---
author:
- 'G. Catanzaro[^1]'
date: 'Received 10 September 2012 / Accepted 7 December 2012 '
title: 'Spectroscopic atlas of H$\alpha$ and H$\beta$ in a sample of northern Be stars[^2]'
---

[Be stars are fast-rotating early-type emission line stars. It is generally assumed that observed emission is generated in a rotating disk-like envelope, as supported by the observed correlation between the stellar projected rotational velocity $v \sin i$ and the width of the emission lines. Then, high-resolution spectroscopic observations of Balmer lines profiles play an important role in putting constraints on Be stars modeling.]{} [We present Balmer lines spectroscopy for a sample of 48 Be stars. For most of them, H$\alpha$ and H$\beta$ have been observed more than two times, in a total period spanning almost two years between 2008 and 2009.]{} [Spectral synthesis of the H$\alpha$ profile was performed following two steps: photospheric contribution was computed by using Kurucz’s code ATLAS9 and SYNTHE, and disk emission was derived by the approach of Hummel & Vrancken (2000, A&A, 302, 751).]{} [For 26 out of 48 stars, a modeling of the total H$\alpha$ emission, i.e. photospheric absorption plus disk net emission, has been attempted. By this modeling we derived an estimation of the disk radius, as well as the inclination angle between the rotational axis with line of sight and the base density at the stellar equator. For the stars observed more than once, we also discuss the variability of H$\alpha$ and H$\beta$ for what concerns both the equivalent width and the spectral profile. We found 16 stars with variable equivalent width and 7 stars with clear signs of profile variations.]{} [For all the stars in our sample, we derive all the fundamental astrophysical quantities, such as, effective temperature, gravity, and projected rotational velocity. We found 13 stars whose equivalent width is variable with a confidence level greater than 80$\%$ and 7 object for which spectral profiles show change with time. According to the commonly used classification scheme, we classified 16 stars as belonging to class 1, 13 to class 2, 11 are shell stars, 6 objects do not show net emission, and 2 stars display transitions from class 1 and 2. For the class 1 stars, we confirm the correlation between $v \sin i$ and peak separation. Concerning the geometry of the disk, we derived the base density at the stellar equator, the radius, and the inclination angle between rotational axis and line of sight. The maximum concentration of stars occurs for disk dimensions ranging in the interval of 6 to 8 stellar radii and for inclination angles going from 23$^\circ$ to $35^\circ$.]{}

Introduction
============

Classical Be stars are early-type B-type stars whose spectra have one or more emission lines in the Balmer series. In particular, the H$\alpha$ emission line is typically the dominant feature in the spectra of such stars, and many authors have modeled H$\alpha$ line profiles to understand the Be star phenomenon better.

The emission lines observed in the spectra are explained in terms of the recombination that occurs in a flattened circumstellar disk, according to the widely accepted model first proposed by Struve ([@struve31]). The disk is a decretion disk; i.e., the source of the disk material is the central star, generated by the equatorial flow of stellar material. One of the key factors in creating the disk is supposed to be the very high value of rotational velocity. In fact, Be stars are known to have higher rotational velocities than a sample of normal B-type stars. From statistical considerations on the $v \sin i$ distribution among Be stars, Porter ([@porter96]) estimated that Be stars rotate at a equatorial velocity equal to 80 $\%$ of the critical rotation velocity:

$$v_{\rm eq}\,=\,0.8\,\sqrt{\frac{GM_*}{R_*}} .$$

The observed emission lines take a variety of shapes, which following the scheme proposed by Hanuschik ([@hanu96]), range from wine bottle profiles, singly or double-peaked profiles, to shell spectra, when the central absorption must extend below the stellar continuum flux. The various shapes are explained as a dependency of $i$, the inclination angle of the star’s rotation axis to the observer’s line of sight. In particular, shell profiles occur only when the disk is viewed equator-on ($i\,=\,90^\circ$), while the single peak and wine bottle occur only for near pole-on ($i\,=\,0^\circ$) viewings, and double-peaked profiles occur at mid-inclination angles.

Double-peaked profiles have been observed both symmetric, which are the two peaks have the same intensity, and asymmetric, the peaks have different height over the continuum level. The current theory is that asymmetry arises from one-armed density waves in the circumstellar disk, which is also known as the global disk oscillation model. In this model, a one-armed oscillation mode is superposed on an unperturbed, axisymmetric disk (Okazaki, [@okazaki97]). Another aspect of Be stars emission is their variability. For example, about one third of all double-peaked profiles exhibit changing asymmetry, with the so-called violet-to-red ratio (V/R) being cyclically variable on timescales of years to decades.

Observations in different spectral regions help astronomers probe different regions of the stellar disk and then put constraints on modeling these stars. For example, recently Meilland et al. ([@meilland07]) have used VLTI/AMBER to observe $\alpha$ Arae in the Br$_\gamma$ line, which was constrained very strongly the rotational property of its disk, concluded that its rotation is purely Keplerian.

In this paper we present an atlas of observed H$\alpha$ and H$\beta$ spectral lines in a sample of bright Be stars. We payed particular attention to modeling the H$\alpha$ profile and to the time variability of Balmer lines profiles.

