The Na I D resonance lines in main sequence late-type stars
Mon. Not. R. Astron. Soc. 000, 000–000 (0000) Printed 3 October 2018 (MN LATEX style file v2.2)
The Na I D resonance lines in main sequence late-type stars
Rodrigo F. Dı́az, Carolina Cincunegui and Pablo J. D. Mauas
Instituto de Astronomı́a y Fı́sica del Espacio, CC. 67, suc. 28, 1428. Buenos Aires, Argentina.
3 October 2018
ABSTRACT
We study the sodium D lines (D1: 5895.92 Å; D2: 5889.95 Å) in late-type dwarf stars. The
stars have spectral types between F6 and M5.5 (B−V between 0.457 and 1.807) and metallicity
between [Fe/H] = −0.82 and 0.6. We obtained medium resolution echelle spectra using
the 2.15-m telescope at the argentinian observatory CASLEO. The observations have been
performed periodically since 1999. The spectra were calibrated in wavelength and in flux. A
definition of the pseudo-continuum level is found for all our observations. We also define a
continuum level for calibration purposes. The equivalent width of the D lines is computed in
detail for all our spectra and related to the colour index (B − V) of the stars. When possible,
we perform a careful comparison with previous studies. Finally, we construct a spectral index
(R′D) as the ratio between the flux in the D lines, and the bolometric flux. We find that, once
corrected for the photospheric contribution, this index can be used as a chromospheric activity
indicator in stars with a high level of activity. Additionally, we find that combining some of
our results, we obtain a method to calibrate in flux stars of unknown colour.
Key words: Stars: late-type - Stars: activity - Stars: chromospheres
1 INTRODUCTION
All through the main sequence, the Na I D resonance lines (D1:
5895.92 Å; D2: 5889.95 Å) are ubiquitous absorption features,
clearly visible in stars of all spectral types. In particular, for cool
stars at the end of the main sequence (late G, K and M) the dou-
blet develops strong absorption wings. In the most active flare stars,
the D lines show chromospheric emission in their core, a telltale of
collision dominated formation processes.
Besides the intrinsic interest in understanding how these lines
behave for different stellar parameters, the sodium doublet provides
a useful diagnostic tool when studying stellar atmospheres. In this
regard, Andretta et al. (1997), Short & Doyle (1998) and Mauas
(2000) showed that in M dwarfs the sodium D lines provide infor-
mation of the conditions in the middle-to-lower chromosphere, and
therefore complements the diagnostics of the upper-chromosphere
and low transition region provided by Hα. Tripicchio et al. (1997)
modelled the equivalent width of the doublet in stars of a wide
range of spectral types (between F6 and M5.5). They concluded
that the chromosphere is not very important in determining the
equivalent width, since it only affects emission in the central core,
which provides a small contribution to the doublet strength. How-
ever, their model fails to reproduce the tendency shown by their
observations for stars with Te f f < 4000
In the present work we study different features of the D lines
using medium resolution echelle spectra covering the entire visi-
ble spectrum. Our study is focused on stars at the end of the main
sequence (from late F to middle M), for which we analyze the con-
tinuum and line fluxes and the equivalent width of the doublet.
In Sect. 2 we describe the observations and calibration pro-
cess. In Sect. 3 we study the continuum flux near the D lines. The
equivalent width is treated in Sect. 4, where we also describe a
method to obtain an approximate flux calibration for stars of un-
known colour index. In Sect. 5 we study the changes observed in
the D lines as a consequence of chromospheric activity. Finally, in
Sect. 6 we discuss the results and present our conclusions.
2 OBSERVATIONS AND STELLAR SAMPLE
2.1 Observations and calibration of the spectra
The observations were obtained at the Complejo Astronómico El
Leoncito (CASLEO), in the province of San Juan, Argentina, in 27
observing runs starting in March 1999. At present, the spectra of
only 19 of these runs were reduced and calibrated.
We used the 2.15-m telescope, equipped with a REOSC
echelle spectrograph designed to work between 3500 Å and 7500
Å. As a detector we used a 1024 x 1024 pixel TEK CCD.
We obtained spectra covering the whole region between 3860
and 6690 Å, which lies in 24 echelle orders. Due to this complete
coverage we can study the effect of chromospheric activity in all the
optical spectrum simultaneously. In the present work we concen-
trate on the sodium D lines. The study of other lines is done some-
where else (see Cincunegui et al. 2006; Buccino & Mauas 2007).
We used a 300 µm-width slit which provided a resolving
power of R = λ/δλ ≈ 26400. This corresponds to a spectral res-
olution of around 0.22 Å at the centre of the D doublet. Addition-
ally, we obtained ThAr spectra for the wavelength calibration and
medium resolution long slit spectra that were employed for the flux
calibration.
c© 0000 RAS
http://arxiv.org/abs/0704.0812v1
2 Dı́az et al.
The observations were reduced and extracted using standard
IRAF1 routines. The details of the flux calibration process are pre-
sented in Cincunegui & Mauas (2004).
2.2 Stellar sample
Since 1999 we have been monitoring around 110 stars of the main
sequence on a regular basis. Each star was observed around three
times a year, weather permitting.
The stellar sample is presented in Table 4. The stars have
spectral types between F6 and M5.5 and colour indexes (B − V)
between 0.457 and 1.807, from the Hipparcos/Tycho catalogues
(Perryman et al. 1997; Hoeg et al. 1997). The metallicity was ob-
tained from different sources, as shown in Table 4 and range from
[Fe/H] = −0.82 to 0.6.
The sample was gathered for different research programmes.
All the stars are field stars, and were included either for being sim-
ilar to the Sun, for exhibiting high levels of chromospheric activ-
ity -as is usually the case for the M stars-, or for having planetary
companions. We have also observed a few sub-giant stars for cal-
ibration purposes, which were excluded from the present analysis.
In previous works we used 18 of the stars included in the sample to
calibrate the S index calculated at CASLEO (Cincunegui & Mauas
2002; Cincunegui et al. 2006) to the one obtained at Mount Wilson
(Vaughan et al. 1978). These 18 stars also belong to the group of
standard stars used by Henry et al. (1996) at Cerro Tololo. Several
stars were included to cover the entire range of effective tempera-
ture. However, the sample is not uniform in metallicity or effective
temperature. Nevertheless, we believe our results are not biassed by
this lack of uniformity in our sample. When such a risk is present,
we binned the observations (see Sect. 3).
Our sample also includes seven stars that fall outside the main
sequence when placed in an HR diagram, even though they are clas-
sified as dwarf stars in the SIMBAD2 database. For these stars, we
calculated the absolute magnitude in the V filter (MV ) using the
measurements of parallax and V from the Hipparcos/Tycho cata-
logues (Perryman et al. 1997; Hoeg et al. 1997). We list these stars
in Table 1. The fourth column shows the luminosity class that cor-
responds to the calculated MV (see Allen 1964, §95), obtained as-
suming that the spectral type is correct. These stars were excluded
from the analysis, together with the rest of the non-main-sequence
stars.
