PROJECTED ROTATIONAL VELOCITIES OF 136 EARLY B-TYPE STARS IN THE OUTER GALACTIC DISK

We measured the FWHM for the He i lines at 4026, 4388, and 4471 Å. The blue wings for some of the He iline profiles are affected by secondary components such as 4023.98 and 4026.2 of He i and 4387.00 and 4469.96 of [He i]. These are distinguishable from the main profile at very low v sin i, but are blended at higher rotation rates. The regions containing the He ilines at 4026, 4388, and 4471 Å were manually normalized to a unit continuum using the splot task in IRAF. The "h," then "b" splot commands measure the right half of the line profile and display the FWHM.

The intrinsic line widths (about 1 Å) are considerably broader than the instrumental resolution (0.08 Å), thus no adjustment was made for the latter. No special treatment was considered for determining the v sin i of the very-broad-lined stars. It should be noted, however, that for those stars with rotational velocities approaching the critical limit, the effect of gravity darkening can lead to systematic underestimation of the projected rotational velocities (see e.g., Townsend et al. 2004; Frémat et al. 2005). Macroturbulence may also contribute to the line widths (see Simon-Diaz & Herrero 2014), although this would affect mostly stars with lower surface gravities, which we ignore in our subsequent analysis. Figure 2 shows examples of both a low (ALS14013) and high (ALS19267) v sin i star for the three helium lines analyzed here.

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As in Paper I, we have used the calibrations in Daflon et al. (2007) to determine v sin i for this sample. We used the same grid of synthetic spectra of B-type stars computed by Daflon et al. (2007) and measured the FWHM for each of the three He i lines: 4026, 4388, and 4471 Å (as in Paper I) . We derived analytical expressions between v sin i and FWHM for each of the three He i lines, for three temperatures: 20,000, 25,000, and 30,000 K. We adopted the conversion formulae appropriate for the temperature nearest to that estimated for each star to represent each He iline. A reasonable estimate of each star's temperature was derived from the parameter Q, listed in Table 1, and the analytical relationship derived between Q and temperature given in Massey et al. (1989). While log g also affects the FWHM, all of the stars used in our statistical analysis are of the luminosity classes IV–V. We will address the effect of surface gravity further in a later analysis (Bragança et al. 2015, in preparation). Our analytical relations follow, in which FWHM is in Å and v sin i is expressed in km s⁻¹: these were used to convert the measured FWHM values for each corresponding line in the program stars given in Table 1.

Table 1.  Observed and Derived Data

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)	(14)	(15)	(16)	(17)
		FWHM (Å)
ALS	V	λ 4026	λ 4388	λ 4471	$\langle {\text{}}v\mathrm{sin}{\text{}}i\rangle$	σvsi	RV	σRV	$n({RV})$	Q	$E(B-V)$	${M}_{{\rm{v}}}$	dKpc	SpType	CAF	Rem
7	10.91	0.98	0.89	0.81	0	0	23.6	1.7	10	−0.8	0.61	−3.7	3.4	B1 IV	F	...
18	10.74	1.59	1.52	1.58	26	11	67.3	2.3	10	−0.79	0.85	−3.6	2.2	B0 V	A	...
19	11.66	1.43	1.62	1.37	27	15	10.4	4.2	9	−0.84	1.18	−5.0	3.9	B0 III neb	A	Sh2–255
45	12.59	1.48	1.11	1.17	11	2	37.8	2.8	10	−0.71	0.49	−2.9	6.2	B1.5 V	A	D07, Bochum 1
48	12.58	2.71	2.25	2.95	81	7	40.3	4.8	10	−0.73	0.57	−3.1	6.0	B2 V	A	Bochum 1
53	12.04	1.73	1.63	1.66	38	6	...	...	...	−0.82	0.57	−3.9	6.8	B1 V	A	SB2?, Bochum 1
54	12.50	3.66	3.92	3.41	126	27	38.5	7.3	8	−0.64	0.51	−2.3	4.5	B2 V	A	Bochum 1
86	11.35	1.10	0.96	0.95	4	4	...	...	...	−0.88	0.50	−4.4	7.0	B0.5 V	A	Sh2–289
208	11.56	1.45	1.18	1.23	12	5	74.8	3.6	10	−0.78	0.48	−4.5	8.1	B1 III	A	Sh2–301
212	12.08	4.66	5.70	5.24	208	32	82.8	10.6	8	−0.71	0.50	−2.9	4.8	B1 V	A	D07, Sh2–301

Only a portion of this table is shown here to demonstrate its form and content. Machine-readable and Virtual Observatory (VOT) versions of the full table are available.