      HD     Spec.         b-y    m$_1$    c$_1$     H$\beta$   T$_{\rm eff}$ (K)     
  -------- ---------- ---------- ------- ---------- ---------- ------------------- -- --
      6811 B7Ve            0.006  0.082    0.697      2.676           12600           
     10516 B2Vep               –    –        –          –             25410           
     11415 B3III        $-$0.059  0.094    0.419      2.665           15680           
     37202 B2IVp           –        –        –          –             21480           
     37490 B3III        $-$0.016  0.060    0.184      2.576           20200           
     41335 B2Vne           0.031  0.020    0.002      2.463           20230           
     43285 B6Ve         $-$0.055  0.104    0.481      2.670           14840           
     44458 B1Vpe               –    –        –          –             26600           
     45542 B6III        $-$0.049  0.106    0.544      2.657           14080           
     47054 B8Ve         $-$0.022  0.096    0.698      2.677           12500           
     50658 B8IIIe       $-$0.015  0.086    0.596      2.626           13600           
     50820 B3IVe+          –        –        –          –             17900           
     52918 B1V          $-$0.072  0.063    0.021      2.591           24720           
     53416 B8              –        –        –          –             12000           
     58050 B2Ve         $-$0.087  0.081    0.169      2.495           20260           
     58343 B2Vne           0.011  0.073    0.264      2.566           18600           
     58715 B8Ve         $-$0.037  0.124    0.791      2.729           11700           
     60855 B2/B3V       $-$0.017  0.059    0.194      2.609           19984           
     61224 B8/9 IV         0.041  0.061    0.773      2.656           12000           
     65875 B2.5Ve          0.004  0.040    0.102      2.451           22540           
     71072 B4IV            –        –        –          –             16550           
     91120 B8/9IV/V        0.005  0.095    0.956      2.742           10600           
    109387 B6IIIpe      $-$0.023  0.072    0.351      2.566           16850           
    138749 B6Vnne       $-$0.040  0.083    0.479      2.683           14910           
    142926 B9pec        $-$0.029  0.109    0.764      2.677           12000           
    142983 B8Ia/Iab     $-$0.022  0.081    0.664      2.590           12860           
    143275 B0.2IVe      $-$0.016  0.036   $-$0.020    2.605           26700           
    162428 A0              –        –        –          –             12200           
    162732 Bpshe        $-$0.045  0.096    0.786      2.669           11740           
    164284 B2Ve            0.057  0.022    0.001      2.495           21650           
    164447 B8Vne        $-$0.013  0.095    0.660      2.721           12900           
    183362 B3Ve         $-$0.009  0.056    0.184      2.528           20260           
    183656 B6sh            0.050  0.037    0.809      2.641           11700           
    183914 B8Ve         $-$0.030  0.109    0.725      2.737           12270           
    187567 B2.5IVe         0.052  0.007    0.093      2.531           23110           
    189687 B3IVe        $-$0.057  0.081    0.281      2.635           17980           
    191610 B2.5Ve       $-$0.039  0.062    0.162      2.553           20600           
    192044 B7Ve         $-$0.032  0.086    0.603      2.632           13460           
    193911 B8IIIne      $-$0.015  0.073    0.644      2.627           13100           
    210129 B7Vne        $-$0.024  0.101    0.476      2.643           15000           
    212571 B1Ve            –        –        –          –             23300           
    214168 B2Ve         $-$0.045  0.055    0.024      2.609           24790           
    216057 B5Vne        $-$0.013  0.088    0.470      2.671           15090           
    216200 B3IVne          0.100  0.040    0.331      2.634           17600           
    217050 B4IIIep      $-$0.006  0.062    0.472      2.501           15090           
    217543 B3Vpe        $-$0.034  0.079    0.241      2.650           18860           
    217675 B6Ve            0.002  0.042    0.477      2.650           15050           
    217891 B6Ve         $-$0.050  0.109    0.476      2.630           14910           

  : Spectral types, luminosity classes, Strömgren photometry, and derived effective temperatures for our program stars. Spectral types and luminosity classes are taken from the SIMBAD database[]{data-label="param"}

  -------- ------ ---------------- ---- --------------------- ----------- ------------- ------------- ----------------------- --------------- --------------- ------------ ----------------------- ------------- -----------
        HD     HR             Name    N                   Cl.   v$\sin i$     M$_*$         R$_*$      $\Delta v_{\rm peak}$       v$_c$       v$_{\rm eq}$       $i$             $\rho _0$          R$_d$/R$_*$         rem
                                                                   (km/s)  (M$_\odot$)   (R$_\odot$)       (km s$^{-1}$)       (km s$^{-1}$)   (km s$^{-1}$)   ($^\circ$)       (g cm$^{-3}$)                    
      6811    335       $\phi$ And    3                     2          80      4.0           3.1                 –                  500             400            12       8.50$\cdot$10$^{-14}$            6.4         3,5
     10516    496       $\phi$ Per    1                     2         240     17.0          10.0                180                 570             450            22       4.20$\cdot$10$^{-12}$            4.3       3,4,5
     11415    542   $\epsilon$ Cas    1                   abs          40      6.5           4.2                 –                   –               –             –                  –                        –           –
     37202   1910      $\zeta$ Tau    2                     2         120     10.5           6.1                290                  –               –             –                  –                        –   1,2,3,4,5
     37490   1934     $\omega$ Ori    2                     1         180      8.9           5.1                190                 580             460            23       8.00$\cdot$10$^{-12}$            3.1     1,2,3,4
     41335   2142         V696 Mon    2                     2         310      8.9           5.1                 –                   –               –             –                  –                        –       1,2,3
     43285   2231           –         1                   abs         230      6.0           4.0                 –                   –               –             –                  –                        –           –
     44458   2284           FR CMa    1                     2         180     18.0          10.5                150                 570             460            23       3.00$\cdot$10$^{-12}$            5.0           3
     45542   2343        $\nu$ Gem    1                    sh         160      5.1           3.5                175                  –               –             –                  –                        –       2,3,4
     47054   2418           –         1                     1         180      4.0           3.1                140                 500             400            27       3.80$\cdot$10$^{-13}$            5.8           3
     50658   2568     $\psi$09 Aur    1                    sh         230      4.5           3.3                150                 510             400            80       3.50$\cdot$10$^{-14}$            8.5         3,5
     50820   2577           –         1                     2         150      7.4           4.6                 –                  550             440            20       7.20$\cdot$10$^{-14}$           13.8           –
     52918   2648           19 Mon    1                   abs         240     17.0          10.0                 –                   –               –             –                  –                        –           –
     53416   –              –         1                     1         190      4.0           3.5                120                 470             370            30       7.60$\cdot$10$^{-14}$            9.1           –
     58050   2817           –         3                     1         110      9.0           5.3                 –                   –               –             –                  –                        –         3,5
     58343   2825           FW CMa    1                     2          50      7.5           4.7                 –                  550             440            6        1.10$\cdot$10$^{-13}$           13.7       2,3,4
     58715   2845      $\beta$ CMi    3                     1         210      3.8           3.0                130                 490             390            32       1.25$\cdot$10$^{-13}$            7.0     2,3,4,5
     60855   2921         V378 Pup    1                     2         240      9.0           5.3                150                  –               –             –                  –                        –         2,3
     61224   2932           –         2                     1         200      4.0           3.1                150                 500             400            30       3.50$\cdot$10$^{-13}$            6.2           3
     65875   3135         V695 Mon    3                     2         180     12.0           7.0                 –                   –               –             –                  –                        –         2,3
     71072   –              –         2                   abs         100      6.5           4.5                 –                   –               –             –                  –                        –           –
     91120   4123           –         9                     1         250      3.0           2.5                180                 480             380            41       1.15$\cdot$10$^{-13}$            6.8         2,3
    109387   4787     $\kappa$ Dra   13   1$\leftrightarrow$2         170      7.0           4.5                140                 540             430            23       4.00$\cdot$10$^{-12}$            5.1         3,5
    138749   5778     $\theta$ CrB   11                   abs         310      6.0           4.0                 –                   –               –             –                  –                        –           5
    142926   5938         V839 Her   10                    sh         275      4.0           3.1                240                 500             400            44       6.00$\cdot$10$^{-12}$            4.3           5
    142983   5941           48 Lib   13                    sh         390      4.1           3.2                 –                   –               –             –                  –                        –         2,3
    143275   5953     $\delta$ Sco    4                     2         165     18.0          10.5                 –                   –               –             –                  –                        –           6
    162428   –              –         5                     1         240      4.0           3.0                180                 500             400            36       9.00$\cdot$10$^{-12}$            6.1           4
    162732   6664      $\zeta$ Her    6                    sh          40      3.8           3.0                260                  –               –             –                  –                        –         3,5
    164284   6712           66 Oph    6                     1         240     10.5           6.1                150                 570             460            32       8.80$\cdot$10$^{-14}$            9.3         2,3
    164447   6720         V974 Her    4                     1         180      4.0           3.5                140                 470             370            28       1.75$\cdot$10$^{-13}$            5.8           5
    183362   7403         V558 Lyr    4                     2         220      9.0           5.3                 –                   –               –             –                  –                        –           3
    183656   7415         V923 Aql    5                    sh         190      3.8           3.0                250                  –               –             –                  –                        –         2,3
    183914   7418    $\beta$ Cyg B    5                     1         240      4.0           3.0                160                 500             400            37       9.00$\cdot$10$^{-14}$            8.2         3,4
    187567   7554        V1339 Aql    4       1$\rightarrow$2         200     13.0           7.7                140                 570             450            26       3.00$\cdot$10$^{-13}$            7.3           –
    189687   7647           25 Cyg    6                    sh         230      7.5           4.7                250                 550             440            31       3.05$\cdot$10$^{-13}$            3.6         3,4
    191610   7708           28 Cyg    4                     1         250      9.0           5.3                270                 570             455            33       2.60$\cdot$10$^{-13}$            3.9         3,4
    192044   7719           20 Vul    3                     1         240      4.5           3.3                150                 510             410            38       1.10$\cdot$10$^{-13}$           10.1           –
    193911   7789           25 Vul    3                     1         170      4.0           3.5                100                 470             370            27       2.30$\cdot$10$^{-13}$            6.0       2,3,5
    210129   8438           25 Peg    8                     1         130      6.0           4.0                70                  530             430            19       1.50$\cdot$10$^{-12}$            5.6       1,2,3
    212571   8539        $\pi$ Aqr    3                     1         220     13.0           7.7                280                 570             450            41       6.00$\cdot$10$^{-13}$            3.9     1,2,3,4
    214168   8603          8 Lac B    3                     2         150     17.0          10.0                 –                   –               –             –                  –                        –           –
    216057   8682           –         4                   abs         260      6.0           4.0                 –                   –               –             –                  –                        –           –
    216200   8690           14 Lac    3                    sh         195     13.0           7.7                 –                   –               –             –                  –                        –           5
    217050   8731           –         1                    sh         240      6.0           4.0                 –                   –               –             –                  –                        –       3,4,5
    217543   8758         V378 And    2                    sh         305      7.5           4.7                 –                   –               –             –                  –                        –           –
    217675   8762          $o$ And    2                    sh         200      6.0           4.0                 –                   –               –             –                  –                        –         4,5
    217891   8773      $\beta$ Psc    6                     2          75      6.0           4.0                 –                  535             430            10       5.20$\cdot$10$^{-13}$            6.1     1,2,4,5
  -------- ------ ---------------- ---- --------------------- ----------- ------------- ------------- ----------------------- --------------- --------------- ------------ ----------------------- ------------- -----------

