arXiv:1101.2372v1 [astro-ph.SR] 12 Jan 2011
Pulsational analysis of V 588 Mon and V 589 Mon observed with
the MOST1and CoRoT2satellites
Institute of Astronomy, T¨ urkenschanzstrasse 17, A-1180 Vienna, Austria
Department of Physics and Astronomy, University of British Columbia, 6224 Agricultural
Road, Vancouver, BC V6T 1Z1, Canada
D. B. Guenther and M. Gruberbauer
Department of Astronomy and Physics, St. Mary’s University, Halifax, NS B3H 3C3,
R. Kuschnig and W. W. Weiss
Institute of Astronomy, T¨ urkenschanzstrasse 17, A-1180 Vienna, Austria
LESIA, Observatoire de Paris-Meudon, 5 place Jules Janssen, 92195 Meudon, France
Laboratoire d’Astrophysique de Marseille, Pˆ ole de l’´Etoile Site de Chˆ ateau-Gombert, 38,
rue Fr´ ed´ eric Joliot-Curie, 13388 Marseille, France
European Space Agency, 8-10 rue Mario Nikis, 75015 Paris, France
Department of Physics and Astronomy, University of British Columbia, 6224 Agricultural
Road, Vancouver, BC V6T 1Z1, Canada
– 2 –
Vienna University of Technology, Institute of Communications and Radio-Frequency
Engineering, Gusshausstrasse 25/389, A-1040 Vienna, Austria
The two pulsating pre-main sequence (PMS) stars V 588 Mon and V 589
Mon were observed by CoRoT for 23.4 days in March 2008 during the Short Run
SRa01 and in 2004 and 2006 by MOST for a total of ∼70 days. We present
their photometric variability up to 1000 µ Hz and down to residual amplitude
noise levels of 23 and 10 ppm of the CoRoT data for V 588 Mon and V 589
Mon, respectively. The CoRoT imagette data as well as the two MOST data sets
allowed for detailed frequency analyses using Period04 and SigSpec. We confirm
all previously identified frequencies, improve the known pulsation spectra to a
total of 21 frequencies for V 588 Mon and 37 for V 589 Mon and compare them
to our PMS model predictions. No model oscillation spectrum with l = 0, 1, 2,
and 3 p-modes matches all the observed frequencies. When rotation is included
we find that the rotationally split modes of the slower rotating star, V 589 Mon,
are addressable via perturbative methods while for the more rapidly rotating
star, V 588 Mon, they are not and, consequently, will require more sophisticated
modeling. The high precision of the CoRoT data allowed us to investigate the
large density of frequencies found in the region from 0 to 300 µHz. The presence
of granulation appears to be a more attractive explanation than the excitation
of high-degree modes. Granulation was modeled with a superposition of white
noise, a sum of Lorentzian-like functions and a Gaussian. Our analysis clearly
illustrates the need for a more sophisticated granulation model.
Subject headings: asteroseismology — techniques: photometric — stars: pre-
main sequence — stars: variables: delta Scuti — stars: individual (V 588 Mon,
V 589 Mon)
1Based on data from the MOST satellite, a Canadian Space Agency mission, jointly operated by Dynacon
Inc., the University of Toronto Institute for Aerospace Studies and the University of British Columbia with
the assistance of the University of Vienna.
2The CoRoT space mission, launched on December 27th 2006, has been developed and is operated by
CNES, with the contribution of Austria, Belgium, Brazil , ESA (RSSD and Science Programme), Germany
– 3 –
V 588 Mon (HD 261331, NGC 2264 2) and V 589 Mon (HD 261446, NGC 2264 20)
are two pre-main-sequence (PMS) pulsating stars for which there exists strong evidence that
they are members of the young open cluster NGC 2264. The proper motions for both stars
are in agreement with the clusters average proper motion (Hog et al. 2000) and both fit
the clusters HR- and color-magnitude diagrams well. A radial velocity measurement only
exists for V 589 Mon (Strom et al. 1971) but it is consistent with the values for other cluster
members. Finally, the radial velocities of emission lines in the optical spectra of the two stars
caused by interstellar gas match the radial velocities of the cluster suggesting that both stars
are indeed embedded in gas clouds belonging to the cluster (Kallinger et al. 2008a).
The cluster has a diameter of ∼39 arcminutes and belongs to the Mon OB 1 association.