Also contained in our sample are four stars which are listed in
a luminosity class other than V in the SIMBAD database that ac-
tually fall well whithin the main sequence. Again, MV values were
obtained and compared with the table in Allen (1964) to confirm
their placement in the HR diagram. These stars are shown in Ta-
ble 2, and were included in the analysis. We also excluded from
the analysis the stars with unknown parallax, since for them abso-
lute fluxes cannot be determined. Our final sample consists of 652
spectra for 84 stars.
1 IRAF is distributed by the National Optical Astronomy Observatories,
which are operated by the Association of Universities for Research in
Astronomy, Inc., under cooperative agreement with the National Science
Foundation.
2 http://simbad.u-strasbg.fr
Spectral type (B − V) MV Lum Class
hd103112 K0 1.05 3.18 IV
hd105115 K2/K3 1.41 -0.68 III
hd119285 K1p 1.04 3.39 IV
hd25069 G9 0.99 2.75 IV
hd5869 K4 1.49 1.05 III
hd94683 K4 1.78 -2.38 II
hd17576 G0 1.78 1.91 III
Table 1. Stars located outside the main sequence in an HR diagram despite
being classified as dwarf-type stars. The fourth column is the luminosity
class we obtained assuming the spectral type is correct
Star Spectral type (SIMBAD) (B − V) MV
hd52265 G0 III-IV 0.57 4.12
hd57555 GO IV/V 0.66 4.18
hd75289 G0 I 0.58 4.1
hd120136 F6 IV 0.51 3.58
Table 2. Stars located in the main sequence despite not being classified as
dwarf-type stars.
3 PSEUDO-CONTINUUM
3.1 Definition
In Fig. 1 we show the spectrum in the region of the D lines for
four stars of different spectral types. As can be seen in the spectra,
in the case of later stars the doublet forms inside a strong molec-
ular band, which extends from 5847 Å to 6058 Å and is due to
TiO (Mauas & Falchi 1994)
Therefore, in order to obtain a reliable estimate of the contin-
uum flux near the lines for all spectral types, the windows chosen
have to be located far away from the line centre, outside the molec-
ular bands. The closest regions are a 10 Å wide window centered
at 5805 Å (window V) and a 20 Å wide window centered at 6090
Å (window R). These windows are indicated in Fig. 1 with solid
lines.
However, even in these regions there are several photospheric
lines, and therefore computing the mean flux would lead to a con-
siderable underestimation of the continuum flux. To deal with this
problem, we considered the mean value of the ten highest points in
each window as an indication of the continuum flux in it. Finally,
to take into account the shape of the continuum in this region, we
computed the flux at the doublet centre (Fcont) as the linear interpo-
lation of the values in each window.
In Fig. 1, the linear interpolation in each spectrum is shown as
a dashed line. We see that this is a good estimation for the contin-
uum flux at the centre of the doublet, even for M-type stars.
3.2 Relation with (B-V)
We calculated Fcont for all the spectra in our sample in the way
explained above. Fcont was normalized to the flux F⊙ , defined in
such a way that Fcont/F⊙ = 1 for a star of solar colour (B − V) =
0.62. In Fig. 2 we plot Fcont/F⊙ in logarithmic scale as a function
of colour index (B − V). The trend is similar to that shown by the
lower end of the main sequence in an HR diagram.
c© 0000 RAS, MNRAS 000, 000–000
The Na I D resonance lines in main sequence late-type stars 3
5800 5850 5900 5950 6000 6050 6100
Figure 1. The region of the sodium doublet for stars of different spectral types. The dotted lines mark the windows used for the calculation of the continuum
flux. The dashed line is the continuum level as defined in Sect. 3.1.
As can be seen in Fig. 2, the stars are not evenly distributed
with colour, a fact that might bias our results. To avoid this, we
binned the observations every 0.05 units in (B − V). For each bin,
we computed the mean value of Fcont , which are plotted as filled
squares in Fig. 2. It can be seen in the figure that there exists a
break at (B − V) = 1.4, where M stars begin. Therefore, we fitted
the binned data with two linear relations:
Fcont
1.18 − 1.86 × (B − V) (B − V < 1.4)
7.55 − 6.55 × (B − V) (B − V ≥ 1.4)
where F⊙ = 5.7334 × 10
−11 erg cm−2 s−1 Å−1.
3.3 Calibration
A relation like that of Eq. 1 can be used to calibrate in flux spectra
of stars of known colour index (B − V). However, most spectro-
graphs only observe a small wavelength range around the line of
interest. For these instruments, the windows at 5805 Å and 6010 Å
might fall outside the observed range. For this reason, we studied a
relation similar to the one in Eq. 1 for a continuum window closer
to the doublet.
First, we note that due to the presence of molecular bands, the
raw spectra of M-type stars are difficult to normalize, in particular
if the observed range is not wide enough. Therefore, we did not try
to find a good pseudo-continuum to calibrate M-dwarfs. For F, G
and K stars, we considered a window 20 Å wide around 5840 Å,
which is indicated in Fig. 1 with dotted lines.
In Fig. 3 we show the ratio between the mean flux F̄ in this
window and the one obtained earlier, for stars with (B − V) < 1.4.
As can be seen, using F̄ underestimates the true continuum, but
the percentual difference between both is smaller than 6 per cent.
Therefore, the first part of Eq. 1 can be used to fit the mean flux
F̄, and to calibrate in flux this region of the spectrum of a star of
known (B − V), increasing the error by less than 6 per cent.
4 EQUIVALENT WIDTH
4.1 Definition
The equivalent width Wλ of a spectral line is defined as
dλ , (2)
where Fc is the continuum flux and Fλ is the value of the flux in the
line. As we pointed out in the preceeding section, the choice of the
continuum level can be subjective, and it can be very difficult for
M-dwarfs.
On the other hand, the limits of the wings of a line are not
always well-defined, and therefore the integration limits λ1 and λ2
also constitute subjective points in the definition of Wλ. In fact,
while in earlier F and G stars the photospheric wings are thin and
well defined, in later stars the wings are extremely wide. There-
fore, the choice of a proper integration window requires a varying
width (∆λ = λ2 − λ1), ranging from 14 to 40 Å around the cen-
tre of the doublet (5892.94 Å), depending on the spectral type of
the star. In Table 3 we list the values of ∆λ we used for differ-
ent colours. A similar technique, with varying widths, was used by
Tripicchio et al. (1997), although it is not clear from their paper
which ∆λ was used for each colour.
Note that in stars with spectral type later than M2.5 the ab-
sorption wings of the D lines become very large and blended with
c© 0000 RAS, MNRAS 000, 000–000
4 Dı́az et al.
0.5 1 1.5
(B-V)
Figure 2. log(Fcont/F⊙) vs. colour index (B − V). The small empty squares
represent the individual observations, and the filled squares are the mean
value in each bin (see text). The solid lines are the best piecewise fit to
the data. Note that in several bins there is only one star, and the individual
observations are therefore hidden by the filled square.
0.6 0.8 1 1.2 1.4
(B-V)
Figure 3. Ratio between Fcont and the mean flux F̄ in the 5830-5850 Å
window, as a function of colour index (B − V). The percentage difference
remains smaller than 6 per cent for F, G and K stars.
the highly-developed absorption bands present (see Fig. 1). There-
fore, for these stars a suitable choice of ∆λ is very difficult and the
calculation of the equivalent width cannot be considered entirely
reliable.
