Download Stellar variability and microvariability II. Spot maps and modelling

The Accepted AP:
Stellar Variability and Microvariability
II. Spot Maps and Modelling
Giuseppe Cutispoto & Antonino F. Lanza
INAF- Catania Astrophysical Observatory, Italy
On behalf of the team of proponents
2-6 November 2005
SECOND COROT- BRASIL WORKSHOP
Ubatuba, SP
Stellar Variability and Microvariability
II. Spot Maps and Modelling
Team of Proponents:
A.F. Lanza (1), P.J. Amado (2,3), S. Aigrain (4), G. Cutispoto (1),
J. R. de Medeiros (5), B. Foing (6), F. Favata (6) , M. Fernandez (7,2) ,
E. Flaccomio (8) , H.-E. Frohlich (9) , R. Garrido (2) , T. Granzer (9) ,
A. Hatzes (10) , E. Janot-Pacheco (11) H. Korhonen (9) , Zs. Kővári (12) ,
S. Messina (1) , G. Micela (8) , K. Oláh (12) , I.Pagano (1) , P.S. Parihar (13) ,
I. Ribas (14) , M. Rodonò †(1,15) , G. Rudiger (9) , S. Sciortino (8) , K.G.Strassmeier
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
14)
15)
INAF - Osservatorio Astrofisico di Catania, Italy
Instituto de Astrofisica de Andalucia, CSIC, Granada, Spain
European Southern Observatory, Santiago, Chile
Institute of Astronomy, Cambridge, United Kingdom
Dept. of Physics, Federal University of Rio Grande do Norte, Natal, Brazil
Research and Science Support Dept. of ESA, ESTEC, Noordwijk, The Netherlands
Max Planck Institut fur Astronomie, Heidelberg, Germany
INAF - Osservatorio Astronomico “G. S. Vaiana”, Palermo, Italy
Astrophysical Institute Potsdam, Potsdam, Germany
Thuringer Landessternwarte Tautenburg, Germany
Universidade de Sao Paulo, Brazil
Konkoly Observatory, Budapest, Hungary
Indian Institute of Astrophysics, Koramangala, Bangalore, India
Institut d'Estudis Espacials de Catalunya, CSIC, Bellaterra, Spain
Dept. of Physics and Astronomy, Università degli Studi di Catania, Italy
(9)
Three Co-ordinated Proposals for the
Corot Additional Program (AO-1)
a) Stellar variability and microvariability. I. An unbiased study
of rotation and stochastic variability and flaring in all Corot
targets (by F. Favata et al.)
b) Stellar variability and microvariability. II. Spot maps and
modelling (by A. F. Lanza et al.)
c) Stellar variability and microvariability. III. Convection and
short-term evolution of photospheric active regions (by S.
Aigrain at al.)
The three proposals are:
• Based on COROT Exofield data;
• Complementary to each other:
– different timescales (from tens of minutes to hundreds of days);
– optimized for different S/N of the data;
– complementary methods of time series analysis and modelling
I shall focus on the second of such proposals, which is dedicated to
“Spot maps and modelling”
Scientific Motivation
Study of solar-like stellar activity in a sample of MS stars
Stellar activity is produced by the interaction
between magnetic fields and plasmas in the
atmospheres of late-type stars (i.e., with an outer
convection zone);
It is characterized by:
• spatial (brightness) inhomogeneities;
• non-stationary time variable phenomena;
• non-radiative heating of the outer atmospheres
Optical passband => magnetic activity in stellar photospheres
Solar photospheric activity:
• Sunspots
• Photospheric faculae
• Magnetic network
Some open key issues
• Magnetic field generation and modulation in stellar
interiors (is aW-dynamo working at the base of the
convection zone or in the overshoot layer ?)
• Processes that drive the magnetic field to the
surface (flux-tube instabilities ?);
• Interaction between magnetic fields and plasma in
the outer layers: modification of convection and
non-radiative heating;
• Magnetic field advection and diffusion by surface
flows (turbulent convection, meridional circulation,
differential rotation,…).
