Blazhko effect in Cepheids and RR Lyr stars

Blazhko effect
in Cepheids and RR Lyrae stars
Róbert Szabó
Konkoly Observatory
Research Center for Astronomy and
Earth Sciences of the
Hungarian Academy of Sciences
22 August 2013
Wroclaw, IAU Symposium 301

Outline
- Introduction – RR Lyrae stars and the Blazhko effect
- What have we learned in the past few years ? - Observations
- What have we learned in the past few years ? - Theory
- Cepheids
- Future directions
- Photometry
- Spectroscopy
- Modeling

RR Lyrae stars and the Blazhko effect
- amplitude and phase
Gilliland et al.
modulation
PASP, 122, 131
2010
- light curve shape
deformation
- ampl. mod.:
dA / A ~ 0.03-0.87
- period var:
1-4 % dP/P
Sosynski et al.
AcA 61, 1, 2011
- Blazhko period:
5 d -- ~10 yr

Mitteilung über veränderliche Sterne
The beginning
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S. Blazhko 1870 - 1956
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RW Dra phase modulation
Astronomische Nachrichten 175, 327, 1907

The beginning
On the changes in the spectrum, period, and lightcurve
of the Cepheid variable RR Lyrae.
●
●
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H. Shapley 1885 - 1972
●
RR Lyr amplitude modulation
Astrophysical Journal 43, 217, 1916

Blazhko effect – pre-Kepler results
-
- occurrence rate: ~50% of the RRab stars are modulated
Konkoly Blazhko Survey (Jurcsik et al. MNRAS 400, 1006, 2009)
- long period modulations (~3000 d )
OGLE (Sosynski et al. AcA 61, 1, 2011)
- tiny and rapid modulations e.g. SS Cnc P BL
= 5.3 d
-
Jurcsik et al. AJ 132, 61, 2006
- stellar structure varies during the cycle
Sódor et al. MNRAS 394, 261, 2009
-
-
- multiple modulation periods , e.g. CZ Lac
Sódor et al. MNRAS 411, 1585, 2011

Kepler and the Blazhko effect
Quasi-continuous data + extreme precision --->
- ~40% of the RRab stars are modulated
- incredible diversity of modulation patterns
- phase modulation in all Blazhko stars
- Blazhko cycles are not strictly repetitive
- long term variations of the modulation cycle
- multiple modulation periods

V445 Lyr aka KIC 618029
Guggenberger et al. MNRAS 424, 649, 2012

Extreme modulation:
V445 Lyr aka KIC 6186029
Q1+Q2+Q3

Kepler Blazhko 'zoo'
Q0-Q12 1061 days
Benkő et al. 2013 in prep.

Multiple modulations
longest P BL
shortest P BL
Benkő et al. 2013 in prep

An unexpected Kepler-discovery:
period doubling (PD) in RR Lyrae stars
Manifestation:
- alternating cycles
- half-integer frequencies
(1/2 f O
, 3/2 f O
, 5/2 f O
…)
Kolenberg, Szabó, Kurtz, et al.
2010, ApJL 713, 198
Szabó, Kolláth, Molnár et al.
2010, MNRAS 409, 1244
RR Lyr Q1 Kolenberg et al. 2010
PD has never been observed in RR Lyr stars nor in RR Lyr models.

Period doubling in RR Lyr (Q1+Q2)

A Kepler RR Lyr short-cadence data set
See Kolenberg's talk

Period doubling in CoRoT data
V1127 Aql Szabó et al. 2013 in preparation

Period doubling
Period doubling:
- interesting nonlinear dynamical phenomenon
- Key to the Blazhko enigma:
- period doubling is seen only in Blazhko stars
- period doubling is seen in most of the Blazhko stars
Models and explanation
Hydrodynamic calculations proved that the cause of the period
doubling effect is a high order resonance (9:2) between the
fundamental mode and the 9 th radial overtone (strange mode).
Szabó, R., Kolláth, Z., Molnár, L. et al. 2010, MNRAS 409, 1244
Kolláth, Z. Molnár, L., Szabó, R. 2011, MNRAS 414, 1111

Hydro results
Kolláth, Molnár, Szabó MNRAS, 414, 1111, 2011
- Florida-Budapest 1D pulsational hydrodynamical code
- PD appears naturally with hydro calculations
- not a transient, bifurcated limit cycle is stable

