Time evolution and rotation of starspots on CoRoT-2 from the modelling of transit photometry

CoRoT-2, the second planet-hosting star discovered by the CoRoT satellite, is a young and active star. A total of 77 transits were observed for this system over a period of 135 days. Small modulations detected in the optical light curve of the planetary transits are used to study the position, size, intensity, and temporal evolution of the photospheric spots on the surface of the star that are occulted by the planetary disk. We apply a spot model to these variations and create a spot map of the stellar surface of CoRoT-2 within the transit band for every transit. From these maps, we estimate the stellar rotation period and obtain the longitudes of the spots in a reference frame rotating with the star. Moreover, the spots temporal evolution is determined. This model achieves a spatial resolution of 2\circ. Mapping of 392 spots vs. longitude indicates the presence of a region free of spots, close to the equator, reminiscent of the coronal holes observed on the Sun during periods of maximum activity. With this interpretation, the stellar rotation period within the transit latitudes of -14.\circ 6 \pm 10 \circ is found to be 4.48 days. This rotation period is shorter than the 4.54 days as derived from the out-of-transit light modulation. Since the transit data samples a region close to the stellar equator, while the period determined from out-of-transit data reflects the average rotation of the star, this is taken as an indication of a latitudinal differential rotation of about 3% or 0.042 rad/d.Comment: 8 pages, 12 figure

Properties of starspots on CoRoT-2

As a planet eclipses its parent star, a dark spot on the surface of the star may be occulted, causing a detectable variation in the light curve. A total of 77 consecutive transit light curves of CoRoT-2 were observed with a high temporal resolution of 32 s, corresponding to an uninterrupted period of 134 days. By analyzing small intensity variations in the transit light curves, it was possible to detect and characterize spots at fixed positions (latitude and longitude) on the surface of the star. The model used simulates planetary transits and enables the inclusion of spots on the stellar surface with different sizes, intensities (i.e. temperatures), and positions. Fitting the data by this model, it is possible to infer the spots physical characteristics. The fits were either in spot longitude and radius, with a fixed intensity, or in spots longitude and intensity, for spots of constant size. Before the modeling of the spots were performed, the planetary radius relative to the star radius was estimated by fitting the deepest transit to minimize the effect of spots. A slightly larger (3%) radius, 0.172 Rstar, resulted instead of the previously reported 0.1667 Rstar . The fitting of the transits yield spots, or spot groups, with sizes of ranging from 0.2 to 0.7 planet radius, Rp, with a mean of (0.41 +/- 0.13) Rp (~100,000 km), resulting in a stellar area covered by spots within the transit latitudes of 10-20%. The intensity varied from 0.4 to 0.9 of the disk center intensity, Ic, with a mean of (0.60 +/- 0.19) Ic, which can be converted to temperature by assuming an effective temperature of 5625 K for the stellar photosphere, the spots temperature ranges mainly from 3600 to 5000 K. The results from the spot modeling are in agreement with those found for magnetic activity analysis from out of transit data of the same star.Comment: 7 pages, 11 figure

