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A Photometric and Spectroscopic Study of 3 Vul
Robert J. Dukes, Jr., William R. Kubinec, Angela Kubinec1
Department of Physics & Astronomy, College of Charleston, 66 George Street, Charleston,
SC 29424
and
Saul J. Adelman2
Department of Physics, The Citadel, 171 Moultrie Street, Charleston, SC 29409
Received ; accepted
1Currently Teacher Specialist On-Site Program, South Carolina Department of Education
2Guest Investigator, Dominion Astrophysical Observatory, Herzberg Institute of Astro-
physics, National Research Council of Canada, 5071 W. Saanich Road, Victoria, BC V9E
2E7 Canada
– 2 –
ABSTRACT
This paper describes photometry of 3 Vulpeculae obtained with the Four
College Automated Photoelectric Telescope and spectroscopy obtained with the
1.22-m telescope of the Dominion Astrophysical Observatory. We have analyzed
differential uvby photometric observations obtained over seven years. Three main
frequencies (f1=0.9719, f2=0.7923, and f3=0.8553 c d−1) were found as well as a
sum frequency (f1+f2 = 1.76420 c d−1). A study of the photographic region using
high dispersion spectrograms obtained with a Reticon detector at the coude spec-
trograph confirms the variable nature of 3 Vul as a 53 Persei star and indicates
that the star’s abundances are normal for main sequence band B stars.
Subject headings: stars: variables: others, stars: abundances, stars: early-type,
stars: individual – 3 Vul
1. Introduction
3 Vulpeculae = HR 7358 = HD 182255 = HIP 95260 (V = 5.2, B6 III) has been
the subject of several studies both as to its variability and its composition. Rountree
Lesh (1968) classified it as a B6 III while Palmer et al. (1968) classified it as a B7 V.
Suggestions, made by some, that 3 Vul might be a chemically peculiar star, have resulted
in SIMBAD’s listing it as a chemically peculiar star. Walker (1952) suspected that 3 Vul
was a photometric variable. Hube & Aikman (1991) analyzed spectroscopic observations
spanning 18 years (JD 2440693 - 2446926) and five nights of differential photometry. They
found 3 Vul to be a single-lined spectroscopic binary (P=367.26 days) whose primary was
probably a member of the 53 Persei class of non-radial pulsators (Smith, Fullerton, & Percy
1987).
– 3 –
Hipparcos measured the parallax to be 8.31 milli-arc-seconds (Perryman 1997).
Combining this with the Hipparcos mean magnitude, converted to an absolute V magnitude
by the Hipparcos data analysis program Celestia 2000 (Turon, Priou, & Perryman 1997),
we find an absolute visual magnitude of –0.24.
Using R = 13000-16000 data of the He I λ5876 line, Catanzaro, Leone, & Catalano
(1999) find the equivalent width is variable with a mean value of 325 mAand an observed
amplitude of about 65 mA. By combining their observations with Hipparcos photometry,
they found a period of 1.26263 days. The variation in their equivalent width is shifted by
0.09 from being in anti-phase with the Hipparcos photometric data. This behavior is not
unexpected for a magnetic chemically peculiar star.
Mathias et al. (2001) included 3 Vul in a group of 10 slowly pulsating B stars which they
monitored spectroscopically for one season. They also analyzed the Hipparcos photometry
and found at least three and possibly five frequencies.
High precision, long time series photometry is required to discover all of the multiple
periods generally present in 53 Persei stars. The Four College Consortium’s Automated
Photoelectric Telescope (APT) located in southern Arizona was designed for just such
observational projects. In March, 1991 (JD 2448334) we initiated Stromgren four color
differential photometry of 3 Vul. In this paper we report on the analysis of seven seasons
of differential photometry and a set of 17 coude spectrograms obtained with the 1.22
m telescope of the Dominion Astrophysical Observatory. We also incorporate the radial
velocities reported by Hube & Aikman (1991), the HeI λ5876 equivalent width measures of
Catanzaro, Leone, & Catalano (1999), and the Hipparcos photometry (Perryman 1997). A
schematic representation of these data sets is shown in Figure 1.
– 4 –
2. Observations
2.1. Photometry
Differential photometric observations were made with the following procedure (standard
for APT observations). The variable star being studied is compared with two reference
stars designated comparison (comp) and check. For the first five seasons these stars were,
respectively, HD 181164 (V=7.5, B5 V) and HD 182865 (V=7.3, B3 V). These were chosen
to be similar in brightness and color and nearby in the sky to the variable. For reasons
discussed below the check star was replaced before the start of season six by HD 181359
(V=7.4, A2).
The four color sequence is similar to that for UVB photometry as described by Boyd,
Genet, & Hall (1984). In this sequence a single differential magnitude determination in one
color requires 11 individual measurements: sky-comp-check-var-comp-var-comp-var-comp-
check-sky. Additionally, one dark count was made after the four-filter sequence. The data
set analyzed for this paper spans 2752 days and includes approximately 1000 four color
observations made on 469 nights. An additional 192 observations in the b filter only were
obtained on 60 nights in the second season.
Since an absentee APT observer has relatively little information on the quality of
a night, extra steps must be taken to eliminate measures affected by cirrus clouds, etc.
The analysis is begun by examining these magnitudes for quality after-the-fact (Dukes,
Adelman, & Seeds 1991). A common method, described in Hall, Kirkpatrick & Seufert
(1986) and Strassmeier & Hall (1988), is to discard observations whose comp minus check
values differ by more than three standard deviations from their mean over the entire data
set. One iterates this process until no more individual values qualify for rejection. The
resulting standard deviation is taken as a measure of the precision of the photometry.
– 5 –
Based on extensive APT experience, we found the initial results of this quality
assurance check (the photometric precision) when applied to the 3 Vul data were less than
acceptable. The source of this problem had to be found, and appropriate corrections made.
Telescope operating logs and data analyses by other Four College Consortium astronomers
indicated no instrumental abnormalities. The next most likely source was the variability of
the comp or the check star (or both stars). Periodogram analysis of the comp minus check
measures revealed a period of around 6.43 days. Similar analyses of the variable minus
comp and variable minus check values verified that the check star (HD 182865) was varying!
Obviously the standard quality assurance check could not be used.
We turned then to the fallback quality check known as the 20 millimagnitude criteria
as described in Hall, Kirkpatrick & Seufert (1986) and Strassmeier & Hall (1988). Each
observation (variable, comp, and check in each filter) consists of two to four individual
measures. If the standard deviation of a measure was greater than two percent (20
millimagnitudes) of the average of the counts incorporated in the measure, the measure was
eliminated. In addition, for a given observation (variable, comp and check), if measures
in two or more colors failed the test, the entire observation was discarded. Although this
method can fail to catch some bad points (Dukes, Adelman, & Seeds 1991) it is a standard
method.
Fortunately one of the authors (RJD) was conducting observations of V473 Lyrae
concurrently with this 3 Vul study. Since these two stars are separated by just over two
degrees in the sky, it was assumed that poor observing conditions (as determined by the
standard comp minus check versus standard deviation of the mean procedure) could exist
in both regions simultaneously or within some time frame. A “20 minute V473 Lyrae”
criterion was developed according to which 3 Vul observations occurring within 20 minutes
of a discarded V473 Lyrae observation were eliminated. Taken together these quality checks
– 6 –
resulted in discarding 910 differential magnitude determinations leaving 991 u measures,
996 v measures, 1172 b measures, and 995 y measures for the entire time span. Table 1
gives the retained differential magnitudes.
