BLAST: THE MASS FUNCTION, LIFETIMES, AND PROPERTIES OF INTERMEDIATE MASS CORES FROM A 50 deg² SUBMILLIMETER GALACTIC SURVEY IN VELA (ℓ ≈ 265°)

The source extraction and source property fitting techniques are similar to those used during analysis of the BLAST05 maps (Chapin et al. 2008). A beam-equivalent-sized Mexican hat wavelet type convolution is applied to the 250 and 350 μm maps, which identifies objects in the confused images by in effect subtracting a local background (e.g., Barnard et al. 2004). Peaks above a threshold in both maps form the candidate source list. This technique finds 1549 candidate sources in the 250 μm band and 1302 candidate sources in the 350 μm band. The 500 μm map is not used for source identification due to the greater source–source and source–background confusion resulting from the lower resolution.

Circular Gaussians are fitted to each candidate source in a 4' diameter area extracted from the flux density map. The center of the Gaussian fit is allowed to move at most by 20'' relative to the candidate source location, and the FWHM to vary from 90% of the beam size to 120''. To eliminate contamination from the other sources, Gaussians are simultaneously fitted to all candidate sources in the fit area. A planar background is also fitted. Any poor fits (e.g., negative amplitudes, or parameters that reach the imposed limits) are discarded. The 250 and 350 μm candidate lists, containing all locations, sizes, and approximate flux densities, are merged. Noise and background confusion may tend to shift the centroids of the fits. Consequently, sources lying within 20'' of each other are considered to be the same and the catalog records the position and size of the higher signal-to-noise ratio (S/N) object. Sources appearing in only one of the two bands are also adopted in the final list. In this procedure, 1109 sources were detected in the 250 μm band and 920 sources were detected in the 350 μm band. There were 703 common to both bands, with a total of 1326 sources.

Gaussians are then refitted using the fixed size (convolved to account for the differing beam sizes) and location parameters from the combined catalog, in all three wavelength maps. Final fluxes are the integrals of these Gaussian fits. Due to the sidelobes in the 250 μm beam, there is a risk of the source finder identifying the sidelobes around bright sources. To prevent this, sources that are in the location and have the appropriate relative amplitude of sidelobes to a bright source are removed from the source list. This removes 44 sources from the 250 μm list, leaving a total catalog of 1282 sources, as shown in Table 1.

Simulations are used to determine the bias and completeness of the source extraction routine. New sources are added to the map by taking the final catalog, convolving them with the measured beam in each band and inserting them into the map. Their locations are chosen to be at least 2' from their original location, but not more than 5', so that the fake sources will reside in a similar background environment to their original location. These added sources are not allowed to overlap each other, but are not prevented from overlapping sources originally present in the map so that the simulation will account for errors due to confusion. The resulting set of maps is run through the source extraction pipeline and the extracted source parameters are compared to the simulation input. To probe completeness at the low flux and large size limit, additional input catalogs are generated with excess numbers of faint and extended sources. The results of these simulations are shown in Figure 3 and are later used to correct the size distribution in Figure 4.

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The mean ratio of the recovered flux to the flux input to the simulation is determined to be 0.731, 0.911, and 1.120 at 250, 350, and 500 μm, respectively. The largest source of this bias is that the telescope beams are not perfectly Gaussian. Two sidelobes of the 250 μm beam contain ∼24% of the power, while the flux extraction procedure only fits a Gaussian to the main lobe. The probability of detection as a function of flux density is shown in Figure 3. The completeness lines derived from this analysis are used to make cuts in mass later in the analysis.

As the artificial sources are placed into the map in the same environments as the real sources lie, we can test the bias of our estimated masses caused by confusion and source mixing. We fit the SED (see Section 3.3) to both the input and recovered source fluxes, and from this determine the mass (see Section 4.3). We find that the recovered masses are biased high by 12%, which is small compared to the other uncertainties. We conclude that confusion is not dominating our fluxes over the mass range of interest.

