STAR FORMATION ACTIVITY IN THE LONG, FILAMENTARY INFRARED DARK CLOUD G53.2

In classification of YSOs, an empirical scheme based on the slope of SEDs was first constructed by Lada & Wilking (1984) and more quantitatively developed by Lada (1987) adopting the definition of spectral index α. Since then, Greene et al. (1994), introducing flat-spectrum (see Section 3.1), has developed the classification system in the study of the ρ Oph YSO population. Whereas the original definition of α used wavelengths between 2 and 20 μm (Lada & Wilking 1984), several recent studies have used only the four IRAC bands to compute α (e.g., Lada et al. 2006; Billot et al. 2010). Regarding differences in the choice of wavelength range, Greene et al. (1994) claimed no deviation between α computed using 2.2–20 μm and 2.2–10 μm, but Evans et al. (2009) classified YSOs in five nearby molecular clouds in the c2d project (Evans et al. 2003, hereafter the c2d clouds) using both 2–24 μm and the IRAC bands and showed that using only the IRAC bands moves sources from earlier to later classes, resulting in 10%–15% difference in inferred lifetimes for the earlier SED phases.

In Section 4, we classified the point sources in IRDC G53.2 by least-squares linear fitting between 2 and 24 μm. In order to examine the difference in classification depending on the use of wavelength range, we classify the sources again using only the IRAC bands and compare the results to the one we have from 2–24 μm in Figure 5. In Figure 5, the histogram of spectral index from only using the IRAC bands, drawn in red, shows a relatively lower number of flat-spectrum and higher number of Class III than the histogram of spectral index from 2–24 μm, drawn in black. When using only the IRAC bands, we get fewer Class I (by ∼7%), fewer flat-spectrum (by ∼40%), comparable Class II, and more Class III (by ∼43%). Since a direct comparison in numbers of each class does not account for uncertainties from fitting in the computation of spectral index, we show a spectral index from 2–24 μm (${{\alpha }_{2-24\,\mu {\rm m}}}$) versus spectral index from the IRAC bands (${{\alpha }_{{\rm IRAC}}}$) plot with their 1σ uncertainties from fitting in Figure 6. As shown in Figure 6, most sources plotted by gray circles have consistent classes from both spectral indices. Red squares in Figure 6 are the sources that are classified as earlier class by ${{\alpha }_{{\rm IRAC}}}$ with its fraction of ∼7%, but they fall into the same classes by ${{\alpha }_{2-24\,\mu {\rm m}}}$ when accounting for uncertainty. Blue triangles in the figure are the sources that are classified as later class by ${{\alpha }_{{\rm IRAC}}}$ with its fraction of ∼20%; however, if we account for the uncertainties, the fraction of sources classified by later class by ${{\alpha }_{{\rm IRAC}}}$ is 12%. From the above comparison, the uncertainty in YSO candidate classification in this study from the choice of wavelength range in determination of spectral index will be ∼12%.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

YSOs are often classified based on mid-IR colors. For example, Gutermuth et al. (2008, 2009) established a mid-IR color-based method that can robustly distinguish YSOs and mitigate the effects of contamination and reddening. Their mid-IR color-based method primarily uses the IRAC magnitudes/colors and additionally uses 24 μm detection for further classifying "Transition Disk" Class II sources, deeply embedded protostars, and highly reddened Class II sources. The color-based classification of YSOs in principle relies on the mid-IR excess emission, as the spectral-index-based classification does, but different criteria between the two may give different classification. In order to check this possibility, we apply the classification scheme described in Gutermuth et al. (2009) to the sources in IRDC G53.2 and compare the results between the color-based and the ${{\alpha }_{2-24\,\mu {\rm m}}}$-based classification. Among 369 sources in Table 2 (excluding the saturated sources in 24 μm), 70 and 189 sources are classified as Class I and Class II, respectively, based on mid-IR colors, where Class I includes 16 deeply embedded protostars and Class II includes 52 transition disk sources and 7 highly reddened Class II sources. The others are the sources with photospheric colors or the sources that lack the IRAC magnitudes. Comparing the number of objects in each class, we find that most Class I ($\gtrsim 80\%$), Class II ($\gt 90\%$), and Class III/photospheric sources (∼100%) from the ${{\alpha }_{2-24\,\mu {\rm m}}}$-based classification are well consistent with the color-based classes. In the case of flat-spectrum sources, however, ∼80% are classified as Class II by the color-based classification, while they are supposed to be included in Class I according to Gutermuth et al. (2009).

