SUBSTELLAR OBJECTS IN NEARBY YOUNG CLUSTERS (SONYC). VI. THE PLANETARY-MASS DOMAIN OF NGC 1333

We begin by showing the spectral type distribution for all spectroscopically classified M- and L-type objects in NGC 1333 in Figure 7. This includes the VLMOs listed in SONYC-IV, new objects identified in the same paper and this new study, plus earlier type objects classified in Winston et al. (2009). Their spectroscopic survey is essentially complete down to the brown dwarf/star boundary (for A_V < 10), and thus ideally complements our own studies, which are not complete above the substellar boundary.

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For the stellar regime, the distribution of spectral types in NGC 1333 resembles those found for other regions (Cha-I, IC348, Taurus; see Luhman 2007), with a peak around M4 and an increase in the frequency between M0 and M5 by about a factor of three. For later spectral types, we observe a second peak around M7, which is not seen in these three other regions.

Another relevant feature in the context of this paper is the sharp drop of the numbers at M9. Based on the COND (Baraffe et al. 2003) and DUSTY (Chabrier et al. 2000) isochrones, M9 corresponds to a mass around the deuterium burning limit. Only two objects (SONYC-NGC 1333-36 at ∼L3 and SONYC-NGC 1333-42 at L1) have later spectral types. Thus, the number of observed planemos in this cluster is very low. This feature will be further discussed in the following subsections.

As an independent check of the distribution shown in Figure 7, we examine the histogram of absolute J-band magnitudes for the population of Class II sources in NGC 1333, as identified by Gutermuth et al. (2008) based on Spitzer data. Of their 137 objects, 94 have photometry in 2MASS. We calculate A_V from J- and K-band photometry, using the same prescription as in SONYC-IV, deredden the J-band photometry and subtract the distance modulus of 7.4 (assuming a distance of 300 pc; see Belikov et al. 2002). We exclude the most reddened objects and consider only the 74 with A_V < 10. In this extinction regime, the distribution of J-band magnitudes does not show a dependence on A_V.

Figure 8 shows again a peak slightly above the substellar limit, which corresponds to the peak around M4–M5 in the spectral type distribution. A second peak is visible in the substellar regime (for M_J of 7–8), but it is much less pronounced than the peak at M7 seen in Figure 7. In fact, within the statistical errors the magnitude distribution is consistent with a broad peak around M_J = 5 and a decline at fainter magnitudes, which agrees with previously published results for Cha-I and IC348 (Luhman 2007). Thus, the second peak in the spectral type distribution could be spurious. One possible explanation is a gap in completeness between the spectroscopic samples from Winston et al. (2009) and ours, causing us to miss objects at ∼M6.

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In Figure 9 we show the Hertzsprung–Russell diagram (HRD) for NGC 1333, focusing on the VLMOs with spectral types of M5 or later. Out of the 41 previously known sources listed in SONYC-IV (crosses), the 10 newly identified in SONYC-IV (plusses), and the seven newly identified in this paper (squares), 51 have estimated effective temperatures and are plotted in the figure.

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Instead of luminosity, we prefer to plot the absolute J-band magnitude to avoid additional errors from the bolometric correction. The absolute J-band magnitudes are calculated in the same way as in Section 5.1, including dereddening of the J-band data⁹ and subtraction of the distance modulus. The typical error bar in the absolute J-band magnitude is ±0.5 mag, which combines the errors in A_V (±1 mag), distance (±20 pc), and photometry (up to ±0.1 mag). The uncertainty in effective temperature, as outlined above, is ±200 K. The approximate mass limits according to the DUSTY and COND isochrones, assuming an age of 1 Myr, are given as well.

