Flat$
Class$II$
Class$III$
14%$
11%$
62%$
13%$
Class$I$
Flat$
Class$II$
Class$III$
Figure 3.13 The pie chart of YSO populations shows the percentage of sources in each class. The left panel is the result of all c2D YSOs (Evans et al., 2009) and right panel is the result of this work.
Table 3.8. Physical Parameters of Opiuchus Cloud.
By taking 2 Myr for the duration of the Class II phase, then the lifetime of the Class I phase, t(I) =1.3 Myr, t(F ) =1.1 Myr for Flat YSOs. As one can see from Table 3.6, the number of Class II YSOs detected in our work is consistent with c2D result. Additionally, we selected more Class I and Flat sources. It is understood the YSO SEDs suffer from the dust extinction. The lifetimes after extinction correction will be shorter 10 – 20 % (Evans et al., 2009). In this case, the best estimation should be 1.0 and 0.9 Myr for Class I and Flat, respectively.
Obviously, our estimates are substantially longer than estimates for the Class I lifetime of 0.1 – 0.2 Myr (Greene et al., 1994) or 0.4 – 0.5 Myr (Evans et al., 2009).
Since we have detected fainter YSOs, the estimated lifetime of a YSO pass from Class I through Class II would be
∼ 4 Myr.
3.4.3 Star Formation in Ophiuchus Cloud
In the study of star formation, it is important to understand how gas turn into stars. Comparison of the mass in YSOs (M
⋆
) to the cloud mass (M (cloud)) gives a measure of the current star formation efficiency, defined as:SF E = M ⋆
M ⋆
+ M (cloud).
(3.3)To calculate the star formation efficiency, we assume a mean mass of 0.5 M
⊙
(Evans et al., 2009). This value is consistent with studies of the IMF (Chabrier 2003, Kroupa 2002, Ninkovic & Trajkovska 2006), but also depending on which evolutionary tracks are used (Oliveira et al., 2009). In Cha II, Spezzi et al. (2008) derive a mean mass of 0.52±0.11 M ⊙
based on spectroscopic data, while the mean stellar mass may be closer to 0.2 M⊙
in the Lupus clouds (Merín et al., 2008) and 0.69 to 0.73 in Serpens (Oliveira et al., 2009). Taking cloud mass, adopted from Evans et al. (2009), into account, the SFE of Ophiuchus cloud is 0.09, which is higher than previous estimation of Evans et al. (2009). However, the assumption of mean YSO mass may change the SFE.As discussed in §3.4.2, the 4 Myr lifetime is the estimation of the time taken to pass from Class I through the Class II. With 4 Myr lifetime for star formation, the star formation rate of Ophiuchus cloud is 54 M
⊙
Myr−1
( 1.7 M⊙
Myr−1
pc−2
).According to a theoretical calculation, a typical GMCs should collapse on its free-fall time scale and results in a SFR of roughly 250 M
⊙
Myr−1
if there is other support(Krumholz & McKee, 2005). Observationally, the SFR in Milky Way is measured as∼ 3 M ⊙
yr−1
(McKee & Williams, 1997).Given the star formation rate ( ˙
M ⋆
), we can calculate a depletion time for the cloud:t dep
= M (cloud)/ ˙M ⋆ .
(3.4)The t
dep ∼ 40 Myr is consistent with the estimation of McKee & Ostriker
(2007), they have suggested the cloud lifetimes range from 10 to 40 Myr. As discussed by Evans et al. (2009), the tdep
is much shorter for the dense core (∼ 0.6
Myr for dense cores in Ophiuchus cloud, Evans et al., 2009) because the dense regions contains more YSOs. If Ophiuchus cloud produce stars at the current rates for 10 Myr, the final efficiency could be as high as∼20%. To reach a high
efficiency would require continued conversion of cloud material into dense cores (Evans et al., 2009).Krumholz & McKee (2005) define the star formation rate per unit free fall time (SF R
f f
) to be the fraction of an object’s mass that turns into stars in a free fall time at the object’s mean density, defined as:SF R f f
= ˙M ⋆ t f f
/M (cloud) = tf f
/tdep ,
(3.5) where tf f
is the free fall time for the mean density of the cloud, calculated fromt f f
= 34Myr/√⟨n⟩.
(3.6)The density
⟨n⟩ in that calculation is the density of all particles, and we
assumed a mean molecular mass of 2.3 amu. Mean densities for Ophiuchus cloud is 387, computed from the mass and surface area by assuming a spherical cloud.We find SF R
f f
is 0.043, which is smaller than the value of Evans et al. (2009).However, this value is close to the average value of all c2D observed regions (0.040).
Comparing with the estimation values from Hsieh & Lai (2013), the SF R
f f
is lower. This is because the lifetime we adopted is 4 Myr instead of 2 Myr. Although the SF Rf f
is lower, yet it is consistent with previous measurements (Evans et al., 2009; Hsieh & Lai, 2013) and implies that the observational data are more consistent with the turbulence model than the magnetic field model (Hsieh & Lai, 2013). The physical parameters derived are listed together with values adopted from literature in Table.3.8.3.4.4 Comparison to Kenncutt-Schmidt Relation
The interaction between interstellar medium and star formation activity is an important prerequisite to understanding galaxy evolution. For theoretical models and observations of galaxy formation, it is important to have a robust measurement for the relation between star formation rate (Σ
SFR
) and gas surface density (Σgas
).Based on theoretical and observational work(Schmidt, 1959; Kennicutt, 1998), it is known as ”Kennicutt–Schmidt relation” and can be expressed as following
equation:
Σ
SFR
= (2.5± 0.7) × 10 −4
(Σgas
)1.4 ±0.15 .
(3.7)As shown in Figure 3.14, our result is consistent with the c2D project although we adopted a new lifetime estimation. Is is clear that all the measurements lie well above the prediction of Kennicutt–Schmidt law, even though these clouds are forming only low mass stars. This may be caused by a reason that the Kennicutt–
Schmidt relation was established using optical observations (Evans et al., 2009).
Wu et al. (2005) found a relation using HCN by observing massive dense core in other galaxies and our Galaxy. This relation extrapolated to lower surface densities comes closest to the observed points. Although recent observation results showed this current relation used in extra-galactic studies may need modification (Heiderman et al., 2010; Wu et al., 2010), yet the Kennicutt–Schmidt relation applies to averages over much larger regions than individual clouds.