Understanding the $\gamma$ Doradus Phenomenon using MONS
F.M. Zerbi$^1$
C. Aerts$^2$
G. Handler$^3$
A.B. Kaye$^4$ and E. Poretti$^1$
We discuss the results expected from observing $\gamma$ Dor stars with the MONS satellite. We first describe how MONS Star Trackers will consistently improve the present knowledge of this new class of variables. We then discuss how the $\gamma$ Dor can be considered possible "bridges" between opacity driven pulsations and stochastically excited solar like oscillations. For this reason the possible inclusion of a $\gamma$ Dor representative in the MONS main target list is suggested and discussed. Three possible candidates are presented: $\gamma$ Dor, 9 Aur and BS 2740.
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\documentclass[11pt]{article}
\usepackage{mons2}
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\lefthead{Zerbi {\it et al}} \righthead{Observing $\gamma$ Dors
with MONS}

\begin{document}

\title{Understanding the $\gamma$ Doradus Phenomenon using MONS}

\author{F.M. Zerbi$^1$, C. Aerts$^2$, G. Handler$^3$, A.B. Kaye$^4$ and
E. Poretti$^1$ }

\affil{$^1$Osservatorio Astronomico di Brera, Via Bianchi 46,
23807 Merate (Lc), Italy \\ $^2$  Instituut voor Sterrenkunde,
Katholieke Universiteit Leuven, \\ Celestijnenlaan 200 B, B-3001
Leuven, Belgium\\ $^3$ SAAO, PO Box 9, Observatory 7935, South
Africa \\ $^4$ Los Alamos National Laboratory, X-TA, MS B-220, Los
Alamos NM 87545, USA}


\begin{abstract}
We discuss the results expected from observing $\gamma$ Dor stars with
the MONS satellite. We first describe how MONS Star Trackers will
consistently improve the present knowledge of this new class of variables.
We then discuss how the $\gamma$ Dor can be considered possible "bridges"
between opacity driven pulsations and stochastically excited solar like
oscillations. For this reason the possible inclusion of a $\gamma$ Dor
representative in the MONS main target list is suggested and discussed.
Three possible candidates are presented: $\gamma$ Dor, 9 Aur and BS 2740.
\end{abstract}

\section{A Brief Introduction to $\gamma$ Doradus Stars}

The $\gamma$ Dor stars have been recently defined (Kaye et al. 1999)  as a
class of variable stars in the lower-red part of the Cepheid instability
strip, undergoing $g$-mode pulsation.  Stars in this group show
(multi)periodic photometric and spectroscopic variability with typical
time scales between 0.3 and 3\,d and typical amplitudes below $0^m.1$. The
definition of the class was based on 12 objects contained in a so-called
{\it master list}. The principal physical properties of these stars are
reported in Table 1. Several objects suspected to belong to the class have
been recently added by Aerts, Eyer \& Kestens (1998) and Handler (1999a)
upon examination of HIPPARCOS light curves. At the present date the
data-base of known $\gamma$ Dor stars and related objects (Handler,
private communication) contains 141 objects divided into {\it Bona Fide}
(12), {\it Prime} (46) and {\it Other} (83) candidates. Bona fide objects
in the master list are stars for which extensive photometric and
spectroscopic data prove that pulsations must be the cause for the
variability. Prime and Other $\gamma$ Dor candidates are stars for which
either a moderate or a limited amount of photometric and/or spectroscopic
data is available, allowing to suspect or speculate that nonradial
pulsation (NRP) is the cause of the observed variations.

\begin{table}[h]
%\begin{minipage}{115mm}
%\scriptsize
\footnotesize
\begin{center}
\begin{tabular}{cccccccccccc}
\tableline Star &$b-y$ & $<V>$ & ST & $v \sin i$ & $\pi$ &
[$Me/H$] & $M_V$ & $L$ & $T_{\rm eff}$ & $R$ & $M$
\\

