Twinkle twinkle massive star, how I wonder what you are - the Kepler Space Telescope
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2nd March 2018
Twinkle twinkle massive star,
how I wonder what you are
Asteroseismology of massive stars with
the Kepler Space Telescope
Dominic Bowman
C. Aerts, T. Rogers, P. V. F. Edelmann, A. Tkachenko,
M. G. Pedersen, C. Johnston, B. Buysschaert
Overview
• An introduction to asteroseismology
• The delta Scuti (δ Sct) stars
• non-linear pulsations
• interior mixing and rotation (a)
• Internal Gravity Waves (IGWs)
• models and observations
• characterising the morphology
• Conclusions and Future Prospects
2nd March 2018
Overview
• A (brief) introduction to asteroseismology
• The delta Scuti (δ Sct) stars
• non-linear pulsations
• interior mixing and rotation (a)
• Internal Gravity Waves (IGWs)
• models and observations
• characterising the morphology
• Conclusions and Future Prospects
2nd March 2018
Asteroseismology
Pulsating stars are unique laboratories which allow
different aspects of physics to be investigated:
• stellar structure
• stellar evolution
•
• rotation
(a)
pulsation driving mechanisms
• chemical mixing
• magnetic fields
• angular momentum transport
Two main types of pulsation modes: pressure (p) and gravity (g).
The Kepler Space Telescope provided 4 yr of continuous observations for
almost 200,000 stars at an unprecedented level of precision.
2nd March 2018
Overview
• A (brief) introduction to asteroseismology
• The delta Scuti (δ Sct) stars
• non-linear pulsations
• interior mixing and rotation (a)
• Internal Gravity Waves (IGWs)
• models and observations
• characterising the morphology
• Conclusions and Future Prospects
2nd March 2018
The δ Sct stars
δ Sct stars lie in the classical instability strip: 6400 ≤ Teff ≤ 8900 K.
p-mode periods of order several hours to several minutes, driven by
the opacity mechanism.
K. Uytterhoeven et al.: The Kepler characterization of the
(Uytterhoeven et al. 2011)
Image credit: Péter Pápics
2nd March 2018
The δ Sct stars
δ Sct stars lie in the classical instability strip: 6400 ≤ Teff ≤ 8900 K.
p-mode periods of order several hours to several minutes, driven by
the opacity mechanism... but Kepler revealed many hybrid pulsators.
K. Uytterhoeven et al.: The Kepler characterization of the variability among A- and F-type stars. I.
(Uytterhoeven et al. 2011)
Image credit: Péter Pápics
2nd March 2018
The δ Sct stars
Approximately 1000 δ Sct stars were observed by Kepler continuously
for 4 years – a unique, high quality and homogeneous data set of stars
with p and g modes for probing stellar interiors.
(Bowman & Kurtz 2018)
Image credit: Péter Pápics
2nd March 2018
The δ Sct stars
Approximately 1000 δ Sct stars were observed by Kepler continuously
for 4 years – a unique, high quality and homogeneous data set of stars
with p and g modes for probing stellar interiors.
(Bowman & Kurtz 2018)
Image credit: Péter Pápics
2nd March 2018
The δ Sct stars
Higher radial order p modes have higher frequencies and are more
sensitive to the surface physics in a star. Higher radial order g modes
have lower frequencies are probe the near-core region.
(Bowman & Kurtz 2018)
Image credit: Péter Pápics
2nd March 2018Non-linear pulsations: amplitude modulation
X
e.g., KIC 7106205 m= Ai cos(2⇡⌫i t + i)
i
4-yr time
span
(Bowman & Kurtz 2014;
Bowman et al. 2015;
Bowman et al. 2016)
2nd March 2018Non-linear pulsations: amplitude modulation
X
e.g., KIC 7106205 m= Ai cos(2⇡⌫i t + i)
i
4-yr time
span
ν1
ν3 high
frequency
resolution (Bowman & Kurtz 2014;
Bowman et al. 2015;
Bowman et al. 2016)
2nd March 2018Non-linear pulsations: amplitude modulation
X
e.g., KIC 7106205 m= Ai cos(2⇡⌫i t + i)
i
4-yr time
span
ν1
ν3 high
frequency
resolution (Bowman & Kurtz 2014;
Bowman et al. 2015;
Bowman et al. 2016)
2nd March 2018Non-linear pulsations: amplitude modulation
AMod
NoMod
Approximately 60 per cent of ~1000
δ Sct stars observed by Kepler are
AMod stars, with significant
amplitude modulation in at least a
single pulsation mode.
