The observations were carried out on 1998 September 22, using the German Gregory Coude Telescope, at the Observatorio

Transcription

1 THE ASTROPHYSICAL JOURNAL, 544:1141È1154, 2000 December 1 ( The American Astronomical Society. All rights reserved. Printed in U.S.A. ANOMALOUS CIRCULAR POLARIZATION PROFILES IN SUNSPOT CHROMOSPHERES1 H. SOCAS-NAVARRO, J. TRUJILLO BUENO,2 AND B. RUIZ COBO3 Instituto de Astrof sica de Canarias, E-38200, La Laguna (Tenerife), Spain Received 2000 May 23; accepted 2000 July 13 ABSTRACT This paper presents a detailed description, analysis, and interpretation of the spectropolarimetric observations recently reported by Socas-Navarro, Trujillo Bueno, & Ruiz Cobo. These observations consist of time series of Stokes I and V proðles above a sunspot umbra. The spectral lines observed simultaneously are the Ca II chromospheric lines at 8498 and 8542 A and the photospheric Fe I line at 8497 A. These spectropolarimetric observations unveil an intriguing time-dependent behavior of the Stokes V proðles in the chromospheric lines. This behavior should be considered as an observational reference for future radiation magnetohydrodynamic simulations of sunspot chromospheres. The analysis of the observed time series shows that a normal,ïï nearly antisymmetric V proðle rapidly evolves toward an anomalous,ïï completely asymmetric proðle, returning later to the normal state. The occurrence of such anomalous circular polarization proðles repeats itself with a periodicity of D150 s. After giving arguments to discard other scenarios, we are able to interpret the anomalous V proðles as a consequence of the development of a second unresolved atmospheric component. This unresolved component seems to be the same that produces the umbral Ñashes observed in other sunspots, where it is present with a larger Ðlling factor. Subject headings: line: proðles È polarization È Sun: chromosphere È Sun: oscillations È sunspots alous, strongly asymmetric proðles only in the chromospheric lines. We study the properties of spatial and temporal distribution of these anomalous proðles and consider their possible physical causes and implications. Three di erent scenarios are explored in order to explain these proðles, namely, (1) strong gradients of magnetic Ðeld and line-of-sight velocity, (2) e ects of atomic orientation, and (3) the e ect of unresolved atmospheric components. After exploring each one of these possibilities, we give arguments to discard 1 and 2. We are able to explain the occurrence of anomalous proðles as due to the development of an active ÏÏ unresolved component. Not only is the active component responsible for the occurrence of the anomalous proðles, but it also explains the oscillation in the line core shift (which is not necessarily an indicator of the chromospheric velocity) and intensity. Finally we show that this active component is also the one that produces UFs in other sunspots where its Ðlling factor is larger than in the present case. 2. OBSERVATIONS AND DATA ANALYSIS 1. INTRODUCTION The sunspot umbral dynamics have been a topic of hot active research during the last decades (see the reviews by Moore 1981; Thomas 1981; Moore & Rabin 1985; Thomas 1985; and more recently by Lites 1993). The most remarkable dynamic process that takes place regularly in the umbral chromosphere is the chromospheric umbral oscillation, which has been observed as changes in the position and intensity of the chromospheric line cores. Some sunspots exhibit umbral Ñashes (hereafter referred to as UFs), sudden brightenings due to the presence of blueshifted emission features, which are often observed in the cores of the Ca II chromospheric lines (see Beckers & Tallant 1969; Wittman 1969). The UFs seem to have a periodicity of D2.5È3 minutes, which suggest some kind of connection between them and the 3 minute