Evidence for Different Disk Mass Distributions Between Early and Late-Type Be Stars in the BeSOS Survey
aa r X i v : . [ a s t r o - ph . S R ] A p r Draft version September 27, 2018
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EVIDENCE FOR DIFFERENT DISK MASS DISTRIBUTIONS BETWEEN EARLY AND LATE-TYPE BESTARS IN THE BESOS SURVEY
C. Arcos , C. E. Jones , T. A. A. Sigut , S. Kanaan and M. Cur´e Instituto de F´ısica y Astronom´ıa, Facultad de Ciencias, Universidad de Valpara´ıso. Av. Gran Bretana 1111, Valpara´ıso, Chile. Department of Physics and Astronomy, The University of Western Ontario. London, Ontario, N6A 3K7, Canada. Centre for Planetary Science and Exploration, The University of Western Ontario. London, Ontario, N6A 3K7, Canada
ABSTRACTThe circumstellar disk density distributions for a sample of 63 Be southern stars from the BeSOSsurvey were found by modelling their H α emission line profiles. These disk densities were used tocompute disk masses and disk angular momenta for the sample. Average values for the disk mass are3.4 × − and 9.5 × − M ⋆ for early (B0-B3) and late (B4-B9) spectral types, respectively. We alsofind that the range of disk angular momentum relative to the star are between 150-200 and 100-150 J ⋆ /M ⋆ , again for early and late-type Be stars respectively. The distributions of the disk mass and diskangular momentum are different between early and late-type Be stars at a 1% level of significance.Finally, we construct the disk mass distribution for the BeSOS sample as a function of spectral typeand compare it to the predictions of stellar evolutionary models with rapid rotation. The observeddisk masses are typically larger than the theoretical predictions, although the observed spread in diskmasses is typically large. Keywords: stars: emission lines, Be — surveys — circumstellar matter INTRODUCTIONA Be star is defined by Collins (1987) as “A non-supergiant B star whose spectrum has, or had at sometime, one or more Balmer lines in emission”. The ac-cepted explanation for the emission lines is the presenceof a circumstellar envelope (CE) of gas surrounding thecentral star analogous to the first model of a Be starproposed by Struve (1931). The material is expelledfrom the central star and placed in a thin equatorialdisk with Keplerian rotation (Meilland et al. 2007). Dif-ferent mechanisms such as rapid rotation (Porter 1996;Townsend et al. 2004; Domiciano de Souza et al. 2003;Fr´emat et al. 2005), mass loss from the stellar wind(Stee & de Araujo 1994; Bjorkman & Cassinelli 1993;Cur´e 2004; Silaj et al. 2014a), binarity (Okazaki et al.2002; Romero et al. 2007; Oudmaijer & Parr 2010),magnetic fields (Donati et al. 2001; Cassinelli et al.2002; Neiner et al. 2003), and stellar pulsations(Rivinius et al. 2003) have been proposed to explain howthe star loses enough mass to form the CE and howthis material is placed in orbit, but it seems that morethan one mechanism is required to reproduce the ob-servations. Such mechanisms must continually supplyenough angular momentum from the star to form andto maintain the disk. Given some mechanism to depositmaterial into the inner edge of the disk, the evolution of the gas seems well described by the viscous disk decre-tion model presented by Lee et al. (1991), with angularmomentum transported throughout the disk by viscosity(Rivinius et al. 2013a).Be stars are variable on a range of different timescales associated with a variety of phenomenon occur-ring in the disk. For example, short-term variations( ∼ hours-days) in the emission lines are associated withnon-radial pulsations, probably due to the high rota-tion rate of the central star (e.g. Rivinius et al. 2003,2013a); intermediate-term variations ( ∼ months-years)are seen in the cyclical variation between the violet andred peaks in doubled-peaked emission lines. Such vari-ations are well represented by the global disk oscilla-tion model (Okazaki 1997; Carciofi et al. 2009). Longerterm variability, in some cases the emission lines disap-pear and/or are formed again on timescales of years todecades, is associated with the formation and dissipationof the disk (see section 5.3.1 of Rivinius et al. 2013b forseveral examples).Spectroscopy of the emission lines can be used to getinformation about the geometry, kinematics and physi-cal properties of the disk. A very convenient model, inagreement with observations, is to assume that the den-sity in the disk’s equatorial plane falls with a power lawwith exponent, n , and follows a Gaussian model in thevertical direction (see details provided in section 3.1).We use the density distribution described above, theradiative transfer code BEDISK and the auxiliary comple-mentary code
BERAY to solve the transfer equation alongmany rays ( ∼ ) through the star/disk configuration.A grid of calculated H α line profiles from models withdifferent disk density distributions and stellar parame-ters are used to match the observed H α line profiles andprovide constraints on the disk parameters. We applythis method to a sample of 63 stars from the BeSOS cat-alogue. We selected a fraction of the best fitting modelsand we obtained the distribution of the disk density pa-rameters, mass and total angular momentum content inthe disk, with results provided for both early- and late-type Be stars.This paper is organized as follows: Our program starsand reduction steps are given in Section 2. Section 3describes our theoretical models including the main as-sumptions of BEDISK and
BERAY codes in Section 3.1. In-put parameters to create the grid of models are providedin Section 3.2. Section 4 describes our results from se-lecting best-fit disk density parameters from all our sam-ple stars in two ways: visual inspection (Subsection 4.2)and a percentage of the best models (Subsection 4.3).Subsection 4.4 gives the mass and angular momentumdistributions of the disks. A discussion and conclusionsof our main results are presented in Sections 5 and 6,respectively. The Appendix displays H α spectra fromour best-fit models for our program stars compared toobservations. SAMPLE AND DATA REDUCTIONWe selected Be stars with B spectral type near oron the main sequence from the Be Stars ObservationSurvey (BeSOS ) catalogue for our study. All Be tar-gets in BeSOS website are confirmed as a Be star inthe BeSS catalogue or have an IR excess in the spec-tral energy distribution. This gives us a total of 63 Bestars. The sample distribution of spectral type is shownin the Figure 1. Approximately 30% of our sample cor-responds to the B2V spectral type. The same distribu-tion was found previously by other authors (Porter 1996;Slettebak 1982), with B2V being the most frequently ob-served spectral type in Be stars.BeSOS spectra were obtained using the Pontifica Uni-versidad Catolica (PUC) High Echelle Resolution Opti-cal Spectrograph (PUCHEROS) developed at the Cen-ter of Astro-Engineering of PUC (Infante et al. 2010).The instrument is mounted at the ESO 50 cm telescopeof the PUC Observatory in Santiago, Chile, and has aspectral range of 390-730 nm with a spectral resolution http://besos.ifa.uv.cl http://basebe.obspm.fr/basebe/ of λ/ ∆ λ ∼ < . The basic steps includedremoving bias and dark contributions, flat fielding, orderdetection and extraction, fitting the dispersion relation,normalization, wavelength calibration, and heliocentricvelocity corrections. Figure 1 . Histogram of the sample of Be stars by spectraltype. The distribution peaks at B2, which corresponds to ∼
30% of the sample.3.
THEORETICAL MODELS3.1.
