Tracing the Magnetic Field of IRDC G028.23$-$00.19 Using NIR Polarimetry

TL;DR

This study used near-infrared polarimetry to map the magnetic field in IRDC G028.23-00.19, revealing its complex role in cloud formation and evolution, with implications for understanding magnetic influence on star formation.

Contribution

First detailed magnetic field mapping of IRDC G028.23-00.19 using NIR polarimetry, analyzing field strength, orientation, and their relation to cloud density.

Findings

Magnetic field strengths ranged from 10 to 165 μG.

B-field strength follows a power law with density, index ~2/3.

Mass-to-flux ratio increases with density.

Abstract

The importance of the magnetic (B) field in the formation of infrared dark clouds (IRDCs) and massive stars is an ongoing topic of investigation. We studied the plane-of-sky B field for one IRDC, G028.23-00.19, to understand the interaction between the field and the cloud. We used near-IR background starlight polarimetry to probe the B field and performed several observational tests to assess the field importance. The polarimetric data, taken with the Mimir instrument, consisted of H-band and K-band observations, totaling 17,160 stellar measurements. We traced the plane-of-sky B-field morphology with respect to the sky-projected cloud elongation. We also found the relationship between the estimated B-field strength and gas volume density, and we computed estimates of the normalized mass-to-magnetic flux ratio. The B-field orientation with respect to the cloud did not show a preferred alignment, but it did exhibit a large-scale pattern. The plane-of-sky B-field strengths ranged from 10 to 165 {\mu}G, and the B-field strength dependence on density followed a power law with an index consistent with 2/3. The mass-to-magnetic flux ratio also increased as a function of density. The relative orientations and relationship between the B field and density imply that the B field was not dynamically important in the formation of the IRDC. The increase in mass-to-flux ratio as a function of density, though, indicates a dynamically important B field. Therefore, it is unclear whether the B field influenced the formation of G28.23. However, it is likely that the presence of the IRDC changed the local B-field morphology.

Tables

Table 1. Table 1: Stellar Polarimetric Properties of G28.23 Field of View

$K$-Band Polarization								$H$-Band Polarization
Star	$l$	$b$	BandaaH: Entry only in $H$-pol, K: Entry only in $K$-pol, HK: Entries in both $H$ and $K$-pol.	PbbUncertainties of quantities are listed in parentheses.ccThe polarization measurements listed are have been corrected for bias, as described in the text.	GPA	QE	UE	P	GPA	QE	UE
Number	(∘)	(∘)	Match	(%)	(deg)	(%)	(%)	(%)	(deg)	(%)	(%)
4216	28.1559	-0.1609	HK	1.6 (0.9)	142 (15)	$-$1.7 (0.9)	0.7 (0.7)	2.3 (3.6)	139 (44)	$-$3.8 (3.5)	2.0 (3.9)
4217	28.1559	-0.0923	H	$\cdots$	$\cdots$	$\cdots$	$\cdots$	7.9 (8.6)	117 (31)	$-$3.7 (6.3)	11.0 (8.8)
4218	28.1560	-0.1861	K	57 (93)	122 (47)	$-$51 (99.9)	96 (63)	$\cdots$	$\cdots$	$\cdots$	$\cdots$
4221	28.1560	-0.2120	HK	10 (15)	100 (42)	5 (22)	18 (15)	6.7 (4.0)	100 (17)	2.0 (4.3)	7.6 (4.0)
4222	28.1560	-0.3196	H	$\cdots$	$\cdots$	$\cdots$	$\cdots$	1.4 (0.7)	88 (14)	1.0 (0.7)	1.2 (0.7)
4223	28.1561	-0.0741	H	$\cdots$	$\cdots$	$\cdots$	$\cdots$	8.6 (3.4)	94 (11)	4.3 (3.2)	8.2 (3.4)

Table 2. Table 2: Stellar Photometric Properties of G28.23 Field of View

Star	NIRaaStellar designations are those listed in the 2MASS/UKIDSS catalogs. Stars brighter than 13th mag in $H$-band were taken from 2MASS, and stars fainter than 13th mag were taken from UKIDSS.	J	H	K	4.5 $\mu$mbb4.5 $\mu$m photometry was retrieved from the GLIMPSE catalog.	H-K	H-4.5 $\mu$m	AV	AV	RelativeccRelative locations of stars with respect to the cloud along the line of sight. B: Background Star, F: Foreground Star, U: Unknown
Number	Desig.	(mag)	(mag)	(mag)	(mag)	(mag)	(mag)	(mag)	Method	Distance
4216	438563875392	16.150 (0.008)	13.390 (0.002)	11.996 (0.001)	11.00 (0.06)	1.394 (0.002)	2.39 (0.06)	18.7 (0.5)	H-4.5	B
4217	438563881028	15.411 (0.005)	14.777 (0.005)	14.424 (0.010)	$\cdots$	0.353 (0.011)	$\cdots$	3.6 (0.2)	H-K	F
4218	438563873228	16.875 (0.015)	14.794 (0.005)	13.537 (0.005)	12.53 (0.26)	1.256 (0.007)	2.26 (0.26)	17.6 (2.1)	H-4.5	B
4221	438563870876	15.200 (0.004)	13.656 (0.002)	12.931 (0.003)	12.23 (0.16)	0.725 (0.003)	1.42 (0.16)	10.9 (1.3)	H-4.5	B
4222	18435111-0423439	13.20 (0.04)	11.58 (0.04)	10.99 (0.03)	10.45 (0.06)	0.60 (0.05)	1.13 (0.07)	8.5 (0.6)	H-4.5	B
4223	438563882475	15.362 (0.004)	13.748 (0.002)	12.940 (0.003)	12.46 (0.11)	0.807 (0.003)	1.29 (0.11)	9.8 (0.9)	H-4.5	U