(Bowman et al. 2016)
2nd March 2018Non-linear pulsations: mode coupling
Theoretical prediction of
resonant coupling
between pulsation modes
(Dziembowski 1982;
Buchler et al. 1997).
Q: Mode coupling or a
combination frequency?
⌫1 = ⌫2 ± ⌫3
1 = 2 ± 3
A1 = µ c A2 A3 µcMixing and rotation in intermediate-mass stars
Asymptotic g modes are almost equally spaced in period:
• gradient indicates the rotation rate in the near-core region
Figure 3. The period spacing patterns of the slowly rotating star KIC 9751996. Left:
• dips are caused by the chemical
zonal gradient caused
(black triangles) and by squares)
retrograde (black the receding
dipole modes are marked separat
(dash–dot lines), zonal (full lines), and retrograde (dashed lines) modes in the Fourier
convective core on the main sequence
before. The dotted lines indicate missing frequencies.
Ongoing task: analysing
period spacing patterns in
δ Sct stars to extend
rotation and mixing studies
to higher masses.
(Miglio et al. 2008;
Bouabid et al. 2013; prograde
Pápics et al. 2015, 2017;
Van Reeth et al. 2015, 2016)
Figure 4. The prograde (left) and retrograde (right) period spacing pattern
2nd March 2018Mixing and rotation in intermediate-mass stars
Most of the intermediate-mass main-sequence stars with a measured radial
rotation profile are approximately rigid rotators.
e Astrophysical Journal Letters, 847:L7 (5pp), 2017 September 20 Aerts, Van Reeth, & Tkachenko
Main Sequence stars:
gamma Dor
SPB
Evolved stars:
RGB
Red Clump
Secondary Red Clump
(Kurtz et al. 2014;
Saio et al. 2015;
(Aerts et al. 2017b)
ure 1. Core rotation rates (circles) as a function of spectroscopically derived gravity for core hydrogen burning stars with a mass between 1.4 and 2.0 Me (green) Van Reeth et al. 2016;
d 3 to ~5 Me (blue) derived from dipole prograde gravito-inertial modes in main-sequence stars. Surface rotation rates (triangles) are deduced from pressure modes
from rotational modulation. Errors on the rotation rates are smaller than the symbol size, while the errors on the gravity are indicated by dotted lines.
eroseismically derived rotation rates and gravities for evolved stars with solar-like oscillations in the mass range 1.4 MeMixing and rotation in intermediate-mass stars
Gravity-mode period spacing patterns constrain the size of the convective
core and the shape ofT.the overshooting
Van Reeth et al.: Rotation of region,
Dor stars and the radial rotation and
mixing profile.
The method: combining time
series photometry, high-resolution
spectroscopy with state-of-the-art
stellar evolution and pulsation
codes to determine interior
physical properties known as
Forward Seismic Modelling.
Fig. 3. Illustration of our method to derive the rotation rate frot and
Brunt-Väisälä frequency N (top) and the rotational kernel Knl asymptotic spacing ⇧ from an observed (Van Reeth et al.
period spacing 2016)
pattern (black
l
for the lowest- and highest-order mode of the stellar model dots). An equidistant spacing series (grey squares) is defined, rotation-
d in Sect. 4.1. The inset shows a zoom of Knl . Both functions ally shifted (white squares), and fitted to the observed pattern using 2 -
e with the sensitivity of the gravity-mode pulsations to the dif- minimisation, optimising for the variables l, m, ⇧ , and f .
l rot
gions inside the star.
