type members. Once the disk systems were identified in each stellar aggregate, we narrowed our selection to those with SpTs roughly between B9 and A5 (equivalent to $-0.2\lesssim {(V-J)}_{0}\lesssim 0.25$). This range corresponds to stars that should be on or very close to the ZAMS. At ages of several, up to ∼20 Myr, they are not so massive as to have started evolving off the ZAMS, and they are not low-mass enough to be located significantly above the ZAMS. In practice, this is equivalent to these stars being located within $\sim \pm 0.12$ mag of the main sequence in a V versus V − J CMD (Siess et al. 2000). We therefore assume that the bright end of the cluster sequence is defined by the ∼B9 to A5 stars with disks. A least-squares fit of the Siess et al. (2000) ZAMS to these stars in each group yielded distances of 337 ± 35 pc for 25 Ori (fit with five stars), 345 ± 35 pc for HR 1833 (fit with five stars), and 343 ± 25 pc for HD 35762 (fit with eight stars). These distances are in agreement with the mean distances derived using available Gaia DR1 (Gaia Collaboration et al. 2016) parallaxes for the B9 to A5 stars in each group, regardless of whether or not they were disk candidates, as long as they were located within ±0.12 mag of the main sequence in the CMD. With the new Gaia DR2 release (Gaia Collaboration et al. 2018), we can now derive individual distances for a sizable subset of the 2062 TTSs in the CVSO sample. This provides a sensitive check on the above distances to the various Orion OB1 groups, with statistically robust samples of well-characterized young stars, and enables us to derive for the first time distances to the non-clustered populations in the OB1a and OB1b subassociations, and the populations projected on the molecular clouds. In Table 4, we compare the three distance determinations for the groups and add the Gaia DR2 distances to the other regions. We removed a few objects with negative parallaxes and used only stars with parallax errors <20%. Note that for the distances derived from the Gaia parallaxes, we show the standard deviation of all measurements in each group. The actual typical measurement error in DR2 for our CVSO TTS is ∼± 25 pc.

Table 4.  Mean Distances for Each Region

Region	MS Fita	Gaia DR1b	Gaia DR2c	Adopted	${N}_{\ast }^{\left({\rm{d}}\right)}$
	(pc)	(pc)	(pc)	pc
Cloud B	⋯	⋯	${395}_{-50}^{+68}$	400	60
Cloud A	⋯	⋯	${398}_{-45}^{+39}$	400	206
1b	⋯	⋯	${{398}_{-51}^{+69}}^{{\rm{e}}}$	400	510
25 Ori	337 ± 35	${347}_{-43}^{+58}$	${352}_{-28}^{+34}$	350	211
HD 35762	343 ± 25	${361}_{-35}^{+44}$	${348}_{-28}^{+34}$	350	78
1a	⋯	⋯	${358}_{-43}^{+60}$	360	797
HR 1833	345 ± 35	${361}_{-36}^{+45}$	${370}_{-40}^{+52}$	360	64

Notes.

^aMain-sequence fitting for B9 to A5 stars, with the σ of the fit. ^bGaia mean distances derived from DR1 parallaxes of B9 to A5 stars. ^cGaia mean distances derived from DR2 parallaxes for CVSO TTSs in each group. ^dNumber of CVSO TTSs involved in each mean Gaia DR2 distance determination. ^eThe distance distribution in OB1b is bimodal; we find two distinct groups of stars, at two different distances.

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The distances derived from our main-sequence fitting, from Gaia DR1 parallaxes for the early-type stars, and from the Gaia DR2 data for the TTS populations, all agree within 1 − σ. In column 5 of Table 5, we provide our adopted distances for each region, and in Figure 23, we show the distribution of distances derived from Gaia DR2. An interesting result is that the OB1b region seems to contain two populations of TTSs, a "near" one at a mean distance of ∼365 pc and a "far" population located roughly at 420 pc. With a sample of over 500 stars in this histogram, this is a rather robust result. The "near" subset distances peak at ∼365 pc, essentially the same distance as the field population of OB1a. In retrospect, this is not surprising, given that we would expect some amount of "contamination" of OB1b star samples by stars from the older and closer OB1a subassociation (B05). In fact, this result is consistent with the suggestion by Jeffries et al. (2006) of an older population of stars from OB1a, which has a mean radial velocity of 23.8 km s⁻¹, offset about 7 km s⁻¹ from the 30 km s⁻¹ mean velocity of the OB1b stars (see also B07a). Further study of the kinematics of these two populations, which is beyond the scope of this work, will help disentangle their nature and origin.