umbral oscillation (see, e.g., Kneer, Mattig, & von Uexku ll 1981; Thomas 1984). Their spatial extent varies between 2000 and 3500 km. Socas-Navarro, Trujillo Bueno, & Ruiz Cobo (2000a) carried out spectropolarimetric observations of time series in the Ca II chromospheric lines at 8498 and 8542 A, as well as in the photospheric Fe I line at 8497 A. This is the Ðrst time that this kind of spectropolarimetric time-series observation is presented, and we have found that the set of data obtained is interesting enough to deserve an in-depth analysis even before any inversion technique is applied to them. This paper describes the observations and presents an analysis of the photospheric and chromospheric umbral oscillations based on direct observational parameters. The observed time series of Stokes V proðles reveals a fascinating behavior, with the periodic occurrence of anom- The observations were carried out on 1998 September 22, using the German Gregory Coude Telescope, at the Observatorio del Teide of the Instituto de Astrof sica de Canarias (see Schro ter, Soltau, & Wiehr 1985 and references therein). On this particular day the instrumental polarization was negligible, since the declination of the Sun was very close to 0 (see Sa nchez Almeida, Mart nez Pillet, & Wittmann 1991). We used a standard circular analyzer (see, e.g., Semel 1980), consisting of a j/4 plate and two crossed calcites, situated after the entrance slit. The light beam splits into two separate beams whose intensities are proportional to (I ] V ) and (I[V ). In order to minimize possible instrumental cross talks between linear and circular polarization, 1 Based on observations obtained with the Gregory Coude Telescope, operated on the island of Tenerife by the Observatory of Go ttingen Uni- the polarimeter was carefully aligned in the laboratory versity, in the Spanish Observatorio del Teide of the Instituto de using an He-Ne laser (see Appendix B in Sa nchez Almeida Astrof sica de Canarias. 2 Consejo Superior de Investigaciones Cient Ðcas, Spain. 1988). 3 Departamento de Astrof sica, Universidad de La Laguna, Tenerife, The seeing conditions were particularly poor that day, Spain. resulting in a rather modest spatial resolution. The slit aper- 1141

2 1142 SOCAS-NAVARRO, TRUJILLO BUENO, & RUIZ COBO Vol. 544 ture was then set to 180 km, which corresponds to about 1A.5, in order to gather as much light as possible. Two CCD cameras were mounted on the focal plane of the spectrograph to simultaneously record the two Ca II lines at 8498 and 8542 A, respectively. The line at 8498 A has an Fe I blend at 8497 A, which is very fortunate for our analysis since it provides information on the photospheric conditions. Unfortunately, we do not have continuum in our images because the Ca II lines are too broad to Ðt in the CCD. The quiet-sun local continuum is estimated by Ðtting averaged quiet-sun proðles taken at disk center to the solar atlas of Neckel & Labs (1984). Lacking an absolute wavelength calibration, we also used this Ðt to provide the wavelength scale for our data. With this instrumental setup we observed two di erent sunspots near the disk center. These are the sunspots cataloged as NOAA 8338 (hereafter referred to as S-A ÏÏ) and NOAA 8340 (hereafter referred to as S-B ÏÏ). While S-A does not exhibit any particularly remarkable feature, S-B shows an asymmetric geometry with two umbrae separated by a light bridge. For our purposes of studying the chromospheric dynamics, an important distinction between both sunspots is that while S-B shows UFs, S-A does not. We will be mainly concerned here with the observations of S-A, although some data from S-B will also be used in 5.3 below. We took time series of about 1 hour for each sunspot, aligning the slit with the center of the umbrae. The exposure time for the images was set to 10 s, and