Solar-like oscillations in low-luminosity red giants: first results from Kepler

0.43 MB·English

by  T. R. Bedding

Accepted by ApJ Letters
PreprinttypesetusingLATEXstyleemulateapjv.11/10/09
SOLAR-LIKE OSCILLATIONS IN LOW-LUMINOSITY RED GIANTS: FIRST RESULTS FROM KEPLER
T. R. Bedding,1 D. Huber,1 D. Stello,1 Y. P. Elsworth,2 S. Hekker,2 T. Kallinger,3,4 S. Mathur,5 B. Mosser,6
H. L. Preston,7,8 J. Ballot,9 C. Barban,6 A. M. Broomhall,2 D. L. Buzasi,7 W. J. Chaplin,2 R. A. Garc´ıa,10
M. Gruberbauer,11 S. J. Hale,2 J. De Ridder,12 S. Frandsen,13 W. J. Borucki,14 T. Brown,15
J. Christensen-Dalsgaard,13 R. L. Gilliland,16 J. M. Jenkins,17 H. Kjeldsen,13 D. Koch,14 K. Belkacem,18
L. Bildsten,19 H. Bruntt,6,13 T. L. Campante,13,20 S. Deheuvels,6 A. Derekas,1,23 M.-A. Dupret,18 M.-J. Goupil,6
A. Hatzes,21 G. Houdek,4 M. J. Ireland,1 C. Jiang,22 C. Karoff,2 L. L. Kiss,1,23 Y. Lebreton,6 A. Miglio,18
J. Montalba´n,18 A. Noels,18 I. W. Roxburgh,24 V. Sangaralingam,2 I. R. Stevens,2 M. D. Suran,25
0 N. J. Tarrant,2 and A. Weiss26
1
Accepted by ApJ Letters
0
2
ABSTRACT

n Wehavemeasuredsolar-likeoscillationsinredgiantsusingtime-seriesphotometryfromthefirst34
a daysofscienceoperationsoftheKepler Mission. Thelightcurves,obtainedwith30-minutesampling,
J
revealclearoscillationsinalargesampleofGandKgiants,extendinginluminosityfromtheredclump

2 downtothebottomofthegiantbranch. Weconfirmastrongcorrelationbetweenthelargeseparation
2 of the oscillations (∆ν) and the frequency of maximum power (ν ). We focus on a sample of 50
max

low-luminosity stars (νmax >100µHz, L.30L⊙) having high signal-to-noise ratios and showing the
]
R unambiguous signature of solar-like oscillations. These are H-shell-burning stars, whose oscillations
should be valuable for testing models of stellar evolutionand for constraining the star-formationrate
S
inthelocaldisk. Weuseanewtechniquetocomparestarsonasingle´echellediagrambyscalingtheir
.
h frequencies and find well-defined ridges corresponding to radial and non-radial oscillations, including
p clear evidence for modes with angular degree l = 3. Measuring the small separation between l = 0
- andl =2 allowsus toplotthe so-calledC-Ddiagramofδν versus∆ν. Thesmallseparationδν of
o 02 01
l=1fromthe midpointofadjacentl =0modesisnegative,contrarytothe Sunandsolar-typestars.
r
t The ridge for l =1 is notably broadened, which we attribute to mixed modes, confirming theoretical
s predictions for low-luminosity giants. Overall, the results demonstrate the tremendous potential of
a
Kepler data for asteroseismologyof red giants.