Table 3. Table 3: Properties of the Pixels in the B-field Map

$l$	$b$	PA Dispersion	Volume Density	${\sigma }_v$ (13CO)	BPOS	M∥/${\Phi }_{⟂}$	LimitsaaIndicates whether the PA dispersion (PA) or density (n) used to calculate BPOS limited the BPOS calculation. “PA” indicates the PA dispersion was greater than 25$°$, but PA dispersion minus its uncertainty was less than or equal to 25$°$. “n” indicates that the volume density was less than 50 H2 cm-3, but the density plus its uncertainty was greater than or equal to 50 H2 cm-3.
(∘)	(∘)	(deg)	(H2 cm-3)	(km s-1)	($\mu$G)	(Normalized)	Used
28.1315	-0.1638	$\cdots$	$\cdots$	2.1 (0.5)	$\cdots$	$\cdots$	$\cdots$
28.1463	-0.1562	$\cdots$	$\cdots$	2.2 (0.3)	$\cdots$	$\cdots$	$\cdots$
28.1612	-0.1486	25.9 (3.9)	$\cdots$	2.7 (0.2)	$\cdots$	$\cdots$	$\cdots$
28.1760	-0.1410	19.7 (2.9)	$\cdots$	3.0 (0.2)	$\cdots$	$\cdots$	$\cdots$
28.1908	-0.1334	11.8 (3.2)	$\cdots$	2.7 (0.5)	$\cdots$	$\cdots$	$\cdots$
28.2056	-0.1258	26.1 (3.1)	$\cdots$	2.4 (0.2)	$\cdots$	$\cdots$	$\cdots$
28.2204	-0.1181	26.1 (2.7)	20 (9)	2.9 (0.4)	$\cdots$	$\cdots$	$\cdots$
28.2353	-0.1105	18.9 (3.0)	59 (25)	2.0 (1.8)	17.5 (4.9)	1.10 (0.33)	$\cdots$
28.2501	-0.1029	13.6 (1.9)	57 (24)	2.4 (0.1)	29.6 (7.4)	0.78 (0.21)	$\cdots$
28.2649	-0.0953	16.0 (2.3)	15 (8)	2.3 (0.1)	$\cdots$	$\cdots$	$\cdots$
28.2797	-0.0877	24.8 (5.0)	55 (25)	2.4 (0.1)	15.6 (4.8)	2.88 (0.93)	$\cdots$
28.1391	-0.1787	$\cdots$	12 (5)	3.1 (0.2)	$\cdots$	$\cdots$	$\cdots$
28.1539	-0.1711	$\cdots$	27 (15)	2.5 (0.2)	$\cdots$	$\cdots$	$\cdots$
28.1688	-0.1634	20.1 (2.9)	31 (17)	1.7 (0.2)	$\cdots$	$\cdots$	$\cdots$
28.1836	-0.1558	14.1 (2.1)	40 (19)	1.4 (0.2)	13.5 (3.8)	1.51 (0.46)	n
28.1984	-0.1482	9.8 (2.3)	41 (21)	3.8 (5.4)	54.8 (20.6)	0.49 (0.19)	n
28.2132	-0.1406	25.8 (2.8)	8 (5)	8.4 (0.4)	$\cdots$	$\cdots$	$\cdots$
28.2281	-0.1330	26.3 (2.6)	28 (10)	13.3 (1.3)	$\cdots$	$\cdots$	$\cdots$
28.2429	-0.1254	16.5 (3.0)	92 (31)	1.9 (2.0)	24.9 (6.8)	0.62 (0.18)	$\cdots$
28.2577	-0.1177	16.2 (2.3)	100 (33)	1.6 (0.1)	22.0 (4.8)	0.57 (0.14)	$\cdots$
28.2725	-0.1101	14.6 (2.1)	90 (35)	2.7 (0.1)	39.5 (9.5)	0.78 (0.20)	$\cdots$
28.2874	-0.1025	19.6 (3.4)	111 (37)	2.5 (0.1)	30.1 (7.2)	2.51 (0.65)	$\cdots$
28.1467	-0.1935	$\cdots$	117 (42)	3.6 (0.3)	$\cdots$	$\cdots$	$\cdots$
28.1616	-0.1859	20.7 (3.3)	132 (44)	3.4 (0.2)	42.0 (9.7)	1.26 (0.32)	$\cdots$
28.1764	-0.1783	18.9 (2.7)	122 (40)	3.3 (0.3)	42.6 (9.3)	1.36 (0.33)	$\cdots$
28.1912	-0.1706	27.3 (2.9)	117 (39)	5.9 (0.5)	51.5 (10.3)	0.50 (0.11)	PA
28.2060	-0.1630	26.5 (2.8)	100 (34)	5.3 (0.7)	43.7 (8.8)	0.28 (0.06)	PA
28.2209	-0.1554	16.6 (2.3)	68 (28)	3.4 (0.5)	36.9 (9.1)	1.56 (0.41)	$\cdots$
28.2357	-0.1478	30.6 (1.8)	39 (17)	2.9 (4.2)	$\cdots$	$\cdots$	$\cdots$
28.2505	-0.1402	29.0 (2.1)	142 (43)	1.3 (0.1)	$\cdots$	$\cdots$	$\cdots$
28.2653	-0.1326	20.0 (2.8)	190 (54)	2.2 (0.1)	33.7 (6.8)	1.25 (0.28)	$\cdots$
28.2802	-0.1249	18.1 (2.2)	217 (63)	2.3 (0.1)	40.9 (7.8)	1.84 (0.39)	$\cdots$
28.2950	-0.1173	18.3 (2.0)	249 (71)	2.1 (0.1)	39.4 (10.7)	3.69 (1.06)	$\cdots$
28.1544	-0.2083	$\cdots$	404 (87)	2.9 (0.6)	$\cdots$	$\cdots$	$\cdots$
28.1692	-0.2007	14.7 (2.6)	461 (96)	3.2 (0.2)	102.1 (21.1)	1.18 (0.27)	$\cdots$
28.1840	-0.1931	15.0 (2.0)	521 (108)	3.5 (0.3)	116.6 (20.0)	1.71 (0.34)	$\cdots$
28.1988	-0.1855	29.0 (3.1)	469 (106)	6.4 (0.5)	$\cdots$	$\cdots$	$\cdots$
28.2137	-0.1779	31.5 (3.6)	283 (82)	5.7 (0.6)	$\cdots$	$\cdots$	$\cdots$
28.2285	-0.1702	17.7 (2.2)	147 (45)	4.5 (0.5)	68.1 (13.6)	1.76 (0.39)	$\cdots$
28.2433	-0.1626	32.2 (1.9)	121 (38)	4.1 (0.5)	$\cdots$	$\cdots$	$\cdots$
28.2581	-0.1550	37.2 (2.4)	261 (72)	1.9 (0.1)	$\cdots$	$\cdots$	$\cdots$
28.2730	-0.1474	16.4 (4.1)	516 (134)	2.5 (0.1)	76.0 (15.6)	4.91 (1.12)	$\cdots$
28.2878	-0.1398	8.6 (2.6)	888 (182)	2.1 (0.1)	163.1 (24.4)	3.17 (0.57)	$\cdots$
28.3026	-0.1322	$\cdots$	672 (135)	1.9 (0.1)	$\cdots$	$\cdots$	$\cdots$
28.1620	-0.2231	$\cdots$	191 (57)	2.3 (1.7)	$\cdots$	$\cdots$	$\cdots$
28.1768	-0.2155	14.4 (3.0)	155 (50)	2.3 (0.2)	44.1 (11.8)	1.79 (0.51)	$\cdots$
28.1916	-0.2079	15.8 (2.0)	287 (79)	3.3 (0.2)	77.7 (14.6)	1.63 (0.35)	$\cdots$
28.2064	-0.2003	14.7 (2.7)	473 (108)	3.1 (0.2)	99.9 (21.5)	2.36 (0.56)	$\cdots$
28.2213	-0.1927	$\cdots$	610 (125)	2.4 (0.5)	$\cdots$	$\cdots$	$\cdots$
28.2361	-0.1851	29.5 (3.0)	535 (110)	2.6 (0.8)	$\cdots$	$\cdots$	$\cdots$
28.2509	-0.1774	24.9 (2.7)	508 (113)	3.5 (1.2)	68.8 (11.0)	2.97 (0.56)	$\cdots$
28.2657	-0.1698	$\cdots$	835 (174)	3.0 (0.0)	$\cdots$	$\cdots$	$\cdots$
28.2806	-0.1622	$\cdots$	1192 (238)	2.6 (0.1)	$\cdots$	$\cdots$	$\cdots$
28.2954	-0.1546	12.2 (3.0)	649 (158)	2.7 (0.1)	123.8 (25.8)	3.54 (0.82)	$\cdots$
28.3102	-0.1470	16.5 (2.9)	271 (78)	2.3 (0.1)	49.8 (11.4)	2.48 (0.62)	$\cdots$
28.1696	-0.2380	$\cdots$	43 (19)	2.0 (0.2)	$\cdots$	$\cdots$	n
28.1844	-0.2304	21.2 (3.3)	46 (23)	4.2 (0.3)	29.6 (8.6)	0.90 (0.28)	n
28.1992	-0.2227	19.0 (2.5)	96 (34)	3.2 (0.2)	36.0 (8.0)	1.35 (0.33)	$\cdots$
28.2141	-0.2151	12.9 (1.7)	127 (40)	3.1 (0.2)	60.3 (12.4)	1.55 (0.35)	$\cdots$
28.2289	-0.2075	27.1 (3.3)	161 (50)	1.6 (0.2)	16.6 (3.3)	6.40 (1.42)	PA
28.2437	-0.1999	26.3 (3.3)	271 (75)	1.2 (1.9)	16.6 (4.0)	7.51 (1.97)	PA
28.2585	-0.1923	11.8 (2.0)	485 (112)	2.9 (8.5)	120.2 (42.6)	1.39 (0.51)	$\cdots$
28.2734	-0.1847	12.5 (2.8)	601 (141)	2.9 (0.1)	125.8 (31.9)	2.81 (0.77)	$\cdots$
28.2882	-0.1770	26.3 (2.2)	399 (107)	3.0 (0.1)	49.8 (7.9)	6.32 (1.18)	PA
28.3030	-0.1694	26.4 (2.3)	242 (67)	3.7 (0.1)	48.5 (7.9)	2.68 (0.51)	PA
28.3178	-0.1618	15.4 (3.5)	113 (36)	3.0 (0.2)	45.0 (12.6)	0.95 (0.28)	$\cdots$
28.1772	-0.2528	$\cdots$	$\cdots$	3.0 (0.3)	$\cdots$	$\cdots$	$\cdots$
28.1920	-0.2452	23.6 (3.4)	4 (2)	4.6 (0.5)	$\cdots$	$\cdots$	$\cdots$
28.2069	-0.2376	19.8 (2.2)	36 (19)	4.5 (0.5)	30.2 (9.0)	0.09 (0.03)	n
28.2217	-0.2299	12.3 (1.3)	52 (23)	5.7 (0.8)	73.3 (18.0)	0.45 (0.12)	$\cdots$
28.2365	-0.2223	10.1 (1.5)	61 (27)	3.0 (0.3)	50.7 (13.7)	1.23 (0.36)	$\cdots$
28.2513	-0.2147	12.5 (2.5)	90 (33)	2.2 (0.2)	36.3 (9.9)	2.17 (0.63)	$\cdots$
28.2662	-0.2071	13.7 (2.2)	122 (41)	2.9 (1.0)	51.2 (12.0)	2.09 (0.53)	$\cdots$
28.2810	-0.1995	23.4 (2.8)	171 (53)	3.5 (0.2)	43.5 (8.5)	2.73 (0.60)	$\cdots$
28.2958	-0.1919	33.6 (9.5)	155 (46)	3.1 (0.1)	25.2 (8.0)	4.11 (1.37)	PA
28.3106	-0.1842	28.1 (8.9)	135 (40)	3.5 (0.2)	32.1 (11.2)	3.06 (1.11)	PA
28.3255	-0.1766	25.6 (3.2)	80 (30)	6.2 (0.5)	47.7 (10.8)	0.50 (0.12)	PA
28.1848	-0.2676	$\cdots$	$\cdots$	6.2 (0.7)	$\cdots$	$\cdots$	$\cdots$
28.1996	-0.2600	16.7 (4.2)	$\cdots$	8.3 (0.8)	$\cdots$	$\cdots$	$\cdots$
28.2145	-0.2524	17.5 (2.3)	$\cdots$	5.3 (0.5)	$\cdots$	$\cdots$	$\cdots$
28.2293	-0.2448	13.5 (1.8)	$\cdots$	5.4 (0.5)	$\cdots$	$\cdots$	$\cdots$
28.2441	-0.2372	10.6 (2.4)	1 (0)	4.2 (0.5)	$\cdots$	$\cdots$	$\cdots$
28.2589	-0.2295	15.3 (2.7)	22 (11)	3.4 (0.6)	$\cdots$	$\cdots$	$\cdots$
28.2738	-0.2219	18.2 (2.7)	54 (24)	3.0 (0.2)	26.6 (7.1)	1.45 (0.41)	$\cdots$
28.2886	-0.2143	34.5 (4.4)	90 (31)	3.3 (0.1)	$\cdots$	$\cdots$	$\cdots$
28.3034	-0.2067	34.9 (17.9)	87 (30)	2.7 (0.1)	15.6 (8.5)	1.19 (0.65)	PA
28.3182	-0.1991	22.1 (15.5)	84 (29)	5.2 (0.3)	47.8 (34.5)	0.61 (0.45)	$\cdots$
28.3331	-0.1915	24.4 (4.9)	67 (25)	11.7 (0.7)	86.8 (23.9)	0.31 (0.09)	$\cdots$
28.1924	-0.2824	$\cdots$	$\cdots$	9.0 (0.6)	$\cdots$	$\cdots$	$\cdots$
28.2073	-0.2748	27.0 (3.8)	$\cdots$	11.2 (1.1)	$\cdots$	$\cdots$	$\cdots$
28.2221	-0.2672	25.7 (2.6)	$\cdots$	6.6 (0.4)	$\cdots$	$\cdots$	$\cdots$
28.2369	-0.2596	25.3 (2.6)	$\cdots$	6.1 (0.5)	$\cdots$	$\cdots$	$\cdots$
28.2517	-0.2520	11.1 (2.6)	$\cdots$	3.2 (0.2)	$\cdots$	$\cdots$	$\cdots$
28.2666	-0.2444	21.5 (2.6)	$\cdots$	2.8 (0.2)	$\cdots$	$\cdots$	$\cdots$
28.2814	-0.2367	26.2 (3.0)	4 (2)	2.2 (0.1)	$\cdots$	$\cdots$	$\cdots$
28.2962	-0.2291	$\cdots$	49 (24)	2.2 (0.1)	$\cdots$	$\cdots$	n
28.3110	-0.2215	$\cdots$	55 (29)	1.8 (0.1)	$\cdots$	$\cdots$	$\cdots$
28.3259	-0.2139	$\cdots$	41 (20)	8.0 (1.5)	$\cdots$	$\cdots$	n
28.3407	-0.2063	$\cdots$	47 (23)	7.9 (12.4)	$\cdots$	$\cdots$	n
28.2000	-0.2973	$\cdots$	$\cdots$	3.9 (0.3)	$\cdots$	$\cdots$	$\cdots$
28.2149	-0.2896	33.2 (3.2)	$\cdots$	5.3 (0.7)	$\cdots$	$\cdots$	$\cdots$
28.2297	-0.2820	32.5 (2.7)	0 (0)	4.9 (0.4)	$\cdots$	$\cdots$	$\cdots$
28.2445	-0.2744	31.8 (4.2)	0 (0)	10.4 (0.8)	$\cdots$	$\cdots$	$\cdots$
28.2593	-0.2668	$\cdots$	0 (0)	6.8 (0.6)	$\cdots$	$\cdots$	$\cdots$
28.2742	-0.2592	22.8 (3.8)	$\cdots$	2.3 (0.1)	$\cdots$	$\cdots$	$\cdots$
28.2890	-0.2516	20.6 (3.6)	$\cdots$	2.0 (0.1)	$\cdots$	$\cdots$	$\cdots$
28.3038	-0.2440	$\cdots$	$\cdots$	1.6 (0.1)	$\cdots$	$\cdots$	$\cdots$
28.3187	-0.2363	$\cdots$	$\cdots$	1.7 (0.1)	$\cdots$	$\cdots$	$\cdots$
28.3335	-0.2287	$\cdots$	$\cdots$	7.9 (18.3)	$\cdots$	$\cdots$	$\cdots$
28.3483	-0.2211	$\cdots$	$\cdots$	6.5 (14.3)	$\cdots$	$\cdots$	$\cdots$
28.2077	-0.3121	$\cdots$	$\cdots$	8.7 (0.8)	$\cdots$	$\cdots$	$\cdots$
28.2225	-0.3045	$\cdots$	$\cdots$	5.3 (0.5)	$\cdots$	$\cdots$	$\cdots$
28.2373	-0.2968	$\cdots$	$\cdots$	6.9 (0.8)	$\cdots$	$\cdots$	$\cdots$
28.2521	-0.2892	$\cdots$	$\cdots$	14.9 (1.8)	$\cdots$	$\cdots$	$\cdots$
28.2670	-0.2816	$\cdots$	$\cdots$	11.4 (1.1)	$\cdots$	$\cdots$	$\cdots$
28.2818	-0.2740	$\cdots$	$\cdots$	4.3 (0.3)	$\cdots$	$\cdots$	$\cdots$
28.2966	-0.2664	$\cdots$	$\cdots$	2.6 (0.2)	$\cdots$	$\cdots$	$\cdots$
28.3114	-0.2588	$\cdots$	$\cdots$	2.4 (0.2)	$\cdots$	$\cdots$	$\cdots$
28.3263	-0.2512	$\cdots$	$\cdots$	2.9 (0.2)	$\cdots$	$\cdots$	$\cdots$
28.3411	-0.2435	$\cdots$	$\cdots$	4.2 (0.3)	$\cdots$	$\cdots$	$\cdots$
28.3559	-0.2359	$\cdots$	$\cdots$	1.8 (2.1)	$\cdots$	$\cdots$	$\cdots$