Regarding the continuum level, we used both values described
in the previous section. The equivalent width computed with F̄,
0.6 0.8 1 1.2 1.4
(B-V)
Figure 4. Ratio between Wλ, calculated with a realistic estimation of the
continuum flux (Fc = Fcont), and Wapprox, computed using the definition of
Fc suitable for the calibration process described in Sect. 4.4 (Fc = F̄). The
percentage difference remains smaller than 20 per cent for almost all stars.
(B − V) interval ∆λ [Å]
≤ 0.8 14
[0.8 − 1) 16
[1.0 − 1.2) 20
[1.2 − 1.3) 24
[1.3 − 1.5) 28
> 1.5 40
Table 3. Wavelength window ∆λ used in the calculation of the equivalent
width for different values of (B − V) (see Equation 2).
the aproximate definition of Fc, will be referred to as Wapprox, and
the one computed with Fcont will be refered simply as Wλ. The ra-
tio between both values is plotted in Fig. 4. Again, using F̄ leads
to an underestimation of the equivalent width. The differences are
larger than for the continuum flux, but even in this case they remain
smaller than 20 per cent.
4.2 Relation with colour index (B − V)
In Fig. 5 we illustrate the behaviour of Wλ as a function of the
colour index (B − V). In the y-axis we plot log(Wλ/λo), where
λo = 5890 Å. The small dots represent the mean value per star and
the filled squares show the results of binning the data as explained
in the previous section. As empty squares we plot the values of
Wapprox, binned in the same way.
A quadratic fit to the binned data gives
= −4.579 + 1.948 (B − V) − 0.3726 (B − V)2 . (3)
c© 0000 RAS, MNRAS 000, 000–000
The Na I D resonance lines in main sequence late-type stars 5
0.5 1 1.5
(B-V)
Figure 5. Equivalent width (logarithmic scale) vs (B − V). The small dots
are the mean values for each star and the filled squares are the mean values
in each bin. The empty squares are the mean values of Wapprox in each bin
(see text). The solid line is the best fit to the binned data. The dotted line
is the fit to Wapprox and the dashed line is the fit given by Tripicchio et al.,
transformed to the colour index scale using Eq 5.
This fit is shown as a solid line in Fig. 5. It can be seen that, as
the temperature decreases, the D lines become wider. It is evident
from Fig. 5 that there is a saturation effect for the reddest stars.
As shown in Fig. 1, for M stars with (B − V) ≥ 1.4, the lines are
so wide that they are almost completely blended. At this point, the
doublet behaves as a single line, and the equivalent width grows
mainly in the outer wings. Additionally, as cooler stars are also
more active, the central line cores are filled in by chromospheric
emission, contributing to the saturation effect.
4.3 Comparison
Tripicchio et al. (1997) also studied the dependence of the equiv-
alent width with effective temperature. They constructed synthetic
profiles of the D lines using a modified version of the MULTI code,
which takes into account the line blending present in the doublet.
They also observed a sample of dwarf and giant stars with spec-
tral type between F6 and M5. They used both the modelled atmo-
spheres and the observed spectra to obtain a relation between Wλ
and effective temperature, given by:
= 2.43 ·
Te f f
− 5.73 , (4)
which reproduces their observations fairly well for effective tem-
peratures higher than 4000 ◦K.
In order to compare this relation to our regression we per-
formed a change of variables in equation 4 using the relation given
by Noyes et al. (1984):
log(Te f f ) = 3.908 − 0.234 · (B − V) , (5)
valid for stars with 0.4< (B − V) < 1.4. In this way we obtain Wλ
as a function of (B − V). The resulting expression is plotted as a
dashed line in Fig. 5.
It can be seen that the values by Tripicchio et al. (1997) are
smaller than ours: in some cases the difference between both ex-
pressions is as large as 40 per cent. Unfortunately, they do not men-
tion how the continuum level or the integration windows were cho-
sen. Although they say they used a wavelength interval of variable
width and that they cleared the spectrum of unwanted lines, no de-
tails are given, so we could not apply their calculation method to
our data.
To check whether our larger values of Wλ are due to the
weak photospheric lines blended in the profiles, we recomputed
the equivalent width in a completely different way, for several of
our stars. We considered the raw spectra of 16 stars from our sam-
ple. The spectroscopic order in which the D lines are found was
extracted, calibrated in wavelegth and normalized. It is worth not-
ing that the doublet is located in the middle of this order, where the
effects of the blaze function are less severe. However, the presence
of molecular bands prevented us from normalizing the spectra of
M-type stars.
We then computed the equivalent width using the IRAF line-
deblending routines included in the SPLOT task, which fit Voigt
profiles to the lines, and perform the calculation over the fits. In
this way, the presence of photospheric lines has no influence on
the obtained value. Due to the severe blending of the D lines, the
routine used by IRAF did not produce acceptable results for stars
with colour larger than ≈ 1.3. Therefore, this method can only be
applied to stars with (B − V) < 1.3.
In Fig. 6 we plot as filled squares the value of Wλ calculated
from our calibrated spectra Vs. the value obtained using IRAF
(WIRAF). The errors in Wλ were calculated assuming a 3 per cent
error in Fλ/Fc (see Eq. 2). The error bars in the x-axis were taken
as the RMS of the fit done by IRAF times the width of the inte-
gration window (see Table 3). The solid line represents the identity
relation, and not a fit to the data. It can be seen that the differences
beween our calculation and the one done with IRAF are well within
the errors. The filled triangles represent the values of Wλ obtained
from our fit, rather than from the individual obervations. Note that
the points still remain very close to the identity line.
As open squares we plot the equivalent width obtained from
Trippichio’s relation (Eq. 4) for the value of (B − V) of the stars
considered, which in all cases fall below the identity relation.
4.4 Determination of (B − V)
The relation shown in Fig. 5 can be used to determine the (B − V)
of a star using the equivalent width of the D lines, measured in non-
calibrated spectra. Since in many cases the spectral region needed
to compute Fcont might fall outside the observed one, we repeat
the fit for Wapprox. The best least square fit to the binned values of
log(Wapprox/λo) Vs. (B-V) is:
Wapprox
= −4.528 + 1.734 (B − V) − 0.2442 (B − V)2 , (6)
which is valid only for (B−V) < 1.4, and where λo = 5890 Å. This
fit is plotted as a dotted line in Fig. 5.
To obtain (B − V) from the measured equivalent width, one
could invert Eq. 6. However, since the least square estimation of
parameters does not treat the dependent and independent variables
symmetrically, a more rigorous procedure would be to fit (B−V) as
a function of Wapprox. We performed this fit and found that within
the errors, both procedures give the same values of (B − V).
c© 0000 RAS, MNRAS 000, 000–000
6 Dı́az et al.
2 4 6 8 10
Figure 6. Wλ computed from the calibrated spectra (filled squares) as a
funtion of the one given by the IRAF deblend routine (WIRAF). The triangles
represent the values obtained from the fit of Eq. 3 and the empty squares
represent the values obtained using the fit from Tripicchio et al. (1997).