Period doubling spin-off
PD led to the discovery of a plethora of other dynamical
phenomena:
- high-order resonances (9:2)
Szabó, Kolláth, Molnár et al. 2010, MNRAS 409, 1244
- presence of high radial overtones (strange modes)
Kolláth, Molnár, Szabó 2011, MNRAS, 414, 1111
- presence of other radial modes (1 st and 2 nd overtones)
in Blazhko stars
Molnár, Kolláth, Szabó et al. ApJL, 2012, 757, 13
- even low-dimensional chaos
Plachy, Molnár, Kolláth 2013, MNRAS 433, 3590
- new explanation of the Blazhko effect
Buchler & Kolláth ApJ 2011, 731, 24

A new explanation for the Blazhko effect
Buchler & Kolláth ApJL, 731, 24, 2011
Irregular amplitude modulations naturally result from the
nonlinear resonant mode coupling between the fundamental
mode and the 9 th overtone using amplitude equations.
Hydro: in BL Her stars Smolec & Moskalik MNRAS 426, 108, 2012

A new explanation for the Blazhko effect
Buchler & Kolláth ApJL, 731, 24, 2011
J. Robert Buchler (1942-2012)

Bifurcation cascades
Bifurcation-cascade
can lead to chaos.
Chaos as found in
RR Lyrae hydro
models.
Indications that
shortest modulation
period Kepler
Blazhko RR Lyrae
stars might be
chaotic.
Kolláth et al. MNRAS, 414, 1111, 2011
Plachy et al. MNRAS, 433, 3590, 2013
Check out R. Smolec's poster

Additional modes in Blazhko stars
Nonradial modes can be excited in RR Lyrae stars
(e.g. Dziembowski 1977, Van Hoolst et al. 1998)
Possible detections in Blazhko stars:
- V1127 Aql CoRoT (Chadid et al. 2010) at least 3 additional
frequencies
- 101128793 CoRoT (Poretti et al. 2010) 2 additional frequencies
Kepler:
- frequency peaks around the first and second overtones in
many Blazhko RRab stars
Benkő et al. 2010 MNRAS 409, 1585
- Detection of the first overtone in RR Lyrae, the prototype
Molnár et al. 2012 ApJL 757, L13
CoRoT
Cf. the poster of J. Benkő et al. and the talk of P. Moskalik

Period-6 state, 3:4 resonance
RR Lyrae, Molnár, Kolláth, Szabó ApJL, 757, L13, 2012

Excited first overtone, triple mode state,
nonlinear asteroseismology
RR Lyrae, Molnár, Kolláth, Szabó ApJL, 757, L13, 2012

Cepheids
Amplitude variation in Cepheids
- Modulations in DM Ceps in anti-phase
- secular(?) variations
- genuine Blazhko-like variation!
Moskalik & Kolaczkowski 2009, MNRAS, 394, 1649
LMC FO/SO Cepheid
Polaris
V473 Lyr
See P. Moskalik's talk
Molnár et al. 2013 AN in press Turner et al. 2005 PASP 117, 207

Cepheids
Amplitude variation in Cepheids
- Modulations in DM Ceps in anti-phase
- secular(?) variations
- genuine Blazhko-like variation!
Moskalik & Kolaczkowski 2009, MNRAS, 394, 1649
LMC FO/SO Cepheid
Polaris
V473 Lyr
See L. Molnár's talk
Molnár et al. 2013 AN in press Turner et al. 2005 PASP 117, 207

Future

Photometry
US: TESS (Transiting Exoplanet Survey Satellite) 2017-
27 d high-precision photometry of bright stars
CoRoT

Photometry
EU: PLATO
(PLAnetary Transits and Oscillations of stars) 2024- ?
Months-years long high-precision photometry of
up to half of the sky
CoRoT

Photometry
EU: PLATO
(PLAnetary Transits and Oscillations of stars) 2024- ?
Months-years long high-precision photometry of
up to half of the sky
CoRoT

Spectroscopy
Detection of He I and He II emission
Preston A&A 507, 1621, 2009, Preston AJ 141, 6, 2011
RR Lyr: Gillet et al. A&A 553, A59, 2013
See E. Guggenberger's and K. Kolenberg's talks
CoRoT
Powerful test for shock-wave formation theories
Radiative hydro, realistic atmosphere computations