Table 4. Table 4: PA Distribution Properties in the four Quadrants

Distribution	Near Median	Far Median	KS Prob.aaProbability that the near and far distributions are drawn from the same parent population.
Quadrant	(deg)	(deg)
$\Delta$PA NE	69	70	0.83
$\Delta$PA NW	37	53	0.02
$\Delta$PA SE	37	71	2$\times$10-6
$\Delta$PA SW	27	26	0.95
GPA NE	104	110	0.43
GPA NW	115	131	0.03
GPA SE	107	104	0.39
GPA SW	98	114	0.01

Equations

$$P_{uncorrected}=\sqrt{U_E^2+Q_E^2},$$

$$P_{corrected}=\sqrt{P_{uncorrected}^2-{\sigma }_P^2}.$$

$$\rho (\mathbf{r},k)=\frac{{\rho }_c}{[1+(\mathbf{r}/R_{flat}{)}^2{]}^{\frac{p}{2}}},$$

$$\Sigma (r)=C_p\frac{{\rho }_{ck}{R}_{flat}}{[1+(r/R_{flat}{)}^2{]}^{\frac{p-1}{2}}},$$

$$C_p={\int }_{-\infty }^{\infty }\frac{(1/R_{flat})dr}{[1+(r/R_{flat}{)}^2{]}^{\frac{p}{2}}},$$

$$B_{POS}=f\sqrt{4\pi \rho }\frac{{\sigma }_v}{{\sigma }_{\varphi }},$$

$$M/{\Phi }_{BN}=7.6\times 10^{-21}{N}_{H_2}/B,$$

$$\overline{M/\Phi }={\int }_0^{\pi /2}\frac{M_{\parallel }\cos \theta }{{\Phi }_{\perp }/\sin \theta }\sin \theta d\theta =f(M_{\parallel }/{\Phi }_{\perp }),$$

Full text

ISM:clouds—ISM:magnetic fields—ISM:dust, extinction—stars:formation—Individual Object:G28.23—techniques:polarimetric

1 Introduction

Infrared Dark Clouds (IRDCs) are dense (H2 column densities $\sim$1022–1023 cm*-2*) filamentary structures that host high-mass star formation (Rathborne et al., 2006). As such, these clouds play important roles in the evolution of the Galaxy. However, much is still not known about IRDC formation and evolution. One open problem is the unknown role of magnetic (B) fields in the formation of IRDCs and any potential star formation they host.

While many studies have probed the B-fields of molecular clouds using techniques such as the Zeeman effect, background starlight polarimetry, and dust emission polarimetry (e.g., Troland & Crutcher, 2008; Chapman et al., 2011; Dotson et al., 2010), studies of the B-fields of IRDCs have mainly focused on the small size scales of cores and clumps (e.g., Cortes et al., 2008; Tang et al., 2009; Girart et al., 2009; Sridharan et al., 2014; Zhang et al., 2014). Several studies have probed the interstellar medium (ISM) between clouds (Heiles, 2000; Li et al., 2009), but few have probed the cloud scales (10s of pc) to study the interaction between the B-field and an IRDC as a whole (e.g., Sugitani et al., 2011; Pillai et al., 2015).

To test whether B-fields play a dominant role in IRDC and massive star formation (e.g., Nakamura & Li, 2008), or are themselves influenced by more dominant forces (e.g., Padoan & Nordlund, 1999), such as turbulence or gravity, B-field properties must be observationally related to other physical cloud properties.

Many models and simulations have studied the formation of filamentary molecular clouds and the forces that control their formation (e.g., Nakajima & Hanawa, 1996; Ostriker et al., 2001; Padoan & Nordlund, 2002; Hennebelle, 2013; Van Loo et al., 2014; Li et al., 2015a). Several of these studies (e.g., Ostriker et al., 2001; Van Loo et al., 2014; Li et al., 2015a) considered the role of B-fields in cloud formation to predict the observational signatures of weak and strong B-fields. One of the most straightforward signatures is the relative orientation of the B-field with respect to the filament orientations. For example, the preferential direction of B-fields relative to cloud orientation can reveal whether material flowed along field lines to create clouds. If the field is more likely found to be either perpendicular or parallel to the cloud orientation, then the B-field very likely played a role in the cloud’s formation (Li et al., 2009).