0.4 0.6 0.8 1 1.2
Figure 7. (B − V) computed from the normalized ([comp]) spectra through
the inverse of Eq. 6 as a funtion of (B − V) from the Hipparchos/Tycho
catalogue ([cat]). The solid line is the identity function. A good agreement
is found between both values.
The method was verified using the same 16 stars used in
the previous section. The raw spectra were extracted, calibrated
in wavelength and normalized using Chebyshev polynomials. All
these procedures were carried out using IRAF. Wλ was calculated
by direct integration of the flux in the appropiate window (see Ta-
ble 3) using SPLOT. Then, the inverse of Eq. 6 was used to obtain
(B − V) for these stars.
In Fig. 7 we plot the value of (B − V) computed in this way
((B − V)comp) as a funtion of the value obtained from the Hippar-
cos/Tycho catalogue ((B−V)cat). To estimate the error in (B−V)comp
we assumed a 5 per cent error in Fλ/Fc , in order to consider errors
in the normalization procedure. The errors in the x-axis were taken
from the Hipparcos/Tycho catalogue. The solid line represents the
identity relation. It can be seen that the method gives, in fact, very
good estimates of the colour of the stars.
Therefore, by measuring the equivalent width of the D doublet
an estimate of the colour index (B−V) can be obtained. Afterwards,
this value of (B − V) can be used to obtain an approximate flux
calibration in the region of the D lines, by means of Eq. 1. In this
way, the spectra of stars of unknown colour can be calibrated in
flux in this spectral region.
5 ACTIVITY INDEXES AND CHROMOSPHERIC
ACTIVITY
In this section, we define different activity indexes using the D
lines, and study their applicability as chromospheric activity indi-
cators.
5.1 N index
First, we constructed an index (N) similar to the Mount Wilson S
index, described by Vaughan et al. (1978).
f1 + f2
fcont
where fi is the mean flux in the Di line, integrated in a square win-
dow 1 Å wide, and fcont is the mean flux of the continuum calcu-
lated as explained in Sect. 3.1.
For the earlier stars in our sample, the N index is highly depen-
dent on the colour (B−V), as can be seen in Fig. 8. This behaviour
changes for stars with (B − V)>
1.1, for which the value of N is
roughly constant. Stars with (B − V) < 1.1 were fitted with a linear
relation, shown in the figure as a solid line:
N(B−V) = −1.584 · (B − V) + 2.027 . (7)
In Fig. 9 we show the result of plotting N as a function of the
S index, which was obtained from our spectra using the calibration
presented in Cincunegui et al. (2006), which relates the S index ob-
tained at CASLEO with the one computed at Mount Wilson. Note
that since our spectra cover the entire visible range, we measure N
and S simultaneously.
It can be seen that stars with (B − V) < 1.1 (shown as filled
triangles) have smaller values of S, and show a weak anticorrelation
between N and S (r = −0.488). We plot the observations for these
stars alone in the upper panel of Fig. 10. Despite the considerable
scatter, the anticorrelation is evident.
However, for these stars the correlation between N and (B−V)
is stronger. To correct for this dependence we substracted N(B−V)
(Eq. 7) from N. In the lower panel of Fig. 10 we plot N − N(B−V)
vs. (B-V). In this case, the correlation dissapears (r = 0.07), imply-
ing that the correlation was due only to the dependence of N with
colour, and the tendency of cooler stars to be more active. Thre-
fore, the N index cannot be used as an activity indicator for stars
with (B − V) < 1.1.
c© 0000 RAS, MNRAS 000, 000–000
The Na I D resonance lines in main sequence late-type stars 7
0.5 1 1.5
(B - V)
Figure 8. N index vs. colour index (B − V). The solid line is the best linear
fit for stars with (B − V) < 1.1. Stars with a larger (B − V) do not show any
correlation.
0 5 10 15
Figure 9. N vs. S. Values for stars with (B − V) < 1.1 are shown as filled
triangles, and those with (B − V) ≥ 1.1 as empty squares.
On the other hand, stars with (B − V) ≥ 1.1 present a good
correlation between both N and S, as can be seen in Fig. 9. Since
for these stars N do not correlate with colour, we do not perform
any correction in this case.
Since we have simultaneous observations of both indexes, we
can explore this apparent correlation for particular stars. In Fig. 11
we plot N vs S for several stars with (B − V) ≥ 1.1, and we show
the linear fits to each individual dataset (the slope of each fit is
given in the legend). It can be seen that the slope of the relation be-
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Figure 10. Upper panel: N vs. S for stars with (B − V) < 1.1. Lower
panel: The dependence on N with colour has been corrected by substracting
N(B−V), shown in Eq. 7. The correlation disappears, as is confirmed by the
small value of the correlation coefficient (r = 0.07).
0 5 10
GJ551 (0.018)
GJ388 (-0.0017)
GJ517 (0.084) 
GJ1 (-0.16)
Figure 11. N vs S for selected stars with (B − V) ≥ 1.1. A linear fit to
the data of each star is also shown (GJ551: solid line; GJ388: dotted line;
GJ517: dashed line; GJ1: dot-dash line). The slope of the fit is given in
parentheses in the legend.
tween S and N changes from star to star, and the behaviour ranges
from correlations with different slopes (GJ551 and GJ517) to cases
where N and S are uncorrelated, either with constant S and vari-
able N (GJ1) or viceversa (GJ388). A similar effect was observed
comparing the flux of the Hα line to the flux in the H and K lines
(Cincunegui et al. 2006). In that case, we found correlations with
c© 0000 RAS, MNRAS 000, 000–000
8 Dı́az et al.
different slopes, anti-correlations, and cases where no correlation
is present.
Therefore, the N index cannot be used to compare activity lev-
els of different stars. However, it can be useful to compare activity
levels on the same star at different times, for those stars which show
a correlation between S and N. For example, N can be used to trace
activity cycles in late-type stars, as we did with Proxima Centauri
using the flux of the Hα emission (see Cincunegui et al. 2007).
5.2 R′D
Noyes et al. (1984, hereafter N84) noted that the S index is sensitive
to the flux in the continuum windows and to the photospheric radi-
ation present in the H and K bandpasses, both of which depend on
spectral type. Despite the apparent independence of N with (B−V)
seen in Fig. 8 for stars with (B − V) ≥ 1.1, the results of the pre-
vious section seem to indicate that N also shows a dependence on
photospheric flux, even for stars with (B − V) ≥ 1.1. This depen-
dence must be corrected more thoroughly in order to compare stars
of different spectral type.
Following N84, we define a new index
R′D = RD − R
D , (8)
where RD = (F1+F2)/σT
e f f , F1 and F2 are the fluxes in the D1 and
D2 windows at the stellar surface, and σ is the Stefan-Boltzmann
constant. Note that RD can be expressed as:
f1 + f2
fcont
· N , (9)
where fbol is the relative bolometric flux. Both expressions in Eq. 9
have the virtue of depending on fluxes on Earth instead of fluxes at
the stellar surface. fbol was computed interpolating the values of the
bolometric correction provided by Johnson (1966). Defined in this
way, RD is independent of the photospheric flux in the continuum
window.