Observation and data reduction
==============================

The idea that underlies this catalog is to create a homogeneous data set of stars observed with the same instrument, the telescope of the [*M.G. Fracastoro*]{} station of INAF-Catania Astrophysical Observatory. For this purpose, we queried the “Catalogue of Be stars” compiled by Jaschek & Egret ([@jaschek82]) selecting all the objects with V$\leq$7 and observable at the latitude of the observatory, which means all the stars with $\delta \ge -22^\circ$. The result of this query is the sample of 48 Be stars reported in Table \[param\]. The limiting magnitude was chosen to obtain a good compromise between the exposure time and the signal-to-noise ratio.

The present catalog is based on new spectroscopic observations of all the stars in our sample, which spectral type are distributed between B1 and A0 (according to the histograms displayed in Fig. \[spect\_type\]), and luminosities classes are III, IV, and V, as in the SIMBAD database[^3]. Some of these stars’ spectra have never been published in other catalogs similar to ours, at least to our knowledge.late

![Histogram showing the distribution of program stars as a function of spectral type. []{data-label="spect_type"}](20357fig1.ps){width="8cm" height="8cm"}

All the spectra of our program stars have been acquired with the 91-cm telescope and FRESCO, the fiber-fed REOSC echelle spectrograph that allows spectra to be obtained in the range of 4300–6800 [Å]{} with a resolution R=21000. The spectra were recorded on a thinned, back-illuminated (SITE) CCD with 1024$\times$1024 pixels of 24 $\mu$m size, whose typical readout noise is of about 8 e$^{-}$ and the gain is 2.5 e$^-$/ADU. All the spectra have been acquired during several observing runs spanning two years between 2008 and 2009.

The reduction of spectra, which included the subtraction of the bias frame, trimming, correcting for the flat-field and the scattered light, the extraction of the orders, and the wavelength calibration, was done by using the NOAO/IRAF package[^4]. The amount of scattered light correction was about 10 ADU. After dividing the extracted spectra by flat-field, the residual shape the spectrum was removed by dividing each spectral order by a Legendre function of a low order. Typical S/N of our spectra is $\sim$100. For some stars this limit has not been reached because its apparent magnitude is close to V$\approx$7, in which case the S/N was about 50.

Finally, the IRAF package [rvcorrect]{} was used to include the velocity correction due to the Earth’s motion, which moved the spectra into the heliocentric rest frame. The task [splot]{} and its facilities were used to measure the peaks separation in the H$\alpha$ profile. Errors in the pixels position were converted in errors on the separations, and were evaluated in $\approx$ 20 km s$^{-1}$.

For each spectrum we measured the equivalent widths (including underlying absorption) of both H$\alpha$ and H$\beta$, where a negative value means the corresponding line shows net emission. All the measured equivalent widths are reported in Table \[eqw\].

