A VLA SURVEY FOR FAINT COMPACT RADIO SOURCES IN THE ORION NEBULA CLUSTER

In each of our VLA maps, we search for sources detected above a certain signal-to-noise threshold. Our maps contain $\gt {10}^{6}$ synthesized beams (see Table 1), and so we must employ a relatively conservative threshold to ensure that we do not select noise spikes in the images as real detections. The noise in each map follows a Gaussian distribution (see Figure 2), so that we expect $\ll 1$ noise spike to fall above a $6\sigma$ detection threshold. We, therefore, use $6\sigma$ as our detection limit.

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We can also use catalogs of previously known source positions to target our search. We search our maps at the positions of >700 near-infrared-detected sources (Hillenbrand & Carpenter 2000) and ∼200 HST-detected proplyds (Ricci et al. 2008, with an overlap of about ∼150 of the near-infrared detected sources). We also search the coordinates of known submillimeter sources detected with the SMA, CARMA, and ALMA that lack counterparts at infrared wavelengths (Eisner et al. 2008; Mann & Williams 2010; Mann et al. 2014). Finally, we search for compact radio sources, which were detected with the VLA by previous surveys (Felli et al. 1993a; Kounkel et al. 2014). Due to the smaller number of synthesized beams being probed (∼800), we expect $\ll 1$ noise spike to fall above a $4.5\sigma$ level. For each previously identified source, we search for a detection above $4.5\sigma$ within a radius of 05, typical of the sizes of beams from these previous studies.

The rms at each pixel is calculated from a 128 × 128 pixel box surrounding that pixel in the residual map. The rms in the map is generally low (∼25 μJy in the 1.3 cm maps, ∼30 μJy at 3.6 cm, and ∼37 μJy at 6 cm). However, the central region of each map exhibits beam artifacts from a cluster of bright sources and poor sampling of large-scale emission. The rms in these regions can be much higher than the rest of the map (∼100 μJy in the 1.3 cm maps, ∼70 μJy at 3.6 cm, and ∼150 μJy at 6 cm; see Table 1).

We list the total number of sources detected in each map in Table 1. For each map, we also provide a breakdown of the number of sources detected in our blind search as well as the additional number of sources detected from the catalog-driven search. We detect 108 objects in our 6 cm map, 98 objects in our 3.6 cm map, and a total of 144 objects across all of our 1.3 cm maps. In all we detect 175 distinct sources across all of our maps. We show the position of every detected source in our maps in the left panel of Figure 1.

Of the 175 unique compact radio sources, 120 sources are associated with YSOs detected in near-infrared surveys (e.g., Hillenbrand & Carpenter 2000), and 67 sources are associated with HST-detected proplyds. 149 have previous radio detections, and 40 have been previously detected at millimeter wavelengths. We also report the detection of 11 sources here for the first time at any wavelength.

We fit every detected source with a two-dimensional Gaussian to determine position, extent, and total source flux. For sources identified in the previously mentioned catalogs that are not detected in our maps, we also integrate over a 1'' aperture centered on the known source position to produce an unbiased estimate of the signal (or noise) toward that position. We include a 10% error on the measurement to account for systematic errors in the band-to-band flux calibration. These intensities, measured toward all cataloged objects in our field of view, are presented in Table 2. The print version of this paper presents only the first page of that table. We also plot images of those sources in Figure 3.

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Table 2.  Source Detections, Identifications, and Fluxes

ID	Proplyd Name	HC00 ID	GMR ID	Z04a ID	Other Names	R.A.	Decl.	${F}_{\nu ,6\mathrm{cm}}$	${F}_{\nu ,3.6\mathrm{cm}}$	${F}_{\nu ,1.3\mathrm{cm},1}$ a	${F}_{\nu ,1.3\mathrm{cm},2}$ a	${F}_{\nu ,1.3\mathrm{cm},3}$ a	${F}_{\nu ,1.3\mathrm{cm},4}$ a	${F}_{\nu ,1.3\mathrm{cm},{mean}}$ a
						(J2000)	(J2000)	(mJy)	(mJy)	(mJy)	(mJy)	(mJy)	(mJy)	(mJy)
1	4538–311	⋯	⋯	⋯	⋯	5h34m5379	−5d23m1073	0.015 ± 0.567	⋯	⋯	⋯	⋯	⋯	⋯
2	⋯	⋯	⋯	⋯	⋯	5h34m5597	−5d23m1300	0.269 ± 0.338	⋯	⋯	⋯	⋯	⋯	⋯
3	4582–635	⋯	⋯	⋯	⋯	5h34m5816	−5d26m3513	−0.245 ± 0.409	⋯	⋯	⋯	⋯	⋯	⋯
4	005–514	⋯	⋯	⋯	⋯	5h35m0047	−5d25m1434	0.114 ± 0.233	⋯	⋯	⋯	⋯	⋯	⋯
5	006–439	⋯	⋯	⋯	⋯	5h35m0058	−5d24m3879	−0.008 ± 0.229	−0.049 ± 1.203	⋯	⋯	⋯	⋯	⋯

Note.