The general trend in this diagram is in good agreement with three sets of isochrones from the Lyon group: DUSTY, COND, and BCAH (Baraffe et al. 1998). Typical for HRDs of star-forming regions, the objects show a large spread due to various effects (e.g., Littlefair et al. 2011). However, only seven objects (14%) are inconsistent with the 1–5 Myr isochrones within the error bars. Some of them could be affected by ongoing accretion or strong magnetic activity (overluminosity)—see Scholz et al. (2012b) for a discussion—or gray extinction by an edge-on disk (underluminosity). Some might experience variability (Scholz 2012). In addition, there remains a small chance that an outlier is a fore- or background source: Perseus is known to have a complex substructure (Enoch et al. 2006; Ridge et al. 2006), i.e., there may be young objects at different distances. Moreover, in some cases the signal to noise in our spectra is not sufficient to confirm low gravity, i.e., we cannot completely exclude older objects in the field. Given these caveats, the overall agreement with the isochrones is good.

Only a very small number of three objects have temperature below 2500 K—SONYC-NGC 1333-31, 36, and 42—(two of them also with spectral type later than M9, see Section 5.1) and would have masses around or below the deuterium burning limit. The plot demonstrates that the frequency of objects per bin in effective temperature drops significantly below 2500 K. There are 19 objects with 2800 ⩽ T_eff < 3100, 13 with 2500 ⩽ T_eff < 2800, but only three with 2200 ⩽ T_eff < 2500. This confirms the finding from the spectral type distribution.

The drop in the frequency of observed objects below 2500 K and spectral type M9, already found in Section 5.1, can either be explained by an actual lack of planemos in this cluster, or by biases in our photometric survey and the selection of objects for follow-up spectroscopy, which will be discussed in the following subsection. In addition, there are three more caveats:

• 1.  
  Extinction might limit the completeness of our survey below 2500 K. To test this, we have overplotted with dash-dotted lines the J-band limit of our survey (J = 19, see Section 2) for A_V = 0 and A_V = 5. We should have been able to find objects with T_eff > 2200 K and A_V ⩽ 5. The clear majority of the confirmed VLMOs have A_V < 5. Also, A_V ∼ 5 is the median extinction for the sample of Class II objects published by Gutermuth et al. (2008), as far as their 2MASS photometry is available. Therefore, we are unlikely to miss a significant number of planemos down to 2200 K due to their high extinction. For extinctions well below A_V of 5 mag, we should be able to find sources even cooler than 2200 K (as proven by the detection of SONYC-NGC 1333-36).
• 2.  
  The isochrones might not accurately reflect the luminosity versus effective temperature relation in young star-forming regions. To explain a lack of planemos in Figure 9, the isochrones would have to turn downward below 2500 K, i.e., cooler objects need to be significantly fainter than expected based on these models. While this cannot be definitely excluded at the moment, the data for the eclipsing binary brown dwarf in Orion—currently the only available empirical test for these isochrones—do not indicate such a trend (Stassun et al. 2007). The luminosities for its components are in agreement with the predictions from the isochrones, in fact, for the lower mass component (M = 0.036 M_☉) the isochrone underestimates the luminosity, the reverse of what would be needed to explain the lack of planemos in NGC 1333. Furthermore, it is difficult to conceive a significant departure from the smooth (almost linear) trend in the isochrones in Figure 4, since this would require an additional and strong source of opacity in the J band. To our knowledge, this is not born out by the available data, for example, the same isochrones fit the optical and near-infrared colors for the substellar population in σ Ori quite well down to the lowest masses (Caballero et al. 2007).
• 3.  
  The effective temperatures—mostly determined with the routines used in this paper, i.e., by fitting DUSTY models to the near-infrared spectra—could be systematically unreliable in a way that T_eff is overestimated for very cool sources. The study by Patience et al. (2012), already mentioned in Section 4, does not indicate any such trend. Specifically, their comparison with the DUSTY models yields effective temperatures below 2000 K when compared with the spectra for 2M1207B, CT Cha B, and GQ Lup B, three very young objects with L spectral types. This seems to work well even when only the H- and K-band spectra are considered, which is the case for our objects in NGC 1333.We conclude that these three caveats cannot be used to explain the lack of observed objects cooler than 2500 K and later than M9.

In this subsection, we will explore the possibility that our survey has missed a significant number of planemos due to a lack of depth or biases in the color cuts.