[
Subject headings: stars: oscillations
2
v
9
2 1Sydney Institute for Astronomy (SIfA), School of
02 Pbehdydsiincsg,@phUynsiivcse.russityyd.edouf.auSydney, NSW 2006, Australia; 17SETI Institute/NASA Ames Research Center, MS 244-30,
1. Bir2mSicnhgohoalmofBP1h5y2siTcsTa,nUdKAstronomy, University of Birmingham, Mo1ff8eItntstFitiueltd,dC’AAst9r4o0p3h5y,siUquSeAet de G´eophysique de l’Universit´e
0 Co3luDmebpiaar,tmVaennctooufvePrh,yCsaicnsadanad Astronomy, University of British de1L9iK`egaev,liAlIln´esetidtuut6eAfooruˆtT1h7eo-reBti4c0a0l0PLhiy`esgiec,sBaenldgiuDmepartment of
10 Au4sItnrisatitute of Astronomy, University of Vienna, 1180 Vienna, Ph2y0sCices,ntUronivdeersiAtystoroffC´ısaicliafodrnaiaU,nSiavnetrasiBdaadrbeadrao,CPAort9o3,10R6u,aUSdAas
v: 56050I3n4d,iaInndiIanstitute of Astrophysics, Koramangala, Bangalore Es2t1reTlahsu,e4r1in50g-e7r62LPanordteos,stPeorrntwuagratle Tautenburg, Sternwarte 5,
rXi DFrea6nnLicsE,eSDIAid,eCroNt,RSO,bUsenrivvaetrosiirte´e PdieerPreareits,M9a2r1i9e5CuMreieu,dUonnivceerdseitx´e, D-2202377DK7eo8pn,akTrotalmyuteOennbtbsouefrrvgAa,stGtorreoyrnmoofmantyhy,eBHeiujinnggarNiaonrmAaclaUdenmivyerosfitSy,ciCenhciensa,
a 94670E2u-3re0k1a7,SUciSeAntific, 2452DelmerStreet Suite100, Oakland,CA H-21452Q5uBeeundaMpaersyt,UP.nOiv.eBrsoixty6o7f,HLounndgoanry, Mile End Road, London
Af8riDcae,pBarotxm3e9n2tUoNf IMSAat0h0e0m3a,tSicoaulthScAiefnricceas, University of South E1254NASst,rUonKomical Institute of the Romanian Academy, Str.
de9TLoaubloouraseto,iCreNRd’SA1st4roapvhEys.iBqueelind3e14T0o0uTloouusleo-uTsaer,bFersanUcneiversit´e Cu2t6itMuladxe-PAlarngcinkt-,In5s,tiRtuOt40fu¨5r57,ABsutcrhoaprheyssti,kR, omKaarnli-aSchwarzschild-
10Laboratoire AIM, CEA/DSM-CNRS, Universit´e Paris 7 Str.1,85748Garching,Germany
Diderot, IRFU/SAp, Centre de Saclay, 91191, Gif-sur-Yvette,
France
11DepartmentofAstronomyandPhysics,SaintMary’sUniver-
sity,Halifax,NSB3H3C3,Canada
12InstituutvoorSterrenkunde, K.U.Leuven,Belgium
13Danish AsteroSeismology Centre (DASC), Department of
Physics and Astronomy, Aarhus University, DK-8000 Aarhus C,
Denmark
14NASAAmesResearchCenter,MS244-30,MoffettField,CA
94035,USA
15Las Cumbres Observatory Global Telescope, Goleta, CA
93117,USA
16Space Telescope Science Institute, 3700 San Martin Drive,
Baltimore,Maryland21218, USA
2 T. R. Bedding et al.
1. INTRODUCTION remaining sample, we used the light curves to measure
the global oscillation parameters, most notably the fre-
Studying solar-like oscillations is a powerful way to
quency of maximum power (ν ) and the mean large
probe the interiors of stars (e.g., Brown & Gilliland max
frequencyseparation(∆ν). Wewereabletofindapower
1994;Christensen-Dalsgaard2004). Oscillationsinmain-
excessin∼1000stars(seealsoFigure5inGilliland et al.
sequence stars and subgiants have been measured us-
2010) and measure the large separation for ∼700 stars.
ing ground-based spectroscopy (for a recent review see
In this Letter we focus on the low-luminosity red giants
Aerts et al. 2008) and more recently by space missions
(corresponding to ν > 100µHz) for which, as dis-
such as CoRoT (e.g., Michel et al. 2008). Red giants max
cussed in the introduction, CoRoT results have not yet
oscillate at lower frequencies and so demand long and
beenreported. AsdiscussedbyMiglio et al.(2009),such
preferably uninterrupted time series to resolve their os-
cillations. stars generally have luminosities below about 30L⊙.
