1. Introduction
A starless core is a key astronomical object. An observational study of starless cores provides insights into the star formation process. A star is born in the core, which is the dense region of a molecular cloud. The ratio of the number of the starless cores to the number of the star-forming cores indicates a timescale from the formation of a molecular cloud core to the birth of a star, assuming that all the molecular cloud cores form a star. The observational study of starless cores also provides insights into the physical properties of an isolated core. A young stellar object (YSO) emanates an energetic outflow, which disturbs the physical condition of a molecular cloud. A starless core maintains the original condition of a quiescent molecular cloud core. Kandori et al. (2005) investigated physical properties of 10 Bok globules [1] . They found that their radial column density profiles are approximated by the Bonner-Ebert sphere model. The radial profiles of the star-forming globules were fitted by the model with the parameter indicating an unstable condition. On the other hand, the radial profiles of the starless globules were fitted by the model with the parameter that was close to the boundary between stable and unstable conditions. In addition, the observational study of starless cores provides insights into chemical processes in a dense, cold region. Chemical conditions are also changed by the YSO. The chemical process in a quiescent, dense, and cold region has been investigated in the starless cores.
Lee and Myers (1999) presented a comprehensive list of starless cores [2] . They made a map of optical extinction on the Digitized Sky Survey and identified 406 dense cores. The major—(a) and minor—(b) axes of the cores were measured. Subsequently, the geometric mean of the FWHM (ab)0.5 of the core was calculated for each core. They searched for IRAS sources within a box twice the size of the geometric mean of the FWHM of the core. It was found that 306 cores did not have IRAS sources. These cores were classified as starless cores. Ninety-four cores have an IRAS source showing the spectral energy distribution signature of an embedded YSO. Six cores have a pre-main sequence star (PMS) only. Assuming that the age of an embedded YSO is 0.1 - 0.5 Myr, they estimated the timescale from the cloud core formation to the birth of the star to be 0.3 - 1.6 Myr.
However, IRAS sensitivity is not sufficient for detecting a sub-solar mass PMS at 150 pc. A low-mass YSO may be missed even if it is associated with the starless cores identified by Lee and Myers (1999) [2] . Consequently, more sensitive searches have then been conducted. Murphy and Myers (2003) conducted near- infrared (J-, H-, and K-bands) photometry of eight dense cores [3] . All cores do not have known PMSs, and most cores do not harbor IRAS sources. These were considered as candidates for the very earliest stage of low-mass star formation. However, they did not find objects with near-infrared excess.
Morita et al. (2006) discovered two classical T Tauri stars and one weak-line T Tauri star associated with the L 1014 dense core through optical broad-band photometry and long-slit spectroscopy [4] . The Spitzer Space Telescope also discovered a very faint infrared source, L 1014-IRS (Young et al. 2004) [5] . Thus, L 1014 is a star-forming core, although it was previously classified as a starless core (Lee and Myers 1999) [2] .
A deeply embedded YSO is very faint in optical and near-infrared wavelengths shorter than 2 μm. This study searched for YSOs associated with starless and star-forming cores at the wavelengths of 3.4 μm, 4.6 μm, and 12 μm (W1-, W2-, and W3-bands) by using the Wide-field Infrared Survey Explorer (WISE) photometric catalog.
2. Dataset
We investigated infrared sources in the ALLWISE photometric catalog for the 288 cores listed in Lee and Myers (1999) [2] , whose major-axis, minor-axis, and distance are known. The searched area for each core is an elliptical centered on the core center. Its semi-major and semi-minor axes are twice those of the core, respectively.
We selected the WISE sources whose photometric signal to noise ratios are larger than 5 in the W1-, W2-, and W3-bands. We eliminated the sources if the contamination and confusion flag was “D” (diffraction spike), “P” (short-term latent image), “H” (scattered light halo), or “O” (optical ghost). Further, we also removed the objects with a saturation value greater than 0.05 in the W1-, W2-, or W3-bands.
Class I and Class II candidates were selected on the color-color diagram. We applied the selection method proposed by Fischer et al. (2016) [6] .
3. Results
Figure 1 shows the color-color diagram of the WISE sources detected in the [LM 99] 69 region. In this diagram, we identified 2 and 6 Class I and Class II candidates, respectively. We detected 132 and 268 Class I and Class II candidates from 139 cores, respectively (Table 1).
We classified 288 cores into 3 types. One is the starless core, which is a molecular cloud core without any associated YSO candidates. We identified 149 cores for this type (Table 2). Second is the molecular cloud core with associated Class I candidates only. We identified 32 cores for this type. Here, the cores with both Class I and Class II candidates are not classified into this type. Third is the molecular cloud core with associated Class II candidates. We identified 107 such cores. The cores with both Class I candidates and Class II candidates are classified into this type. Ninety-one cores that were previously identified as the starless core were found to harbor Class I and/or Class II candidates.