A single-temperature modified blackbody SED is fitted to the three BLAST fluxes for each source, from which we determine the temperature, mass, and luminosity. The routine used here is identical to the one used for BLAST05 results (Chapin et al. 2008; Truch et al. 2008). These fits require knowledge of the dust emissivity index, β. The further determination of mass and luminosity requires knowledge of the dust mass absorption coefficient, κ, the dust to gas ratio, r, and the distance to the sources, d. For the values, we use for these parameters, and for details of the model, see Section 4.

The uncertainties in temperature, mass, and luminosity, not including uncertainties in β, κ, r, and d, are obtained by performing Monte Carlo simulations. Mock fluxes are generated for each source from Gaussian noise using the amplitude of the input source uncertainty and the known correlated and uncorrelated flux density calibration uncertainties. An SED is fitted to each of these mock sources. The distribution of the fit parameters gives the 68% confidence intervals. An additional correction to the uncertainties is calculated based on the reduced χ² for the simulated sources extracted from the map described above. The uncertainties in temperature, luminosity, and mass are then scaled to compensate for any deviation from unity in the reduced χ². The results of these fits are presented in Table 2.

BLAST has a FWHM beam width of 36'' at 250 μm. The high S/N of the map allows us to infer intrinsic source sizes below this scale by deconvolving the BLAST beam from the measured source FWHM. We find that the sizes obtained from the fit (Figure 4) are broader than the intrinsic beam size, with a typical size of 62'', which corresponds to an intrinsic deconvolved source size of 0.15 pc at the distance of the VMR, assuming Gaussian source profiles. These sizes are recorded in Table 2.

The size distribution of the sources is shown in Figure 5. The distribution of source sizes from the BLAST map at 250 μm is broad, with a peak at θ_i/θ_b ≈ 1.1, where θ_b is the BLAST beam size and θ_i = (θ²_fit − θ²_b)^1/2 is the inferred intrinsic source size. The distribution falls off at larger scales faster than our completeness for rotationally symmetric Gaussian sources would imply (Figure 4). From this result, it would be tempting to conclude that we have barely resolved the sources, which would have a typical size of ≈ 0.15 pc at the assumed distance of 700 pc. However, since star-forming objects are not point sources, and are superimposed on structure covering a wide range of scales, one should be careful to test whether sources are really being resolved.

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If we were barely resolving compact sources, then we would expect that if the region we were mapping had been further away, the sources would have appeared smaller, and the size distribution would have peaked at a smaller angular scale. To test this, we have convolved the 250 μm map to a resolution of 60'', and then re-binned it into double-sized pixels, to produce a map as we would have seen it, were the field approximately twice as far away. As confusion becomes more of a problem at the lower resolution, we see fewer sources. The size distribution of the sources we do see does not shift to smaller scales, and there are even fewer sources consistent with being point like. We would have expected that there would be many more.

Results, where θ_i/θ_b is roughly independent of spatial resolution for sources in star-forming regions, has been seen elsewhere, and is a natural consequence of fitting Gaussians to beam-convolved cores which have intrinsic power-law envelopes. Our size distribution is similar to what was seen in Perseus, Serpens, and Ophiuchus (Enoch et al. 2008), and can be interpreted as being consistent with power-law envelopes with exponent −2.0 < p < −1.0 (Young et al. 2003).

To test an entirely different possibility—that apparent source sizes are intrinsic to fitting Gaussians to random Gaussian fluctuations—we created two simulated maps, one with uncorrelated Gaussian fluctuations convolved with the beam and the other with uncorrelated lognormal fluctuations convolved with the beam. The source sizes from the fits to the Gaussian fluctuation map have a qualitatively similar distribution to what is found in star-forming regions, including what we have found here.

To discriminate between these two possible interpretations, we note that if the resolution independent θ_i/θ_b is due to fitting to power-law cores, then the fit size should be roughly independent of mass (as determined in Section 4.3), while if it is due to fitting to random Gaussian fluctuations, we might expect a quadratic mass dependence on the size. Figure 6 shows that our sizes are in fact independent of mass. For this reason, our results are consistent with fitting to cores whose envelopes drop off roughly as power laws. However, note that simple models of cold gravitationally bound but stable prestellar objects, such as Bonner–Ebert spheres, do not have power-law envelopes. Nor are power-law envelopes the only explanation for the lack of a size–mass relationship, but this is beyond the scope of this paper.