^aSubscript 1 indicates the 1.3 cm data were taken on 2013 November 10, 2 on 2014 March 3, 3 on 2014 March 7, 4 on 2014 May 3, and the mean indicates the image from the combined 1.3 cm tracks.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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Our catalog of sources, as presented in Table 2, is sorted by right ascension and then given a catalog "ID," which we list in Table 2. We refer to each source by this ID throughout the remainder of the text and figures. In Table 2 we also list the proplyd name, identification from early ONC radio surveys (e.g., Garay et al. 1987; Felli et al. 1993b), identification from Zapata et al. (2004a), or identification from Hillenbrand & Carpenter (2000), when applicable.

Evidence suggests that the proplyds are undergoing mass loss from photoevaporation by the nearby O star ${\theta }^{1}$ Ori C, so the free–free emission we detect here is likely due to a wind (e.g., Churchwell et al. 1987; Henney & Arthur 1998). For emission from a spherically symmetric wind with an arbitrary $n\propto {r}^{-\alpha }$ density profile the expected spectral dependence of free–free emission is

$$\begin{eqnarray}{F}_{\nu ,{ff}}=\left\{\begin{array}{ll}{F}_{\nu ,\mathrm{turn}}{\left(\displaystyle \frac{\nu }{{\nu }_{\mathrm{turn}}}\right)}^{-0.1} & \nu \geqslant {\nu }_{\mathrm{turn}}\\ {F}_{\nu ,\mathrm{turn}}{\left(\displaystyle \frac{\nu }{{\nu }_{\mathrm{turn}}}\right)}^{(4\alpha -6.2)/(2\alpha -1)} & \nu \lt {\nu }_{\mathrm{turn}}\end{array}\right.\end{eqnarray} \tag{ 1 }$$

(Wright & Barlow 1975). ${\nu }_{\mathrm{turn}}$ is the frequency where the wind becomes partially optically thick, and is determined by the radius of the inner boundary of the ionized envelope. High turnover frequencies indicate more compact inner boundaries. When the wind becomes fully optically thick at very low frequencies the spectrum follows the typical ${F}_{\nu }\propto {\nu }^{2}$ spectrum expected for optically thick thermal emission.

For a fully ionized wind with a constant mass-loss rate, we expect $\alpha =2$ and the spectral dependence of free–free emission is

$$\begin{eqnarray}{F}_{\nu ,{ff}}=\left\{\begin{array}{cc}{F}_{\nu ,\mathrm{turn}}{\left(\displaystyle \frac{\nu }{{\nu }_{\mathrm{turn}}}\right)}^{-0.1} & \nu \geqslant {\nu }_{\mathrm{turn}}\\ {F}_{\nu ,\mathrm{turn}}{\left(\displaystyle \frac{\nu }{{\nu }_{\mathrm{turn}}}\right)}^{0.6} & \nu \lt {\nu }_{\mathrm{turn}}\end{array}\right..\end{eqnarray} \tag{ 2 }$$

Steeper density profiles may lead to steeper spectral dependences below the turnover frequency (e.g., Plambeck et al. 1995). Here, for simplicity, we adopt the solution for a fully ionized wind with a constant mass-loss rate. Many of our sources show evidence for a free–free turnover (see Figure 4), and so we adopt a model including a turnover in the spectrum.

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At higher frequencies, dust emission is expected to dominate. The differences in the expected spectral slopes between dust and free–free emission allow us to characterize each separately by observing our targets at a range of wavelengths. For each of our detected sources we fit a simple model to the known radio, millimeter, and submillimeter photometry:

$$\begin{eqnarray}&&{F}_{\nu }={F}_{\nu ,{ff}}+{F}_{\nu ,\mathrm{dust},230\mathrm{GHz}}{\left(\displaystyle \frac{\nu }{230\mathrm{GHz}}\right)}^{2+\beta }.\end{eqnarray} \tag{ 3 }$$

Here, we assume $\beta =0.7$, consistent with previous studies of protoplanetary disks in other star-forming regions (e.g., Rodmann et al. 2006; Ricci et al. 2010a, 2010b).

We fit the SED of each source by searching a grid over a large range of parameter space of ${\nu }_{\mathrm{turn}}$, ${F}_{\nu ,\mathrm{turn}}$, and ${F}_{\nu ,\mathrm{dust},230\mathrm{GHz}}$ for a minimum in ${\chi }^{2}$. We then use a second, finely spaced, grid search based on the initial search to find the best ${\chi }^{2}$ fit.

${\nu }_{\mathrm{turn}}$, ${F}_{\nu ,\mathrm{turn}}$ and ${F}_{\nu ,\mathrm{dust},230\mathrm{GHz}}$ are left as free parameters in the grid search. If a source has no submillimeter detections ($\geqslant 90\,\mathrm{GHz};$ Eisner et al. 2008; Mann & Williams 2010; Mann et al. 2014), we assume that ${F}_{\nu ,\mathrm{dust},230\mathrm{GHz}}=0$. In that case, we also require $5.5\mathrm{GHz}\leqslant {\nu }_{\mathrm{turn}}\leqslant 22\mathrm{GHz}$, because outside of this range we cannot constrain ${\nu }_{\mathrm{turn}}$. If a source does have submillimeter detections, we only require $5.5\,\mathrm{GHz}\leqslant {\nu }_{\mathrm{turn}}$.

Sources 281, 391, 416, 423, 430, 433, 442, 512, 516, 537, 564, and 595 are all extended sources that are marginally resolved by our 3.6 and 6 cm maps, as well as in our B-configuration 1.3 cm observations. In our A-configuration 1.3 cm observations, however, these sources are very well resolved. In fact, they are so well resolved that much or all of the emission from the source is resolved out. As such, we exclude the A-configuration flux measurements from our SED fitting, as flux variations are likely due to structure being resolved out rather than actual variability.