A change in the observing protocol was made near the beginning of season two. In an
attempt to improve the time resolution we decided to observe in only one filter and selected
b. Since the variable was relatively bright there was some fear that repeated observations of
it would saturate the photomultiplier tube. Thus a neutral density filter of approximately
2.5 magnitudes was used for observations of the variable only. We later decided that this
concern was unfounded and dropped the use of the neutral density filter at the start of
season three. Unfortunately, during the time we were using the neutral density filter we
neglected to make sky observations both with and without this filter. Hence we had to
approximate the sky counts with the neutral density filter by applying a correction based
on our calibration of the neutral density filter. These b observations, although included in
the analysis, should be treated with some suspicion.
Once the new check star was introduced (for seasons six and seven), the reduction
consisted of simply eliminating suspect observations using the three sigma comp - check
criterion described above. Next, seasonal means were removed from the data sets. The
variability of the check star forced us to adopt a different technique to determine the
precision of the photometry for seasons one through five. For these seasons we first
removed the variability of the check star. The check minus comp observations were
fitted with a Fourier series in the period of variation of the check and its first harmonic.
Standard deviations of residuals from this fit measure the precision of the photometry:
u=±0.007, b=v=±0.005, and y=±0.006. For comparison, the V473 Lyrae data (covering
the first four seasons of this study) has errors of u=±0.013, v=b=±0.009, and y=± 0.007
mags. For seasons six and seven the standard deviation of the comp minus check are:
– 7 –
u=±0.0068, v=±0.0059, b=±0.0065, y =±0.0082. Thus, even though the original check
star was variable, we feel that the fact that all these standard deviations are in the same
size range suggests the adopted procedure yields very acceptable results.
2.2. Spectroscopy
Seventeen 2.4 A mm−1 spectrograms with a spectral coverage of 67 A per exposure
and a signal-to-noise ratio of about 200 were obtained with an 1872 element 15µ pixel bare
Reticon detector using the long camera of the coude spectrograph of the 1.22-m telescope
of the Dominion Astrophysical Observatory. The spectra cover approximately λλ3830-4770.
Table 2 lists the central wavelengths and the measured radial velocities. The resolution
was approximately 0.072 A. A 20 A mm−1 spectrogram which included the Hγ line was
also obtained with the Reticon. We flat fielded the spectra using the exposure of a lamp in
the mirror train and then measured them using the interactive computer graphics program
REDUCE (Hill & Fisher 1986). The spectrum is weak-lined with only a few lines measured
per Reticon observation as is usual for middle B stars in the visible region. Lines of H I, He
I, C II, N II, O I, Al II, Al III, Mg II, Si II, S II, Ca II, Ti II, Cr II, Fe II, Fe III, and Ni II
were identified using Moore (1945).
On some spectra the metal lines have rotational profiles corresponding to 19 km s−1
which is half of the value listed by Hoffleit (1982). On others, the lines have distorted
profiles which indicates that this star exhibits non-radial variability. Campos & Smith
(1980) describe stars exhibiting similar behavior. Figures 2 and 3 show some examples of
lines in 3 Vul. These line profile variations are not those of a typical mCP star. As each
spectrum had only a few high quality lines, the deduced radial velocities have one sigma
rms values of order one km s−1. They range from -21 to -34 km s−1 compared with values
between - 10 and 17 km s−1 listed by Abt & Biggs (1972).
– 8 –
3. Period Analysis
Our goals in analyzing the photometric observations were to confirm the periods
reported by Hube & Aikman (1991) and to detect any other periodic variations. The efforts
of all those who labor at period analysis must be in light of two caveats: (a) Even a random
data set will yield some periods. (b) With a sufficient number of sine/cosine terms any type
of variation can be modeled. With these cautions in mind, we analyzed our data using three
different period determination techniques. The first was the Lomb-Scargle periodogram
(Lomb 1976; Scargle 1982) as implemented by Pelt (1992) as part of his Irregularly Spaced
Data Analysis (ISDA) package. Secondly a version of the CLEAN algorithm (Roberts,
Lehar, & Dreher 1987) programmed by Alex Fullerton in IDL and modified by Myron
Smith was applied to help eliminate aliases. Finally, Period 98 (Sperl 1998) was used
to validate the periods found by other methods. In order to identify any variations over
time in the frequencies found, these techniques were applied to various data groupings in
each color. These included the entire 2752 day span, each season individually, and both
adjacent and non-adjacent pairs of seasons. The results discussed below were consistently
found in each of these groupings. The periodogram for the v data shown in Figure 4 is
typical. Two frequencies emerge: f1=0.9719 cycles d−1 (P=1.0289d) and f2=0.7923 cycles
d−1 (P=1.2622d).
Lower amplitude periods were sought by the following method (known as prewhitening).
A simple linear combination of the periods found was fitted to the observations via least
squares. The resulting function was subtracted from the observations. These residuals
were then subjected to periodogram analysis. The prewhitened periodogram of the v
observations illustrates the results (Figure 5). Another frequency (f3=0.8553 cycles d−1,
P=1.1692d) is observed. This process was repeated several times. At each step, a model
with all frequencies found to that point was fitted to the original data and the residuals
– 9 –
examined. A CLEAN analysis (Figure 6) clearly reveals these main frequencies. Note the
reversal of the powers of f1 and f2. ISDA and Period 98 do not show this reversal when
examining the entire data set. There is also a frequency of 1.76 cycles d−1 (P = 0.59d)
which is the sum of f1 and f2. The peak close to 0.0 cycles d−1 is due to residual seasonal
instrumental effects
Determining when to stop this process of adding one frequency at a time needs some
comment. The criteria used to justify the addition of a term included the signal-to-noise
ratio for the term amplitude (greater than 0.5), the size of the amplitude (greater than
or near to the photometric precision), and the amount of reduction in the scatter of the
residuals (greater than 5 %). For the latter item, Waelkens (1991) considers a minimum
of 10% as a conservative and safe limit. However due to the large number of observations
available in this study, we feel that a less conservative (5%) limit is justified. Finally, terms
which consisted of linear combinations of stronger terms were searched for and kept if there
was some confirming indication of their presence. Such coupling is common in multimode
pulsators in Cepheid strip variables. Even though the inclusion of the sum term, f1+f2, does
not satisfy all of the criteria mentioned above for retention, this term consistently shows up
and has been retained.
Table 3 gives the adopted fit by color and by season. In this table σo denotes the
scatter in the observations while σf is the residual scatter after the simple harmonic fit (the
four terms fitted by simple linear least squares). As noted by Waelkens (1991), this residual
scatter is always expected to be somewhat greater than the photometric precision (comp -
check). The percent reduction is the fractional improvement between σo and σf .
Phase diagrams giving the variation in each frequency for v are shown in Figure 7. The
strong variations in f1 and f2 are essentially in phase. The third term, f3, is clearly out of
phase with f1 and f2. The variation in the sum term is weak and appears to show a shift in
– 10 –
phase with respect to its components, f1 and f2.
Individual “seasons” were defined as contiguous groups of observations. This definition
resulted in some observations not belonging to any season. Approximately 1/3 of the 3
Vul observing season is lost to the summer monsoons in Arizona. The few observations
obtained after the end of the monsoons each year were not included in any of the seasonal
data discussed in Section 5.
