X-ray activity cycle on the active ultra-fast rotator AB Dor A? Implication of correlated coronal and photometric variability
aa r X i v : . [ a s t r o - ph . S R ] N ov Astronomy&Astrophysicsmanuscript no. lalitha c (cid:13)
ESO 2018August 7, 2018
X-ray activity cycle on the active ultra-fast rotator AB Dor A?
Implication of correlated coronal and photometric variability
S. Lalitha and J. H. M. M. Schmitt
Hamburger Sternwarte, University of Hamburg, Gojenbergsweg 112, 21029 Hamburg, Germanye-mail: [email protected]
Received XXXX; accepted XXXX
ABSTRACT
Context.
Although chromospheric activity cycles have been studied in a larger number of late-type stars for quite some time, verylittle is known about coronal activity-cycles in other stars and their similarities or dissimilarities with the solar activity cycle.
Aims.
While it is usually assumed that cyclic activity is present only in stars of low to moderate activity, we investigate whether theultra-fast rotator AB Dor, a K dwarf exhibiting signs of substantial magnetic activity in essentially all wavelength bands, exhibits anX-ray activity cycle in analogy to its photospheric activity cycle of about 17 years and possible correlations between these bands.
Methods.
We analysed the combined optical photometric data of AB Dor A, which span ∼
35 years. Additionally, we used ROSATand
XMM-Newton
X-ray observations of AB Dor A to study the long-term evolution of magnetic activity in this active K dwarf overnearly three decades and searched for X-ray activity cycles and related photometric brightness changes.
Results.
AB Dor A exhibits photometric brightness variations ranging between 6 . < V mag ≤ .
15 while the X-ray luminositiesrange between 29 . < log L X [ erg / s ] ≤ . XMM-Newton observations a kind of basal state is attained very often. This basal state probably varies with the photosphericactivity-cycle of AB Dor A which has a period of ∼
17 years, but, the X-ray variability amounts at most to a factor of ∼
2, which is,much lower than the typical cycle amplitudes found on the Sun.
Key words. stars: activity – stars: coronae – stars: late-type – stars: individual: AB Dor
1. Introduction
One of the key characteristics of the Sun is its 11-year activitycycle, which was originally discovered from the periodic varia-tion in the observed sunspot numbers (Schwabe 1844). However,the solar cycle also manifests itself in many other activity indica-tors such as the solar 10.7 cm radio emission, its chromosphericCa ii emission, and its coronal X-ray emission (Gnevyshev 1967;Hathaway 2010). Ever since Hale (1908) discovered strong mag-netic fields in sunspots, the magnetic character of solar activityand its cyclic variations has been beyond dispute. The cycle vari-ations in the solar corona are far more pronounced than thoseobserved in the photosphere, and with the advent of space-basedastronomy vast amounts of solar X-ray data have been collected,which allow a better understanding of the evolution of coronalplasma temperature, emission measure, and structure over thesolar cycle (Orlando et al. 2000). As expected, the solar coronahas a distinctly di ff erent appearance during activity minimumthan encountered at activity maximum. The solar X-ray fluxvaries during a cycle by typically a factor of ∼
200 in the energyrange of 0.6-1.5 keV (Kreplin 1970), while Stern et al. (2003)computed the solar soft X-ray irradiance variations as measuredby the
Yohkoh satellite in the 0.5-4 keV energy range and founda maximum- to minimum- ratio of ∼
30. Tobiska (1994) esti-mated a variation of a factor of ∼
10 in the softer energy rangebetween 0.25-0.4 keV as the solar activity cycle progresses. Thecause for these substantial flux variations is the absence of largeactive regions in the solar corona during its activity minimum,which make it appear much fainter than the solar corona during
Send o ff print requests to : S. Lalitha the activity maximum (Golub 1980). However, the amplitude ofthese variations sensitively depends on the energy range consid-ered and becomes much smaller at softer energies. For example,Ayres (1997) and Ayres et al. (2008) argued that through the 0.1-2.4 keV ROSAT pass band, the Sun was expected to show varia-tions between the minimum and maximum flux of a factor of 5-10. Peres et al. (2000) estimated the X-ray brightness of the Sunduring activity maximum and minimum to be log L X = / sand log L X = / s, respectively, in the ROSAT 0.1-2.4 keVenergy band, which would mean a variation of order of magni-tude variation in the ROSAT band. Their results were supportedby the studies of Orlando et al. (2000) and Judge et al. (2003),who also estimated variations of about a factor of ∼