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With the distances derived for each group, we proceed to plot all of the stars in reddening-corrected V − J CMDs, along with the Siess et al. (2000) isochrones (Figures 24–26). To derive A_V, we preferentially used the V − I_C color, which uses the robust mean V and I_C magnitudes from our CVSO optical photometry, available for ∼86% of the stars. For the remainder of the stars, we used V − J or the R − I_C or I_C − J colors. We used the intrinsic colors from Kenyon & Hartmann (1995), corresponding to the SpT for the star, and the Cardelli et al. (1989) reddening law with R_V = 3.1, which is consistent with recent estimates of the extinction toward the Orion region by Schlafly et al. (2016). We used the colors provided by the Siess et al. (2000) isochrone server: http://www.astro.ulb.ac.be/~siess/pmwiki/pmwiki.php?n=WWWTools.Isochrones, which are derived in the Cousins system using the conversion provided by Kenyon & Hartmann (1995) in their Table A5.

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It is important to note that because we have extensive variability information in the optical bands for each star, we plot the clipped mean average V magnitudes, so that any spread in luminosity because of variability is minimized. Though ideally we would plot the V − Ic CMDs because they contain the optical photometry and variability information from our own data set, we instead chose here the V − J color, with the caveat that the 2MASS J-band is not simultaneous with our optical photometry, in order to include the early-type stars, which mostly lack I-band data. The CMDs for each group show a well-defined cluster sequence running from the early-type stars all the way to the low-mass PMS members, with a gap in the range roughly corresponding to SpTs F to late G. Stars in this range are saturated in our CVSO survey and are hard to discriminate from contaminating field stars based only on the existing information in the SIMBAD and Kharchenko et al. (2005) samples. Though accreting members of this class of objects are easy to find using tracers like strong Hα emission and IR excess, the WTTS counterparts have been traditionally difficult to pinpoint. Because of their shallow convective outer zones, G- and F-type stars do not deplete lithium significantly during their PMS phase. Therefore, in contrast with K and M stars, for these earlier type objects, lithium is not a useful youth indicator. Criteria like X-ray activity are not too useful for finding PMS stars among solar-type stars, because X-ray emission decays slowly during the first ∼100 Myr in G to early-K stars (Briceno et al. 1997). This an outstanding issue in which parallaxes will be crucial to confirm membership, in combination with optical photometry and spectroscopy. The Gaia DR2 release will be of great help in filling in this region of the CMD.

That the new HR 1833 and HD 35762 TTS clusterings exhibit relatively well-defined sequences in the CMD is a compelling suggestion that they are real stellar aggregates, less massive siblings of the 25 Ori cluster. In contrast, the CMD for the general field population across 1a (Figure 27) is much more spread out in luminosity, as expected from stars that likely span a broader range of distances and ages compared to the population of the three clusterings.

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As discussed in Section 3.5, we identify two major overdensities within the Orion OB1b subassociation, which we labeled I and II, each one showing hints of further substructure, which we identified as subgroups a, b, and c. However, to simplify our discussion and in order to have better statistics, here we will consider these two major structures as two single entities. In Figure 28, we plot the TTSs in the V − J CMDs for each of these two groups, together with the early-type stars found within each overdensity. We assumed a distance of 390 pc, consistent with the latest determinations for the σ Ori cluster (Hernández et al. 2014; Schaefer et al. 2016; Caballero 2017), which is generally assumed to be part of the OB1b region. There are 231 TTSs in these two stellar groups: OB1b I contains 93 TTSs, while OB1b II encompasses 138 TTSs. It is interesting that both OB1b groupings exhibit fairly well-defined sequences and that the early-type stars are also roughly located at their expected location in the CMDs, assuming they form part of these two stellar aggregates, although they are clearly more scattered in the CMD compared with their siblings in the OB1a clusterings, maybe in part because of larger extinction in OB1b compared to OB1a. Also apparent is the fact that OB1b I contains a larger fraction of CTTSs than OB1b II, but we defer further discussion to the next section.