Two other data sets were analyzed. The first data set consists of the radial velocities
tabulated in Hube & Aikman (1991) combined with the 17 velocities obtained from the
spectra discussed in Section 2.2. The Hube & Aikman data has 270 data points spanning
6233 days. Our data set of 17 data points spans 1516 days. The total time span for this
combined velocity data set is 9199 days. The resulting orbital period is 366.84 days. A
CLEAN periodogram of this data, Figure 8, clearly shows the orbital variation, f1 and f2.
In this data set f2 is stronger than f1.
The second data set consists of Hipparcos satellite observations (Perryman 1997) of 3
Vul starting on JD 2447901, spanning 1040 days (overlapping the beginning of our APT
data by 587 days and 102 observations), and containing 203 points. Analysis clearly shows
f1 and f2 but again with their amplitudes reversed from those found in the APT data. After
prewhitening, the Hipparcos data verifies that f3 exists although it is not the next strongest
frequency. The reversal in the amplitudes of f1 and f2 in these data sets also occurs in season
four of the APT data. Both the differences in amplitude of the various APT seasons and
the differences among the data sets indicate that the pulsational energy may have shifted
among modes.
Our f3 is not the same as that found by Mathias et al. (2001). They report 0.47233
c d−1 while we find 0.8553 c d−1. In a periodogram of the Hipparcos data these two values
are approximately equal in strength while least squares fitting gives a larger reduction in
– 11 –
the standard deviation using their f3. On the other hand the APT data (see Figure 5)
shows essentially no signal around 0.47 c d−1 even after prewhitening for f1 and f2. An
examination of the observing window transform for the Hipparcos data shows a peak at
0.3775 c d−1. We note that our f3 - 0.3775 c/d is their f3. We thus suggest that they have
found an alias of the true f3. A careful examination of the Period 98 transform for our data
set does not revel any significant power at either the fourth or fifth frequency of Mathias et
al. (2001). Hence we conclude that these frequencies are not real.
4. Spectroscopic Analysis
To derive the photospheric parameters, we assumed that the atmospheric variability
does not have a major effect on them and that we could study the abundances as if the
atmosphere were non-variable. Using the homogenous mean uvbyβ values of Hauck &
Mermilliod (1980) and the calibration of Napiwotzki, Schonberner, & Wenske (1993), which
was a revision of that by Moon & Dworetsky (1985), we estimate Teff = 14343 K and log g
= 4.24. 3 Vul is slightly reddened with E(b-y) = 0.014. The uncertainties are about ±200 K
and ±0.2 dex (Lemke 1989). To improve the value of the surface gravity we used SYNTHE
(Kurucz & Avrett 1981) to synthesize the Hγ region using ATLAS9 LTE plane parallel solar
composition model atmospheres (Kurucz 1993) whose effective temperatures and surface
gravities are close to those found from photometry. We assumed no microturbulence.
Comparison with the Hγ profile as corrected for scattered light (Gulliver, Hill, & Adelman
1996) with the model predictions showed that log g had to be increased to 4.30.
It is somewhat difficult to reconcile the adopted value of the surface gravity with the
spectroscopic luminosity class of III. There appears to be a problem with classification. As
no atomic species had sufficient lines in both number and range of equivalent widths to
deduce a microturbulence, we assumed ξ = 0.0 km s−1 in accord with studies of normal
– 12 –
stars with similar effective temperatures (Adelman 1994).
The helium abundances were derived by comparison of the observed profiles with those
calculated in LTE using SYNSPEC (Hubeny, Lanz, & Jeffrey 1994) and the adopted model
atmosphere. The results (Table 4) indicate that the derived He/H ratio is close to solar. To
convert log N/NT values of the metal lines as found using the program WIDTH9 (Kurucz
1993) to log N/H for comparison with other stars, especially the Sun, we added 0.04 dex.
Table 5 contains the analyses of the metal lines using the program WIDTH9 (Kurucz
1993) and ξ = 0.0 km s−1. Each entry lists the multiplet number (Moore 1945), the
wavelength in A, the gf-value and its reference, the observed equivalent width in mA, and
the log N/NT value. Also included are the average log N/NT values, where N is the number
of atoms of a given species per unit volume and NT is the total number of atoms of all kinds
per unit volume. In deriving the abundances we used a correction of 3.5% to allow for the
scattered light in the direction of the dispersion (Gulliver, Hill, & Adelman 1996).
Table 6 presents our results for 3 Vul alongside those of other normal stars with
consistently performed analyses (see Adelman (1994), Adelman et al. (2001) and references
therein) as well as the corresponding results for the Sun from Grevesse, Noels, & Sauval
(1996). For the 13 values derived from neutral and singly-ionized species, 3 Vul, on the
average, has abundances 0.17±0.10 dex less than solar. These results and the He/H ratio
are consistent with the trends of abundances seen for other normal main sequence band B
stars. The result for Fe III derived from only one line is not consistent with the values from
the Fe II lines. This fact may indicate problems in the equivalent width, gf value, nonLTE
effects, or that the photosphere was disturbed. The derived abundances being those of
normal B stars suggests that it is 3 Vul’s position in the HR diagram rather than chemical
peculiarity which is related to its variability.
An LTE calculation using our derived value of He/H predicts an equivalent width for
– 13 –
the He I λ5876 line of 245 mA. As non-LTE effects increase this line’s equivalent width, the
mean value found by Catanzaro, Leone, & Catalano (1999) is not particularly discordant
with that expected from the derived He/H values. Other strong He I lines, particularly
λ4026 and λ4472, which are even stronger, should also be expected to change their line
profiles and equivalent widths and hence be an important probe of the changing conditions
in the high atmospheres of 3 Vul and similar stars. We cannot confirm this expectation due
to having obtained only one spectrum for this region.
5. Discussion
Figure 9, which shows the variation in the seasonal amplitudes for all colors, suggests
that the distribution of pulsational energy of 3 Vul has shifted in time among the frequencies.
Particularly noticeable is the increase of f2 relative to f1 in season 4 and the drastic decrease
in season 7. These changes in amplitudes are in contrast to what we have found for the
prototype star, 53 Persei, where the amplitudes of the strongest terms have been essentially
constant over ten years (Dukes & Mills 2001).
Color variations were examined (see Table 7). The strongest color variation is in
u-b. There is essentially no variation in b-y. According to (Buta & Smith 1979) the ratio
of the v-y amplitude to v amplitude measures the relative strengths of temperature and
geometrical effects of the variability. Thus the values obtained for f1 and f2 are indicative of
nonradial pulsation.
Figure 10 shows the change in amplitudes of variation of four color indices (u-b, c1, v-y,
and v-b). Both u-b and c1 have significant amplitude and show significant variation. Since
these are temperature sensitive indices in the B stars, we see that the variation due to f1
and f2 is primarily a temperature rather than a geometric effect.
– 14 –
With the increase in accuracy provided by the Hipparcos Satellite, astronomers can
now properly place many nearby stars in the HR diagram. We used the the Hipparcos
data analysis program Celestia 2000 (Turon, Priou, & Perryman 1997) to convert observed
visual magnitudes to absolute visual magnitudes. For that purpose we used the Hipparcos
parallaxes for 29 SPB stars in the literature with errors in the parallaxes of less than 20%.
After the effective temperatures and surface gravities were obtained from the average uvbyβ
photometry given in the SIMBAD database using the program of Napiwotzki, Schonberner,
& Wenske (1993) and subsequently applying the corrections from Adelman et al. (2002), we
obtained the absolute Bolometric magnitudes using Bolometric Corrections from Bessell,
Castelli, & Plez (1998) corresponding to these temperatures and absolute V magnitudes.