the time sampling of the series was 36 s. Since the spectrograph is in a coude focus, there is a rotation of the image on the focal plane with a period of 24 hours. An image rotation compensator is normally used with this telescope, in order to correct for the rotation e ect. Unfortunately, that was not possible in our case, because it would have introduced unwanted instrumental polarization. Consequently, there is a slow drift of the slit through the observed region, taking about half an hour to move from the starting position on the center of the umbra to the umbra-penumbra boundary. During the observation of S-A we let the slit drift until it was close to the umbra border. Then the slit was recentered on the umbra. For S-B, on the other hand, we carried out frequent slight manual corrections in order to keep the slit more or less centered on the same position. As a result of the image motion, it cannot be assured that the observed time series actually corresponds to the same spatial point. However, due to the slowness of the motion and to the high spatial coherence of the phenomena under study (which, as we will show below, involve the whole umbra), the slit drift does not pose a drastic limitation for our analysis. In the process of data analysis we performed a secondorder, Ñat-Ðeld correction similar to that introduced by Sa nchez Almeida & Mart nez Pillet (1994), but with the di erence that we used Ñat-Ðeld images instead of data images to determine the correction. The procedure is basically as follows. The chip is divided into two di erent portions, one of them containing the observed (I ] V ) image and the other containing the observed (I[ V ). Let us denote these as (I ] V )obs and (I[V )obs. After subtracting the dark current level, these images are proportional to the solar signal (assuming a linear behavior of the detector) that we denote by (I ] V )s and (I[V )s, respectively. Ideally, one is able to determine the (pixel dependent) proportionality constant between the observed and solar signals by recording the response of the chip to a Ñat uniform illumination. This response is the Ñat-Ðeld image (F). Since the (I ] V )obs and (I[V )obs are recorded on separate regions of the chip, we have a di erent Ñat Ðeld for each one of them. We denote these by and F. The Stokes parameters I and V are then F` ~ Is \ 1 C(I ] V )obs (I[V )obsd ], (1) 2 F F` ~ V s \ 1 C(I ] V )obs (I[V )obsd [. (2) 2 F F` ~ The problem is that and F are not perfectly known. The measured Ñat Ðelds F` (denoted ~ by Fòbs and F~ obs) are a ected by small inaccuracies, which can be due to noise, imperfections in the uniformity of the incident illumination, variations in the conditions between the measurement of the Ñat Ðeld and the data images, etc. Thus, we can write down Fòbs \ F`(1 ] d`), (3) F obs \ F (1 ] d ), (4) ~ ~ ~ where and d are >1. d` ~ Usually, the Stokes I and V parameters are retrieved through a Ðrst-order, Ñat-Ðeld correction. Denoting these as I1 and V 1 we can write down I1\ 1 C(I ] V )obs (I[V )obsd ], (5) 2 Fòbs F obs ~ V 1\ 1 C(I ] V )obs (I[V )obsd [. (6) 2 Fòbs F obs ~ The polarimetric precision achieved in this manner depends on the inaccuracies of the Ñat-Ðeld measurement. The error in the retrieved Stokes parameters I and V can be estimated using equations (1)È(6): I1[Is \[ 1 2 V 1[V s \[ 1 2 C(I ] V )obs F` C(I ] V )obs F` (I[V )obs d d` ] ~ D, 1 ] F 1 ] d d` ~ ~ (7) (I[V )obs d d` [ ~ D. 1 ] F 1 ] d d` ~ ~ (8) In practice, V > I and 1 ] ^ 1 ] d ^ 1. Taking this into account, if we add and subtract d` equations ~ (7) and (8) and recall equations (1) and (2), we Ðnd that the relative errors in the Stokes parameters are I1[Is C \[ 1 ] d ) ] V s )D Is 2 (d` ~ Is (d` [ d ~ V 1[V s \[ 1 V s 2 ^ [ 1 2 (d` ] d ~ ), (9) ^ [ 1 2 C Is V s (d` [ d ~ ) ] (d` ] d ~ )D Is V s (d` [ d ~ ). (10)