10 in thesolar coronal X-ray emission throughout the solar cycle.The question then immediately arises whether other late-type stars also show such a solar-like cyclic variability in theirmagnetic activity properties (Vaughan et al. 1978; Wilson 1978).Within the context of the Mt. Wilson HK program the long-termvariability of stellar chromospheric activity (as observed in theCa II emission cores) in a large sample of late-type stars wassystematically studied over several decades and the cyclic activ-ity of a larger number of stars in the solar neighbourhood wasestablished (Baliunas et al. 1995). Specifically, Baliunas et al.(1998) found that about 60% of the stars of the Mt. Wilson ob-servatory survey exhibited periodic and cyclic variations, andfurthermore, Lockwood et al. (2004, 2007) found evidence thatthe photospheric and chromospheric activity cycle are related.Baliunas et al. (1995) employed the same technique of studyingstellar activity to also monitor the solar activity-cycle in inte-grated light and showed that the so-called S-index of the Sun
1. Lalitha et al.: X-ray activity cycle on the active ultra-fast rotator AB Dor A? varies between 0.16 and 0.22 between its activity minima andmaxima; in fact, the Sun shows one of the most regular cycles inthe whole stellar sample presented by Baliunas et al. (1998).A related question is whether the stars with di ff erent cyclicproperties in their Ca II emission show a di ff erent behaviour withrespect to their coronal emission. Hempelmann et al. (1996)compared soft X-ray fluxes with Ca emission in a sample oflate-type stars and showed that the stars with cyclic variationsin their calcium flux tend to show less X-ray activity than starswith irregular variability in their Ca II emission. Additionally,X-ray faint stars tend to show flat activity curves or low levelsof short-term variability (see Wright et al. 2010 and referencestherein). On the other hand, X-ray bright, active stars are be-lieved to have no long-term cycles; instead, they are thought toexhibit an irregular variation in their X-ray luminosity (Stern1998). Currently, only fewer than handful of stars have beenfound to have long-term X-ray cycles (cf. Fig.8). With ROSAT,the monitoring of the visual binary 61 Cyg began that subse-quently was continued with XMM-Newton (Hempelmann et al.2006). Four more stars, which are the α Cen system, HD 81809,and τ Boo, were also monitored by XMM-Newton (Favata et al.2004, 2008; Robrade et al. 2007; Ayres 2009; Robrade et al.2012; Poppenhaeger et al. 2012) for possible cyclic variations.Favata et al. (2004) detected a pronounced cycle of 8.2 years anda clear evidence for large-amplitude X-ray variability in phasewith the chromospheric activity cycle for HD 81089. For 61Cyg A, Robrade et al. (2012) found a regular coronal activitycycle in phase with its 7.3 yr chromospheric cycle, whereas noevidence of a clear coronal cycle for 61 Cyg B could be pro-duced. Furthermore, these authors demonstrated that the two α Cen stars exhibit significant long-term X-ray variability, with α Cen A showing a cyclic variability over a period of 12-15years, while the α Cen B data suggest an X-ray cycle of a pe-riod of 8-9 years; the amplitudes of the variability for α Cen Aand B were estimated to be an order of magnitude and about afactor six to eight, respectively. In addition, Robrade and col-laborators also concluded that the coronal activity cycles are acommon phenomenon in older, slowly rotating G and K stars.It is worthwhile noting that most of these stars were moder-ately or low active. However, recently Sanz-Forcada et al. (2013)showed an X-ray cycle of ∼ ι Hor, demonstrating that short cycles in Ca II also have anX-ray equivalent. On the other hand, Poppenhaeger et al. (2012)studied the activity cycle associated with τ Boo, a moderatelyactive F-star displaying a magnetic cycle of ∼
2. Our target star
AB Dor is a quadruple system consisting of the componentsAB Dor A, AB Dor Ba, AB Dor Bb, and AB Dor C. AB Dor A is a magnetically active young dwarf-star of spectral type K0,located at a distance of ∼
15 pc from the Sun as a foregroundstar of the Large Magellanic Cloud (LMC). It is a very rapidrotator with a period of P = v sin i ≈
90 Km / s(see Guirado et al. 2011 and references therein), resulting in veryhigh levels of magnetic activity with an average log ( L x / L bol ) ≈ -3. Located 9.5 ′′ away from AB Dor A is an active M dwarfAB Dor B (Rst 137B; Vilhu & Linsky 1987; Vilhu et al. 1989),about ∼
60 times bolometrically fainter than AB Dor A, andtherefore only little or no contamination due to the presence ofAB Dor B is expected in data that leave both components un-resolved. At radio wavelengths AB Dor B was serendipitouslydetected with the Australian Telescope Compact Array (ATCA)during an observations of AB Dor A (Lim et al. 1992). However,the binarity of AB Dor B itself with a separation of only 0.7 ′′ (called AB Dor Ba and AB Dor Bb) was detected only afterthe advent of adaptive optics. Yet another low-mass companionto AB Dor A is AB Dor C Guirado et al. (1997), located about0.16 ′′ away from AB Dor A.The apparent magnitude of AB Dor A of V = ∼