These values (Table 8) are now compared with the evolutionary tracks from Townsend
(2002) graphically in Figure 11 with the location of 3 Vul emphasized. The Townsend
tracks are for that portion of the evolutionary track for which g-mode pulsation is excited.
Having the Townsend models available allows us to attempt modal identification of the
four terms we have found in our data. First we use the position of 3 Vul on the HR diagram
to narrow our choices to models in the 3.5 - 4.5 M� range. Plotting amplitude ratios versus
phase differences for our observed modes together with those of Townsend’s models, as
shown in Figure 12, suggests that our observed modes are all l = 1 modes.
A comparison of frequencies found by Townsend gives no simultaneous close match
with all three of our strong terms (we exclude the combination term from this discussion).
However comparing the behavior of the same mode between models of different masses
suggests that a model of intermediate mass might have a matching frequency set. Rather
than to attempt our own model calculations we chose to interpolate in the grid of the
Townsend models. Again we used the approximate position of 3 Vul in the HR diagram to
limit our consideration to those models lying within the one sigma limits indicated by the
– 15 –
error bars in Figure 11. For these models (numbers 60-110) we plotted frequency versus
mass for the 3.5, 4.0, and 4.5 M� models. We next considered the frequency range covered
by our observations (about 0.75 to 1.00 c/d). As shown in Figure 13 we then interpolated
to give the bands traversed by the modes existing within this frequency range (g012-g017).
Finally, we identified regions where each of these bands intersected each of our observed
frequencies in order to look for areas where all three frequencies were matched by modes
corresponding to a unique stellar mass. We found three possible mass ranges; one near 3.6
M�, one near 3.9 M�, and one near 4.2 M�. The overlap was poor for 3.6 M� and only
marginal at 3.9 M�. However there is a region from 4.16 to 4.18 M� where our observed
frequencies match respectively the g012, g014, and g015 modes. Thus we conclude that
these modes are present in 3 Vul and that its ”pulsational” mass is approximately 4.16 M�.
We now turn to the question of the age of 3 Vul. Again we use the Townsend models.
We plot the age versus frequency for the 4 and 4.5 M� models. We then look for the
intersection point of the line connecting the same modes in this plot with our observed
frequencies. Next we identify the point on this line corresponding to a 4.16 M� star. We
do this for all lines intersecting our frequencies. We next measure the distance between the
4.16 M� point on the line and the intersection point as shown in Figure 14. Results are
given in Table 9. We pick as the most probable age the one where the sum of the squares of
these distances is the minimum. We find that the most probable age corresponds to model
70 whose log age is 7.4.
Following the methodology described in Straizhis (1992) we can use uvby data from
SIMBAD together with our measured differential amplitudes to determine something about
the temperature change associated with the stronger modes. We calculate the reddening
free [u - b] as 0.672. For B stars (Napiwotzki, Schonberner, & Wenske 1993) the unreddened
– 16 –
[u - b] is a good temperature indicator giving θ where
θ =5040K
T.
Specifically
θ = 0.1692 + 0.2828[u − b] − 0.0195[u − b]2.
Differentiation gives:
∆θ = 0.2828∆[u − b] − 2(0.0195)[u − b]∆[u − b].
Thus for Season one, a range in u - b of 0.0256 gives a ∆ T of 270K. By Season six, the
range has risen to 0.0340 giving a ∆ T of 360K.
Finally, since we now have a value for the mass of the primary we can say something
about the mass of the secondary. Hube & Aikman (1991) give the mass function as 0.0144,
from which we have that the minimum mass of the secondary is 0.7 M�. Only for i � 45
deg can the mass of the secondary exceed 1 M�. Since the primary is young the secondary
must be unevolved if it was formed at the same time. Thus the secondary is most likely a
G-K star which may still be contracting to the main sequence.
6. Conclusions
• 3 Vulpeculae is a member of the 53 Persei class of variables showing both line profile
and light variations similar to the prototype star, 53 Persei.
• Abundances are normal for a mid-B star. As our spectra were taken at different times
they should average out the effect of any variability on compositioon. Hence 3 Vul
should be removed from lists of chemically peculiar stars.
• Like 53 Persei, 3 Vul is multiperiodic.
– 17 –
• Unlike for 53 Persei, for 3 Vul, it is probable that energy is being transferred between
modes as evidenced by the variable amplitudes.
• The three modes excited are tentatively the l = 1 modes g012, g013, and g015.
• The temperature change associated with g012 mode increased by approximately 90 K
over six seasons.
• The primary mass most nearly matching the pulsational frequencies if 4.14 M�.
• The age is approximately 25 million (107.5) years.
• The mass of the secondary is greater than 0.7 M� and probably less than 1 M�.
Certainly, further observation is warranted. Photometry with the APT continues.
We would like to thank Dr. Gianni Catanzaro for supplying velocities based on the
He λ5876 line, Dr. Myron Smith for supplying the IDL code for the CLEAN algorithm,
and Dr. Richard Townsend for rapidly supplying corrected uvby data for his models. We
also thank Lou Boyd of Fairborn Observatory for maintaining the APT. SJA thanks Dr.
James E. Hesser, Director of the Dominion Astrophysical Observatory for the observing
time needed for his contribution to this paper. His work was supported in part by grants
from The Citadel Development Foundation. RJD thanks Dr. Walter S. Fitch, Professor
Emeritus, University of Arizona for many helpful conversations and Dr. Laney Mills for
extensive help in editing the manuscript. AJK submitted a preliminary version of this work
in partial fulfillment for the Bachelor of Science degree. Finally we would like to thank
the numerous College of Charleston undergraduate students who have participated in the
reduction of the APT data during this project. These have included Georgia Richardson,
Rose Forsythe, Francine Halter, Thomas Freismuth, Shadrian Holmes, Kwayera Davis, and
– 18 –
Yvette Mixon. This research has made use of the SIMBAD database, operated at CDS,
Strasbourg, France and has been funded by NSF Grants #AST86-16362, #AST91-15114,
#AST95-28906, and #AST-0071260 all to the College of Charleston.
– 19 –
REFERENCES
Abt, H. A., Biggs, E. S. 1972, Bibliography of Stellar Radial Velocities (New York: Latham
Process Corp.)
Adelman, S. J. 1994, MNRAS, 271, 355
Adelman, S. J., Caliskan, H., Kocer, D., Kablan, H., Yuce, K., & Engin, S. 2001, A&A,
371, 1078
Adelman, S. J., Pintado, O. I., Nieva, F., Rayle, K. E., Saunders, S. E., Jr. 2002, A&A, in
press
Bessell, M. S., Castelli, F., Plez, B. 1998, A&A, 333, 231
Boyd, L. M., Genet, R. M., & Hall, D. S. 1984, IAPPP Comm., No. 15, 20
Buta, R. J. & Smith, M. A. 1979, ApJ, 232, 213.
Campos, A. J. & Smith M. A. 1980 ApJ, 238, 250
Catanzaro, G., Leone, F., & Catalano, F. A. 1999, A&AS, 134, 211
Dukes, R. J., Adelman, S. J., & Seeds, M. A. 1991, in Advances in Robotic Telescopes, ed.