  -------- ------------------- ------ ------ ------------------ ------ ------
        HD               EW(Å)   F      C                 EW(Å)   F      C
      6811       0.87$\pm$0.28  1.84   0.65       6.45$\pm$0.09  1.99   0.67
     37202   $-$15.26$\pm$1.17  1.41   0.49       2.34$\pm$0.01  1.41   0.49
     37490    $-$5.96$\pm$1.09  1.41   0.49       1.83$\pm$0.18  1.41   0.49
     41335   $-$31.92$\pm$0.78  1.41   0.49    $-$1.44$\pm$0.52  1.41   0.49
     58050    $-$4.40$\pm$0.31  1.94   0.66       5.49$\pm$0.04  1.73   0.63
     58715    $-$1.19$\pm$0.36  1.94   0.66       7.96$\pm$0.06  1.98   0.66
     61224    $-$5.59$\pm$0.48  1.41   0.49       5.14$\pm$0.40  1.41   0.49
     65875   $-$43.00$\pm$0.89  1.90   0.66       0.04$\pm$0.60  1.77   0.64
     71072       3.14$\pm$0.08  1.41   0.49       5.22$\pm$0.23  1.41   0.49
     91120    $-$0.40$\pm$0.50  3.49   0.92       8.07$\pm$0.15  3.21   0.91
    109387   $-$19.17$\pm$0.44  3.58   0.94       3.04$\pm$0.06  2.85   0.90
    142926    $-$1.63$\pm$0.45  3.68   0.93       7.05$\pm$0.13  3.06   0.90
    142983   $-$24.66$\pm$0.86  3.31   0.93       3.09$\pm$0.14  3.85   0.95
    143275   $-$10.13$\pm$2.29  2.34   0.76    $-$0.81$\pm$0.20  2.30   0.75
    162428   $-$15.57$\pm$0.14  2.44   0.80       4.78$\pm$0.38  2.40   0.80
    162732    $-$6.61$\pm$0.88  2.52   0.83       5.92$\pm$0.50  2.89   0.85
    164284       1.37$\pm$1.57  2.71   0.84       5.18$\pm$0.08  2.64   0.84
    164447    $-$0.95$\pm$1.13  2.64   0.81       6.68$\pm$0.15  2.68   0.82
    183362   $-$26.39$\pm$0.15  1.88   0.65       1.25$\pm$0.15  1.79   0.64
    183656    $-$7.68$\pm$0.72  2.50   0.80       5.15$\pm$0.18  2.28   0.80
    183914    $-$0.94$\pm$0.22  2.78   0.82       8.10$\pm$0.07  2.53   0.80
    187567   $-$21.82$\pm$0.66  2.14   0.74       0.56$\pm$0.19  2.21   0.74
    189687       0.93$\pm$0.25  2.93   0.86       4.76$\pm$0.05  3.11   0.87
    191610       0.12$\pm$0.24  2.03   0.72       4.69$\pm$0.15  2.04   0.72
    192044    $-$9.96$\pm$0.13  1.97   0.66       5.25$\pm$0.05  1.96   0.66
    193911    $-$5.45$\pm$0.13  1.95   0.66       5.10$\pm$0.05  1.89   0.65
    210129   $-$14.17$\pm$0.21  3.26   0.90       5.11$\pm$0.15  3.13   0.89
    212571    $-$5.40$\pm$0.04  1.99   0.67       1.98$\pm$0.14  1.98   0.66
    214168   $-$14.79$\pm$0.35  2.00   0.67       1.87$\pm$0.52  1.82   0.65
    216057       4.62$\pm$0.15  2.36   0.76       7.19$\pm$0.10  2.21   0.74
    216200       1.15$\pm$0.43  1.98   0.66       5.08$\pm$0.21  1.97   0.66
    217543       2.35$\pm$0.76  1.41   0.49       5.31$\pm$0.11  1.41   0.49
    217675       3.05$\pm$0.28  1.41   0.49       5.64$\pm$0.18  1.41   0.49
    217891   $-$12.94$\pm$0.64  2.70   0.84       4.70$\pm$0.19  2.70   0.84
  -------- ------------------- ------ ------ ------------------ ------ ------

  : Program stars for which we have more than two spectra. We reported for both lines mean equivalent widths, their F values, computed according Eq. \[Fval\], and the confidence levels of the detected variability.[]{data-label="eqw_test"}

Classification and fit of the H$\alpha$ line profiles
=====================================================

Almost all the stars in our sample were found with emission in the H$\alpha$. Then, considering the shape of their profile and according to the classification scheme proposed by Hanuschik ([@hanu88]), we classified our stars as belonging to

-   class 1 when they exhibit a rather symmetrical double peak structure with V/R$\approx$1,

-   class 2 when they have an asymmetric single peak or a dominant peak with a much weaker secondary peaked,

-   shell stars when the central reverse is deeper than the continuum level,

-   [*abs*]{} when there is not emission above the continuum level.

Our classification is reported in the fourth column of Table \[summary\].

Only for the stars belonging to class 1, plus stars from other classes but with V/R ratio close to unity, we attempt an estimation of the disk dimension. The approach we used was to minimize the difference between observed and synthetic profiles, computed in two separate steps. First of all, we calculated the photospheric H$\alpha$, then the contribution due to the net emission of the disk and then we added these two synthetic profiles obtained separately. These two steps are described in the following:

-   [*Computation of the photospheric profile*]{}

    We first computed the photospheric H$\alpha$ profiles for all our program stars. They were generated in three steps: [*i)*]{} first, we computed an LTE model atmosphere using the ATLAS9 code (Kurucz [@kur93]), [*ii)*]{} the stellar spectrum was then synthesized using SYNTHE (Kurucz & Avrett [@kur81]), and [*iii)*]{} the spectrum was convolved with the instrumental and rotational profiles.

    First of all we had to obtain an estimation of the effective temperature for each target. Considering that the continuum energy distribution of Be stars is typical of normal early-type stars both in the visual and UV, but not in the IR, where an excess could be present because of the hot circumstellar dust (Zickgraf [@zick00]), effective temperatures were computed from Strömgren photometry (Hauck & Mermilliod [@hauck98]) using the algorithm coded by Moon ([@moon85]), with the exception of eight stars for which photometry is not available. This method is allowed because it does not involve any IR filter. For seven of them we adopted the temperatures from the literature: HD10516, HD37202, and HD44458 from Soubiran et al. ([@soubiran10]), HD58020 and HD71072 from Hohle et al. ([@hohle10]), HD162428 from Moujtahid et al. ([@mouj99]), and HD212571 from Wu et al. ([@wu11]), while for HD53416 we derived an estimation of temperature from spectral type and the calibration by Kenyon & Hartman ([@kenyon95]). Since our targets have luminosity class IV/V (as reported in the SIMBAD database), we fixed the surface gravity to $\log g $=4.0, except for HD11415, HD37490, HD45542, HD50658, HD109387, HD193911, and HD217050 (luminosity class III) for which $\log g$=3.0 has been preferred. Radii and masses were adopted following the calibration in Drilling & Landolt ([@drill99]). Assuming these atmospheric parameters, we computed the v$\sin i$ of each star by spectral synthesis of the observed Mg[i]{} $\lambda$4481 [Å]{}. This line was chosen because in the spectral range of our targets, it reaches its maximum depth and therefore it is better suited to determining the rotational velocity. Errors on the projected rotational velocities are $\approx$ 15 km s$^{-1}$.