Some of our sources are variable across our multiple epochs of 1.3 cm data (see Section 4.2). We account for this variability in our modeling by including the measured flux at each epoch and allowing the variability to influence the uncertainty of our parameter estimation. Sources that are more variable will also have more uncertainty in model fits.

We list the parameters of our best fitted models to each source detected in our maps in Table 3. The photometry, along with the best fit model, for each source is plotted in Figure 4.

Table 3.  Free–Free Emission Model Parameters and ALMA Band Fluxes for Detected Sources

ID	${\nu }_{\mathrm{turn}}$	${F}_{\nu ,\mathrm{turn}}$	${F}_{\nu ,\mathrm{dust},230\mathrm{GHz}}$	${F}_{\nu ,\mathrm{Band}1}$ a	${F}_{\nu ,\mathrm{Band}2}$ a	${F}_{\nu ,\mathrm{Band}3}$ a	${F}_{\nu ,\mathrm{Band}4}$ a	${F}_{\nu ,\mathrm{Band}5}$ a	${F}_{\nu ,\mathrm{Band}6}$ a	${F}_{\nu ,\mathrm{Band}7}$ a	${F}_{\nu ,\mathrm{Band}8}$ a	${F}_{\nu ,\mathrm{Band}9}$ a	${F}_{\nu ,\mathrm{Band}10}$ a
	(GHz)	(mJy)	(mJy)	(mJy)	(mJy)	(mJy)	(mJy)	(mJy)	(mJy)	(mJy)	(mJy)	(mJy)	(mJy)
11	$\lt 5.5$	3.188 ± 0.161	⋯	2.65	2.44	2.39	2.29	2.23	2.19	2.11	2.05	1.98	1.93
18	$\lt 5.5$	0.582 ± 0.078	⋯	0.48	0.45	0.44	0.42	0.41	0.40	0.38	0.37	0.36	0.35
69	$\gt 22.0$	0.265 ± 0.181	⋯	0.25	0.23	0.23	0.22	0.21	0.21	0.20	0.20	0.19	0.18
76	$\lt 5.5$	0.237 ± 0.021	⋯	0.20	0.18	0.18	0.17	0.17	0.16	0.16	0.15	0.15	0.14
77	11.477 ± 6.002	0.382 ± 0.055	⋯	0.34	0.31	0.31	0.30	0.29	0.28	0.27	0.26	0.25	0.25

Note.

^aBand 1 = 35 GHz, Band 2 = 80 GHz, Band 3 = 100 GHz, Band 4 = 150 GHz, Band 5 = 200 GHz, Band 6 = 230 GHz, Band 7 = 345 GHz, Band 8 = 450 GHz, Band 9 = 650 GHz, Band 10 = 850 GHz

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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The origin of the radiation ionizing these sources has been the subject of much debate. Early radio studies of the region disagreed as to whether these sources were externally ionized by radiation from ${\theta }^{1}$ Ori C or ionized internally by a young massive star, and as to whether these objects are dense neutral condensations or protoplanetary disks (e.g., Churchwell et al. 1987; Garay et al. 1987), although these studies are complicated by the fact that only projected, and not actual, distances from ${\theta }^{1}$ Ori C are known. Since these early studies, HST imaging (e.g., O'Dell et al. 1993) and detailed modeling of those images (e.g., Henney & Arthur 1998) has favored protoplanetary disks ionized by ${\theta }^{1}$ Ori C.

Free–free emission powered by ionizing radiation from ${\theta }^{1}$ Ori C should decrease with increasing separation from ${\theta }^{1}$ Ori C. We show the measured flux versus distance in the left panel of Figure 5. For most sources there is a trend of decreasing radio flux with increasing separation, suggesting that they are exhibiting free–free emission from gas ionized by ${\theta }^{1}$ Ori C. We also find that the difference in their 1.3 and 6 cm flux is close to zero, as expected for optically thin free–free emission, which has a roughly flat spectrum (see the right panel of Figure 5). We note that here we report projected distances. Actual separations are greater than or equal to this number. We discuss the outliers of these trends below, in Section 4.3.

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For this study, we are only concerned with whether these sources are emitting thermal free–free emission or not, so that we can characterize the emission and remove it from dust emission for disk mass studies, but on the surface Figure 5 would seem to suggest that these sources are externally ionized by ${\theta }^{1}$ Ori C. The detailed structure of these compact objects is beyond the scope of this paper, as the radio emission can be well characterized without that knowledge, but we will revisit the subject in a more detailed study in the future.

Many compact radio sources have previously been identified at a range of wavelengths in the ONC through VLA surveys of the region. The earliest searches for compact radio sources in the ONC were conducted primarily at 20, 6, 2, and 1.3 cm (e.g., Churchwell et al. 1987; Garay et al. 1987; Felli et al. 1993a, 1993b). These surveys were state of the art at the time, with rms as low as 0.18 mJy beam⁻¹ at 2 cm (Churchwell et al. 1987; Felli et al. 1993a), 0.23 mJy beam⁻¹ at 6 cm (Felli et al. 1993b), or 1.0 mJy beam⁻¹ at 1.3 cm (Garay et al. 1987). These searches identified 49 compact radio sources in the ONC.