Our initial candidate selection was based on a (i, i − z) color–magnitude diagram (the IZ catalog, see Section 2). From the set of 196 candidates, more than half are now covered by follow-up spectroscopy. In particular, 27 out of 43 IZ candidates with i > 22 and 9 out of 15 with i > 24 have been verified spectroscopically. As illustrated in Figure 2, the spectroscopy covers the entire color–magnitude space of this selection down to the faint end. This candidate sample contains two likely planemos (SONYC-NGC 1333-31 is not found in this survey). Statistically, the remaining candidates that have not been verified yet are expected to contain one more.

This selection, however, might have missed planemos, because the depth of the IZ survey is not sufficient. As argued in SONYC-IV, this is a distinct possibility; while the nominal completeness limit is i = 24.8, it might be lower in some parts of the cluster with strong background emission.

To overcome the depth limitation of the IZ survey, we have used the JKS catalog, which contains all objects with J- and K-band photometry from our own survey and Spitzer photometry in the first two IRAC bands at 3.6 and 4.5 μm (see Section 2). As illustrated in Figure 3, this survey is much deeper and extends significantly beyond the limiting magnitude for follow-up spectroscopy (J = 19). It should be complete down to J = 20.8. The near-infrared images do not show strong background structure due to the cloud, i.e., the completeness should be uniform across the cluster. The JKS catalog contains about two-thirds of the confirmed VLMOs in NGC 1333; most of the ones that are not in this catalog are relatively bright and therefore affected by saturation in our deep near-infrared images. This catalog contains two likely planemos (SONYC-NGC 1333-42 does not have a Spitzer counterpart).

The color–magnitude diagram from this catalog is shown in Figure 3. Our spectroscopic follow-up covers a large fraction of this diagram to the J = 19 limit. According to the COND and DUSTY 1 Myr isochrones, this should correspond to a mass of 0.003–0.004 M_☉ for A_V = 0 and 0.006–0.008 M_☉ for A_V = 5. For 15 < J < 17, the entire color range in I1 − I2 has been probed by spectroscopy; it turns out that most of the confirmed objects in this magnitude range (11/13) have I1 − I2 > 0.2. As the IRAC color can be affected by excess emission due to a disk, this simply might reflect the high disk fraction in NGC 1333 (see SONYC-IV). For 17 < J < 19, we verified about three quarters of the objects with I1 − I2 > 0.3. Thus, in these color domains the spectroscopic survey is sufficiently complete to rule out the existence of more than 1–2 additional planemos.

To further analyze the color space from the JKS catalog, we show a (J − K, I1 − I2) color–color diagram in Figure 10. In comparison with other color combinations in this catalog, this plot shows a relatively clear distinction between objects confirmed as very low mass cluster members and those rejected. All confirmed objects are marked with squares, all objects verified with spectroscopy with crosses. For this plot, we estimate the expected position of planemos based on the photometry of known young ultracool objects: In the σ Ori cluster (Scholz & Jayawardhana 2008), the average color of 16 M9-L5-type objects is I1 − I2 = 0.2, albeit with a spread of ±0.2 mag due to photometric uncertainties. Among 10 young field dwarfs with L0–L4 spectral type, the average color is I1 − I2 = 0.17 with a spread of 0.05 mag (Luhman et al. 2009). Based on these two samples, we adopt I1 − I2 = 0.2 as typical intrinsic color of planemos.

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The dashed line in Figure 10 shows the reddening path for A_V = 0–15 starting with this intrinsic color. Shifting this line by 0.1 mag to the left is in good agreement with the left boundary for most of the confirmed VLMOs in NGC 1333 (dash-dotted line). This line combined with a limit of J − K > 1.0 is adopted as the color space where brown dwarfs and planemos are expected.

In this regime, we have 250 objects out of which 103 have 16 < J < 19 and are thus sufficiently faint to be planemos (J = 16 corresponds to ∼0.015 M_☉ for zero extinction in COND/DUSTY isochrones) and sufficiently bright to be accessible for spectroscopy. About one quarter of them have been observed spectroscopically. Thus, the catalog could contain a few additional planemos—up to six, statistically, which would yield a total of up to eight. This analysis shows that one particular bias in the selection of candidates, the cutoff at I1 − I2 = 0.3 which was necessitated by the large amounts of contaminating objects at bluer colors, might affect our ability to find planemos.