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We conclude that size and envelope are poorly defined concepts for these sources. They cannot be regarded as isolated objects with well-defined boundaries on a uniform background. In determining the SED of such an object when the resolution varies between bands, it is important to insure that the flux is integrated assuming the same spatial size in each band (see Section 3.1).

Source temperatures are determined by fitting the BLAST SEDs to an optically thin, modified blackbody:

$$\begin{equation} S_{\nu } = A \left(\frac{\nu }{\nu _0}\right)^{\beta } B_{\nu }(T), \end{equation} \tag{ 1 }$$

where A is the fit amplitude, B_ν(T) is the Planck function, β is the dust emissivity index, and c/ν₀ = 250 μm.

Simple dust emission models predict that the dust emissivity index will approach β = 2 at long wavelengths. More complex models, which include the properties of disordered materials (Meny et al. 2007) provide a context within which β can be less than 2, but only at temperatures above T ≈ 20 K.

Observationally, β ≈ 2 is common, though the value of the effective dust emissivity index has been observed to be as low as β ≈ 1 in higher density or warmer regions (Meny et al. 2007). While it is very difficult to determine the intrinsic dust β without data significantly longward of the peak in the Rayleigh–Jeans regime, Dupac et al. (2002) suggest a temperature/emissivity index inverse correlation, with low-temperature cores having β ≈ 2.

Observations of β < 2 for cold regions have been interpreted as being the result of temperature variations within the observed beam and along the line of sight. A self-shielded core with possible star formation within it will almost certainly not be isothermal. Simulations (Gonçalves et al. 2004; Li et al. 2003) predict temperature gradients in cold cores of up to 10 K, which will lead to an effective best-fit β < 2, even if the intrinsic properties of the dust have the theoretically expected β = 2. In these cases, use of the effective best-fit β rather than the intrinsic β will cause the mass to be significantly underestimated; we have found by simulations that when using the approximation of an isothermal fit, using the intrinsic β rather than fitting for it minimizes the error in derived mass, even in the case of significant temperature variations.

We chose to use the theoretically motivated value of β = 2. For reference, if we were to choose β = 1.5, the best-fit temperatures would increase by ≈10%.

BLAST is most effective at determining the temperatures of cooler (< 20 K) sources, with typical uncertainties of 10% for 11 K sources, rising to over 40% for 20 K sources, as the peak of the modified blackbody SED moves shortward of the BLAST bands. This uncertainty includes noise, confusion, and calibration uncertainty, but not systematic uncertainty from β. The temperature distribution (Figure 7) has a strong peak at 12.5 K, with a cutoff at the low end around 10 K, and a tail extending to higher temperatures, with 19% of the sources warmer than 20 K.

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Source mass is related to the amplitude fit in Equation (1) by

$$\begin{equation} M_{\rm c} = \frac{Ad^2}{\kappa r}. \end{equation} \tag{ 2 }$$

The value of κr has not been well determined. A summary of the values of κ at 250 μm from the literature is shown in Table 3. The large spread of values follows the theoretically motivated variation in κ between different regions and classes of objects. We have determined κr for our region by comparing the BLAST dust emission to estimated gas mass from C¹⁸O data. This technique for empirically verifying κr by comparing submillimeter derived masses to those from CO has been applied previously by PRONAOS (Dupac et al. 2002). Although they do not calculate their own value of κr, the PRONAOS team calculated masses based on both the Draine & Li (2007) and Ossenkopf & Henning (1994) κr values, which bracket the mass estimates from external CO data for a few cold clouds.

The NANTEN instrument observed the J = 1–0 ¹²CO and ¹³CO emission lines in the entire BLAST Vela field and the J = 1–0 C¹⁸O emission line for several targeted regions therein (Yamaguchi et al. 1999). One of these, the NANTEN cloud 28, is a well-isolated, nearly isothermal 1400 M_☉ cold cloud, shown in the 250 μm BLAST band in Figure 8. A single-temperature SED was fitted to the BLAST-estimated fluxes and compared to the CO-derived mass to give us our BLAST-derived value of κr. In order to remain consistent with the NANTEN derived masses, we adopt a distance of d = 700 pc (Liseau et al. 1992).