Disk density and temperature structure
We calculated theoretical H α line profiles using twocodes: BEDISK , a non-local thermodynamic equilibrium(non-LTE) code developed by Sigut & Jones (2007), and
BERAY (Sigut 2011), an auxiliary code that uses
BEDISK ’soutput to solve the transfer equation along a series ofrays ( ∼ ) to produce model spectra.There are two significant components that must bespecified to model the physics of a star+disk system: thedensity distribution of the gas in the disk and the inputenergy provided by the photo-ionizing radiation field ofthe central star. Assuming both, BEDISK code solvesthe statistical equilibrium equations for the ionizationstates and level populations using a solar chemical com-position. Then, the code calculates the temperature dis-tribution in the disk by enforcing radiative equilibrium.All calculations are made under the assumption that the vertical density distribution is fixed in approximate hy-drostatic equilibrium, and the geometry of the disk isaxisymmetric about the stars’s rotation axis and sym-metric on the midplane of the disk.The assumed density distribution has the form: ρ ( R, Z ) = ρ (cid:18) RR ⋆ (cid:19) − n exp (cid:0) − ( Z/H ) (cid:1) , (1)where Z is the height above the equatorial plane, R isthe radial distance from the stars’ rotation axis, ρ isthe initial density in the equatorial plane, n is the indexof the radial power law, and H is the height scale in the Z -direction and is given by H = H (cid:18) RR ⋆ (cid:19) / , (2)with the parameter H defined by, H = (cid:18) R ⋆ kT GM ⋆ µ m H (cid:19) / , (3)where M ⋆ and R ⋆ are the stellar parameters, mass andradius, respectively; G is the gravitational constant, m H is the mass of a hydrogen atom, k is the Boltzmannconstant, µ is the mean molecular weight of the gasand T is an isothermal temperature used only to fix thevertical structure of the disk initially. This parameterwas fixed at T = 0 . T eff (Sigut et al. 2009). Since Bestars are fast rotators, the rotational velocity of the starwas assumed to be 0.8 v crit for all spectral types, where v crit is given by v crit = r GM ⋆ R ⋆ . (4)Finally, the rotation of the disk is assumed to bein pure Keplerian rotation (Meilland et al. 2007). Formore details the reader is referred to Sigut & Jones(2007).3.2. Input parameters and grid of models
We computed a grid of models using
BEDISK/BERAY for a range of spectral classes from B0 to B9 in integersteps in spectral subtype in the main sequence stage. Forearly spectral types, we also computed models for B0.5and B1.5 due to the large number of B2V stars in ourprogram stars (see Figure 1). We also included turbu-lent velocity ( v tur = 2.0 km s − ) into the disk for a morerealistic model, since thin disks are likely to be turbulent(Frank et al. 1992) which increases the Doppler width inline profiles. The stellar parameters were interpolatedfrom Cox (2000) and are displayed in the Table 1. Eachdisk model was computed using 65 radial ( R ) and 40vertical ( Z ) points. The spacing of the points in thegrid is non-uniform, with smaller spacing near the star and in the equatorial plane where density is the great-est. Jones et al. (2008) studied the disk density of clas-sical Be stars by matching the observed interferometricH α visibilities with Fourier transforms of synthetic im-ages produced by the BEDISK code. In their study, theysuggest that the base density ρ is typically between10 − to 10 − g cm − and the index power-law, n , nor-mally ranges from 2 to 4 (Waters et al. 1987). The outerradius of the H α emitting region has been estimatedby several authors considering samples of Be stars aswell as studies for individual stars (see Discussion Sec-tion 5.2). Hanuschik (1986) found that a typical outerradius of the envelope region producing the secondaryH α component is 20 R ⋆ and a similar value was foundby Slettebak et al. (1992) of 18.9 R ⋆ for strong lines and7.3 R ⋆ for weak lines. Measurements obtained using in-terferometric techniques determine the H α emitting re-gion to be between ∼ R ⋆ (e.g. Tycner et al.2005; Grundstrom & Gies 2006). Given this, we com-puted models for a disk truncation radius, R T , of: 6.0,12.5, 25.0 and 50.0 R ⋆ , with base densities of : (0.1, 0.25,0.5, 0.75, 1.0, 2.5, 5.0, 7.5, 10.0, 25.0) × − g cm − and n from 2.0 to 4.0 in increments of 0.5, to adequatelycover the full range of parameters space reported in theliterature. Finally, the inclination angle i was variedfrom 10 ◦ to 90 ◦ , in steps of 10 ◦ , with 90 ◦ replaced by89 ◦ to avoid an infinity value. Thus with 9 ρ values, 5 n values, 9 i values and 4 R T values, each spectral typeis represented by a library of 1620 individual H α modelline profiles. To properly compare the synthetic profileswith our observations, every model was convolved witha Gaussian to match the resolving power of 18000 of ourspectra. Table 1 . Adopted Stellar ParametersST T eff log g R ⋆ M ⋆ (K) ( R ⊙ ) ( M ⊙ )B0V 30000 4.0 7.40 17.50B0.5V 27800 4.0 6.93 15.43B1V 25400 3.9 6.42 13.21B1.5V 23000 4.0 5.87 11.04B2V 20900 3.9 5.33 9.11B3V 18800 4.0 4.80 7.60B4V 16800 4.0 4.32 6.62B5V 15200 4.0 3.90 5.90B6V 13800 4.0 3.56 5.17B7V 12400 4.1 3.28 4.45B8V 11400 4.1 3.00 3.80B9V 10600 4.1 2.70 3.29 Behaviour of the H α emission line F / F c (a) 1030507090 -500 -250 0 250 500 V (km/s)02468 F / F c (c) 1.0e-125.0e-121.0e-115.0e-111.0e-10 (b) 6.012.525.050.0 -500 -250 0 250 500 V (km/s) (d) 2.02.53.03.54.0 Figure 2 . Example of the variation of the emission H α line profiles by varying disk parameters. The reference model is shownin black in each panel for ease of comparison and corresponds to the disk parameters of n = 2.5, ρ = 5.0 × − g cm − , R T = 25.0 R ⋆ and i = 50 ◦ . The fluxes are normalized to the continuum star+disk flux outside of the line. Top left: inclinationvariation.
Top right: disk truncation radius variation.
Bottom left: base density variation.
Bottom right: power-law exponentvariation. F ( Jy ) (a) 1030507090 -500 -250 0 250 500 V (km/s)050010001500 F ( Jy ) (c) 1.0e-125.0e-121.0e-115.0e-111.0e-10 (b) 6.012.525.050.0 -500 -250 0 250 500 V (km/s) (d) 2.02.53.03.54.0 Figure 3 . Same as Figure 2 but with the H α lines plotted as absolute fluxes in Janskys. Prior to beginning our statistical analysis, we illus-trate the behavior of the predicted H α emission lineprofile as each of the four model parameters, ρ , n , R T and i , are varied. Figure 2 shows the results, with theline profiles convolved down to a nominal resolution of λ/ ∆ λ = 20000. The fluxes are normalized by the con-tinuum star+disk flux outside of the line. The referencemodel, shown in black in each panel, was chosen to bea disk with parameters n = 2 . ρ = 5.0 × − gcm − , i = 50 ◦ and R T = 25 . R ⋆ surrounding a central B2Vstar. Panel (a) shows the predicted lines obtained byvarying the inclination from 10 ◦ to 90 ◦ in steps of 20 ◦ .The profile goes from a singly-peaked,“wine bottle” pro-file at 10 ◦ , to a doubly-peaked profile for higher inclina- tions. While the profile at line centre does not dropbelow the continuum at i = 90 ◦ , it does strongly sat-isfy the shell-star definition of Hanuschik et al. (1996)in which the peak to line centre flux ratio exceeds 1.5.Absorption below the continuum would result for lessmassive disks. Panel (b) shows the result of varyingthe disk truncation radius; the flux increases stronglywith the disk size and the emission peak separation be-comes smaller for larger disks, as expected by the Huang(1972) relation. Panel (c) shows the effect of increas-ing the base density of the disk, ρ . The emission linestrength increases with increasing ρ up to the refer-ence value of 5 . × − gcm − , but then decreases forhigher densities. This occurs because the line profile isthe ratio of the total flux, line-plus-continuum, to thecontinuum flux alone. The line flux saturates with den-sity first, causing the ratio to then decrease with increas-ing ρ as the unsaturated continuum flux then increasesfaster. Finally, panel (d) shows the effect of varying thepower-law index of equatorial plane drop-off. The be-haviour reflects both the effect of increased density seenin panel (c) combined with a reduction in the emissionpeak separation since the disk density is concentratedcloser to the star for larger n .As noted in the previous paragraph, the H α line pro-files shown as relative fluxes, i.e. divided by the pre-dicted star+disk continuum, can show a more complexbehaviour than might be expected because the line andcontinuum fluxes often have a different dependence on,say, the disk density. To clarify this point, Figure 3shows the same line profiles as Figure 2 but plotted asabsolute fluxes in Janskys without continuum normal-ization. In panel (a) of Figure 3, the i = 90 ◦ profile isnow the weakest and the i = 0 ◦ profile, the strongest.The disk contribution to the normalizing continuum de-creases in proportion to the disk’s projected area, i.e.cos( i ), while for large inclinations, i ∼ ◦ , the stellarcontinuum can be significantly obscured by the circum-stellar disk. In panel (b), there is a strong dependenceof the line flux on R T , whereas the continuum flux isessentially independent of R T . This is because the con-tinuum forms very close to the central star (inside of the6 R ∗ , the smallest disk considered) whereas the opticallythick H α line emission forms over a much larger portionof the disk. In panel (c), the fluxes are now seen to scalein order with increasing ρ o , and the saturation of theline flux as compared to the continued increase in thecontinuum flux is clear. Finally in panel (d), the linefluxes are ordered with increasing flux with decreasing n , and the dependence of the continuum flux with thedensity-drop off in the disk is as expected.Figure 2 suggests that there is some degeneracy amongthe calculated H α line profiles, i.e. very similar relativeflux line profiles can result from different combinationsof the model parameters ( n, ρ o , R T , i ). To explore thisfurther, we have used the reference profile of Figure 2corresponding to ( n = 2 . , ρ = 5 × − gcm − , R T =25 R ∗ , i = 50 ◦ ) as a simulated observed profile andsearched the B2V profile library for the top nine closestmodel profiles as defined by the smallest average per-centage difference between the model and “observed”profile across the line: this figure-of-merit for the close-ness of two line profiles is further discussed in thenext section. Figure 4 shows the results. While allnine profiles share the same R T , there are small dif-ferences among the returned parameters, with n rang-ing between 2 . . ρ o , between 5 . × − and7 . × − g cm − , and i between 40 ◦ and 60 ◦ . The variations in the parameters are correlated: typically,smaller ρ o values are associated with larger n values.In the next section, we describe how we deal with thisdegeneracy in assigning model parameters to each star. RESULTS4.1.