20 years along with a flip-flop cycle of ∼ ∼
20 year periodsuggested by J¨arvinen et al. (2005).AB Dor A has not only been a target of interest for opticalobservations, but has been observed with many space-based ob-servatories across the UV, EUV, and X-ray wavebands. The firstX-ray detection of AB Dor A was obtained with the
Einstein
Observatory (Pakull 1981; Vilhu & Linsky 1987), and ever sincethen AB Dor A has been observed repeatedly by almost allX-ray observatories (Collier Cameron et al. 1988; Vilhu et al.1993; Mewe et al. 1996; Maggio et al. 2000; G¨udel et al. 2001;Sanz-Forcada et al. 2003a; Hussain et al. 2007; Lalitha et al.2013). The long-term X-ray behaviour of the X-ray emissionfrom the AB Dor system is dominated by AB Dor A (G¨udel et al.2001; Sanz-Forcada et al. 2003a). AB Dor Ba and Bb cannot beseparated with current X-ray telescopes; the combined luminos-ity of the B-components is ∼ . × erg / s in the 0.2-4.0 keV(Vilhu & Linsky 1987). Sanz-Forcada et al. (2003a) obtained aluminosity of ∼ . × erg / s in the 0.5-2.0 keV with Chandra
ACIS observations. Hence, the contribution of the companionsto the X-ray emission of AB Dor A can be considered negligible,essentially because the quiescent X-ray emission of the compan-ions scales as their bolometric luminosity.The time evolution of AB Dor A has previously been studiedby Kuerster et al. (1997), who compared the V-band brightnesswith X-ray observations (5 1 / / XMM-Newton that cover about sixyears of observations.
2. Lalitha et al.: X-ray activity cycle on the active ultra-fast rotator AB Dor A?
3. Observations and data analysis
Because it is a foreground star of the LMC, AB Dor has theadvantage of being easily observable at all times with most X-ray satellites, and therefore quite a number of often serendipi-tously taken X-ray data of this source exist. We used
ROSAT ob-servations listed in the ROSAT
Position Sensitive ProportionalCounters (PSPC) source catalogue from pointed observationswith typical exposure times of between 1 ksec and 3 ksec, andthe
ROSAT
High Resolution Imager (HRI) source catalogueagain from pointed observations with typical exposure times ofbetween 1 ksec and 6 ksec. Since the ROSAT satellite was in alow Earth orbit, the typical contiguous and uninterrupted view-ing intervals of a source are typically in the range 1 - 2 ksec,therefore longer exposures are composed of a number of shorterexposures with sometimes very long intervening temporal gaps.We specifically used the PSPC observations obtained between1990 and 1993 and the HRI observations obtained between 1990and 1998; the total PSPC exposure is 74.4 ksec, the total HRIexposure is 106.2 ksec; thus, the ROSAT observations comprisea relatively short total exposure time when compared with the
XMM-Newton observations listed in Table 1.We also carried out a detailed analysis of AB Dor A, us-ing the data obtained by
XMM-Newton
Observatory. On board
XMM-Newton three telescope are co-aligned with three CCDcameras (i.e., one PN and two MOS cameras) with a sensitiv-ity range between ≈ /∆ E ≈ XMM-Newton
RGS. Hence this target has been repeatedly ob-served over the last decade, giving us an ideal opportunity toassess the long-term behaviour of AB Dor A. In these data thereare either no observations or typically much shorter observationtime covered by the EPIC instrument than that of the RGS (seeTab. 1); we therefore restricted our analysis to the available RGSdata. The data were reduced using the standard
XMM-Newton
Science Analysis System (SAS) software V12.0.1. We used themeta-task rgsproc + RGS2) the task rgslccor .In Fig. 1, we provide all RGS light curves used for ouranalysis, and indicate the times of quiescence and strong flaring.Because AB Dor A is an active star, flaring is indeed observedin almost all observations. When investigating the long-term be-haviour of AB Dor A, we focused on the quiescent emission.Hence we excluded time periods of enhanced activity or strongflaring, particularly when the count rate increased from the qui-escent level by about 50 or more percent for each observation.We thus excluded larger flares on the basis of the respective X-ray light curve and calculated the mean or median count rate for The ROSAT observation log is provided in electronic form at CDS. A detailed description of the XMM packages is available athttp: // xmm.esac.esa.int / sas / current / doc / packages.All.html After revolution 135, the CCD 7 in RGS1 su ff ered a failure; thisfailure does a ff ect comparisons between observations using count rates. the combined RGS (RGS1 + RGS2) observations (see Col. 4 inTab. 1).
Table 1.