A possible reason for this discrepancy is an ambiguity of flat-spectrum. Since flat-spectrum is an evolutionary stage between Class I and Class II, separating flat-spectrum sources from either class will be highly uncertain. The wavelength range used in classification can be a reason as well. Although the color-based classification is made from IRAC to MIPS 24 μm wavelengths, classes are mainly determined by IRAC colors because the 24 μm magnitudes are only additionally used to classify anomalies such as transition disk or highly reddened Class II. Therefore, a source with an SED slope in the IRAC wavelengths close to the boundary between flat-spectrum and Class II but bright in 24 μm may be classified as Class II by the color-based scheme, whereas it would be classified as flat-spectrum (i.e., Class I) by the ${{\alpha }_{2-24\,\mu {\rm m}}}$-based scheme. This trend is also seen in the comparison between the ${{\alpha }_{2-24\,\mu {\rm m}}}$-based and ${{\alpha }_{{\rm IRAC}}}$-based classification discussed above (Section 6.1.1). We note that extinction may be an another factor that moves flat-spectrum to Class II, and it will be discussed below in detail. In summary, the mid-IR color-based classification of YSOs is consistent with the ${{\alpha }_{2-24\,\mu {\rm m}}}$-based classification scheme in general, except when classifying flat-spectrum sources. In such objects, there is some ambiguity between Class I and Class II sources, which is likely dependent on the wavelength ranges used. The difference between the two classifications will affect the number ratio of Class II to Class I objects by a factor of two or three (Section 6.2.1).

On the other hand, Robitaille et al. (2006) adopted a "Stage" classification. Stage is based on the physical properties of SEDs, thus referring to the actual evolutionary stage rather than Class, which is only based on the slope of SEDs. Although Stage 0/I/II/III is analogous to Class 0/I/II/III, it is not a one-to-one correspondence because of the inclination effect. For example, pre-main-sequence stars with an "edge-on" disk can be classified as flat-spectrum or Class I by their SED slopes, and Crapsi et al. (2008), in their study on the nature of embedded YSOs using radiative transfer modeling, claimed that 34% of the Stage II sources could be misclassified as flat-spectrum. Despite the possible misclassification, however, the classes of the YSO candidates in IRDC G53.2 classified based on spectral index ${{\alpha }_{2-24\,\mu {\rm m}}}$ agree fairly well with the stages in a color–color diagram as presented in Figure 7. In Figure 7, Class I, II, and III objects mostly fall into the areas of Stage I, II, and III (Robitaille et al. 2006), respectively. Flat-spectrum sources again show an ambiguity between Stages I and II, but ∼65% are located in the Stage I area. The others placed in the Stage II area may represent the ones with large inclination angle. Comparison of "Class" and "Stage" classification from the [3.6]−[5.8] versus [8.0]−[24] color–color diagram indicates a general agreement between the two, although there are some exceptions. Detailed investigation on the physical properties of the YSO candidates in IRDC G53.2 based on the analysis of the individual SEDs will be addressed in our forthcoming paper.

Zoom In Zoom Out Reset image size

Embedded star-forming regions in a dense molecular cloud suffer high extinction from dust and reddening. High column density, and thus high extinction, toward IRDC G53.2 may affect the classification of YSOs based on SED shapes, but it may not be significant because of much smaller extinction in mid-IR than in optical. Previous studies using Spitzer data also show that the effects from extinction on the overall YSO classification are small. Evans et al. (2009) compared spectral index of YSOs in the c2d clouds before and after extinction correction and found that the effect from extinction was small (10%–20%), probably smaller than other sources of uncertainty. Billot et al. (2010) also found that the YSO census in the Vulpecula OB association (hereafter Vul OB1) based on the mid-IR color method showed only a marginal difference after they corrected for extinction. This indicates that classification schemes based on mid-IR excess are only moderately affected by extinction. However, it is also possible that extinction effects in our analysis of IRDC G53.2 YSO population, which is much further away and embedded in a denser molecular cloud, may not be as negligible as in the above studies, and we will briefly discuss expected effects from extinction on the YSO census in IRDC G53.2 below.