Selection of the best disk models
The H α spectrum of each star in our sample was com-pared to the theoretical library for that spectral type us-ing a script that systematically finds the best match tothe observed profile. For each comparison, the percent-age flux difference between the model and observationwas averaged over the line to assign each comparison afigure-of-merit value (hereafter called F ), defined as F ≡ i = N X i =1 w i | F obs i − F mod i | F mod i (5)where F obsi is the observed relative line flux, F mod i isthe model relative line flux, w i is a weight, discussedbelow, and the sum is over all wavelengths spanningthe line. Several different weights were examined: uni-form weighting w i = 1, line-center weighting w i = | F mod i /F mod c − | , and uniform weighting but using thesum of the square of flux differences divided by flux.For each spectrum, we tested the second option first,but also calculated the quality of the fits for other op-tions as well, and by visual inspection we selected thebest F method to adopt for each spectrum (which maybe different for each star) to use in our results.Initially the best 50 matches out of the 1620 profilesusing the smallest F / F min values were identified, where F min is the minimum figure-of-merit of the best-fittinglibrary profile. We show an example for a B2 spectraltype in Figure 5 for the Be star HD58343. The upperleft panel shows the best 50 models sorted by F / F min (black dots) with the best 5 models in red, blue, green,yellow, and cyan colors corresponding to F / F min of1.00, 1.20, 1.30, 1.40 and 1.45, respectively. The best5 models are different in the disk density parameters,but they have the same inclination angle, i = 10 ◦ , andthe same disk truncation radius of R T = 25.0 R ⋆ for thisstar. The upper right panel shows models of H α lineprofiles corresponding to each respective color as wellas the observed profile shown in black. The main dif-ference between these models appears in the flanks ofthe emission line. Hanuschik (1986) classified typicalemission profiles seen in Be stars at different inclinationangles, where this particular “wine bottle shape” is usu-ally seen at low inclinations. Moreover, Hummel (1994)reproduced emission line profiles using a Keplerian diskmodel for an optically thick disk ( ∼ − g cm − ) andhe found for inclinations between 5 ◦ . i . ◦ , emissionline profiles show inflection flanks. For high inclination -500 -250 0 250 500012345 F / F c (1) -500 -250 0 250 500012345 (2) -500 -250 0 250 500012345 (3) -500 -250 0 250 500012345 F / F c (4) -500 -250 0 250 500012345 (5) -500 -250 0 250 500012345 (6) -500 -250 0 250 500 V (km/s) F / F c (7) -500 -250 0 250 500 V (km/s) -500 -250 0 250 500
V (km/s)
Figure 4 . The top nine most similar profiles in the B2V H α line library to the reference profile of Figure 2. The first panelis an identical match, whereas panels (2) through (9) represent increasing differences as measured by the average percentagedifference between the two profiles. The model parameters ( n, ρ o , R T , i ) are as indicated at the bottom of each panel, and thereference parameters are those given in panel 1. angles, i & ◦ , he noticed that a central depressionplus a double peak profile is generated due to the veloc-ity field present in the disk. The lower left panel showsthe behavior of log ρ vs F / F min where, in this partic-ular case, we can see that higher values of ρ dominate.The lower right panel is the same as the lower left panelexcept for n . In Figure 5, the best model (red color) iswell constrained by F / F min = 1.00, however we noticethat similar values of ρ combined with different valuesof n give us similar profiles of the emission line (for thesame inclination angle and same disk truncation radius).For this reason we consider a range of models within apercentage of F / F min as described in Subsection 4.3.4.2. Best fit models by visual inspection
We chose the best model by visual inspection of thecomparison plots between the models and the observa-tions; such plots are shown in Appendix A, and themodel parameters corresponding to this best fit are dis-played in Table 2 in the columns 4 to 8. Targets witha superscript a indicate an Hα absorption line in thatstar’s spectrum. In some cases, the script was not ableto suitably reproduce the core and wings of the emis-sion line profile (see discussion section 5.6 for possibleexplanations). However, we chose the fit that best rep-resents the wings of the line (instead of the core) andclassified them as poor fits. These cases are indicatedwith the superscript pf in the Table 2 and they are notconsidered in our analysis. Targets are sorted by HD number indicating the dateof the observation and the F / F min value of the chosenmodel. Table 2 also lists the H α equivalent width, EW,and the emission double-peak separation, ∆ V p , mea-sured from the observations. Some of the targets arerepresented by more than one observation due to vari-ability, and they show changes in the line profile (peakheight, violet-to-red peak ratio, etc). There are 22 suchvariable cases indicated by an asterisk symbol beside thestar name below the plot (14 of these are in emissionand 8 in absorption), and they were treated by keepingthe inclination angle constant for the system, and eachtime fit with different models. In our program starsthere are 15 Be stars with H α in absorption. We no-tice that in our sample all targets are confirmed as Bestars, so absorption profiles presented here are Be starsin disk-less phase or currently without a disk. We didnot include absorption profiles in our analysis, never-theless, our spectral library contains profiles with purephotospheric H α profiles. We display the values for sys-tems with absorption in Table 2 and in the plots in Ap-pendix B.We provide our results separately for the emission pro-files, absorption lines, and for the targets with poor fits.Overall, we have 42 Be stars with H α emission, 15 withabsorption profiles, and 6 with poor fits. The systemswith poor fits are displayed in Appendix C. Figure 5 . Example of the selection method. The results correspond to the Be star HD58343 with an inclination angle of i = 10 ◦ and R T = 25 R ⋆ . The first 5 best models are indicated with the F / F min value starting at 1.00 (red), 1.20 (blue), 1.30 (green),1.40 (yellow) and 1.45 (cyan) in all panels. Top left: F / F min of the 50 best models. Top right: H α line profiles models comparedwith the observation (black solid line). Bottom left: log ρ values for the best 50 models. Bottom right: n values for the best 50models. Distribution of the disk density parameters:representative models
In the previous section, we determined the best-fitdisk density models for each of our program stars withH α in emission. In this section, we wish to look at thedistribution of disk density parameters in this sample.From now on, every spectrum in emission for each target(if there is more than one) is considered by a separate,unique model. This give us a total of 61 emission mod-els. As we explained in the previous section, there is arange of models for each star that fit the observed pro-file nearly as well as the best-fit model selected by visualinspection. Thus for any given star, we can systemati-cally define a “set” of best fit parameters by selecting allmodels with F ≤ . F min resulting in N models be-ing selected. We note that by selecting a slightly largerrange of F , as Figure 5 demonstrates, the base den-sity and the exponent of the disk surface density span awide range of values especially for F ≥ .
50. To definerepresentative disk density parameters for each star, wechoose a weighted-average over the N selected models.For the disk parameter X , which could be ρ or n , etc.,we define < X > ≡ W N X i =1 w i X i , (6) where W ≡ P Ni =1 w i and the weights are chosen as w i ≡ ( F / F min ) m . (7)The index m was chosen to be equal to -10 so that sig-nificantly different weights are given to models rangingfrom 1 to 1.25, i.e. the weight assigned to F = 1 .
25 is1 . − ≈ n and ρ inEq. 1) of emission profiles are displayed in Figure 5. Themost frequent pairs are concentrated between < n > ≃ < ρ > ≃ (4 . − . × − g cm − or < log ρ > ≃ -10.4 to -10.2.We note that we detect emission profiles in the upperleft triangular region of Figure 6. With increasing valuesof the density exponent and decreasing base density, cor-responding to the lower right in Figure 6, it would be in-creasing difficult to detect emission due to reduced diskdensity. The lack of disk material for these stars made itimpossible to constrain our models as mentioned above Figure 6 . Distribution of the representative < n > and < log ρ > model values for systems with emission profiles. so we did not analyze any features for them. Moreover,some absorption profiles seemed to be pure photosphericlines, and some showed evidence of a possible forma-tion/dissipation disk phase (see HD33328’s spectrum,for example, in Appendix B).4.4. Distribution of disk mass and angular momentum
From each star’s fitted disk density parameters, wecan estimate the mass of the disk by integrating thedisk density law, Eq. 1, over the volume of the disk.For the radial extent of the disk, we chose the radiusthat encloses 90% of the total flux of the H α line in an i = 0 ◦ (i.e. face-on disk) image computed with BERAY .This measure of the H α disk size was used in favor ofthe fitted R T as the latter was computed on a verycoarse grid of only four values. To compute each diskmass, < M d > , the representative values of the diskparameters were used which included the models with F < . F min . In addition to disk mass, the repre-sentative value of the total angular momentum content, < J d > , of each disk was also computed, using the samedisk density parameters and assuming pure Keplerianrotation for the disk. Representative values of the diskmass and angular momentum in stellar units are dis-played in Table 2 in columns 12 and 13, respectively.Figure 7 shows the distribution of both representativevalues, disk mass and disk specific angular momentum, < J d > / < M d > , for early and late stellar types. Tonormalize by the stellar angular momentum, the centralstar was assumed to rotate as a solid body at 0 . v crit with the critical velocity computed using Eq. 4. (Seealso Section 5.3 for a discussion about the effect of thestellar rotation on J d ).The distribution of the disk mass in early types rangesfrom 1 . × − to 3 . × − M ⋆ (see top panel in Fig-ure 7). For late types, values range from 1 . × − to1 . × − M ⋆ . The mean disk mass for the early-typesis 3 . × − M ⋆ , while for the late-types, the mean disk Figure 7 . Distribution of the representative values of thedisk mass (top panel) and angular momentum of the disk(bottom panel) compared to the central star. mass is 9 . × − M ⋆ .The bottom panel in Figure 7 shows the distributionof the specific angular momentum < J d > / < M d > of the disk in units of stellar specific angular mo-mentum. For early types, the most frequent range is < J d > / < M d > ≃
150 - 200 and corresponds to a < J d > ∼ (1 . − . × − J ⋆ and a total mass of < M d > ∼ (3 . − . × − M ⋆ . For late types themost frequent values ranges from 100 to 150 correspond-ing to a range value of < J d > ∼ (1 . − . × − J ⋆ and < M d > ∼ (1 . − . × − M ⋆ . In general, latetypes have lower values of < M d > and < J d > incomparison with early types. It should be kept inmind that while the model disk masses vary overa large range (with M d /M ∗ spanning 1 . × − to 1 . × − ), the range of model specific angularmomentum is much less owing to the assumption ofKeplerian rotation. The minimum and maximumvalues of < J d > / < M d > in units of J ∗ /M ∗ are49 and 306, for a total variation of just over a factor of 6.4.5. Relation between H α equivalent width and diskmass Figure 8 . Equivalent widths of the H α emission line profilesas a function of mass. The relation between H α EW, and disk mass, < log M d > , separated by early and late-type Be stars,is shown in Figure 8. Negative values indicate that thenet flux of the emission line is above the continuum level.While there is an overall trend for the most massive disksto have the largest H α EW, there is an extremely largedispersion. This is not unexpected; for any given powerlaw index n in Eq. 1, the H α EW will first increase with ρ , reach a maximum, and then decline (see, for exam-ple, Sigut et al. 2015). This decline occurs because oncethe density becomes large enough, the continuum fluxfrom the disk at the wavelength of H α rises more quicklythan the line emission, so the equivalent width actuallydecreases with ρ and so does the corresponding diskmass. The exact value of ρ at which the H α equivalentwidth peaks is dependent on n ; therefore, in a mix ofmodels with differing ( ρ , n ), there will not be a directrelationship between disk mass and H α EW. Finally, wenote that the most massive disks and largest H α equiv-alent widths (absolute value) are found most frequentlyamong the early-type Be stars. DISCUSSION5.1.