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In Section 3.6.1, we showed that the OB1b region is composed of two populations separated in distance. In Figure 29, we show the distribution of distances derived from the Gaia DR2 parallaxes for each of the two groups of TTSs in OB1b. This plot shows that the bimodality in the distance (or parallax) distribution in the OB1b subassociation arises from the northern OB1b I group, which has a near (∼355 pc) component and a far (∼415 pc) component. By contrast, the majority of the TTSs in the southern OB1b II group are at distances within the range $d\sim 390\mbox{--}450$ pc, with a median distance of ∼420 pc. As we discuss in Section 3.6.1, we speculate that this "near" component may be part of the field population of OB1a stars. If so, we would expect these TTSs to share other properties with their OB1a siblings.

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In order to study any evolutionary trends, we must first estimate ages for each region and group of stars. The dereddened CMDs provide a useful tool to do this. For each star, we obtained the observed V − I_C color from the CVSO robust mean V- and I-band magnitudes and then derived the color excess by comparing with the intrinsic color corresponding to our SpT, obtained from Table A5 in Kenyon & Hartmann (1995). We derived A_V assuming the Cardelli et al. (1989) reddening law; we could derive extinctions for over ∼88% of the CVSO stars using V − I_C. Because V − I_C comes from our quasi-simultaneous CVSO photometry, we adopted this band to perform the reddening correction in preference over the V − J color. The small fraction of stars dropped because of lack of V − I_C information does not affect in a significant way our final mean age estimates. We then performed a linear interpolation within the Baraffe et al. (1998) and Siess et al. (2000) model isochrones, using their published V − J colors and deriving absolute V-band magnitudes with the reddening-corrected distance modulus corresponding to the adopted distances for each group and region shown Table 4. Finally, we computed clipped mean ages to derive a single age for each region. Because the distribution of log (age) tends to have more symmetric, Gaussian shapes than the distribution in age, we used these to derive the mean age and standard deviations (and perform the outlier rejection). The values, standard deviation of the fits, and number of stars involved in each calculation are provided in Table 5.

The Siess et al. (2000) models yield older ages compared to the Baraffe et al. (1998) ones, but both agree in the sequence of ages, indicating, as expected, that the youngest stars are the ones projected onto the A and B molecular clouds. Within the uncertainties, these two regions can be assumed to be of the same age, ∼3 Myr, a value which is somewhat higher but consistent with estimates for regions like L1641 in the A cloud (Hsu et al. 2012; given the large uncertainties in age determination, particularly for the youngest star-forming regions). We also point out that because our candidate selection was optical, we are reddening-limited toward the molecular clouds, resulting in a modest number of stars compared to the low-extinction OB1b and OB1a regions. Therefore, we are more susceptible to contamination from OB1b and OB1a. Such slightly older stars would bias the mean age toward a slightly higher value. The second oldest population is located in the OB1b region, and the oldest stars are those in the OB1a subassociation, consistent with the historic picture of the progression of ages across Orion OB1. Within the OB1a region, 25 Ori seems to be the youngest group (∼6–9 Myr), similar in age to HD 35762, while HR 1833 comes out as the oldest one (12–14 Myr). The "field" population has an average age of ∼11 Myr.

Despite the large uncertainties in the absolute ages of each region, which come from a complex combination of observational errors that include determination of SpTs, transformation to an effective temperature scale, the adoption of dwarf temperatures and colors for PMS stars, the use of a particular reddening law, the uncertainty in the assumed distances, and finally, but not least, limitations in the theory behind model isochrones and differences between various models, for the purpose of our analysis here onwards, what is important is the age sequence between the various regions. Even with the improved distances that will come with the second release of Gaia, differences between models or differing methods, and the various other assumptions mentioned above, will likely still introduce significant systematic offsets, in addition to scatter. For example, Bell et al. (2013) found ages that are older by a factor of ∼2 compared to the most commonly assumed ages for several nearby young regions. Further discussion of PMS ages and their uncertainties is beyond the scope of this work.