& (mag) &  (mag) & & (kms$^{-1}$) & (mas)  & & (mag) &$[L_\odot]$
& (K) & $[R_\odot]$ & $[M_\odot]$
\\

\tableline

HD 224945 & 0.192 & 6.93 & F0 {\sc v} &  55 & 16.92 & $-0.30$ &
3.07 & 5.1 & 7250 & 1.43 & 1.51
\\

$\gamma$ Dor & 0.201 & 4.25 & F0 {\sc v} &  62 & 49.26 & $-0.02$ &
2.72 & 7.0 & 7200 & 1.70 & 1.57 \\

9 Aur & 0.217 & 5.00 & F0 {\sc v} &  18 & 38.14 & $-0.19$ & 2.89 &
6.0 & 7100 & 1.62 & 1.52 \\

BS 2740 & 0.219 & 4.49 & F0 {\sc v} &  40 & 47.22 & $-0.15$ & 2.86
& 6.2 & 7100 & 1.64 & 1.53 \\

HD 62454 & 0.214 & 7.15 & F1 {\sc v} &  53 & 11.18 & ~~0.16 & 2.39
& 9.5 & 7125 & 2.02 & 1.66 \\

HD 68192 & 0.227 & 7.16 & F2 {\sc v} & 85 & 10.67 & ~~0.05 & 2.30
& 10.5 & 7000 & 2.20 & 1.71 \\

HD 108100 & 0.234 & 7.14 & F2 {\sc v} & 68 & 12.10 &  $-0.03$ &
2.53 & 8.5 & 6950 & 2.01 & 1.62
\\

HD 164615 & 0.226 & 7.06 & F2 {\sc iv} & 66 & 14.36  & ~~0.20 &
2.82 & 6.5 & 7000 & 1.73 & 1.53 \\

BS 6767 & 0.183 & 6.40 & F0 {\sc v}n & 135 & 17.44  & $-0.10$ &
2.59 & 7.9 & 7300 & 1.76 & 1.61 \\

BS 8330 & 0.225 & 6.20 & F2 {\sc iv} & 38 & 19.90 & $-0.01$ & 2.67
& 7.4 & 7000 & 1.85 & 1.57 \\


BS 8799 & 0.181 & 5.99 & kA5 & 45 & 25.04 & $-0.36$ & 2.96 & 5.7 &
7375 & 1.46 & 1.54 \\

HD 224638 & 0.198 & 7.49 & F1 {\sc v}s & 24 & 12.56 & $-0.15$ &
2.98 & 5.5 & 7200 & 1.51 & 1.52 \\

\tableline \normalsize
\end{tabular}
\end{center}
\vskip-0.8truecm \caption{Observational parameters of the
confirmed $\gamma$ Dor variables and calculated or inferred
basic properties. Table taken from Kaye et al. (1999).
\label{deftab1} }
\end{table}

The most relevant problems in the observation of $\gamma$ Dor stars
concern the amplitudes and time scales of their variability. Amplitudes
are small and the clustering of the typical frequencies around 1\,d$^{-1}$
creates conflicts with the 1\,d$^{-1}$ alias typical of ground-based
single-site observations and requires to organize multi-longitude
campaigns. At the same time even in these campaigns problems of alignment,
improper correction for atmospheric extinction and fluctuation in the
instrumental setup often introduce spurious low-frequency terms that have
the chance to be misinterpreted as signal. For this reason $\gamma$ Dor
stars will benefit as many other classes of variables of continuous
out-of-atmospheric coverage as the one provided by a space mission like
MONS.

The interested community has largely discussed if $\gamma$ Dor stars
have any relevance for asteroseismology. These stars pulsate in $g$-modes
that in some sense carry more information on the stellar interior than
$p$-modes, but the low number of modes excited and the intrinsic
uncertainties in the application of standard mode-identification
techniques seem to make a seismic interpretation rather difficult. The
$\gamma$ Dor stars give us however two additional possibilities for
seismological investigations which other classes of pulsating star cannot
provide.