The local extinction in star-forming regions may be derived using the near-IR colors of stars observed in each region and comparing these with their intrinsic colors (e.g., Evans et al. 2009; Gutermuth et al. 2009). However, since this method is limited to nearby regions, we cannot apply it to IRDC G53.2. Extinction in IRDC G53.2 is also not uniform; it is larger in the central parts of the molecular cloud, where the ¹³CO integrated intensity map peaks in Figure 2 (left). To investigate the effects of extinction on our YSO census, we therefore consider the extreme case of one of the clumps in IRDC G53.2 (from Butler & Tan 2012) and examine how it could possibly affect the YSO classes. Butler & Tan (2012) estimated physical properties of starless and early-stage cores and clumps in 10 IRDCs, including the one in IRDC G53.2 (MSX G053.11+00.05 in Figure 1; core J1 in Butler & Tan 2012) based on the mid-IR extinction mapping technique. Their estimation, using the IRAC 8 μm images, gave a mean mass surface density of ∼0.15 g cm⁻² or ${{\tau }_{8\mu {\rm m}}}\sim 1.1$ (according to their Equation (1)) for a clump in the MSX G053.11+00.05. From the mid-IR extinction law derived by Spitzer data (Flaherty et al. 2007; Chapman et al. 2009), we estimate the extinction at each IRAC and MIPS 24 μm band as follows, although extinction at 24 μm is highly uncertain owing to a small sample size in Flaherty et al. (2007) and Chapman et al. (2009): ${{A}_{[3.6]}}\;=\;$ 1.6–1.7 mag, ${{A}_{[4.5]}}\;=\;$ 1.3–1.4 mag, ${{A}_{[5.8]}}\;\sim$ 1.2 mag, ${{A}_{[8.0]}}\;\sim$ 1.2 mag, and ${{A}_{[24]}}\;\sim$ 1 mag. If we apply extinction correction to these values in Figure 7, about half of the flat-spectrum sources in the Stage I area move to the Stage II area, whereas Class I and Class II sources show only small changes. However, we note that this extinction will be close to the upper limit in IRDC G53.2. The clump in the MSX G053.11+00.05 is located where the ¹³CO emission is strong, corresponding to the innermost contour in Figure 2, and extinction of most of the area in the IRDC should be much lower. For example, the mass surface density (or extinction) of the outer part of the clump in the MSX G053.11+00.05 is ∼10% of the mean value (Figure 12 of Butler & Tan 2012), which does not make any remarkable changes in Figure 7. Therefore, extinction in IRDC G53.2 may affect the YSO classification in a way to decrease the number of flat-spectrum objects and increase the number of Class II objects, but the effect on the overall classification is likely insignificant.

We first compare the census of YSO candidates in IRDC G53.2 and other star-forming regions because the number of YSOs in each class can provide an estimation of the relative age of a star-forming region, assuming a constant birthrate (Gutermuth et al. 2009). For example, the number ratio of Class II to Class III objects, which can be a diagnostic of a fraction of YSOs with disks (i.e., disk fraction), gives the age of a star-forming region since disk fraction exponentially decreases with the age of a star-forming region (Mamajek 2009; Ybarra et al. 2013). The use of the ratio of Class II to Class III, however, would be inappropriate in the case of IRDC G53.2. In IRDC G53.2, the fraction of Class I and flat-spectrum sources that may not even form accretion disks is rather high ($\lesssim 50\%$), and the census of Class III objects and photospheric sources is likely to be incomplete because of their weak IR-excess emission and faintness at 24 μm (see Section 5.2). Instead, we use the number ratio of Class II to Class I objects (${{N}_{{\rm Class}\,{\rm II}}}/{{N}_{{\rm Class}\,{\rm I}}}$, hereafter) to compare the relative age of IRDC G53.2 with other star-forming regions. As mentioned in Section 4, the evolutionary status of flat-spectrum is rather uncertain, and the objects with SEDs of flat-spectrum are often included in Class I if they are not separately classified (e.g., Gutermuth et al. 2009). Following this, we include flat-spectrum in Class I in the discussion below.

Figure 8(a) presents ${{N}_{{\rm Class}\,{\rm II}}}/{{N}_{{\rm Class}\,{\rm I}}}$ of IRDC G53.2 and other star-forming regions from the literature. In the figure, ${{N}_{{\rm Class}\,{\rm II}}}/{{N}_{{\rm Class}\,{\rm I}}}$ of IRDC G53.2, which is 0.9 after removing field star contamination, is marked with a filled red star, and the ratios of other star-forming regions from different literature are marked with different filled symbols. Filled gray circles are from a systematic Spitzer survey on 36 young, nearby, star-forming clusters within 1 kpc by Gutermuth et al. (2009), and a gray dashed line indicates the median value of ${{N}_{{\rm Class}\,{\rm II}}}/{{N}_{{\rm Class}\,{\rm I}}}$ (3.7) for these clusters. ${{N}_{{\rm Class}\,{\rm II}}}/{{N}_{{\rm Class}\,{\rm I}}}$ of the c2d clouds (Evans et al. 2009) and Vul OB1 (Billot et al. 2010) are also presented by a filled blue square and filled purple downward-pointing triangle, respectively. Filled green triangles are ${{N}_{{\rm Class}\,{\rm II}}}/{{N}_{{\rm Class}\,{\rm I}}}$ of YSOs that are spatially associated with dark filamentary structures in the inner Galactic region of $10{}^\circ \lt l\lt 15{}^\circ$ and $-1{}^\circ \lt b\lt 1{}^\circ$ using GLIMPSE data (Bhavya et al. 2013). While nearby, low-mass star-forming regions (Evans et al. 2009; Gutermuth et al. 2009) and Vul OB1 (Billot et al. 2010) show higher ${{N}_{{\rm Class}\,{\rm II}}}/{{N}_{{\rm Class}\,{\rm I}}}$ than that of IRDC G53.2, YSOs likely related to IRDCs (Bhavya et al. 2013) show similar or lower ${{N}_{{\rm Class}\,{\rm II}}}/{{N}_{{\rm Class}\,{\rm I}}}$ compared to IRDC G53.2. Direct comparison of the number ratios from different studies, however, is not appropriate because (1) different classification schemes affect the fraction of each class, as discussed in Section 6.1, and (2) different distances affect the detection limit so that the number of faint sources at 24 μm (i.e., later-class YSOs) decreases as the distance to the star-forming region increases.

