Quasi-biennial oscillations (QBOs) are considered as a fundamental mode of solar magnetic activity at low latitudes ($\leq50^\circ$). However, the evolutionary aspect and the hemispheric distribution of solar QBOs at high latitudes ($\geq60^\circ$) are rarely studied. Here, a relatively novel time-frequency analysis technique, named the synchrosqueezed wavelet transform, is applied to extract the main components of the polar faculae in the northern and southern hemispheres for the time interval from August 1951 to December 1998. It is found as the following: (1) Apart from the 22-year Hale cycle, the 17-year extended activity cycle, and the 11-year Schwabe cycle, the QBOs have been estimated as a prominent timescale of solar magnetic activity at high latitudes; (2) the QBOs of the polar faculae are coherent in the two hemispheres, but the temporal (phase) and the spatial (amplitude) variations of solar QBOs occur unevenly on both hemispheres; and (3) for the 11-year period mode, the northern hemisphere begins three months earlier than that in the southern one. Moreover, the spatial and temporal distributions of the hemispheric QBOs differ from those of the 11-year Schwabe cycle mode in the two hemispheres. Our findings could be helpful to improve our knowledge on the physical origin of the spatial distribution of solar QBOs at high latitudes, and could also provide more constraints on solar dynamo models introduced to characterize the different components of the solar magnetic activity cycle.
We studied new simultaneous observations of the flux variations of the photospheric and chromospheric emissions of 33 solar-type stars and Sun during the HK-project that were conducted over the past 20 years. In addition to the known cyclic chromospheric emission variations of stars at the 11-year time scale, which were discovered at the Mount Wilson Observatory, we found a recurrences that are similar to the quasi-biennial variations of solar radiation. The results of calculations of the radiation fluxes variations periods of stars at the quasi-biennial scale are given.
Quasi-biennial oscillation (QBO) of solar magnetic activities is intrinsic to dynamo mechanism, but still far from fully understood. In this work, the phase and amplitude asymmetry of solar QBO of Halpha flare activity in the northern and southern hemispheres is studied by the ensemble empirical mode decomposition, the cross-correlation analysis, and the wavelet transform technique. The following results are found: (1) solar QBO of Halpha flare index in the two hemispheres has a complicated phase relationship, but does not show any systematic regularity; (2) the solar cycle mode of solar Halph…
Spatio-temporal analysis of helioseismic quasi-biennial oscillations
Centre for Fusion, Space and Astrophysics, Department of Physics, University of Warwick（华威大学物理与天体物理融合空间与天文研究中心）；Engineering Research Institute “Ventspils International Radio Astronomy Centre (VIRAC)”, Ventspils University of Applied Sciences（文茨皮尔斯应用科学大学文茨皮尔斯国际射电天文中心（VIRAC）工程研究所）
In this work, we apply multichannel singular spectrum analysis (MSSA), a data-adaptive, multivariate, non-parametric technique that simultaneously exploits the spatial and temporal correlations of the input data to extract common modes of variability, to investigate the intermediate quasi-periodicities of the Fe XIV green coronal emission line at 530.3 nm for the period between 1944 and 2008. Our analysis reveals several significant mid-term periodicities in a range from about one to four years that are consistent with the so-called quasi-biennial oscillations (QBOs), which have been detected …
We investigate the spherical harmonic degree (l) dependence of the "seismic" quasi-biennial oscillation (QBO) observed in low-degree solar p-mode frequencies, using Sun-as-a-star Birmingham Solar Oscillations Network (BiSON) data. The amplitude of the seismic QBO is modulated by the 11-yr solar cycle, with the amplitude of the signal being largest at solar maximum. The amplitude of the signal is noticeably larger for the l=2 and 3 modes than for the l=0 and 1 modes. The seismic QBO shows some frequency dependence but this dependence is not as strong as observed in the 11-yr solar cycle. These …
We looked for signatures of Quasi-Biennial Periodicity (QBP) over different phases of solar cycle by means of acoustic modes of oscillation. Low-degree p-mode frequencies are shown to be sensitive to changes in magnetic activity due to the global dynamo. Recently have been reported evidences in favor of two-year variations in p-mode frequencies. Long high-quality helioseismic data are provided by BiSON (Birmingham Solar Oscillation Network), GONG (Global Oscillation Network Group), GOLF (Global Oscillation at Low Frequency) and VIRGO (Variability of Solar IRradiance and Gravity Oscillation) in…
