Observation of the period ratio P_1/P_2 of transversal oscillations in solar macro-spicules
aa r X i v : . [ a s t r o - ph . S R ] A p r Observation of the period ratio P /P of transversaloscillations in solar macro-spicules H. Ebadi, and M. KhoshrangbafAbstract
We analyze the time series of oxygen lineprofiles (O vi A and O vi A ) obtainedfrom SUMER/SOHO on the solar south limb. We cal-culated Doppler shifts and consequently Doppler veloc-ities in three heights 4 ′′ , 14 ′′ , and 24 ′′ from the limbon a coronal hole region. Then, we performed waveletanalysis with Morlet wavelet transform to determinethe periods of fundamental mode and its first harmonicmode. The calculated period ratios have departuresfrom its canonical value of 2. The density stratificationand magnetic twist are two main factors which maycause these departures. Keywords
Sun: spicules · MHD waves: period ratio
Observation of oscillations in solar spicules may beused as an indirect evidence of energy transport fromthe photosphere towards the corona. Transverse mo-tion of spicule axis can be observed by both, spec-troscopic and imaging observations. The periodicDoppler shift of spectral lines have been observed fromground based coronagraphs (Nikolsky & Sazanov 1987;Kukhianidze et al. 2006; Zaqarashvili et al. 2007). ButDoppler shift oscillations with period of ∼ SOHO ) by Xia et al. (2005). Direct peri-odic displacement of spicule axes have been found byimaging observations on Solar Optical Telescope (SOT)on
Hinode (De Pontieu et al. 2007; Kim et al. 2008;He et al. 2009).
H. Ebadi, and M. KhoshrangbafAstrophysics Department, Physics Faculty, University of Tabriz,Tabriz, Irane-mail: [email protected]
The observed transverse oscillations of spicule axeswere interpreted by kink (Nikolsky & Sazanov 1987;Kukhianidze et al. 2006; Zaqarashvili et al. 2007; Kim et al.2008; Ebadi et al. 2012a) and Alfv´en (De Pontieu et al.2007) waves. All spicule oscillations events are sum-marized in a recent review by Zaqarashvili & Erd´elyi(2009). They suggested that the observed oscillationperiods can be formally divided in two groups: thosewith shorter periods ( < > P /P be-tween the period P of the fundamental mode and theperiod P of its first harmonic (Andries et al. 2009;Karami & Bahari 2012; Orza et al. 2012; Erd´elyi et al.2013). Different factors such as the effect of den-sity stratification (Andries et al. 2009) and magnetictwist (Karami & Bahari 2009) can cause the devia-tion of the period ratio from its canonical value of2. The observed values of this ratio in coronal loopsis either smaller or larger than 2 (Verwichte et al.2004; Andries et al. 2009). Srivastava et al. (2008)Using simultaneous high spatial and temporal res-olution H α observations studied the oscillations inthe relative intensity to explore the possibility ofsausage oscillations in the chromospheric cool post-flare loop. They used the standard wavelet tool, andfind P /P ∼ .