The age of NGC 2264 is reported in the literature to lie between 3 (e.g., Walker 1956;
Sung et al. 2004) and 10 million years (e.g., Sagar et al. 1986). With such a young age,
the cluster’s main sequence only consists of massive O and B type stars, while stars of later
spectral types are still in their pre-main sequence (PMS) phase. Therefore, V 588 Mon and
V 589 Mon having spectral types of A7 and F2, respectively, have not arrived on the zero-age
main sequence (ZAMS) yet.
The δ Scuti like variability of V 588 Mon and V 589 Mon was first reported by Breger
(1972). Hence, they were the first pulsating PMS stars discovered. In the meantime the
number of known δ Scuti like PMS pulsators has increased from 36 (Zwintz 2008) to ∼ 60
(Zwintz, K., private communication) due to dedicated observations from ground and from
Pulsating PMS stars have intermediate masses, i.e. between ∼1.5 and 4 M⊙and can
become vibrationally unstable when they cross the instability region in the Hertzsprung-
Russell (HR) diagram on their way to the ZAMS. Pre- and post-main sequence evolutionary
tracks for the same stellar mass intersect several times close to the ZAMS which makes the
determination of the evolutionary stage of a field star from only its effective temperature,
luminosity and mass ambiguous. Additional information such as typical observational evi-
dence for the PMS evolutionary stage (i.e. emission lines, IR excess, an X-ray flux, located
in an obscured region on the sky etc.) or membership to very young open clusters is needed
to resolve this ambiguity. Another way to distinguish the evolutionary stages can come
from the asteroseismic interpretation of the observed pulsation frequencies (Guenther et al.
Time series photometry for V 588 Mon and V 589 Mon has been obtained from a multi-
site ground based campaign (Kallinger et al. 2008a) and from two observing runs of the
– 4 –
Canadian MOST space telescope (Walker et al. 2003) in 2004 and 2006 (Guenther et al.
2009). The 8 and 12 frequencies common to these three data sets for V 588 Mon and V 589
Mon, respectively, were submitted to a first asteroseismic analysis (Guenther et al. 2009).
The accuracy of the MOST observations is higher than that of the ground based data. Hence
it is not surprising that the two MOST data sets yield more significant frequencies at lower
amplitudes that were not found in the ground based observations. The CoRoT observations
of the two PMS pulsators are new and independent data sets of unprecedented accuracy that
allow us for the first time to investigate other effects (e.g., granulation) in PMS stars. As
both MOST data sets and the CoRoT data are available to us, we use them together for a
detailed pulsational analysis.
2. Observations and Data Reduction
2.1. MOST observations
The MOST (Microvariability and Oscillations of STars) space telescope (Walker et al.
2003) was launched on June 30, 2003, into a polar sun-synchronous circular orbit with an
orbital period of ∼ 101 minutes (corresponding to an orbital frequency of 14.2 d−1). From
its orbital vantage point, MOST can obtain uninterrupted observations of stars located in
its Continuous Viewing Zone (CVZ) for up to 8 weeks. The MOST satellite houses a 15-cm
Rumak-Maksutov telescope feeding a CCD photometer through a single, custom broadband
optical filter (covering wavelengths from 350 to 750nm).
MOST can supply up to three types of photometric data simultaneously for multiple
targets in its field. The mission was originally intended only for Fabry Imaging, in which an
image of the entrance pupil of the telescope - illuminated by a bright target star (V < 6) - is
projected onto the instrument’s Science CCD by a Fabry microlens (see Reegen et al. 2006)
for details. After MOST was operating in orbit, the pointing performance of the satellite was
improved so much that a new mode of observing, Direct Imaging, was made practical. Direct
Imaging is much like conventional CCD photometry, in which photometry is obtained from
defocussed images of stars in the open area of the CCD not covered by the Fabry microlens
array field stop mask. In the original design, no scientific information was available from
the Guide Stars used for the ACS (Attitude Control System), but now precise photometry
is possible for these stars as well (see e.g., Walker et al. 2005; Aerts et al. 2006).