-   [*Computation of net disk emission*]{}

    We have adopted the Be disk model approach of Hummel & Vrancken ([@hummel00]) that is based on models developed by Horne & Marsh ([@horne86]) and Horne ([@horne95]) for accretion disks in cataclysmic variables. The disk is assumed to be axisymmetric and centered over the equator of the underlying star, and the gas density varies as

    $$\rho(R,Z)\,=\,\rho_0R^{-n} exp\left[-\frac{1}{2}\left(\frac{Z}{H(R)}\right)^2\right]$$

    where R and Z are the radial and vertical cylindrical coordinates (in units of stellar radii), $\rho_0$ is the base density at the stellar equator, [*n*]{} a radial density exponent, and H(R) the disk vertical scale height. The neutral hydrogen population within the disk is found by equating the photo-ionization and recombination rates (Gies et al. [@gies07]). The disk gas is assumed to be isothermal and related to the stellar effective temperature T$_{\rm eff}$ by T$_d$=0.6T$_{\rm eff}$ (Carciofi & Bjorkman [@carciofi06]).

    This approach take the contribution of the central star’s finite size on the H$\alpha$ line formation process into account, i.e. the obscuration of the disk by the central star at any given inclination. The numerical model represents the disk by a large grid of azimuthal and radial surface elements, and the equation of transfer is solved along a ray through the center of each element according to

    $$I_\lambda\,=\,S_\lambda^L\,(1-e^{-\tau_\lambda})\,+\,I_\lambda^S\,e^{-\tau_\lambda}$$

    where I$_\lambda$ is the derived specific intensity, S$_\lambda^L$ the source function for the disk gas (taken as the Planck function for the disk temperature T$_d$), I$_\lambda^S$ the specific intensity for the H$\alpha$ of the star, and $\tau_\lambda$ the integrated optical depth along the ray. The first term applies to all the disk area elements that are unocculted by the star, while the second term applies to all elements that correspond to the projected photospheric disk of the star. The absorption line adopted in I$ _\lambda^S$ is Doppler-shifted according to solid-body rotation for the photospheric position in a star that is rotating at 80$\%$ of the critical value.

    Electron scattering is not taken into account in the line profile computation. So we do not expect to reproduce the wings of strong lines well, since for these lines the broadening of the wings due to the electron scattering can not be neglected. Disk kinematic is taken into account using a rotational velocity law written as

    $$V(R)\,=\,V_{\rm rot}^*R^{-j}$$

    (Hutchings [@hutch70]), where R represents the radial coordinate that has its origin at the center of the star, and $V_{\rm rot}^*$ denotes the actual rotational velocity at the stellar surface. The exponent ranges from $j\,=\,1/2$ for pure Keplerian rotation and $j\,=\,1$ corresponding to conservation of angular momentum. Likewise the value of $j$ is still matter of debate, recent studies seem to converge toward the Keplerian value (Hummel & Vrancken [@hummel00], Meilland et al. [@meilland07]). Thus, in this study we assumed the disk to be in pure Keplerian rotation.

Once we obtained and combined these two contributions, we started the minimization algorithm using as goodness-of-fit test the parameter

$$\chi^2 = \frac{1}{N} \sum (\frac{I_{\rm obs} - I_{\rm th}}{\delta I_{\rm obs}})^2$$

where $N$ is the total number of points, $I_{\rm obs}$ and $I_{\rm th}$ are the intensities of the observed and computed profiles, respectively, and $\delta I_{\rm obs}$ is the photon noise.

As initial guesses for the inclination angle $i$ and for the disk radius, we used the equations

$$v_{\rm eq} \sin i\,=\,0.8\,\sqrt{\frac{GM_*}{R_*}}\,\sin i 
\label{incl}$$

where $v_{\rm eq} \sin i$ is the value measured in our spectra, and

$$\frac{\Delta v_{\rm peak}}{2\,v \sin i}\,=\,r_d^{-j}
\label{rad}$$

(equation \[6\] in Hanuschik et al. ([@hanu88])) where $\Delta v_{\rm peak}$ is the separation between violet and red peaks, as measured in each profile and reported in Table \[summary\].

Then, fine tuning was carried out using the [*amoeba*]{} minimization[^5] algorithm between observed and computed profiles. In our procedure two assumptions have been made: radial density exponent has been fixed to $n$=3 and, as stated before, the Keplerian rotation of the disk has been considered ($j$=1/2). The first hypothesis, regarding the value of the density exponent can be justified by considering the work of Grundstrom & Gies ([@grund06]). These authors computed several theoretical curves that described the dimension of the disk radius as a function of the H$\alpha$ equivalent width, for different values of the inclination angle i and different values of n. They concluded that the overall shape of those curves for different n and equal i are almost the same, since it is a small difference of $\approx 3 \%$ in correspondence of equivalent widths between -2 and -15 [Å]{} when n change from 3 to 3.5. They then suggest that the particular choice of n is not as important as the choice of the right i. Moreover, Porter & Rivinius ([@porter03]) from IR flux excess in Be stars suggested that n falls in the interval $n\,= \,2\div4$. Thus, on the basis of these results, we fixed the value of the density exponent to the middle value of n=3. Total H$\alpha$ profiles, star+disk, are presented in Figs. \[halpha1\], \[halpha2\], and \[halpha3\].

To derive an estimation of the disk radius, we used the method developed by Grundstrom & Gies ([@grund06]) to form a synthetic image of the system star+disk in the plane of sky by summing the intensity over a 2.8 nm band centered on H$\alpha$. We collapsed this image along the projected major axis to get the summed spatial intensity, and we adopted the value for which the summed intensity drops to half its maximum value as effective disk radius.

We estimated the errors on the disk dimensions and on the inclination angles to be $\pm$2R$_*$ and $\pm$3$^\circ$, respectively. These determinations have been estimated by varying in Eqs. \[incl\] and in \[rad\] the observed quantities $v \sin i$ and peak separation by their experimental errors and considering as uncertainties the semi-amplitude of this variation.

All the adopted and derived parameters are reported in Table \[summary\].

![Correlation between measured v $\sin i$ and peaks separation. The points have been grouped on the basis of the mean equivalent width: EW$\le$-20 [Å]{} (filled squares), -20[Å]{}$<$EW$\le$-15[Å]{} (filled circles), -10[Å]{}$<$EW$\le$-5[Å]{} (filled triangles), -5[Å]{}$<$EW$\le$0[Å]{} (open circles), and EW$\ge$0 [Å]{} (open squares). []{data-label="corr"}](20357fig2.ps){width="8cm"}

H$\alpha$ and H$\beta$ Variability {#variab}
==================================

Usually Be stars display variability in their equivalent width (EW) and/or in their spectral profile.

To find whether a star presents equivalent width variation, we applied to both H$\alpha$ and H$\beta$ equivalent widths the statistical method called F-test. When more than one observation was present for a given target, we calculated the amplitude of the variation, $\Delta\,EW$, and the standard deviation of the sample using

$$\sigma\,=\,\sqrt{ \frac{1}{N-1} \sum (EW_i - \overline{EW})^2 }\\$$

where N is the number of points, and the (N-1) corresponds to the degree of freedom used for the F-test. Having obtained $\Delta EW$ and $\sigma$, we calculated a simple observable to assess the variability for a given target using a ratio of the form:

$$F\,=\,\frac{\Delta\,EW}{\sigma} .
\label{Fval}$$

This simple ratio represents the number of times that the amplitude of the variation is greater than the standard deviation.