68. They suggested that the oscil-lations represent the fundamental and the first har-monics of the fast-sausage waves in the cool post-flareloop. Verwichte et al. (2004) have detected interesting phenomenon of simultaneous existence of fundamentaland first harmonics of fast-kink oscillations (see alsoDe Moortel & Brady (2007); Van Doorsselaere et al.(2007); Zaqarashvili et al. (2013a)). However, the ratiobetween the periods of fundamental and first harmon-ics P /P was significantly shifted from 2, which laterwas explained as a result of longitudinal density strat-ification in the loop. The rate of the shift allows us toestimate the density scale height in coronal loops, whichcan be a few times larger compared to its hydrostaticvalue.Observed oscillation periods can be used to esti-mate the Alfv´en speed and consequently magnetic fieldstrength in macro-spicules (Zaqarashvili et al. 2013b).The mentioned studies in the previous paragraph areall devoted to the coronal loop transversal oscillations.To my knowledge there is no any work related to theperiod ratio of spicules oscillations. So, the presentstudy is an attempt to check this ratio observationally.We will study the same problem theoretically in ourfuture works. SUMER is a high-resolution normal incidence spectro-graph operating in the range 666-1610 ∼ ˚A (first order)and 333-805 ∼ ˚A (second order). The angular pixel sizeis ∼ ˝1. The spectral pixel size depends slightly on thewavelength. Contriving normally allows sub-pixel reso-lution. It can vary from about 45 m˚A/pixel at 800 ∼ ˚Ato about 41 ∼ m˚A/pixel at 1600 ∼ ˚A (Wilhelm et al.1995).A coronal hole region in the south pole of the sunwas observed with SUMER (detector B) on 21 Feb1997. The pointing coordinates were X = 0 ′′ , Y =-985 ′′ . The slit, which was used for observations, hasthe dimensions of 0.3 ′′ × ′′ . The observation was per-formed from 01:36 UT to 01:52 UT and the exposuretime was 15 seconds. In Figure 1 we presented the im-ages of the studied region which were observed by 304˚A SOHO/EIT (top) on 21 February 1997. The rect-angular shows the region of south limb macro-spicules.We used the “madmax” algorithm to enhance the fineststructures (Koutchmy & Koutchmy 1989). As it isclear from down panel of Figure 1, the length of thestudied spicule is 25 Mm which means that the studiedspicule is macro-spicule. Since the EIT images have afixed pixel resolution of 2 . Fig. 1
Image of the studied region which were observedby 304 ˚A SOHO/EIT (top) on 21 February 1997. The slit isin the North – South direction. The rectangular shows theregion studied. We used the “madmax” algorithm to en-hance the finest structures (down). The white arrow showsthe studied macro-spicule.
Software (SSW) database. We performed the radio-metric calibration, so the specific intensity unit is Wm − sr − ˚A − through this analysis(Ebadi et al. 2007;Vial et al. 2009).We calculated the integrated intensity for O vi (1031.93 ˚ A ) line along the SUMER slit. The limb islocated in pixel number 86 and the spicule region islied from pixel 87 to 117 which is shown in Figure 2.Moreover, we plotted integrated profile of O vi (1031.93˚ A ) line in Figure 3. Fig. 2
The integrated intensity along the SUMER slit forO vi (1031.93 ˚ A ) line. The spicule region is lied from pixel87 to 117. Fig. 3
The integrated profile of O vi (1031.93 ˚ A ) line. We analyze O vi (1031.93 ˚ A ) and O vi (1037.61 ˚ A ) lineprofiles from the time series by fitting to a Gaussian.Then we calculated Doppler shifts and consequently Doppler velocities (Zaqarashvili et al. 2007). we usedthe two stable photospheric neutral oxygen emissionlines (i.e. O i (1027.43 ˚ A ) and O i (1028.16 ˚ A )) thathappen to be in the same spectral window with theO vi lines. Doppler velocities and proper wavelet anal-ysis results are presented in Figures 4, 5, and 6 for O vi (1031.93 ˚ A ). We perform wavelet analysis with Mor-let wavelet transform in three heights for both lines.On the other hand, wavelet analysis results for the lineO vi (1037.61 ˚ A ) are showed in Figures 7, 8, and 9. Thewavelet power spectrum, the cone of influence, and theglobal wavelet power spectrum are plotted in each fig-ure. The contour levels are chosen so that 75%, 50%,25%, and 5% of the wavelet power is above each level,respectively.We determined the fundamental mode and its firstharmonic periods for each line and in three heights (4 ′′ ,14 ′′ , and 24 ′′ from the limb). For comparison we pre-sented results in Table 1 for both lines. Table 1 P (fundamental mode period), P (first harmonicperiod), and P /P (fundamental to its first harmonic pe-riod ratio) are presented for both oxygen lines. line height P (s) P (s) P /P O vi (1031 . A ) 4 ′′