V 588 Mon and V 589 Mon were observed in the Direct Imaging mode, first from
December 6, 2004, to January 24, 2005, and second within the NGC 2264 observations
(see Zwintz et al. 2009) from December 7, 2006, to January 4, 2007. The light curves have
– 5 –
therefore time bases of 48.13 days in 2004 and 22.77 days in 2006. In 2004 on-board exposures
were 15 seconds long sampled 2 times per minute. A 5-day subset light curve of V 588 Mon
from 2004 is shown in panel a of Figure 1, the respective V 589 Mon 5-day subset light curve
in panel d. The 2006 data had exposure times of 1.5 seconds, 16 consecutive images were
added on top of each other and the sampling time was 24 seconds (Zwintz et al. 2009).
5-day subsets of the light curves for V 588 Mon and V 589 Mon from the 2006 data are given
in panels b and e of Figure 1, respectively.
Data reduction of the MOST Direct Imaging photometry was conducted using the
method developed by Rowe et al.(2006) which combines classical aperture photometry
and point-spread function fitting to the Direct Imaging subrasters.
2.2. CoRoT observations
The CoRoT satellite (Baglin 2006) was launched on December 27, 2006, from Baikonur
aboard a Soyuz rocket into a polar, inertial circular orbit at an altitude of 896 km. With
its 27-cm telescope, CoRoT can observe stars within a field of view of about 1.3 × 2.6deg2
located inside two cones of 10-degree radius, one at a right ascension of 06:50 (galactic
anticenter direction) and the other at 18:50 (galactic center direction).
The CoRoT space telescope originally had two CCDs devoted to asteroseismology for
stars with 5.7 < mV < 9.5 mag and two CCDs dedicated to the search for exoplanets
where ∼6000 stars in the magnitude range from 10 to 16 mag in R per CCD are monitored.
Observations of the young open cluster NGC 2264 were conducted as dedicated Short Run,
SRa01, uninterrupted for 23.4 days in March 2008 within the framework of the Additional
Programme (AP; Weiss 2006). At the middle of SRa01 the ascending mode of the orbital
plane was 15.67◦. The complete cluster was placed in one of the two Exofield-CCDs and
data were taken for all stars in the accessible magnitude range. The 100 observed brightest
stars in the field of the cluster were primary targets to search for stellar pulsations in PMS
stars. A detailed description will be given in Zwintz et al. (2010, in preparation).
With V =9.7 mag and V =10.3 mag, V 588 Mon and V 589 Mon are nominally too bright
to be observed in the CoRoT Exofield. Obtaining data for these two stars was only possible
using the method of the so-called CoRoT imagettes.
Per observing run up to 20 imagettes, 15 × 10 pixel large CCD subwindows, can be
defined in each of the two CoRoT Exo-field CCDs. SRa01 was the first CoRoT observing run,
for which the imagette data were requested for scientific use and allowed to observe stars that
normally would be too bright for the Exo-field. Each of the imagettes is submitted to a special
– 6 –
data reduction pipeline developed by the Laboratoire d’Astronomie de Marseille (LAM) and
the Laboratoire d’´Etudes Spatiales et d’Instrumentation en Astrophysique (LESIA). The
reduction includes the flagging of data obtained during passes of the satellite through the
South Atlantic Anomaly (SAA), the calculation of a photometric mask, the detection of
cosmics, contaminants, outliers due to the satellite jitter and hot pixels and filtering of the
orbital signal. A detailed description will be given in Auvergne et al. (2010, in preparation).
In preparation for the NGC 2264 observations, a prioritized target catalog consisting
only of the stars brighter than the Exo-CCD magnitude limit was generated. From the 20
possible windows on the Exo-field CCD1, 14 were used to observe some of the previously
selected objects including the two known PMS pulsators V 588 Mon and V 589 Mon. Figure
1 shows 5-day subsets of the respective light curves (panels c and f). Note that the different
filter bandwidths of the CoRoT (from 370 to 1000 nm) compared to the MOST (from 350
to 750 nm) data are caused by the different passbands used in the two satellites.
2.3. Frequency Analysis
Frequency analyses were conducted using Period04 (Lenz & Breger 2005) which com-
bines Fourier and least-squares algorithms. Frequencies are prewhitened subsequently and
are considered to be significant if their amplitudes exceed 4 times the local noise level in the
amplitude spectrum (Breger et al. 1993; Kuschnig et al. 1997).
For the MOST data sets, the formally significant frequencies were checked against the
instrumental frequencies related to the orbit of the satellite, its harmonics and 1 d−1sidelobes
within the frequency resolution (computed according to Kallinger et al.
CoRoT data the influence of the satellite’s orbital and related frequencies is negligible.