(Paxton et al. 2011, 2013, 2015, 2017; Townsend & Teiter 2013)
llot et al. 2012, Fig. 2), with and m, while the asymptotic spacing ⇧l is dependent on the
2nd March 2018Mixing and rotation in intermediate-mass stars
Gravity-mode period spacing patterns constrain the size of the convective
core and the shape of the overshooting region, and the radial rotation
profile. M. G. Pedersen et al.: The shape of convective core overshooting from gravity-mode period spacings
(a) (b) (c) (d)
f2
ov fov
D0 D0 D0 f1
log Dmix [cm2 s 1]
D2
Dext Dext Dext
m/M m/M m/M m/M
Fig. 1: Di↵erent shapes of internal mixing profiles. Grey marks the convective core, blue the overshooting region and green the extra
di↵usive mixing in the radiative envelope. Panel (a) to (c) has been zoomed in on the near core region while panel (d) shows the
Withprofile
mixing hundreds
from center toofthe δ Sctofstars
surface the star. still
In bothto analyse!
panel
(Pedersen et al. 2018)
(a) and (b) the extra di↵usive mixing in the radiative envelope
has been set constant. Panel (a): step overshoot. Panel (b): exponential overshooting. Panel (c): Extended exponential overshoot
where the extension replaces the constant di↵usive envelope mixing in panels (a) and (b). Panel (d): Exponential overshoot coupled
to an extra di↵using mixing profile Dext (r) from Rogers & McElwaine (2017) instead of a constant mixing (green dashed line).
2nd March 2018The δ Sct stars: the work still to do!
Searching for g-mode period spacing patterns in hundreds of δ Sct
stars will constrain the properties of stellar interiors on the upper main
sequence.
(Bowman & Kurtz 2018)
Image credit: Péter Pápics
2nd March 2018Overview
• A (brief) introduction to asteroseismology
• The delta Scuti (δ Sct) stars
• non-linear pulsations
• interior mixing and rotation (a)
• Internal Gravity Waves (IGWs)
• models and observations
• characterising the morphology
• Conclusions and Future Prospects
2nd March 2018Mixing and Angular Momentum tranSport of massIvE stars
We only have a handful of in-depth Observations Models
The Astrophysical Journal Letters, 815:L30 (5pp), 2015 December 20
studies of interior mixing and rotation
in main sequence stars
(see, e.g., Aerts et al. 2017b).
One missing aspect from evolutionary Figure 1. Time snapshot of M4. (Left) Temperature perturbation with white hot and black cool perturbations. (Right) Vorticity with black negative vortic
positive.
models is angular momentum Table 1
Model Parameters
substantial variation and certainly none outside the
quoted.
transport caused by Model
M1
M2
Ωi (rad s−1)
10−7
5×10−7
Q cv
1.5
1.5
Ωc/Ωe
2.5±2.3
0.5±1.9
áAMñ AMi
1.005
1.021
In Figure 2, we immediately see that the range of d
rotation profiles seen in the simulations (−0.03–5) is
that observed (−0.3–5). More specifically, our low fl
with a variety of low rotation rates converge to core
10−6
Internal Gravity Waves (IGWs).
M3 1.5 3.73±3.46 1.010 differential rotation values between ∼1–5, similar t
M4 10−6 3.0 −0.06±0.14 1.021 the eight observations of differential rotation (H
M5 5×10−6 1.5 0.60±0.81 0.998
HD29248, HD157056, KIC9244992, KIC
M6 5×10−6 2.2 1.24±1.56 1.020
M7 5×10−6 3.0 −0.14±0.65 0.990
KIC10080943). These models show a slight preferen
10−5 values closer to one than to five, similar to the ob
Improved Stellar Evolution theory
M8 1.5 1.06±0.34 1.000
M9 10−5 3.0 0.20±0.11 1.010 Simply, we expect HD129929, HD29248, and HD
M10 4×10−5 1.5 0.97±0.10 1.001 be described by high flux rather than low flu
M11 4×10−5 3.0 0.21±0.18 1.008 However, numerous other effects (such as stratificati
Only a few detections of IGWs exist M12
M13
8×10−5
8×10−5
1.5
3.0
0.93±0.06
0.12±0.03
1.000
1.011
Note. Ωi is the initial rotation rate given in rad s−1. Q cv represents the
Vaisala barrier, etc.—see the Discussion) could
surface flux of waves contributing to these stars appea
like low flux models. Low flux, high rotation models
values very close to one. Notably though, the averag
(Aerts & Rogers 2015; convective forcing in units K s−1, where cv is the specific heat at constant
volume. The values 1.5 and 3 result in root-mean-squared convective velocities
of ∼2.9 and 4.5 km s−1, respectively, values ∼10 and ∼20 times larger than
predicted by mixing length theory. The differential rotation, Ωc/Ωe, represents
exactly one. Therefore, in these low flux models, the
angular momentum transport by waves but not enoug
the system significantly away from its initially unif
This is particularly true in faster rotating models, w
Aerts et al. 2017a).