RphotD is the photospheric contribution to the flux in the win-
dows of the D lines. For the H and K lines, N84 integrated the flux
outside the H1 and K1 minima, and used these values to calculate
Rphot, which is substracted from RHK . However, the D lines are usu-
ally in absorption. For this reason, we had to correct for the photo-
spheric contribution in a different way. Since even for very inactive
stars the D lines are not completely dark, the minimum line flux in
a very inactive star must be photospheric in origin. Therefore, we
assumed that the basal flux of the D lines is a reasonable estimation
of the photospheric contribution.
In Fig. 12 we plot the flux in the D1 line as a function of the
colour index (B−V), in logarithmic scale. The solid line represents
the basal flux, computed using a third order polynomial. The spec-
tra with the D lines in emission were excluded from the fit. The
resulting expression is:
log(Fmin1 ) = −6.527 − 11.86· (B − V) + 10.87 · (B − V)
−4.218 · (B − V)3 .
For the D2 line, a similar expression is obtained:
log(Fmin2 ) = −6.374 − 12.48· (B − V) + 11.37 · (B − V)
−4.344 · (B − V)3 .
Contrary to what happens for the H and K lines, this term is
appreciable for all the range of our observations. Even for stars with
Balmer lines in emission, the photospheric correction can be up to
50 per cent of the value of RD.
0.5 1 1.5
(B-V)
Figure 12. Flux in the D1 line as a function of colour index (B − V). The
solid line represents our estimation of the minimum flux. Those spectra with
D lines in emission were not considered for the fit.
Following N84, we substracted the same value of RphotD to all
stars of the same spectral type. In this way, we have constructed
an index eliminating the dependence on spectral type which arises
from the photospheric flux in the integration bandpasses. R′D should
therefore depend exclusively on chromospheric flux and be inde-
pendent of spectral type.
5.3 Chromospheric activity
According to N84, R′HK = RHK−Rphot is proportional to the fraction
of nonradiative energy flux in the convective zone. Since this flux
then heats the chromosphere by means of the magnetic field, R′HK
should be a good activity indicator.
We computed R′HK for all our spectra using a relation analogue
to Eq. 9. As Rphot we used the expression given in N84, valid in the
range 0.44 < (B − V) < 0.82,
log(Rphot) = −4.02 − 1.4 (B − V) . (12)
As noted by N84 the photospheric correction is unimportant for
active stars. Indeed, we found that the correction is less than 10 per
cent virtually for all stars with B − V > 1.1. Therefore, we used
Eq. 12 for all the range of our observations.
To study its applicability as an activity indicator, R′D was plot-
ted against R′HK . The result is presented in Fig. 13, where the filled
triangles represent stars which exhibit the Balmer lines in emission.
No correlation seems to be present when we consider the complete
stellar sample. Indeed the correlation coefficient is r = 0.094. How-
ever, if we consider only the most active stars –those which exhibit
Balmer lines in emission – an excelent correlation is found between
both indexes. This is shown in Fig. 14, where we plot R′D vs R
only for these stars. The solid line is the best linear fit to the data:
R′D = 2.931 × 10
+ 0.1388 · R′HK , (13)
with correlation coefficient r = 0.978. This result demonstrates that
c© 0000 RAS, MNRAS 000, 000–000
The Na I D resonance lines in main sequence late-type stars 9
0 0.0001 0.00015 0.0002
0.0001
Figure 13. R′D vs R
HK . Filled triangles represent stars with Balmer lines in
emission. No clear correlation is present, and the correlation coefficient for
the complete sample is r = 0.094.
R′D can be used as an activity indicator for active stars. Note that de-
spite presenting the Balmer lines in emission, not all stars in Fig. 14
present the D lines in emission, and this does not seem to be a con-
dition for the use of R′D as an activity indicator. R
D is particularly
useful to study the cooler stars, which tend to be more active and
where the emission in the region of the H and K Ca II lines is sub-
stantially smaller (even an order of magnitude) than the flux in the
region of the D doublet.
6 SUMMARY
A program was started in 1999 to study chromospheric activity and
atmospheres of main sequence stars in the Southern Hemisphere.
In this paper we analyze the sodium D lines. We use medium reso-
lution echelle spectra, obtained in CASLEO, which were calibrated
in wavelength and in flux.
We constructed an HR diagram for all the stars in our sample
taking the colour index (B−V) and the visual magnitude V from the
Hipparcos/Tycho catalogues. We found that several stars, in spite of
being classified as dwarfs in the Simbad database, fall outside the
main sequence. We present these stars in Table 1 and defer a more
detailed analysis for future work. Conversely, in Table 2 we show
four stars that were not classified as dwarfs even though they fall
within the main sequence.
In Sect. 3 we define a pseudo-continuum level useful for all
spectral types. Since in M stars the D lines are formed inside a
TiO molecular band, we consider two windows located quite far
from the doublet. In each window, the mean value of the ten high-
est points was calculated and the pseudo-continuum was defined as
the linear interpolation between both windows. The continuum flux
obtained in this way shows a very tight correlation with colour in-
dex (B − V). Since most observations do no include regions too far
from the lines, for stars with (B− V) < 1.4 we also defined another
pseudo-continuum, which uses a window located closer to the D
0 0.0001 0.00015 0.0002
Figure 14. R′D vs R
HK for stars with Balmer lines in emission. The solid
line is the best linear fit to the data, with correlation coefficient r = 0.977.
The excelent correlation indicates that R′D is a good chromospheric activity
indicator.
lines, and also correlates strongly with (B − V). We showed that
this correlation can be used to obtain an approximate calibration in
flux in this spectral region.
In Sect. 4 we describe in detail the computation of the equiv-
alent width. We use a wavelength interval which range from 14 Å
for F6 stars to 40 Å for the coolest stars in our sample. In M-type
stars, the large photospheric wings, blended with deep molecular
bands, difficult an accurate calculation. We find a good correlation
between equivalent width and colour index (B−V) for all the range
of observations.
The relation obtained was then used to determine the colour of
dwarf-type stars from the equivalent width of the D lines. We find
values of (B − V) in good agreement with those from the Hippar-
cos/Tycho catalogues. Since equivalent width is a characteristic of
line profiles that do not require high resolution spectra to be mea-
sured, this fact could become a useful tool for subsequent studies.
Finally, in Sect. 5 we study how the flux in the D lines changes
with changing levels of chromospheric activity. We define an index
(N) analogue to Mount Wilson S index and find it is strongly cor-
related with colour for stars with (B − V) < 1.1. This fact produces
an apparent correlation between N and S, which disappears when
the colour dependence is taken into account. On the other hand, in
stars with (B−V) ≥ 1.1, N is independent of colour and is correlated
with the S index. However, the slope between N and S varies when
different stars are studied individually, varying from tight correla-
tions to cases where no correlation is present. This fact restricts the
use of the N index as an activity indicator when different stars are
compared. However, the N index may be useful when comparing
different activity levels on individual stars, specially in later stars
with little emission in the region of the CaII H & K lines.
