\citet{2009ApJ...697.1103T} presented an extensive kinematic study of the ONC, covering about 2\(^\circ\) of Declination centered on the Orion A cloud, from NGC 1977 down to L1641N. This survey builds on previous work by \citet{2008ApJ...676.1109F} and constitutes the most complete and highest precision kinematic survey of this region to date, offering a unique possibility to characterize kinematically the ONC foreground population identified in this paper. In Figure \ref{fig:vdispprofile} we present the North-South velocity dispersion profile of the ONC region, taken from Table 13 of \citet{2009ApJ...697.1103T}. The filled circles represent the sources in this paper with reliable radial velocities. The NGC 1977, the OMC2/3, the Trapezium cluster, and NGC 1980 are indicated, as well as the extent of the Orion nebula (light open circle). The thick red line represents the north-south velocity dispersion profile measured in bins of Declination (indicated by the thin horizontal lines).
It is striking that the velocity dispersion profile has a minimum at the location of NGC 1980. This is perhaps the strongest indication we have that the stellar population of NGC 1980 is a distinct population from the reddened population inside Orion A. The measurement of the velocity dispersion in the bin that mostly includes NGC 1980 (FWHM\(=\)2.1 km/s) was not optimized to isolate the most probable members of this cluster and should then be seen as an upper limit to the true velocity dispersion in this cluster. Still, this value is close to the velocity dispersion of the Trapezium cluster as measured from the proper motion of stars within one half degree of the center of the Trapezium, namely, 1.34\(\pm\)0.18 km/s for a sample of brighter stars \citep{1988AJ.....95.1744V} and 1.99\(\pm\)0.08 km/s for a larger sample including slightly fainter stars \citep{1988AJ.....95.1755J}. Both velocity dispersions were corrected to the more recent estimate of the distance to the Orion A cloud (400 pc).
Given the striking differences in the velocity dispersion profile, we then calculated the mean radial velocity per bin from the subsample of single sources (not directly available in the Tobin et al. 2009 paper) and found that although showing variations from bin to bin, these variations are of the order of the measured dispersions. In particular, the mean velocity for the bin including the Trapezium (\(-5.3^\circ < \delta < -5.4^\circ\)) and NGC 1980 (\(-5.8^\circ < \delta < -6.0^\circ\)) is \(25.7\pm3.0\) km/s and \(24.3\pm2.7\) km/s, respectively. Within the errors, estimated as the median absolute deviation in each bin, the NGC 1980 cluster has virtually the same radial velocity as the ONC. We note, however, that we were taking the bins as simple slices at constant declination, without trying to optimize their boundaries to better separate the different populations.
Because of the importance of measuring the velocity differences between the Trapezium and NGC 1980, especially for discussing the origin of NGC 1980, we made an alternative source selection and created two new subsamples that are in principle more pure, but have about three times fewer sources. For the NGC 1980 subsample we matched the Tobin et al. 2009 catalog with the foreground population identified in this paper. For the Trapezium we matched the Tobin et al. 2009 catalog with the COUP sample \citep{2002ApJ...574..258F}, which is dominated by Trapezium sources, and removed sources that matched the foreground population. Because this Trapezium subsample was meant to be of “high confidence”, we used the radial velocity limits found in this subsample (6.2 km/s and 36.6 km/s) to exclude five extreme outliers in the NGC 1980 sample (with velocities of \(\sim -40\) and \(\sim 90\) km/s). In these subsamples, the mean velocity for the Trapezium and NGC 1980 clusters is \(25.4\pm3.0\) km/s and \(24.4\pm1.5\) km/s, respectively, or essentially the same values as derived above, with the important difference that the dispersion of velocities in NGC 1980 is now reduced by about a factor of two, once again suggesting that this cluster is a population distinct from the reddened population inside Orion, as argued above. Still, the measured velocity difference of 1 km/s is not statistically significant even with the decreased velocity dispersion.