Solar quasi-biennial oscillations with period range 0.6 to 4 years, are prominent in records of solar activity. Here we show that the 1.6 year quasi-biennial oscillation in solar activity has the exceptional feature of phase inversion between each solar cycle in the sequence of four solar cycles, 20 to 23. The hypothesis advanced is that this feature is due to synchronicity between solar activity and planetary alignment. An index of alignment between Earth and Mercury, Venus, Jupiter and Saturn is shown to have dominant peaks of alignment separated by 1.6 years in each solar cycle with, howeve…
The cyclicity of 33 solar-type stars that are similar to 11-year and to the quasi-biennial variations of solar radiation have studied. Our calculation were based on new simultaneous observations of the flux variations of the photospheric and chromospheric emissions of 33 solar-type stars and the Sun during the HK project that were conducted over the last 20 years. The method of Fast Fourier Transform was applied to these observed data. In addition to the known cyclic chromospheric emission variations of stars at the 11-year time scale, which were discovered at the Mount Wilson Observatory, we …
Quasi-biennial oscillations (QBO) are frequently observed in the solar activity indices. However, no clear physical mechanism for the observed variations has been suggested so far. Here we study the stability of magnetic Rossby waves in the solar tachocline using the shallow water magnetohydrodynamic approximation. Our analysis shows that the combination of typical differential rotation and a toroidal magnetic field with a strength > 10^5 G triggers the instability of the m=1 magnetic Rossby wave harmonic with a period of 2 years. This harmonic is antisymmetric with respect to the equator and …
Manifestations of the solar magnetic activity through periodicities of about 11 and 2 years are now clearly seen in all solar activity indices.In this paper, we add information about the mechanism driving the 2 year period by studying the time and latitudinal properties of acoustic modes that are sensitive probes of the subsurface layers. We use almost 17 years of high quality resolved data provided by the Global Oscillation Network Group (GONG) to investigate the solar cycle changes in p-mode frequencies for spherical degrees l from 0 to 120 and 1.6 mHz < nu < 3.5 mHz. For both periodic compo…
This study aims to provide further evidence for the potential influence of the global solar magnetic field on localised chromospheric jets, the macrospicules (MS). To find a connection between the long-term variation of properties of MS and other solar activity proxies, including e.g. the temporal variation of the frequency shift of solar global oscillations, sunspot area, etc., a database overarching seven years of observations was built up. This database contains 362 MS, based on observations at the 30.4 nm of the Atmospheric Imaging Assembly (AIA) on-board the Solar Dynamics Observatory (SD…
Contex: Solar magnetic activity exhibits variations with periods between 1.5--4 years, the so-called quasi-biennial oscillations (QBOs), in addition to the well-known 11-year Schwabe cycles. Solar dynamo is thought to be the responsible mechanism for generation of the QBOs. Aims: In this work, we analyse sunspot areas to investigate the spatial and temporal behaviour of the QBO signal and study the responsible physical mechanisms using simulations from fully nonlinear mean-field flux-transport dynamos. Methods: We investigated the behaviour of the QBOs in the sunspot area data in full disk, an…
We investigated the solar cycle dependency on the presence and periodicity of the Quasi-Biennial Oscillation (QBO). Using helioseismic techniques, we used solar oscillation frequencies from the Global Oscillations Network Group (GONG), Michelson Doppler Imager (MDI) and Helioseismic & Magnetic Imager (HMI) in the intermediate-degree range to investigate the frequency shifts over Cycles 23 and 24. We also examined two solar activity proxies, the F10.7 index and the MgII index, for the last four solar cycles to study the associated QBO. The analyses were performed using Empirical Mode Decomposit…
We study and compare characteristics of sunspot group latitude distribution in two catalogs: the extended Greenwich (1874--2014) and Schwabe ones (1825--1867). We demonstrate that both datasets reveal similar links between latitude and amplitude characteristics of the 11-year cycle: the latitude dispersion correlates with the current activity and the mean latitude of sunspots in the cycle's maximum is proportional to its amplitude, It agrees with conclusions that we made in previous papers for the Greenwich catalog. We show that the latitude properties of sunspot distribution are much more sta…
Quasi-biennial oscillation (QBO) is a well-known quasi-periodical variation with characteristic time 0.5-4 years in different solar, heliospheric and cosmic ray characteristics. In this paper a hypothesis is checked on the causes of the apparent lack of correlation between solar and heliospheric QBOs, then the possible mechanisms of QBO in the GCR intensity are discussed as well as the idea of the same nature of the step-like changes and Gnevyshev Gap effects in the GCR intensity. Our main conclusions are as follows: 1) In the first approximation the hypothesis is justified that the change in …