In order to compare activity levels on stars of different spectral
types we define an improved index taking into account the photo-
spheric contribution to the flux both in the lines and in the contin-
uum windows. First we construct RD as the ratio between absolute
c© 0000 RAS, MNRAS 000, 000–000
10 Dı́az et al.
line fluxes and stellar luminosity. Then, the photospheric contribu-
tion in the lines bandpasses, which was computed using the basal
flux in the D lines, was substracted from RD to define R
D. As was
expected, the earlier stars in our sample do not show any sign of
correlation between both indexes. Indeed, it has been known for a
long time that the cores of the Na I D lines in the solar atmosphere
remain dark from center to limb while the Ca II H&K lines show
increasing line reversal. Only in stars with higher atomic densities,
as the M-dwarfs, the D lines can be expected to have collision rates
high enough to respond to the temperature changes in the chromo-
sphere (e.g. Mauas 2000). Because of this, earlier theoretical works
(see Andretta et al. 1997; Short & Doyle 1998) have restricted their
attention to this type of stars. However, in this work the new R′D in-
dex was found to correlate well with R′HK for the most active stars
in our sample (those which exhibit the Balmer lines in emission),
even though some of these stars do not present a line reversal at the
core of the D lines. Therefore, R′D is also a good activity indicator
for these stars. For the rest of the spectra, no correlation was found.
The CCD and data acquisition system at CASLEO has been
partly financed by R. M. Rich through U.S. NSF grant AST-90-
15827. This research has made use of the SIMBAD database, op-
erated at CDS, Strasbourg, France. We thankfully acknowledge the
comments and suggestions of the referee (Ian Short), which helped
us to improve our original manuscript.
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Table 4. List of stars used in the analysis and average measurements. Nobs is the number of times the star has been observed. V is the visual magnitude in the UBV system. [Fe/H] is the iron abundance relative to
the Sun, obtained from references (a): Cayrel de Strobel et al. (2001); (b): Nordström et al. (2004); (c): Cayrel de Strobel et al. (1997). < Fcont > is the continuum flux (see Sect. 3.1). < F̄ > is the mean flux in a
window 20 Å wide around 5840 Å. < Wλ > is the equivalent width of the sodium doublet and < Wapprox > is the equivalent width computed using F̄ as pseudo-continuum (see Sect. 4.1), in angstroms. Cols. 10
and 11 give the average absolute flux in a 1 Å window centered at the D1 and D2 lines, respectively. All fluxes are in units of [erg cm−2 s−1]. < N > is the value of the N index, calculated as explained in Sect. 5.1.
Columns 13 and 14 give average value for the RD index and the corresponding photospheric correction R
D (see Sect. 5.2). Finally, in the last column we present the mean values of R
HK . Colour index (B − V),
magnitude V and spectral type have been obtained from the Hipparcos/Tycho catalogues (Perryman et al. 1997; Hoeg et al. 1997).
Star Nobs Sp. type (B − V) V [Fe/H] < Fcont > < F̄ > < Wλ > < Wapprox > < FD1 > < FD2 > < N > < RD > R
D < R
hd28246 5 F6V 0.457 6.380 0.02b 9.651e-12 9.591e-12 1.189 1.108 6.330e-12 5.7 3 9 e - 1 2 1.251 1.825e-04 1.761e-04 5.737e-05
hd38393 12 F7V 0.481 3.590 -0.12a 1.293e-10 1.286e-10 1.222 1.153 8.595e-11 7 . 8 6 2e-11 1.272 1.897e-04 1.780e-04 3.084e-05
hd120136 3 F6IV 0.508 4.500 0.32a 5.665e-11 5.618e-11 1.602 1.500 3.622e-11 3 .270e-11 1.217 1.829e-04 1.037e-04 4.078e-05
hd16673 9 F6V 0.524 5.790 -0.01a 1.711e-11 1.704e-11 1.243 1.192 1.098e-11 9. 567e-12 1.201 1.784e-04 1.529e-04 4.929e-05
hd114762 3 F9V 0.525 7.300 -0.82a 4.346e-12 4.325e-12 1.069 1.008 2.913e-12 2 .641e-12 1.278 1.938e-04 1.716e-04 2.693e-05
hd35850 5 F7V 0.553 6.300 0.00a 1.063e-11 1.057e-11 1.374 1.296 7.466e-12 6.6 73e-12 1.330 1.940e-04 1.198e-04 1.376e-04
hd17051 5 G0V 0.561 5.400 -0.04a 2.536e-11 2.505e-11 1.679 1.526 1.423e-11 1. 233e-11 1.047 1.582e-04 1.176e-04 4.635e-05
hd45067 11 F8V 0.564 5.880 -0.16a 1.572e-11 1.562e-11 1.340 1.255 9.635e-12 8 .603e-12 1.160 1.686e-04 4.831e-05 2.549e-05
hd52265 2 G0III-IV 0.572 6.290 0.21a 1.108e-11 1.091e-11 1.541 1.347 5.911e-1 2 5.201e-12 1.003 1.490e-04 9.101e-05 2.567e-05
hd19994 9 F8V 0.575 5.070 0.15a 3.438e-11 3.385e-11 1.736 1.543 1.932e-11 1.7 17e-11 1.062 1.587e-04 4.529e-05 3.132e-05
hd130948 6 G1V 0.576 5.860 -0.20a 1.640e-11 1.622e-11 1.885 1.744 9.382e-12 8 .210e-12 1.072 1.582e-04 1.445e-04 5.599e-05
hd75289 8 G0Ia 0.578 6.350 0.28a 1.054e-11 1.039e-11 1.651 1.472 6.067e-12 5. 247e-12 1.074 1.596e-04 8.565e-05 3.365e-05