Zoom In Zoom Out Reset image size

To make an appropriate comparison, we first compute ${{\alpha }_{2-24\,\mu {\rm m}}}$ of YSOs in the star-forming clusters from Gutermuth et al. (2009) and Vul OB1 (Billot et al. 2010) using their flux catalogs and reclassify them. Gutermuth et al. (2009) classified YSOs using their mid-IR colors. Since the color-based classification results in fewer Class I and more Class II sources than the ${{\alpha }_{2-24\,\mu {\rm m}}}$-based classification (Section 6.1.2), ${{N}_{{\rm Class}\,{\rm II}}}/{{N}_{{\rm Class}\,{\rm I}}}$ will become higher if one uses the color-based classification scheme. After reclassification of their sources based on ${{\alpha }_{2-24\,\mu {\rm m}}}$, the median of ${{N}_{{\rm Class}\,{\rm II}}}/{{N}_{{\rm Class}\,{\rm I}}}$ for all the clusters becomes smaller, as expected, from 3.7 to 2.0. New ${{N}_{{\rm Class}\,{\rm II}}}/{{N}_{{\rm Class}\,{\rm I}}}$ distribution and the median value are presented in Figure 8(b) with filled gray circles and a gray dashed line, respectively. Billot et al. (2010) classified the YSOs in Vul OB1 using ${{\alpha }_{{\rm IRAC}}}$, so they also have fewer flat-spectrum and more Class II sources and thus higher ${{N}_{{\rm Class}\,{\rm II}}}/{{N}_{{\rm Class}\,{\rm I}}}$ (Section 6.1.1 and Figure 5). Our ${{\alpha }_{2-24\,\mu {\rm m}}}$-based classification scheme to the sources in Vul OB1 decreases ${{N}_{{\rm Class}\,{\rm II}}}/{{N}_{{\rm Class}\,{\rm I}}}$ from 1.9 to 1.2, and the new ratio is marked with an open purple downward-pointing triangle in Figure 8(b). For the c2d clouds (Evans et al. 2009), we use their results because they used ${{\alpha }_{2-24\,\mu {\rm m}}}$ in classification.

Next, we correct for distance by assuming that the nearby regions from Evans et al. (2009) and Gutermuth et al. (2009) are at the same distance as IRDC G53.2 (at 1.7 kpc). To do this, we scale the fluxes of the YSOs and extract the sources brighter than a threshold at 24 μm. For the threshold, we use 8.41 mag, the faintest 24 μm magnitude in IRDC G53.2. Larger distance may affect the classification itself as well owing to higher extinction, but such an effect will be negligible in the overall statistics (Section 6.1.4). We mark distance-corrected ${{N}_{{\rm Class}\,{\rm II}}}/{{N}_{{\rm Class}\,{\rm I}}}$ in Figure 8(b) using open orange circles for the clusters in Gutermuth et al. (2009) with their median value of 0.8 (orange dashed line) and an open blue square for the c2d clouds. For the clusters in Gutermuth et al. (2009), we only consider the clusters with total number of YSOs > 10. In the c2d clouds, ∼50% of Class I sources including flat-spectrum remain after distance correction, whereas only ∼26% of Class II sources remain. This indicates that in a region at larger distance, the YSO census is likely biased to an earlier class so that ${{N}_{{\rm Class}\,{\rm II}}}/{{N}_{{\rm Class}\,{\rm I}}}$ becomes lower. We do not correct distance for Vul OB1 since it is at a similar distance (2.3 kpc) to IRDC G53.2. We summarize the newly computed ${{N}_{{\rm Class}\,{\rm II}}}/{{N}_{{\rm Class}\,{\rm I}}}$ for each region after correcting classification and distance in Table 5. Number ratio of Class II to Class I in a star-forming region is sensitive to both classification scheme and distance, and each factor changes the ratio by a factor of two. We do not make any correction for the IRDC-associated YSOs from Bhavya et al. (2013) because their catalog is not available. The IRDCs in their samples are mostly farther away (3–6 kpc) than IRDC G53.2, so ${{N}_{{\rm Class}\,{\rm II}}}/{{N}_{{\rm Class}\,{\rm I}}}$ will become higher by a factor of two if assuming the distance of 1.7 kpc. On the other hand, they classified the sources based on ${{\alpha }_{{\rm IRAC}}}$, so the use of ${{\alpha }_{2-24\,\mu {\rm m}}}$ will make ${{N}_{{\rm Class}\,{\rm II}}}/{{N}_{{\rm Class}\,{\rm I}}}$ lower by a factor of two. Therefore, their corrected ${{N}_{{\rm Class}\,{\rm II}}}/{{N}_{{\rm Class}\,{\rm I}}}$ may not be very different from the uncorrected ones.