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We find κr= 0.16 cm² g⁻¹, or κ = 16 cm² g⁻¹ assuming r = 0.01. The procedure was repeated to see how much the compact source affects the result, by first removing the bright point source in Figure 8, fitting its mass separately, and adding it back into the total. This had a negligible (≲2%) effect on our value for κr.

As a consistency check, we repeated this analysis with the largest cloud in Yamaguchi et al. (1999)—cloud 25, region C in Figure 1—though it is not as isothermal as cloud 28. We separately fit the entire hot central region (centered on RCW 36) and the rest of the cloud. When we do this we derive a temperature of 20.2 K for the central region and 11.5 K for the rest of the cloud and a κr value of 0.14 cm² g⁻¹, quite consistent with the results from cloud 28, which we use in our analysis.

The value of κr is independent of the distance to the cloud, as both the C¹⁸O and BLAST dust measurements have the same dependence on distance. However, the value is strongly dependent on our assumed β = 2. Changing our assumption to β = 1.5 changes κr by about 50%. However, if the dust properties are the same for our sources as for the clouds we have used for this calibration of κr, then this will not affect their final masses. Our biggest source of uncertainty is from the CO mass estimates—these uncertainties are typically a factor of 1.5–2, corresponding to an uncertainty in κ and our derived source masses by the same factor.

The masses, luminosities, and temperatures of the cores are presented in Figure 9. The sources span the mass range from 1 to 100 M_☉, with most of the sources centered around their Jeans mass (see Section 7), which is several solar masses. Due to confusion with background structure, the survey is incomplete for cooler sources at low mass. Above 14 M_☉, it is complete for even the coolest sources.

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In the same way that the power-law envelopes of these cores make size a poorly defined concept, the mass that we measure is a function of our spatial resolution. This needs to be taken into consideration when comparing our masses to those measured in other fields. Under the model that we are fitting to beam-convolved p ≈ −1.6 power-law envelopes, simulations show that if we had mapped the same sources with the same (improved) spatial resolution as was done by Bolocam in Serpens (Enoch et al. 2008), we would have found ≈1/2 of the mass that we found with our spatial resolution in Vela, because the fit would not have picked up as much of the envelopes.

In Figure 10, we present the same information for sources within cloud 25 (object C in Figure 1) which is a large cold cloud not visible in IRAS (Helou & Walker 1988) at 100 μm. This is the largest of a class of objects visible in the map which are characterized by large numbers of cold sources with few mid-IR or far-IR counterparts.

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Comparing the mass we find in cold cores with the molecular gas mass found in the same region in ¹²CO, we can determine the fraction of mass in cold cores. As distance uncertainty affects both the core mass estimates and the gas mass estimates in the same way, this ratio is independent of our assumed distance, as long as the cores are well associated with structures in CO (visually, they are) and as long as our sample is not contaminated by distant objects of another type posing as cold cores. The fact that the mass function falls so steeply (faster than d²) means that the density of high-mass distant objects is spatially much lower than the density of low-mass closer objects—reducing the probability that this is a dominant effect. Our catalog contains 6000 M_☉ of cores with T < 14 K. To estimate the total mass in our cold cores, compensating for completeness, we integrate the lognormal mass function from Figure 11 to find a total mass in cores of 12,000 M_☉, compared with a total gas mass in CO in the VMR (Yamaguchi et al. 1999) of 5.6 × 10⁵ M_☉. The total gas fraction in cold cores is thus estimated at 2%. Given the large and heterogeneous nature of the field, we suggest that this fraction can be taken as representative of the Galaxy as a whole.