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He i 4026:

$$\begin{eqnarray*}20,000\;{\rm{K}}:v\mathrm{sin}i & = & -0.13{(\mathrm{FWHM})}^{2}+56.91(\mathrm{FWHM})-84.4\\ 25,000\;{\rm{K}}:v\mathrm{sin}i & = & -0.43{(\mathrm{FWHM})}^{2}+59.28(\mathrm{FWHM})-78.6\\ 30,000\;{\rm{K}}:v\mathrm{sin}i & = & -0.60{(\mathrm{FWHM})}^{2}+59.64(\mathrm{FWHM})-68.7\end{eqnarray*}$$

He i 4388:

$$\begin{eqnarray*}20,000\;{\rm{K}}:v\mathrm{sin}i & = & -1.29{(\mathrm{FWHM})}^{2}+60.16(\mathrm{FWHM})-60.5\\ 25,000\;{\rm{K}}:v\mathrm{sin}i & = & -1.18{(\mathrm{FWHM})}^{2}+58.55(\mathrm{FWHM})-50.8\\ 30,000\;{\rm{K}}:v\mathrm{sin}i & = & -1.27{(\mathrm{FWHM})}^{2}+59.42(\mathrm{FWHM})-48.6\end{eqnarray*}$$

He i 4471:

$$\begin{eqnarray*}20,000\;{\rm{K}}:v\mathrm{sin}i & = & +0.65{(\mathrm{FWHM})}^{2}+38.91(\mathrm{FWHM})-38.7\\ 25,000\;{\rm{K}}:v\mathrm{sin}i & = & -0.47{(\mathrm{FWHM})}^{2}+41.24(\mathrm{FWHM})-37.9\\ 30,000\;{\rm{K}}:v\mathrm{sin}i & = & -0.20{(\mathrm{FWHM})}^{2}+44.46(\mathrm{FWHM})-38.8.\end{eqnarray*}$$

All of the star designations, observed parameters, and derived quantities are listed in Table 1: column 1, their number in the ALS catalog (Reed 2003); column 2, their apparent V magnitude; columns 3–5, the measured line FWHMs discussed above; columns 6 and 7, the average v sin i and error; columns 8–10, the radial velocity, error, and number of lines measured; column 11, the reddening free quantity Q; column 12, the color excess $E(B-V)$; column 13, the absolute V magnitude used to compute the photometric distance in column 14; column 15, the spectral type found in the literature; and column 16, the classification as Cluster (C), Association (A), or Field (F), as described in Section 3.1. Remarks about Hα emission, suspected binary stars, and membership in an association or cluster are found in column 17.

A subset of eight stars included in this study were previously observed in a study of v sin i by Daflon et al. (2007): they are indicated in Table 1, column 17 as D07. Additionally, six of our stars were observed by Huang & Gies (2006), who derived v sin i values: they are indicated as HG06. A comparison of our results with these published values is shown in Figure 3. It is worth remarking that the largest outlier from the one-to-one relationship in Figure 3, ALS 15340 with v sin i of 102 km s⁻¹, was noted by HG06 to be a SB1. Both HG06 and this work note Hα emission. None of the other stars shown in Figure 3 are suspected of being binary systems in the literature.

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As would be expected, some stars show evidence of double lines or line profiles that suggest the star is a binary. For completeness, these stars are listed in Table 1 with a notation in column 17, though no values for v sin i are given. Sample spectra of the stars with clear double lines are shown in Figure 4.

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Although spectra were only taken at a single epoch, the measured heliocentric radial velocities of the apparently single stars may be useful in future dynamical studies or to establish binarity.

There are also 18 stars that show noticable Hα emission, indicated with a remark in column 18. Hα line profiles for these candidate Be stars show a range of morphology, as shown in Figure 5.

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Previous work has shown that v sin i appears to depend on the stellar environment, and, in particular, that on average v sin i is lower for field stars as compared with stars in clusters or associations (Wolff et al. 2007). With no new kinematic data available to address this, we have searched the literature to find the classification arrived at by previous authors. Classifying a particular star as a cluster or association member within the Milky Way Galaxy is non-trivial. In many cases in the literature stars have been assigned membership in open clusters or associations based solely on photometry, much of which was done many decades ago. While the existence of the entire cluster is clear, the membership of any particular star can be much less certain.