Two important sources of information about sunspots in the Maunder minimum are the Spörer catalog and observations of the Paris observatory, which cover in total the last quarter of the 17th and the first two decades of the 18th century. These data, in particular, contain information about sunspot latitudes. As we showed in previous papers, dispersions of sunspot latitude distributions are tightly related to sunspot indices, so we can estimate the level of solar activity in this epoch by a method which is not based on direct calculation of sunspots and is weakly affected by loss of observation…
We applied the method of continuous wavelet-transform to high-quality time-frequency analysis to the sets of observations of relative sunspot numbers. Wavelet analysis of these data reveals the following pattern: at the same time there are several activity cycles whose periods vary widely from the quasi biennial up to the centennial period. These relatively low-frequency periodic variations of the solar activity gradually change the values of periods of different cycles in time. This phenomenon can be observed in every cycle of activity.
The activity of the Sun as a result of cyclic changes of the global magnetic field is studied. As a consequence of the analysis of magnetic activity of solar-type stars the following power dependencies were found: the dependence between the rotation periods and the effective temperatures, the dependence between the duration of the "11-year" cycles of activity and the effective temperatures, and the dependence between the duration of quasi-biennial cycles and the effective temperatures. It is shown that the physical nature of these dependencies associated with the observed properties of solar-t…
The Ca-K spectroheliograms obtained at the Kodaikanal observatory (KO) are used to generate a uniform time series using the equal contrast technique (ECT) to study the long and short-term variation in the solar chromosphere. The percentage of plage, Enhanced network (EN), Active network (AN), and Quiet network (QN) area at various latitudes is compared with the activity at 35$^{\circ}$ latitude and also with the sunspot number for the period of 1907 -- 1984. The values of phase differences indicate that the activity begins at $\sim$45$^{\circ}$ latitude and shift progressively to the lower lat…
We applied the method of continuous wavelet-transform to the time-frequency analysis to the sets of observations of relative sunspot numbers, sunspot areas and to 6 Mount Wilson HK-project stars with well-defined magnetic cycles. Wavelet analysis of these data reveals the following pattern: at the same time there are several activity cycles whose periods vary widely from the quasi-biennial up to the centennial period for the Sun and vary significant during observations time of the HK-project stars. These relatively low-frequency periodic variations of the solar and stellar activity gradually c…
We present a long-term study of the secondary star in the cataclysmic variable AE~Aqr, using Roche tomography to indirectly image starspots on the stellar surface spanning 8~years of observations. The 7 maps show an abundance of spot features at both high and low latitudes. We find that all maps have at least one large high-latitude spot region, and we discuss its complex evolution between maps, as well as its compatibility with current dynamo theories. Furthermore, we see the apparent growth in fractional spot coverage, $f_{\mathrm{s}}$, around $45^{\circ}$~latitude over the duration of obser…
We have analysed the Ca-K images obtained at Kodaikanal Observatory as a function of latitude and time for the period of 1913 - 2004 covering the Solar Cycle 15 to 23. We have classified the chromospheric activity into plage, Enhanced Network (EN), Active Network (AN), and Quiet Network (QN) areas to differentiate between large strong active and small weak active regions. The strong active regions represent toroidal and weak active regions poloidal component of the magnetic field. We find that plages areas mostly up to 50 deg latitude belt vary with about 11-year Solar Cycle. We also find that…
Studies on the periodic variation and the phase relationship between different solar activity indicators are useful for understanding the long-term evolution of solar activity cycle. Here we report the statistical analysis of grouped solar flare (GSF) and sunspot number (SN) during the time interval from January 1965 to March 2009. We find that, 1) the significant periodicities of both GSF and SN are related to the differential rotation periodicity, the quasi-biennial oscillation (QBO), and the eleven-year Schwabe cycle (ESC), but the specific values are not absolutely identical; 2) the ESC si…