Disk density
We found a distribution of the representative valuesof the disk density parameters for early and late spec-tral types, which are displayed in Figure 6. Early stellartypes cover values of < n > between 2.0 and 3.0, whilelate stellar types reach values near 3.7. It appears thathigher values of the power-law exponent are found forstars with lower effective temperature. This could ex-plain the small emission disks seen in late type starssince with increasing n , the disk density falls faster withdistance from the star. However, the average value ofthe representative values of the power-law exponent areessentially the same for early and late spectral types: < ¯ n early > = 2 . ± . < ¯ n late > = 2 . ± . BEDISK was com-pleted by Silaj et al. (2010). They created a grid of diskmodels for B0, B2, B5 and B8 stellar types at three in- clinations angles i = 20 ◦ , 45 ◦ and 70 ◦ for different diskdensities. They modeled H α line profiles of a set of 56Be stars (excluding Be-shell stars) and studied the ef-fects of the density and temperature in the disk. Theirresults show a higher percentage of models ranging ρ between 10 − and 10 − g cm − and a significant peakof n ∼ .
5, which is slightly larger than the values of n found in this study. We attribute this difference to thedifferent methods used to compute the H α line profile.Silaj et al. (2010) used BEDISK to compute the line in-tensity escaping perpendicular to the equatorial planein each disk annulus (i.e. rays for which i = 0 ◦ ). Theythen assumed that this ray was representative of otherangles considered, i = 20, 45 ◦ and 70 ◦ , and combinedthe i = 0 ◦ rays with the appropriate Doppler-shifts andprojected areas. Clearly this computation method be-comes limited with larger viewing angles. In contrast, BERAY , used here, does not make any of these approxi-mations, and it has been successfully used to model theH α lines of Be shell stars for which the inclination angleis large (Silaj et al. 2014b). Eight Be-shell spectra wereanalyzed and values for ρ between 10 − and 10 − gcm − and n between 2.5 and 3.5 were found.Touhami et al. (2011) used the assumption of anisothermal disk and the same density prescription asEquation 1 to reproduce the color excess in the NIR ofa sample of 130 Be stars. For the central star, they as-sumed an early-type star and adopted n = 3.0 for all themodels. They varied ρ between 10 − and 2.0 × − g cm − , which is very similar to our range of ρ varia-tion. They set the inclination angle at i =45 ◦ and 80 ◦ used an outer disk radius of ∼ R ⋆ . Otherstudies also use the same scenario for the density distri-bution, where the base density of the disk is found tobe between 10 − and 10 − g cm − and the power-lawexponent n is usually in the range 2 - 4 (for a review ofrecent results the reader is referred to the section 5.1.3of Rivinius et al. 2013b).Recently Vieira et al. (2017) determined the disk den-sity parameters ρ and n for 80 Be stars observed in dif-ferent epochs, corresponding to 169 specific disk struc-tures. They used the viscous decretion disk model to fitthe infrared continuum emission of their observations,using infrared wavelengths. They found that the ex-ponent n is in the range between 1.5 and 3.5, whereour most frequent values are between 2.0 and 2.5 forboth early and late spectral types. They also found ρ to range between 10 − and 10 − g cm − , whichcompares favorably with our average values of between(4.00-6.30) × − g cm − , again for both early andlate spectral types. Vieira et al. (2017) also establishedthat the disks around early-type stars are denser thanin late-type stars, consistent with our finding of moremassive disks for the earlier spectral types.0Finally, we also notice that our models sometimes donot reproduce the wings of our H α observations. Thismay reflect our assumption of a single radial power lawfor the equatorial density variation in this disk. Al-ternatively, for earlier spectral types, this may reflectneglect of non-coherent electron scattering in the for-mation of H α (Poeckert & Marlborough 1979). For ex-ample, Delaa et al. (2011) performed an interferometricstudy of two Be stars using a kinematic disk model ne-glecting the expansion in the equatorial disk. They wereable to fit the wings and the core of the H α emission lineby introducing a factor to estimate the incoherent scat-tering to their kinematic model.5.2. Size of the emission region
The outer extent of the disk considered in the mod-elling of this work was assumed to be one of four values,6.0, 12.5, 25.0 and 50.0 R ⋆ . From these values, the bestfitting models have a disk truncation radius of 25.0 R ⋆ followed by 50.0 R ⋆ . Nevertheless, as noted previously,a better estimate of the size of the H α emitting regionis the equatorial radius that contains 90% of the inte-grated H α flux in an i = 0 ◦ image computed with BERAY ,a quantity we denotes as R . We provide R values inthe column 11 on Table 2. These values, based on theintegrated flux from our models, could used by otherstudies to conveniently compare with our results.As an additional check, we compare our R disk sizeswith a measure based on the observed separation of theH α emission peaks, as first suggested by Huang (1972),and tailored to our model assumptions. The basic idea ofthis method is that the double-peak separation is set bythe disk velocity at it’s outer edge, which we will denote R H . If the observed peak separation is ∆ V p km s − , wehave 12 (cid:18) ∆ V p sin i (cid:19) = r GMR H , (8)assuming Keplerian rotation for the disk and correctingthe observed peak separation for the viewing inclination i . Hence, ∆ V p = 4 (cid:18) GMR H (cid:19) sin i . (9)In this work, we assumed that all Be stars rotate at 80%of their critical velocity; therefore, each star’s equatorialvelocity is V eq = 0 . s GM (3 / R ⋆ , (10)where R ⋆ is the stellar (polar) radius. Using this toeliminate ( GM ) from the previous equation and solvingfor the disk size we have R H R ⋆ = 9 . (cid:18) V eq sin i ∆ V p (cid:19) (11) ■■ ■■ ■■■ ■ ■■■ ■■ ■■ ■■■ ■ ■ (cid:1)(cid:2)(cid:3)(cid:4)(cid:5) ■ (cid:6)(cid:2)(cid:7)(cid:8) < R H > ( R (cid:1) ) < R > ( R ★ ) Figure 9 . Relation between the emitting size containing 90%of the integrated H α emission, R , and the emitting sizeobtained from Huang’s law, R H . A linear fit is representedby the solid line. As V eq sin i is the star’s v sin i value, we have approxi-mately R H R ⋆ ≈ (cid:18) v sin i ∆ V p (cid:19) . (12)This equation is very similar to the form used by manyauthors to derive approximate disk sizes from observedspectra (e.g. Hanuschik 1986; Hummel 1994). We notethat the way we use Eqn. 12 is slightly non-standard: wedo not measure v sin i directly from our spectra; instead,we adopt the v sin i of the best fit-model. As the H α profiles are essentially insensitive to v sin i , we are usingthe observed peak separation ∆ V p and the best-fit valueof i for the viewing inclination.The correlation between R H and R is displayed inFigure 9. For a few of our targets, we do not ob-tain a R H value because of a small ∆ V p or small in-clination where Huang’s law is not valid. The solidline indicates the linear fit over both early (blue cir-cles) and late (red squares) stellar types considering val-ues not larger than 50.0 R ⋆ and greater than 1 R ⋆ tobe consistent with the input values used in the BERAY model. The relation between the representative val-ues of the mentioned sizes is given by the linear equa-tion < R > = (0.53 ± < R H > + (3.45 ± r corr = 0.611 with confidence intervals calculated usinga bootstrapping method. We notice that the most fre-quent disk sizes values calculated by Huang’s relation forearly and late spectral types are concentrated less than5 R ⋆ and the values containing 90% of the H α flux forearly and late spectral types are concentrated between10 and 15 R ⋆ .Many other measurements of the Be star disk sizeshave been reported in the literature. Hanuschik (1986)measured the ∆ V p and the FWHM in the H α emissionline of 24 southern Be stars and using Huang’s law he1estimated an outer emitting size of ∼ R ⋆ . Similar val-ues were found by Slettebak et al. (1992) for 41 Be stars,they obtained an outer emitting size in the range ∼
7- 19 R ⋆ for the H α emission line. Using interferometrictechniques Tycner et al. (2005) studied the relation be-tween the total flux emission of H α line and the physicalsize of the emission region in 7 Be stars, finding for thefirst time a clear correlation between these both quan-tities. For early stellar types they found an extendedemitting size of ∼ R ⋆ while for stars withlower effective temperatures they found smaller valuesof ∼ R ⋆ to 14.0 R ⋆ (with an exception for ψ Per of ∼ R ⋆ ). An alternative way to estimate the emit-ting region based on the H α half-width at half-maximumwas proposed by Grundstrom & Gies (2006). They com-pared their results with the interferometric measures ofthe H α emitting size in the literature and they obtainedlower values between ∼ R ⋆ .Our very low values of R H from observed emissionprofiles (less than 1 R ⋆ and not considered in the anal-ysis) come from very large ∆ V p values. If the star isrotating near its critical rotation, the gas could accumu-late near the star and consequently the emission regionof the H α line could be of the order of a few stellar radii.Overall, our results for R T , either from the represen-tative models or from Huang’s law, show general agree-ment with previous works in the literature, giving highervalues for early stellar types and lower values for late-Betypes.5.3. Mass and angular momentum of the disk
In Section 4.4 we provided the range of the total diskmass and the total disk angular momentum for earlyand late stellar types. Our results gave us higher valuesof < J d > and < M d > for early types in comparisonwith late types. This was expected considering that latestellar types have, in general, smaller disks. Consideringthe whole sample without distinction between early andlate stellar types, we estimate that the total angularmomentum content in the disk is approximately 10 − times the angular momentum of the central star andthe mass of the disk is approximately 10 − times themass of the central star.Sigut et al. (2015) studied the disk properties of thelate Be shell star Omicron Aquarii (o Aqr, B7IVe)combining contemporaneous interferometric and spec-troscopy H α observations with near-infrared (NIR) spec-tral energy distributions. They compared the values ob-tained by each technique for different disk parameters.From H α spectroscopy, values of R T , M d and J d arehigher than those obtained from the NIR, while ρ and n are lower than NIR. From their results, the compar-ison between values obtained from spectroscopy, inter-ferometry and NIR spectral distributions, give similar or consistent values for M d and J d , but the disk densityparameters ( ρ , n ), showed in a range of values. As a re-sult, for o Aqr, Sigut et al. (2015) found values of J d ∼ × − J ⋆ and a total mass of M d ∼ × − M ⋆ .These values are consistent with our results in Figure 6,but are at lower end of the distribution for late stellartypes.As we mentioned earlier in Section 4.3, we distinguishour results between early (B0-B3) and late (B4-B9) typeBe stars. Recall that the parameters associated withthese stars are listed in Table 1. In order to study theeffects of the central star on the distributions of diskmass and angular momentum for early and late spectraltypes, we performed a two-tailed Kolmogorov-Smirnov(KS) test with the null hypothesis that both samplescome from the same distribution. Figure 10 shows thecumulative distribution functions (CDFs) for disk mass(upper panel) and total disk angular momentum perdisk mass (bottom panel). For disk mass, the maximumdistance, D m , between CDFs for early and late typesgives D m = 0 .
