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

The Accepted AP: 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 (9)

1) INAF - Osservatorio Astrofisico di Catania, Italy2) Instituto de Astrofisica de Andalucia, CSIC, Granada, Spain3) European Southern Observatory, Santiago, Chile4) Institute of Astronomy, Cambridge, United Kingdom5) Dept. of Physics, Federal University of Rio Grande do Norte, Natal, Brazil6) Research and Science Support Dept. of ESA, ESTEC, Noordwijk, The Netherlands7) Max Planck Institut fur Astronomie, Heidelberg, Germany8) INAF - Osservatorio Astronomico “G. S. Vaiana”, Palermo, Italy9) Astrophysical Institute Potsdam, Potsdam, Germany10) Thuringer Landessternwarte Tautenburg, Germany11) Universidade de Sao Paulo, Brazil12) Konkoly Observatory, Budapest, Hungary13) Indian Institute of Astrophysics, Koramangala, Bangalore, India14) Institut d'Estudis Espacials de Catalunya, CSIC, Bellaterra, Spain15) Dept. of Physics and Astronomy, Università degli Studi di Catania, Italy

Stellar Variability and Microvariability

II. Spot Maps and Modelling

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.)

Three Co-ordinated Proposals for the Corot Additional Program

(AO-1)

The three proposals are:

• Based on COROT Exofield data;

I shall focus on the second of such proposals, which is dedicated to “Spot maps and modelling”

• 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

Scientific Motivation

Study of solar-like stellar activity in a sample of MS stars

It is characterized by: • spatial (brightness) inhomogeneities; • non-stationary time variable phenomena;• non-radiative heating of the outer atmospheres

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);

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 -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,…).

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 11-yr sunspot cycle, providing evidence for a migrating dynamo wave;

The turbulent diffusivity of magnetic field can be estimated from sunspot group lifetimes

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):

• 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 tothat 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):

: 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))

• AR formation: 8-10 days (B-C); • Rotational modulation: 25-30 days (C-D);• AR decay (facular component): 60 days (D-E)

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 (to account for long-term variations of the mean flux level)

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

The situation may be better for stars more active than the Sun (Messina et al. A&A in press)

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)

Active region longitudes

(Lanza, Bonomo, Rodonò, in progress)

(Lanza et al. 2003, A&A 403, 1135)

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)

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

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;

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)

Absolute values are model dependent, but the cycle period is well retrieved

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 rotationSpot 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. (2003, A&A 405, 1137), we can estimate:

• 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 timeFrom 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

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);

About the limitations of a spot modelling based only on wide-band

flux modulation

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

(Lanza et al., in progress) (Vogt et al. 1999, ApJS 121, 547)

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)

Dinamo -

(Rodonò et al. 2004, AN 325, 483)