Given the masses, sizes, and temperatures of the cores, we can calculate whether they can form pressure-supported structures which are stable against the Jeans instability (Jeans 1902). The maximum mass, M, enclosed within a radius, R, of such a structure is given by

$$\begin{equation} \left(M/R\right)_{\rm J} = 4.2 \frac{c_{\rm s}^2}{G}, \end{equation} \tag{ 4 }$$

where $c_s = \sqrt{kT/2.3 m_{\rm p}}$ is the speed of sound in the medium, k is Boltzman's constant, T is the gas temperature, which we assume to be equal to the dust temperature, and m_p is the proton mass. For a Gaussian source, the enclosed M/R has a peak at 2.135σ where the enclosed mass is 79.3% of the total fit mass. A truncated power-law core has a larger M/R than a Gaussian, with a maximum which is dependent on the size of the inner knee. Since we are fitting Gaussians, and do not have the resolution to determine the inner knee radius, we take the conservative position that the maximum M/R for our cores is greater than that of a Gaussian. The criterion for Gaussian cores is plotted in Figure 9 for our median-sized (0.15 pc) sources.

Restricting ourselves to sources with temperatures that are consistent with an early stage of star formation (T < 14 K), and considering the size of each source, we find a median M/M_J = 1.8, meaning that the distribution peaks near the Jeans criterion, but that most of the sources (80%) are unstable. If we further restrict ourselves to the mass range for which the survey is complete (M>14 M_☉), our sources exceed their Jeans masses by a median factor of M/M_J = 4. This ratio is linear in the assumed distance, so even if the cloud were at 500 pc, rather than 700 pc, the majority of the sources would still be unstable. Sources more distant than the assumed 700 pc exceed their Jeans mass by an even larger factor.

Without some other form of support, cores that exceed the Jeans mass would collapse to form stars in a free-fall time, given by McKee & Ostriker (2007),

$$\begin{equation} t_{\rm {ff}} = 1.37 \times 10^{6}\rm {\,yr}\left[\frac{10^3 \rm {\,cm}^{-3}}{\it {\bar{n}}}\right]^{1/2}. \end{equation} \tag{ 5 }$$

For the M>14 M_☉, T < 14 K intermediate mass cores in our catalog, the median density is $\bar{n}=1.7\times 10^4$ cm⁻³. The free-fall times are roughly Gaussian distributed as $t_{\rm {ff}} = (3.4 \pm 1.2) \times 10^5$ yr. This is a lower limit to the lifetimes of cold cores, in that it is possible that many of them may contain pre-Class II protostars.

These characteristic times do not fit comfortably with the character of the GMCs within which the sources lie. Within region C in Figure 1, one large cluster containing more than 350 stars has formed two to three million years ago (Baba et al. 2004), which implies that the GMC is older than this. Given this age, the free-fall times, and the large number of cold cores in region C, one would expect that the GMC would contain stars at various stages of evolution. However, besides two very small candidate star clusters, and ∼30 candidate protostars identified in the mid-IR by MSX and confirmed in the NIR (Baba et al. 2006), there is little sign of ongoing star formation. Only 6% of the cores with mass over 14 M_☉ in this cloud have mid-IR (MSX) counterparts, compared to 22% considering the entire map. Since Baba et al. (2006) argue that MSX has the sensitivity to find the intermediate mass protostars which our M>14 M_☉ will become, the cloud appears to be in a very early stage of evolution. This suggests that we are either seeing the cloud at a very special time, or that the lifetimes of the cores are much longer than the free-fall times, and more on the order of the few million year minimum age of the GMC.

The characteristic time for cold cores to become stars can also be estimated from the fraction of the molecular gas in cold cores, by assuming that all cold cores eventually become stars with a mass-independent efficiency, and from the molecular gas depletion time, $t_{{\rm H}_2} = M/\hbox{SFR}$.

A study of star formation in several nearby galaxies has found that H₂ in spirals forms stars at constant efficiency over a range of scales and physical conditions, with a molecular gas depletion time of $t_{{\rm H}_2} = (2 \pm 0.8) \times 10^{9}$ yr (Bigiel et al. 2008). The Galaxy averaged molecular gas depletion time for the Milky Way, including the consumption of helium, can be estimated from the total molecular gas mass $M_{{\rm H}_2}\approx 1.3\times 10^9$ M_☉ and star formation rate R_MW ≈ 2.7 M_☉ yr⁻¹ (Misiriotis et al. 2006) to be $t_{{\rm H}_2} = M_{{\rm H}_2}/0.73R_{{\rm MW}} \approx 6.6\times 10^8$ yr. This estimate for the Milky Way gas depletion time is substantially less than for the nearby galaxies, but given the considerable uncertainties, roughly consistent. For the analysis that follows, we will use the Milky Way gas depletion time, but note that using $t_{{\rm H}_2}$ from the nearby galaxies would give a substantially larger characteristic times.