3 No. 2, 2000 ANOMALOUS STOKES V PROFILES IN SUNSPOT CHROMOSPHERES 1143 Equations (9) and (10) show that the accuracy in Stokes I is roughly that of the Ñat-Ðeld measurement, which is usually below 1%. However, the relative error in the Stokes V proðle is multiplied by a factor IS/V S, which typically lies between 10 and 100. Therefore, while the I1 is usually a fairly accurate estimation of Is, limited only by the noise in the data, V 1, on the other hand, is limited by the accuracy in the Ñat-Ðeld measurement. If we had any means to determine the factor [ d ) in equation (10), we could use that information (d` to further ~ correct our proðles in order to obtain a better approximation for V s. The images used for the determination of the Ñat Ðeld were observed immediately after the series of S-A and before that of S-B. These are images of the disk-center quiet Sun, which are taken moving the telescope along the northsouth direction during the exposure time. It is, therefore, reasonable to assume that there should not be any solar Stokes V signal in them (i.e., V s ^ 0). With this assumption, equation (10) yields flatfield V 1 \[1 [ d )Is. (11) flatfield 2 (d` ~ flatfield Neglecting second-order terms in [ d ) in equation (9), (d` ~ we can write Is \ I1. Substituting it in equation flatfield flatfield (11), we Ðnd that [ d ^ [2 d` V 1 flatfield. (12) ~ I1 flatfield It is now straightforward to use equation (12) to correct our data: V s \ V 1]1 2 (d` [ d ~ )Is. (13) As above, using equation (9) to write Is in terms of I1 and neglecting second-order terms in [ d ), equation (13) (d` ~ Ðnally yields V s \ V 1]1 [ d )I1. (14) 2 (d` ~ In this manner, we use equation (14) to correct the Ðrstorder estimate V 1, thus achieving a better accuracy in the measurement of the polarization signals. Figure 1 shows an image of the S-A series after the data analysis process. The noise in the resulting Stokes I and V proðles is between 5 ] 10~4 and 10~3, in units of the quiet-sun continuum. Residual interference fringes still remain on the data, but they can be easily removed with a suitable spatial Ðltering. A diamond-shaped large-scale structure from the camera shutter is also visible in the Stokes V image. Since the umbral region is either una ected or only a ected far in the wings, those points can be removed from the data set without any signiðcant loss of information. 3. TEMPORAL VARIATION OF THE PROFILES Figure 2 shows the temporal variation of the Stokes I and V proðles emergent from the umbra. Each proðle corresponds to the center of the umbra portion covered by the slit. The image drift is clearly visible as a gradual brightening of the intensity in the line wings from the beginning of the series. It can also be seen around the middle of the series, the point where the slit position was corrected to place it again on the center of the sunspot. Another remarkable feature is the presence of alternating light and dark horizontal lines in the Stokes I image, extending from the wings to the core. We cannot, in principle, guarantee that this is a solar e ect because each proðle in Figure 2 corresponds to a given time and is obtained from the corresponding image. The quiet-sun continuum intensity, used for the normalization of the proðles, had to be estimated by indirect means (as described above) for each one of the images. The uncertainty in the normalization value for the individual proðles introduces some random intensity Ñuctuations when the whole time series is put together in Figure 2. We estimate the error in our continuum determination to be around 1%, which is of the order of the observed di erences between the bright and dark horizontal FIG. 1.ÈStokes I (bottom) and V (top) images of S-A after the data analysis process with second-order Ñat-Ðeld correction. The two horizontal lines at 8A and 29A are hairline marks.