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Figure 1. Color-color diagram of WISE point sources in the [LM 99] 69 region. Sources plotted in the region labeled as I are identified as Class I candidates. Sources in the region II are Class II candidates. Other sources are identified as field stars.
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Table 1. WISE point sources associated with the optically selected cores. The letters in the parentheses following the core name indicate the core classification in Lee and Myers (1999) [2] . N: starless core, I: core with an embedded YSO, II: core with a PMS.
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Table 2. Starless cores. The numbers indicate the core number labeled in Lee and Myers (1999) [2] .
a: Lee and Myers (1999) listed IRAS 04005 + 5647 as an associated embedded YSO; however, it is classified as a field star in this study. b: Lee and Myers (1999) [2] listed IRAS 04248 + 2612 as an associated embedded YSO; however, it is located outside the searched region in this study. c: Lee and Myers (1999) [2] listed IRAS 05522 + 0146 as an associated embedded YSO; however, it is located outside the searched region in this study. d: Lee and Myers (1999) [2] listed IRAS 14,451 − 6502 as an associated embedded YSO; however, it is classified as a field star in this study. e: Lee and Myers (1999) [2] listed IRAS 15,534 − 3740 as an associated embedded YSO; however, it is saturated in the W1-band. f: Lee and Myers (1999) [2] listed IRAS 16,285 − 2355 as an associated embedded YSO; however, it is saturated in the W1-band. g: Lee and Myers (1999) [2] listed IRAS 16,305 − 2425 as an associated embedded YSO; however, it is a low-S/N in the W3-band. h: Lee and Myers (1999) [2] listed IRAS 16,451 − 0953 as an associated embedded YSO; however, it is a low-S/N in the W2- and W3-band. i: Lee and Myers (1999) [2] listed IRAS 16,451 − 1045 as an associated embedded YSO; however, it is a low-S/N in the W2- and W3-band. j: Lee and Myers (1999) [2] listed IRAS 16,455 − 1405 as an associated embedded YSO; however, it is saturated in the W1-band. k: Lee and Myers (1999) [2] listed IRAS 17,193 − 2705 as an associated embedded YSO; however, it is identified as a planetary nebula (Henize 1967) [10] . l: Lee and Myers (1999) [2] listed IRAS 19345 + 0727 as an associated embedded YSO; however, it is classified as a field star in this study. m: Lee and Myers (1999) [2] listed IRAS 20353 + 6742 as an associated embedded YSO; however, it is classified as a field star in this study.
4. Discussion
For the star-forming cores, Lee and Myers (1999) [2] listed the associated IRAS sources. Among them, 16 IRAS sources were identified as Class I candidates, and 5 as Class II candidates in our study. Six sources were identified as field stars. Further, 22 sources were saturated mostly in the W1-band. Eleven sources were low S/N mainly in the W3-band. Two sources possessed the contamination and confusion flag, and five sources were located outside the searched region. Based on these discrepancies in the source identification, 13 cores previously classified as star-forming cores were reclassified as starless cores in this study (Table 2).
The associated WISE sources are thought to be very low-mass objects. For example, the J-band apparent magnitudes of the Class II sources associated with [LM 99] 10 are approximately 16 mag, which corresponds to absolute magnitudes of approximately 10 mag. Based on the evolutionary track of Baraffe et al. (2003) [7] , a 0.005 M⊙ object has 10th absolute magnitude in the J-band at 1 Myr old. Because 400 YSO candidates were found in 141 cores, each core has 3 YSO candidates on average. Assuming that the average mass of the core is ~1 M⊙ (e.g., Dunham et al., 2016 [8] ; Tokuda et al., 2019 [9] ), the star formation efficiency is obtained as low as 1%.
Extremely low-mass YSOs and deeply embedded YSOs may not be detected even with WISE. A portion of the starless cores classified in this study may indeed have YSOs. We detected 132 and 268 Class I and Class 2 candidates, respectively. The number of Class II sources should be 10 times that of the Class I sources if stars form constantly. This is because the age of a Class II source is 10 times that of a Class I source. The small number of the detected Class II candidates indicates the shallow detection limit for the Class II source even using the WISE photometric catalog. Another interpretation for the deficit in the Class II sources is based on the proper motion of the YSOs. Esplin and Luhman (2019) showed that YSOs associated with the Taurus molecular cloud have a dispersion of proper motion as large as ~10 mas/yr [11] . The distances of the nearest cores in this study are similar to that of the Taurus molecular cloud. Thus, a Class I source born in the nearest core spreads out as ~17' in 105 yr and a Class II source spreads out as ~2.8˚ in 106 yr. Because the size of the cores in this study is only a few arcminutes, we may miss the scattered YSOs, particularly the Class II sources associated with the nearby cores. If this is the case, the ratio of the number of Class II sources to that of the Class I sources (hereafter, the Class ratio) is low for the nearby cores. We investigated this detection bias by dividing the star-forming cores into three groups according to their distance (Table 3). The Class ratio is low for the cores in the distant group, compared to the cores in the medium distance group. The apparent sizes of the cores in the distant group are, on average, smaller than those of the cores in the other groups. Many Class II sources scattered from the distant cores may not be detected in this study, resulting in the low Class ratio for the distant cores. The average apparent sizes are comparable for the cores in the nearby and medium distance groups; however,
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Table 3. Ratio of the number of Class II candidates to that of the Class I candidates associated with the star-forming cores. a and b represent the average semi-major and semi-minor axes, respectively.