2008b). In the
3. Pulsation and granulation of V 588 Mon and V 589 Mon
3.1. Modeling the stellar background in the CoRoT data
Assuming white, i.e.
CoRoT time series for V 588 Mon and V 589 Mon showed 106 and 197 formally significant
frequencies, respectively, after the initial frequency analysis with the methods described
above. Although the number of frequencies are lower than the many hundreds of frequencies
reported for classical Scuti stars observed by CoRoT (e.g., Poretti et al. 2009, observed
>1000 frequencies in HD 50844), they are still too many to be accounted for as simply
frequency independent, background noise, the 23.4 days long
– 7 –
individually excited low l-valued p-modes. Asteroseismic models predict some tens of p-
modes with degrees l < 4, which are potentially excited in the frequency range of δ Scuti-
type oscillations. A substantially larger number of modes would have to include modes of
degree l > 4 and/or rotationally split modes and/or the possibility that the detected modes
are part of the intrinsic background noise due to granulation.
If all l-valued p-modes are driven to similar amplitudes then the geometric cancelation
effect reduces the observable amplitude by more than an order of magnitude for l > 3 p-modes
(see, for example, the spatial response functions in Christensen-Dalsgaard & Gough 1982).
But Daszynska-Daszkiewicz et al. (2006) note, though, that some stars exhibit more than
two orders of magnitude variations in pulsation amplitudes. In addition, when observing in
luminosity the geometric cancelation effect is offset by an l2factor. Regardless, the variation
in amplitude of the modes in the short run data (23 d) from CoRoT and in the MOST data
is a little more than one order of magnitude. We are not yet reaching the lower amplitude
modes, for which these effects become important. Furthermore, we note that unlike the
example of HD 50844 observed by Poretti et al. (2009) we do have data for V 588 Mon and
V 589 Mon from different instruments obtained at different epochs. If all the frequencies were
due to pulsation modes then they (or at least the majority) should appear in all data sets.
However, apart from the frequencies listed in Tables 2 and 3 we find 5 to 10 frequencies that
coincide (within the frequency uncertainties) in the CoRoT and MOST data sets for both
stars. The number depends on the considered frequency range, the chosen significance limits,
and how the coincidence and frequency error is defined in detail. But even for two totally
unrelated data sets it would not be surprising to find a few coincident frequencies. In case of
V 588 Mon, for example, most of the 106 formally significant frequencies in the CoRoT data
are distributed between about 5 and 15 d−1in about 700 independent frequency bins. The
frequency bin-size is one over the data set length times the square root of the significance
(Kallinger et al. 2008b). For our analysis we use an average significance of 10. Even if the
formally significant frequencies in the CoRoT data set were just random numbers one could
expect to find by chance matches for at least a few of them with the 179 formally significant
frequencies determined from the MOST data. Hence, at this time, we argue that many of the
low amplitude frequencies in the CoRoT data are due to granulation and a (rare) coincidence
with low amplitude MOST frequencies is not indicative for pulsation.
Kallinger & Matthews (2010) concluded that many of the low-amplitude frequencies in
δ Scuti stars are consistent with a strongly frequency-dependent intrinsic background signal
due to granulation or some effect similar to granulation. This is well known for cool stars with
convective envelopes. The turbulent motions in their outer convective envelopes generate
quasi-stochastic power, with amplitudes strongly decreasing for shorter time scales. Although
the signal is quasi-stochastic in the time domain, its Fourier transform is Lorentzian-like,
– 8 –
where different physical processes on (or near) the stellar surface produce the same type of
signal but on different amplitude and time scales. For the Sun and other Sun-like stars,
the different signal components are usually assigned to stellar activity, activity of the pho-
tospheric/chromospheric magnetic network, and granulation, with time scales ranging from
months for active regions to minutes for granulation (see e.g., Michel et al. 2008, 2009).
The presence of a granulation background signal depends of course on the presence of
a surface convection zone, which is usually attributed to stars cooler than the red border
of the classical instability strip. On the other hand, it is known that stellar evolutionary
models for stars in the instability strip predict a thin convective surface layer and they should
therefore show a similar signature of granulation as cool stars in their power spectra. We
believe that this was not recognized before in classical δ Scuti stars, but also in PMS δ Scuti
stars because the amplitudes are small and a clear detection requires long and uninterrupted
observations to achieve a high-frequency instrumental noise well below 100ppm, which have
become available only recently. Although the MOST observations of V 588 and V 589 Mon
are of unprecedented length and completeness the granulation signal with a low-frequency
amplitude of roughly 100ppm (see Figure 2 and 3) is hidden in the instrumental noise (see
Table 1). Only the CoRoT observations are sufficient to reveal the strongly frequency-
dependent background signal.