Other tests rely on the relative strength of the B-field. The relative strength of the gravitational potential compared to the local B-field (‘Mass-to-Flux’ ratio, M/$\Phi_{B}$, Crutcher, 2012) of a clump reveals the importance of the B-field compared to gravity. Additionally, if the power-law dependence of the B-field strength on cloud gas volume density is shallower than 2/3, the field likely influenced the flow of material during cloud formation (Li et al., 2015a).

Near-Infrared (NIR) background starlight polarimetry provides a way to probe the B-field on scales of $\sim$1 to tens of pc at the distances to most IRDCs. The polarization signal is caused by aspherical dust grains spinning with their long axes aligned mostly perpendicular to the intervening B-field (Lazarian & Hoang, 2007). The linear polarization signal imparted on background starlight by the asymmetric dichroic extinction of the dust grains follows the orientation of the B-field in the plane of the sky. Therefore, the orientations of the NIR polarizations trace the plane-of-sky B-field. NIR polarimetry can reveal the plane-of-sky B-field morphology over large fields of view and wide ranges of column and volume densities (e.g., Clemens et al., 2012b). In addition, the plane-of-sky B-field strength can often be inferred by using the Chandrasekhar-Fermi Method (Chandrasekhar & Fermi, 1953, hereafter CF Method), which combines the polarization measurements with complementary cloud density and gas velocity information.

1.1 IRDC G28.23

In this study, we evaluated the plane-of-sky B-field toward IRDC G028.23-00.19 (hereafter referred to as G28.23) ($l$ = 28$\fdg$23, $b$ = $-$0$\fdg$19; Rathborne et al., 2006), using NIR polarimetric observations, to determine the role in the formation of the IRDC. Figure 1 shows a 3-color GLIMPSE and MIPSGAL (Benjamin et al., 2003; Carey et al., 2009) image of G28.23. The IRDC can be seen as the dark extinction feature against the bright background emission111The bright IR point source at the top left of the cloud is an unassociated OH/IR foreground star, at a LSR radial velocity of $\sim$52 km s*-1* (Bowers & Knapp, 1989), which is different from the 80 km s*-1* velocity of G28.23 (Sanhueza et al., 2013).. Located at a distance of 5.1 kpc, G28.23 is a dense, quiescent IRDC that hosts one of the most massive quiescent cores found in an IRDC, and is a likely candidate to host future high-mass star formation. Because of its quiescent nature, G28.23 is an ideal laboratory in which to study the interaction between an IRDC and the surrounding B-field. With no signs of active star formation, G28.23 provides an opportunity to study the interaction between an IRDC and the surrounding B-field before any potential disruption by active star formation.

1.2 Methodology

We pursued answers to four questions regarding the plane-of-sky B-field, as revealed by deep NIR observations, to ascertain the field’s importance in the formation of G28.23.

1. Do polarization percentages, as probed by NIR background starlight polarimetry, increase as a function of extinction? If the polarization percentages do not increase with extinction, then it is possible that the NIR polarization measurements only probe the skin of the cloud (Arce et al., 1998) and do not reveal the B-field properties deeper into the cloud. Depolarization along the line of sight, where different layers of material exhibit different polarization orientations that cancel when summed, can also cause this effect. If the polarization increases with extinction, then this is evidence that the material in G28.23 positively increases the measured polarization percentage. Therefore, the B-field can be probed by NIR polarization of background stars.

2. Is the plane-of-sky B-field preferentially aligned with the orientation of G28.23? Because the angle of the cloud major axis orientation with respect to plane of the sky is not known, we will use the cloud elongation as a proxy for the cloud’s major axis. If the B-field is perpendicular or parallel to the cloud , then the field likely played a role in the cloud formation. Otherwise, if the field is randomly oriented with respect to the cloud, the field likely did not strongly influence cloud formation.

3. What is the power-law dependence between B-field strength and cloud volume density? A weak B-field frozen into isotropically collapsing material would follow a power law of 2/3 (Crutcher et al., 2010), .

4. How does M/$\Phi_{B}$ vary across the cloud? While NIR polarimetry will not probe the densest cloud interiors, it will probe the B-field in the outer cloud regions. The M/$\Phi_{B}$ estimates will reveal the relative changes of the B-field strength with respect to gravity in the outer layers of G28.23 .

Using a combination of new and archival NIR polarimetry, archival submm and far-IR (FIR) dust emission, and published molecular line data, we studied the magnetic and physical properties of G28.23. The paper is organized as follows. Section 2 describes the observations and archival data products used. Section 3 outlines the data analysis and results. Section 4 discusses the implications of the results on the importance of the B-field, and Section 5 summarizes the study.

2 Observations

2.1 NIR Polarimetry

NIR polarimetric observations in both $H$-band (1.6 $\mu$m) and $K$-band (2.2 $\mu$m) of G28.23-00.19 were obtained using the Mimir instrument (Clemens et al., 2007) on the 1.8m Perkins Telescope in Flagstaff, AZ. The instrument field of view (FOV) was 10x10 arcmin with a plate scale of 0.58 arcsec per pixel. Mimir used a compound half-wave plate (HWP) in conjunction with a fixed, cold wire-grid. The $H$-band data were taken from Data Release 2 of the Galactic Plane Infrared Polarization Survey (GPIPS, Clemens et al., 2012b)222http://gpips0.bu.edu/Data_Release/. GPIPS spanned 76 sq. degrees of the inner Galaxy, from 18–56*∘* in Galactic longitude and $\pm$1*∘* in latitude, which fully covered the location and extent of G28.23. The survey region consists of 3,237 individual pointings, each covering a 10x10 arcmin area. Each GPIPS observation consisted of 96 images (one each at 16 unique HWP positions at six dither positions on the sky) with an exposure time of 2.5 seconds. The total integration time of each observation was $\sim$4 minutes. Sky conditions were clear, and each GPIPS field was required to meet a 2 arcsec seeing criterion.

The $H$-band data for a 20$\times$20 arcmin region (the region shown in Figure 1) covering the IRDC, as well as its environment, were extracted from the GPIPS database. This region is aligned in Galactic coordinates, with center ($l$, $b$) = (28.244, $-$0.200).

Targeted $K$-band observations, covering about 10.4$\times$10.8 arcmin, centered on coordinates $l$ = 28$\fdg$247 and $b$ = $-$0$\fdg$19, and aligned in R.A. and decl., were obtained over five nights in 2013 September and 2014 June. These consisted of 14 separate observations, each with 96 individual 15 second exposures. The total integration time was 5.6 hours. These deep $K$-band observations probed the more extincted regions, while the $H$-band data covered a larger FOV. The $K$-band sky coverage is outlined as the black box in Figure 1. Hereafter, references to the 10$\times$10 arcmin FOV centered on the cloud refer to this 10.4$\times$10.8 arcmin region.

The calibration of the NIR polarimetric data is described in Clemens et al. (2012a). The data were reduced using the custom IDL packages Mimir Software Package Basic Data Processing (MSP-BDP) and Photo POLarimetry (MSP-PPOL) (Clemens et al., 2012a). The main reduction and processing steps included taking dome flat fields at each HWP position to correct for variation across the Mimir FOV, accounting for instrumental polarization by observing globular cluster stars, and converting the instrumental polarization position angles to Equatorial coordinates via observations of polarimetric standard stars from Whittet et al. (1992). The resulting combined polarimetric catalog contains the properties of individual stars down to magnitudes of $\sim$13 for $H$-band and $\sim$14-14.5 for $K$-band, as measured by Mimir. The polarization position angles, PAs, are measured as the angle East of North in Equatorial coordinates, and can be transformed to Galactic coordinates (Galactic PAs or GPAs) by adding 62.8*∘*.

2.2 Additional Datasets

In addition to NIR polarimetry, we used NIR and mid-IR (MIR) photometry from the 2MASS (Skrutskie et al., 2006), UKIDSS (UKIRT Infrared Deep Sky Survey; Lawrence et al., 2007), and GLIMPSE (Benjamin et al., 2003) catalogs, dust continuum data from the Herschel infrared Galactic Plane Survey (Hi-GAL) (Molinari et al., 2010) and the APEX Telescope Large Area Survey of the Galaxy (ATLASGAL) (Schuller et al., 2009), and molecular line data from the 13CO Galactic Ring Survey (GRS; Jackson et al., 2006). The NIR and MIR photometry were used to estimate the extinctions to the polarization stars. The dust continuum data were used to create an H2 column density map of the cloud. The 13CO data, which have an angular resolution of 46 arcsec, were used to find the gas velocities and line widths in the less dense regions of the cloud.

3 Analysis and Results

Because the B-field of G28.23 can only be probed by stars lying beyond it, we first found the polarimetric stars that were background to the cloud. The relative locations of the stars with respect to the cloud (background, foreground), were determined by comparing the stellar extinctions to the dust emission-traced cloud extinction. We also accounted for foreground extinction and polarizing layers. The column density map of the cloud was found by using the Herschel Hi-GAL and ATLASGAL dust emission data. The polarization PA orientations were found and compared to the cloud orientation. The cloud volume density was derived from the column density, and used in estimating the plane-of-sky B-field strength. These steps are described in more detail below.

3.1 Catalog of NIR Polarimetric and Photometric Stars

A list of NIR stars was created using the 2MASS and UKIDSS photometric data within the $20\times 20$ arcmin region of Figure 1. Stars with $H$-band magnitudes brighter than 13th mag were selected from 2MASS, and stars fainter than 13th mag were selected from UKIDSS. Only stars with $H$-band uncertainties less than 0.3 mag were retained. These stars were then matched to the $H$ and $K$-band polarization catalogs. The number of 2MASS+UKIDSS stars within the 20$\times$20 arcmin FOV with polarizations in either $H$, $K$, or both was 17,160. Of these, 3,280 stars had both $H$ and $K$-band polarization entries ($H$-pol, $K$-pol), while 12,554 stars were found only in $H$-pol and 1,326 were found only in $K$-pol. The number of $H$-pol entries is much higher because the $H$-pol data span a larger area . This catalog of stars was then matched to the GLIMPSE catalog. Of the 17,160 stars, 12,490 were positionally-matched to GLIMPSE 4.5 $\mu$m point sources.