the Class ratio is low for the nearby group. We consider that a portion of the Class II sources associated with the nearby cores may be located outside the searched region, resulting in the low Class ratio for the nearby cores. Thus, completeness in this study may be different for the Class I and Class II sources owing to their proper motion.
Lee and Myers (1999) [2] recognized that the sizes of the star-forming cores are larger than those of the starless cores, while they did not find significant differences in the distances and aspect ratios between these two types of cores. However, we did not find any differences in size, distance, and aspect ratio. Because both starless and star-forming cores have a large variety, we took the sigma clipping average for these parameters. We calculated the average and standard deviation of the parameters, and subsequently removed the values beyond ±3 sigma from the average. We iterated this procedure until there were no more values to remove. The projected areas were 0.024 ± 0.018 pc2 and 0.066 ± 0.043 pc2 for the starless cores and star-forming cores, respectively. Further, the distances were 195 ± 56 pc and 215 ± 82 pc, and the aspect ratios were 1.99 ± 0.61 and 2.09 ± 0.74 for the starless cores and star-forming cores, respectively. As evident, the differences between all the parameters for the starless and star-forming cores are not significant.
The ratio of the number of starless cores to that of the star-forming cores suggests the timescale from the formation of the cloud core to the birth of the star. We estimated this timescale to be 0.5 Myr from the ratio of the number of starless cores (149) to that of the cores with Class I candidates only (32), assuming that the age of a Class I source is 0.1 Myr. Otherwise, the timescale was estimated to be 1.4 Myr when considering the ratio of the number of the starless cores (149) to that of the cores with Class II candidates (107), assuming the age of a Class II source as 1 Myr. Lee and Myers (1999) [2] found 306 starless cores and 94 cores with embedded YSOs. The embedded YSO corresponds to a Class 0 or Class I source. Assuming 0.1 - 0.5 Myr for the age of the embedded YSO, they estimated the typical lifetime of the starless cores to be 0.3 - 1.6 Myr. This value is consistent with the timescale derived in this study. On the other hand, they detected only six PMSs. However, because the age of a Class II source is 10 times that of a Class I source, the number of Class II sources should be 10 times that of the Class I sources, assuming a constant star formation rate. Thus, the small number of PMSs implies a shallow detection limit of IRAS for a PMS.
We claim that the timescale of low-mass star formation in a core is approximately 1 Myr. Shu (1977) considered the gravitational collapse of an isolated core, and derived the collapse timescale of 1 Myr [12] . Whereas, Palla and Galli (1997) considered ambipolar diffusion during the collapse of a core, and then derived a collapse timescale of several tens of Myr [13] . Our statistics are consistent with the collapse timescale presented by Shu (1977) [12] .
Kim et al. (2010) examined the association of infrared dark cloud cores with YSOs [14] . They used the Spitzer GLIMPSE, MSX, and IRAS point source catalogs. The infrared dark clouds are as massive as 102 - 104 M⊙ and are considered to be the forming site of a massive star. They identified YSO candidates for 1072 cores, while 8102 cores had no YSO candidates. Based on the ratio of these numbers and the typical lifetime of a high-mass embedded YSO of 103 - 104 yr, they suggested that the cores spend 104 - 105 years to form high-mass stars. This value is shorter than the timescale estimated in this study. Thus, the lifetime of massive starless cores may be shorter than that of low-mass starless cores.
5. Conclusion
We searched for infrared sources associated with the molecular cloud cores listed in Lee and Myers (1999) [2] , by using the WISE photometric catalog. One hundred and forty-nine cores do not have associated sources and are starless cores. Further, 32 cores have only Class I candidates, and 197 cores have Class II candidates. The estimated timescale from the core formation to the birth of a star is approximately 1 Myr. This is consistent with the gravitational collapse model of a core.
Funding
This work was supported by JSPS KAKENHI Grant Number 22K03677.