M. A.Seeds and J. L. Richard (Mesa: Fairborn Press), 281
Dukes, R. J. & Mills, L. R. 2001, American Astronomical Society Meeting 197, #46.11
Fuhr, J. R., Martin, G. A., & Wiese, W. L. 1988, J. Phys. Chem. Ref. Data, 17, Suppl. 4
Fuhr, J. R., & Wiese, W. L. 1990, in CRC Handbook of Chemistry and Physics, ed. D. R.
Lide (Cleveland, Ohio, CRC Press)
Grevesse, N., Noels, A., & Sauval, A. J. 1996, ASP Conf. Ser. 99: Cosmic Abundances, 117
– 20 –
Gulliver, A. F., Hill, G., & Adelman, S. J. 1996, ASP Conf. Ser. 108: M.A.S.S., Model
Atmospheres and Spectrum Synthesis, 232
Hall, D. S., Kirkpatrick, J. D., & Seufert, E. R. 1986, IAPPP Comm., No. 25, 32
Hauck, B., & Mermilliod, M. 1980, A&AS, 40, 1
Hill, G. & Fisher, W. A. 1986, Publications of the Dominion Astrophysical Observatory
Victoria, 16, 193
Hoffleit, D. 1982, The Bright Star Catalogue, 4th revised edition, (New Haven, CT: Yale
University Observatory)
Hube, D. P., & Aikman, G. C. L. 1991, PASP, 103, 49
Hubeny, I., Lanz, T., & Jeffery, C. S. 1994, Daresbury Lab. News, Anal. Astron. Spectra,
No. 20, 30
Kurucz, R. L. 1993, Atlas 9 Stellar Model Atmospheres Programs and 2 Km/s Gravity,
Kurucz CD Rom No. 13, (Cambridge, MA: Smithsonian Astrophysical Observatory)
Kurucz, R. L. & Avrett, E. H. 1981, SAO Special Report No. 391 (Cambridge, MA:
Smithsonian Astrophysical Observatory)
Special Report No. 391
Kurucz, R. L. & Bell B. 1995, Atomic Data for Opacity Calculations, Kurucz CD-Rom No.
23, (Cambridge, MA: Smithsonian Astrophysical Observatory)
Lanz, T. & Artru, M. -C. 1985, Phys. Scripta. 32, 115
Lemke, M. 1989, A&A, 225, 125
Lomb, N. R 1976, Ap&SS, 39, 447
– 21 –
Martin, G. A., Fuhr J. R., & Wiese W. L. 1988, J. Phys. Chem. Ref. Data, 17, Suppl. 3
Mathias, P., Aerts, C., Briquet, M, De Cat, P., Cuypers, J., Van Winckel, H., Le Contel, J.
M. 2001, A&A, 379, 905
Moon, T. T. & Dworetsky, M. M. 1985, MNRAS, 217, 305
Moore, C. E. 1945. Rev. ed., (Princeton, N.J.: The Observatory)
Napiwotzki, R., Schonberner, D, & Wenske, V. 1993,A&A, 268, 653
Palmer, D. R., Walker, E. N., Jones, D. H. P., & Wallis, R. E. 1968, Royal Greenwich
Observatory Bulletin, 135, 385
Pelt, J. 1992, Irregularly spaced data analysis, User manual and program package, (Helsinki:
Univ. Helsinki)
Perryman, M. A. C. 1997, The Hipparcos and Tycho Catalogues (ESA SP-1200: Noordwijk:
ESA)
Roberts, D. H., Lehar, J., & Dreher, J. W. 1987, AJ, 93, 968
Rountree Lesh, J. 1968, ApJS, 17, 371
Scargle, J. D. 1982, ApJ, 263, 835
Smith, M. A. 1989, in Automatic Small Telescopes, ed. D. S. Hayes & R. M. Genet (Mesa:
Fairborn Press). 143
Smith, M. A., Fullerton, A. W., & Percy, J. R. 1987, LNP Vol. 274: Stellar Pulsation,
Sperl, M. 1998, Comm. in Asteroseismology (Vienna) 111, 1
Straizhis, V. 1992, (Tucson : Pachart Pub. House)
– 22 –
Strassmeier, K. G. & Hall, D. S. 1988, ApJS, 67, 439
Townsend, R. H. D. 2002, MNRAS, 330, 855
Tuton, C., Priou, D., Perryman, M. A. C. 1997, Proc. of the ESA Symposium ‘Hipparcos –
Venice ’97’ (ESA SP-402: Venice:ESA)
Waelkens, C. 1991, A&A, 246, 453
Walker, M. F. 1952, AJ, 57, 227
Wiese, W. L., Fuhr J. R., & Deters T. M. 1996, J. Phys. Chem. Ref. Data, Monograph 6
Wiese, W. L. & Martin, G. A. 1980, NSRDS-NBS 68, Part 2 (Washington, DC: U. S.
Government Printing Office)
Wiese, W. L., Smith, M. W., & Glennon, B. M. 1966, NSRDS-NBS 4 (Washington, DC: U.
S. Government Printing Office)
Wiese, W. L., Smith, M. W., & Miles, B. M. 1969, NSRDS-NBS 22 (Washington, DC: U.
S. Government Printing Office)
This manuscript was prepared with the AAS LATEX macros v5.0.
– 23 –
2451000245000024490002448000
Julian Date
He I 5876 Å Equivalent Widths
Hipparcos Photometry
Radial Velocities
APT Photometry
Earlier Velocities
Stromgren b
Stromgren uvy
Season 1 2 3 4 5 6 7
Fig. 1.— The time coverage of the data sets considered.
447.8 448.0 448.2 448.4 448.6 448.8 449.0 449.2Wavelength (nm)
0.50
0.60
0.70
0.80
0.90
1.00
Res
idua
l Int
ensi
ty
Fig. 2.— The 447.8-449.3 nm region of 3 Vul showing normal line profiles.
– 24 –
450.5 451.0 451.5 452.0 452.5Wavelength (nm)
0.50
0.60
0.70
0.80
0.90
1.00
Res
idua
l Int
ensi
ty
Fig. 3.— This 450.5-452.5 nm region of 3 Vul showing line profiles distorted by pulsations.
0.020
0.015
0.010
0.005
0.000
Pow
er
2.01.51.00.50.0
Frequency (cyles/day)
f1f2|f2-1|
|f1-1|
f2+1
f1+1
|f1-2||f2-2|
Fig. 4.— Periodogram by Period 98 of the differential v magnitudes. The main frequencies
f1 and f2 are indicated along with several aliases.
– 25 –
0.006
0.005
0.004
0.003
0.002
0.001
0.000
Pow
er
2.01.51.00.50.0
Frequency (cycles/day)
f3f3+1
|f3-1||f3-2|
f1+f2f1+f2-1|f1+f2-2|
Fig. 5.— Periodogram of the prewhitened v differential magnitudes (f1 and f2 were removed).
Note that f3 and the sum term (and their aliases) are clearly revealed.
7x10-5
6
5
4
3
2
1
0
Pow
er
2.01.51.00.50.0Frequency(cycles/day)
f1f2
f3
Fig. 6.— CLEAN periodogram of v differential magnitudes. The peak close to zero c/d is
due to residual seasonal instrumental effects. It is not the orbital frequency.
– 26 –
-0.04-0.020.000.020.04
Del
ta v
2.01.51.00.50.0Phase of f1+f2
0.040.020.00
-0.02-0.04
Del
ta v
2.01.51.00.50.0Phase of f3
-0.04-0.020.000.020.04
Del
ta v
2.01.51.00.50.0Phase of f2
-0.04-0.020.000.020.04
Del
ta v
2.01.51.00.50.0Phase of f1
Fig. 7.— Phase diagrams for the v magnitudes. Each panel is prewhitened for all frequencies
except for the indicated phasing frequency.
