Report on research work

1.1       Information on the development of the research project

  • Overall scientific concept and goals:

This project is aimed at search and analysis of the effects of deep convection in the integral photometry of main sequence stars. The magnetic flux tubes, which form the observable solar active regions, have to traverse the entire convection zone before they reach the photosphere. According to the predictions of numerical modelling of this process as well as our solar studies (Arkhypov et al. 2011, 2012, 2013 and references therein), the large-scale convection cells above the tachocline could be imprinted in the surface magnetic field and affect the global distribution of active regions. The project included the analysis of stellar light curves and extraction from that of hidden information about the structure and dynamics of the surface activity pattern (i.e., starspots and faculae) of stars, as well as the interpretation and application of the obtained data. For this purpose, a set of most suitable for the analysis light curves of main sequence stars with the rotational periods 0.5<P<30 days, effective temperatures 3227<Teff<7171 K and clear starspot variability has been selected from the data archive of the orbital observatory Kepler.

 

  • Was there a change in research orientation between the start and the end of the project? If so, what form did the change take, what effect did it have on the work?

In addition to the originally planned work, the project scope has been expanded to analyze a larger data set (1998 stars were studied instead of “a few hundreds” foreseen). That enabled investigation of several additional related topics, such as the starspot diagnostics; diffusivity of magnetic elements in stellar photosheres; short-period activity cycles; and X-ray / EUV emissions of stars.  

1.2       Most important results and brief description of their significance (main points)

  • Contribution to the advancement of the field

The developed approaches, analysis methods and obtained results open a new way to study the stellar interior plasma motion, inaccessible yet for asteroseismology. In particular, the manifestation of turbulence is discovered at global scales (i.e., azimuthal numbers m=1,2 and 3). This super-large scale turbulence is an attribute of deep convection, because the known typical sub-photosheric convective cells (granules to supergranules) are much smaller (m>100) in accordance with a local height scale (Arkhypov et al. 2011, 2012, 2013, 2015a,b). The G-dwarfs KIC 7765135, 7985370 and 8429280 were studied in details to obtain the power spectra Wm of longitudinal distribution of their surface activity, corrected for integral photometry distortion (according to the method developed in sub-task 1a). The predicted quasi-Kolmogorov’s scaling Wm ∝ m -5/3±0.1 was found for the azimuthal numbers 1≤m≤3 (Arkhypov et al. 2016).

         Another prediction of the Kolmogorov’s theory of turbulence, confirmed by the project study, is the scaling index of the “size-lifetime” relation: b12≡[log(t2)-log(t1)]/[log(2)-log(1)]=-2/3, where t1 and t2 are the variability timescales of the most reliable first (m=1) and second (m=2) rotational harmonics of a light curve, respectively.  The b12-histograms, constructed for hundreds of stars with different rotation periods all have maxima at the predicted value b12=-2/3 (Fig. 8a, 13a,b in Arkhypov et al. 2016; Fig. 3 in Arkhypov et al. 2017b). Since the index b12 describes only the global (m=1 and 2) turbulence, it confirms the manifestation of deep-convection in the starspot emergences (Arkhypov et al. 2016, 2017a).

         The aforementioned results show an evidence of a super-large scale turbulent cascade in the stellar convection zone consistent with the prediction of turbulence theory. Such cascade originates from the global (m=1) turbulent vortices decaying into smaller and smaller sub-vortices. It has been found that the extrapolation of this cascade to the scale of laminar convection transforms the time scales t1 and t2 of harmonics into the laminar  timescales tlam1≈tlam2, which, as shown in Fig. 5 in Arkhypov et al. 2017b , appear as a proxy of the turnover time tMLTof the standard mixing length theory (MLT) (Arkhypov et al. 2015a, 2016, 2017b). This successful theory is based on the hypothesis of identity of all convection cells, which formally correspond to the laminar convection, and the discovered timescale proximity tlam1≈tlam2≈tMLT can be interpreted as an indirect detection of gigantic convection cells. The presence of the giant laminar convection in the Sun with a certain scale, decaying in a turbulent cascade, was confirmed also with our methods (Arkhypov et al. 2012, 2013). With the measured timescales tlam1 and tlam2 instead of the turnover time tMLT, one can obtain the classical relations between stellar activity level and the Rossby number P/tMLT (Arkhypov et al. 2016).