A more recent survey mapped a 4' × 4' region of the the ONC at 3.6 cm using the VLA. This survey achieved a sensitivity of 0.03 mJy beam⁻¹ and uncovered 77 compact radio sources (Zapata et al. 2004a). Of these 77 sources, 38 were previously known from the earlier studies mentioned above, while 39 were new centimeter detections. Zapata et al. (2004b) also mapped a 30'' × 30'' region in OMC-1 South at 1.3 cm with the VLA. They achieved an rms of 0.07 mJy beam⁻¹, but due to the limited area of their maps only detected 11 sources.

A recent survey mapped out a large region encompassing λ Ori, Lynds 1622, NGC 2068, NGC 2071, NGC 2023, NGC 2024, σ Ori, the ONC, and Lynds 1641 with the VLA at 4.5 and 7.5 GHz with a 60 μJy sensitivity (Kounkel et al. 2014). They found $\gt 350$ sources over the area of their map, 54 of which overlap with the area we survey. The majority of their detected sources also have spectral indices consistent with flat spectra.

Here, we compare these previous surveys with our own JVLA maps. In Figure 6 we plot the distribution of fluxes for compact sources detected in our maps as well as the distribution of fluxes for previously identified compact radio sources at the same wavelength. The most extensive existing studies at 1.3 cm are limited by either survey area or sensitivity so we also compare our 1.3 cm detections with previous 2 cm detections.

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Of the 49 compact radio sources detected by initial surveys (e.g., Churchwell et al. 1987; Garay et al. 1987; Felli et al. 1993a, 1993b), we have detected 37 in our maps. We have also recovered 64 of the 77 sources detected by Zapata et al. (2004a), 9 of the 11 sources found by Zapata et al. (2004b), 42 of the 54 sources found by Kounkel et al. (2014), and 144 of the 556 sources found by Forbrich et al. (2016). We detect 29 of the 35 sources that were previously detected at 2 cm. We also report the detection of 135 sources that have not previously been detected at 1.3 cm, 34 at 3.6 cm, 4 at 6 cm, and 26 sources that have not previously been detected at any radio wavelengths. The sources that were previously detected, but that we do not detect in our maps, are likely variable given the deeper sensitivity in our JVLA data.

Previous radio studies of the ONC have explored multiple epochs of data to search for evidence of source variability. Felli et al. (1993b) monitored the ONC at 2 and 6 cm for a period of 7 months and found 13 sources to be variable over that time with flux variability of 20%–80%. Zapata et al. (2004a) tracked the ONC at 3.6 cm over 4 years, and identified 36 sources that are time variable by more than 30%. More recently, Kounkel et al. (2014) mapped a large region of the Gould Belt at 4.5 and 7.5 GHz over three epochs each separated by a month, and found 32 variable sources in the ONC. Furthermore, Rivilla et al. (2015) studied a field in the ONC at 0.7 and 0.9 cm and found 19 sources which are variable over long-term (monthly) timescales, and five sources which are variable on short timescales (hours to days). Moreover, very short timescale radio flares have been observed toward a number of pre-main sequence stars (e.g., Bower et al. 2003; Forbrich et al. 2008; Rivilla et al. 2015)

Here, we compare previously measured fluxes for detected compact radio sources with the fluxes in our maps. Time-baselines are ∼10 years at 1.3 cm and 3.6 cm and $\gtrsim 20$ years at 6 cm, and we cannot characterize shorter timescales for variability. We thus seek to identify sources that may not have been detected as variable in previous, shorter time-baseline studies (Felli et al. 1993b; Zapata et al. 2004a). We also use our multiple epochs of 1.3 cm data to search for variability on timescales of ∼7 months, between 2013 November 10 and 2014 May 3.

As discussed earlier, Sources 281, 391, 416, 423, 430, 433, 442, 512, 516, 537, 564, and 595 are very well resolved with the A-configuration at 1.3 cm. As such, we exclude these sources from our variability considerations at 1.3 cm, as flux variations may be due to structure being resolved out rather than actual variability.

We define a variable source as one for which the flux measurements are 3σ discrepant from one epoch to the next, at any observed wavelength. ΔF/F quantifies how variable a source is, where F is the mean flux of the source and ΔF is the standard deviation of the fluxes. We show the results of this search in Table 4. For the sources detected in Zapata et al. (2004a) and Zapata et al. (2004b) we include a 10% uncertainty on the flux on top of the uncertainties they quote to account for a systematic flux calibration uncertainty across the data sets.