Firstly, the domain of $\gamma$ Dor stars in the HR diagram partly
overlaps with that of the $\delta$ Scuti stars (Handler 1999a). It can
therefore be suspected that stars showing both types of pulsation could be
present. This will allow to constrain the physical properties of a star
tightly from the $\delta$ Scuti-type $p$ modes, which helps in identifying
the $\gamma$ Dor-type $g$ modes which can then be used to probe the
star's deep interior. Indeed, short-period light variations have already
been detected for two $\gamma$ Dor stars (see Handler 1999b for
the first discovery).

Secondly, Guzik et al. (2000) pointed out the major role played by
convection in $\gamma$ Dor pulsation theory. These authors
calculated nonadiabatic pulsation properties of evolutionary
models lying near the $\gamma$ Dor instability region in the H-R
diagram. The models considered have relatively deep envelope
convection zones. By using the Pesnell (1990) non-adiabatic
pulsation code these authors calculated the $l=0,1,2$ pulsation
frequencies and found unstable high order $g$-modes with
frequencies between 4 and 25 $\mu$Hz (periods $\sim$ 0.4 to 3
days). Furthermore the mode kinetic energy was found to reach a
minimum at a frequency of about 11 $\mu$Hz (period of $\sim$ 1 d),
i.e. near the most commonly observed $\gamma$ Dor period. The
frequency spacing between modes with same $l$ and subsequent $n$
was found to be $\sim 0.1$ d$^{-1}$, exactly matching the typical
frequency spacing observed in multiperiodic $\gamma$ Dor stars.
These results strongly suggest that asteroseismology of $\gamma$
Dor stars might be easier as it seemed until very recently.

Another interesting outcome of the model calculations originates from the
"frozen-in convection" approximation used, in which fluctuations in the
convective luminosity are set to zero during the pulsation cycle. Because
convection does not adapt to transport the luminosity in this
approximation, the radiation is periodically blocked by the high opacity
at the convection zone base, resulting in pulsational driving. Therefore
the overstable $g$-modes in $\gamma$ Dor stars are first maintained by an
opacity bump at the basis of the convective layer which has nothing to do
with the classical $\kappa/\gamma$ mechanism and "tunnel" to the surface
through a convective envelope which is "lazy"  enough not to adjust and
damp them. Second the turbulent motion in the convective envelope could
trigger solar-like oscillations as in any other stars of this mass,
temperature and luminosity. Indeed the temperature and luminosity range
occupied by $\gamma$ Dor stars completely overlaps with the one in which
solar-like oscillations are predicted. In this sense $\gamma$ Dor stars
might represent a sort of "bridge" between overstable pulsation and
stochastically generated solar-like oscillations. The MONS primary
telescope represents an unique opportunity to investigate such a possible
link. For this reason we encourage the MONS science team to consider the
inclusion of an object of this kind in the primary target list.

\section{Observing $\gamma$ Doradus stars with the star trackers}

MONS star trackers will observe their targets continuously for about 30
days; this will greatly reduce the size of alias peaks. A computed MONS
spectral window predicts the strongest alias at .02 mHz ($\sim
1.7$\,d$^{-1}$) with an amplitude of $0.2\times 10^{-6}$. This number has
to be compared to the typical size of the 1\,d$^{-1}$ alias of
ground-based multisite campaigns for $\gamma$ Dor stars, which is of about
$3.1\times10^{-1}$ in amplitude or higher. Most of the available
literature on $\gamma$ Dor stars contains discussions of accurate
time-series analysis fighting against aliasing. In this sense the superb
quality of MONS spectral window will likely allow major improvements in
frequency recognition.