To determine whether or not this number is meaningful and whether the star shows variability, we evaluated the corresponding confidence level; see last column of Table \[eqw\_test\]. We considered all the stars for which C$\ge$80$\%$ as definitively variable (13 stars, that is 41$\%$ of the sample), while we cannot say anything for the target with C$\le$50$\%$ (22$\%$ of the sample) due to the small number of points. The 37$\%$ of the stars, are probably variable but within a confidence level ranging from 50$\%$ to 80$\%$. In any case, all the targets show the same behavior in both spectral lines.

In this atlas we show the full set of our profiles (H$\alpha$ and H$\beta$) for the 48 observed stars. In Figs. \[variab1\] to \[variab5\], we show the Balmer profiles observed for program stars with multiple measurements, In each panel we reported for each profile also the last four digits of the heliocentric julian date of the observation. In some cases to improve the visualization, profiles have been blown up according to

![image](20357fig3a.ps){width="8cm" height="7cm"} ![image](20357fig3b.ps){width="8cm" height="7cm"}

$$F'_\lambda = [(F_\lambda - 1) * k] + 1$$

where F$_\lambda$ denotes the observed flux, F$'_\lambda$ the displayed flux, and k is the magnification factor.

In Fig. \[one\_shell\] we show all the stars for which we collected one spectrum only. Most of the stars have been measured several times during the 2008/2009 period, but only few stars showed significant variations in their spectral profiles. These objects are discussed separately in the following:

[*HD37202 -*]{} This star has been observed in two nights separated by 205 days. It is clearly visible an increase in flux in the violet peak in both spectral lines, even if it is more evident in H$\beta$.

[*HD41335 -*]{} As for the previous object, only two observations have been acquired for this star in a range of 207 days. The star exhibits V/R variations in both lines.

[*HD58050 -*]{} The triple-peaked structure visible in the H$\alpha$ observed in the first night is missing in the other two spectra. No features are seen in the H$\beta$.

[*HD109387 -*]{} This star was observed for 13 nights in a period spanning 110 days. The top part of the H$\alpha$ emission profiles shows irregular variability, with back and forth changing from class 2 toward class 1, but no evident sign of day-by-day variability has been observed. No variations have been detected in H$\beta$ double-peaked profile.

[*HD142926 -*]{} During 110 days this shell star was observed 10 times showing a slight V/R variability in the H$\alpha$.

[*HD143275 -*]{} In the four spectra acquired by us, $\delta$Sco shows important changes in the emission of H$\alpha$. The V/R changes over the observational period and it shows a flat core in the first spectrum.

[*HD164284 -*]{} Observed for six times in 536 days, this star exhibits equivalent width variability. The double-peaked emission of the H$\alpha$ profile decrease with time, although the V/R remains constant and $\approx$1. Also the H$\beta$ shows a change in the shape, since it is the last profile without any peak.

[*HD183362 -*]{} This star shows an increased emission level on the red side of its profile.

[*HD183656 -*]{} V/R variability has been observed, both in H$\alpha$ and in H$\beta$ profiles, in the six spectra acquired in a range of 358 days.

[*HD187567 -*]{} This star show variability in the H$\alpha$ profile, and evolves from class 1 toward class 2.

[*HD189687 -*]{} In the H$\alpha$, this star does not show any sign of variability for the first month of observations. In the last spectrum taken after 32 days from the second to last, it starts to show an increase of the flux in the red peak. No H$\beta$ variability has been detected.

[*HD191610 -*]{} This star shows a gradual increment of the flux in the red peak.

Discussion and conclusions
==========================

In this paper we presented a homogeneous sample of H$\alpha$ and H$\beta$ line profiles observed in 32 Be stars, which show emission at least in the H$\alpha$ line. According to Hanuschik ([@hanu88]), we classified our targets on the basis of the following scheme:

-   16 stars, 33$\%$ of the sample, in class 1;

-   13 stars, 27$\%$ of the sample, in class 2;

-   11 stars, 23$\%$ of the total, has been classified as shell stars;

-   6 stars, 12$\%$ of the total, do not show net emission.

In this list we do not include the two stars that show any phase transition between classes 1 and 2.

This frequency distribution shows that the majority of our sample of 48 Be stars, randomly distributed in spectral type, belongs to class 1 profiles. Regarding the 13 stars classified as class 2, seven of them are single peak, while six show structured profiles.

Two stars showed variability from one class to another. HD187567 has undergone an evolution from class 1 to class 2, while the behavior of HD109387 is more complicated. In 110 days, this star has been observed 13 times, and it showed a transition from class 2 to class 1 and back again to class 2.

In Fig. \[corr\] we compared the behavior of the H$\alpha$ peaks separation to $v \sin i$ for the stars of the class 1 (included the class 2 HD60855). A linear correlation seems to exist, as expected from the work of Hanuschik et al. ([@hanu88]), although two stars discarded from this trend, namely HD191610 and HD212571. To verify this correlation we computed the Pearson [*r*]{} coefficient, obtaining [*r*]{}=0.72 and the linear fit given by the equation:

$$y = (0.56 \pm 0.13) \cdot x + (29.94 \pm 26.80) .$$

Thus, we confirm that $v \sin i$ and H$\alpha$ peaks separation are in linear correlation, confirming the disk-like geometry of Be star envelopes and, probably this assumption is not valid for HD191610 and HD212571.

For all the stars belonging to the class 1, we attempted to model the emission with the purpose of deriving some parameters such inclination angle, base density at the stellar equator and disk radius. In Fig. \[hist\] we show the distribution of stars as a function of the disk radius (right panel) and of the inclination angle (left panel). The histograms were built considering a binning equal to the estimated errors, that is, 2R$_*$ and 3$^\circ$ in the disk dimension and inclination angle, respectively. They show as there is a major concentration of stars for disk around $6 \div 8$ R$_*$ (about 17$\%$ of our sample) and for angles around $23^\circ \div 35^\circ$ (about 28$\%$ of the sample).

Moreover, with the aim of inferring line profile variability, for most of the stars of our sample we obtained more than one spectrum in a period spanning two years between 2008 and 2009. All but seven stars, those discussed in Sect. \[variab\], do not show any evident sign of variability in both Balmer lines.

This research made use of the SIMBAD database, operated at the CDS, Strasbourg, France.