Figure 1 shows the measured values of ∆ν and ν
The first indications of solar-like oscillations in G max
for these stars. The symbols show results obtained
and K giants were based on ground-based observa-
using the pipeline described by Huber et al. (2009),
tions in radial velocity (see Merline 1999 and ref-
who also described the method used to fit and sub-
erences therein; Frandsen et al. 2002; De Ridder et al.
tract the background. Similar results were found using
2006) and photometry (Stello et al. 2007), and on
pipelines developed by four other groups (Hekker et al.
space-based photometry from the Hubble Space Tele-
2010b; Mosser & Appourchaux 2009; Kallinger et al.
scope (HST; Edmonds & Gilliland 1996; Gilliland 2008;
2010; Mathur et al. 2010), and the dotted lines in Fig-
Stello & Gilliland 2009), WIRE (Buzasi et al. 2000;
ure 1 show the region inside which ∼80% of those mea-
Retter et al. 2003; Stello et al. 2008), Microvariability
surementslay. Adetailedcomparisonofthe resultsfrom
and Oscillations of Stars (MOST; Barban et al. 2007;
the different pipelines is ongoing.
Kallinger et al. 2008a,b), and Solar Mass Ejection Im-
ThetightcorrelationinFigure1between∆ν andν
ager (SMEI; Tarrant et al. 2007). A major break- max
was discussed by Hekker et al. (2009) and Stello et al.
through came from observations over about 150 days
(2009),andisseenheretoextendtoredgiantswithmuch
with the CoRoT space telescope, which produced clear
higher ν . This and other correlations between global
detections in numerous stars of both radial and non- max
oscillation parameters, and their connection to funda-
radial oscillations in the frequency range 10–100µHz
mentalstellarparameters,willbediscussedinfuturepa-
(De Ridder et al. 2009;Hekker et al. 2009; Carrier et al.
pers.
2010). This increased the number of known pulsating G
and K giants to nearly 800, and enabled the first sys-
3. RESULTS
tematic study of oscillations in a large population of
red clump stars (Hekker et al. 2009; Miglio et al. 2009; 3.1. Frequency analysis
Kallinger et al. 2010). Note that the red clump com- We now consider a subset of 50 of the low-luminosity
prises core He-burning stars and is the metal-rich coun- red giants for more detailed analysis, chosen as having
terpart to the horizontal branch. the best signal-to-noise ratios. These stars are indicated
Detecting oscillations in lower-luminosity red giants, in Figure 1 with filled symbols. Figure 2 (left panel)
which are H-shell-burning stars at the base of the giant shows power spectra for six of them, spanning the full
branch,isverydesirablefortestingmodelsofstellarevo- range of ν being considered. Each power spectrum
max
lutionandalsoforconstrainingthestar-formationratein shows a regular series of peaks, which is the clear signa-
the local disk (Miglio et al. 2009). However, such detec- ture of solar-like oscillations.
tions are even more challengingthan for clump stars be- Solar-like oscillations are p modes with high order
causetheamplitudesaresubstantiallylower. Inaddition, and low degree, and the observed frequencies in main-
theoscillationfrequenciesarehigherandarecomparable sequence stars are reasonably well-described by the fol-
to the orbital frequency of a satellite in low-Earthorbit. lowing relation:
ThesefactorsmadeitdifficultforCoRoTtoachievesuch
detections. νn,l ≈∆ν(n+ 21l+ǫ)−l(l+1)D0. (1)
In this Letter, we present data from the aster-
Here, n (the radial order) and l (the angular degree)
oseismology program of the NASA Kepler Mission
are integers. The form of Equation 1 is motivated by
(Gilliland et al. 2010) that reveal clear oscillations in a
theoreticalcalculations: forrelativelyunevolvedstars,an
large sample of red giants, extending in luminosity from
asymptoticexpansion(Tassoul1980;Gough1986)shows
the red clump down to the bottom of the giant branch.
that∆ν is approximatelythe inverseofthe soundtravel
2. GLOBALOSCILLATIONPARAMETERS time across the star, while D is sensitive to the sound
0
The observations were obtained over the first 34 days speed gradient near the core and ǫ is sensitive to the
of science operations of the Kepler Mission (Q1 data). surface layers.