535 and considering a significance level at0.01, the critical value, D c , is 0.50 for the 61 emissionmodels. Hence we conclude that early and late sam-ples of disk mass come from different distributions. Thelargest value for the maximum distance between CDFsfor < J d > / < M d > , gives D m = 0 . v crit for all theluminosity classes in our models. Various studies haveattempted to determine these rates more precisely, witha consensus that they are rapid rotators, but it is stillnot clear how close to critical these rates are. Porter(1996) compared the observational distribution of asample of v sin i values of Be-shell stars (sin i ∼
1) witha theoretical distribution. He determined that these Be-shell stars rotate at 70%-80% of their critical rotation.Huang et al. (2010) studied the effect of the stellarrotation on the disk formation in “normal” B stars as afunction of stellar mass, by comparing with Be stars inthe literature. They found that the rotational velocityneeded to create a Be star varies strongly with thestellar mass. For low-mass B stars (less than 4 M ⊙ orlater than B6 V) the upper-rotational limit is very closeto the break-up velocity ∼ M ⊙ or earlier than B2 V) theupper-rotational limit is near to 0.63 v crit . To test thesignificance of our choice of 0.8 v crit on our angularmomentum distribution of our sample, we adopted bothlimiting values of the break-up velocity, 0.63 and 0.962 Figure 10 . Cumulative distribution functions for the massand total angular momentum of the disk. Blue (lower curve)and red (upper curve) colors represent early and late spec-tral types, respectively. Maximum distance between CDFsis indicated in each plot. The upper panel shows the CDFscomparison of both samples for the < log M d > and the lowerpanel shows the same, but for the < J d > / < M d > dis-tribution. A KS test demonstrated for both, disk mass anddisk angular momentum, that early and late samples comefrom different distributions at 1% level. for early and late stellar types, respectively. For earlytypes, the disk angular momentum is under-estimated( J ⋆ ∼ . / . ≃ .
3) by J disk /J ⋆ ∼ . / . ≃ < J d > / < M d > , respec-tively, we found a total range distribution between ∼ D m = 0 . M ∗ , R ∗ ), a portion of the variation in disk specificangular momentum must simply reflect the change of p ( MR ) ∗ ( J / M ) d i s k Late BeEarly BeLinear Fit
Figure 11 . The disk specific angular momentum of the Be-SOS sample stars versus the square root of the stellar masstimes the stellar radius. All qunatities are in solar units.The linear fit to the data has a correlation coefficient of r = +0 . stellar mass and radius with spectral type. To quan-tify this, we note that the disk specific angular mustscale as J/M ∼ r v K ( r ) where r is a characteristic ra-dius for the disk, and v K is the Keplerian velocity at thispoint. We may write this as J/M ∼ p GM ∗ R ∗ ( r/R ∗ )by introducing the stellar radius R ∗ . If the character-istic disk size ( r/R ∗ ) is constant with spectral type, wehave J/M ∼ √ M ∗ R ∗ . Figure 11 plots the disk spe-cific angular momentum found for our sample versus thequantity √ M ∗ R ∗ from Table 1. While there is a widedispersion, the linear trend is very clear, with a corre-lation coefficient of r = +0 .
63. Therefore, as expected,a significant portion of the variation in the disk specificangular momentum is due to the variation of the cen-tral star parameters via the overall scale of the disk’sKeplerian rotation. The large scatter about this lineartrend, typically a factor of 2 −
3, must then reflect thedifferent disk sizes and the distribution of the disk masswith radius, controlled mainly by the parameter n .5.4. Cumulative distribution of the inclination angles
An interesting consequence of the H α modelling isthat the inclination of the system can be determined.Figure 12 shows the CDF of the derived representa-tive values of the inclination angles versus the expected1 − cos( i ) distribution, assuming that the rotation axesare randomly distributed. Using a one-sample KS test,we find that our data do not follow the expected distri-bution. Defining the null hypothesis H : “the inclina-tion data comes from the 1 − cos( i ) distribution” and at We are thankful to the anonymous referee for suggesting thisline of reasoning. Figure 12 . Cumulative distribution of the representative in-clination angles (solid line) versus the expected distribution1 − cos( i ) (dashed line). A KS test showed that the sample isnot drawn from the expected distribution with a significancelevel of α =0.01. significance level α =0.01, the maximum distance, D m is0 . D c = 0 . D m > D c , H is rejected with a 1% level. This rejection, that ourinclination angles distribution is not random, is not sur-prising as the selection criteria for Be stars in surveys areoften biased against shell stars seen at high inclinations(Rivinius et al. 2006). This indeed seems to be the casefor our sample as the observed CDF of Figure 12 doesnot contain the expected fraction of high-inclination ob-jects; in particular, our sample has only 8 Be shell stars.5.5. Comparison with disk mass predictions of modelsof stellar evolution with rotation
In this section, we compare the disk mass distributionderived for the BeSOS sample as a function of spec-tral type with the predictions of Granada et al. (2013).While the hydrodynamical origin of the Be star diskejection mechanism(s) is unknown, there is a broad con-sensus that rapid stellar rotation, likely reaching thecritical value, is the ultimate driver for disk ejection inisolated Be stars (Rivinius et al. 2013a). Models of stel-lar evolution with rotation do predict episodes of criti-cal rotation during main sequence evolution due to theinternal transport of angular momentum. Under the as-sumption that disk ejection removes the excess surfaceangular momentum at critical rotation, and using theformalism of Krtiˇcka et al. (2011) for the ejected diskand its angular momentum transport, Granada et al.(2013) compute the main sequence evolution of B starswith masses from 2 to 9 M ⊙ and follow the required diskejections over the main sequence. While these modelsmake many assumptions (such as the details of the an-gular momentum transport and the initial ZAMS rota-tion rate and profile) which may not be realistic, theydo predict average disk masses as a function of spec- tral type. In Figure 13, we compare the disk massesobtained from the BeSOS survey stars with the predic-tions of Granada et al. (2013). Shown are the averagedisk mass, its 1 σ variation, and the minimum and max-imum disk masses, all for each spectral type. In theobservational sample, there is often a very wide rangeof disk masses at each spectral sub-type, typically atleast an order of magnitude. The observed average diskmass is always above the Granada et al. (2013) predic-tion, although the theoretical prediction typically fallswithin the observed range of disk masses. The predictedcurve shows an increasing trend with earlier spectraltype (or increased stellar mass). This is reflected in theBeSOS sample, although the number of stars with spec-tral types earlier than B2 is small (6 out of 63 stars).Also shown in the figure are the disk mass estimatesfor o Aqr (Sigut et al. 2015) and 48 Per (Grzenia et al.2017), based on modelling of the H α emission profile (asin the current work), coupled with simultaneous mod-eling of interferometric visibilities and near-IR spectralenergy distributions. These two, higher-precision diskmass estimates fall closer the predicted trend, althoughagain within the observed variation of the BeSOS sam-ple. We note that the current disk mass estimates arereally lower limits as we are sensitive only to the H α emitting gas. Given the uncertainties in the theoreticalmodeling, a more detailed a comparison may be unwar-ranted at this point. However, the distribution of Bestar disk masses may develop into a powerful diagnosticconstraint on rotating models of stellar evolution.5.6. Observed profiles with poor fits
Appendix C contains all the fits that we consider poorand do not reproduce the features in the observed H α line profiles. All targets are in emission and are early-type stars (between B0 and B2), with the exception ofHD83953, a B5V star. The shape of the emission profilesare very similar, showing wide profiles reaching velocitiesof the order of 600 - 700 km s − . Our methodology wasnot able to find a good agreement between the observa-tions and the models because these profiles do not havea symmetric central emission and are very wide. Forexample, in the entire sample of emission profiles (Ap-pendix A), only three stars are classified between B0 andB1.5 and these three are evolved: HD68980 (B1.5 III),HD143275 (B0.3 IV) and HD212571 (B1 III-IV), withvelocities between ∼
300 - 500 km s − , and with almostsymmetric profiles. On the other hand, we note thatHD35439 (B1 Vn), HD50013 (B1.5 V) and HD110432(B0.5 IVpe) show variation in the intensity peak, whereHD35439 shows a clear V/R variation. In the literaturetwo of the six stars are binary stars classified as a φ Per-type. These types of systems consist of an early B-typemain sequence star as the primary and a hot subdwarf4 * (Solar Masses)-11-10.5-10-9.5-9-8.5-8-7.5-7-6.5 l og ( M d / M * ) B0.51B13B1.52B218B39B46B50B67B72B88B95 B0.51B13B1.52B218B39B46B50B67B72B88B95 B0.51B13B1.52B218B39B46B50B67B72B88B95 BeSOS SampleGranada et al (2013) Predictiono Aqr (Sigut et al 2015)48 Per (Grzenia et al 2017)
Figure 13 . Comparison of the average H α disk masses found in the current work (shaded blue circles) as a function of stellarmass (bottom axis) or spectral type (top axis). The average decretion disk masses of Granada et al. (2013) (Table 6), predictedfrom stellar evolutionary models rotating at Ω crit = 0 .