Table 1 lists the polarimetric properties of the stars - the polarimetric bands in which the stars were observed, polarization percent, Galactic polarization PAs (GPAs), and Equatorial Stokes Q and U parameters (QE, UE), along with uncertainties. The reported GPAs are measured from the North Galactic Pole with GPAs increasing along the East of North direction, where 90$\arcdeg$ is parallel to the Galactic plane and 0 and 180$\arcdeg$ are perpendicular to the plane. These GPAs were derived by rotating the Equatorial PAs computed from Stokes UE and QE parameters. Table 2 lists the photometric properties of these stars in the same order, including the 2MASS or UKIDSS designation, stellar colors and magnitudes, and the relative extinctions and distances (discussed below).

The polarization percentages reported and used in the analysis have been Ricean corrected (Wardle & Kronberg, 1974) to account for positive bias:

[TABLE]

All polarization measurements reported in Table 1 and in the results are Pcorrected. Stars with Pcorrected signal-to-noise ratios (SNR) greater than 2.5 and uncertainties less than 5% were classified as “high SNR” stars.

\floattable

\floattable

Because many of the stars in the catalog had both $H$ and $K$-pol entries, it was possible to compare the difference in PAs between the two wavelengths ($\delta$PAK-H) for each star. Of the stars with both $H$ and $K$-pol matches, 137 showed high SNR in both bands. Figure 2 shows the distribution of $\delta$PAK-H of these high SNR stars. The variance-weighted mean $\delta$PAK-H is $-$2.1$\pm$0.6$\arcdeg$ , with a weighted standard deviation of 16$\arcdeg$. The standard deviation is close to the uncertainty in PA of a star with polarization signal-to-noise of 2.5 (11.5$\arcdeg$). Therefore, the measured $H$ and $K$-pol PAs are judged to be identical to within their uncertainties.

3.2 Selecting Background Stars

To probe the B-field of G28.23, it was necessary to select stars that are background to the cloud. Foreground stars probe material between the cloud and the observer, and therefore, do not probe the cloud B-field. Finding distances to field stars, however, is difficult using only photometric information. Therefore, for the purpose of finding stars background to G28.23, we compared the photometrically determined stellar extinctions to the thermal dust emission-derived cloud column density (converted to an extinction map) along the same lines of sight. Stars exhibiting larger extinctions than the cloud extinction were selected as background stars.

3.2.1 Stellar Extinctions

Each polarimetric star in Table 1 contains a photometric entry in Table 2. Not all entries contain a match to the GLIMPSE catalog, as stated in Section 3.1. The extinctions of the stars that were matched to GLIMPSE were estimated via the Rayleigh-Jeans Color Excess (RJCE, Majewski et al., 2011) method if their 4.5 $\mu$m magnitude uncertainties were less than 0.3 mag. The RJCE method uses the NIR $H$-band and MIR 4.5 $\mu$m magnitudes of stars to determine their color excesses, E($H-4.5$ $\mu$m), following the extinction law of Indebetouw et al. (2005). We adopted an intrinsic ($H-4.5$ $\mu$m)∘ equal to 0.08 mag (Majewski et al., 2011) for all stars. For stars that could not be matched to the GLIMPSE catalog, or were matched but their 4.5 $\mu$m magnitude uncertainties were greater than 0.3 mag, we used the Near-Infrared Color Excess (NICE, Lada et al., 1994) method, which uses the E$(H-K)$ color excesses of stars to estimate their extinctions. We adopted an intrinsic $(H-K)_{\circ}$ of 0.13 mag for these stars.

3.3 Cloud Extinctions

We used public Herschel data from the Hi-Gal project (Molinari et al., 2010) and data from ATLASGAL (Schuller et al., 2009) to estimate the cloud column density. Herschel data for G28.23 are identified with the obs-ID numbers 1342218694/5 and were observed during April 2011 using the parallel mode, which observed in five wavebands simultaneously (70, 160, 250, 350, and 500 $\mu$m). The ATLASGAL data provide additional sub-mm measurements at 870 $\mu$m.

The data were reduced and processed following the procedure described in detail in Guzmán et al. (2015). All maps were convolved to the resolution of the 500 $\mu$m maps ($37$ arcsec) and projected to a common pixel grid. To study filamentary IRDCs, it is important to subtract the diffuse far-IR emission of the Galactic plane that is not associated with the filament. The subtraction procedure is described in Guzmán et al. (2015) and is similar to that used in other IRDC studies performed using Herschel data (e.g., Battersby et al., 2011). At 500 $\mu$m, the diffuse component subtracted around G28.23 amounts to 250–300 MJy sr*-1*, which is comparable to the emission expected from the IRDC itself.

Dust column density and temperature maps were obtained by fitting a single temperature gray-body model to each pixel. These densities and temperatures were converted to gas column densities using theoretical dust opacity curves (Ormel et al., 2011). The dust model used contained no ice coatings and had 3$\times$104 years of coagulation for silicate-graphite grains, . The uncertainties of the dust temperatures and column densities are given in Guzmán et al. (2015), and are on the order of 10%. Following Heiderman et al. (2010), the gas column densities were converted to extinctions via the relation AV [mag] = N${}_{H_{2}}$ [cm2]/1.37$\times$1021 [cm2/mag], where AV = 1.086 CEXT (Draine, 2003), RV is equal to 5.5, and CEXT at $V$-band is equal to 6.715$\times$10*-22* cm2 H*-1* (Weingartner & Draine, 2001)333http://www.astro.princeton.edu/ draine/dust/dustmix.html..

Figure 3 shows the GLIMPSE and MIPSGAL 3-color image of G28.23, with column density-based AV contours overlaid. An AV of 10 mag corresponds to an H2 column density of 1.37$\times$1022 cm*-2*. The dark extinction feature within the 50 mag AV contour in Figure 3 corresponds to the densest region of the IRDC. The long axis of the cloud, including both the densest regions of the cloud between longitudes 28$\fdg$25 and 28$\fdg$32 and the less dense filament at longitudes less than 28$\fdg$25, extends approximately 12 arcmin. Due to the proximity of G28.23 to the Galactic mid-plane, it is located in a region of non-negligible, and variable, extinction. At latitudes below that of the cloud, farther from the mid-plane, the extinction decreases, whereas at latitudes closer to the midplane, the extinction increases.

3.3.1 Accounting for Foreground Extinction and Polarization

Because the dust emission-based cloud extinction estimates accounted for foreground and background extinction through removal of diffuse emission, a similar type of correction needed to be done for the stellar extinctions prior to the assignment of stellar locations. To estimate the foreground extinction, we examined the extinctions of the polarization catalog stars that were spatially coincident with the regions of the cloud that had column densities larger than AV = 30 mag (N{}_{H_{2}}$$\sim4.11$\times$1022 cm*-2*). These stars are most likely to be foreground stars because, even with deep exposures, it would be very difficult to detect stars in the NIR through such large extinctions.

Figure 4 plots the distribution of stellar extinctions of stars in the Table 1 polarimetry catalog and are located within the region outlined by AV = 30 mag in Figure 3. These stars show predominantly low extinctions, with a small tail in the distribution extending to larger extinctions. The distribution of extinctions was fit using a Gaussian plus a constant background. The peak of the fit occurs at 2.06 mag with a Gaussian width ($\sigma$) of 1.01 mag. Based on the fit, we estimated that the foreground extinction is strongly bounded to be no more than 4.5 mag ( peak plus $\sim$2.5$\sigma$).

All stellar extinctions were estimated following the steps described in Section 3.2.1. Based on their relative extinctions compared to the cloud extinctions at their locations, the stars were classified into three categories: ‘foreground,’ ‘background,’ and ‘unknown.’ Any star with extinction less than 4.5 mag was classified as ‘foreground.’ The extinctions of the remaining stars were reduced by 4.5 mag and compared to the cloud extinction at the stellar coordinates. Stars with foreground-modified extinctions larger than the cloud extinction plus cloud extinction uncertainty (10%) were classified as ‘background.’ Stars with modified extinctions less than the cloud extinction minus cloud extinction uncertainty were classified as ‘foreground.’ Stars with extinctions that fell within the cloud extinction $\pm$ the cloud extinction uncertainty received distance classifications of ‘unknown.’ These stars were not included in further analysis because their relative locations with respect to the cloud could not be well-determined.

The estimated stellar extinction (not reduced by 4.5 mag) of each star, along with the extinction estimation method used, and its distance assignment are listed in columns 9, 10, and 11, respectively, in Table 2.

Because foreground material is present along the line-of-sight to G28.23, the polarization measurements of the background stars needed to be corrected for any foreground polarization signal. To remove this effect, we assumed the foreground polarization was contained in a uniform layer.

We computed the variance-weighted average Stokes UE and QE parameters of all foreground stars. This foreground polarization signal was $\sim$0.5 %. The average foreground UE and QE values ($\overline{U}$E = 0.40 %, $\overline{Q}$E = -0.28 %) were subtracted from the UE and QE parameters of the individual background stars . The foreground, weighted U, Q uncertainties (of order $\sim$0.02 %) were propagated into the foreground-subtracted UE and QE uncertainties of the background stars. We note that the polarization properties of the stars listed in Table 1 have not been foreground-modified, but can be by following the above procedure. The foreground-corrected polarization properties are used in the rest of the analyses.