In the Sun we can obtain information on such processes by tracing
the evolution and the motion of active regions (ARs; i.e., sunspot
groups):
 Sunspot groups can be used as tracers of surface
differential rotation;
 Their bipolar structure suggests that the magnetic field
emerges in the form of magnetic flux tubes;
 Their mean latitude varies according to the phase of the 11yr sunspot cycle, providing evidence for a migrating dynamo
wave;
 The turbulent diffusivity of magnetic field can be estimated
from sunspot group lifetimes
• Sporer’s law (butterfly diagram of sunspot groups);
• 11-yr cycle in sunspot areas
The contribution from COROT
Solar-stellar connection for activity levels similar to
that of the Sun
Impact of high-precision (F/F ~ 10-4 - 10-3) “short”term
(up to 150 days) observations:
–
AR growth and decay;
–
–
–
–
preferential longitudes for AR formation;
thermal properties of AR;
surface differential rotation in solar analogues;
Rieger-type activity cycles (with 10 < P < 150 days)
The Sun as a star
VIRGO/SoHO time series:
Total Solar Irradiance (TSI)
Spectral Solar Irradiance (SSI)
Active region evolution
Pooled variance analysis allows us to indentify the relevant timescales
of variation in the TSI and SSI related to active regions (cf. Donahue
et al.1997, Sol. Phys. 171,191; Lanza et al. 2004, A&A 425, 707):
• AR formation:  8-10 days (B-C);
• Rotational modulation:  25-30 days (C-D);
• AR decay (facular component):  60 days (D-E)




: 402 nm SSI;
: 500 nm SSI;
: Total Solar Irradiance (TSI)
: 862 nm SSI
(Time series consisting of one
point per hour; Lanza et al. 2004))
Spot modelling of the
TSI and SSI variations
We fitted the variations of the TSI and SSI (at 402, 500 and 862 nm)
by assuming:
a) Three discrete ARs (to fit the rotational modulation of the flux)
b) An uniform background component
the mean flux level)



(to account for long-term variations of
each AR contains both cool spots and bright faculae;
the area and the coordinates of the ARs and of the uniform background
are adjusted in order to fit the simultaneous variations of the flux in the
bolometric (total) and spectral bands along sections of the solar light
curves of 14-d duration;
the temperatures of spots and faculae are fixed by fitting the rotational
modulation produced by a single AR
(Lanza et al. 2004, A&A 425, 707)
Thermal properties of ARs
Degeneracy between AR area, position and the mean
temperatures of sunspots and faculae
It can be reduced to
some extent when the
flux variations are
dominated by a single
AR (Eker et al. 2003, A&A
404, 1107; Lanza et al.
2004, A&A 425, 707)
(Lanza et al. 2004, A&A 425, 707)
The situation may be better for stars more active than the Sun
(Messina et al. A&A in press)
Active region longitudes
Longitudes of observed sunspot
groups (blue dots) and longitudes
of the ARs of our 3-spot model
(red triangles) for the period
1999.2-2000.2
Distribution of the angle between the
observed mean sunspot longitude and
the mean longitude of the 3 ARs of our
spot model from the best fit to the
26-yr time series of TSI (1978-2004)
(Lanza et al. 2003, A&A 403, 1135)
(Lanza, Bonomo, Rodonò, in progress)
Variation of the total AR area
 The total area of the ARs in our model of the TSI
varies in phase with the 11-yr cycle;
 Absolute values are model dependent, but the cycle
period is well retrieved
Open triangles: total area of the ARs
from our model of the 26-yr TSI
time series;
Solid line: Actual variation of the
total sunspot group area from the
Greewich Photoheliographic Results.