The presence of the Li i 6707 Å line strongly in absorption is a reliable indicator of youth in K- and M-type stars (Section 3.1.1). Because this light element is burned at temperatures of $\sim 2\times {10}^{6}\,$ K, which roughly corresponds to the temperature at the base of the convective envelope in a solar-type star at the ZAMS (Siess et al. 2000), lithium is steadily depleted during the PMS phase in low-mass stars, and its surface abundance decreases over time, with the known spread caused by effects like rotation and the details of physical processes used in the stellar interior codes (Sestito & Randich 2005; Tognelli et al. 2012; Bouvier et al. 2016, 2018).

Having measured Li equivalent widths (W[Li i]) in a homogeneous way for a large number of PMS K- to M-type stars, we are in a vantage position to explore from a statistical perspective the depletion of Li during the PMS phase. In order to avoid the uncertainties associated with the derivation of Li abundances (see Sestito & Randich 2005; Tognelli et al. 2012), we restrict ourselves to looking at a purely observational measure, W(Li i). This approach was considered by Jeffries et al. (2014) in their discussion of PMS Li depletion. We adopt the ONC data from Sicilia-Aguilar et al. (2005) and the Taurus Li measurements from Basri et al. (1991), as representative of what can be considered as a "pristine" or "undepleted" Li sample of optically visible, 1–2 Myr old, low-mass PMS stars. Both data sets were obtained with similar spectral resolution to that of our spectra, so we expect a reasonable comparison with our own measurements, though it is important to bear in mind that even in very young regions like Taurus and the ONC, there is a considerable spread in Li abundances.¹⁵ Still, past studies indicate that most members in these very young regions have undergone little, if any, Li depletion; see Palla et al. (2005, 2007) and Sestito & Randich (2005). Thus, we define the "undepleted" or "young" Li locus in the W(Li i)–T_eff diagram, following Briceño et al. (2007), as the region above the line

$$\begin{eqnarray*}&&W{(\mathrm{Li}{\rm{i}})}_{\mathrm{young}}\gt 1.0591-(1.52\times {10}^{-4})\times {T}_{\mathrm{eff}},\end{eqnarray*}$$

with W(Li i) in Å and T_eff in K. Over 70% of Taurus and ONC TTSs fall in the young Li locus.

In Figure 30, we show the surface density of Li equivalent widths for two populations at different evolutionary stages, the ∼5 Myr old OB1b and the ∼11 Myr old OB1a "field" population. We use these two subsets because they have the largest number of stars, 556 in OB1b and 843 in OB1a, so that statistics are less affected by differences in sample sizes. We derived the surface density using the Two-dimensional Kernel Density Estimation recipe in R (Venables & Ripley 2002). We can see how as we go from a young region to an older one, even allowing for the large spread in W(Li i) at any given T_eff, in part intrinsic and in part due to measurement errors, a population-wide trend is evident; the K and M stars slowly move downwards in the diagram, to smaller values of W(Li i). This effect was already suggested by us in Briceño et al. (2007), and later shown by Jeffries et al. (2014) in the γ Velorum cluster. However, here we provide robust observational evidence of Li depletion with large samples of young populations of low-mass stars, all belonging to the Orion OB1 association.

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In the left panel of Figure 31, we show the evolution of the ensemble Li i for each population, parametrized by the number of TTSs in each group lying within the "young" Li locus, as indicated in Table 6. The decrease in the ensemble W(Li i) across different populations can be fit by an exponential decline with a characteristic timescale τ_Li = 8.5 ± 2.3 Myr in M-type stars, which constitute the bulk of the samples shown in Figure 30. This is in rough agreement, within a factor of ∼2, with theoretical predictions of Li depletion (Stahler & Palla 2005). For example, Bildsten et al. (1997) estimated that a $0.3\,{M}_{\odot }$ PMS star (approximately an M3 TTS) will have depleted its Li by ∼50% at 16 Myr. Though few studies similar to ours have been done, our findings seem consistent with the differences between the overall W(Li i) for M stars shown by Jeffries (2014) in their comparison of the ONC with γ Vel. The HD 35762 group is an outlier in Figure 31, with an unusually low Li-young fraction that does not fit the trend, though it is only a 1σ deviation. This group merits further investigation in order to determine better its full membership and derive better parameters for the stellar aggregate. Large-scale spectroscopic studies in increasingly older populations, carried out in a systematic way, could shed light on the evolution of Li in young stellar populations in the little studied 10–50 Myr age range. If this behavior could be calibrated, it may prove to be a useful tool for dating PMS populations in the next era of large-scale photometric and spectroscopic studies, ushered by the possibility of combining the power of facilities like DECam on the CTIO Blanco telescope, the Zwicky Transient Factory (Smith et al. 2014), and LSST (Ivezic et al. 2008) with highly multiplexed spectroscopic discovery and characterization machines like DESI (DESI Collaboration et al. 2016a, 2016b).