– 27 –
6
5
4
3
2
1
0
Pow
er
1.00.80.60.40.20.0
Frequency (cycles/day)
forb
f1
f2
Fig. 8.— Periodogram by CLEAN of the radial velocities in Hube & Aikman (1991) and
those reported here. Note that both f1 and f2 are present although the relative amplitudes
are significantly different from those found in the photometric data. We also see a peak
corresponding to the orbital frequency.
– 28 –
0.040
0.030
0.020
0.010
0.000
u am
plitu
de
1 2 3 4 5 6 7
Season
0.020
0.015
0.010
0.005
0.000
v am
plitu
de
0.020
0.015
0.010
0.005
0.000
y am
plitu
de
0.020
0.015
0.010
0.005
0.000
b am
plitu
de
f1 f2 f3 f1+f2
Fig. 9.— Temporal variation in the amplitudes of the frequencies reported. The dates
used were the midpoints of the seasons. One sigma error bars have not been included since
generally the symbol sizes are larger than the errors.
– 29 –
0.018
0.016
0.014
0.012
0.010
0.008
0.006
0.004
0.002
0.00024500002448400
u-b 0.018
0.016
0.014
0.012
0.010
0.008
0.006
0.004
0.002
0.00024500002448400
c1
0.018
0.016
0.014
0.012
0.010
0.008
0.006
0.004
0.002
0.00024500002448400
v-y 0.018
0.016
0.014
0.012
0.010
0.008
0.006
0.004
0.002
0.00024500002448400
v-b
f1 f2 f3 f4
Fig. 10.— Seasonal amplitudes of color index variations for the frequencies reported. The
dates used were the midpoints for the seasons. One sigma error bars are shown.
– 30 –
3.4
3.2
3.0
2.8
2.6
2.4
2.2
2.0
Log
Lum
inos
ity
4.30 4.25 4.20 4.15 4.10 4.05 4.00Log Effective Temperature
3 Mo
3.5 Mo
4.0 Mo
4.5 Mo
5.0 Mo
5.5 Mo
6.0 Mo
6.5 Mo
3 Vulpeculae
Fig. 11.— HR Diagram showing evolutionary tracks for Townsend models where g mode
pulsation occurs. The positions and one sigma error bars for 25 SPB stars as well as for 3
Vul are shown
– 31 –
4x10-1
5
6
7
Am
pV
U
403020100-10PhiVU
4.5 Mo
f1f2
f3 f1+f2
l = 1 l = 2 l = 3 Observed Values
4x10-1
5
6
7
Am
pvu
403020100-10Phivu
4.0 Mo
f1
f2f3 f1+f2
l = 1 l = 2 l = 3 Observed Values
Fig. 12.— Amplitude ratios versus phase differences for the Stromgren v and u bands. Filled
circles are observed values. Other symbols are models.
– 32 –
4.6
4.4
4.2
4.0
3.8
3.6
3.4
1.000.980.960.940.920.900.880.860.840.820.800.780.76Frequency (c/d)
g017 g016 g015 g014
g013
g012
f1f3f2
Fig. 13.— Plot of frequency versus mass from Townsend’s models. The diagonal strips are
various pulsation modes and are interpolated from the 3.5, 4.0, and 4.5 values. As described
in the text the position of 3 Vul on the HR diagram with one sigma error bars was used
to limit the models plotted to Townsend’s numbers 60 - 110. The horizontal bars represent
the intersection of each diagonal strip with one of the observed frequencies. The only mass
range with all three frequencies simultaneously matching a theoretical mode is from 4.14 to
4.18 M�.
– 33 –
7.60
7.55
7.50
7.45
7.40
7.35
7.30
7.25
Log(
Age
)
1.051.000.950.900.850.800.750.70Frequency (c/d)
f1
f2
f3
Model 080
Model 060
Model 070
g015 g014 g013 g012
f2
d2,70
d3,70
d1,70
4.0 Mo
4.5 Mo
Fig. 14.— Plot of log age versus mass. The diagonal lines running from upper right to lower
left are interpolated between the 4.0 M� and the 4.5 M� models. The short diagonal lines
intersecting them indicate the interpolated position of a 4.16 M� model. The vertical lines
correspond to our observed frequencies. The distance in arbitrary units each 4.16 M� model
is from the nearest observed frequency is given in Table 9. Three examples of these distances
are labeled as d-frequency,model number . The most probable age is assumed to be the one
with the smallest sum of the squares of these distances.
– 34 –
Table 1. uvby Photometry of 3 Vul
Mean Julian Date Delta u Delta v Delta b Delta y
2448334.0115 -2.1248 -2.4500 -2.4225 -2.3294
2448348.9690 -2.1493 -2.4677 -2.4337 -2.3404
2448350.9635 -2.149 -2.4659 -2.4332 -2.3405
2448351.9610 -2.1866 -2.487 -2.4516 -2.3600
2448353.9555 -2.1321 -2.4559 -2.4239 -2.3315
2448354.9530 -2.1227 -2.4505 -2.4172 -2.3283
2448355.9505 -2.1474 -2.4596 -2.4297 -2.3332
2448356.9476 -2.1713 -2.4792 -2.4458 -2.3557
2448357.9449 -2.1972 -2.4907 -2.4567 -2.3594
2448359.9398 -2.1113 -2.4413 -2.413 -2.3225
2448360.9371 -2.1172 -2.4526 -2.4202 -2.3288
2448361.9342 -2.1234 -2.4486 -2.4215 -2.3271
2448363.9764 -2.0709 -2.422 -2.3914 -2.3028
aTabular values are differential magnitudes between the vari-
able and the comparison, HD 181164.bThe complete version of this table is in the electronic edition
of the Journal. The printed edition contains only a sample. Ju-
lian Dates for each observation are given in the electronic version
rather than the mean of the values for the four filters given in the
sample.