3.1.1. V 588 Mon
The CoRoT light curve of V 588 Mon consists of 56978 data points sampled with 32
seconds and has a noise level of 47 ppm in the original amplitude spectrum from 0 to 100
d−1(see Table 1). The first frequency analysis resulted in 106 formally significant frequencies
with signal-to-noise values larger than 4. Among those are also the previously published 8
pulsation frequencies (Guenther et al. 2009).
A visual inspection of the power spectrum of V 588 Mon reveals that the average power
per frequency bin (e.g. 10µHz) is roughly constant at low frequencies and drops by more than
one magnitude beyond about 500µHz, which is a clear indication for a frequency-dependent
noise. To model the background signal, the pulsation power has to be taken into account as
well. This is relatively straight forward for cool stars, where the envelope of the pulsation
power excess is well approximated by a Gaussian. This is more complicated for stars in the
instability strip where the excess envelope can be quite different from a Gaussian (or any
other simple function). We follow the approach of Kallinger & Matthews (2010) and first
prewhiten the 10 frequencies with the most significant peaks (i.e., the highest amplitudes)
and assume the residual pulsation power excess to be at least Gaussian like. Although NGC
– 9 –
2264 was observed continuously for the 23.4 days, several data points were removed during
the reduction process mostly due to high energy particle hits during the satellites passes
through the South Atlantic Anomaly (SAA) leading to regular gaps in the time series. The
resulting alias peaks would significantly distort a fit to the power spectrum. We therefore
filled the gaps – but only for the time series used to investigate the background characteristics
which requires uninterrupted data – with linearly interpolated values to receive the needed
clean window function. The power spectrum of the gap-filled data is shown in Figure 2. The
residual power spectrum is modeled with a superposition of white noise, two Lorentzian-
like functions, and a Gaussian. The resulting global fit (solid line in Figure 2) reproduces
the overall shape of the residual power spectrum and demonstrates the strong frequency
dependence of the background signal. The residual power spectrum is then corrected for
the background signal by using the global fit without the pulsation component. Finally, we
use the height-to-background ratio (HBR; middle panel of Figure 2) to rate the significance
of the individual frequencies received from the initial frequency analysis and consider only
frequencies that exceed an HBR value of 9 to originate from pulsation. For V 588 Mon four
frequencies match this criterion (see Table 2 and Figure 2). Together with the 10 prewhitened
frequencies of highest amplitudes, a total of 14 pulsation frequencies remain after granulation
modeling. There are a number of peaks in the middle panel of Figure 2 between about 70
and 200µHz that have a higher HBR value than the peaks in the surrounding frequency
ranges but which do not exceed our formal limit of HBR ≥ 9. This indicates that there
are additional pulsation frequencies but our simplistic model of the pulsation power excess
underestimates their significance.
3.1.2.V 589 Mon
The CoRoT light curve of V 589 Mon has 57092 data points also obtained with an
exposure time of 32 seconds and the noise level in the amplitude spectrum of the original
data set is 61 ppm from 0 to 100 d−1(Table 1). After the initial frequency analysis, 197
frequencies were identified to be formally significant. Similar as for V 588 Mon, all previously
published 12 pulsation frequencies (Guenther et al. 2009) were also detected in the CoRoT
The same method as described for V 588 Mon was used for V 589 Mon. In this case the
15 frequencies with the highest amplitudes were prewhitened before the gaps in the residuals
were filled by linear interpolation (Table 3). The top panel of Figure 3 shows the power
spectrum of the gap filled data (grey), the global model fit (solid line), the model without the
pulsational component (dotted line), and the two Lorentzian-like functions (dashed lines). 22
– 10 –
frequencies show an HBR value larger than 9 in power (middle panel in Figure 3). Together
with the 15 frequencies of highest amplitudes that were prewhitened, a total of 37 frequencies
are attributed to be caused by pulsation (see Figure 5 and Table 3).