If we further extrapolate from our observations over a broad region that 2% of molecular gas in the entire Milky Way is in cold cores, and if we assume that these cores will eventually form stars with an efficiency = 0.3 (Matzner & McKee 2000), the mass-independent lifetime for cold cores is given by

$$\begin{equation} t_c = 0.02\epsilon \,t_{{\rm H}_2} = 4\times 10^6\,\mbox{yr.} \end{equation} \tag{ 6 }$$

If a large fraction of cold cores never becomes stars (effectively reducing the efficiency), then this lifetime would be an overestimate of those that do produce a star.

We can further develop a toy model to determine the mass-dependent lifetime for the cores using the CMF. We first estimate the expected star formation rate per mass interval for our region by assuming that star formation follows gas mass, reversing the steps in the previous section. Measurements of ¹²CO give a total molecular gas mass in the VMR (Yamaguchi et al. 1999) of 5.6 × 10⁵ M_☉, compared to a total molecular gas mass in the Galaxy of 1.3 × 10⁹ M_☉. Since star formation follows molecular gas, our map accounts for 0.043% of the total star formation of the Galaxy. So, given a Galactic star formation rate of 2.7 M_☉ yr⁻¹, this region of the Galaxy produces stars at a rate of 1.2 × 10⁻³ M$_\odot \,\rm {yr}^{-1}$. With a canonical initial stellar mass function for stars, neglecting multiplicity (Kroupa 2007), normalized by the total star formation rate in Vela, the star formation rate per mass interval per year in Vela is

$$\begin{equation} F_{{\rm vela}} = \frac{{\it dN}_s}{{\it dM}_sdt} = 2.6\times 10^{-4} M_s^{-2.3}\, (M_{\odot}^{-1}\; \mbox{yr}^{-1}\mbox{)} \end{equation} \tag{ 7 }$$

over the mass interval 0.5 M_☉ < M < 150 M_☉.

Assuming a power-law CMF, dN_c/dM_c = n₀M^α_c, and that each core will form k stars of mass M_s with efficiency , the mass function of stars which will eventually be created from the cores which currently exist is

$$\begin{eqnarray} \left(\frac{{\it dN}_s}{{\it dM}_s}\right)_P &=& \left(\frac{{\it dN}_c}{{\it dM}_c}\right)\left(\frac{{\it dN}_s}{{\it dN}_c}\right)\left(\frac{{\it dM}_c}{{\it dM}_s}\right) \\ &=& \big(n_0M_c^\alpha\big)(k)\left(\frac{k}{\epsilon }\right) \\ &=& \frac{n_0k^{\alpha +2}}{\epsilon ^{\alpha + 1}}M_s^\alpha. \end{eqnarray} \tag{ 8 }$$

Further assuming a steady state for both the CMF and the normalized star formation rate, R_vela, when averaged over the whole region, the characteristic time for the cores to form stars is

$$\begin{eqnarray} t_c(M) &= \frac{({\it dN}_s/{\it dM}_s)_P}{F_{\rm vela}} \\ &= \frac{n_0\epsilon ^{1.3}}{2.6\times 10^{-4} k^{0.3}} M_{{\rm core}}^{\alpha + 2.3}. \end{eqnarray} \tag{ 11 }$$

In Section 6, we showed that over the range $14<M/\mbox{\mbox{\it M}}_\odot <100$, n₀ = 9.0 × 10⁴ and α = −3.22. Assuming k = 2 and = 0.3, we find

$$\begin{eqnarray} &&t_c(M) = 4 \times 10^6 (M/20{\,M}_\odot)^{-0.9}\,\mbox{\,yr.} \end{eqnarray} \tag{ 13 }$$

The CMF being steeper than the Salpeter mass function for stars implies that high-mass cores evolve more quickly than low-mass cores. This time dependence is reliant on the highly uncertain IMF spectral index. A steeper IMF would imply less time dependence.