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An important indicator related to the evolutionary state of a population of low-mass PMS stars is the fraction of stars still accreting from their circumstellar disks. As we have discussed in Section 3.3, CTTSs are low-mass PMS stars considered to be actively accreting from a circumstellar disk. We have introduced an additional class of objects, namely, the C/W stars, which we argue are objects in a stage intermediate between that of actively accreting CTTS and the largely diskless, chromospherically active WTTSs. These C/W stars are likely undergoing modest and/or variable accretion, in some cases at levels below what can be readily detected in low-resolution spectra. Such low accretors can be diagnosed through high-resolution spectroscopy that can resolve the Hα line profile or near-IR spectra that can look at other accretion diagnostics like the He i $\lambda 10830$ line (Thanathibodee et al. 2018). In Table 7 we show the accretor fractions derived for each region, in order to gauge how accretion is progressing from one population to another. We determine the percentage of accreting TTS in each region as % Accretors = (No. CTTSs/No. TTSs) × 100.

The percentage of CTTSs averaged over our full sample is 11%, but this is a strongly location-dependent value, which is due to the very different ages of each group. It varies from at least 70% in the ∼1 Myr old ONC (Hillenbrand et al. 1998), to ∼30% in the A and B clouds, decreasing to 14% in the OB1b region and finally down to ∼5%–8% once we reach the ∼10 Myr age range of the OB1a subassociation. However, even within the OB1b region, there are considerable differences; the OB1b I group has a much higher fraction of CTTSs (∼22%) compared with OB1b II (3.8%).

As disks evolve and dissipate, fewer TTSs are still actively accreting at a given age, and the fraction of CTTSs diminishes as an increasing fraction of the PMS population tends to be composed of non-accreting WTTSs. This well-known trend (Hartmann 2008) can now be tested with improved statistics across populations characterized in a uniform and consistent way. In the right panel of Figure 31, we show the decrease of the accretor fraction with age, for all of the populations and groups in our sample. As in previous sections, for this analysis we consider OB1b as a single population, in order to provide more robust statistics. We have included the ONC as reference, taking the value of 70% provided by Hillenbrand et al. (1998), with the caveat that this number has not been derived in the same way as the rest of the regions and groups. Still, this value agrees well with the exponential fit to the data, described by the dashed red line,

$$\begin{eqnarray*} &&\% \mathrm{Accretors}={C}_{\mathrm{acc}}\times \exp (-t/{\tau }_{\mathrm{acc}}),\end{eqnarray*}$$

with C_acc = constant and $T=$ age, and C_acc normalized so that the percentage of accretors at t = 0 is 100%.