4 1144 SOCAS-NAVARRO, TRUJILLO BUENO, & RUIZ COBO Vol. 544 FIG. 2.ÈTemporal variation of the Stokes I (lower image) and V (upper image) proðles. The slow drift of the slit, moving from the center of the umbra toward the penumbra, is visible as a gradual brightening of the intensity in the wings. The slit is recentered on the umbra at t \ 30 minutes. lines. Nevertheless, as we will see below, these intensity Ñuctuations show a clear period of D3 minutes, which indicates that they probably have a solar origin V ariations in the ProÐles Shape The Stokes V image in Figure 2 shows that the chromospheric Ca II lines are crossed at regular time intervals by horizontal lines that do not show up in the photospheric Fe I line at 8497 A. A closer look at these horizontal lines reveals that they consist of bright features embedded within the dark V lobes and dark features within the bright V lobes. We have depicted a time sequence of I and V proðles in Figures 3 and 4. It turns out that, while the red lobe of the Stokes V remains more or less unchanged during the series, the blue lobe undergoes dramatic shape changes, to the point of completely destroying the well-known antisymmetry that is characteristic of the Stokes V signals. We will refer to these asymmetric proðles as anomalous ÏÏ V proðles. Note that the photospheric Fe I line at 8497 A barely changes, thus evidencing the chromospheric origin of the mechanism that originates the anomalous proðles T emporal and Spatial Distribution of Anomalous ProÐles In order to analyze the distribution of anomalous proðles we must Ðrst set an objective criterion to deðne what we understand by this term. It is obvious from Figure 4 that a measurement of the proðle asymmetry should be a good objective indicator. Among several di erent deðnitions that we tried, we found that a very suitable one is given by the following formula: A \ 100 ] / = (V [ V )2 dj ~= obs ant, (15) / = V 2 dj ~= ant where V is the observed Stokes V proðle and V is a obs ant perfectly antisymmetric proðle (with respect to the zerocrossing wavelength), whose red lobe is identical to that of V obs. The above deðnition somehow represents a percentage of asymmetry. In order to study its time behavior, we plot the parameter A versus time in Figure 5 (upper panel). As we anticipated in the discussion of Figure 4, we can see that the normal, more or less antisymmetric, V proðles periodically turn into anomalous proðles. The power spectrum (see lower panel in Fig. 5) reveals two distinct peaks, at 2.5 and 3.3 minutes, respectively. Due to the drift of the slit through the image, the interpretation of these results as a real time-dependent behavior of the polarization signal would be questionable if the spatial coherence of the phenomenon under study were small. It is therefore crucial to study the spatial distribution of the anomalous proðles along the slit and how this distribution changes with time. To that aim, we have adopted the convention that a proðle whose asymmetry (deðned by eq. [15]) exceeds 25% is considered as anomalous. With this convention we calculate the number of anomalous proðles that are present along the slit direction at a given time in the series. Figure 6 shows, as a function of time, the percentage of anomalous proðles in the umbra along the slit. If there is no preferred azimuthal direction in the sunspot, this number should be representative of the percentage of points on the whole umbra which produce anomalous proðles at a given time. It turns out that the physical process which is originating these proðles is characterized by a large-scale spatial coherence. This means that at some moments the umbra is quiet,ïï and at other moments almost the whole umbra is producing anomalous proðles, as can be seen in Figure 6. Observations of Stokes I in chromospheric lines indicate that the umbral oscillation is characterized by a periodicity of 2È3 minutes and a large-scale spatial coherence (see, e.g., Thomas 1984). The observed properties of anomalous pro-

5 No. 2, 2000 ANOMALOUS STOKES V PROFILES IN SUNSPOT CHROMOSPHERES 1145 FIG. 3.ÈTime series of Stokes I proðles normalized to the quiet-sun continuum (the time sampling is 36 s). Successive proðles are shifted in ordinates by 0.1. The dotted lines connect the proðles of Ca II jj8498 and 8542, which are simultaneous. Ðles discussed above, of time periodicity and spatial coherence, seem to indicate a connection with the chromospheric umbral oscillation. We will therefore concentrate on the study of the oscillatory properties of this umbra in the next section. 4. UMBRAL OSCILLATIONS With our set of data we have the possibility of analyzing the oscillations in the photosphere using the Fe I line at 8497 and in the chromosphere with the Ca II infrared A lines. The main limitation has to do with the slit drift, due to the image rotation produced by the telescope. This prevents us from observing at the same spatial position through the whole time series. Nevertheless, we can safely study all those properties that exhibit a large-scale spatial coherence, as we did above with the occurrence of anomalous proðles. The variation of a given quantity along the slit direction should be a good indicator of whether such quantity has a local or