the mean ratio of core-to-envelope rotation. The time and spatial averaging are
discussed in the text. Errors quoted are due to variations in time, which are also transport is less efficient.
discussed in the text. áAMñ/AMi represents the integrated angular momentum High flux models, on the other hand, converg
compared to the initial angular momentum content of the system, demonstrat- envelope differential rotation values generally betwe
ing the level at which angular momentum is conserved in the system. this case, IGWs are particularly efficient at spinni
amplitude) the radiative envelopes and hence,
generally spin faster than cores. For slow rotators thi
there is some deviation and skewness. The values of Ωc/Ωe
is efficient enough and predominantly due to retrogra
quoted in Table 1 are the mean values with errors of one
so that negative values are common. On the other ha
standard deviation. The variability due to differences in spatial rotators, prograde waves dominate and bring about
averaging are smaller than those in time, so long as Ωc is positive rotation in the envelope. It is worth notin
measured within the radiative region and away from convective general, slow rotators tend to favor retrograde wave
overshoot. If the core value includes the convection zone, the at the surface and hence, retrograde envelope rotat
ratio Ωc/Ωe becomes significantly more variable, tends to fast rotators favor prograde wave deposition at the s
increase and its distribution is often not Gaussian. This may be hence, prograde envelope rotation. At the mo
due to inadequate time resolution or reduced dimensionality, but theoretical reason for this tendency is unknown.
is more likely due to the stochastic nature of turbulent The high flux, slow rotator behavior seen in these s
convection. Each of the models is run for at least 20 wave is similar to the differential rotation pattern observed
crossing times of the entire radiative envelope for a typical wave KIC10526294 (Triana et al. 2015). In Figure 3, we
(horizontal wavenumber 10 and frequency 10 μHz), or ∼100 rotation profile inferred for KIC10526294 (Triana et
convective turnover times, which amounts to ∼107 s. We note with error bars, along with time-averaged rotation pro
that some models are run substantially longer and do not show M4, which was initiated with a rotation rate
3
2nd March 2018Models of Internal Gravity Waves (IGWs)
Currently, we have 2D numerical simulations of convectively-driven IGWs in
a 3 M⊙ ZAMS star, but driving is at least 100 times stronger than expected
so likely resemble a 30 M⊙ instead (Rogers et al. 2013; Rogers 2015).
The morphology of the
predicted low-frequency power
excess (red noise) can be
scaled in frequency for different
stellar masses and ages.
This frequency scaling is
approximately a factor of 0.75
for 3 to 30 M⊙ ZAMS stars.
Temperature perturbation with white hot and black cool perturbations. (Right) Vor
" M = " A and # ⌫
(Shiode et al. 2013)
2nd March 2018Observations of Internal Gravity Waves (IGWs)
/2/L33 A&A 602, A32
doi:10.1088/2041-8205/806 (20
(5pp), 2015 June 20
DOI: 10.1051/00 17)
nal Letters, 806:L33 04-6361/201730
The Astrophysical Jour reserved.
c ESO 2017 571
rights
Astronomical Society. All
© 2015. The American
TIVELY DRIVEN WA
VES IN MASSIVE STA
RS Astronomy
NATURES OF CONVEC &
OBSERVATIONAL SIG Astrophysic
3,4
C. Aerts and T. M.
1,2 Rog ers
Belgium s
de, KU Leuven, Celestijnen
laan 200D, 3001 Leuven,
The Netherlands Kepler shed
Instituut voor Sterrenkun
1
APP, Radboud Univ ersity Nijm egen, 6500 GL Nijmegen,
upon Tyne, UK s new and un
2
Departmen t of Astro physi cs/IM
Statis tics, Newcastle Univ ersity, Newc astle
of a blue sup precedented
3
Department of Math
4
emati cs and
Tucson, AZ 85721, USA
Planetary Science Institute, May 23; published 2015 June 19 ergiant: Grav light on the va
Received 2015 April 30;
accepted 2015 it y waves in the riability
C. Aerts 1, 2, S.
Símon-Díaz 3, 4 O9.5Iab star
ABSTRACT waves (IGWs) M. H. William 7
, S. Bloemen 1, 2
, J. Debosscher 1 H D 188209 ?