96 45 2.13O vi (1031 . A ) 14 ′′
100 48 2.08O vi (1031 . A ) 24 ′′
110 50 2.2O vi (1037 . A ) 4 ′′
108 52 2.07O vi (1037 . A ) 14 ′′
118 58 2.03O vi (1037 . A ) 24 ′′
100 49 2.04As it is clear from the Table 1, the fundamental modeand its first harmonic period ratios have departuresfrom its canonical value of 2. They are greater than 2 inboth lines in 4 ′′ , 14 ′′ , and 24 ′′ from the limb. The fun-damental mode periods are determined as 96 −
118 s andits first harmonic periods are lied in the range 45 − Hinode ob-servations determined the variation of magnetic field strength and plasma density along a spicule by seis-mology. They studied a kink wave propagating alonga spicule by estimating the spatial change in phasespeed and velocity amplitude as a novel approach.Suematsu et al. (2008); Tavabi et al. (2011) by usingthe SOT/
Hinode observations reported twisted motionsin spicules.Since we determined the oscillation periods of funda-mental mode and its first harmonic in macro-spicules,it is possible to estimate the Alfv´en speed and conse-quently magnetic field strength through them. Kinkwaves are transverse oscillations of magnetic tubes andthe phase speed for a straight homogenous tube can bewritten as: c k = λT obs = V A s
21 + ρ e /ρ , (1)where V A ≡ B / √ µ ρ is the Alfv´en speed inside thetube, λ is the wavelength, and T obs is the observedoscillation period. ρ e and ρ are the plasma densityoutside and inside of tube, respectively. The densityin spicules is 3 × − kg m − and ρ e /ρ ≃ . λ = 2 L ( L is the length ofthe macro-spicule which determined as 25 Mm in thiswork). The mean fundamental mode period is deter-mined as ∼
105 s. By using these parameters in Equa-tion 1 the Alfv´en speed and magnetic field strength isestimated as ∼
340 km/s and ∼
65 G in macro-spicules,respectively.
We analyze the time series of O vi (1031.93 ˚ A ) and O vi (1037.61 ˚ A ) line profiles obtained from SUMER/SOHOin order to uncover the oscillations in the solar macro-spicules. We concentrate on particular coronal holeregion which contains the macro-spicules and foundthat their axis undergo quasi-periodic transverse dis-placement. This is done by calculating Doppler shiftsand consequently Doppler velocities in three heights 4 ′′ ,14 ′′ , and 24 ′′ from the limb. By performing waveletanalysis with Morlet wavelet transform in three heightswe determine the fundamental mode and its first har-monic periods and their ratios. Our findings show smalldepartures of this value from its canonical value of 2 inboth lines and three mentioned heights. In other words,they are greater than 2 in both lines in 4 ′′ , 14 ′′ , and24 ′′ from the limb. These departures may be causedby the density stratification and magnetic twist whichis observed in spicules. Observed oscillation periods are used to estimate the Alfv´en speed and consequentlymagnetic field strength in macro-spicules as ∼
340 km/sand ∼
65 G, respectively.
Acknowledgements
The authors thank anonymousreferee for his/her useful and instructive comments inimproving the document. The authors are gratefulto the
SOHO
Team for providing the observationaldata. SUMER is financially supported by DLR, CNES,NASA and the ESA PRODEX program (Swiss contri-bution). SOHO is a mission of international coopera-tion between ESA and NASA. We appreciate the ISSIsupport in the frame of the ”Spectroscopy and Imagingof coronal hole spicules from Space” Team.
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Fig. 4 a. Doppler velocity variations of the studied spicule 4 ′′ above the limb in O vi (1031.93 ˚ A ) line. b. The waveletpower spectrum. The contour levels are chosen so that 75%, 50%, 25%, and 5% of the wavelet power is above each level,respectively. The cross-hatched region is the cone of influence, where zero padding has reduced the variance. c. The globalwavelet power spectrum. Fig. 5
The same as in Fig. 3 but 14 ′′ above the limb. Fig. 6
The same as in Fig. 3 but 24 ′′ above the limb. Fig. 7 a. Doppler velocity variations of the studied spicule 4 ′′ above the limb in O vi (1037.61 ˚ A ) line. b. The waveletpower spectrum. The contour levels are chosen so that 75%, 50%, 25%, and 5% of the wavelet power is above each level,respectively. The cross-hatched region is the cone of influence, where zero padding has reduced the variance. c. The globalwavelet power spectrum. Fig. 8
The same as in Fig. 6 but 14 ′′ above the limb. Fig. 9
The same as in Fig. 6 but 24 ′′′′