This fit gives an accretion e-folding timescale τ_acc = 2.1 ± 0.5 Myr, consistent with the findings of Fedele et al. (2010), but obtained in a single star-forming region, with ∼2000 stars measured in a consistent and uniform way. For reference, we also plot the disk fractions for each region, derived using the ${Ks}-W2$ color, by matching the CVSO sample with the ALLWISE catalog (Wright et al. 2010; Mainzer et al. 2011). Following Luhman & Mamajek (2012; who used ${Ks}-[4.5]$, from Spitzer data), we derived the disk fraction as the number of stars falling above the upper envelope of the distribution of WTTSs in a ${Ks}-W2$ versus V − J color–color diagram, divided by the total number of TTSs with a ${Ks}-W2$ measurement in each region. The disk fraction is systematically higher than the accretor fraction. A possibility is that at every age, there are systems in which accretion has stopped due to the clearing of an inner gap in the disk, but enough dust remains to produce an IR excess. Alternatively, there may be a number of low accretors that have not yet been found. An exponential fit to the decline in disk-bearing systems as a function of age results in a timescale of 3.2 Myr for the depletion of dust in the innermost parts of the disk. Our derived values for ${\tau }_{\mathrm{acc}}$ and ${\tau }_{\mathrm{disk}}$ are in very good agreement with previous studies looking at disk fractions using similar indicators (e.g., Fedele et al. 2010), the main differences being that, first, we have derived this result for a large sample within the same star-forming region, thus we can expect the stars to have a common origin, and second, all of the stars in each of the groups spanning the entire ∼3–10 Myr age range have been selected, confirmed as members, and characterized in the same way. We defer further discussion on the ensemble properties of disks in Orion OB1 to a forthcoming paper, in which we carry out an extensive analysis of Spitzer and WISE infrared data for the CVSO sample.

We now examine the variability among the various groups of stars in our sample. In Table 8, we show the mean and median amplitudes (peak-to-peak) of the variation in each of the V, R, and I_C bands, together with the mean and median standard deviation of the variability for each type of TTS: CTTS, C/W, and WTTS, as well as for the active and non-active subsets of the field star sample described in Section 3.3. As can be seen in Figure 32, the amplitude of the mean V-band amplitude decreases from the more active CTTSs, to the C/W class, and finally to the more quiescent WTTSs, which are still more variable than the population of active field stars. These active field stars are an important contaminant of photometric surveys like ours, even when folding in variability, because they are active K- and M-type stars, which are significantly variable, so they pass all our selection criteria. They differ from WTTSs only in the lack of the Li i λ 6707 absorption feature, and their weaker Na i λλ 8183, 8195 absorption. In fact, the active group of field stars has a higher $\overline{{\rm{\Delta }}(V)}=0.29$ compared to the non-active group ($\overline{{\rm{\Delta }}(V)}=0.22$). A Welch Two-sample T-test finds that the amplitude of variability in these two groups is different at the 95% confidence level. Thus, the active group, defined on the basis of Hα emission, also has a higher photometric variability in the V-band; moreover, because these stars are mostly foreground to regions like Orion, they naturally appear above the main sequence in CMDs. These young main-sequence dKe and dMe need to be accounted for when mapping star-forming regions in future large-scale surveys of the galactic disk.

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Table 8.  Optical Variability in Orion OB1

	TTS	CTTS	C/W	WTTS	Field stars
No. of Stars	2062	218	150	1694	2418
$\overline{{\rm{\Delta }}(V)}$	0.403	0.722	0.474	0.356	0.240
median ${\rm{\Delta }}(V)$	0.302	0.500	0.378	0.290	0.191
$\overline{{\rm{\Delta }}(R)}$	0.28	0.590	0.349	0.242	0.154
median ${\rm{\Delta }}(R)$	0.215	0.381	0.281	0.202	0.113
$\overline{{\rm{\Delta }}({I}_{C})}$	0.244	0.419	0.261	0.225	0.160
median ${\rm{\Delta }}{I}_{C}$	0.190	0.273	0.218	0.183	0.107
$\overline{\sigma (V)}$	0.091	0.179	0.118	0.078	0.049
median $\sigma (V)$	0.067	0.136	0.089	0.064	0.036
$\overline{\sigma (R)}$	0.064	0.145	0.081	0.054	0.032
median $\sigma (R)$	0.048	0.095	0.064	0.045	0.025
$\overline{\sigma ({I}_{C})}$	0.045	0.091	0.049	0.040	0.027
Median $\sigma ({I}_{C})$	0.033	0.055	0.047	0.032	0.021

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The trend in Figure 32, combined with that seen in Figure 16, provides support to the idea that the C/W class is indeed a transition stage between the more active CTTSs and the WTTSs, which in turn can be clearly distinguished as a group from their young main-sequence counterparts. Further details on the optical variability of the CVSO TTS sample can be found in Karim et al. (2016), where we presented optical light curves for 1974 stars and derived periods for 564 of them, the large majority WTTSs.