hd215768 5 G0V 0.589 7.490 -0.20b 3.678e-12 3.642e-12 1.466 1.342 2.083e-12 1 . 7 9 5 e - 1 2 1.054 1.550e-04 1.193e-04 6.666e-05
hd213240 2 G0/1V 0.603 6.810 0.13b 6.975e-12 6.907e-12 1.975 1.856 3.737e-12 3 . 2 1 1 e - 12 0.996 1.484e-04 5.347e-05 2.894e-05
hd43587 7 F9V 0.610 5.700 -0.08a 1.932e-11 1.908e-11 1.812 1.656 1.103e-11 9. 575e-12 1.067 1.583e-04 8.101e-05 2.246e-05
hd197076 6 G5V 0.611 6.430 -0.20b 9.906e-12 9.812e-12 1.560 1.440 5.488e-12 4 . 6 9 6 e - 1 2 1.028 1.533e-04 1.334e-04 2.160e-05
hd202996 2 G0V 0.614 7.460 0.00b 3.735e-12 3.690e-12 1.778 1.629 2.355e-12 2. 0 4 7 e - 1 2 1.179 1.711e-04 5.219e-05 6.028e-05
hd45270 6 G1V 0.614 6.530 -0.14b 9.022e-12 8.913e-12 1.770 1.620 5.030e-12 4. 4 6 4 e - 1 2 1.052 1.567e-04 1.141e-04 8.372e-05
hd165185 10 G5V 0.615 5.940 -0.06a 1.540e-11 1.523e-11 1.727 1.589 8.778e-12 7.63 2e-12 1.066 1.573e-04 1.203e-04 6.079e-05
hd48189 6 G1.5V 0.624 6.150 -0.18b 1.259e-11 1.248e-11 1.878 1.770 7.036e-12 6 . 3 7 0 e - 1 2 1.065 1.559e-04 8.756e-05 8.837e-05
hd147513 11 G5V 0.625 5.370 0.03a 2.656e-11 2.618e-11 1.754 1.577 1.508e-11 1 .271e-11 1.046 1.576e-04 1.201e-04 6.066e-05
hd150433 7 G0 0.631 7.210 -0.47b 4.702e-12 4.649e-12 1.753 1.613 2.666e-12 2. 294 e - 1 2 1.055 1.530e-04 1.185e-04 2.568e-05
hd219709 7 G2/3V 0.632 7.500 -0.02a 3.607e-12 3.572e-12 1.925 1.808 1.922e-12 1.6 48e-12 0.990 1.438e-04 8.602e-05 4.212e-05
hd30495 11 G3V 0.632 5.490 -0.13a 2.326e-11 2.304e-11 1.696 1.576 1.228e-11 1 .047e-11 0.978 1.439e-04 1.187e-04 6.058e-05
hd202628 9 G2Va 0.637 6.750 -0.14a 7.346e-12 7.261e-12 1.954 1.812 3.955e-12 3.401e-12 1.001 1.480e-04 1.141e-04 4.981e-05
hd38858 5 G4V 0.639 5.970 -0.25b 1.511e-11 1.492e-11 1.872 1.710 8.241e-12 7. 0 4 6 e - 1 2 1.011 1.498e-04 1.279e-04 2.778e-05
hd20766 12 G2.5V 0.641 5.530 -0.22a 2.242e-11 2.225e-11 1.833 1.742 1.199e-11 9.930e-12 0.978 1.430e-04 1.384e-04 4.897e-05
hd59967 5 G4V 0.641 6.660 -0.19b 8.012e-12 7.884e-12 1.826 1.629 4.420e-12 3. 7 6 3 e - 1 2 1.021 1.512e-04 1.214e-04 7.739e-05
hd187923 10 G0V 0.642 6.160 -0.20a 1.368e-11 1.350e-11 1.809 1.646 7.548e-12 6.660e-12 1.038 1.655e-04 4.708e-05 2.116e-05
hd19467 10 G3V 0.645 6.970 -0.13b 5.923e-12 5.861e-12 1.736 1.607 3.277e-12 2 . 8 7 4 e - 1 2 1.039 1.508e-04 7.483e-05 2.271e-05
hd189567 8 G3V 0.648 6.070 -0.30a 1.395e-11 1.377e-11 1.752 1.595 7.994e-12 6 .906e-12 1.068 1.592e-04 1.008e-04 3.051e-05
hd210918 11 G5V 0.648 6.230 -0.18a 1.154e-11 1.139e-11 1.788 1.623 6.353e-12 5.686e-12 1.043 1.491e-04 7.484e-05 2.604e-05
hd173560 9 G3/5V 0.649 8.690 -0.21b 1.272e-12 1.248e-12 1.667 1.427 7.344e-13 6 . 3 8 5 e - 13 1.079 1.637e-04 4.757e-05 3.793e-05
hr6060 15 G2Va 0.652 5.490 0.05a 2.369e-11 2.331e-11 1.962 1.765 1.221e-11 1. 033e-11 0.951 1.408e-04 9.134e-05 2.526e-05
hd11131 9 G0 0.654 6.720 -0.06a 7.558e-12 7.474e-12 1.726 1.587 4.098e-12 3.4 39e-12 0.997 1.460e-04 1.038e-04 7.184e-05
hd20619 11 G1.5V 0.655 7.050 -0.20a 5.339e-12 5.293e-12 1.738 1.632 2.916e-12 2.486e-12 1.012 1.417e-04 1.212e-04 3.218e-05
hd217343 2 G3V 0.655 7.470 -0.18b 3.768e-12 3.711e-12 1.995 1.810 2.075e-12 1 . 8 0 5 e - 1 2 1.030 1.499e-04 1.060e-04 1.057e-04
hd4308 12 G5V 0.655 6.550 -0.47a 8.907e-12 8.808e-12 1.652 1.513 4.651e-12 3. 991e-12 0.970 1.431e-04 9.757e-05 2.719e-05
hd1835 13 G3V 0.659 6.390 -0.01a 1.067e-11 1.049e-11 2.116 1.921 5.225e-12 4. 551e-12 0.917 1.393e-04 9.379e-05 6.410e-05
hd213941 9 G5V 0.670 7.580 -0.42a 3.335e-12 3.313e-12 2.057 1.977 1.759e-12 1 .508e-12 0.979 1.386e-04 1.031e-04 3.985e-05
Table 4 – continued
Star Nobs Sp. type (B − V) V [Fe/H] < Fcont > < F̄ > < Wλ > < Wapprox > < FD1 > < FD2 > < N > < RD > R
D < R
hd197214 10 G5V 0.671 6.950 -0.5b 6.138e-12 6.048e-12 1.983 1.804 3.224e-12 2 . 7 1 9 e - 1 2 0.968 1.411e-04 1.186e-04 3.608e-05
hd172051 13 G5V 0.673 5.850 -0.29b 1.699e-11 1.677e-11 2.078 1.923 8.668e-12 7 . 3 6 7 e - 1 2 0.944 1.380e-04 1.266e-04 2.725e-05
hd19034 8 G5 0.677 8.080 -0.39b 2.167e-12 2.148e-12 1.870 1.767 1.128e-12 9.4 4 3 e - 1 3 0 .957 1.389e-04 1.297e-04 2.861e-05
hd203019 3 G5V 0.687 7.840 0.07b 2.710e-12 2.652e-12 2.330 2.078 1.256e-12 1. 1 2 3 e - 1 2 0.878 1.272e-04 9.105e-05 9.492e-05
hd202917 5 G5V 0.690 8.650 -0.16b 1.269e-12 1.250e-12 2.377 2.198 6.377e-13 5 . 5 0 5 e - 1 3 0.936 1.338e-04 1.183e-04 1.416e-04
hd12759 4 G3V 0.694 7.300 -0.13b 4.585e-12 4.501e-12 2.245 2.026 2.427e-12 2. 0 9 3 e - 1 2 0.986 1.465e-04 2.882e-05 7.779e-05
hd128620 7 G2V 0.710 -0.010 0.22a 3.844e-09 3.777e-09 2.123 1.912 1.943e-09 1 . 5 9 1e-09 0.919 1.355e-04 4.082e-05 2.221e-05