(Lanza, Bonomo, Rodonò, in progress)
Rieger sunspot cycles
Periods of about 156 days (and possibly of 180 days) are
sometimes apparent in the variation of sunspot area (as
shown by wavelet analysis, Krivova & Solanki 2002, A&A 394, 701)
Shorter-term cycles (50-90 days) may be present in the
solar flare occurrence rate (see, e.g., Lou 2000, ApJ 540, 1102)
Surface differential rotation
Spot modelling can be used to derive the presence and amplitude of
surface differential rotation
• In the Sun the lifetime of ARs is too short to trace the surface shear
from the disk-integrated flux modulation (Lanza et al. 2003, A&A 403,1135);
• In more active stars lifetime is long enough to allow to estimate the
amplitude of the differential rotation (Strassmeier & Oláh 2004, ESA SP-538 p.149)
G5V star k1 Ceti observed by MOST
(Rucinski et al. 2004, PASP 116,1093):
Single-spot model (Period: 8.3 days)
Residuals indicate a second spot with a
rotation period of 9.3 days
Predicted Ca II H&K flux variations on
the basis of previous ground-based
observations not simultaneous with MOST
Observational requirements
From the analysis of the solar TSI and SSI, we found the
following requirements to study activity on solar analogues:
• Time sampling: from 1 hour (faster rotating stars)
to 1 day (for slowly rotating stars like the Sun);
• Uninterrupted observations (duty cycle > 80-90 %);
• Photometric accuracy: 0.5  2 • 10-4 mag for an
amplitude of 1  2.5 • 10-3 mag (for the more active stars a
smaller accuracy is adequate, with a light curve amplitude of 0.04 mag,
k1 Ceti, an accuracy of 7 • 10-4 mag is enough)
• Multi-band data (to allow a characterization of AR properties
such as temperatures, areal ratio of cool spots to warm faculae)
Expected COROT samples
According to Bordé et al.
estimate:
(2003, A&A 405, 1137),
we can
• about 45 objects/field with 11<V<12.5 in the F7V-G7V
spectral range - exp. accuracy: (1-1.5)•10-4 in 1-hr integration time;
• about 20 objects/field with 11<V<12.5 in the G8V-K5V
range - exp. accuracy: (0.9-1.3)•10-4 in 1 hr integration time
From the Hipparcos photometry (Eyer & Grenon 1997, ESA SP-402 p.
467), we estimate that 200 solar-type (F7V-G7V) and 400
F5V-M0V objects/field with 11<V<14 will show an
amplitude of variability of about 10-2 mag. or larger
Conclusions-I
COROT will provide us with an unprecedented view of
solar-like activity in late-type MS stars;
For at least 40-50 solar analogues and a few hundreds
F5V-M0V stars/field, we expect to obtain:
• AR evolution time scales and contrast properties;
• preferential longitude for AR formation (if any);
• surface differential rotation (SDR);
• possible short-term activity cycles
Conclusions-II
SDR and turbulent diffusion of magnetized plasma as a function of
stellar global parameters and rotation rate will provide us with key
ingredients for dynamo models
Our results will have an impact also on the core program and other
additional science proposals in order to study, e.g.:
• the role of magnetic activity on transit detection and
transit shape;
• the perturbation of p-mode oscillations by magnetic activity;
• stellar rotation;
• microvariability on time scales from minutes to hours;
• the evolution of activity and rotation during the MS life
of the Sun
About the limitations of a spot modelling
based only on wide-band flux modulation
Light curve inversion is an inherently ill-posed problem, because of
the low information content of wide-band light curves on the
pattern of surface brightness
Maximum Entropy or Tikhonov regularizations can be
applied to reduce the impact of non-uniqueness and
instability:
• sound results for very active stars (only cool spots are needed; e.g.,
Lanza et al. 1998, A&A 332,541):
– spot longitudes in photometric and DI maps are comparable;
• for less active stars, the facular component must be included;
• it is difficult to introduce spots and faculae in MEM models
(however, work is in progress);
Comparison between MEM maps based on V-band light curve
fitting (left) and Doppler Imaging + light curve fitting (right) for
the epoch 1988.07 (HR 1099 K1 IV component star, pole-on view)
(Lanza et al., in progress)
(Vogt et al. 1999, ApJS 121, 547)
Note that the largest circle on the left map is the equator, while on the right map marks
latitude –30°; the radial ticks indicate the direction of the observer at the labelled phases
and, in the right panel, phases of spectroscopic observations
Dinamo
a-W
the a- dynamo
Rotation
+
Convection
Differential
Rotation
Poloidal
Field
B diffusion
a-effect
Reaction
Toroidal Field
intensification
Toroidal
Field
Regeneration of the poloidal field
Reaction
B diffusion
(Rodonò et al. 2004, AN 325, 483)