         The project study additionally opens the new perspectives for the investigation of starspots. It has been shown that the parameter b12 allows distinguishing between various mechanisms of the starspot variability. In particular, b12=-2/3 indicates the presence of deep convection (for the stars with moderate magnetism, when the typical starspot lifetime is shorter than the deep-convection timescale), whereas b12=-2 and b12<-2.3 appear a signature of the dominating diffusional or sub-diffusional decay of starspots, respectively (for the highly magnetized stars, when the long lifetime of starspots smooths and masks the modulation of the starspot dynamics caused by deep convection). The case of b12»-1 corresponds formally to a hypothetical (unconfirmed in our study) erosion of activity complexes by the stellar differential rotation. As a result of undertaken study, a diagnostic diagram (Fig. 1 in Arkhypov et al. 2017a) has been constructed, which indicates the regions of dominance of abovementioned mechanisms in the stellar P-Teff parameters frame. Using the b12-based approach, the diffusivity of the magnetic elements in stellar photosphere has been estimated (see Eq.(22) and Fig. 14 in Arkhypov et al. 2016) for the unprecedentedly broad interval of stellar effective temperatures from 3300 to 6600 K. Note, that hitherto the spot decay and the deep-convection effect (unknown before) were undistinguished in the starspot literature.

         The study of the short-period (<1000 days) activity cycles in 462 stars (Arkhypov et al. 2015b) appears an important achievement of the project. Hitherto such Rieger-like periodicities were found only in dozens of Kepler’s stars. As a result, we have found the unknown so far continuation of the inactive stars branch in the Saar-Brandenburg diagram (Saar & Brandenburg 1999), as shown in Fig. 16 in Arkhypov et al. 2015b, and the manifestation of a-quenching effect in the short-period activity cycle periods Pcyc (Arkhypov et al. 2015b).

         The average level of stellar activity has been studied with a proposed new activity index A12, which is the squared amplitude of the first (or fundamental, m=1) rotational harmonic of a light curve. The advantage of this index consists in its statistical proportionality to the starspot number (confirmed for the Sun) and suitability to the Kepler data. It has been shown, that the index A12 might be used as a proxy of the ratio RX between the stellar X-ray and the bolometric LX luminosities (Arkhypov et al. 2016, 2017c). As a result, the regression LX(P,Teff) was obtained to predict the average LX for the stars which have X-ray fluxes below the sensitivity thresholds of orbital observatories.  

 

  • Breaking of new scientific / scholarly ground

In summary, the project breaks the common belief on completely turbulent convection zones with unobservable at photosphere largest (i.e., deepest) convective motions. Our results rather support the classical MLT idea on the significance of standardized (laminar) convective cells at the bottom of the convection zone.

 

  • Most important hypotheses / research questions developed

This project raises a question on laminar component in turbulent convection zones of stars. This seems a new experimental input in a theory of magnetic dynamo which influences the whole range of the stellar activity phenomena including the starspot global dynamics, activity cycles; and X-ray / EUV emissions of stars. 

 

  • Development of new methods

An original method for processing and analysis of stellar light curves was developed to investigate the timescale of stochastic variations of the longitudinal distribution of starspots (Arkhypov et al. 2015a). In fact, this approach is a set of methodologic routines ranging from data pre-processing and preparing of the analyzed light-curves up to the calculation of variability timescales t1 and t2 of the most reliable first and second rotational harmonics, respectively, and their following up study. The new histogram and spectral-autocorrelation methods were developed for the estimating of periods Pcyc of short cycles of stellar activity, which usually are non-dominating in activity power spectrum on the background of long-period cycles. Each methodology was tested, modernized and fine-tuned. The developed algorithms and theirs modifications (Arkhypov et al. 2015b, 2016, 2017abc) can be used in future automatized surveys of stellar activity and deep mixing.