We analyzed light curves having 29.4-minute sampling Weconventionallydefinethreesmallfrequencysepara-
(long-cadence mode) for about 1500 stars listed as red tions: δν02 is the spacing between adjacent modes with
giants in the Kepler Input Catalog (KIC; Latham et al. l = 0 and l = 2, δν13 is the spacing between adjacent
2005). About 20% of the Q1 light curves showed large modes with l = 1 and l = 3, and δν01 is the amount by
variations (>1%) on long timescales, mostly due to M- which l=1 modes are offset from the midpoint between
giant pulsations, and are not analyzed here.27 For the the l=0 modes on either side. If Equation 1 holds then
itfollowsthatδν =6D ,δν =10D andδν =2D .
02 0 13 0 01 0
27 Oneofthesewassubsequently foundtobeanoscillatingred We shalluseEquation1 asa guide to the analysisofthe
giantinaneclipsingbinarysystem(Hekkeretal.2010a). observedfrequencies,althoughitsphysicalinterpretation
Oscillations in low-luminosity red giants with Kepler 3
may be open to question in the case of red giants. a boxcar of width 0.01∆ν) to give the result shown in
To determine oscillation frequencies for each of the Figure 3c.
50 stars in our subset, we needed to locate the highest The clarity of the ridges in Figure 3 allows us to
peaks in the power spectra. We did this using conven- make some statements about mode lifetimes. As men-
tional iterative sine-wave fitting, sometimes called pre- tioned in Section 3.1, damping causes each mode to
whitening or CLEAN. This involves finding the highest be spread into multiple peaks under a Lorentzian en-
peakinthepowerspectrum,subtractingthecorrespond- velope with a full-width at half maximum (FWHM) of
ingsinusoidalvariationfromthetime seriesandthenre- 1/(πτ), where τ is the mode lifetime. There has been
calculating the power spectrum in an iterative process. considerable discussion of the lifetimes of red-giant os-
We retained only those peaks that lay in the frequency cillations, particularly regarding whether the modes are
rangeν ±5∆ν andhadheightsgreaterthan4.5times sufficiently long-lived to allow their frequencies to be
max
the fitted background level (in amplitude). measured with sufficient accuracy to be useful for aster-
Damping of solar-like oscillations causes the observed oseismology (Houdek & Gough 2002; Stello et al. 2006;
power from each mode to be spread into multiple peaks Barban et al. 2007; Dupret et al. 2009). The CoRoT re-
under a Lorentzian envelope. If the length of the ob- sultshaveclearlydismissedthisworryforredclumpstars
servations is significantly greater than the typical mode (De Ridder et al. 2009; Carrier et al. 2010) and our Ke-
lifetime, one therefore expects several peaks to be ex- pler data do the same for the low-luminosity stars. This
tractedforeachmode. Infact,themodesareonlybarely is excellent news for asteroseismology.
resolved(seeSection3.3)andsoweexpectiterativesine- Figure 3 was constructed by aligning the radialmodes
wave fitting to give good results. on the vertical solid line. However, the resulting width
of the l = 0 ridge is not zero, which arises from at least
3.2. Semi-scaled E´chelle Diagram threefactors: (1)theresolutionlimitsetbytheduration
of the observations (34d), which leads to peaks in the
A powerful method to study the mode frequencies of
power spectrum having FWHM 0.3µHz; (2) variations
solar-like oscillations is to plot them modulo the large
in ∆ν with frequency in individual stars over the range
separation, in a so-called ´echelle diagram (Grec et al.
being considered(curvature in the´echellediagram);and
1983). We have displayed the frequencies of all 50 stars
(3)broadeningofpowerdueto finite mode lifetimes (see
in a single ´echelle diagram by using the scaling tech-
above). The observed narrowness of the l =0 ridge sets
nique describedby Bedding & Kjeldsen(2010), in anef-
upper limits on the second and third of these effects.
fort to carry out “ensemble asteroseismology”. The re-
Here, as discussed above, we are particularly interested
sult is shown in Figure 3a. To make this diagram, we
in the mode lifetimes.