Table 4.  Variability of ONC Sources

ID	1.3 cm Variable?	${({\rm{\Delta }}F/F)}_{1.3\mathrm{cm}}$	3.6 cm Variable?	${({\rm{\Delta }}F/F)}_{3.6\mathrm{cm}}$	6 cm Variable?	${({\rm{\Delta }}F/F)}_{6\mathrm{cm}}$
11	N	⋯	Y	20 ± 28	⋯	⋯
76	N	⋯	⋯	⋯	0	⋯
77	N	⋯	Y	144 ± 25	⋯	⋯
102	⋯	⋯	N	⋯	⋯	⋯
103	N	⋯	⋯	⋯	⋯	⋯
115	Y	78 ± 102	N	⋯	⋯	⋯
134	N	⋯	⋯	⋯	⋯	⋯
151	N	⋯	N	⋯	⋯	⋯
154	Y	37 ± 10	Y	152 ± 3	⋯	⋯
173	N	⋯	⋯	⋯	⋯	⋯
199	N	⋯	⋯	⋯	⋯	⋯
200	N	⋯	Y	71 ± 7	⋯	⋯
209	⋯	⋯	N	⋯	⋯	⋯
213	Y	158 ± 68	Y	77 ± 29	⋯	⋯
219	N	⋯	⋯	⋯	⋯	⋯
222	N	⋯	⋯	⋯	⋯	⋯
229	Y	29 ± 574	N	⋯	⋯	⋯
235	N	⋯	⋯	⋯	⋯	⋯
236	N	⋯	⋯	⋯	⋯	⋯
237	N	⋯	⋯	⋯	⋯	⋯
238	Y	64 ± 9	⋯	⋯	⋯	⋯
243	N	⋯	⋯	⋯	⋯	⋯
246	Y	45 ± 22	⋯	⋯	⋯	⋯
253	N	⋯	⋯	⋯	⋯	⋯
257	Y	122 ± 72	⋯	⋯	⋯	⋯
259	Y	125 ± 74	⋯	⋯	⋯	⋯
262	N	⋯	⋯	⋯	⋯	⋯
265	Y	129 ± 21	⋯	⋯	⋯	⋯
270	⋯	⋯	N	⋯	⋯	⋯
271	N	⋯	⋯	⋯	⋯	⋯
275	⋯	⋯	⋯	⋯	Y	100 ± 4
278	⋯	⋯	⋯	⋯	N	⋯
279	Y	20 ± 26	N	⋯	⋯	⋯
280	N	⋯	N	⋯	⋯	⋯
281	⋯	⋯	Y	28 ± 12	N	⋯
284	N	⋯	⋯	⋯	⋯	⋯
286	N	⋯	⋯	⋯	⋯	⋯
287	N	⋯	N	⋯	⋯	⋯
289	N	⋯	⋯	⋯	⋯	⋯
294	N	⋯	Y	52 ± 22	⋯	⋯
297	N	⋯	Y	25 ± 21	⋯	⋯
301	Y	29 ± 27	⋯	⋯	⋯	⋯
307	Y	38 ± 19	Y	67 ± 8	N	⋯
308	Y	19 ± 30	Y	38 ± 14	⋯	⋯
313	N	⋯	⋯	⋯	⋯	⋯
315	N	⋯	⋯	⋯	⋯	⋯
319	N	⋯	⋯	⋯	⋯	⋯
325	N	⋯	⋯	⋯	⋯	⋯
330	N	⋯	⋯	⋯	⋯	⋯
331	⋯	⋯	N	⋯	⋯	⋯
332	N	⋯	⋯	⋯	⋯	⋯
333	⋯	⋯	N	⋯	⋯	⋯
341	Y	51 ± 10	Y	55 ± 13	N	⋯
344	⋯	⋯	N	⋯	⋯	⋯
357	⋯	⋯	N	⋯	⋯	⋯
358	⋯	⋯	N	⋯	⋯	⋯
364	⋯	⋯	Y	73 ± 16	⋯	⋯
365	⋯	⋯	N	⋯	⋯	⋯
371	⋯	⋯	N	⋯	⋯	⋯
373	⋯	⋯	⋯	⋯	Y	91 ± 7
374	N	⋯	N	⋯	⋯	⋯
380	N	⋯	⋯	⋯	⋯	⋯
382	N	⋯	⋯	⋯	⋯	⋯
383	N	⋯	Y	39 ± 17	⋯	⋯
384	⋯	⋯	N	⋯	⋯	⋯
386	⋯	⋯	Y	36 ± 20	⋯	⋯
389	N	⋯	Y	70 ± 4	⋯	⋯
391	⋯	⋯	N	⋯	N	⋯
393	N	⋯	⋯	⋯	⋯	⋯
394	Y	72 ± 9	⋯	⋯	⋯	⋯
399	⋯	⋯	N	⋯	⋯	⋯
400	⋯	⋯	Y	60 ± 16	⋯	⋯
401	N	⋯	⋯	⋯	⋯	⋯
407	⋯	⋯	⋯	⋯	Y	101 ± 3
408	N	⋯	Y	31 ± 21	N	⋯
409	N	⋯	⋯	⋯	⋯	⋯
411	⋯	⋯	⋯	⋯	N	⋯
413	Y	41 ± 14	Y	23 ± 15	N	⋯
414	⋯	⋯	N	⋯	⋯	⋯
416	⋯	⋯	N	⋯	N	⋯
418	Y	88 ± 5	Y	63 ± 10	⋯	⋯
421	N	⋯	N	⋯	⋯	⋯
423	⋯	⋯	N	⋯	N	⋯
427	N	⋯	Y	33 ± 13	⋯	⋯
428	N	⋯	⋯	⋯	⋯	⋯
430	⋯	⋯	N	⋯	N	⋯
433	⋯	⋯	Y	39 ± 13	⋯	⋯
437	Y	284 ± 45	Y	215 ± 46	N	⋯
438	N	⋯	N	⋯	N	⋯
439	Y	24 ± 32	N	⋯	N	⋯
440	Y	299 ± 89	⋯	⋯	⋯	⋯
442	⋯	⋯	Y	29 ± 17	⋯	⋯
444	N	⋯	N	⋯	⋯	⋯
460	N	⋯	N	⋯	N	⋯
465	N	⋯	N	⋯	⋯	⋯
466	N	⋯	Y	51 ± 13	⋯	⋯
469	Y	108 ± 21	⋯	⋯	⋯	⋯
473	N	⋯	Y	55 ± 11	⋯	⋯
477	⋯	⋯	Y	60 ± 16	⋯	⋯
481	N	⋯	⋯	⋯	⋯	⋯
483	N	⋯	N	⋯	⋯	⋯
484	N	⋯	N	⋯	⋯	⋯
491	N	⋯	N	⋯	N	⋯
492	Y	57 ± 13	⋯	⋯	⋯	⋯
493	⋯	⋯	⋯	⋯	Y	102 ± 3
494	N	⋯	N	⋯	⋯	⋯
499	Y	28 ± 22	N	⋯	⋯	⋯
501	N	⋯	N	⋯	⋯	⋯
512	⋯	⋯	Y	27 ± 22	N	⋯
516	⋯	⋯	N	⋯	N	⋯
518	N	⋯	N	⋯	N	⋯
519	⋯	⋯	N	⋯	⋯	⋯
529	Y	99 ± 11	⋯	⋯	⋯	⋯
530	⋯	⋯	N	⋯	⋯	⋯
535	N	⋯	Y	31 ± 19	⋯	⋯
537	⋯	⋯	N	⋯	⋯	⋯
544	Y	102 ± 4	⋯	⋯	⋯	⋯
546	N	⋯	N	⋯	⋯	⋯
549	N	⋯	⋯	⋯	⋯	⋯
555	N	⋯	N	⋯	N	⋯
564	⋯	⋯	N	⋯	N	⋯
587	Y	136 ± 3	Y	69 ± 6	⋯	⋯
595	⋯	⋯	N	⋯	N	⋯
599	N	⋯	⋯	⋯	⋯	⋯
605	N	⋯	⋯	⋯	⋯	⋯
608	N	⋯	Y	38 ± 18	⋯	⋯
616	N	⋯	⋯	⋯	⋯	⋯
617	Y	24 ± 14	Y	49 ± 12	⋯	⋯
621	N	⋯	⋯	⋯	⋯	⋯
649	N	⋯	⋯	⋯	⋯	⋯
658	N	⋯	⋯	⋯	⋯	⋯
665	N	⋯	⋯	⋯	⋯	⋯
668	N	⋯	⋯	⋯	⋯	⋯
690	N	⋯	⋯	⋯	⋯	⋯
715	Y	92 ± 24	⋯	⋯	⋯	⋯
730	Y	51 ± 9	Y	50 ± 6	Y	47 ± 11
737	Y	905 ± 487	⋯	⋯	⋯	⋯
760	N	⋯	⋯	⋯	⋯	⋯
786	N	⋯	⋯	⋯	⋯	⋯
821	N	⋯	⋯	⋯	⋯	⋯
835	N	⋯	⋯	⋯	⋯	⋯
842	N	⋯	⋯	⋯	⋯	⋯
848	N	⋯	⋯	⋯	⋯	⋯
859	N	⋯	⋯	⋯	⋯	⋯
862	N	⋯	⋯	⋯	⋯	⋯
891	N	⋯	⋯	⋯	⋯	⋯
897	N	⋯	⋯	⋯	⋯	⋯