Observation log of
XMM-Newton data. Columns 4 and5 provide the mean RGS / median RGS count rate and the datadispersion for the RGS data. Obs. ID Date Obs. time Mean / median σ of thePN / RGS RGS count rate RGS data points[ks] [cts / s] [cts / s]20000123720201 01 /
05 60.0 / / /
06 41.9 / / /
10 55.7 / / /
12 6.2 / / / / / / /
01 48.6 / / /
05 48.2 / / /
10 — / / /
04 15.9 / / /
06 4.9 / / / / /
11 — / / /
11 — / / /
12 — / / /
12 — / / /
01 — / / /
03 — / / /
05 — / /
10 — / / /
12 — / / /
11 — / / /
04 — / / /
10 — / / /
12 — / / /
07 — / / /
01 — / / /
01 47.0 / / /
11 57.9 / / /
01 9.9 / / /
01 9.9 / / /
12 9.9 / /
3. Lalitha et al.: X-ray activity cycle on the active ultra-fast rotator AB Dor A? R a t e [ c oun t s / s ]
01 May 2000 R a t e [ c oun t s / s ]
07 Jun 2000 R a t e [ c oun t s / s ]
27 Oct 2000 R a t e [ c oun t s / s ]
11 Dec 2000
10 20 30 40 50 60 70Time [ks]0246810 R a t e [ c oun t s / s ]
11 Dec 2000
70 80 90Time [ks]0246810 R a t e [ c oun t s / s ]
11 Dec 2000 R a t e [ c oun t s / s ]
20 Jan 2001 R a t e [ c oun t s / s ]
22 May 2001 R a t e [ c oun t s / s ]
13 Oct 2001 R a t e [ c oun t s / s ]
12 Apr 2002 R a t e [ c oun t s / s ]
18 Jun 2002
20 30 40 50 60Time [ks]0246810 R a t e [ c oun t s / s ]
18 Jun 2002 R a t e [ c oun t s / s ]
05 Nov 2002 R a t e [ c oun t s / s ]
15 Nov 2002 R a t e [ c oun t s / s ]
03 Dec 2002 R a t e [ c oun t s / s ]
30 Dec 2002 R a t e [ c oun t s / s ]
23 Jan 2003 R a t e [ c oun t s / s ]
30 Mar 2003 R a t e [ c oun t s / s ]
31 May 2003 R a t e [ c oun t s / s ]
23 Oct 2003 R a t e [ c oun t s / s ]
08 Dec 2003 R a t e [ c oun t s / s ]
27 Nov 2004 R a t e [ c oun t s / s ]
18 Apr 2005 R a t e [ c oun t s / s ]
16 Oct 2005 R a t e [ c oun t s / s ]
31 Dec 2006 R a t e [ c oun t s / s ]
19 Jul 2007 R a t e [ c oun t s / s ]
03 Jan 2008 R a t e [ c oun t s / s ]
04 Jan 2009 R a t e [ c oun t s / s ]
25 Nov 2009 R a t e [ c oun t s / s ]
11 Jan 2010 R a t e [ c oun t s / s ]
02 Jan 2011 R a t e [ c oun t s / s ]
31 Dec 2011
Fig. 1.
XMM-RGS light curves of AB Dor A plotted in counts per second. Quiescent time intervals are marked by arrows; see textfor details. A log of the observations is provided in Table 1.
4. Lalitha et al.: X-ray activity cycle on the active ultra-fast rotator AB Dor A?
We compiled all publicly available photometric V-band data ofAB Dor A, covering nearly 34 years of observations taken be-tween 1978-2012 with a short gap between 1998-1999 and 2000-2001. The data taken between 1978-2000 have been presentedby J¨arvinen et al. (2005); most of the observations were carriedout using the standard Johnson
UBVRI filters. Additionally, weused an – unpublished – data set collected between 2001-2012obtained in the context of the all-sky automated survey (ASAS) in the V band (Pojmanski 1997; Pojmanski et al. 2005), which ispublicly available.ASAS is a CCD photometric sky survey, monitoring thesouthern as well as a part of the northern sky ( δ < + ◦ )since 2000 up to now. The ASAS telescope is located in Chile,Las Campanas Observatory (LCO), at an altitude of 2215 mabove sea level and consists of two wide field (9 ◦ × ◦ ) cam-eras equipped with both V and I filters. For AB Dor A, we usedobservations carried out using only V-band data with exposuretimes of 180s for each frame; in general, the photometric accu-racy of ASAS data for AB Dor A is about 0.05 mag.
4. Long term light curves
In Figure 2, we plot the V-band brightness of AB Dor A as afunction of time. We then subdivided the entire ∼
34 years ofV-band observations into smaller time periods and estimated amedian V magnitude over each of these time bins (depicted asblack and blue circles).To search for periodic variability we performed a peri-odogram analysis on the entire optical dataset using the gen-eralised Lomb-Scargle periodogram in the form introduced byZechmeister & K¨urster (2009), which is a variant of the Lomb-Scargle periodogram. In Figure 3, we show the resulting pe-riodogram from the entire optical data set spanning nearly 34years of observations. A clear peak around ≈ ∼ .