ely driven internal gravity son , F. Gr , P. I. Pápic 1 s
rvati onal evid ence for the occurrence of convectiv e photometry. This evidence results from 8 undahl , M. Fr
edslund Anderse 8 , S. Bryson 5, M. Still 5, 6, E. M
We demonstrate obse rved with high -pre cisio n CoR oT spac
simulatio of IGWs in
ns a J. Christensen-
Da n , V. Antoci 8, oravveji 1,
sive O-ty pe stars obse nal hydr odyn amic al lsg aa rd 8
, and T. M. Roge 9, 10 P. L. Pallé 3, 4,
in young mas on two-dimensio caused by
velocity spectra based that the velocity spectra rs
1
betw een also show Instituut voor Ste
a com paris on spec tra. We obse rved rrenku nde, KU Leuve
sive star and the observed of macroturbulence in the bright, e-mail: Conny.
One of three O stars observed
differentially rotating mas line-profile variability and explain the occurrence
line profi les of OB stars .
le
IGWs may lead to detectab findings provide predictions that can readily be teste mission accompanied by high-
Our
type stars in the scien tific prog ram of the K2
d by including a sample
simu latio ns of IGW
of
s for
3
4
2
Department of
Ins titu to
Departamento
Aerts@ster.k
Astrophysics/IM euven.be
de Astrofísica
de Ca
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AP P, Ra
n, Celestijnenl
narias, 38200 La
dboud Universit
aan 200D, 300
y Nijmegen, 650
1 Leuven, Belgi
0 GL Nijmegen
um
ing OB- onal hydr odyn amic de Astrofísica, Un La guna, Tenerife,
slowly and rapidly rotat mult i-dim ensi 5 , The Netherla
by CoRoT (Blomme et al.
precision spectroscopy
various mas ses and ages
and their confrontation
.
logy – line: profiles –
with
stars : mas sive – stars : oscillatio ns – tech niqu es: phot ometric – 7
6
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Ce
SA Ames Research
Bay Area Envir
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Center, Mo
in Information
rch
ive rsid ad de La Lagun
onmental Resea ↵ett Field, CA 94095, USA
Institute, 560 Th
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a, 38205 La La
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guna, Tenerife,
Sp ain
nds
Key words: asteroseismo
TN 37209, US
A Systems, Tennes eet W., Sonoma, CA 95476,
see State Unive US
2011), to have IGW signal: rsity, 3500 Joh A
8
Stellar Astrophy
waves 9 sics Centre, De n A. Merritt Blv
drive De par tm ent of Mathema par tm ent of Physics and d., Box 9501,
ectiv e core s likel y 10 tics As tro Nashville,
large conv Planetary Scienc and Sta nom
are not excited, while their is therefore focused on the search e Institute, Tucso tistics, Newcastle Universit y, Aarhus University, 8000 Aa
n, AZ 85721, US y, Newcastle upo rhus C, Denmark
1. INTRODUCTION IGWs efficiently. This work convection in photometric and Received 6 Feb A n Tyne NE1 7R
U, UK
core ruary 2017 / Ac
er gravity-mode (g-mode)
oscilla- for IGWs driven by observed cepted 3 March
The existence of high-ord of a few carefully selected 2017
ating B (SPB ) stars , which are core- spectroscopic observations s are impo rtant beca use the
tions in slowly puls een 3 and 7 O-type stars. Such sign
ature
nced angular
with masses roughly betw es could point to enha
• Excess of "red noise"
hydrogen-burning stars
M (her eafte r SPB
than two decades ago,
s; Wae lkens 1991), was estab
prior to understanding their
llations
lished more
are
exci
driv
tatio
en by
n
existence of these wav
momentum
inclu sion of
trans
thes
port
e proc
and
esse
chem ical mixing, and hence guid
s into future theoretical
models.
e Stellar evolution
photometry has
but not yet to
models are mo
st
become a new uncertain for evolved massive
way to test the
ABSTRACT
stars. Asterose
know that thes e osci ma ism
mechanism. We now bump due to out
O9.5 Iab star HD ssive evolved supergiants.Our come of stellar evolution the ology based on high-precisio
• Line profile variations
the heat mechanism asso
iron-group elements in
ciated with the opacity
the stell
Saio 1993
ar
).