To estimate an age to the NGC 1980 cluster we compared the evolutionary status of class II sources in various clusters analyzing the median spectral energy distribution (SED) of late-type (spectral type later than K0) members. We followed the \citet{2005ApJ...629..881H} definition of Class II, namely objects with \(0.2<[3.6]-[4.5]<0.7\) mag and \(0.6<[5.8]-[8.0]<1.1\) mag. To compute the median SED for the different clusters we retrieved the optical, near-infrared (2MASS) and mid-infrared (Spitzer and WISE) photometry for samples of confirmed members of Taurus , IC 348 , NGC1333 , \(\lambda-\)Ori , and \(\eta-\)Cha . To compute the median SED for the Trapezium cluster we first defined a “high confidence” Trapezium member catalog, as we did in the previous section, by cross-matching the X-ray COUP sample from \cite{2008ApJ...677..401P} with the foreground (NGC 1980) sample, and excluding all matches as unrelated foregrounds. The individual SEDs within each cluster were normalized to the \(J\)-band flux, and the median cluster SED of each cluster was computed. Figure \ref{fig:medsed} shows the result. One can see from this Figure \ref{fig:medsed} that the optical part of the SED varies from cluster to cluster, mostly because of dust extinction. More striking, the mid-infrared (\(>3\) \(\mu\)m) excesses, related to the presence of a disk, decrease systematically with age.
The median SED of NGC 1980 seems to fit between the median SED of Taurus (1–3 Myr) and \(\lambda-\)Ori (5–7 Myr), suggesting an age in between that of these regions. But another constraint is given by the massive stars in the center of the cluster. Of the five brightest stars at the peak of the spatial distribution in Figure \ref{fig:density}, only the brightest, iota Ori (O9 III, V\(=\)2.77 mag), seems to have evolved from the main sequence. This implies an age of about 4-5 Myr for this star, assuming it started its life as a 25 M\(_\odot\) star \citep[e.g.][]{Massey:2003fk}. This age fits well within the inferred age from the median SED and also agrees with the estimate of \citet{1978ApJS...36..497W} for the age of Ori OB 1c subgroup (of about 4 Myr).
To estimate the size of the cluster population we focused on the distribution of foreground sources from the center of the cluster to the south in order to avoid incompleteness problems caused by the bright Orion nebula. We counted the number of sources falling on a 20\(^\circ\) “pie-slice” inside the A\(_V \geq 5\) mag region, centered on the cluster and with a radius of 7 pc. This radius approximately corresponds to the extent of the 10% contour in Figure \ref{fig:density}, chosen to account for contamination from the Galactic field between Earth and Orion (estimated to be 6–9% of the foreground population in Section \ref{sec:unrel-galact-field}). Note that this radius is not the half-mass radius but simply the radius to which we can trace the enhancement of sources over the unrelated foreground field. We repeated this measurement several times to account for uncertainties in the location of the cluster center and counted about 100 to 110 sources in the 20\(^\circ\) “pie-slice”. Assuming spherical symmetry for the distribution of sources in NGC 1980, we expect a total of about 1800-2000 sources in NGC 1980, or a total cluster mass of about 1000 M\(_\odot\) (assuming an average mass per star of 0.5 M\(_\odot\)).
Assuming NGC 1980 has a normal initial mass function (IMF), we can make a consistency test on the likelihood of the number of sources in this cluster being of the order of 2000. For this we constructed 200000 synthetic clusters of 1000 M\(_\odot\) each by randomly sampling the Kroupa and Chabrier IMFs \citep{Kroupa2001,2003PASP..115..763C} and tracked the mass of the most massive star in each synthetic cluster. The mean mass of the most massive star was 54\(\pm\)26 M\(_\odot\) (Kroupa) and 22\(\pm\)11 M\(_\odot\) (Chabrier). Assuming there were no supernovae in NGC 1980 yet, and that iota Ori is the most massive star in the cluster, then, to first approximation, a population of about 2000 sources seems a plausible estimate of the size of the NGC 1980 population.