Litiumioniakkujen kierrätysteknologiat – kriittinen kirjallisuustutkimus

The purpose of this thesis is to offer a critical review of existing and emerging recycling technologies for lithium ion batteries (LiBs), based on a literature research. Additionally LiBs as sources of secondary raw materials are described, and the current status and possibilities of mechanical processing methods in LiBs recycling is studied. Five industrial and four emerging technologies are analysed in detail based mainly on information provided by scientific articles and patents. LiBs are used increasingly for providing energy to portable applications and electric mobility. The opera-tion principle of LiB is based on the layered active electrode materials that enable Li-ion insertion and transfer between the electrodes during discharge and charge. The performance and properties of LiB are especially dependent on the active cathode material. In present commercial LiB cells it consists of one of the five different compound types containing Co, Ni, Mn and Fe in different proportions, in addition to Li. Other materials in LiBs are graphite, Al and Cu foils, polymeric separator, electrolyte consisting of Li salt and organic materials, and the cell casing of stainless steel, Al or polymer. End-of-life batteries can have charge left, they can produce flammable and toxic gases, and they can contain flammable elemental Li – facts that have to be considered in recycling process. In the studied technologies, mechanical, pyrometallurgical and hydrometallurgical techniques are utilized in different combinations for the recovery of LiB materials. Usually pyrometallurgical or mechanical treatment starts the process, followed by hydrometallurgical recovery of the cathode materials. Pyrometallurgical treatment loses Al and Li in slag but has the capability of treating mixed feed. In mechanical treatment, more materials can be saved but extra attention is needed for safe handling of the batteries: the batteries are discharged prior to crushing, and/or comminution is carried out in protective medium. The crushed materials are separated with magnetic (Fe, SS) and density based materials (Al, Cu, polymers), and differing particle size of particular materials. Combination of several crushing and separation steps or thermal treatment can be used for improved detachment of active cathode material from the foil which is crucial for the success of the recovery of cathode materials in the following hydrometallurgical treatment. Only part of the once high-cost primary materials of the cell can be feasibly recycled to be used again. Co has been the driving force for recycling LiBs. Li is usually recovered in the end as a carbonate. For graphite and electrolyte recovery there exists methods, but the economic feasibility is questionable. Different organic materials have in general lost their value in the end-of-life of the cell. In some emerging technologies the goal is to produce cathode precursor material directly as an outcome of the mechanical and hydrometallurgical steps. This potentially saves more of the original cathode compound value, but requires also stricter processing conditions and control of the feed. Novel technologies consider the recovery other cathode compound materials than just Co, but are not able to treat the mixed cathode materials at the same time. Especially LiFePO4 is challenging material, because it has a low recycling value, and constitutes an impurity in the leaching process.Työssä analysoidaan teollisia ja orastavia litiumioniakkujen kierrätysteknologioita sekä mekaanisten prosessointimenetelmien asemaa ja mahdollisuuksia niiden osana. Analysoitavana on viisi teollista ja neljä orastavaa teknologiaa, ja tietolähteinä ovat pääasiassa tieteelliset artikkelit ja patentit. Litiumioniakkuja käytetään energialähteenä kannettavissa sovelluksissa ja sähkökäyttöisissä liikennevälineissä. Kennon toiminta perustuu elektrodimateriaaleihin, joiden kerroksittainen rakenne mahdollistaa litiumionien liikkumisen elektrodilta toiselle akkua purettaessa ja ladattaessa. Tämänhetkisissä kaupallisissa litiumioniakuissa aktiivinen katodimateriaali on yleensä jokin viidestä vaihtoehtoisesta siirtymämetalliyhdisteestä, jotka sisältävät litiumin lisäksi kobolttia, nikkeliä, mangaania tai rautaa eri yhdistelminä. Kenno sisältää myös grafiittia, kuparia ja alumiinia, litiumsuolasta ja orgaanisista yhdisteistä koostuvan elektrolyytin sekä polymeerierottimen elektrodien välissä. Kennokotelon materiaalina voi olla alumiini, ruostumaton teräs tai polymeeri. Kierrätysprosessissa on huomioitava, että kennoissa on useimmiten latausta jäljellä, ja anodille on käytön aikana voinut pelkistyä herkästi syttyvää alkuainelitiumia. Lisäksi kennoissa voi käsittelyn aikana muodostua herkästi syttyviä ja myrkyllisiä kaasuja. Tutkituissa kierrätysprosesseissa käytetään mekaanisten, pyrometallurgisten ja hydrometallurgisten tekniikoiden erilaisia yhdistelmiä. Katodimateriaalien talteenotto toteutetaan lähes aina hydrometallurgisella menetelmällä. Pyrometallurgian epäkohtana on, että alumiini ja litium menetetään kuonaan. Toisaalta pyrometallurgisen prosessin syötteenä voi olla laajempi materiaalien kirjo. Mekaanisessa prosessoinnissa suurempi osa materiaaleista voidaan ottaa talteen, mutta toisaalta akkujen turvallinen käsittely vaatii erityistä huomiota. Akut on purettava ennen murskausta, joka on lisäksi suoritettava suojakaasussa tai -liuoksessa. Murske voidaan jaotella eri materiaaleihin (rautapohjaiset materiaalit, alumiini, kupari, polymeerit) seulonnan sekä magneettisuuteen ja tiheyteen perustuvien menetelmien avulla. Useammilla murskaus- ja luokittelukerroilla tai lämpökäsittelyllä voidaan parantaa katodijauheen erottamista alumii-nista ja kuparista, mikä on tärkeää hydrometallurgisen liuotusprosessin onnistumiseksi. Vain osa alun perin arvokkaista kennon materiaaleista voidaan kannattavasti ottaa talteen. Erityisesti koboltti on ollut kannustin litiumioniakkujen kierrätykselle. Litium otetaan yleensä talteen karbonaattina. Grafiitin ja elektrolyytin talteenotolle on olemassa menetelmiä, mutta se ei ole taloudellisesti kannattavaa. Suurin osa orgaanisista materiaaleista on menettänyt arvonsa käytetyssä kennossa. Osassa nousevia teknologioita pyritään tuottamaan suoraan mekaanisen ja hydrometallurgisen käsittelyn tuloksena katodiyhdisteen esiastetta, kuten siirtymämetallioksidia. Näin menetellen säilytetään mahdollisesti enemmän alkuperäisen katodiyhdisteen arvosta, mutta haittapuolena on, että prosessointiolosuhteita ja syötteen koostumusta on vastaavasti kontrolloitava tarkemmin. Nousevat teknologiat pyrkivät pääsääntöisesti ottamaan talteen myös muita katodiyhdistemateriaaleja kuin koboltin, mutta ne eivät pysty käsittelemään erilaisia katodiyhdisteitä samalla kertaa. Haastavin katodimateriaali on litiumrautafosfaatti, jonka kierrätysarvo on alhainen ja jonka sisältämä rauta on epäpuhtaus koboltin, nikkelin ja mangaanin liuotusprosessissa

Dependence of stellar differential rotation on effective temperature and rotation: an analysis from starspot transit mapping

Stellar rotation is crucial for studying stellar evolution since it provides information about age, angular momentum transfer, and magnetic fields of stars. In the case of the Sun, due to its proximity, detailed observation of sunspots at various latitudes and longitudes allows the precise estimate of the solar rotation period and its differential rotation. Here, we present for the first time an analysis of stellar differential rotation using starspot transit mapping as a means of detecting differential shear in solar-type and M stars. The aim of this study is to investigate the relationship between rotational shear, $\Delta\Omega$, with both the star's effective temperature ($T_{\text{eff}}$) and average rotation period ($P_{\text{r}}$). We present differential rotation profiles derived from previously collected spot transit mapping data for 13 slowly rotating stars ($P_{\text{rot}} \geq 4.5$ days), with spectral types ranging from M to F, which were observed by the Kepler and CoRoT satellites. Our findings reveal a significant negative correlation between rotational shear and the mean period of stellar rotation (correlation coefficient of -0.77), which may be an indicator of stellar age. On the other hand, a weak correlation was observed between differential rotation and the effective temperature of the stars. Overall, the study provides valuable insights into the complex relationship between stellar parameters and differential rotation, which may enhance our understanding of stellar evolution and magnetic dynamos.Comment: 9 pages, 2 figure