2D/3D modeling
- Modeling nonradial modes
- Realistic turbulent convection
- Interaction between pulsation
and convection
- Mode selection
- Interaction between modes
Geroux & Deupree
ApJ 731, 18, 2011
Geroux & Deupree
ApJ 771, 113, 2013
F. Kupka's talk yesterday
Geroux & Deupree
poster
CoRoT

Blazhko effect – proposed mechanisms
1. Magnetic oblique 2. Resonance model 3. Stothers’ idea
rotator /pulsator model Van Hoolst et al. 1998 Stothers 2006
Shibahashi 2000 Dziembowski & Mizerski 2004 Stothers 2010
Strong magnetic field 1:1 nonlinear resonance Magnetic dynamo effect altering
deforms the purely between the radial fundamental the stellar structure by causing
radial pulsation mode and a nonradial mode variable turbulent convection
Strong magnetic field was Too high amplitude required for Complex turbulent and
ruled out Chadid et al. 2004, the nonradial mode in some cases magnetic dynamo interaction
Kolenberg & Bagnulo 2009
hard to model. Requires
Blazkho period is the rot. period
nonphysical changes
Smolec et al. 2011
Molnár et al. 2012

Latest proposed Blazhko mechanisms
Radial resonance model
Buchler & Kolláth 2011
Shockwave interaction
Gillet 2013 A&A, 554, A46
9:2 resonance between the First overtone perturbs the
fundamental mode and a
fundamental mode creating
high radial (strange) overtone
an additional shock wave
supported by full hydro calculations
cause or consequence?
Figures: courtesy of K. Kolenberg

Conclusions
- Space photometry revived the field of Blazhko studies
by shedding new light on the problem
- Blazhko effect : anything but regular
- Period doubling provided a good handle to tackle the problem
- Additonal modes: complicated nonlinear dynamics,
role of resonances, chaos
- Some Cepheids may show the Blazhko effect as well
- We hope for the continuation of the space based revolution:
TESS, PLATO, even a re-purposed Kepler

Conclusions
- Space photometry revived the field of Blazhko studies
by shedding new light on the problem
- Blazhko effect : anything but regular
- Period doubling provided a good handle to tackle the problem
- Additonal modes: complicated nonlinear dynamics,
role of resonances, chaos
- Some Cepheids may show the Blazhko effect as well
- We hope for the continuation of the space based revolution:
TESS, PLATO, even a re-purposed Kepler
High-amplitude variable star fans (RR Lyr, Cep, DSCT, ...)
should join forces to propose a Kepler white paper.
5:30pm splinter session today

Thank you

Linear 'diagnostic' diagram
of half-integer resonances
Notation: o6 7
:
6 th overtone
with a 7:2
resonance
with the
fundamental
mode
Candidates:
o9 9
o6 7
o4 5
Kolláth, Molnár, Szabó MNRAS, 414, 1111, 2011

Nonlinear 'diagnostic' diagram
Blue region:
resonant
positive
Floquet
exponent
(PD)
It follows
the 9:2
resonance
with the 9 th
strange
overtone.
Kolláth, Molnár, Szabó MNRAS, 414, 1111, 2011

Strange modes
Kolláth, Molnár, Szabó MNRAS, 414, 1111, 2011
Strange modes:
- extra modes compared to the adiabatic eigenspectrum
- trapped surface modes
- can be excited, despite being high order overtones.

In collaboration with
- K. Kolenberg – co-chair of KASC RRL & Cep WG
+ other members of
KASC (Kepler Asteroseismic Science Consortium)
- Z. Kolláth, J. Benkő, L. Molnár, E. Plachy
+ other KIK-members,
Kepler Investigations at Konkoly Observatory
http:www.konkoly.hu/KIK/

Acknowledgements
Acknowledging the support from
- IAU
- the Lendület Young Researchers' Program
- the Bolyai Scholarship of the Hungarian Academy of Sciences
- Hungarian OTKA grant K83790
- HUMAN MB08C 81013 grant of the MAG Zrt
- KTIA URKUT_10-1-2011-0019 grant
- EU FP7 IRSES/ASK grant no. 269194