3.3.2 Properties of the Background Stars

The number of background stars with a high SNR in $K$-pol was 318, of which 90 were also detected as high SNR $H$-pol stars. Within the entire 20$\times$20 arcmin FOV, 574 background stars were detected as high SNR $H$-pol stars, including those 90 stars. Four high SNR $H$-pol stars in the 10$\times$10 arcmin FOV did not have corresponding $K$-pol entries.

Figure 5 shows a GLIMPSE and MIPSGAL 3-color image of G28.23 overlaid with the column density-derived AV contours and the high SNR $H$ and $K$ stellar polarization vectors. The polarizations probe to cloud AV values between 35 to 40 mag. While the $K$-band polarizations cannot probe into the dense, inner regions of the IRDC, where AV values reach $\sim$100 mag, they probe to the intermediate densities. Using a combination of $H$-pol and $K$-pol data, we trace the cloud plane-of-sky B-field orientation from the outer diffuse regions into the intermediate regions of the cloud. The large-scale polarization orientation across the FOV is preferentially parallel to the Galactic plane, although some changes to this overall pattern are seen near the IRDC.

The following analysis and results use only the sample of $H$-pol and $K$-pol background stars.

3.4 Polarization Efficiency

Because the mechanism of spinning up dust grains to be oriented perpendicular to the intervening B-field relies on an anisotropic radiation field (Lazarian & Hoang, 2007), one concern in using stellar polarimetry to probe B-fields in dense regions is whether the grains remain aligned with the field deep within the cloud (Arce et al., 1998).

3.5 UQ Averaging

Using only high SNR stars ignores the stars with lower signal-to-noise ratios. While these stars are not significant individually, they can be averaged to boost average polarization signal-to-noise (Clemens et al., 2012b). Therefore, we spatially averaged the polarimetric information of all of the background stars, to create smoothed polarization maps of the cloud. The maps were gridded into pixels of 30$\times$30 arcsec, and all stars classified as background were used. The variance-weighted average UE and QE Stokes parameters of the stars located within each pixel were computed , from which debiased (Section 3.1) average polarization and Equatorial PAs were estimated. The polarizations computed for each pixel were therefore independent. These Equatorial PAs were rotated into GPAs.

Figure 7 is similar to Figure 5, but with the spatially-averaged polarization vectors plotted. Only the polarization values of pixels where the polarizations were equal to or greater than 2.5 times their propagated uncertainties are shown. In this average polarization map, the large-scale patterns of the polarizations become more evident than in Figure 5. The polarization GPAs are preferentially perpendicular to the cloud major axis farther from the cloud and, especially at larger longitudes, twist to become more parallel to the cloud .

3.6 Relative GPA Orientations

To explore the PA orientation patterns further, we separated the polarization map into four cloud-centered quadrants and compared the GPA distributions of the individual background stars in each of these regions.

An F-test supported 7th order polynomial was fit to the column density map to define a cloud ‘spine’ along its long axis (e.g., Marchwinski et al., 2012; Cashman & Clemens, 2014). The polynomial was fit to the pixel locations of the peak values of the column density map along the declination axis, so the spine points were spaced $\sim$37 arcsec apart. Figure 8 shows the cloud column density-derived AV contours, with this spine overlaid. The spine splits the cloud into ‘Northern’ and ‘Southern’ (Galactic) components. In addition, we also separated the cloud into ‘Eastern’ and ‘Western’ sections by a line running parallel to the R.A. axis through the spine midpoint. This line separates the northern dense region of the cloud, which hosts several massive starless cores (Sanhueza et al., 2013) from the less dense, southern elongated extension .

For each high SNR $K$-pol and $H$-pol star in the 10$\times$10 arcmin FOV, was found relative to the orientation of the cloud spine at the closest point to the star. The PA differences ranged from 0 to 180$\arcdeg$, where 90$\arcdeg$ signifies PAs that are perpendicular to the cloud spine, and 0 or 180$\arcdeg$ signify PAs that are parallel to the spine. Figure 9 shows the distributions of relative PA orientations for stars in the four quadrants.

The four distributions show different relative PA patterns. The standard deviation of each distribution was found by shifting the whole distribution by increments of 10$\arcdeg$ and wrapping PAs greater than 180$\arcdeg$ , finding the standard deviation of each shifted distribution, and selecting the least deviation. The Northeast (larger $l$ and $b$ values) distribution peaks around a relative orientation of 69$\arcdeg$ ( more perpendicular) with a standard deviation of 30$\arcdeg$. The Southwest distribution peaks around 26$\arcdeg$ (more parallel), with a standard deviation of 15$\arcdeg$. The Northwest and Southeast distributions are not strongly skewed toward either parallel or perpendicular, though the majority of stars in both distributions have relative PAs between 0 and 90$\arcdeg$. The Southeast distribution is somewhat more preferentially perpendicular, though it has a larger standard deviation of 36$\arcdeg$.

3.7 PA Dispersion

As a partial proxy for the plane-of-sky B-field strength under the CF method, we calculated the PA dispersion across the cloud. This dispersion calculation used the 322 high SNR $K$ and $H$ polarizations in the 10$\times$10 arcmin FOV .

A large-scale PA pattern was removed from the polarization PAs prior to calculating the PA dispersions, as the estimated dispersion of the B-field should only include the turbulent motions of the gas (e.g., Ostriker et al., 2001). To create the large-scale pattern, the individual stellar PAs were smoothed using variance weighting. Bin centers separated by 45 arcsec . $\sigma$ equal to $\sim$38 arcsec to achieve Nyquist sampling. A range of center separations and corresponding Nyquist-sampled Gaussian kernel sizes were tested, but the results did not vary significantly. The resulting smoothed PA map was then interpolated to the size of the Mimir instrument platescale, 0.58 arcsec per pixel. The smoothed and interpolated PA map values were then subtracted from the individual stellar GPAs .

The PA dispersions of these large-scale corrected GPAs were calculated using large, overlapping 120$\times$120 arcsec bins with center separations of 60 arcsec. Such large bins were necessary to ensure that enough stars with high signal-to-noise were used in the dispersion calculations. Dispersions ( standard deviations of the PA distributions) and propagated uncertainties were calculated only for bins with at least seven high SNR stars.

Following Hildebrand et al. (2009), the uncertainties of the PA dispersions were subtracted in quadrature from the dispersions. This step was performed to correct the dispersions for the bias added by observational uncertainties, for which the median uncertainty was $\sim$3$\arcdeg$. The median post-correction signal-to-noise of the PA dispersions was seven.

The corrected PA dispersion map is shown in Figure 10. The blue regions show where PA dispersions were below 25$\arcdeg$. The light gray regions indicate bins where the PA dispersions themselves were above 25$\arcdeg$, but the PA dispersions minus their uncertainties were less than or equal to 25$\arcdeg$. These blue and light gray regions are where the plane-of-sky B-field strengths were calculated using the CF method . The dispersions could not be calculated in the dense center regions of the cloud due to the lack of stars, which are shown in white. Regions where the PA dispersions minus their uncertainties were above 25$\arcdeg$ are shown as dark gray pixels .

3.8 Cloud Volume Density

A Plummer-like model was fit to the normalized column density profile, following Equation 1 of Arzoumanian et al. (2011):

[TABLE]

where $k$ is the distance along the cloud spine, ${\bf r}$ is the 3D distance to the cloud spine, $r$ is the projected distance to the closest location, $k$, to the cloud spine, $\rho_{ck}$ is the central gas volume density of the cloud, and $p$ is the profile index. Rflat represents the radius of the central flat portion of the column density profile. $\Sigma(r)$ is the mass surface density, equal to $\mu$mH$N_{H2}$. The volume density, which depends on the distance from the cloud spine, is $\rho_{p}({\bf r},k)$. The central density was allowed to vary with $k$. It was constrained by the fit to the column density profile, and was fit point by point along the cloud spine to reproduce the column density values. The best Rflat and $p$, fit using all of the pixels in the column density map (within the central 10x10 arcmin box in Figure 3), were found to be 0.8$\pm$0.3 pixels ($\sim$30 arcsec) and 2.0${}^{+0.1}_{-0.3}$, respectively. In comparison, the profile index would be equal to 4 for an isothermal cylinder in equilibrium (Ostriker, 1964), indicating that there may be some magnetic support for G28.23 (Fiege & Pudritz, 2000). The central densities along the cloud spine were found to range from 4.2$\times$103 to 3.1$\times$104 H2 cm*-3*, with uncertainties of about 200 H2 cm*-3*.

This method returned a 3D volume density data cube, with voxel side sizes equal to the column density pixel size (37 arcsec $\sim$ 0.9 pc at a distance of 5.1 kpc).

To calculate an average volume density map, a cloud boundary was needed, since the Plummer profile of the cloud extended to infinity. The cloud boundary was assumed to be located where the column density radial profile reached a plateau. This plateau occurs at an estimated extinction level of AV$\sim$2 mag, indicative of the fact that G28.23 is not an isolated cloud, but is instead embedded in diffuse material. Using the 3D density model, we determined that the AV contour of 2 mag corresponds to a median volume density of 50 H2 cm*-3* in the plane of the sky. Based on this correspondence, the cloud boundary was assumed to be where the maximum volume density along the line of sight just reached 50 H2 cm*-3*.