Table 5.  Comparison of Number Ratio of Class II to Class I Objects (${{N}_{{\rm Class}\,{\rm II}}}/{{N}_{{\rm Class}\,{\rm I}}}$) between IRDC G53.2 and Other Star-forming Regions

Region	Distance (kpc)	Without Correction	${{\alpha }_{2-24\,\mu {\rm m}}}$-based Class	At 1.7 kpca
IRDC G53.2b	1.7	0.9	0.9	0.9
Gutermuth et al. (2009)	<1	3.7	2.0	0.8
c2d cloudsc	<0.3	2.1	2.1	1.1
Vul OB1d	2.3	1.9	1.2	∼1.2e

Notes.

^aClassification is based on ${{\alpha }_{2-24\,\mu {\rm m}}}$. ^bThe numbers are after removing field star contamination. ^cEvans et al. (2009). ^dBillot et al. (2010). ^eSince Vul OB1 is at a similar distance to IRDC G53.2, we use ${{N}_{{\rm Class}\,{\rm II}}}/{{N}_{{\rm Class}\,{\rm I}}}$ without correction.

Download table as:  ASCIITypeset image

Under the same classification criteria and assuming the same distance, all of the compared regions and IRDC G53.2 show similar ${{N}_{{\rm Class}\,{\rm II}}}/{{N}_{{\rm Class}\,{\rm I}}}$, which indicates that they are similar in age or at a similar evolutionary stage. We note that there may be more Class I objects in IRDC G53.2 that are too deeply embedded to be detected even in 24 μm because of high column density of the central part of the IRDC. Such sources are, however, beyond the scope of this study, and further investigation including longer wavebands will be helpful to search for them.

Star formation activity in IRDCs has mostly been studied on core (10⁻²–10⁻¹ pc) or clump (10⁻¹–10⁰ pc) scales, so a direct comparison of the stellar population in different IRDCs, as in Section 6.2.1, is difficult. Some studies, however, address the issues on protostars detected at 24 μm in the vicinity of IRDCs and their association. The 24 μm point-source detection is one of the signs to trace star formation activity in IRDC clumps and related to their evolutionary phase. IRDC clumps are suggested to evolve from a quiescent clump to an active/red clump with an intermediate clump in between. As clumps evolve, they become warmer and show tracers of star formation such as embedded 24 μm point sources or H₂O/CH₃OH maser emission (Chambers et al. 2009; Battersby et al. 2010). A large number of YSO candidates detected in 24 μm in IRDC G53.2, with the associated "green fuzzies (extended 4.5 μm enhancement)" and H₂O/CH₃OH masers previously found (e.g., Chambers et al. 2009), indicates that stars are actively forming in IRDC G53.2 and IRDC G53.2 is likely at a later evolutionary stage among IRDCs.

Ragan et al. (2009) investigated stellar content around 11 IRDCs at 2.4–4.9 kpc using Spitzer data. They found many Class II and a few Class I objects, but only ∼10% of them were associated with the IRDC clumps identified by the absorption in 8 μm. From the clump mass function, which is shallower than the Salpeter mass function, and a lack of association between the clumps and mid-IR sources, the authors suggested that IRDCs are the precursors to stellar clusters in an early phase of fragmentation. In the IRDC G011.11-0.12, Henning et al. (2010) found ∼20 embedded cores in a diverse mass range (1–240 ${{M}_{}}$), half of which were associated with the 24 μm detection. From large spacings between the cores, well in excess of the Jeans length in the IRDC (see Section 6.3.2 below), the authors also concluded that IRDC cores are at an early stage in protostar formation with a capability of forming massive stars and clusters. These IRDC clumps in the early phase of fragmentation (Henning et al. 2010; Ragan et al. 2009) are very weakly associated with 24 μm point sources with lower surface density of sources in mid-IR compared to IRDC G53.2. This again implies a more evolved status for IRDC G53.2. The cores in the IRDC G011.11-0.12 or in the IRDCs in Ragan et al. (2009) may represent an earlier stage than that seen in IRDC G53.2, before active star formation has turned on. Future studies on stellar mass function in IRDC G53.2 or on physical properties of the clumps harboring bright 24 μm sources will be helpful for further comparison between IRDC G53.2 and other IRDCs at various evolutionary stages.