96 years to the the entire data set presented inFig. 2 after correcting for the linear trend in the J¨arvinen et al.(2005) and the ASAS data set (plotted as orange curve in Fig. 2).Additionally, in Fig. 4 we plot the mean of optical data foldedwith the cycle period of ≈
17 years.In addition to the main peak in Fig. 3, we note another peakwith a period of ≈ ≈ = ≈ Lockwood et al. (1997) and Radick et al. (1998) studied the rela-tionship between the photometric variability and chromosphericactivity of Sun-like stars by combining the Mount Wilson HK The ASAS data are available at http: // / asas / V m a gn i t ud e JD-2,400,0001980 1985 1990 1995 2000 2005 2010Year
Fig. 2.
AB Dor A long-term V-band brightness evolutionadapted from J¨arvinen et al. (2005) and ASAS observations. Thebrown circles denote all individual V-band observations. The es-timated median magnitudes are denoted as black and blue circlesfor the data from J¨arvinen et al. (2005) and the ASAS observa-tions, respectively. Plotted as a thick line is the sinusoidal fit tothe entire dataset with a period of ≈
17 years. P o w e r Optical data complete bin
Fig. 3.
Periodogram of complete data set of optical V-magbrightness. The highest peak indicates activity-cycle period val-ues of 16.96 years.activity observations with 11 years of Str¨omgren b and y pho-tometry taken at Lowell Observatory. The latter authors foundthat on cycle time-scales young active stars show an inverse cor-relation between photometric brightness and chromospheric ac-tivity, while older stars such as the Sun show a direct correlationbetween brightness and activity. Radick et al. (1998) explainedthis finding by arguing that the stars switch from spot-dominatedto facular-dominated brightness variations at an age of ≈ ∼
50 Myr (Close et al. 2005).Hence, according to Fig. 2, one would expect an increase in X-ray activity from minimum to maximum between 1996-2004,and a decline in X-ray activity between 1990-1996 and also since2005. In this section we therefore investigate to what extent theavailable X-ray data support the view of such cyclic coronal ac-tivity in AB Dor A.
5. Lalitha et al.: X-ray activity cycle on the active ultra-fast rotator AB Dor A? V m a g Jaervinen et al. 2005ASAS Observations
Fig. 4.
Optical V-band brightness data of Fig. 2 folded with acycle period of 16.96 years versus the phase interval [0.0,1.0].Plotted in green and blue are the mean of the J¨arvinen et al.(2005) and ASAS observations, respectively; the plotted errorbar depicts the brightness measurement distribution due to rota-tional modulation.
In Figure 5, we show the temporal behaviour of the soft X-rayluminosity as observed between 1990 and 2011 by various X-raysatellites. Assuming that AB Dor-A’s X-ray spectrum can be de-scribed with temperature components 2 and 5 MK and an equiv-alent absorption column N H of 10 cm − , we computed energyconversion factors (ECF) to convert the observed count rates intofluxes. Using XSPEC v12.6.0 and WebPIMMS v4.6, we esti-mated ECF
PS PC = . × − erg / cm / counts, ECF
HRI = . × − erg / cm / counts, ECF
RGS = . × − erg / cm / counts,and ECF
RGS = . × − erg / cm / counts in the canonicalROSAT energy band 0.1-2.4 keV; the resulting X-ray luminosi-ties (L X ) were finally calculated using a distance of 14.9 ± To examine whether the trends in the X-ray and optical are reallycorrelated, we carried out a correlation analysis of the two datasets. To relate an optical magnitude to each X-ray observation,we used the value of the fitted optical light curve (see Fig. 2)at the time of each X-ray observation. The resulting scatter plotis shown in Fig. 6, where we show logarithmic X-ray luminos-ity vs. V-band magnitude. A linear fit between those quantitiesgives a slope of 0.9 ± X with V mag ,implying that the X-ray luminosity is higher when the photo-spheric brightness is lower. Furthermore, we also computed alinear Pearson correlation coe ffi cient ( ρ ) of 0.40 between theX-ray luminosity and photospheric brightness with a two-tailed L x [ e r g / s ] JD-2,400,0001990 1995 2000 2005 2010Year
Fig. 5.
Temporal behaviour of the soft X-ray luminosity with1 σ deviation as observed by several X-ray missions between1990 and 2011. ROSAT
PSPC data are plotted as light-blue filledcircles;
ROSAT
HRI data are depicted as navy-blue filled cir-cles. The red circles represent
XMM-Newton
RGS observations.Plotted as a thick black curve is sinusoidal fit to the X-ray datawith an optical-cycle period of ≈
17 years.probability value of 0.0001%. These findings are clearly consis-tent with the picture that the star is X-ray bright when the surfacebrightness is low. L x [ e r g / s ] Fig. 6.