We present a new method for determining the location of active bands of latitude on solar-type stars, which uses stellar-cycle-induced frequency shifts of detectable solar-like oscillations. When near-surface activity is distributed in a non-homogeneous manner, oscillation modes of different angular degree and azimuthal order will have their frequencies shifted by different amounts. We use this simple concept, coupled to a model for the spatial distribution of the near-surface activity, to develop two methods that use the frequency shifts to infer minimum and maximum latitudes for the active b…
Context. The study of young solar type stars is fundamental for a better understanding of the magnetic activity of the Sun. As a planet in transit crosses in front of its host star, a darkspot on the stellar surface may be occulted, causing a detectable variation in the light curve. Kepler-63 is a young solar-like star withan age of only 210 Myr that exhibit photometric variations compatible with spot signatures. Since its orbiting planet is in an almostpolar orbit, different latitudes of the star can be probed by the method of spot transit mapping. Methods. A total of 150 transits of Kepler-6…
We present observational signatures of solar cycle 25 onset. Those signatures are visibly following a migratory path from high to low latitudes. They had starting points that are asymmetrically offset in each hemisphere at times that are 21-22 years after the corresponding, same polarity, activity bands of solar cycle 23 started their migration. Those bands define the so-called "extended solar cycle." The four magnetic bands currently present in the system are approaching a mutually cancelling configuration, and solar minimum conditions are imminent. Further, using a tuned analysis of the dail…
We study the variability of solar activity using new photospheric proxies originally developed for the analysis of stellar magnetism with the CoRoT and Kepler photometric observations. These proxies are obtained by tracking the temporal modulations in the observations associated to the spots and magnetic features as the Sun rotates. We analyze here 21 years, spanning solar cycles 23 and 24, of the observations collected by the space-based photometric VIRGO and radial velocity GOLF instruments on board the SoHO satellite. The photospheric activity proxy Sph is then calculated for each of the th…
A solar-type dynamo model in a spherical shell is developed with allowance for random dependence of the poloidal field generation mechanism on time and latitude. The model shows repeatable epochs of strongly decreased amplitude of magnetic cycles similar to the Maunder minimum of solar activity. Random dependence of dynamo-parameters on latitude brakes the equatorial symmetry of generated fields. The model shows the correlation of the occurrence of grand minima with deviations in the dynamo-field from dipolar parity. An increased north-south asymmetry of magnetic activity can, therefore, be an…
The Solar Cycle is reviewed. The 11-year cycle of solar activity is characterized by the rise and fall in the numbers and surface area of sunspots. A number of other solar activity indicators also vary in association with the sunspots including; the 10.7cm radio flux, the total solar irradiance, the magnetic field, flares and coronal mass ejections, geomagnetic activity, galactic cosmic ray fluxes, and radioisotopes in tree rings and ice cores. Individual solar cycles are characterized by their maxima and minima, cycle periods and amplitudes, cycle shape, the equatorward drift of the active la…
The most important parameter in the coupling between solar wind and geomagnetic activity is the $B_z$-component of the interplanetary magnetic field (IMF). However, recent studies have shown that IMF $B_y$ is an additional, independent driver of geomagnetic activity. We use here local geomagnetic indices from a large network of magnetic stations to study how IMF $B_y$ affects geomagnetic activity at different latitudes for all solar wind and, separately during coronal mass ejections (CMEs). We show that geomagnetic activity, for all solar wind, is 20% stronger for $B_y>0$ than for $B_y<0$ at s…
We report on simulations of turbulent, rotating, stratified, magnetohydrodynamic convection in spherical wedge geometry. An initially small-scale, random, weak-amplitude magnetic field is amplified by several orders of magnitude in the course of the simulation to form oscillatory large-scale fields in the saturated state of the dynamo. The differential rotation is solar-like (fast equator), but neither coherent meridional poleward circulation nor near-surface shear layer develop in these runs. In addition to a poleward branch of magnetic activity beyond 50 degrees latitude, we find for the fir…
The results of determinations of the azimuthal and meridional velocities by time-distance helioseismology from Helioseismic and Magnetic Imager (HMI) onboard Solar Dynamics Observatory (SDO) from May 2010 to September 2020 at latitudes from -60° to +60° and depths to about 19 Mm below the photosphere are used to analyze spatiotemporal variations of the solar differential rotation and meridional circulation. The pattern of torsional oscillations, or latitudinal belts of alternating `fast' and `slow' zonal flows migrating from high latitudes towards the equator, is found to extend in the time--l…