Myers (2012) developed an analytic model of protostar mass and luminosity evolution in clusters that provides estimates of cluster age, protostar birthrate, accretion rate, and mean accretion time, under the assumptions of constant protostar birthrate, core-clump accretion, and equally likely accretion stopping. Based on the model, the age of a star-forming cluster can be described as $t\simeq \bar{a}/[\nu (1+{{\nu }^{2}}/2(1-\nu ))]$ (Equation (38) of Myers 2012), where $\bar{a}$ is the accretion timescale and ν is the fraction of protostars among total YSOs in the cluster. From this, Myers (2012) estimated the ages and birthrates of 31 nearby clusters and complexes using the observed numbers of protostars and Class II YSOs assuming the accretion timescale of 0.17 Myr and equal numbers of Class II and Class III sources (see Section 5 of Myers 2012 for details). In the above equation, the term ${{\nu }^{2}}/[2(1-\nu )]$ becomes negligible as ν decreases, so that the equation can be approximated by ${{N}_{{\rm Class}\,{\rm II}}}/{{N}_{{\rm Class}\,{\rm I}}}$ and the age of a star-forming cluster as $t\simeq 2\bar{a}({{N}_{{\rm ClassII}}}/{{N}_{{\rm ClassI}}}+1/2)$. We apply this relation to IRDC G53.2, assuming the same accretion timescale of 0.17 Myr, and the estimated age of IRDC G53.2 is ∼0.5 Myr. This age may be highly uncertain because of several assumptions used in the model, particularly the accretion timescale, which varies from 0.12 to 0.4–0.5 Myr (Myers 2012 and references therein). The age of the nearby star-forming clusters in Gutermuth et al. (2009) using ${{N}_{{\rm Class}\,{\rm II}}}/{{N}_{{\rm Class}\,{\rm I}}}$ after correcting for classification and distance (Section 6.2.1) ranges from 0.2 to 1.1 Myr, with a median of 0.5 Myr. This is comparable to the estimated age of IRDC G53.2.

As Figure 1 shows, bright mid-IR sources in IRDC G53.2 are located along dark filaments in 24 μm. Based on the classification in Section 4, we examine the spatial distribution of the YSO candidates in IRDC G53.2 in relation to the associated CO molecular cloud and far-IR emission. Figure 9 shows the distribution of the YSO candidates in each class on a ¹³CO column density map we construct from the GRS ¹³CO $J\;=\;$ 1–0 image integrated at $v\;=\;$ 15–30 km s⁻¹ (Section 2). Overall, the YSO candidates are dispersed within the boundary of IRDC G53.2 as drawn by the magenta contour, though they are also more concentrated where the ¹³CO column density is higher.

Zoom In Zoom Out Reset image size

Column density of the molecular cloud shows a good correlation with far-IR continuum emission as well. For comparison, intensity contours from the Herschel ¹⁴ SPIRE (Griffin et al. 2010) 500 μm image¹⁵ with levels of 3, 5, and 8 Jy beam⁻¹ are presented in white on the column density map in Figure 9, and three peak positions (one in the eastern and two in the western part of the IRDC) in both column density and 500 μm intensity are spatially coincident. We note that there is far-IR emission outside of IRDC G53.2 boundary to the north and west of the IRDC. This emission is probably not related to IRDC G53.2 but, rather, to foreground emission from CO clouds at another velocity observed along the same line of sight (see Figure 2).

In Figure 9, Class I objects are clustered within the 500 μm contours, particularly higher intensity levels, whereas Class II or III objects are rather randomly distributed. We examine the degree of clustering by comparing the numbers of objects in each class within the 500 μm contours. Table 6 presents the numbers of the YSO candidates in each class within the 500 μm contours of 8, 5, 3, and 2 Jy beam⁻¹. If we compare Class I and II objects, $\gtrsim 40\%$ of the Class I objects are distributed within 5 Jy beam⁻¹, where only ∼22% of the Class II objects are placed. This indicates that Class I objects or YSOs in earlier classes are more concentrated where the 500 μm intensity is higher, although flat-spectrum objects are more widely distributed. Clustering of Class I YSOs at high-extinction regions or the regions with high column density is often shown in other star-forming regions as well (e.g., Gutermuth et al. 2009; Myers 2012 and references therein; Chavarría et al. 2014).

Table 6.  Number of Young Stellar Object Candidates in IRDC G53.2 in the Herschel 500 μm Contours

Class	8 Jy beam−1	5 Jy beam−1	3 Jy beam−1	2 Jy beam−1	All IRDCa
I	15 (19%)	33(42%)	56(72%)	74(95%)	78(100%)
Flat-spectrum	4 (6%)	18 (27%)	36 (55%)	53 (80%)	66 (100%)
II	11 (8%)	30 (22%)	54 (40%)	84 (62%)	135 (100%)
III	0 (0%)	0 (0%)	2 (3%)	15 (24%)	62 (100%)
${{N}_{{\rm Class}\,{\rm II}}}/{{N}_{{\rm Class}\,{\rm I}}}$ b	0.6	0.6	0.6	0.7	0.9

Notes.