We should not miss any significant number of planemos with enhanced mid-infrared colors due to the presence of a disk. If the disk fraction for planemos is as high as for brown dwarfs, as shown for the σ Ori cluster (Scholz & Jayawardhana 2008), excess emission should be expected for about half of the planemos in NGC 1333 (see SONYC-IV for more information on disk fractions). These objects should be located to the right of the dashed line. In this area, we find 39 objects from which about half have been verified spectroscopically (including the two planemos). This implies that we might miss about two more objects in this color domain. Assuming a disk fraction of around >50%, this again gives a total number of up to eight planemos.

The JKS catalog can further be used to probe the regime J > 19, which is not accessible for spectroscopy. The JKS catalog contains 292 objects with J > 19, 124 in the color space expected for planemos (dash-dotted lines in Figure 10). However, this sample is dominated by strongly reddened objects with high J − K color. Only about 30 of them have J − K colors consistent with A_V < 5 and only seven are below A_V = 3. Given that two-thirds of the confirmed brown dwarfs have an optical extinction below 5 mag and about half below 3 mag, this basically rules out that the candidates too faint for spectroscopy down to J ∼ 21 contain a sizable population of planemos. According to the COND and DUSTY isochrones, this limit corresponds to object masses of 0.002–0.003 M_☉ (for A_V of 0–5 and age of 1 Myr).

In the following, we will use the survey results in NGC 1333 to give a quantitative constraint on the frequency of planemos, which can be compared with other star-forming regions. To do this, we estimate the fraction of brown dwarfs that have a mass in the planemo domain, f_P = N_P/N_BD. This quantity serves as a proxy for the shape of the mass function in the substellar regime. Here, we treat the population of planemos as a subsample of the population of brown dwarfs.

Our survey in NGC 1333 yields only three objects with effective temperatures below 2500 K or spectral types later than M9. According to the currently available 1–5 Myr isochrones, these objects have masses below the deuterium burning limit of 0.015 M_☉ and are thus good candidates for planemos. As outlined above, we might miss about six more planemos due to our cutoff in the mid-infrared color.

The total number of brown dwarfs can be calculated as follows. Adding the objects listed in SONYC-IV and this paper, there are 58 with spectral type M5 or later or effective temperatures of 3200 K or below. From these around 10–20 are likely to be above the substellar boundary, which leaves 38–48 brown dwarfs. Following the same statistical arguments that we have used in Section 4.1. of SONYC-IV, we estimate that we might miss up to 13 more brown dwarfs, plus six planemos (see above), i.e., the total is 57–67.

Thus, for NGC 1333 we estimate that f_P is 12%–14%. Just counting the number of confirmed objects, the ratio becomes 6%–8%. This includes all planemos down to masses of 0.006–0.008 M_☉ (the mass limit for J = 19 and A_V = 5).

This value can be compared with other star-forming regions. This comparison comes with three caveats. (1) Only σ Ori and UpSco have been surveyed with a depth comparable to our survey in NGC 1333, i.e., all other ratios should be considered lower limits. (2) While the general survey strategy is similar in all cases (candidate selection based on optical/near-infrared photometry plus follow-up spectroscopy), the details of the strategy differ from region to region, which might introduce unknown biases. To be conservative, we focus in the following mostly on samples with spectroscopic confirmation. (3) Most of the studies listed below do not make an attempt to estimate the total substellar population, by taking into account possible survey biases.

We note that all existing surveys use the COND/DUSTY isochrones for mass estimates, as in our paper. In the case, these isochrones turn out to be systematically off, the results of the comparison should still be valid and merely shifted to different mass regimes.

σ Ori. The summary paper by Caballero et al. (2007) lists 46 confirmed brown dwarfs, out of which 12 are expected to be in the planemo regime, i.e., f_P ∼ 26%. Not all of these objects are spectroscopically confirmed, but the contamination in this cluster is generally low due to the negligible extinction. The surveys in this region are similarly deep as in NGC 1333, i.e., the numbers should be comparable.