enve
How
lope
ever
(Dzi emb
, the detection of
owski
2. MODEL ING CON VEC
ively few
TIV ELY
theo
DRIVEN WAVES
retic al pred ictio ns for the
pho tom
we assembled
etr y obt
188209 from Ke
ained by the nom
and ana
ple r spa ce
inal mission dur
aim is to detect
photometry and
ing 146
, ana lys e and
ory and was rec
int
ently applied to
long-term high-r erpret the photospheric and a multitude of stars,
eso lut ion
n uninterrupted
win d variability of
space
et al. 1993; Gautschy & stan ding wav es, Ther e have been relat ectio n in int erp ret
lysed high-reso
lut
0 d to deduce the spectroscopy. We the
associated with those IGWs excited by core conv
the temporal spectr ion high signal-to-no pho tometric variab used Kepler sca
g-mode period spacings ired for spectra and amplitudes of photom oscopic var ise spectr
ning et al. (2004) provided that is etry is in full in agreement wit iability of the star. The variabilit oscopy taken with four spectr O-type supergiant. In addition,
ility of this ttered-light
icted from theo ry (Tassoul 1980) and requ the . On the one hand , Brow h ogr
as pred
stars, remained impossibl
e from massive stars 2 M star, but consistently det the one found in y of this blue sup aphs during som
asteroseismology of such the core convection for a similar ected in all spe the ground-ba ergiant derive e 1800 d to
fully planned long-term
dedicated the first 3D simulations of and hence omitted and spe frequencies but slightly higher ctral lines of HD 188209. The sed spectroscopy. We find signifid from the scattered-light space
ground, even after care ). This is these only cove red the inner 30% in radius, theo retic al ctroscopy points amplitudes. Th photospheric var cant low-freque
Q: can we detect such waves
campaigns (Aerts et al.
partly due to the low amp
1999; De Cat & Aert
litudes of g-modes and
ds of g-m odes in mas
s 2002
is also made
sive stars are of
much of the wave prop
agation region. More
e radius of the star but are
models do consider the entir rotation, and must make assump-
ect
rece nt star.
ility.
towards a spe
vity waves exc
e morphology
limited to variabConvectively-driven internal gra ctrum of travelling waves wit of the frequency spectra derive ates into the wind, where it has
h fre
ited in the stellar quency values in the range
int
iab ility propag
d from the lon
exp ect
ncy variability
g-term photom
etry
difficult because the perio contamination one-dimension (1D), negl n and convective-oversh
oot Key words. techni erior o↵er the
most plausible ed for an evolved O-type
e timescales have strong t the nature of convectio e stars: individual: HDques: photometric – technique explanation of
in intermediate-mass stars?
the order of days and thes
by daily aliases in the
photometry and high-reso
amplitude spec
lution spectroscopy. g-m
tra of grou nd-b ased
ode aster-
terru pted
tions abou
de et al.
(Samadi et al. 2010; Shio nolds stresses in the convection
theo retic al mod els assume Rey
2013 ). Gen erall y,
give
thos
ency 1. Introdun by
188209 s: spectroscopic –
stars: massive
– waves – stars:
osc illa tio ns –
the det ect ed
saw its birth due to the unin zone that generate waves
with a predominant frequ ction
oseismology of SPBs only the CoRoT frequency and with frequ Sta
ency and
ometry assembled with the convective turnover
high-precision space phot to the dete ction of perio d
ted by the assu med prop ertie s of rs theborn wi
th sufficiently hig in the predictions
e data led wavelength spectra dicta
and Kepler missions. Thes es of consecutive radial order and es of the waves are dete
rmined at bythetheend of
their life h mass to explo
de as supernov stellar evolution of massive star evolution fro
turbulence. The amplitud ical evolution of have major impact on the dy
mod
spacings caused by dipole nece ssary for seismic modeling gy is trans ferred from convectio chem n to a
the
code
main-sequence s even occur already well be
m various mode
rn
tifica tion whic h ener ga lax ies na mi cal
offered the mode iden al. 2012, 2014, 2015).
efficiency with
depe ndent on assumptions
abousupt erntheovae
are thus highly . Appropriate models of suc
and (MS) phase (e.
g.
fore the end of
et al. 2010 ; Pápi cs et es and are high ly
tcomings , the
nately, the theory rel evant for astrop h pre - Ma rtin s & Palacios 2013).