It has often been noticed in published frequency analyses (even among
$\gamma$ Dor candidates) that after subtraction of known signals from the
data suprisingly high residuals remained. In the best cases the mean
internal error achievable from the ground is 2000 ppm, on the average 4000
ppm is probably a more reliable value; this translates into noise levels
around 1000 ppm in the amplitude spectra in the frequency region of
interest. At the typical magnitudes of the proposed $\gamma$ Dor targets
MONS Star Trackers will allow clear 3$\sigma$ detections of signals with
amplitudes of the order of a few tens of ppm, providing information more
accurate by orders of magnitude with respect to the best observations from
Earth. In the case of {\it prime} or {\it other} candidates the suspected
presence of g-mode pulsation is mostly deduced from survey quality light
curves (see for example the left box of Figure 1). The residual scatter in
the light curves is typically a few percent ($\sim 10^4$ ppm). MONS STs
will improve the measurement accuracy by a factor of at least 100 allowing
to confirm the detection and to give an insight into the behaviour of the
star at the same time. Obviously, possibly superposed $\delta$~Scuti-type
pulsations would be easily detectable as well.

\section{Observation of $\gamma$ Doradus stars with the main CAM}

A star which is to be observed as a MONS prime target must be as bright as
possible and its $\gamma$ Dor nature must be well established. By
examination of Table 1 we can see that 3 of the bona fide $\gamma$ Dor
stars have apparent magnitudes between 4 and 5, i.e. in the typical
magnitude range of the solar-type variables included in MONS' prime
program. Those are $\gamma$ Dor, 9 Aur and BS 2740. The three stars have
been observed at least through one successful multi-longitude multi-colour
photometric campaign and the presence of NRP is established beyond any
reasonable doubt. The cases of $\gamma$ Dor and 9 Aur are particularly
interesting since these are the most thoroughly observed and studied
$\gamma$ Dor stars so far. We now turn to short descriptions of these
objects.

The bright star {\bf $\gamma$ Dor} was observed in the sixties during
survey work dedicated to some chemically peculiar A stars and was
suspected to show variations with an amplitude $\Delta V=0^m.05$. Cousins
(1992) observed it with high precision in 1983/84 (55 measurements in 120
nights). The analysis provided evidence of two close frequencies at 1.32
and 1.36\,d$^{-1}$, which was confirmed, together with their beat
frequency at 0.04\,d$^{-1}$, by a further intensive observing run in 1989.
The star has since then been object of two multi-longitude photometric and
one multi-longitude spectroscopic campaign (Balona et al. 1994, 1996). The
first campaign confirmed the two close frequencies at $f_1=1.32098$ and
$f_2$=1.36354\,d$^{-1}$ and provided evidence for the presence of a third
frequency at $f_3$=1.47447\,d$^{-1}$. The second campaign resulted in
clear evidence of line profile variations due to NRP.

The availability of line profiles sampled with sufficient resolution
allowed these authors to apply the {\it moment method} (Balona 1987, Aerts
et al. 1992) to this star. Such a method constructs a {\it discriminant},
the minimum value of which indicates the most suitable combination of
$i,l,m$ to fit the observed oscillation. The discriminant diagrams for
$\gamma$ Dor computed by Balona et al. (1996) are reported in
Figure~\ref{monfig2} (right box). Clearly the results are non-conclusive
since they do neither point to a unique solution nor, as they should, to a
unique value for the inclination. However, Balona et al. (1996) state that
the most probable angle of inclination for the star is $i=70^o$ and the
best estimate for the pulsational quantum numbers ($l, m$) are (3,3) for
$f_1$ and (1,1) both for $f_2$ and $f_3$.

\begin{figure}
\label{Ccurves} \psfig{figure=monfig2.ps,width=17cm}
\caption{Left box: phased Hipparcos light curves of suspected $\gamma$ Dor
stars reported by Aerts, Eyer \& Kestens (1998). Right box: results
of the moment analysis of $\gamma$ Dor presented by Balona et al.
(1996). The figure shows the discriminants in arbitrary units as a
function of the angle of inclination (in degrees) for various
modes ($l,m$). $f_1$, $f_2$ and $f_3$ are represented in the top,
mid and bottom panel, respectively.\label{monfig2}}
\end{figure}