first divided the frequencies of each star by ∆ν (that
The FWHM of the l = 0 peak in Figure 3c, found
is, scaling them to have a largeseparationof unity). We
by subtracting the background and fitting a Lorentzian,
usedthe´echellediagramtoidentifytheradialmodesand
is 0.033∆ν. This sets an upper limit on the intrinsic
then fine-tuned the scaling factor (∆ν) by up to a few
linewidths ofthese modes. However,so far ourmeasure-
percent to align them on a single line in the ´echelle dia-
ment is in terms of ∆ν, which varies over the sample.
gram,shownasasolidlineinFigure3a. Asdiscussedby
The median ∆ν is 11.5µHz, in which case the measured
Bedding & Kjeldsen(2010,theirMethod2),thisequates
width equates to a lower limit on the mode lifetimes of
to assigning all stars the same value of ǫ. The fact that
about 10days. To investigate further, we divided the
all the stars can be aligned indicates this is a valid ap-
sample into four bins according to ∆ν and formed the
proximation. This alignment is also clearly seen in the
collapsed´echelle diagram for each subset, as before. We
right-handpanelofFigure2, whichshowspowerspectra
foundthewidthsofthel=0ridgesinallfourcasestobe
plotted against scaled frequencies (i.e., divided by ∆ν). about the same in absolute terms (∼0.4µHz), which is
The ´echelle diagram in Figure 3a differs from those
only slightly greater than the FWHM set by the resolu-
shown by Bedding & Kjeldsen (2010) in one important
tionofthe data(seeabove). Weconcludethatthe mode
respect: only the horizontal axis has been scaled. In the
lifetimes in these red giants is at least 10days, possibly
vertical direction, we have plotted the original frequen-
much greater.
cies without scaling, which spreads out the points and
allows us to look for variations with ν . Such a plot
max 3.4. Small Separations and the C-D Diagram
might be called a semi-scaled´echelle diagram.
The l = 2 ridge is closely parallel to the l = 0 ridge,
3.3. Collapsed E´chelle Diagram and Mode Lifetimes implying that δν is a nearly constant fraction of ∆ν
02
for the stars in our sample, with δν ≈ 0.125∆ν (Fig-
We can collapse the ´echelle diagramin the verticaldi- 02
ure 3c). This frequency scaling indicates that, to a good
rection in order to define the ridges more clearly. Fig-
approximation,the stars are homologous.
ure 3b shows this using a simple histogram of the peaks
We were able to measure the mean small separation
in Figure 3a, and the ridges are clearly visible. Rather
δν for 38 stars in our sample. Figure 4a shows the re-
than counting the number of peaks above a threshold, 02
sults in a so-calledC-D diagram(Christensen-Dalsgaard
another approach is to sum the total power. To do this,
1988), which plots δν versus ∆ν. The dashed line in
werestrictedeachbackground-correctedpowerspectrum 02
tothesamefrequencyrangeasbefore(ν ±5∆ν),then Figure 4a shows a linear fit, which has parameters
max
dividedthefrequencyscalebythelargeseparation(using δν =(0.122±0.006)∆ν+(0.05±0.08)µHz. (2)
02
the samefine-tuned valueas above)andfoldedthe spec-
trum modulo unit spacing. These folded spectra were The spread of points about this relation presum-
summedforall50starsandthensmoothedslightly(with ably reflects a spread in stellar masses, and is better
4 T. R. Bedding et al.
seen by plotting the ratio of the two separations, as and by the less efficient trapping due to the smaller
shown in Figure 4b (see Roxburgh & Vorontsov 2003; density contrast between the core and the envelope.
Ot´ı Floranes et al. 2005; Mazumdar 2005). As a consequence, more non-radial modes could be ob-
The dotted line in Figure 3 marks the midpoint be- served than only those trapped in the envelope. This
tween l = 0 modes. Interestingly, the l = 1 ridge is is particularly expected to affect l = 1 modes because
centered slightly to the right of this line. This indicates the evanescent region just above the H-burning shell
that the average small separation δν in these red gi- is smaller for these modes (see also Dziembowski et al.