This boundary is more liberal than ones used in previous studies, which used the cloud FWHM to estimate the cloud depth along the line of sight (e.g., Crutcher et al., 2004). For G28.23, cloud column density FWHM corresponds spatially to a median volume density in the plane of the cloud spine of $\sim$550 H2 cm*-3*. Using the FWHM boundary in calculating the average volume density map might be overly restrictive in the case of G28.23. The selected boundary of 50 H2 cm*-3* corresponds to a cloud width of $\sim$4$\sigma$.

The average H2 volume density map of G28.23 is shown in Figure 12 . The outermost density boundary indicates where the average volume density just reaches 50 H2 cm*-3*. The maximum average volume density is 1.9$\times$103 H2 cm*-3*. If the boundary of 550 H2 cm*-3* corresponding to the FWHM of the column density were used instead, the maximum average volume density becomes 6.1$\times$103 H2 cm*-3*. The larger boundary of 50 H2 cm*-3* allows the B-field across a larger area to be computed.

3.9 Plane-of-Sky B-field Strength

To estimate the plane-of-sky B-field strength (BPOS), we used the CF method, modified as recommended by Ostriker et al. (2001):

[TABLE]

where $\rho$ is the mass density (in grams cm*-3*), $\sigma_{v}$ is the one-dimensional non-thermal gas velocity dispersion (in cm s*-1*), $\sigma_{\phi}$ is the polarization PA dispersion (in radians), $f$ is a correction factor, and $B_{POS}$ is the plane-of-sky B-field strength in units of Gauss. Following Ostriker et al. (2001), $f$ is closest to 0.5, and the method is only valid along directions where the PA dispersion is less than 25$\arcdeg$ (0.44 radians).

The gas velocity dispersion were estimated by evaluating the GRS 13CO spectral data cubes, which have an angular resolution of 46 arcsec and spectral resolution of 0.2 km s*-1* (Jackson et al., 2006).

The vlsr of G28.23 peaks at about 81 km s*-1* (Sanhueza et al., 2013). A secondary smaller peak at 73-34 km s*-1* can be detected in the 13CO spectra in some regions near the cloud. The 81 km s*-1* line feature was fit with a Gaussian profile for each GRS spatial pixel falling within the 10$\times$10 arcmin FOV. Where detected, the secondary component at 73 km s*-1* was also fit with a Gaussian profile.

The median of the velocity dispersions was $\sim$3 km s*-1*, and the median SNR of the velocity dispersions was 12.

The angular resolutions of the 13CO velocity dispersion, average volume density, and PA dispersion maps were 46 arcsec, 37 arcsec, and 60 arcsec, respectively. Because the PA dispersion angular resolution was the largest of the three, the other two maps needed to be changed to this resolution. The velocity dispersion and volume density maps were regridded to the resolution of the PA dispersion map, with 60$\times$60 arcsec pixels, where the value of each output pixel was the average of the values of the input pixels that overlapped the output pixel area, weighted by the fraction of the input pixel area falling into the output pixel.

Equation 6 was used to calculate BPOS in each of these matched pixels and combined into a map of G28.23. The matched maps consisted of 11$\times$11 pixels. Of these, BPOS was calculated in the 51 pixels where PA dispersions, minus their uncertainties, were less than or equal to 25$\arcdeg$ and where the volume densities plus their uncertainties were greater than or equal to 50 H2 cm*-3*. Uncertainties in the BPOS estimates were found by propagating the uncertainties from the PA dispersions, velocity dispersions, and volume densities. We assumed no uncertainty in the kinematic distance of 5.1 kpc. The dependence of the B-field strength on distance (and any distance uncertainty) is discussed in Section LABEL:systematicuncertaintiesall. The BPOS SNR values ranged from 1.4 to 6.7, with a median of 4.2.

The properties of each bin, including PA dispersion, volume density, 13CO gas velocity dispersion, BPOS, and the normalized Mass-to-Flux ratio (discussed in the following section), along with their uncertainties, are listed in Table 3. The last column of Table 3 lists whether the PA dispersion, density, or both limited the BPOS calculated for each pixel. If the PA dispersion of a pixel was above 25$\arcdeg$, but the dispersion minus its uncertainty was less than or equal to 25$\arcdeg$, . Similarly, the volume density of a pixel was below 50 H2 cm*-3*, but the density plus its uncertainty was greater than or equal to 50 H2 cm*-3*, .

\onecolumngrid

\twocolumngrid

Figure 13 the derived field strengths range from 10–165 $\mu$G, and probe extinctions up to AV$\sim$30 mag. The field strength estimates are predominantly lower in the lower density regions of the upper left (NE) quadrant of Figure 13. The field strength could not be probed in the densest regions of the cloud because of the lack of stars with polarimetric detections.

3.9.1 B-field Strength versus Density

One test of whether a B-field influenced the flow of material into a cloud is dependence of the field strength on cloud density. This relation between B-field strength and average volume density is shown for G28.23 in Figure 14, which is based on, and uses data from, Figure 1 of Crutcher et al. (2010). The BPOS strengths of G28.23 were scaled to represent the mean B-field strength in only one dimension ($B_{x}=B_{POS}/\sqrt{2}$), and are shown as the black diamonds. The volume density ($n$) used in this relation is the volume density of atomic hydrogen, found by doubling the molecular hydrogen volume density. The Zeeman measurements and upper limits from Crutcher et al. (2010) are shown as the blue triangles. Also shown is a red, dashed line representing the equation of Bmax from their Equation 21. Most of the Bx values for G28.23 exceed the corresponding Bmax values at the given densities. We note that the Bx points of G28.23 are for a single cloud, while the BZ points of Crutcher et al. (2010) consist of one point per cloud for various samples of clouds and Zeeman probes.

A single power law of the form $B{\sim}n^{\alpha}$ was fit to the G28.23 Bx versus $n$ points. The best-fit power law had a slope $\alpha$=0.73 $\pm$ 0.06 (black solid line in Figure 14). The implications of this result will be discussed in Section 4.2.

3.10 Mass-to-Flux Ratio

The M/$\Phi_{B}$ of a region determines whether gravitational or magnetic energy dominates (Crutcher, 2012). The normalized M/$\Phi_{B}$ (M/$\Phi_{BN}$), is equal to (Crutcher et al., 2004):

[TABLE]

where N${}_{H_{2}}$ is in cm*-2* and B is in $\mu$G. A normalized M/$\Phi_{B}$ equal to unity indicates that gravitational energy is equal to the magnetic energy.

The B-field strength used in the M/$\Phi_{BN}$ calculation is nominally BTOT, which is the amplitude of the 3-D vector B-field strength (Crutcher et al., 2004). However, because we measure BPOS, the M/$\Phi_{BN}$ calculated here is actually M*∥*/$\Phi_{\perp}$ (Planck Collaboration et al., 2016b), . Based on the geometry of the cloud and whether the B-field is perpendicular or parallel to the cloud major axis, the average M/$\Phi_{BN}$ over all possible inclination angles (with respect to the line of sight) will be (Crutcher et al., 2004; Planck Collaboration et al., 2016b):

[TABLE]

where $\theta$ is the inclination of the cloud with respect to the line of sight. Limiting geometries include: the B-field being perpendicular to the cloud major axis, and, the B-field being parallel to the cloud major axis. The correction factor, $f$, applied to M*∥/$\Phi_{\perp}$ to yield the average M/$\Phi_{BN}$, will be bounded by 1/3 (perpendicular) and 3/4 (parallel) (Planck Collaboration et al., 2016b). Therefore, the M∥*/$\Phi_{\perp}$ values presented for G28.23 need correction, depending on geometry, to infer M/$\Phi_{BN}$.

Figure 15 shows the M*∥/$\Phi_{\perp}$ map of G28.23. The M∥/$\Phi_{\perp}$ ratios range from $\sim$0.09–7.5, with a median of $\sim$1.55. The M∥*/$\Phi_{\perp}$ values appear to increase with increasing cloud density.

Figure 16 plots the M*∥/$\Phi_{\perp}$ values against atomic hydrogen volume density. The horizontal dashed line represents unity for M∥/$\Phi_{\perp}$. A positive correlation is seen between density and M∥/$\Phi_{\perp}$, where regions that are less dense tend to have lower M∥/$\Phi_{\perp}$ values, and regions that are denser tend to have larger M∥/$\Phi_{\perp}$ values. Applying the geometric correction factor lowers the M∥/$\Phi_{\perp}$ estimated M/$\Phi_{BN}$ values and changes the average volume density at which the cloud goes from subcritical (B-field dominated) to supercritical (gravitationally dominated). Similar to the B-field strength, a power law was fit to M∥/$\Phi_{\perp}$ versus $n$. The best-fit power-law has an index of 1.02$\pm$0.08. The uncorrected volume density that corresponds to criticality is 225 H cm-3*, whereas the corrected volume density ranges from $\sim$300 to 670 H cm*-3*, depending on the correction factor.

4 Discussion

To test the importance of the B-field in IRDC G28.23, we examined the relationships between the B-field and other cloud properties. In this section, we discuss the implications of the results.

4.1 Plane-of-sky B-field Morphology: Relative PA Orientations

The first test of the importance of the B-field in the formation of G28.23, Question 2, examines the relative orientation of the polarization PAs with respect to the projected cloud orientation. For this IRDC, the relative PA orientations were neither preferentially perpendicular nor parallel to the cloud major axis orientation. The relative PA orientations do, however, show a large-scale pattern, and appear to have distinct distributions in the Northern and Southern regions of the cloud, as seen in Figure 9, . The PAs in the North are more likely to be perpendicular to the cloud elongation, especially in the Northeast, whereas in the South , PAs are more likely to be parallel to the cloud elongation.