 

Arkhypov, O.V., Antonov, O.V., & Khodachenko, M.L. 2011, SoPh,270, 1-8

Arkhypov, O.V., Antonov, O.V., & Khodachenko, M.L. 2012, SoPh,278, 285

Arkhypov, O. V., Antonov, O. V., & Khodachenko, M. L. 2013, SoPh, 282, 39

Arkhypov, O. V., Khodachenko, M. L., Güdel, M., et al., 2015a, A&A, 576, A67

Arkhypov, O. V., Khodachenko, M. L., Güdel, M., et al., 2015b, ApJ, 807, 109

Arkhypov, O. V., Khodachenko, M. L., Güdel, M., et al., 2016, ApJ, 826, 35

Arkhypov, O. V., Khodachenko, M. L., Güdel, M., et al., 2017a, MNRAS, accepted

Arkhypov, O. V., Khodachenko, M. L., Güdel, M., et al., 2017b, A&A, submitted

Arkhypov, O. V., Khodachenko, M. L., et al., 2017c, MNRAS in preparation

Saar, S. H., & Brandenburg, A. 1999, ApJ, 524, 295

 

  • Relevance for other (related) areas of science (transdisciplinary issues).

The standard mixing length theory (MLT) describes the phenomenon of convectional mixing of material in various circumstances, from planetary interiors and atmospheres to stars and the interstellar medium. However, its applicability to the turbulent environments (e.g., in stars) is often questionable. Nevertheless, MLT has been empirically proven to give consistent results which made it a standard method in the stellar modeling. The project study sheds certain light on this. In course of the project, we have derived a method for measuring the turnover time in stellar convection vortexes. This is one of key parameters in the stellar physics, which has so far only been calculated theoretically or estimated semi-empirically using the MLT paradigm. Therefore, our results contribute a broad spectrum of related fields: modeling of stellar convection, activity and evolution.

         Another important result is the new experimental argumentation for the existence of undetectable (with direct measurements) gigantic convection cells in the Sun-like stars. Such convection is associated with the physical problem of laminar-turbulent transition, related to an old enigma of "active longitudes". Altogether this is relevant to the whole scope of solar-terrestrial interactions.

         The stellar activity, analysed in the project, is one of key factors in a wide spectrum of astrophysical problems, space weather, geophysics, astrobiology, and apparently medicine. In particular, signatures of the short cycles of the Sun are found in the geomagnetic activity (Singh and Badruddin, 2017), in variation of atmospheric electric potential gradient and neutron count rate (Silva and Lopes, 2017), and even in nuclear decay rate (Sturrock et al. 2011). Consequently, revealing and understanding of the analogous modulations of activity in other stars play the key role in understanding of this phenomenon in general, which is in its turn important for space weather prediction at solar and exasolar planets.

 

Silva, H. G., Lopes, I. 2017, Astrophysics and Space Science, 362, 44

Singh, Y. P., Badruddin. 2017, Planetary and Space Science, 138, 1

Sturrock, P.A., Fischbach, E., Jenkins, J.H. 2011, Solar Physics, 272, 1

 

1.3       Information on the execution of the project, use of available funds and (where appropriate) any changes to the original project plan relating to the following:

  • Duration: The project was prolonged (cost-neutral) for one more year to analyse a new (larger) stellar data set with regard to the starspot lifetime, diffusivity of magnetic elements in stellar photosheres, as well as X-ray emission of stars.
  • Use of personnel

Dr. Arkhypov O. (01.08.2013 – 31.07.2017) – the main co-worker, all tasks;

Dr. Zaquarashvili T. (01.08.2013 – 31.10.2013) – contribution to Task 1.