Upper Scorpius. Based on photometry and proper motions from UKIDSS, the total number of brown dwarfs in this region is 68 in the UKIDSS covered area, out of which 49 are in the northern area where follow-up spectroscopy is available (Dawson et al. 2011). The currently ongoing spectroscopic verification shows that essentially all these objects are indeed members of UpSco (Lodieu et al. 2008, 2011a). Converting the photometry to masses, this sample should cover the mass range down to 0.01 M_☉ and contains about half a dozen objects below 0.015 M_☉. A deeper survey by Lodieu et al. (2011b) does not find new members in the planemo domain.¹⁰ This yields f_P ∼ 10%.

ρ-Ophiuchus. This region is affected by very high and variable extinction, which strongly hampers any survey. The existing census is not nearly complete below 0.03 M_☉. So far, there are around 40 confirmed objects with spectral types later or equal M6 from Wilking et al. (2008), Geers et al. (2011), Marsh et al. (2010a), Mužić et al. (2012), Alves de Oliveira et al. (2010), and Alves de Oliveira et al. (2012). Out of these, eight might be in the planemo regime based on spectral type and effective temperature, which results in f_P ∼ 20%.

Chamaeleon-I. The census by Luhman (2007) and Luhman & Muench (2008) contains 35 objects with spectral type of M6 or later that are to be considered brown dwarfs. Five of these have estimated masses below 0.015 M_☉, i.e., f_p ∼ 14%. We note that our own deep survey work in Cha-I has not revealed any additional planemos yet down to 0.008 M_☉ (Mužić et al. 2011).

Taking into account the caveats listed above, the values for f_P in the various regions are consistent with each other and in the range between 10% and 20%; only σ Ori might have a slightly larger planemo fraction. Focusing on the confirmed objects, NGC 1333 has a relatively low planemo fraction compared with other star-forming areas.

We can also estimate the fraction of planemos with respect to the population of young stars, g_P = N_P/N_S. For NGC 1333, we have recently determined that the star-versus-brown dwarf ratio, defined as R₁ = N(0.08–1.0 M_☉/N(0.03–0.08 M_☉), is 2.3 ± 0.5, for most other regions this ratio is larger. Taking this into account, for NGC 1333 the fraction of planemos with respect to the total cluster population is in the range of 2%–3%. For the other regions where this type of census is available this number becomes 2%–5%, i.e., stars are 20–50 times more frequent than planemos. This is consistent with the planemo fraction of <10% (Lucas et al. 2005) and 1–14% (Lucas et al. 2006) derived for the Orion Nebulae Cluster (ONC), albeit for slightly different mass limits. Thus, the number of planemos is insignificant compared with the total population of stars and brown dwarfs. The planemo contribution to the mass budget of young clusters is negligible (well below 1%).

With the available database of spectroscopically confirmed objects in NGC 1333, we are in the position to construct the initial mass function (IMF) in the low-mass regime. We choose to express the IMF as a mass spectrum dN/dM ∝ M^−α. To do that, we use the same spectroscopic samples as in Section 5.1, combining the confirmed low-mass stars from Winston et al. (2009) with the census of VLMOs. We select all M and L dwarfs, in total 107 objects, out of which 100 have an estimate for the effective temperature, either from our survey or from Winston et al. (2009).

Masses were derived for this sample by comparing the temperatures with theoretical evolutionary tracks. Temperatures do not significantly depend on age in the 1–10 Myr phase, as opposed to luminosities and magnitudes, and thus provide a mass estimate that is insensitive to age spread. We use the 1 Myr isochrone from the BCAH models for M ⩾ 0.1 M_☉ and the 1 Myr isochrone from the DUSTY models for M < 0.1 M_☉. For each object with a given T_eff, we selected the isochrone data points within ±200 K around T_eff, fitted this section either linearly (if there are less than five data points) or with a second order polynomial, and used that function to calculate the mass corresponding to T_eff. All masses are tied to this isochrone and should not be compared with values derived using other models.