hd41824 11 G6V 0.712 6.600 -0.09b 9.098e-12 8.924e-12 2.456 2.231 4.401e-12 3 .864 e - 1 2 0.909 1.394e-04 3.642e-05 1.074e-04
hd117176 3 G4V 0.714 4.970 -0.11a 3.835e-11 3.783e-11 1.947 1.780 2.074e-11 1 .897e-11 1.036 1.492e-04 2.157e-05 1.581e-05
hd3443 9 K1V 0.715 5.570 -0.16c 2.212e-11 2.186e-11 2.440 2.305 1.051e-11 8.7 90e-12 0.872 1.259e-04 5.059e-05 2.837e-05
hd3795 9 G3/5V 0.718 6.140 -0.70a 1.299e-11 1.288e-11 1.692 1.584 7.208e-12 6 .159e-12 1.029 1.472e-04 2.478e-05 2.282e-05
hd203244 1 G5V 0.723 6.980 -0.21a 6.150e-12 6.069e-12 2.284 2.128 3.265e-12 2 .754e-12 0.979 1.434e-04 1.010e-04 7.445e-05
hd10700 11 G8V 0.727 3.490 -0.59a 1.490e-10 1.475e-10 2.344 2.227 6.720e-11 5 .630e-11 0.829 1.180e-04 1.243e-04 3.117e-05
hd152391 11 G8V 0.749 6.650 -0.06b 8.579e-12 8.407e-12 2.613 2.379 3.882e-12 3.26 3 e - 1 2 0.833 1.238e-04 9.103e-05 6.268e-05
hd36435 5 G6/8V 0.755 6.990 -0.02a 6.071e-12 5.984e-12 2.425 2.255 2.798e-12 2.433e-12 0.862 1.235e-04 8.948e-05 6.689e-05
hd13445 5 K1V 0.812 6.120 -0.21a 1.365e-11 1.338e-11 3.400 3.147 4.822e-12 3. 947e-12 0.643 8.931e-05 8.795e-05 3.455e-05
hd26965 10 K1V 0.820 4.430 -0.25a 6.876e-11 6.776e-11 3.413 3.228 2.547e-11 2 .081e-11 0.673 9.885e-05 8.235e-05 2.275e-05
hd177996 9 K1V 0.862 7.890 -0.28b 2.876e-12 2.798e-12 4.034 3.699 1.131e-12 9 .836 e - 1 3 0.735 1.048e-04 3.767e-05 7.872e-05
hd17925 7 K1V 0.862 6.050 0.10a 1.648e-11 1.608e-11 3.898 3.596 5.892e-12 4.9 04e-12 0.655 9.825e-05 6.478e-05 8.305e-05
hd22049 13 K2V 0.881 3.720 -0.14a 1.318e-10 1.292e-10 3.905 3.653 4.355e-11 3 .628e-11 0.606 8.335e-05 6.921e-05 5.299e-05
hd128621 8 K1V 0.900 1.350 0.24a 1.220e-09 1.183e-09 4.576 4.216 3.709e-10 3. 049e-10 0.554 7.802e-05 3.906e-05 2.154e-05
gl349 12 K3V 1.002 7.200 -0.15b 5.535e-12 5.373e-12 6.086 5.667 1.353e-12 1.1 42e- 1 2 0 .451 5.558e-05 4.579e-05 5.335e-05
gl542 9 K3V 1.017 6.660 0.26a 9.770e-12 9.361e-12 7.693 7.154 1.959e-12 1.678 e-12 0.372 4.834e-05 2.846e-05 1.566e-05
hd188088 6 K3/4V 1.017 6.220 – 1.499e-11 1.433e-11 7.920 7.369 3.456e-12 2.903e-12 0.425 5.636e-05 1.315e-05 4.730e-05
hd131977 9 K4V 1.024 5.720 0.03 2.381e-11 2.322e-11 8.199 7.903 4.477e-12 3.802e-12 0.348 4.588e-05 4.552e-05 2.660e-05
gl610 9 K3/4V 1.043 7.390 -0.03a 4.892e-12 4.719e-12 7.510 7.054 1.128e-12 9. 638e-13 0.428 5.266e-05 1.849e-05 1.505e-05
hd32147 10 K3V 1.049 6.220 0.34a 1.468e-11 1.415e-11 7.691 7.232 2.773e-12 2. 353e-12 0.349 4.360e-05 2.653e-05 1.978e-05
gl845 8 K4.5V 1.056 4.690 -0.23a 6.041e-11 5.768e-11 7.782 7.203 1.179e-11 1. 008e-11 0.362 4.505e-05 3.618e-05 2.748e-05
gl435 8 K4/5V 1.064 7.770 – 3.576e-12 3.467e-12 7.456 7.062 7.230e-13 6.108e-13 0.373 4.640e-05 4.852e-05 2.499e-05
hd216803 2 K4V 1.094 6.480 – 1.181e-11 1.159e-11 6.814 6.562 2.636e-12 2.258e-12 0.414 4.993e-05 3.080e-05 6.597e-05
hd156026 7 K5V 1.144 6.330 -0.21a 1.398e-11 1.357e-11 8.456 8.105 2.623e-12 2 .313e-12 0.353 4.114e-05 2.798e-05 3.156e-05
gl416 7 K4V 1.203 9.060 – 1.178e-12 1.121e-12 10.178 9.482 2.018e-13 1.851e-13 0.329 3.623e-05 1.301e-05 2.745e-05
gl517 7 K5Ve 1.210 9.240 -0.15c 9.272e-13 8.849e-13 9.795 9.116 2.115e-13 1.9 72e-13 0.441 4.464e-05 1.877e-05 1.643e-04
hd157881 9 K5 1.359 7.540 -0.20a 5.122e-12 4.868e-12 13.782 13.040 8.167e-13 7.218e-13 0.300 2.634e-05 3.709e-06 3.227e-05
gl526 5 M1.5 1.435 8.460 – 2.297e-12 – 15.084 – 3.925e-13 3.433e-13 0.320 2.379e-05 4.811e-06 1.880e-05
gl536 5 M1 1.461 9.710 – 7.087e-13 – 14.472 – 1.436e-13 1.307e-13 0.387 2.547e-05 2.607e-06 1.920e-05
gl1 9 M1.5 1.462 8.560 – 2.062e-12 – 15.579 – 2.574e-13 2.163e-13 0.230 1.520e-05 4.825e-06 6.587e-06
hd180617 8 M2.5 1.464 9.120 – 1.220e-12 – 16.324 – 1.837e-13 1.661e-13 0.287 1.866e-05 4.279e-06 2.185e-05
gl479 6 M2 1.470 10.650 – 3.116e-13 – 16.527 – 5.484e-14 5.032e-14 0.338 2.246e-05 5.738e-06 3.258e-05
hd36395 8 M1.5 1.474 7.970 0.60c 3.719e-12 – 15.876 – 6.313e-13 5.648e-13 0 .32 2 2.133e-05 1.291e-06 4.688e-05
hd42581 8 M1/2V 1.487 8.150 – 3.000e-12 – 14.864 – 5.104e-13 4.495e-13 0.320 1.895e-05 1.113e-06 2.533e-05
gl388 6 M3.5Ve 1.540 9.430 – 9.761e-13 – 22.636 – 2.003e-13 2.289e-13 0.440 1.987e-05 1.501e-06 1.122e-04
gl699 11 M4Ve 1.570 9.540 – 9.174e-13 – 26.649 – 7.240e-14 6.531e-14 0.150 4.653e-06 4.012e-06 1.006e-05
gl551 13 M5.5Ve 1.807 11.010 – 2.303e-13 – 28.131 – 4.582e-14 5.835e-14 0.452 5.566e-06 2.657e-08 1.883e-05
	Introduction
	Observations and stellar sample
	Observations and calibration of the spectra
	Stellar sample
	Pseudo-continuum
	Definition 
	Relation with (B-V)
	Calibration
	Equivalent width
	Definition 
	Relation with colour index (B-V)
	Comparison
	Determination of (B-V)
	Activity indexes and chromospheric activity
	N index 
	Chromospheric activity
	Summary