We performed a literature search using SIMBAD for each star and then checked the references to determine what was known about the association or cluster membership. This was straightforward for stars for which the literature search indicated cluster membership. However, associations and field stars are more difficult. For example, we observed 13 stars that had been observed by Fitzgerald & Moffat (1980) in the vicinity of the putative open cluster NGC 2414, and which they identified as a new association, "association NGC 2414" at a distance of 4.2 kpc. Their color–magnitude diagram for the proposed association members is poorly defined. Our photometric distances for these 13 stars average 5.0 kpc, but the individual distance estimates range from 3.5 to 6.6 kpc. We have listed these stars as field stars. Twenty-three of the stars we observed are located in H ii regions first discussed by Sharpless (1959): in most of these examples the distance of the H ii region is based on the spectroscopic distance of just a few stars presumed to be exciting the H ii region. We have classified these Sharpless region stars as association members unless there existed later studies of the star in question.

An early study by Deutsch (1970) demonstrated that, for a limited sample of field B-stars, Maxwellian distributions can reasonably represent the observed projected rotational velocities. Subsequent work by a variety of researchers indicates that other statistical distributions could fit the data better if the sample sizes are large enough, but there is no a priori knowledge of the true shape of the underlying distribution function. Given the limited sample size in our study, Maxwellian distributions are adequate for making qualitative comparisons, especially when the data are divided into small subsamples. In the discussion that follows, the distributions of the subsamples were each fit with two Maxwellian functions representing sharp-lined and broad-lined components. The bi-modal Maxwellian distributions are defined by the two values of the mode parameter and the relative fraction of the two data sets being modeled. Artificial histograms were generated having the same total number of objects as the observed data, and the modes and relative frequencies of the two functions were varied to minimize the differences between the artificial and the observed distributions in the least-squares sense. The choice of histogram bin sizes is limited by the relatively small size of the subsamples: after some experimentation, 50 km s⁻¹seemed like the most reasonable choice.

Figure 6 shows comparisons of the distributions of the combined data of "Field" B0-B2-type stars with luminosity classes V–IV from this work plus GB2012 to the distribution for B0-B2-type stars in the Bright Star Catalog observed by Abt et al. (2002, hereinafter ALG02) plus Levato & Grosso (2013, hereinafter LG13). The fitted bimodal Maxwellian distributions are nearly identical, each showing a significant fraction of slow rotators. This gives added support to the idea that there are multiple mechanisms producing Field B-type stars. Note that a large number of evolved and binary stars in GB2012 were excluded from the analysis. Although we excluded from the analysis objects with luminosities of class III or higher, little is known about binarity for our targets and its impact on the distributions. ALG02 argued that the inclusion of close binaries would have little effect on the distributions; however, Langer (2012) argues that there are theoretical considerations that predict that the projected rotational velocities of massive main-sequence stars can be strongly affected by the presence of a close companion. The same is true for stars with strong magnetic fields (e.g., Stepién 2002). Because the fraction of massive close binaries is large (e.g., Sana et al. 2012) and because magnetic fields seem to be ubiquitous among B-type stars (Langer 2012), binarity and magnetic fields could, in principle, affect the distributions derived here.

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Figure 7 shows the plots of the v sin i distributions for our three groupings ("Cluster," "Association," and "Field," as defined above) of stars having luminosities of class IV or V described in the preceding section, along with the bimodal Maxwellian fits to each. Since Figure 6 shows that the distributions for the Field star subgroup is very similar to the distributions of objects from ALG02 and LG13, we adopted the averages of the modes shown in Figures 6, 23, and 116 km s⁻¹, to fit the three subgroup distributions. Only the relative fraction of the two Maxwellian distributions was varied to best fit the data. The relative fractions of the low v sin i component, 32%, 44%, and 18% for the Field, Association, and Cluster subsets, respectively, are consistent with earlier studies of early B-type stars that found large fractions of slow rotators in the Field and large fractions of rapid rotators in Clusters.

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Independent of the Maxwellian fits, a relative comparison of the observed distributions using a Kolmogoroff–Smirnoff test give probabilities of 0.34 and 0.25 that the "Cluster" v sin i's come from the same population as the "Field" and "Association" objects, respectively. The same comparison gives a probability of 0.87 that the "Field" and "Association" stars come from the same population. Note that neglecting gravity darkening would underestimate the values of the largest v sin i 's (see Frémat et al. 2005) but would not explain the large fraction of slow rotators.