The mass spectrum was calculated in a way to achieve similar statistical uncertainties in each mass bin, i.e., with varying bin size. For M > 0.7 M_☉, the sample sizes are too small for a meaningful analysis, the 10 objects above this limit were excluded. The lowest mass bin includes all objects with M < 0.03 M_☉. In Figure 11, we plot our result. The data points in this diagram are consistent with dN/dM∝M^−α with α = 0.61, overplotted as dashed line. For the substellar regime alone, the best-fitting slope is α = 0.46. For the stellar regime above 0.1 M_☉ the slope becomes α = 1.0. The uncertainty in the slope is in the range of 0.1.

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To verify how the uncertainties in the effective temperatures (±200 K) affect these results, we carried out the following test. For half of the objects, randomly selected, we increased T_eff by 200 K, and for the other half we reduced it by 200 K. This effectively scrambles the values within the error bars. Then the mass spectrum was calculated again using the same procedure. This yields α = 0.66 for the entire sample and 0.55 for the brown dwarfs, slightly higher as before but well within the error bars. This test also shows that the peak around 0.2 M_☉ seen in the figure is spurious.

Also shown is the Kroupa IMF, an empirical description of the mass spectrum as a segmented power law, as a solid line (Kroupa 2001). This function follows α = 1.3 ± 0.5 in the stellar regime up to 0.5 M_☉ and α = 0.3 ± 0.7 in the substellar domain. Within the uncertainties, the Kroupa IMF is consistent with the mass spectrum in NGC 1333.

The slope derived here is broadly consistent with values derived for most other star-forming regions and young clusters. For example, for the very VLMOs in σ Ori, values of 0.6–0.7 have been published in the literature (Caballero et al. 2007; Béjar et al. 2011). For the domain from 0.03 to 0.6 M_☉, the cluster Blanco 1 has a mass function with α = 0.69 ± 0.15 (Moraux et al. 2007). For Upper Scorpius and the mass regime 0.01–0.3 M_☉, a value of α = 0.6 ± 0.1 has been published (Lodieu et al. 2007). For the Pleiades, α is found to be in the range of 0.6–1.0 in the low-mass regime (e.g., Moraux et al. 2003, and references therein). For the α Per cluster, the slope is 0.59 ± 0.05 (Barrado y Navascués et al. 2002). In Collinder 69, the slope has been found to be between 0.2 and 0.4 for the low-mass regime (Bayo et al. 2011).

To our knowledge, the only young region where a significantly different slope of the mass spectrum has been determined is the ONC. In a recent paper, Da Rio et al. (2012) find Γ of −1.1 to −3.1 for the substellar regime, which corresponds to a negative α (α = Γ + 1). Similar results have been found in previous studies in the ONC (e.g., Muench et al. 2002). These numbers appear to be anomalous compared with the other regions mentioned above.

Apart from the overall slope, we can examine the shape of the mass spectrum in NGC 1333. In equal sized bins, the numbers per bin increase continuously with decreasing mass, with the exception of a slight minimum around 0.1–0.2 M_☉. However, the test with the modified temperatures (see above) indicates that this minimum is spurious, the data are indeed consistent with a monotonically rising histogram. The same result has been obtained for Upper Scorpius and σ Ori, while some other regions show a peak in the mass spectrum around 0.1–0.2 M_☉ and a smaller slope for lower masses (IC348, Cha-I, ρ-Oph; Luhman 2007; Alves de Oliveira et al. 2012). One consequence of this difference is a smaller star-to-brown-dwarf ratio (i.e., a large number of brown dwarfs relative to stars) in regions with monotonically rising mass spectrum—as it is indeed found for NGC 1333. As discussed in SONYC-IV, a comparison of these ratios possibly indicates environmental differences in the formation of brown dwarfs.