95, is given by the red line. The 1 σ variation in the disk masses of thecurrent work are shown as the error bars (shown only if the number of sample stars at that spectra type is 3 or more), and theassociated triangles give the maximum and minimum disk masses found. The number directly below each spectra type is thenumber of stars in the BeSOS sample at that spectral type. The black square and black diamond are H α disk mass estimatesfor o Aqr (Sigut et al. 2015) and 48 Per (Grzenia et al. 2017), respectively. star as the secondary, both surrounded by an envelope.It is believed that the secondary at some time was a moremassive star that has lost a large percentage of its mass(by mass-transfer to the primary) leaving a hot heliumcore. The primary star is increasing its mass and angularmomentum, due to the mass-transfer interaction, as re-sult a large v sin i value is observed. HD41335 (HR2142)was recently highly studied by Peters et al. (2016), whoused a large set of ultraviolet and H α observations tomeasure radial velocities of the primary star to com-pute an orbit. For the system, Be + sdO, they find amass ratio M /M = 0 . ± .
02 and for the compan-ion they found a projected rotational velocity v sin i <
30 km s − , an effective temperature greater than 43 ± M ⊙ and radius greater than0.13 R ⊙ with a luminosity of log L/L ⊙ > .
7. To explainthe variations of the shell line absorption they proposeda circumbinary disk model, where the companion inter-sects with the boundaries of a gap in the disk of theprimary star causing a tidal wave. Thus the gas movingin these regions interacts with the dense gas producingshocks. Peters et al. (2016) state that this model couldoperate in other Be binaries only if the disk of the pri-mary star is massive enough with considerable densitynear the companion, if it has a high orbital inclination( i = 90 ◦ ) and if the companion has low mass to create awide gap so the gas can move across it. For HD41335 we have four observations between 2012 November and 2015February. The H α emission line does not show peak in-tensity variations in this period. From the HeI 6678 ˚Aline we cannot determine if variability is present. Thesecond φ Per-type star proposed is HD63462 (OmicronPuppis), a bright B1 IV type. This star shows intensityvariations in H α and from the V/R variation two quasi-period are obtained: 2.5 and 8 years. Koubsk´y et al.(2012) also found a particular variation in the HeI 6678˚A line. They described this variation as: “an emissioncomponent swaying from the red side of the profile to theblue one and back”. Their observations were obtainedbetween 2011 November and 2012 April. We inspectedour spectra, which are observed in 2013 February and2015 October, and while there are no variations in theH α emission line, the HeI 6678 ˚A line shows the samepattern described by Koubsk´y et al. (2012). A red peakis seen at 6682 ˚A in 2013 and a blue peak is seen at 6675˚A in 2015. Koubsk´y et al. (2012) estimated the period-icity of the radial velocities obtained at H α , HeI 6678 ˚Aand Paschen emission lines (P14, P13 + Ca II and P12)determining an orbital period of 28.9 days. They alsofound a relation between the velocity and the emissionintensity of the HeI line, as the velocity increases theintensity is strongest and vice versa. They did not findany direct evidence of spectral lines from the hot subd-warf companion, and for this reason they suggest that5Omicron Puppis is a Be + sdO type. φ Per-type systemscould potentially test the hypothesis that Be stars couldbe formed by binary interactions, however these systemsare difficult to detect due to the faint companion and forthis reason observations in the ultraviolet range are re-quired. The disk density parameters for the best-fittingmodels for all of these objects were not included in ouranalysis. CONCLUSIONSWe modeled the observed H α line profiles of 63 Bestars from the BeSOS catalogue. Compared to syntheticlibraries computed with the BEDISK and
BERAY codes,good matches were found for 57 objects, 42 with H α inemission and 15, in absorption. The remaining 6 objectshad poor fits that did not reproduce the features of theemission line. From the 41 H α emission line objects,we modeled each available observational epoch giving atotal of 61 matched line profiles. Our results were usedto constrain to the range of values for the base densityand power-law exponent of the disk density model givenin Eq. 1 for all 61 observations. We determined thebest fit model for each observation which are displayedin Table 2 and in the corresponding plots shown in theAppendix section. Moreover, we obtained a distributionof the best representative models with F ≤ . F min onwhich we base our average results.The most frequent values for the base density are be-tween < log ρ > ∼ -10.4 and -10.2 and for the power-law exponent are between < n > ∼ α disk, thesample distribution for disk mass and disk angular mo-mentum (assuming Keplerian rotation for the disk) werefound, with typical values of < M d > / < M ⋆ > ∼ − and < J d > / < J ⋆ > ∼ − . We find that diskmass and angular momentum distributions were differ-ent between early (B0 - B3) and late (B4 - B9) spectraltype at 1% level of significance. Finally, we compareour disk masses as a function of spectral type in Fig-ure 13 with the theoretical predictions of Granada et al.(2013) based on stellar evolution calculations incorpo-rating rapid rotation. Our average H α disk masses(which are lower limits to the total disk masses) arealways larger than the theoretical predictions, althoughthe variation at each spectral type is quite large, typi-cally more than an order of magnitude.Our estimates for the H α disk radius ( R , the ra-dius that encloses 90% of the line emission) are com-pared to Huang’s well-known law relating the disk sizeto the double-peak separation in the profile. A lin-ear correlation is found with a correlation coefficient of r corr = 0 . V p and/or smallest v sin i values from the mod- els used in the Huang’s relation. The concentration ofsuch values is less than 5 R ⋆ for Huang’s law and between15 and 20 R ⋆ for R and is dominated by early-typeBe stars. Several studies about similarities and differ-ences between early and late type Be stars have beencarried out recently. Kogure & Leung (2007) suggestedthat early-type Be stars have more extended envelopescompared with the late-type Be stars from their analy-sis of H α equivalent