3.2. Comparison of the MOST 2004 and 2006 data to the CoRoT data
The MOST 2004 light curves of V 588 Mon and V 589 Mon have 59344 and 60386 data
points, respectively. The noise levels in the original amplitude spectra computed from 0 to
100 d−1(i.e., 0 to 1157 µHz) are 125 and 133 ppm (see Table 1). In 2006 V 588 Mon and
V 589 Mon were observed only less than half the time as for 2004, hence the light curves
consist only of 23137 and 23113 data points, respectively, and the resulting noise levels from
0 to 100 d−1in the original amplitude spectra are 405 and 429 ppm (Table 1).
For each star a separate frequency analysis was conducted and the frequencies common
to both data sets were then used for the further analysis and for comparison to the CoRoT
data. The modeling of the background noise was not possible due to the lower quality of the
MOST data compared to the CoRoT observations.
For V 588 Mon 20 significant frequencies are common to the MOST data sets of 2004
and 2006. A cross identification with the 14 CoRoT frequencies that remain after granulation
modeling showed that 12 of them are also present in the MOST data (Table 2). A further
cross-check of the formally significant CoRoT frequencies before the background noise model-
ing to the 20 frequencies appearing in the MOST 2004 and 2006 data resulted in 7 additional
common frequencies (F15 to F21 in Table 2). Although these peaks have HBR values lower
than 9, hence would be attributed to be caused by background noise, they have to be con-
sidered as pulsational. Such stable frequencies that are present in three independent data
sets obtained in three different years are unlikely to be caused by granulation. Additionally
the shape of the pulsational power excess is very likely more complicated than a Gaussian
that is used in the power spectrum model (Kallinger & Matthews 2010) and in the future
a more realistic approach will be needed. Therefore, for V 588 Mon 19 pulsation frequencies
are in common between the MOST 2004, MOST 2006 and CoRoT data sets (Table 2) and
are marked as black lines in the bottom panel of Figure 4. A comparison between the 106
formally significant frequencies and the identified 21 pulsation frequencies for V 588 Mon
is given in the bottom panel of Figure 2 and illustrates the influence of granulation to the
For V 589 Mon 19 significant frequencies are common to the MOST data sets of both
years. 17 of those were also identified in the CoRoT data after granulation modeling and
– 11 –
are marked as black lines in the bottom panel of Figure 5. The two additional frequencies
appearing in the MOST data were identified likely to be aliases or caused by instrumental
effects. The comparison between the formally significant 197 frequencies and the identified
37 pulsational peaks is shown in the bottom panel of Figure 3.
Using both MOST data sets and the COROT data, in total 21 pulsation frequencies are
identified for V 588 Mon (black lines in the top panel of Figure 4) and 37 for V 589 Mon
(black lines in the top panel of Figure 5) where 2 and 20 of them, respectively, are unique
discoveries obtained with CoRoT. All MOST frequencies have a counterpart in the CoRoT
4. Asteroseismic analysis of V 588 Mon and V 589 Mon
For any seismic modeling of a star to be successful it is critical that the identified
frequencies are, in fact, p-modes (or g-modes) intrinsic to the star. Errant or spurious
frequencies are difficult to isolate by modeling alone. Because viable models are based on
a large parameter space many possible solutions for various combinations and selections of
the observed frequencies can be produced. In specific terms, when, as is often the case, it
is impossible to find a model fit to all the observed frequencies, there usually exist multiple
possibilities to fit some subset of the observed frequencies and no decisive way to prefer one
solution over the others.
CoRoT observations of both V 588 Mon and V 589 Mon have yielded a large number of
frequencies, many of which were also seen by MOST (Guenther et al. 2009). The two inde-
pendent observations go a long way toward confirming the intrinsic, i.e., non-instrumental,
nature of the frequencies. Furthermore, since the MOST and CoRoT observations are sep-
arated in time by several years, they imply the modes are stable over a period of at least 4
Both stars show significant v · sini velocities, high enough, to produce resolvable split-
tings in the frequency domain. Unfortunately, the mode identification is complicated by
the fact that the predicted splitting frequencies are comparable to the characteristic (i.e.,
asymptotic large) spacing that separates p-mode frequencies, thereby, making it difficult
to distinguish the split sidelobes from the parent frequencies. Furthermore, if the stars
are rapidly rotating then the splittings are not linearly spaced about the reference fre-
quency (Espinosa et al. 2004). Recent studies (Reese et al. 2009b; Deupree & Beslin 2010;
Ouazzani 2008) show that non-perturbative multi-dimensional approaches are necessary to
predict the frequency spacings. Although the direct modeling of these frequencies is compli-
– 12 –
cated, Reese et al. (2009a) show how an empirical formula can be used to fit the frequencies
assuming the interior rotation profile is simple enough. Needless to say, as long as mode iden-
tification depends on the interior rotation curve, there will always be some ambiguity in the
Finally, we note that the observed frequencies are low, corresponding to model modes
near the fundamental frequency of the star. Although the frequencies of these modes are
more sensitive to the interior structure of the star than higher frequency modes, hence,
better suited to constraining the evolutionary state of the model, they are also subject to a
mode bumping-like effect. As a consequence, the regular spacing between adjacent p-modes
is perturbed, hindering mode identification.