Carciofi, A. C., & Bjorkman, J. E. 2006, ApJ, 639, 1081 Drilling, J., & Landolt, A. U. 1999, in: Allen’s Astrophysical Quantities, Fourth Edition, Edited by Arthur N. Cox, Los Alamos, NM Gies, D. R., Bagnuolo, W. G. Jr., Baines, E. K., et al. 2007, ApJ, 654, 527 Grundstrom, E. D., & Gies, D. R. 2006, A&A, 651, 53 Hanuschik, R. W. 1996, A&A, 308, 170 Hanuschik, R. W., Hummel, W., Sutorius, E., Dietle, O., & Thimm, G., 1996, A&ASS, 116, 309 Hanuschik, R. W., Kozok J. R., & Kaiser, D. 1988, A&A, 189, 1988 Hauck, B., & Mermilliod, M. 1998, A&AS, 129, 431 Hohle, M. M., Neuhauser, R., & Schutz, B.F. 2010/ AN, 331, 349 Horne, K. 1995, A&A, 297, 273 Horne, K., & Marsh, T. R. 1986, MNRAS, 218, 761 Hummel, W., & Vrancken, M. 2000, A&A, 302, 751 Hutchings, J. B. 1970, MNRAS, 150, 55 Jaschek, M., & Egret, D., 1982, A catalogue of Be stars. In: Be stars, IAU Symp. 98, 261 Ed. M. Jaschek and H.-G. Groth, Munich Kurucz, R.L. 1993, A new opacity-sampling model atmosphere program for arbitrary abundances. In: Peculiar versus normal phenomena in A-type and related stars, IAU Colloquium 138, M.M. Dworetsky, F. Castelli, R. Faraggiana (eds.), ASP Conference Series Vol. 44, p.87 Kenyon, S. J., & Hartmann, L., 1995, ApJS, 101, 117 Kurucz, R. L., & Avrett, E. H. 1981, SAO Special Rep., 391 Meilland, A., Stee, Ph., Vannier, M. et al. 2007, A&A, 464, 59 Moon, T. T. 1985, Comm. from the Univ. of London Obs., 78 Moujtahid, A., Zorec, J., & Hubert, A. M. 1999, A&A, 349, 151 Nelder, J. A., & Mead, R., 1965, Computer Journal, Vol 7, pp 308-313. Okazaki, A. T. 1997, A&A, 318, 548 Porter , J. M., & Rivinius, Th., 2003, PASP, 115, 1153 Porter, J. M. 1996, MNRAS, 280, L31 Saad, S.M., Kubát J., Korcáková, D., et al., 2006, A&A, 450, 427 Silaj, J., Jones, C. E., Tycner, C., Sigut, T. A. A., & Smith, A.D., 2010, ApJS, 187, 228 Slettebak, A., Collins, G. W., Truax, R., 1992, ApJS, 81, 335 Soubiran, C., Le Campion, J.-F., Cayrel De Strobel, G., & Caillo, A. 2010, A&A, 515, 111 Struve, O. 1931, ApJ, 73, 94 Wu, Y., Singh, H. P., Prugnel, P., Gupta, R., & Koleva, M. 2011, A&A, 525, 71 Zickgraf, F.-J., 2000, The connection with B\[e\] stars. In: The Be phenomenon in Early-Type stars, IAU Colloquium 175, M. A. Smith, H. F. Henrichs, J. Fabregat (eds), ASP Conference Series Vol. 214, p. 26

Fit emission
============

$
   \begin{array}{cc}

   \includegraphics[width=8cm]{20357figA1a.ps} &
   \includegraphics[width=8cm]{20357figA1b.ps} \\
   \includegraphics[width=8cm]{20357figA1c.ps} & 
   \includegraphics[width=8cm]{20357figA1d.ps} \\
   \includegraphics[width=8cm]{20357figA1e.ps} &
   \includegraphics[width=8cm]{20357figA1f.ps}\\
   \includegraphics[width=8cm]{20357figA1g.ps} &
   \includegraphics[width=8cm]{20357figA1h.ps}
   \end{array}$

$
   \begin{array}{cc}

   \includegraphics[width=8cm]{20357figA2a.ps} &
   \includegraphics[width=8cm]{20357figA2b.ps} \\
   \includegraphics[width=8cm]{20357figA2c.ps} & 
   \includegraphics[width=8cm]{20357figA2d.ps} \\
   \includegraphics[width=8cm]{20357figA2e.ps} &
   \includegraphics[width=8cm]{20357figA2f.ps}\\
   \includegraphics[width=8cm]{20357figA2g.ps} &
   \includegraphics[width=8cm]{20357figA2h.ps}
   \end{array}$

$
   \begin{array}{cc}

   \includegraphics[width=8cm]{20357figA3a.ps} &
   \includegraphics[width=8cm]{20357figA3b.ps} \\
   \includegraphics[width=8cm]{20357figA3c.ps} & 
   \includegraphics[width=8cm]{20357figA3d.ps} \\
   \includegraphics[width=8cm]{20357figA3e.ps} &
   \includegraphics[width=8cm]{20357figA3f.ps}\\
   \includegraphics[width=8cm]{20357figA3g.ps} &
   \includegraphics[width=8cm]{20357figA3h.ps}
   \end{array}$

$
   \begin{array}{cc}

   \includegraphics[width=8cm]{20357figA4a.ps} &
   \includegraphics[width=8cm]{20357figA4b.ps} 
  \end{array}$