widths by spectral type consistentwith the findings presented here.Finally we find that the derived inclination anglesfrom the H α profile fitting do not follow the expectedrandom distribution. This is attributed to the under-representation of Be shell stars in the BeSOS survey.Numerous studies have found that the mean v sin i val-ues increase for late-type main sequence Be stars (e.g.Zorec & Briot 1997; Yudin 2001; Cranmer 2005). In ourcase, we fixed the rotation of the star to be 80% of thecritical value, consistent with Chauville et al. (2001).Clearly, the study of Be stars is still in continuous devel-opment. In future we plan to re-analyze the sample byincluding more lines in the visible range (i.e., H β , H γ ),as well as investigating the spectral energy distributionsand v sin i values.The authors would like to thank the anonymous ref-eree for insightful questions and suggestions that helpedimprove this paper. This research was supported by theDFATD, Department of Foreign Affairs, Trade and De-velopment Canada, International scholarship programChile-Canada; C.A acknowledges Gemini-CONICYTproject No.32120033, Fondo Institucional de Becas FIB-UV, Becas de Doctorado Nacional CONICYT 2016 andPUC-observatory for the telescope time used to ob-tain the spectra presented in this work. C.E.J andT.A.A.S acknowledge support from NSERC, NationalSciences and Engineering Research Council of Canada.S.K thanks the support of Fondecyt iniciaci´on grant N11130702. C.A, S.K and M.C acknowledges the supportfrom Centro de Astrof´ısica de Valpara´ıso.6 Table 2 . Summary of the best fit model by visual inspection and representative models ( F / F min ≤ Best model Observation Representative modelHD Sp.T date F / F min i n ρ R T EW ∆ V p < R > < M d /M ⋆ > < J d /J ⋆ > (yyyy-mm-dd) (deg) (g cm − ) ( R ⋆ ) (˚A) (km s − ) ( R ⋆ )(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)10144 B6 Vpe 2012-11-13 - - - - - -0.8 719.5 - - -2013-01-18 1.2 70 3.0 7.5e-12 6.0 -0.9 485.1 10.4 1.8e-11 8.5e-102013-07-24 1.0 70 3.5 2.5e-11 6.0 -0.5 361.8 13.5 2.8e-10 2.2e-082013-10-29 1.0 70 4.0 7.5e-11 6.0 -1.2 353.6 14.6 4.0e-10 3.0e-082014-01-29 1.0 70 2.0 5.0e-11 6.0 -1.7 345.3 12.9 3.3e-10 2.3e-0833328 a B2 IVne 2012-11-13 1.0 60 4.0 7.5e-12 25.0 1.7 703.0 - - -2013-01-18 1.0 60 4.0 2.5e-12 6.0 0.1 534.5 - - -2015-02-25 1.0 60 4.0 7.5e-12 25.0 1.9 657.8 - - -35165 B2 Vnpe 2014/2015 blue 1.0 80 2.0 5.0e-11 12.5 -12.1 283.7 45.0 8.4e-10 1.0e-072014/2015 red 1.1 80 2.0 1.0e-11 6.0 -12.8 312.4 45.0 8.4e-10 1.0e-0735411 a B1 V + B2 2012-11-13 1.0 80 4.0 7.5e-12 25.0 2.15 0 - - -2013-01-18 1.0 80 3.5 1.0e-12 50.0 3.1 0 - - -2013-02-26 1.0 80 4.0 1.0e-12 6.0 3.0 0 - - -2015-02-25 1.0 80 4.0 7.5e-12 25.0 2.4 0 - - -35439 pf B1 Vpe 2012-11-13 1.0 50 2.5 2.5e-11 50.0 -27.7 209.7 - - -2013-01-18 1.0 50 2.5 2.5e-11 50.0 -28.6 185.0 - - -2013-02-26 1.0 50 2.5 2.5e-11 50.0 -30.2 193.2 - - -2015-02-25 1.0 70 2.0 5.0e-12 50.0 -25.6 152.1 - - -37795 B9 V 2012-11-13 1.0 40 3.0 2.5e-10 50.0 -9.3 106.9 46.4 3.8e-10 4.5e-082013-01-18 1.0 40 3.0 2.5e-10 50.0 -9.7 82.2 53.3 4.5e-10 5.9e-082015-02-25 1.0 40 3.0 2.5e-10 50.0 -9.0 82.2 50.2 4.0e-10 5.4e-0841335 pf B2 Vne 2012-11-13 1.0 80 2.0 5.0e-12 25.0 -25.9 152.1 - - -2013-01-18 1.0 80 2.0 5.0e-12 25.0 -27.1 111.0 - - -2013-02-26 1.0 80 2.0 5.0e-12 25.0 -26.7 115.1 - - -2015-02-27 1.0 80 2.0 5.0e-12 25.0 -26.9 115.1 - - -42167 B9 IV 2014-01-30 1.0 70 2.0 2.5e-10 6.0 -2.0 160.3 32.6 5.8e-10 5.3e-082015-02-25 1.0 70 2.0 2.5e-10 6.0 -1.7 209.7 32.6 5.8e-10 5.3e-0845725 B4 Veshell 2015-02-26 1.0 70 2.0 5.0e-12 25.0 -30.2 164.4 87.4 2.1e-09 3.7e-0748917 B2 IIIe 2014-01-29 1.0 60 2.0 5.0e-12 25.0 -24.6 86.3 103.7 3.3e-09 6.3e-072015-10-23 1.0 60 2.0 5.0e-12 25.0 -27.1 90.4 103.7 3.3e-09 6.3e-0750013 pf B1.5 Ve 2012-11-13 1.0 50 2.5 2.5e-11 50.0 -24.1 94.6 - - -2013-02-26 1.0 60 2.0 5.0e-12 50.0 -22.2 98.7 - - -2014-03-21 1.0 50 2.5 2.5e-11 50.0 -24.0 65.8 - - -2015-02-25 1.0 60 2.0 5.0e-12 50.0 -25.2 65.8 - - -2015-10-23 1.0 60 2.0 5.0e-12 50.0 -28.9 74.0 - - -52918 a B1 V 2014-01-29 1.0 60 4.0 1.0e-11 25.0 1.37 678.4 - - -56014 B3 IIIe 2014-01-29 red 1.0 80 2.5 1.0e-11 6.0 -2.0 390.6 23.4 3.0e-10 2.7e-082014-01-29 blue 1.0 80 2.5 5.0e-12 12.5 -2.0 390.6 23.4 3.0e-10 2.7e-0856139 B2 IV-Ve 2013-02-27 1.0 30 2.0 2.5e-11 25.0 -20.7 0 105.5 9.1e-09 1.7e-062015-02-27 1.0 30 2.0 2.5e-11 25.0 -16.7 0 105.5 9.1e-09 1.7e-062015-11-14 1.0 30 2.0 5.0e-11 25.0 -10.2 0 73.7 1.4e-08 2.3e-0657150 B2 Ve + B3 IVne 2014-01-29 1.0 60 2.0 5.0e-12 50.0 -30.2 0 189.2 6.8e-09 1.8e-0657219 a B3 Vne 2014-01-29 1.0 80 3.5 7.5e-12 25.0 2.3 0 - - -58343 B2 Vne 2013-02-27 1.0 10 2.5 7.5e-11 25.0 -7.2 0 71.7 7.7e-09 1.2e-06
Table 2 continued Table 2 (continued)
Best model Observation Representative modelHD Sp.T date F / F min i n ρ R T EW ∆ V p < R > < M d /M ⋆ > < J d /J ⋆ > (yyyy-mm-dd) (deg) (g cm − ) ( R ⋆ ) (˚A) (km s − ) ( R ⋆ )(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)58715 B8 Ve 2013-02-27 1.0 50 3.5 2.5e-10 25.0 -7.2 127.4 35.6 1.2e-09 1.2e-072015-02-25 1.0 50 3.5 2.5e-10 25.0 -7.3 115.1 35.6 1.2e-09 1.2e-0760606 B2 Vne 2012-11-13 1.0 70 3.0 1.0e-10 25.0 -21.3 143.9 62.2 3.2e-09 5.1e-072013-01-19 1.0 70 3.0 1.0e-10 25.0 -22.8 152.1 62.2 3.2e-09 5.1e-072013-02-26 1.0 70 3.0 1.0e-10 25.0 -18.9 135.7 62.2 3.2e-09 5.1e-0763462 pf B1 IVe 2013-02-27 1.0 70 2.0 5.0e-12 12.5 -10.9 94.6 - - -2015-10-23 1.0 50 2.5 1.0e-11 50.0 -11.6 94.6 - - -68423 B6 Ve 2014-03-21 1.0 10 2.0 2.5e-10 50.0 -6.2 49.3 49.1 1.1e-08 1.4e-0668980 B1.5 III 2013-02-27 1.0 40 2.0 5.0e-12 50.0 -23.2 41.1 214.2 1.1e-08 2.9e-062015-02-26 1.0 40 2.5 2.5e-11 50.0 -19.6 45.2 130.2 1.3e-08 3.0e-0671510 a B2 Ve 2014-01-29 1.0 70 3.0 2.5e-12 12.5 2.6 0 - - -2014-03-19 1.0 70 4.0 7.5e-12 6.0 2.6 0 - - -2015-02-26 1.0 70 2.0 1.0e-12 6.0 2.25 0 - - -75311 B3 Vne 2014-03-19 1.0 60 3.0 7.5e-11 50.0 -0.6 287.8 26.0 2.8e-09 2.7e-0778764 B2 IVe 2014-01-30 1.0 40 2.5 7.5e-11 12.5 -4.8 131.6 42.1 3.6e-09 5.3e-072014-03-19 1.0 40 2.5 7.5e-11 12.5 -4.2 139.8 42.1 3.6e-09 5.3e-0783953 pf B5V 2013-02-27 1.0 70 3.0 1.0e-10 50.0 -20.6 160.3 - - -89080 B8 IIIe 2013-02-27 1.1 70 2.0 2.5e-12 25.0 -7.2 164.4 35.6 8.8e-10 8.8e-082014-05-09 1.1 70 2.0 2.5e-12 25.0 -7.0 143.9 35.6 8.8e-10 8.8e-0889890 a B3 IIIe 2014-01-30 1.0 70 3.0 5.0e-12 50.0 1.7 0 - - -2014-03-19 1.0 80 3.5 7.5e-12 25.0 2.3 0 - - -2015-02-27 1.0 80 3.0 5.0e-12 50.0 1.7 0 - - -2015-05-06 1.0 70 3.5 7.5e-12 25.0 1.9 0 - - -91465 B4 Vne 2013-02-26 1.0 70 