Variation of X-ray luminosity as a function of the (calcu-lated) V magnitude. The symbols here are the same as in Fig. 5;see text for details. Plotted as brown lines are the linear regres-sion with 2 σ confidence band. While the overall X-ray light curve might be a ff ected by errorsin the instrumental cross calibrations, trends in individual instru-ments should be free from such e ff ects and be real. In the follow-ing we therefore concentrated on the data taken with the ROSAT
PSPC and the
ROSAT
HRI, from which a multitude of obser-vations is available, to determine count-rate trends individuallyfor each instrument. We found a negative slope with respect tothe time evolution of the count rates for the ROSAT PSPC data,
6. Lalitha et al.: X-ray activity cycle on the active ultra-fast rotator AB Dor A?
Table 2.
Results from the search for a long-term variation inthe X-ray data. The errors and the false-alarm probability (FAP)are obtained from bootstrapping the observed distribution of themeasurements (BS).
Data set best fit slope Error FAP[cts / sec / yr] BS % ROSAT
PSPC -0.22 0.47 72HRI 0.05 0.05 61
XMM
RGS -0.04 0.02 63 while for the ROSAT HRI data we found a faint positive slope(see column 2 in Table 2).We used a simple bootstrap technique to estimate the errorof the slope. For this purpose we ran a Monte Carlo simulationfor the observing times, carrying out linear fits to the simulateddata sets. The count rates and their individual errors were ran-domly redistributed over the range of available observing times.A regression analysis on the re-sampled data was performed andrepeated several times (5 × times), thus providing an error at1 σ probability associated with the determined slope. The resultsof this analysis are listed in column 3 of Table. 2. For the PSPCdata we found that in 72% of the cases slopes as small as theobserved one are obtained by pure chance, whereas for the HRIdata this is estimated to be true in 61% of the cases.Comparing the optical light curve (Fig. 2) and the X-ray lightcurve (Fig. 5), one expects the ROSAT PSPC observations to beat activity minimum during the 17-year cycle, the ROSAT HRIobservations to be during the constant or rise phase from mini-mum to maximum activity level and the XMM-Newton observa-tions cover almost half an activity-cycle period. Our regressionanalysis of the individual PSPC and HRI data is consistent withthis picture, but the statistical significance is low.
Since AB Dor A was used as a calibration source for
XMM-Newton , many datasets with much enhanced quality and longtemporal coverage of AB Dor A have become available, whichcan be used for cycle studies. In contrast to the ROSAT obser-vations, those of XMM-Newton are much longer, which allowsus to identify periods of flaring in the data stream and excludethese periods from analysis. In Fig. 7 we plot the evolution ofthe XMM-RGS count rate taking into consideration only thequiescent emission. In addition, we re-plot Fig. 2 to comparethe optical and X-ray light curves (the lower panel of Fig. 7). Ifthe XMM-RGS data show a variation similar to the optical data,2000-2006 should represent the activity maximum. Because vi-sual inspection suggests an anti-correlation between the opticaland the X-ray data, we carried out some statistical tests to deter-mine whether these trends are significant or not.A (parametric) regression analysis on these data similar tothe ROSAT data was performed, and the results are presented inTable 2 as well. We obtained a negative slope for the observedXMM-RGS count rates as a function of time, and again, similarto the ROSAT data, we performed a simple bootstrap techniqueto estimate the error of the slope and FAP. A slope as small as theobserved one for the XMM-RGS data that occurs by pure chanceis estimated to be 63%. The negative slope fits with the overallpicture of an expected decline in the activity, but the significanceof this slope is again very low.
JD-2,400,000 135 X -r a y c oun t r a t e V m agn i t ude Fig. 7.
Top panel: Temporal behaviour of the XMM-RGS countrate binned to 100 s (as brown circles) after removing the flaresfrom each observation. The median count rate over the durationof each observational run is depicted as black circles. Bottompanel: V-band data for AB Dor A (same as Fig. 2).We then decided to apply non-parametric correlation testssuch as the Spearman ρ and Kendall τ test (Press 1992) on themean and the median XMM-RGS data presented in Table. 1.For this purpose we divided the XMM-RGS data into two sub-sets, one covering the years 2000-2005, that is, towards the an-ticipated maximum, and the second set between 2005-2011 withdeclining activity. The Spearman rank correlation coe ffi cient ρ is defined as ρ = P ( R i − ¯ R )( S i − ¯ S ) pP ( R i − ¯ R ) pP ( S i − ¯ S ) , (1)where R i and S i are the ranks of time and the minimum count-rate values respectively. The significance of a non-zero value of ρ is computed from a parameter t defined as t = ρ s N − − ρ , (2)where ρ is the Spearman rank and N is the sample size. Note thatthe significance t is distributed approximately as a Student dis-tribution with N-2 degrees of freedom (Press 1992); a low valueof significance ( p in Tab. 3) indicates a significant correlation.An alternative non-parametric test is the Kendall τ -test,which uses the relative ordering of the rank instead of the numer-ical di ff erence of the ranks. Consider two samples (with n itemseach) of physical quantities, in our case the observing times t i ( i = , N ) and the minimum count rate r i ( i = , N ); we assumed
7. Lalitha et al.: X-ray activity cycle on the active ultra-fast rotator AB Dor A?
Table 3.