(Degroote osci llatio ns in SPB s are strictly wav
face . Desp ite these shor of the hy sics. Unfortu- ing
Despite the im
me
While heat-driven g-mode effect on convective–radiative inter al. (201 that of low-mass ir evolution is a lot less we
tha0)n and of stellar mode nse progress in the astero
-known and quantifiable s predicted by Samadi et
periodic and have a well
observed time -seri es phot ome
De Cat & Aert
try and spectral line-profi
s 2002 ;
Observations
Aert s et
le
al.
theoretical spectra of IGW
Shiode et al. (201 3) are cons
stars
istent with the observed ? vary
. How ever , their amp
frequency
litudes Based on photometr
stars that die as
ic
ll est
white dwarfs. Di ablished precision uninterrupted
↵e ren ces (e.g. Chaplin
& Mi
ls of various
types
space photome of stars from high-
try in
seismic tun-
the past decad
variations (LPVs; e.g., y by core ranges of variable OB
be inconsistent with obse the No
satons.
rvati elliteForand on spectrosc observations made with the Hekker & Chris glio 2013; Charpinet et al. e
es excited stochasticall 2014;
2014), the effect of wav
convection (Belkace m et al. 2010 ; Sam
rvations is relatively unkn
(scaled) IGW model
adi et al. 2010; Shiode
own. This
significantly and appear to
example, the amp litud es pred icted in Shiode et al. (201
nitude lower than those rio del
more than an order of mag those are too small to As
Tel esc
arec Optical Tel opic observations made with NASA Kepler lack sui
3) rdi
ope in
predicted operated by the Flemi
explainRo
escope operated
by NOTS
sh Community, A and the Mercator
four telescopes
: stars and their
tensen-Dalsgaard
table data to
ach ieve thi
2016, for review Aerts 2015;
evolved descend s stage for massive O-typ
s), we still
et al. 2013) on such obse with internal
theque de los Mucha both at the Ob
servato- while the MOST and ants, the B sup e
of obse rvati onal diagnostics connected ext Sam adi et al. (2010), and even nerti al mod estroin
físiHD
ca de Canarias
, the
chos (La Palma
, Sp ain ) of the pe rgiants for week Co Ro T mi ssi
ergiants. Indeed
,
lack in the cont excited gravito-i scope (AST) ope T13 2.0 m Au Ins
tomatic Spectros tituto de s to months (e. ons observed a few B su-
is particularly relevant detection of stochastically
gravity waves (IGWs) rated by Tennes
Figure
2nd2.March 2018 amplitude spectra (gray) overplotted with the predictio
Measured
whic h heat -driv en mod es ser vatory, and the see State Universit cop ic Tel e- 20 10 , 20 13; Moravveji g. Sa io et al. 2006;
of O-ty pe stars , in He rtz y at et Ae rts
of the variability telescope operat Fairborn Ob- cies were not measured al. 2012), their pulsationa et al.
ish Observatori sprung SONG the
o
and Copenhag del Teide on the island of ed on the Span- gular
wavenumb with sufficient
precision
l frequen-
en U TenerSelecting candidate stars with IGWs
• Any star with a convective core
is predicted to excite IGWs.
• No direct observations of stars
with M > 5 M⊙ by Kepler.
• Other telescopes (K2, CoRoT)
have more massive stars, but do
not have as good frequency
resolution.
Ongoing task: carry out a
systematic search for
signatures of IGWs in main
sequence stars with M > 1.4 M⊙
2nd March 2018A "constant" main sequence A star
Te↵ = 9500 ± 100 K
1 month of SC
log g = 3.8 ± 0.1 Kepler data:
1
v sin i = 20 ± 2 km s A noise level of less than
M ' 2.5 M 1 micro-mag
4 yr of LC
Kepler data:
2nd March 2018Characterising red noise T. Kallinger et al.: The connection bet
Astrophysical red noise is typically
modelled as a Lorentzian:
↵0
↵= +C
µ
1 + (2⇡⌧ ⌫)
For example, granulation
background in Red Giants
requires multiple components.
Ongoing task: create a
parameter-space for IGWs across
a wide mass range for main
µ
sequence stars.