^aThe numbers without removing field star contamination. ^bFlat-spectrum is included in Class I.

Download table as:  ASCIITypeset image

We also compare ${{N}_{{\rm Class}\,{\rm II}}}/{{N}_{{\rm Class}\,{\rm I}}}$ in each level of the 500 μm contours. Flat-spectrum objects are again included with the Class I objects. If Class I objects are concentrated in a denser region surrounded by more evolved YSOs, ${{N}_{{\rm Class}\,{\rm II}}}/{{N}_{{\rm Class}\,{\rm I}}}$ will increase as larger regions are considered, from the densest region to the outer region, and there will be a gradient in the ratios. Myers (2012), using the protostar fraction, investigated age structures in well-studied star-forming regions, Serpens north/south clusters and the CrA cluster, and found that there are local age variations from 0.3 to 0.9 Myr. In Table 6 we present ${{N}_{{\rm Class}\,{\rm II}}}/{{N}_{{\rm Class}\,{\rm I}}}$ in the 500 μm contours of each level in IRDC G53.2. The central region with higher (>8 Jy beam⁻¹) 500 μm intensity or higher ¹³CO column density shows smaller ${{N}_{{\rm Class}\,{\rm II}}}/{{N}_{{\rm Class}\,{\rm I}}}$ of 0.6, compared to 0.9 for the whole IRDC. The difference is small, and a local gradient among the intensity levels is hardly seen, likely owing to a small sample size. Compared to the area of the IRDC, the number of YSO candidates is rather small, which makes a statistical comparison of the number of sources in each contour zone difficult. However, we still see that Class I objects are likely concentrated along the denser filament in IRDC G53.2. If we apply the relation between ${{N}_{{\rm Class}\,{\rm II}}}/{{N}_{{\rm Class}\,{\rm I}}}$ and age we derive in Section 6.2.3 from Myers (2012), it gives ∼0.2 Myr of age variation in IRDC G53.2

On the other hand, several recent studies have shown clustering of Class I YSOs along filamentary structures or pre- and protostellar core formation along IRDCs, many of which are likely massive (Teixeira et al. 2006; Henning et al. 2010; Jackson et al. 2010; Bhavya et al. 2013). Therefore, spatial concentration of earlier-class objects along the bright emission in the Herschel image supports star formation in very early phases occurring in IRDC G53.2 and gives a possibility that a fraction of the early-phase YSOs are massive. Detailed modeling of the objects using a full SED including longer wavebands in the future will be necessary to investigate physical characteristics of YSOs forming in IRDC G53.2.

In analysis of the spatial distribution of YSOs in star-forming regions, an average spacing between sources is often used to investigate the fragmentation processes in relation with the Jeans fragmentation and the subsequent dynamical evolution of the stars since YSOs are expected to move away from their birth sites as they evolve (Teixeira et al. 2006; Kumar et al. 2007; Winston et al. 2007; Gutermuth et al. 2009). One indicator to examine spacings between YSOs is a nearest-neighbor distance, which is the projected distance to the nearest YSO, often noted as NN2 distance (Gutermuth et al. 2009). In the study of the "Spokes" cluster in the young cluster NGC 2264, Teixeira et al. (2006) found a clear peak in their histogram of NN2 distances and suggested that the peak indicates the Jeans fragmentation of dense, dusty filaments. A peak at small spacings with a relatively long tail of large spacings in NN2 distance histograms is shown in young, nearby, star-forming clusters as well, and when the histograms show a pronounced peak and tail, the cumulative distributions have a steep inner slope and a shallow outer slope (e.g., Figure 2 of Gutermuth et al. 2009).

The histogram of the NN2 distances of the YSO candidates in IRDC G53.2 also shows a well-defined peak, as presented in Figure 10(a), with a median value of 0.2 pc. The dashed line in the figure marks the 5'' (or 0.04 pc at 1.7 kpc) boundary below which the source confusion becomes significant (Gutermuth et al. 2009), which means that the most frequent spacing (∼0.2 pc) is not an effect of resolution. As Gutermuth et al. (2009) pointed out, the cumulative distribution of the NN2 distance has a steep slope at small spacings and a shallow slope at large spacings. In Figure 10(b), we compare the NN2 distances of each YSO class. We include flat-spectrum objects in Class I, and they still show a clear peak at ∼0.2 pc. The NN2 distances of Class II objects also have a peak, but not as sharp as that of Class I, and the NN2 distances of Class III are rather broadly distributed at larger spacings. We present the median of the NN2 distances of each class in Table 7. The NN2 distance histograms of each class indicate that Class I objects are more highly clustered with smaller spacings (0.2 pc in median) than later classes (0.4 and 0.7 pc in median for Class II and Class III, respectively), and their normalized cumulative distributions presented in Figure 10(c) more clearly show this. In Figure 10(c), the cumulative distribution of Class I has much steeper slope at small spacings than the other two classes. The NN2 distances that contain 70% of the sources in each class are 0.3, 0.5, and 0.7 pc for Class I, II, and III, respectively (see Table 7).