Variability
===========

  -------- ------------ ------------- ------------ -------- ------------ ------------- ------------ -------- ------------ ------------- ------------
     HD         JD          EW([Å]{})    EW([Å]{})    HD         JD          EW([Å]{})    EW([Å]{})    HD         JD          EW([Å]{})    EW([Å]{})
            (2450000+)    H$\alpha$     H$\beta$             (2450000+)    H$\alpha$     H$\beta$             (2450000+)    H$\alpha$     H$\beta$  
      6811  4714.6282            1.06         6.53   142926  4543.6113         $-$2.82         7.14   187567  4654.5327       $-$ 21.09         0.81
            4747.5640            0.99         6.46           4554.6243         $-$1.61         7.04           4655.5890       $-$ 21.46         0.59
            4749.6417            0.55         6.36           4555.6541         $-$1.68         6.84           4678.5234       $-$ 22.24         0.40
     10516  4749.6602        $-$25.21         0.37           4556.6487         $-$1.40         6.80           4714.4153       $-$ 22.50         0.44
     11415  4749.6753            4.25         5.83           4575.5709         $-$1.61         7.11   189687  4654.5758            0.76         4.70
     37202  4544.2610        $-$16.09         2.33           4576.5771         $-$1.68         7.14           4655.5411            0.93         4.75
            4749.7298        $-$14.44         2.35           4586.5501         $-$1.49         7.12           4677.5324            0.62         4.77
     37490  4544.2799         $-$5.19         1.95           4588.5402         $-$1.38         7.05           4681.5430            1.01         4.76
            4749.7175         $-$6.73         1.70           4616.4682         $-$1.46         7.03           4682.5777            0.89         4.76
     41335  4542.3012        $-$31.37      $-$1.81           4653.3880         $-$1.18         7.20           4714.4602            1.35         4.84
            4749.7436        $-$32.48      $-$1.07   142983  4543.5309        $-$26.32         3.24   191610  4712.3812            0.48         4.81
     43285  4543.3009            5.06         7.57           4555.5462        $-$23.71         3.15           4713.3568         $-$0.00         4.63
     44458  4544.3009        $-$31.82      $-$0.80           4556.5508        $-$24.48         3.08           4747.3386         $-$0.01         4.81
     45542  4542.3231         $-$0.91         5.93           4575.5004        $-$24.74         3.03           4749.4744         $-$0.00         4.51
     45725  4542.3417            9.38        11.36           4576.4808        $-$24.61         3.15   192044  4712.4081         $-$9.93         5.21
     47054  4543.3275         $-$6.86         6.17           4585.4945        $-$25.81         3.07           4713.3805        $-$10.10         5.24
     50658  4542.3850            1.34         5.67           4586.4283        $-$25.08         3.16           4747.3594         $-$9.84         5.30
     50820  4544.3397         $-$8.32      $-$2.73           4587.4507        $-$24.20         2.75   193911  4712.4526         $-$5.42         5.04
     52918  4542.4174            2.77         3.78           4588.4201        $-$23.85         3.24           4713.4085         $-$5.34         5.12
     53416  4556.2808         $-$4.66         6.42           4599.4307        $-$24.62         3.03           4747.3837         $-$5.60         5.14
     58050  4544.3849            4.31         5.44           4616.3757        $-$25.63         3.05   210129  4654.5979        $-$13.86         4.85
            4554.2984            4.74         5.51           4653.4399        $-$23.49         3.29           4677.5640        $-$14.28         5.02
            4556.3476            4.14         5.51           4654.4038        $-$24.03         2.97           4678.5672        $-$14.30         5.24
     58343  4543.3636        $-$19.29         2.75   143275  4677.3348        $-$11.01      $-$0.78           4681.5694        $-$14.18         5.04
     58715  4542.4392         $-$0.79         7.91           4681.3050         $-$6.94      $-$0.64           4682.6018        $-$14.14         5.11
            4554.3634         $-$1.29         7.95           4682.3327        $-$10.28      $-$0.73           4714.4878        $-$14.01         5.23
            4556.3986         $-$1.49         8.02           4714.2604        $-$12.30      $-$1.09           4747.4096        $-$14.54         5.33
     60855  4543.3894        $-$38.59      $-$0.95   162428  4586.5791        $-$15.50         5.03           4749.5015        $-$14.04         5.04
     61224  4555.2948         $-$5.93         5.42           4588.5667        $-$15.72         4.12   212571  4712.4805         $-$5.37         2.11
            4556.4231         $-$5.25         4.85           4677.3624        $-$15.69         4.99           4714.5117         $-$5.44         2.00
     65875  4543.4116        $-$42.00      $-$0.28           4681.3258        $-$15.58         4.80           4749.5255         $-$5.40         1.83
            4544.4331        $-$43.32         0.74           5011.4665        $-$15.38         4.96   214168  4713.4584        $-$15.13         2.12
            4554.4361        $-$43.69      $-$0.33   162732  4586.6250         $-$7.24         6.13           4747.4338        $-$14.44         2.22
     71072  4555.3404            3.20         5.05           4616.5402         $-$6.95         5.91           4749.5512        $-$14.80         1.27
            4576.3047            3.09         5.38           4654.4306         $-$6.00         6.40   216057  4713.4828            4.48         7.25
     91120  4543.4858         $-$1.39         8.32           4677.4028         $-$7.04         4.94           4714.5419            4.60         7.15
            4554.3985         $-$0.31         8.19           4682.3762         $-$7.31         6.07           4747.4580            4.84         7.29
            4555.4708         $-$0.40         8.15           5011.5115         $-$5.09         6.04           4749.5750            4.58         7.07
            4556.4743         $-$0.52         8.02   164284  4575.5993         $-$0.01         5.19   216200  4713.5068            1.07         5.04
            4576.3563         $-$0.66         7.90           4576.6058         $-$0.00         5.04           4714.5693            1.61         5.31
            4585.3822         $-$0.66         8.02           4616.5681            0.91         5.23           4749.6007            0.76         4.90
            4586.3393         $-$0.01         7.84           4677.4774            1.43         5.12   217050  4747.5172        $-$27.42         1.82
            4587.3192         $-$0.01         8.05           4682.4266            1.64         5.26   217543  4713.5577            1.81         5.38
            4588.3168            0.37         8.16           5011.5620            4.25         5.23           4747.5433            2.89         5.23
    109387  4543.5060        $-$20.01         3.05   164447  4575.6219         $-$2.03         6.62   217675  4713.6001            3.24         5.51
            4554.4814        $-$19.83         3.01           4677.4415         $-$1.24         6.64           4747.4769            2.85         5.77
            4555.5156        $-$19.34         3.07           4681.3697         $-$1.44         6.68   217891  4678.6041        $-$12.16         4.93
            4556.5191        $-$19.09         2.97           4749.3442         $-$1.02         6.93           4681.6008        $-$12.46         4.86
            4575.4348        $-$19.43         3.02           5011.5811            0.96         6.52           4713.6187        $-$12.85         4.76
            4576.4464        $-$19.42         2.98   183362  4653.5050       $-$ 26.22         1.35           4714.6005        $-$12.80         4.66
            4585.4577        $-$19.09         3.02           4682.5161       $-$ 26.45         1.08           4747.4941        $-$13.47         4.57
            4586.3921        $-$19.00         2.98           4714.3334       $-$ 26.50         1.33           4749.6231        $-$13.90         4.42
            4587.3898        $-$18.78         2.99   183656  4653.5999         $-$8.27         5.24                                     
            4588.3867        $-$18.77         3.07           4681.4527         $-$7.59         5.25                                     
            4599.3878        $-$18.45         3.14           4714.3630         $-$8.01         5.35                                     
            4616.3342        $-$19.11         3.13           4749.3742         $-$8.07         4.98                                     
            4653.3303        $-$18.84         3.12           5011.6055         $-$6.48         4.94                                     
                                                     183914  4653.5454         $-$1.01         8.03                                     
                                                             4681.4958         $-$0.91         8.09                                     
                                                             4682.5518         $-$0.96         8.20                                     
                                                             4714.3886         $-$0.61         8.14                                     
                                                             4749.4339         $-$1.23         8.06                                     
  -------- ------------ ------------- ------------ -------- ------------ ------------- ------------ -------- ------------ ------------- ------------

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![image](20357figB7a.ps){width="9cm"} ![image](20357figB7b.ps){width="9cm"} ![image](20357figB7c.ps){width="9cm"}

[^1]: I wish to dedicate this paper to my child never born, to keep track of his passage through my life.

[^2]: Table B.1 and all observed spectra are available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/

[^3]: http://simbad.u-strasbg.fr/simbad/

[^4]: IRAF is distributed by the National Optical Astronomy Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc.

[^5]: The amoeba routine implements the simplex method of Nelder & Mead ([@nelder65]).