One specific cloud configuration in a strong B-field regime is the hub-filament system, where the B-field helps funnel material to a central dense hub along one or more filaments (Myers, 2009; Chapman et al., 2011; Li et al., 2014; Pillai et al., 2015). Such a configuration would exhibit B-fields perpendicular to the dense hub and parallel to the less dense connecting filaments.

Based on the relative PA orientations with respect to locations in the cloud, it is unclear whether the B-field played a dominant role in the formation of G28.23.

We note the presence of a bright 8 $\mu$m feature in the Southeast region ($l\sim$28$\fdg$3, $b\sim-$0$\fdg$2) of the cloud, which may have disrupted the B-field in that area. As seen in Figure 7, the polarization measurements appear to form a shell around this bright ring-like structure. Fewer high SNR stars are present near the structure, compared to the rest of the region. This structure may correspond to a large bubble in the Catalog of bubbles from the Milky Way Project, centered at $l$ = 28$\fdg$297 and $b$ = $-$0$\fdg$202 (Simpson et al., 2012). The bubble may have disrupted either the B-field or the dust grains in the region such that polarizations cannot easily be measured. Spectral information targeting this structure was unavailable at the time of this study. While GRS 13CO line emission at different radial velocities toward this region (lines at 74 and 81 km s*-1*) can be detected, this feature is not seen as a coherent structure in the 13CO data. We conclude that the distance to this bubble is not known, and its association with G28.23 remains circumstantial.

4.2 B-field, Cloud Density, and Mass-to-Flux

For the regions where BPOS strengths were estimated for G28.23, the relation between Bx and volume density was best fit with a single power law of slope 0.73$\pm$0.06, which addresses Question 3. This slope is approximately equal to the slope of 0.65 found by Crutcher et al. (2010) for B vs. $n$ at densities larger than 300 H cm*-3*.

Our best-fit slope, which is greater than 2/3, implies that the B-field was not the dominant force in the formation of G28.23. However, the slope of 2/3 corresponds to a temporal evolution of the B-field with density as material undergoes collapse (Li et al., 2015a). The B vs. $n$ relation of G28.23 characterizes instantaneous structure: the present-day dependence of the B-field strength on density across the cloud. If the temporal test of B-field importance can be applied to the structural relation, indicates that the B-field did not affect the formation of G28.23 to a large degree. However, the influence of the B-field in the future evolution of the cloud is not known.

Simulations run by Li et al. (2015b) of clump collapse using both initially strong B-fields (Alfvén Mach number \mathcal{M}_{a}$$\sim1) and weak B-fields (\mathcal{M}_{a}$$\sim10) found similar dependences of the B-field strength on density to those found in this study. Their strong-field simulations exhibited a power law index of 0.7, which is very similar to the 0.73 found here. In contrast, their power law dependence in the weak-field simulation was 0.57. The 2/3 dependence of Mestel (1966) applied to weak B-fields, which is not the case for G28.23, but the similar dependence on density is still seen.

The median uncorrected M*∥/$\Phi_{\perp}$ of the cloud is $\sim$1.5, for which M/$\Phi_{BN}$ will range from 0.5 to 1.125 when corrected (Question 4). M∥/$\Phi_{\perp}$ was found to correlate with density with a power law index of $\sim$1. This result indicates that there is a critical density, $n_{crit}$, above which the cloud is supercritical and no longer B-field supported. The gray region in Figure 16 indicates where M/$\Phi_{BN}$ = 1 would be if a geometric correction factor is applied. The best-fit line between density and M∥/$\Phi_{\perp}$ intercepts this region for densities in the range $\sim$300-670 H cm-3*. The lower limit of this range is similar to the threshold density of 300 H cm*-3* that Crutcher et al. (2010) associated with a molecular cloud becoming self-gravitating.

4.2.1 Systematic Uncertainties due to Volume Density

The average volume density characterizing lines of sight through a cloud can be calculated using different methods (e.g., Marchwinski et al., 2012). These will result in different density estimates. In the present study, the selection of the cloud boundary affects the average volume density estimates. Our chosen boundary of 50 H2 cm*-3* might be considered somewhat liberal, whereas selecting a boundary corresponding to the FWHM of the cloud column density may be overly restrictive and would result in ignoring a substantial amount of cloud material and associated B-field.

To determine the effects of the assumptions made in calculating the average volume densities, we recomputed the BPOS strengths and M*∥/$\Phi_{\perp}$ values using average volume densities derived from other boundary values. Volume density boundaries of 550, 200, and 100 H2 cm-3* corresponded to the cloud column density widths equal to the FWHM, 2$\sigma$, and 3$\sigma$, respectively, where $\sigma$ was derived from fitting the cloud column density perpendicular to the cloud spine, as described in Section 3.8. The best-fitting power law indices of Bx vs. $n$ ranged from 1.24$\pm$0.24 to 0.82$\pm$0.08 for widths equal to the FWHM and 3$\sigma$. The best fits to the relations found by using the FWHM boundary are more uncertain because the number of pixels meeting the criteria to calculate B-field strengths decreased drastically (to 15 pixels) compared to the case of the larger boundary out to 50 H2 cm*-3* .

The use of different boundaries to calculate the average volume densities for G28.23, while changing the indices of the best-fitting power laws to the B vs. $n$ relation, does not change the interpretation that the B-field was not likely to be the dominant force in the formation of the cloud. The power law indices of the B vs. $n$ relations are still above the 2/3 threshold, which indicate that gravity was likely the dominant force. This result is still subject to the assumption that the density index for temporal evolution of the B-field matches the density index for present-day structure.

Based on the dependence of the B-field strength on density, the B-field morphology, and the M*∥*/$\Phi_{\perp}$ values of the cloud, it is unclear whether the B-field was the dominant force in the formation of G28.23.

5 Summary

The importance of the B-field in IRDC formation is not yet understood. To determine whether the B-field played a role in the formation of one IRDC, G28.23, we analyzed archival and new NIR polarimetric observations, . We posed four questions to investigate the role of B-fields in the formation of G28.23. One question addressed whether NIR polarizations could probe the B-field in the intermediate layers of clouds as opaque as IRDCs, and three questions addressed the importance of the B-field in cloud formation. We examined the behavior of NIR polarization percentage with extinction, the relative cloud to B-field PA orientations, the relationship of the B-field strength with density, and finally, the Mass-to-Magnetic Flux ratio across the cloud.

Using a combination of shallow $H$-band and deep $K$-band polarimetric observations, along with dust continuum data from the Herschel Hi-GAL and ATLASGAL surveys, and spectral line data from GRS 13CO, we analyzed the properties of the plane-of-sky component of the B-field of G28.23. We found:

1. The polarization percentages increase as a function of extinction, indicating that our observations do probe the B-field of the outer and intermediate layers of G28.23.

2. The overall relative orientation of the plane-of-sky B-field was neither preferentially perpendicular nor parallel to the projected cloud orientation. Therefore, it is unclear from the B-field morphology alone whether the B-field affected the formation of the cloud. The PAs do, however, show a large-scale pattern. The distinct relative PA distributions found in different locations around the cloud indicate that the B-field morphology in the region is affected by the presence of the cloud.

3. The dependence of the B-field strength on cloud density was fit with a power law. The index of the best-fitting power law was 0.73$\pm$0.06, very similar to the slope of 2/3 that would imply that the B-field was not dynamically important in the formation of the IRDC.

4. The relation between M*∥/$\Phi_{\perp}$ and density, fit with a power law, indicates that the cloud is magnetically dominated at lower densities and becomes gravitationally dominated at higher densities. Applying a correction factor to M∥/$\Phi_{\perp}$ to account for the unknown geometry of the system shows that the M/$\Phi_{BN}$ vs. density relation crosses unity in the density range $\sim$300–700 H cm-3*.

Based on the B-field properties found by NIR polarimetry in this study, it is unclear whether the B-field influenced the formation of IRDC G28.23. It is likely, though, that the local B-field in the vicinity of G28.23 was influenced by the presence and/or formation of the cloud.

6 Acknowledgement

We thank J. Montgomery, T. Hogge, and I. Stephens for constructive discussions on the analysis. We are grateful to R. Crutcher for permission to include his Zeeman data. This research was conducted in part using the Mimir instrument, jointly developed at Boston University and Lowell Observatory and supported by NASA, NSF, and the W.M. Keck Foundation. This research made use of the NASA/IPAC Infrared Science Archive, which is operated by the Jet Propulsion Laboratory, California Institute of Technology (Caltech), under contract with NASA. This publication made use of data products from the Two Micron All Sky Survey, which was a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/Caltech, funded by NASA and NSF. This work is based in part on data obtained as part of the UKIRT Infrared Deep Sky Survey. The ATLASGAL project is a collaboration between the Max-Planck-Gesellschaft, the European Southern Observatory (ESO) and the Universidad de Chile. It includes projects E-181.C-0885, E-078.F-9040(A), M-079.C-9501(A), M-081.C-9501(A) plus Chilean data. This publication makes use of molecular line data from the Boston University-FCRAO Galactic Ring Survey (GRS). The GRS is a joint project of Boston University and Five College Radio Astronomy Observatory, funded by the National Science Foundation under grants AST-9800334, 0098562, 0100793, 0228993, & 0507657. A.E.G acknowledges support from FONDECYT 3150570. This work was supported under NSF grants AST 09-07790 and 14-12269 and NASA grant NNX15AE51G to Boston University.