The solar cycle onset at mid-latitudes, the slow down of the sunspot drift toward the equator, the tail-like attachment and the overlap of successive cycles at the time of activity minimum are delicate issues in $αΩ$ dynamo wave and flux transport dynamo models. Very different parameter values produce similar results, making it difficult to understand the origin of these solar cycle properties. We use GONG helioseismic data to investigate the progression of the solar cycle as observed in intermediate-degree global $p$-mode frequency shifts at different latitudes and subsurface layers, from the…
The Sun is a variable star whose magnetic activity and total irradiance vary on a timescale of approximately 11 years. The current activity minimum has attracted considerable interest because of its unusual duration and depth. This raises the question: what might be happening beneath the surface where the magnetic activity ultimately originates? The surface activity can be linked to the conditions in the solar interior by the observation and analysis of the frequencies of the Sun's natural seismic modes of oscillation - the p modes. These seismic frequencies respond to changes in activity and …
The combined Greenwich and Solar Optical Observing Network (SOON) sunspot group data during 1874-2013 are analyzed and studied the relatively long-term variations in the annual sums of the areas of sunspot groups in 0-10 deg, 10-20 deg, and 20-30 deg latitude intervals of the Sun's northern and southern hemispheres. The variations in the corresponding north-south differences are also studied. Long periodicities in these parameters are determined from the fast Fourier transform (FFT), maximum entropy method (MEM), and Morlet wavelet analysis. It is found that in the difference between the sums …
For the period of 1997-2006, coronal holes detected in the SOHO/EIT 195 $Å$ full disk calibrated images are used to compute the rotation rates of high latitude and near polar coronal holes and, their latitudinal variation is investigated. We find that, for different latitude zones between $80^{o}$ north and $75^{o}$ south, for all their area, the number of days observed on the solar disk, and their latitudes, coronal holes rotate rigidly. Estimated magnitudes of sidereal rotation rate of the coronal holes are: $13.051 \pm 0.206$ deg/day for the equator, $12.993 \pm 0.064$ deg/day in the region…
The Sun is a variable star whose magnetic activity varies most perceptibly on a timescale of approximately 11 years. However, significant variation is also observed on much shorter timescales. We observe a quasi-biennial (2 year) signal in the natural oscillation frequencies of the Sun. The oscillation frequencies are sensitive probes of the solar interior and so by studying them we can gain information about conditions beneath the solar surface. Our results point strongly to the 2 year signal being distinct and separate from, but nevertheless susceptible to the influence of, the main 11 year …
A mission to view the solar poles from high helio-latitudes (above 60$^\circ$) will build on the experience of Solar Orbiter as well as a long heritage of successful solar missions and instrumentation (e.g. SOHO \cite{SOHO}, STEREO \cite{stereo}, Hinode \cite{Hinode}, SDO \cite{SDO}), but will focus for the first time on the solar poles, enabling scientific investigations that cannot be done by any other mission. One of the major mysteries of the Sun is the solar cycle. The activity cycle of the Sun drives the structure and behaviour of the heliosphere and is, of course, the driver of space we…
The ongoing 11-year cycle of solar activity is considerably less vigorous than the three cycles before. It was preceded by a very deep activity minimum with a low polar magnetic flux, the source of the toroidal field responsible for solar magnetic activity in the subsequent cycle. Simulation of the evolution of the solar surface field shows that the weak polar fields and thus the weakness of the present cycle 24 are mainly caused by a number of bigger bipolar regions emerging at low latitudes with a `wrong' (i.e., opposite to the majority for this cycle) orientation of their magnetic polaritie…
Based on the extended Greenwich-NOAA/USAF catalogue of sunspot groups it is demonstrated that the parameters describing the latitudinal width of the sunspot generating zone (SGZ) are closely related to the current level of solar activity, and the growth of the activity leads to the expansion of SGZ. The ratio of the sunspot number to the width of SGZ shows saturation at a certain level of the sunspot number, and above this level the increase of the activity takes place mostly due to the expansion of SGZ. It is shown that the mean latitudes of sunspots can be reconstructed from the amplitudes o…