01
ants is negative, whereas it is positive in the Sun and 2001; Christensen-Dalsgaard 2004). Our observation
thehandfulofothermain-sequencestarsforwhichithas of a broadened l = 1 ridge with a small cluster of
beenmeasured: αCenA(Bedding et al.2004), αCenB modes per order supports the theoretical predictions by
(Kjeldsen et al. 2005), γ Pav (Mosser et al. 2008), and Dupret et al. (2009). Observations of frequency spectra
τ Cet (Teixeira et al. 2009). A negative value for δν in a sample of higher luminosity red giants would be a
01
also indicates that Equation 1 is not satisfied in detail desirable follow-up study.
for these red giants, a point already noted for the G8
giantHR 7349byCarrier et al. (2010), basedonCoRoT 3.6. Detection of l =3 Modes
observations.
In addition to ridges corresponding to l = 0, 1 and 2,
3.5. Mixed Modes with l=1 we see clear evidence in Figure 3 for modes with l = 3.
Thedetectionofthesemodeswithphotometryisdifficult
The l = 1 ridge in Figure 3 is notably broader than
because of the very low amplitudes that result from ge-
theothers. Wedonotattributethistoshortermodelife-
ometric cancellation. The only previous report of solar-
times, but rather to the presence of mixed modes whose
like oscillations with l = 3 from photometry (except for
frequencies are shifted by avoided crossings. Mixed
the Sun) is a probable detection using CoRoT in the G0
modesoccurinevolvedstarsandhavethecharacteristics
main-sequence star HD 49385 (Deheuvels et al. 2010).
of p modes in the envelope of the star and of g modes in The ability to detect l = 3 modes from Kepler obser-
the interior (e.g., Aizenman et al. 1977). A typical ex-
vations of red giants is a significant bonus.
ample is the star KIC 5356201 (see Figure 2 and filled In Figures 3a and b there are 12 peaks that fall along
blue symbols in Figure 3a). The l = 0 and 2 modes are
the ridge that we identify with l = 3, and these arise
quite close to their respective ridges, whereas there is
from10starsin the sample of50. These are presumably
much more scatter about l = 1. A more extreme exam-
peaksthat,duetothestochasticnatureoftheexcitation,
ple is the star KIC 4350501 (see Figure 2 and filled red
happen to rise above our detection threshold in these
symbols in Figure 3a), which shows a particularly high
observations. A more objective approach is to sum the
peak at 87µHz, well below νmax. The proximity of this powerfromallstars,asshowninFigure3c,andweagain
peak to the l =1 ridge indicates that it is likely to be a
see clear evidence for the l=3 ridge.
mixed mode. A similar situation is seen in the F5 sub-
Howdoes the position ofthe l=3 ridgecomparewith
giant Procyon,for which ground-basedvelocity observa-
expectations? As mentioned in Section 3.1, it is conven-
tions show a narrowpeak well below ν that lies close
max tional to measure l = 3 relative to l = 1, via the small
to the l =1 ridge in the ´echelle diagram (Bedding et al.
separationδν . However,giventhatthepositionofl =1
13
2010). Thelargepeakheightcanbeexplainedbythefact
fortheseredgiantsisanomalous,itseemssensible toin-
that mixed modes are expected to have longer lifetimes
stead measure l = 3 relative to l = 0. We therefore
(smaller linewidths) than pure p modes because they
suggest using a new small separation, δν , defined (by
03
have larger mode inertias (e.g., Christensen-Dalsgaard
analogytoδν )astheamountbywhichthel=3modes
01
2004).
areoffsetfromthe midpointbetweenthel =0modeson
Another good example is KIC 5006817, shown in Fig-
either side. If followsthatδν =δν +δν . FromFig-
03 01 13
ure 5, where we clearly see multiple l = 1 peaks in each ure3cweseethatδν ≈0.28∆ν. Iftheasymptoticrela-
03
order (see also KIC 9904059 = KOI 145 in Figure 1 of
tionheld(Equation1),wewouldexpectδν =12D . In
03 0
Gilliland et al. 2010). Each of these clusters of peaks
that case the ratio between δν and δν would be 2.0,
03 02
is reminiscent of a single mode that is heavily damped
whereas we observe a ratio of 2.2. These results should
(see Section 3.3). However, as mentioned above, mixed
provide valuable tests for theoretical models.