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At 1.3 cm, we find 30 sources that show some indication of variability, with ΔF/F ranging from 20%–900%. At 3.6 cm, we identify 32 sources whose fluxes are variable, including three sources not identified as variable in Zapata et al. (2004a), because they were too faint to be detected in individual epochs. The variability, as defined by ΔF/F, of these sources ranges from 20%–200%. Finally, at 6 cm we identify five variable sources with ΔF/F ranging from 50%–100%.

There were 13 sources detected by previous radio surveys of the ONC (e.g., Felli et al. 1993a, 1993b). Most of those sources were not detected in the same bands as our observations, and so they are excluded from our variability analysis. However, the five variable sources with 6 cm fluxes from Felli et al. (1993b) were undetected in our maps, and have ΔF/F ranging from 50%–100%. Given the high fluxes of the remainder of the sources, we would have expected to detect them in our maps, and so those sources likely have similarly high variability amplitudes.

In all, we find that 55 of our sources are variable at one or more wavelengths. Of the variable sources, 11 are characterized as variable at multiple wavelengths. 20 are found to be variable at one wavelength, but not another, although many of our constraints on ΔF/F are not strong. The remaining sources could only be analyzed at a single wavelength.

We show the location of each variable source in the right panel of Figure 1, with the strength of the variability (ΔF/F) represented by the size of the plot symbol. We find that variability amplitude does not follow the same trend as free–free flux, with variability decreasing with increased separation from ${\theta }^{1}$ Ori C. Instead, we find sources that are significantly variable out to large radii. Some of the most variable objects can be found at large separations.

Variability of radio emission from these sources is likely to arise from a few different mechanisms. It may be the result of gyrosynchrotron emission produced by magnetospheric activity in young stars (e.g., Feigelson & Montmerle 1999). These flares may be the result of magnetic reconnections on the protostellar surface, which would produce radio flares on the timescales of minutes (e.g., Dulk 1985; Bower et al. 2003; Forbrich et al. 2008). Interactions between the magnetic fields of the protostar and its disk could also produce flares on the timescales similar to the rotation periods of young stars, which are typically days to weeks in the ONC (e.g., Shu et al. 1997; Forbrich et al. 2006; Rodríguez-Ledesma et al. 2009).