Zoom In Zoom Out Reset image size

We perform a Kolmogorov–Smirnov (K-S) test to examine the probability that the parent distributions of each class are the same. Table 8 presents the K-S probabilities of the normalized cumulative distributions of the NN2 distances between each class. The results show $\lt 1\%$ chance of similarity between any two classes, implying that Class I objects are typically closer to their nearest neighbors than Class II or III objects. Such a tendency was more obviously shown in a study on the Serpens cloud core, where the median NN2 distances of Class I, flat-spectrum, Class II, and Class III are 0.024, 0.079, 0.097, and 0.132 pc, respectively (Winston et al. 2007). An increase in the median distance between YSOs for more evolved sources/classes supports the idea that stars are born in a dense region and dispersed away from the birth site as they evolve, and the smaller spacing of Class I objects in IRDC G53.2 indicates that such a process is occurring in IRDC G53.2 as well.

On the other hand, the median NN2 distance of IRDC G53.2 is about a factor of two larger than that of nearby star-forming clusters. For comparison, the mean value of the median NN2 distances of 36 nearby, young clusters in Gutermuth et al. (2009) is 0.07 pc. The relatively larger spacing of the sources in IRDC G53.2 is likely due to its larger distance. As discussed in Section 6.2.1, there is a selection effect in the sources in IRDC G53.2 from distance so that the NN2 distances of the sources in the IRDC can be biased to higher values by the smaller number of the sources compared to the whole area (and hence a lower surface density of sources). Although the mean of the median NN2 distances of the clusters in Gutermuth et al. (2009) is 0.07 pc, the median NN2 distances of the individual clusters are spread up to ∼0.4 pc, and they in general show a good correlation with the distance to the clusters as we present in Figure 11. In this plot, although there are a few outliers that are not easily explained, the NN2 distance of the sources in IRDC G53.2, lying on the tendency of the relation between distance and NN2 distance, is not particularly large when one takes into account its distance.

Zoom In Zoom Out Reset image size

In the Spokes cluster at a distance of 800 pc, Teixeira et al. (2006) found a typical separation of ∼0.1 pc for protostars distributed along its dusty filaments. This length scale is in very good agreement with the Jeans length in the cluster, so they suggested thermal fragmentation of the dense filamentary material. The NN2 distance of the Spokes cluster is also smaller than that of IRDC G53.2. The assumption that the Spokes cluster is at the same distance as IRDC G53.2 does not change the result because Teixeira et al. (2006) only used the bright 24 μm sources that are detectable at 1.7 kpc. However, the surface density of sources in the Spokes cluster is higher owing to its smaller area than IRDC G53.2, and we need to analyze the NN2 distance in a subregion with high source surface density in IRDC G53.2 to make a suitable comparison. There are three subregions where the YSO candidates are concentrated in Figure 9 that are consistent with the 3 Jy beam⁻¹ of the 500 μm contour, as well as dark filaments in 24 μm. We derive the NN2 distances of one of the subregions marked with an arrow "A" in Figure 9, where the YSO candidates are located along the dark filament in 24 μm (see Figure 1). The number of the YSO candidates in region A is 41, and the median NN2 distance is ∼0.1 pc, resulting in a similar length scale to that of the Spokes cluster.

The NN2 distance in region A is also comparable with the Jeans length, given as ${{\lambda }_{{\rm J}}}={{(\pi c_{s}^{2}/G{{\rho }_{0}})}^{1/2}}\;=\;$ 0.21 pc ${{(T/10{\rm K})}^{1/2}}\times {{({{n}_{{{{\rm H}}_{2}}}}/{{10}^{4}}{\rm c}{{{\rm m}}^{-3}})}^{-1/2}}$ (McKee & Ostriker 2007; Winston et al. 2007) for initial temperature ∼20 K and density $\sim {{10}^{5}}\;{\rm c}{{{\rm m}}^{-3}}$, which are typical values in IRDCs (Pillai et al. 2006; Rathborne et al. 2006; Ragan et al. 2011). Comparing with the mean core separation of ∼0.9 pc in the IRDC G011.11-0.12 (Henning et al. 2010), this indicates that IRDC G53.2, in which Jeans fragmentation is likely dominant, is more evolved than the IRDC G011.11-0.12. More detailed investigation on this subregion using far-IR data and/or molecular line maps such as HNC (1–0) (e.g., Jackson et al. 2010) will be useful to explore the fragmentation and star formation processes occurring in dense filamentary IRDCs.