During the solar magnetic activity cycle the emergence latitudes of sunspots change, leading to the well-known butterfly diagram. This phenomenon is poorly understood for other stars as starspot latitudes are generally unknown. The related changes in starspot rotation rates caused by latitudinal differential rotation can however be measured. Using the set of 3093 Kepler stars with activity cycles identified by Reinhold et al. (2017), we aim to study the temporal change in starspot rotation rates over magnetic activity cycles, and how this relates to the activity level, mean rotation rate, and …
The Split Janus-faced Sun: Magnetic Rhythm and Duality in the Solar Cycle
Yunnan Observatories, Chinese Academy of Sciences（中国科学院云南天文台）；University of Chinese Academy of Sciences（中国科学院大学）；Yunnan Key Laboratory of Solar Physics and Space Science（云南省太阳物理与空间科学重点实验室）；Key Laboratory of Solar Activity, National Astronomical Observatories, CAS（中国科学院国家天文台太阳活动重点实验室）
Solar activity has significantly changed over the last two Schwabe cycles. After a long and deep minimum at the end of Cycle 23, the weaker activity of Cycle 24 contrasts with the previous cycles. In this work, the response of the solar acoustic oscillations to solar activity is used in order to provide insights on the structural and magnetic changes in the sub-surface layers of the Sun during this on-going unusual period of low activity. We analyze 18 years of continuous observations of the solar acoustic oscillations collected by the Sun-as-a-star GOLF instrument onboard the SoHO spacecraft.…
We studied the effect of the perturbation of the meridional flow in the activity belts detected by local helioseismology on the development and strength of the surface magnetic field at the polar caps. We carried out simulations of synthetic solar cycles with a flux transport model, which follows the cyclic evolution of the surface field determined by flux emergence and advective transport by near-surface flows. In each hemisphere, an axisymmetric band of latitudinal flows converging towards the central latitude of the activity belt was superposed onto the background poleward meridional flow. …
Using a time series of high-resolution spectra and high-quality multi-colour photometry, we reconstruct surface maps of the primary component of the RS CVn type rapidly rotating eclipsing binary, SV Cam (F9V + K4V). We measure a mass ratio, q, of 0.641(2) using our highest quality spectra and obtain surface brightness maps of the primary component, which exhibit predominantly high-latitude spots located between 60-70-degree latitudes with a mean filling factor of about 35%. This is also indicated by the R-band light curve inversion, subjected to rigourous numerical tests. The spectral subtract…
The frequencies of the solar acoustic oscillations vary over the activity cycle. The variations in other activity proxies are found to be well correlated with the variations in the acoustic frequencies. However, each proxy has a slightly different time behaviour. Our goal is to characterize the differences between the time behaviour of the frequency shifts and of two other activity proxies, namely, the area covered by sunspots and the 10.7cm flux. We define a new observable that is particularly sensitive to the short-term frequency variations. We then compare the observable when computed from …
We present observations of the extended solar cycle activity in white-light coronagraphs, and compare them with the more familiar features seen in the Fe XIV green-line corona. We show that the coronal activity zones seen in the emission corona can be tracked high into the corona. The peak latitude of the activity, which occurs near solar maximum, is found to be very similar at all heights. But we find that the equatorward drift of the activity zones is faster at greater heights, and that during the declining phase of the solar cycle, the lower branch of activity (that associated with the curr…
Numerous analyses suggest the existence of various quasi-periodicities in solar activity. The power spectrum of solar activity recorded in sunspot data is dominated by the $\sim$11-year quasi-periodicity, known as the Schwabe cycle. In the mid-term range (1 month -- 11 years) a pronounced variability known as a quasi-biennial oscillation (QBO) is widely discussed. In the shorter time scale a pronounced peak, corresponding to the synodic solar rotation period ($\sim$ 27 days) is observed. Here we revisited the mid-term solar variability in terms of statistical dynamic of fully turbulent systems…
Using data of fast-rotating active dwarf stars in the Kepler database, we perform time-frequency analysis of the light curves in order to search for signs of activity cycles. We use the phenomenon that the active region latitudes vary with the cycle (like the solar butterfly diagram), which causes the observed rotation period to change as a consequence of differential rotation. We find cycles in 8 cases of the 39 promising targets with periods between of 300-900 days.