Free–free emission may also be variable if the density distribution of material being ionized is non-uniform, causing the amount of ionized material to vary, or if the incident ionizing radiation varies. Studies have found that O-type stars have winds that exhibit cyclical variability on timescales of hours to days (see review by Fullerton 2003). The visible, UV and X-ray intensity of ${\theta }^{1}$ Ori C varies with a period of 15.4 days (e.g., Stahl et al. 1993, 1996; Caillault et al. 1994; Walborn & Nichols 1994), and so the ionization level and, therefore, free–free flux might be expected to vary on a similar timescale. The ionized region, however, is likely to be many light days across or larger, and so this variability may be washed out.

Inhomogeneities in the disk are unlikely to be brought into the ionized region on timescales shorter than the dynamical timescale. For disks, the dynamical timescale varies depending on location in the disk and the mass of the central star (e.g., Kenyon 2001). Inner disk radii for young stars are found to be in the order of 0.1–1 AU (e.g., Eisner et al. 2007), so that the smallest dynamical timescales we can expect are in the order of weeks to half a year. Photoevaporation in disks tends to produce winds at radii larger than the critical radius, where the photoionized material has sufficient velocity to escape. For ionization by EUV photons, this tends to occur at radii of $\gtrsim 5\,\mathrm{au}$ (e.g., Hollenbach et al. 1994; Gorti & Hollenbach 2009), corresponding to dynamical timescales of a few years. Non-uniformities in the disk are, therefore, likely to cause longer-term variability in the free–free emission.

Aside from the timescale of variability, the SED of the source at each epoch might be used to distinguish between free–free and synchrotron emission. As described in Section 3.2, free–free emission is characterized by a flat spectrum with ${F}_{\nu }\propto {\nu }^{-0.1}$. Gyrosynchrotron emission, however, is expected to have a spectral index that is significantly negative, typically ${F}_{\nu }\propto {\nu }^{-0.7}$. We discuss constraints on the nature of some of these sources in Section 4.3. Further studies with concurrent flux measurements at multiple wavelengths, however, are needed to fully distinguish between these sources of emission.

Here, we do not have simultaneous flux measurements at all bands for each epoch of data, and so it is difficult to constrain the spectral index of the emission at each epoch. There are, however, a few sources which change flux significantly between the 1.3 cm observations on 2014 March 3 and 7. For example, on March 3, Source 529 had a 1.3 cm flux of 7 mJy, but on March 7 it was down to a flux of 4.5 mJy. By May 7th the flux was all the way down at 0.5 mJy. Such an extreme change in flux may be indicative of gyrosynchrotron emission from a magnetic flare. Source 544 also shows a similar pattern. Source 587 has a flux of 1.7 mJy on March 3, but on March 7 its flux increased significantly to 22 mJy, again possibly indicative of a magnetic flare. For most sources, however, we do not have sufficient time resolution to distinguish between daily, weekly, or even longer variability timescales.

We detected emission in at least one of our maps from 67 HST-identified proplyds (Ricci et al. 2008; Mann & Williams 2010; Mann et al. 2014). Furthermore, we have detected radio emission toward 120 sources that have been identified by near-infrared imaging (Hillenbrand & Carpenter 2000). We also detect radio emission from two sources dubbed "MM" by Eisner et al. (2008), indicating that they have previously only been detected at wavelengths longer than 1 mm. Finally, we have detected 51 sources that are not associated with a known proplyd or near-infrared detected source.

The majority of our targets, including all of the sources identified as proplyds, are well fitted by our free–free and dust emission model, in agreement with previous conclusions that these objects are disks with winds driven by photoevaporation (e.g., Churchwell et al. 1987; Henney & Arthur 1998). We detect a turnover in the free–free emission spectrum for 40 objects, as evidenced by $5.5\,\mathrm{GHz}\lt {\nu }_{\mathrm{turn}}\lt 22\,\mathrm{GHz}$. There are at least three sources (Sources 374, 465, 473) that might even have ${\nu }_{\mathrm{turn}}\gt 22\,\mathrm{GHz}$, indicating that our maps are insufficient to fully characterize their emission. With such high turnover frequencies, these objects must have small inner boundaries to their ionized envelopes and are likely very compact and dense. Further short wavelength observations are necessary to better constrain the free–free emission spectrum.

Some sources have SEDs that appear to be fitted well by our free–free + dust model with some variability included. Fluxes at all three wavelengths were measured concurrently on 2014 March 3, and if we just consider those flux measurements, all of our sources are fitted well by free–free emission models. Without simultaneous 3.6 and 6 cm measurements for the other 1.3 cm epochs it is impossible to say whether the SEDs at those epochs remain consistent with free–free emission, although it seems probable.

Below, we split the sources whose SEDs are not fitted well by our model and, therefore, are not indicative of being free–free emission, or do not follow the expected trend of decreasing centimeter flux with increasing separation from ${\theta }^{1}$ Ori C:

4.3.1. Strong Free–Free Sources

4.3.2. Dust-only Sources

4.3.3. Non-thermal Radio Sources

4.3.4. Extragalactic Sources

At submillimeter, millimeter and radio wavelengths, the light emitted by dust grains is expected to be largely optically thin and the flux is directly proportional to the amount of dust present (e.g., Beckwith et al. 1990). As such, submillimeter flux measurements of protoplanetary disks are commonly used to measure the mass of those disks (e.g., Andrews & Williams 2005; Eisner et al. 2008; Mann & Williams 2010; Andrews et al. 2013; Mann et al. 2014). A number of previous surveys across millimeter and submillimeter wavelengths have employed this method to measure disk masses for protoplanetary disks in the ONC (e.g., Mundy et al. 1995; Bally et al. 1998b; Williams et al. 2005; Eisner & Carpenter 2006; Eisner et al. 2008; Mann & Williams 2010; Mann et al. 2014).