modes are expected to have longer lifetimes than pure p
modes and hence to produce narrower – not broader – 4. CONCLUSIONS
peaks. Indeed, this phenomenon of multiple l =1 peaks
These results, based on the analysis of only 34 days
is probably what led previous authors to report short
of data, show the tremendous potential of Kepler long-
modelifetimesinredgiants(seeSection3.3). Guidedby
cadence data for the study of solar-like oscillations in
the theoretical work of Dupret et al. (2009), we instead
red giants. As more data become available, the longer
interpret the observed properties of the l = 1 ridge in
time series will allow detailed studies of stars covering
terms of mixed modes.
the whole range of evolutionary states along the red gi-
Dupret et al. (2009) discussed theoretical amplitudes
ant branch and provide stringent observational tests for
of solar-like oscillations for a range of models on the
theories of stellar structure and evolution in this part of
red giant branch. Their models show mostly regular
the H-R diagram.
frequency patterns for evolved giants (ν < 80µHz),
max
but predict more complex spectra for low-luminosity gi-
ants. This is mainly explained by the less efficient ra- We gratefully acknowledge the entire Kepler team,
diative damping in the cores of these stars, leading to whose outstanding efforts have made these results pos-
a stronger interaction of p-mode and g-mode cavities, sible. Funding for this Discovery mission is provided
Oscillations in low-luminosity red giants with Kepler 5
Fig.1.—Large frequency separation versus frequency ofmaximum power for 78low-luminosityredgiants. Filledsymbolsindicate the
50 stars that were selected for more detailed analysis. The dotted lines enclose the region containing ∼80% of measurements by the five
pipelines(seetext).
by NASA’s Science Mission. Grants were received (GOA/2008/04).
from the European Research Council (ERC/FP7/2007–
2013 n◦227224, PROSPERITY), and K.U.Leuven
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Fig.2.— Left: Power spectra of six representative low-luminosity red giants. Right: The same power spectra plotted against scaled
frequency(seeSection3.2). Thedottedlinesareequallyspaced,havingunitseparationandbeingalignedwiththel=0modes. Starsare
labelledwithidentification numbersfromtheKeplerInput Catalog (KIC;Latham etal.2005).
Fig. 3.— (a) Semi-scaled´echelle diagram for the sample of 50 low-luminosity red giants (see Section 3.2). Symbols indicate extracted
frequencies, with symbol sizes proportional to amplitude. Filled blue and red symbols are frequencies of the stars KIC 5356201 and
KIC4350501,respectively(seeFigure2andSection3.5). Thevalueof∆ν foreachstarwasfine-tunedinordertoalignthel=0modeson
theleft-mostvertical dotted line. Theother dotted lineliesexactly 0.5away, markingthemidpointbetween l=0modes. (b)Histogram
of the points shown in panel a. (c) Folded and scaled power spectra, collapsed over all stars in the sample and smoothed slightly (see
Section3.2). Thearrowsshowthedefinitionsofthesmallseparationsδν01,δν02,δν03,andδν13,withthesignconventionthatleft-pointing
arrowscorrespondtopositiveseparations (seeSection3.1).
Oscillations in low-luminosity red giants with Kepler 7
Fig. 4.—(a) Theso-calledC-Ddiagram (Christensen-Dalsgaard1988)of δν02 versus ∆ν forthe 38stars inoursampleforwhichboth
quantitieswerereliablydetermined. Thedashedlineshowsalinearfit. (b)Theratioδν02/∆ν versus∆ν forthesamestars,tobettershow
thescatter aboutthetrend.
Fig. 5.—Powerspectrumand´echellediagramforthestarKIC5006817,illustratingmultiplel=1peaksperorder. Notethatthehighest
peakinthepowerspectrumextends beyondtheplotlimits(to8400ppm2).
This figure "fig02.jpg" is available in "jpg"(cid:10) format from:
http://arxiv.org/ps/1001.0229v2
This figure "fig03.jpg" is available in "jpg"(cid:10) format from:
http://arxiv.org/ps/1001.0229v2
This figure "fig04_final.jpg" is available in "jpg"(cid:10) format from:
http://arxiv.org/ps/1001.0229v2