  • Major items of equipment purchased: -- NO
  • Other significant deviations.[1] -- NO

2.      Personnel development – Importance of the project for the research careers of those involved (including the project leader)

 

The project provided a nice opportunity for its team members (mainly Drs. Arkhypov O. and Khodachenko M.L.) to intensify international research collaboration links with international partners. During the project time Khodachenko, M.L. successfully passed the evaluation at the Austrian Academy of Sciences and got a permanent job position there, and Lammer, H. made his habilitation.

                

3.      Effects of the project beyond the scientific field

      • Brief comments on specific effects beyond the research field, including activities outside the sphere of academia.

              (A)    Besides of the research work for the project, its participants took part in the RTD consortia of several European FP7/H2020 projects:

     - IMPEx (http://impex-fp7.oeaw.ac.at Integrated Medium for Planetary Exploration)

- Europlanet 2020 RI (http://www.europlanet-2020-ri.eu European Planet. Science)  

- SOLSPANET (http://solspanet.eu/solspanet Solar & Space Weather Network)

     (B)    The investigations, performed within the project gave rise to several research directions, which will be continued (see III Attachements Sect 7.1). Investigation and probing of the stellar activity and XUV radiation with high precision photometry observations and the methods, developed within the project appear an important contribution for the exoplanetary studies.

4.      Other important aspects (examples)

  • Project-related participation in national and international conferences
  1. Khodachenko, M.L. Physics of exoplanetary systems, Evaluation talk at Austrian Academy of Sciences, Mar.19, 2014
  2. Arkhypov, O.V., and Khodachenko, M.L. 2014. On largest scale of magnetic flux emergence in the Sun and stars. 40th COSPAR Scientific Assembly. August 2014, in Moscow, Russia.
  3. Khodachenko, M.L. Invited review lecture: “Exoplanetary Magnetic Fields and Magnetospheres: Atmosphere Mass-loss and Magnetospheric Protection” on Phys. Colloquium at the Dept of Phys., Univ. of Warwick, UK, Oct. 2014
  4. Arkhypov, O.V., Khodachenko, M.L., et al., 2016. New results on stellar deep mixing and starspot dynamics from the Kepler photometry. The Astrophysics of Planetary Habitability. Patways to Habitability, 8-12 February 2016.
  5. Arkhypov, O.V., Khodachenko, M.L., Güdel, M., et al., 2016. Short-period cycles of stellar activity in Kepler photometry. The Astrophysics of Planetary Habitability. Patways to Habitabilit, 8-12 February 2016.
  6. Khodachenko, M.L., Exoplanets – frontiers of modern planetology, Invited lcture series on School of Modern Astrophysics (SOMA), at Moscow Inst. Of Phys. And Techn., Dolgoprudny, Russia, June-July, 2016
  7. Khodachenko, M. L.,Exoplanetary Magnetic Fields and Magnetospheres, Invited presentation on Physics seminar at Moscow State Univ., Feb 2017, Russia.
  8. Arkhypov, O.V., Khodachenko, M.L. Invited review: Probing of stellar activity with high precision photometry. FWF NFN, Pinkafeld, Austria, 16-17 May 2017.

 

  • Organisation of symposiums and conferences:

Drs. Lammer, H., Güdel M., and Khodachenko M.L. participated in SOC of “The Astrophysics of Planetary Habitability”, held 8-12 February 2016, Wien

  • Any other aspects: The project team members (Drs. Khodachenko M.L. and Arkhypov O.V.) served as referees in: Astron. & Astrophys.; Journal of Geophysical Research (JGR); Astrophys. Journ.; Solar Phys.; MNRAS.

         In 2017 Dr. Khodachenko M.L. served as ERC Advanced Grants remote reviewer, for the European Research Council, EC.

 

[1]     The decision as to what should be regarded as a “significant deviation” is the responsibility of the project leader. As a guideline, any deviation of more than 25% from the original financial plan or work schedule should be accounted for.