The proplyds, however, are located near the Trapezium Cluster of young massive stars that are photoevaporating the disks (e.g., Churchwell et al. 1987). The ionized material produced in the proplyds emits free–free emission, which can be bright at the same wavelengths used to measure disk masses. In order to accurately measure disk masses, it is, therefore, important to separate the dust and free–free contributions to submillimeter and millimeter fluxes. This is particularly true with the advent of ALMA, which will detect disks in the ONC much fainter than those that have been previously detected.

In this work, we characterized the free–free emission from a collection of compact radio sources in the ONC. In Table 3 we use the best fit free–free emission spectrum model from Section 3.2 to calculate the expected free–free flux at all ALMA bands. This table can be used to correct measured millimeter fluxes for free–free contamination, and accurately measure the submillimeter dust flux and thereby the dust mass.

For most sources, this extrapolation provides a good estimate of the free–free contribution of the source at ALMA wavelengths. This is not true, however, of sources for which the model fit is poor, as was discussed in the previous section. Furthermore, the extrapolation to ALMA bands for sources whose turnover frequency is designated as $\gt 22\,\mathrm{GHz}$ is also very uncertain. Many of these sources were only detected at 1.3 cm, and a few have radio photometry that is best fitted by a ${\nu }^{0.6}$ power law. Our extrapolation for these sources assumes ${\nu }_{\mathrm{turn}}=22\,\mathrm{GHz}$, but if ${\nu }_{\mathrm{turn}}\gt 22\,\mathrm{GHz}$ the free–free flux at ALMA bands would be greater than our current prediction. Further radio or millimeter observations are necessary to constrain ${\nu }_{\mathrm{turn}}$ before accurate ALMA free–free fluxes can be predicted.

Variability is also a significant source of uncertainty in determining how well free–free emission from disks can be constrained and removed from disk mass measurements, if the free–free flux to dust flux ratio is large. For example, the measured 230 GHz flux of Source 439 is 8.8 mJy and the model free–free flux at 230 GHz is 2.8 mJy, with a variability of 24%. So free–free emission makes up 32 ± 8% of the total 230 GHz flux. Source 466, however, has a measured 230 GHz flux of 7.7 mJy, 0.3 mJy of which is due to free–free emission with 50.8% variability, so the free–free emission makes up 5 ± 2% of that flux. Because of the smaller free–free flux to total flux ratio of Source 466, the dust flux can be better constrained, even though Source 466 is more variable.

ALMA, however, will be able to detect disks which are much fainter than has previously been possible, For these sources, variability may be a significant problem. Source 469 has a 230 GHz free–free flux of 0.33 mJy with a variability of 108%. Although it has no previous millimeter detections, if it were found to have a millimeter flux of 0.5 mJy, the dust mass calculation would be highly uncertain, because the free–free flux would make up 65 ± 70% of the total 230 GHz flux.

An accurate estimate of the uncertainty associated with variability of our sources, however, likely requires further monitoring of the sources to characterize the timescale and amplitude of the variability. Sources with significant variability may even require concurrent millimeter and radio flux measurements in order to measure the free–free contribution to millimeter flux measurements.

While not important for some objects, the correction for free–free emission is often crucial for correctly measuring disk mass. For example, the free–free emission from sources 391, 408, 416, 418, 421, 423, 430, 438, 439, 442, 446, 460, 465, 484, 491, 494, 499, 512, 516, 518, 535, 537, 555, 564, 605, 612, and 617 contributes >50% of the measured 3 mm fluxes. Free–free emission also contributes >40% of the measured 1.3 mm fluxes for sources 408, 416, 418, 421, 423, 438, 442, 460, 465, 484, 491, 494, 499, 516, 518, 535, 564, and 617 and >30% of the measured 850 μm fluxes for sources 408, 421, 423, 438, 460, 465, 484, 491, 494, 499, and 617. Without these corrections, disk mass estimates from these submillimeter bands would be off by a significant amount.

While our radio data set is tremendously useful for finding radio sources and characterizing their free–free emission for ALMA disk mass studies in the ONC, the data also have a number of other applications which we will explore in future work.

Due to the high resolution of our maps, particularly at 1.3 cm, many of the sources detected in our maps are well resolved. The morphology of these objects show interesting features, particularly when matched up with high-resolution HST images of the proplyds. For many sources, structure in the HST maps is well matched with features in our maps.

Furthermore, we can use resolved images to measure mass-loss rates for the protoplanetary disks. The free–free emission we detect here originates from ionized cocoons of gas, which are flowing away from their associated disks under the intense radiation pressure from the star ${\theta }^{1}$ Ori C. The flux of this free–free emission coupled with measured sizes of these cocoons of gas is sufficient to measure disk mass-loss rates. Mass-loss rates have previously been measured for a handful of disks in the ONC (e.g., Churchwell et al. 1987), but the improved sensitivity and resolution of our maps will allow us to make this measurement for many more sources.