Fig. 7. Power density spectra of three typical starset
(Kallinger with
al.νmax ≃ 22, 220,
2014)
and 2200 µHz, respectively, showing that all timescales and amplitudes
(granulation as well as pulsation) scale simultaneously. Grey and black
2ndlines
March 2018 the raw and heavily smoothed spectrum, respectively. The
indicateCharacterising red noise: Bayesian MCMC
Using the 30 solar mass ZAMS O
star HD46223, fit a global red noise
power law:
↵0
↵= +C
1 + (2⇡⌧ ⌫)
~ 6 c/d
(Bowman et al. in prep)
2nd March 2018Characterising red noise: Bayesian MCMC
Limitations of the IGW simulation:
• Low frequencies are not resolved
computationally.
• The predicted IGW spectrum is
quite structured.
~ 6 c/d
(Bowman et al. in prep)
2nd March 2018Characterising red noise: quality of the fit
• A Bayesian MCMC framework for fitting red noise is robust with
appropriate uncertainties using (asymmetric) posterior distributions.
• Also, allows quality of fit to be determined at different stages iterative
pre-whitening for stars with pulsation modes.
• Model testing with log-likelihood ratio statistics, for example:
h i
ˆ
TLR = 2 ln `(✓) `(✓0 )
where: ˆ
`(✓) is the log-likelihood of the red noise model
and: `(✓0 ) is the log-likelihood of the null hypothesis – a simpler model
(e.g., white noise)
(Bowman et al. in prep)
2nd March 2018Are there other physical explanations?
The O supergiant rho Leo has a large-scale Te↵ ' 22 000 K
tangential velocity field and photometric log g ' 2.55
variability consistent with:
v sin i = 50 km s 1
• IGWs
• dynamical aspherical wind M ' 18 M
• sub-surface convection (Crowther et al. 2006;
Simón-Díaz & Herrero 2014)
(Aerts, Bowman et al. 2018)
2nd March 2018Models of Internal Gravity Waves: in 3D!
3D IGW simulations of 3 M⊙ ZAMS star:
⇥1011 l=4
105
1.2
104
1.0
103
0.8
1
r/cm
vr /cm s
102
0.6
101
0.4
100
0.2
1
10
0 100 200 300 400 500
f /µHz
Image courtesy of May Pedersen Image courtesy of Philipp Edelman
... to be continued!
2nd March 2018Models of Sub-Surface Convection: in 3D!
3D surface convection simulations of 30 M⊙ ZAMS star: Image courtesy of
Philipp Edelman
Ongoing task:
use convection
simulations to
R? (cm)
predict photometric
T (K)
and spectroscopic
variability and
disentangle IGW
signatures.
... to be continued!
R? (cm)
2nd March 2018Overview
• A (brief) introduction to asteroseismology
• The delta Scuti (δ Sct) stars
• non-linear pulsations
• interior mixing and rotation (a)
• Internal Gravity Waves (IGWs)
• models and observations
• characterising the morphology
• Conclusions and Future Prospects
2nd March 2018Conclusions and Future Prospects
Delta Scuti stars:
• Hybrid δ Sct stars are excellent laboratories for testing physics within
intermediate-mass stars, with gravity-mode period spacing patterns
able to extend mixing and rotation studies beyond B and F stars.
(a)
Internal Gravity Waves:
• Ongoing work to characterise observational signatures of IGWs in main
sequence stars with a convective core observed by Kepler and K2.
• Asteroseismic constraints of IGWs informing 3D IGW simulations and
prescriptions of mixing and angular momentum transport in stellar
evolutionary models.
• TESS launch in mid-2018 promises exciting results for the most massive
stars, including hundreds of pulsating O and B stars!
2nd March 2018Conclusions and Future Prospects: TESS
Planets: TESS will find many
transiting exoplanets orbiting
bright stars. It will eventually
observe a large fraction of the sky.
Stars: a rich and unique data set
of many high-mass and pre-main-
sequence stars. Also, follow-up of
original Kepler field.
Image credit: NASA (tess.gsfc.nasa.gov)
2nd March 20182nd March 2018
Twinkle twinkle massive star,
how I wonder what you are
Asteroseismology of massive stars with
the Kepler Space Telescope
Dominic Bowman
C. Aerts, T. Rogers, P. V. F. Edelmann, A. Tkachenko,
M. G. Pedersen, C. Johnston, B. BuysschaertYou can also read