In the next section we provide a general overview of the modeling methodology and
theoretical considerations used to interpret the oscillation spectra. In sections 4.2. and 4.3.
we discuss each star separately beginning with V 589 Mon.
4.1.1. Stellar mode and model calculation
All of our modeling and seismic analyses are based on a dense set of models that cover
the HR-diagram. The PMS models start above the birthline on the Hayashi track and extend
to the ZAMS (zero-age main sequence). Model masses range from 0.81 M⊙ to 4.99 M⊙ in
increments of 0.01 M⊙. The models themselves were constructed using the Yale Stellar
Evolution Code (YREC: Demarque et al. 2008) incorporating the latest opacities, nuclear
physics, and equation of state. Each model is resolved into ∼2000 shells with two-thirds
of the shells covering the outer envelope and Eddington gray atmosphere. We estimate the
model frequency uncertainty to be 0.1%. The grid density is such that ∼2000 models lie
within 2-sigma of each star’s position in the HR-diagram, of the ∼400000 models computed
in total (Guenther et al. 2009).
The adiabatic p-mode frequencies for l = 0, 1, 2, and 3 of the models were computed
using Guenther’s stellar pulsation code (Guenther 2004). We have assumed that geometric
cancelation will occur for higher order p-modes making them more difficult to see above the
background noise level (see discussion in section 3.1).
– 13 –
4.1.2. Mode bumping in PMS stars
When the oscillation frequencies of our PMS models are plotted in an echelle diagram
(i.e., frequency modulo the large spacing plotted opposite the frequency of the modes) they
reveal the vertical alignment characteristic of common l-valued p-modes. But maybe surpris-
ing at first glance, the lowest radial order, n, modes do not stay aligned with the modes at
higher frequencies but zigzag. This behavior is common to evolved post-main sequence stars
and is attributed to the increased density gradients in the region surrounding the isothermal
helium core near the base of the hydrogen burning shell. The effect is called mode bumping
and is well documented in texts on stellar pulsation (e.g., Cox 1980; Unno et al. 1989).
PMS stars do not show the same large gradients in density because nuclear burning has not
Regardless, for some PMS stars there exists a slight peak in the Brunt-V¨ ais¨ al¨ a frequency
in the deep interior (see Figure 6 for V 589 Mon). This bump is enough to perturb the p-
mode eigenfunction in the interior and affect its frequency. Note, only nonradial p-modes
show mode bumping since they need to couple with g-modes (for which l = 0 modes are
undefined). The perturbation in frequency can be seen in a plot of p-mode frequency versus
(evolutionary) time as shown in Figure 7 for l = 1 p-modes for models along a 2.65M⊙track
(corresponding to V 589 Mon, see section 4.2.). The large spacing varies as the star evolves,
changing inversely with the radius of the star. The n = 0 large spacing deviates slightly
from the large spacing of the other modes at various times during the evolution of the star.
Unlike the mode bumping that is seen in post-main sequence stars, the PMS bumping
does not occur abruptly in time: it is only slowly varying as the model evolves toward the
ZAMS. Consequently, it is not necessary to increase the resolution of the grid to follow
this behavior as is the case of post-main sequence bumping. Although it complicates the
identification of the modes at low frequencies, it also provides an additional feature of the
oscillation spectrum that can be used to confirm the interior structure and evolutionary state
of the PMS model.