Results from the correlation test performed on themean and median XMM-RGS data. Column 3 shows the sig-nificance of a non-zero value of the Spearman rank, and Column5 shows whether the observed value of τ is significantly di ff erentfrom zero. Data set Spearman ρ test Kendall τ test ρ t p-value τ σ Mean RGS data2000-2005 -0.01 -0.07 0.94 0.02 0.022005-2011 -0.45 -1.33 0.22 -0.28 0.072000-2011 -0.36 -2.15 0.04 -0.22 0.01Median RGS data2000-2005 -0.05 -0.22 0.82 0.01 0.022005-2011 -0.33 -0.94 0.37 -0.22 0.072000-2011 -0.35 -2.05 0.04 -0.20 0.01 the times to be sorted so that t i < t i + . The total number of pos-sible pairs of time and count rates is n(n-1) /
2. We considered apair of values of time t and count rate r . If the relative orderingof the ranks of two observing times is the same as the relativeordering of the two rates, the pair is called concordant, other-wise the pair is called discordant. Ignoring the problem of howto treat timed observations, the basic idea is to compare the num-ber of concordant and discordant pairs, since that number shouldbe statistically equal in the absence of correlations. Specifically,the Kendall τ is given by τ = n c − n d n ( n − / , (3)where n c is the number of concordant and n d the number of dis-cordant pairs, normalised by the total number of pairs. Clearly,for a perfect correlation τ =
1. On the null hypothesis of in-dependence of time and count rate, that is, no correlation, τ isexpected to be normally distributed with zero expectation and avariance of Var ( τ ) = N + N ( N − . (4)The results of our correlation analysis are provided in Tab. 3,where we also quote the two-sided probability value (p-value)for a given t-value (Eqn. 2). Clearly, the two tests on the me-dian and mean RGS data yield no significant correlations for the2000 - 2005 data, while they suggest significant correlations forboth the median and mean RGS data between 2000 - 2011. Ifonly the 2005 - 2011 data are considered, the τ -test suggests asignificant correlation, while the correlation is marginal at bestusing the Spearman rank ρ . In all cases, however, there is ananti-correlation, that is, the X-ray rate is decreasing accordingto expectation. These results suggests that there is an influenceof the activity cycle on the X-ray emission, but the observed X-ray variation is quite di ff erent from the X-ray variation measuredfor the Sun. It is of course di ffi cult to assess this influence quan-titatively, but inspecting the values provided in Tab. 1, we finda maximum count-rate of 3.93 / / s from XMM-RGS dataand a minimum count-rate of 2.15 / / s, from which we cal-culate a variation amplitude of at most ∼ While a clear cyclic behaviour with a cycle length of ∼
17 yearsis observed for AB Dor A in its optical brightness variations, asimilar variation in the available X-ray data is not immediatelyapparent. However, Fig. 6 suggests an anti-correlation betweenoptical and X-ray brightness in support of the view of a varia-tion in X-ray flux with the optical cycle. The extensive and con-tiguous observations carried out with the XMM-Newton RGSallow a much more refined assessment of the temporal variabil-ity of AB Dor A than all previously available X-ray data. Aninspection of Fig. 1 demonstrates that AB Dor A is variable atall times and does indeed produce frequent and significant flar-ing. However, the
XMM-Newton
RGS data also demonstrate thatAB Dor A returns to a basal state at around approximately 3RGS cts / sec. This basal state can be observed only in reasonablylong and contiguous observations, and even then it may not be at-tained. At any rate, in short and non-contiguous data, as availablefrom satellites in low Earth orbit such as ROSAT, it is di ffi cult toidentify such basal state periods; still, taking the ROSAT data atface value, the data support a variation of X-ray flux with opticalcycle in the anticipated way, although the obtained correlationsare not statistically significant.Since the available XMM-Newton observations now coverthe period between optical activity maximum and minimum, wecarried out several statistical tests to study a possible activitycycle associated with the XMM-RGS data. The results indeedindicate an increase and decline in activity with an activity maxi-mum around 2002-2003 (cf. Fig.7). This change in activity man-ifests itself in a change in the flux of the basal state level, but thechange in amplitude is at most a factor of two, and possibly evenlower. As a consequence, the relative change is far less than therelative change observed in the Sun and other late-type stars andtherefore the variability of the star’s basal state is weaker thanthe typical X-ray variability (outside flares) in less active coolstars. The low-amplitude variability observed in AB Dor A maybe attributed to the fact that we are dealing with an ultra-fastrotator that has a saturated corona.
