Spitzer-IRAC GLIMPSE of high mass protostellar objects II - SED modelling of a bonafide sample,
In this paper, we estimated and analysed the physical properties of infrared counterparts (IRC) of high mass protostellar objects by comparing their spectral energy distributions (SED) with those predicted by radiative transfer accretion models of young stellar objects (YSOs). The SED of the IRCs were fitted by models of massive protostars with a range of masses between 5-42 M☉ and ages between 103 and 106 years. The observed data favours protostars of low effective temperatures (4000-8000 K) with correspondingly large effective photospheres (2-200 R☉) for the observed luminosities. The envelopes are large with a mean size of ~0.2-0.3 pc and show a distribution that is very similar to the distribution of the sizes of 8 µm nebulae discussed in a previous paper. The estimated envelope accretion rates are high with a mean value of 10-3 M☉/yr and show a power law dependence on mass with an exponent of 2, suggesting spherical accretion at those scales. Disks are found to exist in most of the sources. The modelled sources mostly represent proto-B stars although, considering the high accrection rates observed, some of them could become O stars in the future. We demonstrate that many of these results may represent a realistic picture of massive star formation, despite some of the biases resultant from the assumptions within the models.
In a previous work , we used the GLIMPSE data (Galactic Legacy Infrared Mid-Plane Survey Extraordinaire, a legacy program of the Spitzer Space Telescope) to study a sample of 381 high mass protostellar objects (HMPOs). We have identified several infrared counterparts (IRCs) of these mm/submm cores, corresponding to point sources and compact nebulae. The GLIMPSE data showed that several point sources present spectral indices and magnitudes similar to those of protostars with over 8 M☉ and that the compact nebulae have strong morphological resemblances to ultra-compact HII regions.
In this paper, we modeled the spectral energy distribution (SED) of the IRCs found with the previous work, using the best data available complementary to GLIMPSE. Since the first paper was published, a new version of the GLIMPSE catalog has been released, which allowed us to extend our study to a total of 68 bona fide infrared counterparts of HMPOs. The SED of these sources allowed the derivation of several physical parameters and also the determination of their evolutionary stage.
In order to obtain as much photometric data as possible, we used GLIMPSE, 2MASS, MSX and IRAS catalogs, for the wavelengths between the near- and far-infrared, and the catalogs on which the HMPO sample was based (SCUBA, MAMBO and SIMBA) for the mm and submm data. This grants us photometric data in a total of 18 bands within the range 1.2 µm to 1.2 mm.
The SED fitting tool developed by Robitaille et al. (2007) was used to fit the data with a grid of YSO models presented by Robitaille et al. (2006). In order to qualify as a “data point”, photometry data must belong to a single source and the measurement errors must be known. The GLIMPSE and 2MASS data - which have the best spatial resolution - were typically used as data points with associated errors set to 10% and 50%, respectively, while the remaining data was typically used as upper limits.
For each run, the SED fitting tool provided a best fitting model (which presents the smallest χ2 value) as well as all models whose χ2 per data point is less than 3 units bigger than the best χ2 per data point. This fitting degeneracy is useful because the model grid is too sparse to effectively determine the minima of the χ2 surface and consequently obtain the confidence intervals; an example of such fits is presented in Fig. 1. This example illustrates how different physical components dominate the emitted radiation at different wavelengths. The disk emission almost overplots the total flux in the near-IR domain whereas the envelope emission dominates the mid-IR to the millimeter range.
As each tested model corresponds to a different set of physical parameters, we are able to derive the parameters from the models which present low χ2 values and are outputted by the SED fitting tool. So, for each source, we calculated means and standard deviations of the parameters from the successful fitted models, weighted by the χ2 value of each model. We noted that the distributions of the stellar mass, the age and the luminosity generally show clear peaks that are independent of the model grid sampling characteristics. However, parameters such as disk mass or envelope accretion rate do not show such clear concentrations and usually have skewed distributions, mimicking the entire model grid distribution, or are spread over a wide range of values.
The interstellar extinction, which is also provided by the SED fitting tool, is estimated to span a range between 0-150, with a peak between 10 and 25 mag. The distribution of the extinction values internal to the modeled YSO is found to peak between 30 and 300 mag, which is roughly similar to the extinction estimated from the millimeter continuum observations of such cores. Most of the sources are fitted as massive protostars with a mean stellar mass of ~10-20 M☉ (with some reaching up to 40 M☉), with total luminosities between 103 and 105 L☉. Many of them are very young, with ages of ~103-104 years. The radii of the photospheres are usually large, between 20-200 R☉ and the stellar temperature is found typically to be 4000-8000 K.
Our sources, which were best fitted by models with disks, present a spread of disk masses around ~0.1 M☉ with no visible trend for the youngest sources; the few older sources, at ~106 yrs, have less massive disks and with bigger uncertainties, as one would expect. Most of the modeled sources show the presence of both disks and envelopes and protostars without envelopes have ages greater than one million years. As expected from the physics assumed in the models, the disk accretion rate (~10-6 M☉yr-1) is lower than the envelope accretion rate (~10-3 M☉yr-1). The dependence of the envelope accretion rate as a function of stellar mass corresponds to a power law, with an exponent of 2, suggesting that these objects are undergoing spherical accretion.
We must also note that, due to limitations in the models used in the SED fitting tool, we may be overestimating the mass of at least some of the stars with more than ~20M☉, which means we may be looking instead to proto-B stars. However, due to the large accretion rates obtained, some of them could evolve to O stars. Besides, in order to grasp the true nature of the different protostellar components, we may need better observational constraints on the toroid sizes, cavity opening angles and densities at larger distances, which will be of importance for future model grids. Nevertheless, the observed SEDs are well explained in the framework of an accretion scenario model.
 Spitzer-IRAC GLIMPSE of high mass protostellar objects. I Infrared point sources and nebulae, Astronomy and Astrophysics, Volume 472, Issue 1 (2007)