These times are sensitive to uncertainties in the ¹²CO masses used to estimate the fraction of gas in molecular clouds, and the molecular gas depletion time for Vela. Using $t_{{\rm H}_2} = (2\,\,{\pm}\,\, 0.8)\times 10^9$ yr from Bigiel et al. (2008) instead of the estimate from the very uncertain values from the Milky Way gives t_c = (12 ± 5) × 10⁶ yr. These uncertainties could substantially change the estimate, but nevertheless, it would be very difficult to reconcile our counts with free-fall times.

The few million year lifetime is roughly consistent with a naive crossing time based on 0.1  km s⁻¹ infall velocities measured in low-mass cold cores (Bergin & Tafalla 2007).

The lifetimes of these intermediate cold cores are longer but roughly consistent with previous estimates for low-mass cores. A compilation of previous data reported in Ward-Thompson et al. (2007) finds lifetimes for densities like we find of around a million years, which is several times the free-fall time. Similarly, lifetime estimates of low-mass starless and protostellar cores in Perseus, Serpens, and Ophiuchus based on the ratio of starless, Class 0 and Class I cores to Class II cores give starless core lifetimes of a half million years, and combined starless and Class 0/I protostellar lifetimes of a million years (Enoch et al. 2008). If we assume that our cold cores are mainly starless, our lifetime estimates exceed this half million year estimates by an order of magnitude. On the other hand, if we assume that our cold cores are a combination of starless, and Class 0/I type protostars, then this estimates is shorter than ours by a factor of a few, though, given the considerable uncertainties, perhaps marginally consistent with what we see.

It should be noted that many of these surveys have been made in regions of known star formation. Since they typically depend on the observed ratios of less evolved cores to more evolved cores, selection on the existence of evolved objects could bias the estimates low. BLAST has shown that there can be considerable populations of cold cores far from any evidence of heating by later stages of star formation. For example, region C in Figure 1 contains 169 cold cores, with a mean temperature of 13 K, including one of over 80 M_☉, and with no cores over the 20 K temperature expected for envelopes being blown off from Class II protostars (Molinari et al. 2008), other than three associated with RCW 36.

An even more striking contrast is with high-mass star formation lifetime estimates found from an analysis of Cygnus X. Motte et al. (2007) find lifetimes for starless and protostellar cores of less than 10⁴ yr for cores with M>40 M_☉, based on the ratio of the early cores to more evolved types within the map.

Though we do not currently have a complete census of all O stars in our region, we can evaluate the consistency of our lifetimes by applying a similar reasoning to our data. Taking the definition of high-mass star-forming cores from Motte et al. (2007) as cores with M>40 M_☉, we integrate our fit to the mass function in Figure 11. We predict 7.8 high-mass cold cores in our map (we actually see 8). Integrating our estimated normalized star formation rate from our region given in Equation (7), we predict that there should have been nine stars with $M>40\epsilon \,\mbox{\mbox{\it M}}_\odot = 12\,\mbox{\mbox{\it M}}_\odot$ formed in our region over the past two million years, which is consistent with the visual impression of hot (blue) spots in Figure 1. Averaging over very large areas, we find that the lifetimes for cold cores is on the order of millions of years, and far in excess of the free-fall times, even for the high-mass tail of our distribution.

The existence of even these small numbers of high-mass cores in Vela is strong evidence for a long lifetime. However, our lifetime estimate could be compromised because we may have misidentified these objects as high-mass star-forming cores; for example, these objects could be the result of the blending of many low-mass cores, or our mass estimates could be significantly off. But our resolution is close to what Motte et al. (2007) use to define an object as a core rather than a clump, and our sources are all well below the clump scale. Our masses are calibrated to C¹⁸O masses, and an underestimated distance (more likely than an overestimate) would produce underestimated source masses, making the discrepancy even larger. On the other hand, since Cygnus X was chosen as a region undergoing significant amounts of high-mass star formation (which is a very rare event), lifetime estimates based on statistics of the region could be strongly biased toward shorter values—the region is being observed at a very special time.