The focus of this study is the planetary-mass domain. Assuming a monotonic continuation of the power law shown in Figure 11 with α = 0.6 ± 0.1, we would expect 8 ± 3 objects with 0.005 M_☉ < M < 0.015 M_☉, i.e., in the planemo domain and detectable in our survey. For comparison, in Section 5.3 we derive an upper limit of eight planemos in this mass regime from our survey, taking into account the incompleteness in the spectroscopic follow-up of our candidates. Thus, the data are consistent with a monotonic power-law mass spectrum across the deuterium burning limit, but a smaller slope is possible as well. Our survey rules out that the slope of the mass spectrum in NGC 1333 increases in the planemo regime.

Again this is in agreement with previous findings for other regions. In σ Ori, the census of substellar objects is well approximated by a monotonic slope down to planetary masses (Caballero et al. 2007; Béjar et al. 2011; Peña Ramírez et al. 2012), with a possible turnover (i.e., a lower α) in the mass spectrum below 0.006 M_☉. For Upper Scorpius, the results by Lodieu et al. (2011b) favor a turndown below 0.01 M_☉. We note that Marsh et al. (2010b) show a mass function of ρ-Ophiuchus covering the entire planemo regime based on a photometrically selected candidate sample, which resembles the one in σ Ori. Taken together, it seems safe to conclude that the slope of the mass function in the planemo domain is α ≲ 0.6.

We note that α ≲ 0.6 corresponds to a planemo fraction as defined in Section 5.4 of f_P ≲ 20% (if the entire planemo domain is considered) or f_P ≲ 30% (with a lower mass cutoff at 0.005 M_☉). Indeed, no regions show a larger planemo fraction: Most surveys indicate significantly lower values, including our own work in NGC 1333.

Thus, the current census of star-forming regions provides support for the idea that planemos are an extension of the population of stars and brown dwarfs and form through the same mechanisms. The observations indicate that free-floating objects with planetary masses exist down to at least 0.006 M_☉, but, as pointed out in Section 5.4, their numbers and their mass budget are insignificant compared with the total population of stars and brown dwarfs.

Some theoretical estimates for the lower mass limit in the star formation process—the opacity limit for fragmentation—are 0.007 (Low & Lynden-Bell 1976) or 0.01 M_☉ (Silk 1977) from analytical arguments and <0.001 (Boss 2001) or 0.003–0.009 M_☉ (Bate 2005) from numerical simulations. Except for the lowest-mass values, all these estimates are consistent with the current observational picture.

Sumi et al. (2011) recently determined the slope of the mass spectrum based on microlensing surveys, and find 1.3 ± ^0.3_0.4 for M < 0.01 M_☉, significantly higher than for brown dwarfs (0.49 in their work), indicating that Jupiter-mass objects are almost twice as common as stars. Their estimate includes planetary-mass objects without host stars (i.e., free-floating) and those on wide orbits, but they argue that the majority of them are indeed unbound (but see Quanz et al. 2012 for a criticism of this claim). This is in clear disagreement with the results from the surveys in star-forming regions, where the number of planemos per star is much smaller (see Section 5.4) and the slope in the mass spectrum is not rising (see above). If the microlensing result holds, the additional planemos would have to be in the mass regime <0.005 M_☉, which is not sufficiently probed by the cluster surveys. This would imply a break in the slope of the mass spectrum in the planemo domain, favoring a scenario where the Jupiter-mass objects form in a different way than the planemos and brown dwarfs seen in the star-forming regions—as indeed concluded by Sumi et al. (2011). Larger samples of short-period microlensing events and deeper surveys in star-forming regions are critical to understand whether they are in fact different populations or not.

In another recent paper, Strigari et al. (2012) estimate that there may be up to 10⁵ objects with masses between 10⁻⁸ and 10⁻² M_☉ (called "nomads" in their paper) per-main-sequence star. To arrive at this number, they use the slope of the mass spectrum in the brown dwarf/planemo regime as a constraint. Their upper limit of 10⁵ can only be obtained by using α = 2. As shown above, this is inconsistent with the surveys in star-forming regions. For a more realistic value of α = 0.5, the result given in their paper is ≳ 1 nomads per-main-sequence star. Given the enormous difficulties in extrapolating the mass function over six orders of magnitude in mass and different modes of formation, these estimates remain highly speculative.