5. Comparison of AB Dor A’s activity cycle with thatof other stars
In the following section we view our findings on the activitycycle on AB Dor A in the context of stellar activity cycles asseen in X-rays and other activity indicators. In Fig. 8, we plot thecycle period (in years) vs. the stellar rotation period (in days) forthe sample stars. We use the stellar sample discussed in detail byBrandenburg et al. (1998) and B¨ohm-Vitense (2007) (blue andgreen triangles), the stars with confirmed X-ray cycles discussedin the introduction section (magenta circles) and individual fastrotators with activity cycles as discussed by Bernhard & Frank(2006), Taˇs (2011), and Vida et al. (2013) (red circles); the datapoint for AB Dor A is also shown, using its 0.52-day rotationperiod and 17-year activity-cycle period.Brandenburg et al. (1998) showed that active and inac-tive stars follow di ff erent branches in a P cyc - P rot -diagram.B¨ohm-Vitense (2007) suggested that the time taken for thetoroidal magnetic field to reach the stellar surface is determinedby the length of the activity cycle associated with the star. Hencestudying the relation between the rotation period and the lengthof the activity cycle may shed light on the relevant dynamomechanisms.Most of the X-ray cycle stars fit the active or in-active sequence proposed by Brandenburg et al. (1998) and
8. Lalitha et al.: X-ray activity cycle on the active ultra-fast rotator AB Dor A?
B¨ohm-Vitense (2007) reasonably well. Note that the short-period systems follow yet di ff erent branches in the P cyc - P rot -diagram. We hypothesise that AB Dor A and other ultra-fast ro-tators have somewhat di ff erent dynamo processes that are notreadily comparable to more slowly rotating stars. Clearly, sub-stantial work needs to be done to demonstrate the reality of ac-tivity cycles in ultra-fast rotators as a class. rot [days]110 P cyc [ yea r s ] Active InactiveUFR
LO PegGSC 2038−00293GSC 3377−0296V405 AndEY Dra SunAB Dor A α Cen A61 Cyg B61 Cyg A α Cen BHD 81809 ι Hor
Fig. 8.
Rotation period plotted as a function of the activity-cycle period. Depicted as blue and green triangles are stars be-longing to inactive and active sequence (B¨ohm-Vitense 2007).Represented as a magenta circles are stars with X-ray cycles (cf.see introduction). The place of AB Dor A is represented as ma-genta star. Depicted as red circles are the activity cycles reportedin other ultra-fast rotators reported by Bernhard & Frank (2006),Taˇs (2011), and Vida et al. (2013).
6. Rotational modulation
Out of the wealth of data of available
XMM-Newton data onAB Dor A, we chose the subsets of data that cover more thanone stellar rotation and are therefore well suited for a short-termvariability study. In Fig. 9, we depict the X-ray light curve af-ter flares were removed by eye for all XMM-RGS data sets withmore than one rotational period and plot this vs the rotationalphase interval. We note substantial fluctuations as a result of anactive corona. The seemingly irregular variability seen in indi-vidual light curves can be attributed to the low energy and shorttime-scale flares, with no obvious sign of rotational modulation.We point out that the data shown in Fig. 9 extend over ten years,yet the dispersion of the data is very low, re-emphasizing theexistence of a possible basal coronal state in AB Dor A.
7. Summary
The available X-ray observations of AB Dor A, compiled for aperiod of more than two decades, show X-ray variability on avariety of time scales. Since AB Dor A is a very active star, itexhibits substantial short-term variability and in particular fre-quent flaring activity. This flaring activity may last for severalhours and can be observed in
XMM-Newton data where the ex-posure time ranges over several tens of kilo-seconds (cf. Fig. 1).But in short and non-contiguous snapshot observations typicallyavailable from low Earth-orbit satellites such as the ROSAT ob-servations, which typically have individual exposure times of a R a t e [ c t s / s ] Fig. 9.
X-ray light curve after removing the flares from a subsetof XMM-RGS observation on AB Dor A folded with rotationalperiod and plotted vs. the phase interval. Each colour representsdi ff erent observations / di ff erent rotation. Represented as blackfilled circles are mean count rate at a certain rotation phase with2 σ deviation.few kilo-seconds at best, this variability is di ffi cult to distinguishfrom variability on longer time-scales. In the optical, long-termvariability with a period of 16-17 years that is highly reminis-cent of the solar sunspot cycle could be established; with 20%the amplitude of the optical cyclic variations is quite substantial.Because of its substantial variability on short time-scales, acorrelation between X-ray and photospheric activity is di ffi cultto establish with snapshot X-ray data. However, in su ffi cientlylong X-ray observations of AB Dor A, we were able to estimatea basal state of ≈ XMM-Newton
RGS cts / sec. Furthermore, wepresented evidence that this basal state flux may vary with theoptical cycle of AB Dor A in analogy to the solar activity cycle;note that the Sun appears faintest when large Sun spot group(s)are on its visible hemisphere. However, for AB Dor A we esti-mated a factor of only ∼ Acknowledgements.
S. L. acknowledges funding by the DFG in the frameworkof RTG 1351 ”Extrasolar planets and their host stars”.
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