4.1.3. Searching for the best fitting model spectra
To find the best-fit model oscillation spectrum to the observed spectrum we searched
our grid of models (Guenther & Brown 2004) looking for local minima in χ2defined by:
– 14 –
where νobs,iis the observed frequency for the ithmode, νmod,i is the corresponding model
frequency, σobs,iis the observational uncertainty for the ithmode, and N is the total number
of modes that match the observed frequencies. We estimate the model uncertainty σmod,iby
fitting models to the solar oscillation spectrum (Guenther 2004). Here we set it to 0.1% the
frequency of the mode.
As we will describe in sections 4.2. and 4.3., we were unsuccessful in finding p-mode
frequency fits to all the observed modes. Owing to the not insignificant rotation rates of the
two stars, we considered the possibility that the oscillation spectrum of each star contains
rotationally split modes. We included only the lowest order approximations in these attempts
since full nonlinear rotational splitting computations are too laborious to be applied to a
grid searching methodology.
As a first attempt we considered a range of fixed width splittings. These are not model
constructed splittings that depend on the eigenfunction of the mode and the interior structure
but are simply a constant frequency added to and subtracted from the model frequency in
order to simulate, approximately, the expected set of frequency splittings. In other words,
when searching our grid of models we looked for frequency matches between model and
observations at ν ± m∆ν, where ν is a model computed p-mode, m is the order of the
splitting, and ∆ν is the splitting frequency itself.
We also computed rotational splittings for a selected set of models, using the formulation
of Gough (1981), for a solid body rotation curve and for a rotation curve that rises near the
surface. Here we wanted to see if we could perceive any difference between the two different
rotation curves, e.g., one curve produced slightly lower χ2spectrum fits than the other. Note
that Gough’s formula is applicable to slow rotation rates only.
4.2. V 589 Mon
V 589 Mon is located just below the birthline in the HR-diagram along our 2.65 M⊙
PMS evolutionary track as shown in Figure 8. Note that its location in the HR-diagram and
its association with the cluster NGC 2264 precludes it from being a post-main sequence star.
The birthline (Stahler 1983; Palla & Stahler 1999) corresponding to a mass in-fall rate of
– 15 –
∼ 10−5M⊙/year is shown. Following Guenther et al. (2009) we take the luminosity of V
589 Mon to be log L/L⊙ = 1.58 ± 0.1, the effective temperature to be 6800 ± 350K, and
we note that the observed v·sini is 60 ± 10 km s−1(see Kallinger et al. 2008a, their Table
2, values adopted from 2MASS photometry).
4.2.2. Mode Analysis
Figure 9 shows the model computed characteristic spacing (approximately equal to the
average large spacing in the asymptotic limit of large radial order n, Tassoul 1980) as
function of position in the HR-diagram in the vicinity of V 589 Mon (and V 588 Mon). The
average small spacing, over the observed frequency range, computed from our model grid is
1.7 ± 0.3µHz.
We plot the observed frequencies in an echelle diagram to reveal the vertical alignment
characteristic of common l-valued p-modes. Models show that the regular spacing between
p-modes extends all the way to n = 1 for PMS stars. Based on the model results shown in
Figure 9 we see that the large spacing for V 589 Mon should lie between 20 µHz and 26 µHz.
The CoRoT frequencies have amplitudes down to 0.27 mmag where the MOST frequencies
have amplitudes at or above 0.46 mmag. Note that this set of MOST frequencies include low
amplitude frequencies that were excluded in the analysis of Guenther et al. (2009) where
only the 8 frequencies common to MOST and ground-based observations were presented and
analyzed. We proceed with our model analysis using the CoRoT frequencies.
In an echelle diagram, there is some suggestion for vertically aligned sequences of modes
in the observations, but the effect is confused by the presence of many additional apparently
randomly scattered frequencies (see Figure 10). What strikes us most are the many more
frequencies observed by CoRoT between 50 µHz and 150 µHz than can be accounted for
from just l = 0, 1, 2, and 3 p-modes. As noted in section 4.1 we believe geometric factors
and the limited S/N of our data rule out the possibility of identifying higher l-values in our
CoRoT (and MOST) data.
We searched through all ∼400,000 PMS models in our grid comparing their oscillation
spectra to the observed spectrum and identified those models that had χ2≤ 1. We could
find no model whose oscillation spectrum fit (with χ2≤ 1) more than 9 of the 37 frequencies
at a time with l = 0, 1, 2, and 3 modes and which falls within the uncertainty box of V 589
Mon’s position in the HR-diagram. The observed frequencies cannot all be accounted for by
l = 0, 1, 2, and 3 p-modes alone.