Photometric variability of the bright northern star {\bf 9 Aurigae} was
reported by Krisciunas \& Guinan (1990). The star was then observed by
Krisciunas et al. (1995) through a multi-longitude campaign, however only
comprising sites in the continental US and Hawaii.  The analysis of these
data resulted in the detection of two frequencies at $f_1=0.794$ and
$f_2$=0.345\,d$^{-1}$.  Radial velocity measurements were also collected
during the campaign with the CORAVEL instrument in France.  Radial
velocity curves gave evidence for variability with frequency $f_2$, but no
sign of $f_1$, whereas the second output quantity of CORAVEL, the line
width, was dominated by $f_1$, as the photometry. This prompted Aerts and
Krisciunas (1996) to apply the moment method to the same CORAVEL data.
These authors reported a possible identification of the two frequencies as
the manifestation of an $l=3$, $|m|=1$ spheroidal mode and its toroidal
correction due to stellar rotation.

In order to overcome the aliasing problem, 9 Aur was re-scheduled for a
multi-longitude photometric campaign; the results were published by Zerbi
et al. (1997). This time a coverage of more than $18^h$ over $24^h$ was
achieved in a number of nights resulting in a substantial decrease of the
1\,d$^{-1}$ alias. The main frequency $f_1$ was confirmed and a new
frequency at $f_3$=0.7681\,d$^{-1}$ was discovered well above the level of
detection. However, the previously known mode at $f_2=0.3454$ could not be
clearly resolved. Its power was distributed into two peaks at
$f_{2a}$=0.2788d\,$^{-1}$ and at $f_1/2$=0.3975\,d$^{-1}$, the latter
causing the phased curve of the main signal to be double-wave-shaped. Most
of the measurements in this campaign were collected in the Str\"omgren
system. This made it possible to observe how the oscillations manifested
themselves in the $c_1$ index (tracing the luminosity) and the $(b-y)$
index (tracing the effective temperature) for the principal frequency. It
was found that they occurred in phase within the errors. This means that
geometrical displacements are not relevant for the oscillations, which can
be assumed as due basically to temperature variations. To some extent this
is what one would expect for a low-order $g$-mode oscillation.

The light variability of the F0 IV star {\bf BS 2740} was discovered by
Hensberge et al. (1981), who used it as a comparison star for Ap star
observations. On the basis of 20 $uvby$ measurements collected in 16
nights spanning 41 days, these authors derived a period of 0.936\,d$^{-1}$
and classified BS 2740 as a ``mild Ap star''. This evidence and the star's
position in the HR diagram combined with the detection of line-profile
variations in unpublished spectrograms prompted Poretti et al. (1997)  to
investigate its possible $\gamma$ Dor nature through a multi-longitude
campaign. The light curve of BS 2740 was explained with four frequencies,
$f_1=1.0434$, $f_2=0.9951$, $f_3=1.1088$ and $f_4$=0.9019\,d$^{-1}$ and
white noise. All the frequencies above are very close to 1\,d$^{-1}$,
which means that roughly the same phase of the oscillations would be seen
by a single-site observer. Multisite campaigns or space observations are
therefore required for this star.

\section{Conclusions}

The $\gamma$ Dor stars are known to exhibit $g$-mode pulsations at
time scales that make their observation difficult from the ground because
of aliasing problems. The location of the class in the HR diagram and some
theoretical arguments imply that solar-like oscillations could be excited
in these stars as well. The MONS satellite is then the ideal tool to
investigate both aspects taking profit of the clean spectral window of the
STs and the precision of the CAM. We therefore strongly support the
inclusion of a suitable candidate in the main target list and the
recording of as many targets as possible with the STs.

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\end{document}

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