– 35 –
Table 2. Journal of Spectrographic Observations
Central Wavelength(A) Mid-Exposure Julian Date Exposure Time (min.) Radial Velocity (km s−1)
3860 2449201.712 40 -25.2
3915 2449280.617 45 -20.8
3970 2449203.790 60 -27.2
4025 2448848.738 38 -21.4
4080 2449894.905 57 -28.4
4135 2449276.675 63 -24.0
4190 2449200.768 22 -28.8
4245 2448379.936 31 -22.2
4300 2449893.882 59 -32.9
4355 2449621.667 23 -24.0
4410 2449892.816 49 -32.3
4465 2448474.803 26 -27.6
4520 2449531.844 52 -34.0
4575 2449895.928 66 -31.2
4630 2448479.812 37 -25.0
4685 2448845.710 37 -24.8
4740 2449891.884 59 -24.0
– 36 –
Table 3. Frequency Determination
color/season Start JD End JD N Amplitude Amplitude Amplitude Amplitude σo σf Reduction
f1=0.9719 f2=0.7923 f3=0.8553 f1+f2
u all 2448334 2451086 991 0.030 0.026 0.008 0.004 0.033 0.017 48%
u1 2448334 2448440 125 0.029 0.026 0.014 0.005 0.034 0.013 62%
u3 2449055 2449168 170 0.032 0.025 0.009 0.005 0.031 0.011 65%
u4 2449418 2448548 114 0.032 0.034 0.013 0.001 0.036 0.014 61%
u5 2449786 2449910 171 0.034 0.031 0.004 0.011 0.035 0.013 63%
u6 2450506 2450620 87 0.036 0.031 0.011 0.005 0.035 0.018 49%
u7 2450875 2450993 175 0.035 0.019 0.009 0.001 0.032 0.014 56%
v all 2448334 2451086 996 0.020 0.016 0.005 0.003 0.021 0.011 48%
v1 2448334 2448440 124 0.018 0.015 0.008 0.004 0.021 0.008 62%
v3 2449055 2449168 170 0.019 0.015 0.006 0.003 0.019 0.007 63%
v4 2449418 2448548 112 0.020 0.020 0.008 0.001 0.021 0.008 62%
v5 2449786 2449910 172 0.021 0.019 0.003 0.006 0.022 0.008 64%
v6 2450506 2450620 87 0.021 0.019 0.007 0.002 0.022 0.012 45%
v7 2450875 2450993 174 0.021 0.011 0.005 0.000 0.020 0.009 55%
b all 2448334 2451086 1172 0.016 0.015 0.004 0.003 0.019 0.011 42%
b1 2448334 2448440 125 0.017 0.015 0.007 0.003 0.020 0.009 55%
b2 2448702 2448809 181 0.014 0.017 0.002 0.005 0.020 0.011 45%
b3 2449055 2449168 170 0.018 0.014 0.006 0.003 0.017 0.007 59%
b4 2449418 2339548 112 0.018 0.019 0.008 0.001 0.020 0.007 65%
b5 2449786 2449910 173 0.019 0.017 0.002 0.006 0.020 0.008 60%
b6 2450506 2450620 86 0.019 0.017 0.006 0.002 0.019 0.010 47%
b7 2450875 2450993 171 0.019 0.011 0.005 0.001 0.018 0.009 50%
y all 2448334 2451086 995 0.016 0.014 0.004 0.003 0.018 0.010 44%
y1 2448334 2448440 124 0.016 0.014 0.007 0.002 0.018 0.008 56%
y3 2449055 2449168 170 0.017 0.013 0.005 0.003 0.017 0.007 59%
y4 2449418 2339548 114 0.017 0.018 0.007 0.001 0.019 0.007 63%
y5 2449786 2449910 173 0.018 0.016 0.003 0.005 0.019 0.008 58%
y6 2450506 2450620 84 0.019 0.018 0.005 0.002 0.019 0.010 47%
y7 2450875 2450993 172 0.017 0.010 0.004 0.001 0.016 0.008 50%
– 37 –
Table 4. He/H Values
Wavelength(A) He/Ha
4009 0.10
4026 0.10
4120 0.10:
4143 0.10:
4169 0.08
4388 0.10
4438 0.08
4472 0.11
4713 0.08
Mean 0.09±0.01
aNote: The two lines with
uncertain (:) values were given
one-half weight.
– 38 –
Table 5: Metal abundances of 3 Vul
Mult. λ(A) log gf Ref. Wλ(mA) log N/NT
C II log C/NT = -3.68±0.12
4 3918.98 -0.53 WF 27 -3.66
3920.68 -0.23 WF 36 -3.66
6 4267.02 +0.56 WF 43 -3.56
4267.26 +0.74 WF 39 -3.84
N II log N/NT = -4.34±0.26
5 4630.54 +0.09 WF 6 -4.15
12 3995.00 +0.21 WF 6 -4.52
OI log O/NT = -3.28±0.08
3 3947.29 -1.77 WF 12 -3.22
5 4368.30 -1.71 WF 7 -3.34
Mg II log Mg/NT = -4.67±0.09
4 4481.23 +0.97 FW 273 -4.59
5 3848.24 -1.60 WM 10 -4.76
3850.39 -1.88 WM 8 -4.58
9 4428.00 -1.20 WS 10 -4.67
4433.99 -0.90 WM 18 -4.69
10 4384.64 -0.78 WS 17 -4.81
4390.58 -0.53 WS 36 -4.59
Al II log Al/NT = -5.98
2 4663.10 -0.28 FW 20 -5.98
Al III log Al/NT = -5.47
3 4529.18 +0.67 WS 7 -5.47
– 39 –
Table 5: -continued
Mult. λ(A) log gf Ref. Wλ(mA) log N/NT
Si II log Si/NT = -4.51±0.09
1 3853.66 -1.44 LA 61 -4.64
3856.02 -0.49 LA 108 -4.45
3862.59 -0.74 LA 91 -4.58
3 4128.07 +0.38 LA 103 -4.48
4130.89 +0.53 LA 119 -4.42
Si III log Si/NT = -4.37±0.13
2 4552.65 +0.29 WM 15 -4.26
4567.82 +0.07 WM 8 -4.52
4574.76 -0.41 WM 5 -4.34
S II log S/NT = -4.94±0.24
9 4716.23 -0.42 FW 7 -5.19
30 4524.95 +0.17 WM 11 -4.94
43 4463.58 -0.02 WS 6 -4.79
4483.58 -0.43 FW 5 -4.53
44 4153.10 +0.62 WS 16 -4.97
4162.70 +0.78 WS 21 -4.86
49 4278.50 -0.12 WS 6 -4.75
4294.40 +0.56 WS 8 -5.22
55 3923.46 +0.44 WS 8 -5.20
Ca II log Ca/NT = -5.41
1 3933.66 +0.13 WM 139 -5.41
Ti II log Ti/NT = -7.26
31 4501.27 -0.75 MF 3 -7.26
– 40 –
Table 5: -continued
Mult. λ(A) log gf Ref. Wλ(mA) log N/NT
Cr II log Cr/NT = -6.44±0.09
44 4558.66 -0.66 MF 15 -6.40
4588.22 -0.63 MF 13 -6.54
4618.82 -1.11 MF 4 -6.58
4634.10 -1.24 MF 5 -6.41
Fe II log Fe/NT = -4.71±0.24
3 3945.21 -4.19 MF 7 -4.14
27 4173.45 -2.65 MF 21 -4.68
4233.17 -2.00 MF 35 -4.88
4303.17 -2.49 MF 22 -4.75
4351.76 -2.10 MF 26 -5.02
4385.38 -2.57 MF 18 -4.94
4416.82 -2.60 MF 22 -4.61
28 4178.86 -2.48 MF 19 -4.90
4296.57 -3.01 MF 11 -4.63
37 4489.18 -2.97 MF 9 -4.74
4491.40 -2.77 MF 17 -4.58
4515.34 -2.48 MF 16 -4.90
4520.22 -2.60 MF 16 -4.82
4534.17 -3.47 MF 9 -4.23