2.0 5.0e-12 25.0 -28.4 131.6 82.4 2.4e-09 3.8e-072014-05-09 1.0 70 2.0 1.0e-10 50.0 -24.9 135.7 63.1 2.1e-09 3.1e-072015-02-27 1.0 70 2.0 1.0e-10 50.0 -22.9 94.6 63.1 2.1e-09 3.1e-072015-05-06 1.1 70 2.0 5.0e-12 25.0 -30.4 98.7 97.4 2.9e-09 5.0e-0792938 a B4 V 2014-01-30 1.0 80 4.0 7.5e-12 12.5 2.4 0 - - -2015-02-27 1.0 80 4.0 7.5e-12 12.5 2.6 0 - - -2015-05-06 1.0 80 4.0 7.5e-12 12.5 4.3 0 - - -93563 B8.5 IIIe 2014-01-30 1.2 70 3.5 1.0e-10 50.0 -8.1 296.0 22.5 6.3e-11 5.0e-09B8.5 IIIe 2015-05-06 1.2 70 3.5 1.0e-10 50.0 -9.7 135.7 22.5 6.3e-11 5.0e-09102776 B3 Vne 2014-01-30 1.0 60 3.0 5.0e-11 50.0 -12.2 98.7 52.1 9.6e-10 1.2e-072014-03-19 1.0 60 2.5 1.0e-11 50.0 -9.7 185.0 90.6 9.4e-10 1.7e-072015-02-27 1.1 60 2.0 2.5e-12 25.0 -7.1 185.0 85.5 1.3e-09 2.3e-072015-05-06 1.0 60 2.0 2.5e-12 50.0 -7.4 119.2 91.4 2.0e-09 3.5e-07103192 B9 IIIsp 2014-03-19 1.2 60 3.0 7.5e-12 50.0 -1.4 259.0 13.4 4.6e-10 3.4e-082015-02-26 1.2 60 3.0 7.5e-12 50.0 1.2 263.1 13.4 4.6e-10 3.4e-082015-05-07 1.2 60 3.0 7.5e-12 50.0 2.0 234.3 13.4 4.6e-10 3.4e-08105382 a B6 IIIe 2014-01-30 1.0 80 3.5 5.0e-12 25.0 1.3 0 - - -2015-05-07 1.0 80 3.0 2.5e-12 25.0 2.5 0 - - -105435 B2 Vne 2014-01-30 1.0 60 2.5 1.0e-10 50.0 -37.0 0 157.9 1.0e-08 2.3e-062015-02-25 1.0 60 2.0 5.0e-12 50.0 -33.1 0 198.5 9.1e-09 2.4e-062015-05-06 1.0 60 2.0 5.0e-12 50.0 -31.0 0 198.5 9.1e-09 2.4e-06107348 B8 Ve 2014-01-30 1.0 50 3.0 2.5e-10 25.0 -10.2 82.2 30.1 1.5e-09 1.5e-072015-05-07 1.1 50 3.0 5.0e-11 25.0 -6.9 123.3 37.4 1.0e-09 1.0e-07110335 B6 IVe 2014-01-30 1.1 70 3.0 2.5e-10 25.0 -19.3 69.9 55.8 2.1e-09 2.8e-07
Table 2 continued Table 2 (continued)
Best model Observation Representative modelHD Sp.T date F / F min i n ρ R T EW ∆ V p < R > < M d /M ⋆ > < J d /J ⋆ > (yyyy-mm-dd) (deg) (g cm − ) ( R ⋆ ) (˚A) (km s − ) ( R ⋆ )(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)2015-05-07 1.1 70 3.0 2.5e-10 25.0 -18.3 90.4 55.8 2.1e-09 2.8e-07110432 pf B0.5 IVpe 2014-01-31 1.0 80 2.0 7.5e-12 25.0 -30.2 197.3 - - -2015-05-06 1.0 80 2.0 7.5e-12 25.0 -28.6 102.8 - - -112078 a B3 Vne 2014-01-31 1.0 30 2.5 1.0e-12 50.0 2.2 0 - - -120324 B2 Vnpe 2014-01-31 1.0 50 2.0 5.0e-11 25.0 -14.8 74.0 72.8 7.6e-09 1.2e-062015-02-25 1.0 50 2.5 7.5e-11 25.0 -18.6 66.8 78.4 3.9e-09 5.7e-072015-05-06 1.1 50 2.5 5.0e-11 25.0 -21.0 0 97.0 4.0e-09 7.2e-07124195 a B5 V 2014-03-21 1.0 70 4.0 7.5e-12 50.0 2.2 0 - - -124367 B4 Vne 2014-01-31 1.1 70 2.0 5.0e-12 50.0 -38.9 98.7 21.7 1.4e-09 1.2e-07124771 a B4 V 2014-03-21 1.1 70 4.0 5.0e-12 6.0 2.1 0 - - -127972 B2 Ve 2014-01-31 1.0 80 2.5 7.5e-12 12.5 -5.3 259.0 26.9 3.0e-10 2.8e-082015-02-25 1.0 80 2.5 7.5e-12 12.5 -3.7 349.5 26.9 3.0e-10 2.8e-082015-07-15 1.0 80 2.5 7.5e-12 12.5 -2.9 365.9 26.9 3.0e-10 2.8e-08131492 B4 Vnpe 2014-03-21 1.0 70 3.0 1.0e-11 6.0 -0.9 489.2 21.7 1.4e-09 1.2e-07135734 B8 Ve 2013-07-24 1.1 60 2.0 2.5e-12 25.0 -7.0 168.6 40.2 1.1e-09 1.2e-072015-02-25 1.1 60 2.5 1.0e-11 25.0 -8.3 135.7 40.2 1.1e-09 1.2e-072015-07-15 1.1 60 2.5 1.0e-11 25.0 -8.2 152.1 40.2 1.1e-09 1.2e-07138769 a B3 IVp 2013-07-24 1.0 80 2.5 1.0e-12 12.5 4.2 0 - - -2015-07-15 1.0 80 3.5 5.0e-12 50.0 3.1 0 - - -142184 a B2 V 2013-07-24 1.0 60 4.0 5.0e-12 12.5 2.0 698.9 - - -2014-03-21 1.0 80 4.0 2.5e-12 6.0 3.5 698.9 - - -143275 B0.3 IV 2014-03-19 1.1 20 3.0 7.5e-11 50.0 -11.3 0 143.6 1.0e-07 3.1e-05148184 B2 Ve 2013-07-24 1.0 30 2.0 1.0e-11 25.0 -35.9 0 152.8 2.4e-08 5.5e-062015-02-25 1.0 30 2.0 1.0e-11 25.0 -34.9 0 152.8 2.4e-08 5.5e-062015-05-06 1.0 30 2.0 1.0e-11 25.0 -39.9 0 152.8 2.4e-08 5.5e-06157042 B2 IIIne 2013-07-24 1.1 70 2.5 2.5e-11 12.5 -20.2 160.3 55.0 1.6e-09 2.1e-072015-05-06 1.1 70 2.5 2.5e-11 12.5 -22.9 213.8 55.0 1.6e-09 2.1e-07158427 B2 Ve 2015-05-06 1.0 70 2.0 5.0e-12 50.0 -36.1 32.9 188.1 7.5e-09 2.0e-06167128 B3 IIIpe 2013-07-24 1.0 40 3.5 7.5e-11 50.0 -3.8 164.4 32.6 3.1e-09 3.9e-07205637 B3 V 2012-11-14 1.1 89 2.0 1.0e-11 6.0 -1.9 337.1 27.3 8.8e-10 8.4e-08209014 B8 Ve 2013-07-24 1.0 89 2.0 2.5e-10 12.5 -8.0 242.6 29.3 1.1e-09 1.1e-072015-10-23 1.0 89 2.0 2.5e-10 12.5 -8.5 209.7 29.3 1.1e-09 1.1e-07209409 B7 IVe 2012-11-13 1.0 80 2.0 5.0e-12 25.0 -18.9 143.9 58.2 7.9e-10 1.1e-072015-10-24 1.2 80 2.0 5.0e-12 50.0 -20.0 152.1 55.6 2.0e-09 2.4e-07212076 B2 IV-Ve 2012-11-13 1.3 30 2.0 2.5e-11 25.0 -18.2 28.8 85.1 3.1e-09 4.8e-072015-10-23 1.0 30 2.0 2.5e-12 50.0 -14.3 24.7 118.2 6.8e-09 1.2e-06212571 B1 III-IV 2012-11-14 1.1 60 2.5 1.0e-11 12.5 -7.7 283.7 84.1 9.3e-10 1.5e-072013-07-24 1.1 60 2.5 7.5e-12 12.5 -4.0 304.2 74.4 6.4e-10 9.6e-082015-10-24 1.0 60 2.5 1.0e-11 12.5 -10.7 209.7 83.9 1.6e-09 2.6e-07214748 B8 Ve 2012-11-15 1.3 50 3.5 2.5e-10 12.5 -4.0 131.6 28.7 2.8e-09 2.2e-072013-07-24 1.3 50 3.5 2.5e-10 12.5 -4.9 123.3 28.7 2.8e-09 2.2e-072015-07-15 1.3 50 3.5 2.5e-10 12.5 -5.7 123.3 28.7 2.8e-09 2.2e-072015-10-24 1.3 50 3.5 2.5e-10 12.5 -5.7 135.7 28.7 2.8e-09 2.2e-07217891 B6 Ve 2012-11-13 1.0 40 2.0 5.0e-11 50.0 -21.1 0 94.1 1.7e-08 2.9e-062013-07-25 1.0 40 2.0 5.0e-11 50.0 -22.8 0 94.1 1.7e-08 2.9e-06219688 a B5 V 2015-10-24 1.0 50 3.0 2.5e-12 12.5 2.6 0 - - -221507 a B9.5 IIIpHgMnSi 2013-07-24 1.0 89 3.0 2.5e-12 6.0 2.5 0 - - -
Table 2 continued Table 2 (continued)
Best model Observation Representative modelHD Sp.T date F / F min i n ρ R T EW ∆ V p < R > < M d /M ⋆ > < J d /J ⋆ > (yyyy-mm-dd) (deg) (g cm − ) ( R ⋆ ) (˚A) (km s − ) ( R ⋆ )(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)2015-07-15 1.0 89 3.0 2.5e-12 6.0 3.5 0 - - -2015-10-23 1.0 89 3.0 2.5e-12 6.0 4.1 0 - - -224686 B8 Ve 2012-11-13 1.0 80 2.0 2.5e-10 6.0 -2.0 275.4 28.7 2.8e-9 2.8e-07 a Absorption profiles pf Poor fit − Not agreement model
Note —The information displayed in this table are for the best (visual inspection) and representative ( F / F min ≤ REFERENCES
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APPENDIX A. EMISSION PROFILESObserved emission line profiles from our program stars (black lines) shown with the best-fit model (red dashed lines).Variable stars in our sample are indicated an asterisk symbol beside the star name.1
HD10144* HD35165* HD37795HD42167 HD45725 HD48917HD56014* HD56139* HD57150 HD58343 HD58715 HD60606HD68423 HD68980* HD75311HD78764 HD89080 HD91465* HD93563 HD102776* HD103192HD105435* HD107348* HD110335HD120324* HD124367 HD127972 HD131492 HD135734* HD143275HD148184 HD157042 HD158427HD167128 HD205637 HD209014 HD209409* HD212076* HD212571*HD214748 HD217891 HD224686 B. ABSORPTION PROFILESThe same as Appendix A except for absorption profiles.6