4555.89 -2.29 MF 24 -4.83
4629.34 -2.37 MF 22 -4.83
38 4508.28 -2.21 MF 20 -5.02
4522.63 -2.03 MF 27 -5.00
4541.52 -3.05 MF 7 -4.74
– 41 –
Table 5: -continued
Mult. λ(A) log gf Ref. Wλ(mA) log N/NT
Fe II (continued)
38 4576.33 -3.04 MF 12 -4.52
4583.83 -2.02 MF 46 -4.40
4620.51 -3.28 MF 8 -4.52
172 4048.83 -2.09 KX 7 -4.59
173 3935.94 -1.86 MF 11 -4.57
186 4635.33 -1.65 MF 16 -4.40
190 3938.97 -1.85 MF 7 -4.72
- 4451.54 -1.82 KX 7 -4.58
4455.26 -1.99 KX 4 -4.68
4596.02 -1.82 KX 6 -4.64
Fe III log Fe/NT = -3.97
45 4022.35 -2.05 KX 4 -3.97
Ni II log Ni/NT = -6.06±0.19
11 3849.58 -1.88 KX 12 -6.00
4067.05 -1.83 KX 15 -5.91
12 4015.48 -2.42 KX 2 -6.27
Note. — References for gf values
FW = Fuhr & Wiese (1990)
KX = Kurucz & Bell (1995)
LA = Lanz & Artru (1985)
MF = Martin, Fuhr & Wiese (1988) and Fuhr, Martin & Wiese (1988)
WM = Wiese & Martin (1980)
WF = Wiese, Fuhr & Dieters (1996)
WS = Wiese, Smith & Glennon (1966) and Wiese, Smith & Miles (1969)
– 42 –
Table 6: Comparison of Derived and Solar Abundances (log N/H)
Stars
Ion γ Peg ι Her τ Her 3 Vul ξ Oct π Cet 21 Aql 134 Tau ν Cap α Dra Sun
He I -1.02 -1.07 -0.96 -1.03 -1.07 -1.07 -1.05 -1.00 -1.19 -1.40 -1.01
CII -3.81 -3.49 -3.53 -3.64 -3.64 -3.77 -3.92 -3.45 -3.39 -3.78 -3.45
N II -4.03 -3.84 -4.09 -4.30 -4.33 -3.88 -4.15 ... ... ... -4.03
O I ... ... ... -3.24 -3.30 -3.30 -3.24 ... -3.33 -3.49 -3.13
Mg II -4.55 -4.78 -4.60 -4.63 -4.73 -4.52 -4.59 -4.53 -4.61 -4.82 -4.42
Al II -5.94 -6.03 ... -5.94 ... ... ... ... ... ... -5.53
Al III -5.90 -5.49 -5.59 -5.43 ... -5.32 -5.93 ... ... ... -5.53
Si II -5.31 -5.16 -4.490 -4.47 -4.77 -4.52 -4.40 -4.51 -4.69 -4.89 -4.45
Si III -4.67 -4.45 -4.42 -4.33 ... -4.99 -4.58 ... ... ... -4.45
S II -5.04 -4.91 -4.76 -4.90 -4.92 -4.82 -5.04 -4.53 -4.85 -5.03 -4.67
Ca II -6.20 -6.03 -5.74 -5.37 -6.24 -5.72 -5.66 -5.33 -5.55 -5.61 -5.64
Ti II ... ... -6.76 -7.22 -7.28 -7.17 -7.46 -7.06 -7.05 -7.10 -6.98
Cr II ... ... ... -6.40 -6.62 -6.54 -6.64 -6.41 -6.13 -6.61 -6.33
Fe II -4.44 -5.14 -4.72 -4.67 -4.81 -4.62 -4.80 -4.63 -4.47 -4.93 -4.50
Fe III -4.33 -4.35 -4.62 -3.93 ... -4.78 -4.77 ... ... ... -4.50
Ni II ... ... -6.72 -6.02 -5.96 -5.98 -6.04 -5.85 -5.67 -5.92 -5.75
Teff 21000 16500 15000 14343 13625 13150 12900 10825 10250 10075
log g 4.25 4.0 4.10 4.30 4.00 3.85 3.35 3.88 3.90 3.30
ξ(km s−1) 4.9 2.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.4
– 43 –
Table 7. Color Fits
Indices N Amplitude Amplitude Amplitude Amplitude σo σf
f1=0.9719 f2=0.7923 f3=0.8553 f1+f2
v 969 0.01805 0.01558 0.00463 0.00287 0.02048 0.01092
u-b 969 0.01324 0.011588 0.00321 0.00161 0.01527 0.00847
b-y 969 0.00095 0.00087 0.00016 0.00027 0.00391 0.00380
u-v 969 0.01174 0.01065 0.00266 0.00141 0.01390 0.00794
v-b 969 0.00155 0.00100 0.00053 0.00019 0.00423 0.00400
v-y 969 0.00244 0.00178 0.00067 0.00041 0.00505 0.00454
m1 969 0.00082 0.00059 0.00040 0.00022 0.00639 0.00634
c1 969 0.01020 0.00979 0.00212 0.00123 0.01375 0.00929
(v-y)/v 969 0.13519 0.11435 0.14493 0.14327
– 44 –
Table 8. Slowly Pulsating B Stars
HIP HD Parallax Mbol log L log Teff
15988 21071 5.41±0.79 -1.41 2.46±0.13 4.172±0.006
18216 24587 8.46±0.75 -1.75 2.60±0.08 4.146±0.006
19398 26326 4.49±0.78 -2.59 2.93±0.15 4.194±0.006
20354 27396 7.03±0.79 -2.34 2.83±0.10 4.205±0.005
20493 27742 6.77±0.76 -0.65 2.16±0.10 4.104±0.007
20715 28114 5.46±1.02 -1.40 2.46±0.16 4.166±0.006
23833 33331 3.20±0.57 -1.37 2.44±0.15 4.107±0.007
29488 42927 3.47±0.70 -2.46 2.88±0.18 4.258±0.005
34000 53921 6.77±0.54 -1.34 2.43±0.07 4.139±0.006
34798 55522 4.54±0.61 -2.45 2.88±0.12 4.252±0.005
34817 55718 3.67±0.63 -2.74 2.99±0.15 4.222±0.005
38455 64503 5.09±0.52 -3.61 3.34±0.09 4.250±0.005
40285 69144 3.36±0.56 -3.58 3.33±0.14 4.202±0.005
43763 76640 3.75±0.48 -1.94 2.67±0.11 4.173±0.006
45189 79416 5.23±0.68 -1.90 2.66±0.11 4.151±0.006
47893 84809 3.75±0.70 -2.07 2.72±0.16 4.212±0.005
48182 86659 3.00±0.51 -2.88 3.05±0.15 4.220±0.005
52043 92287 2.55±0.51 -3.56 3.32±0.17 4.224±0.005
61199 109026 10.07±0.52 -2.55 2.92±0.04 4.212±0.005
66607 118285 3.51±0.56 -1.60 2.54±0.14 4.082±0.007
72800 131120 8.49±0.76 -2.11 2.74±0.08 4.271±0.005
76243 138764 9.30±0.86 -1.05 2.32±0.08 4.150±0.006
77227 140873 7.99±0.68 -1.25 2.40±0.07 4.149±0.006
79992 147394 10.37±0.53 -2.31 2.82±0.04 4.175±0.006
90797 169978 6.81±0.75 -2.00 2.70±0.10 4.102±0.007
– 45 –
Table 8—Continued
HIP HD Parallax Mbol log L log Teff
107173 206540 4.68±0.81 -1.62 2.54±0.15 4.147±0.006
108022 208057 6.37±0.70 -2.41 2.86±0.10 4.294±0.004
112781 215573 7.35±0.47 -1.38 2.45±0.06 4.148±0.006
Table 9. Deviations of frequency from interpolation between 4 and 4.5 M� Models to 4.14
M�
mode d1,mode d2,mode d3,mode σ2
g050 0.45 0.55 1.35 3.328
g060 0.25 0.90 0.27 0.945
g070 0.35 0.13 0.00 0.139
g080 1.0 0.45 0.25 1.265
g090 0.6 0.05 2.65 7.839
g100 1.15 0.35 2.89 9.797
g110 0.90 0.00 2.85 8.123