6 1146 SOCAS-NAVARRO, TRUJILLO BUENO, & RUIZ COBO Vol. 544 FIG. 4.ÈTime series of the Stokes V proðles, simultaneous to those in Fig. 3, normalized to the quiet-sun continuum intensity. Successive proðles are shifted in ordinates by Note the oscillation between normal antisymmetric and anomalous asymmetric proðles in the chromospheric lines. a global character and, therefore, whether it is or not useful for our analysis Photospheric Oscillations One of the obvious indicators of the photospheric oscillation is the line core Doppler shift, which gives an estimate of the velocity in the atmosphere with the oscillation cycle. In our case this task is extremely difficult, mainly for two reasons. First, the Fe I line is so weak in the umbra that the noise makes it almost impossible to accurately determine the line minimum position. The fact that the line is completely split by the Zeeman e ect contributes to its weakness. Second, the contamination with stray light coming from the surroundings of the umbra masks the real shape of the line, and it would be difficult to disentangle its e ect. Fortunately, we also count on the information provided by the Stokes V proðle. This signal is strong (see Fig. 4) and fairly una ected by stray light. The zero-crossing wavelength of Stokes V is often used to determine velocities in the line formation region. In our case, however, this is not possible because the Fe I line is blended in the blue wing of the Ca II line at 8498 A. We then estimate the line center

7 No. 2, 2000 ANOMALOUS STOKES V PROFILES IN SUNSPOT CHROMOSPHERES 1147 the peaks. The shift of the peaks depends on the slope of the Ca II Stokes V proðle at the wavelengths of the Fe I line. We have corrected for this e ect by Ðtting a straight line to the Ca II proðle around A. This gradient is then subtracted from the Fe I Stokes V proðle. The velocities obtained with the procedure described above are coherent through the whole umbra. The spatial average of these velocities as a function of time is depicted in Figure 7 (upper panel). The velocities in this Ðgure had to be corrected for the SunÏs rotation velocity ([125 m s~1 at the coordinates of S-A), because the wavelength calibration was carried out using Ñat-Ðeld images taken at disk center (see 2), and the sunspot is at 7 east and 35 north from disk center. The power spectrum of the derived average photospheric velocity is presented in Figure 7 (lower panel). We can see that the umbral photosphere is oscillating with a very clear period of 5 minutes (i.e., with a frequency of 3.33 MHz). This result, as well as the amplitude of the oscillation, is in agreement with previous work by other authors using di erent lines (see, e.g., Lites 1993 and the references therein). In contrast to the velocity Ðeld, the power spectrum of the time series of magnetic Ðeld strengths (determined from the wavelength separation between the red and blue Stokes V peaks) looks like a noise spectrum with no single peak that dominates over the others. FIG. 5.ÈAsymmetry of an umbral V proðle as a function of time (upper panel) and its power spectrum (lower panel). The anomalous proðles repeat themselves periodically every D150 s. wavelength as the average of the blue and red peak wavelengths, which are calculated by Ðtting a second-order polynomial to each peak. The fact that the Fe I Stokes V proðle is blended in the Ca II wing might produce a slight shift of FIG. 6.ÈFraction of anomalous proðles in the umbra at any time. Their occurrence is characterized by a large-scale spatial coherence, as can be deduced from this plot. FIG. 7.ÈUpper panel: Spatially averaged photospheric velocities, determined from the Stokes V proðles of the Fe I line at 8497 A. Positive values correspond with redshift. L ower panel: Power spectrum of the photospheric velocity.

8 1148 SOCAS-NAVARRO, TRUJILLO BUENO, & RUIZ COBO Vol Chromospheric Oscillations The chromospheric oscillation is normally studied by interpreting the core Doppler shifts of strong chromospheric lines as due to chromospheric velocities. This approach, however, is dangerous (as pointed out by Athay 1970) and can even be misleading. In this section we will analyze some properties of the Ca II line minima shift, but the reader is warned against interpreting these directly as Doppler shifts of the line core. Figure 8 shows the temporal variation of the line minimum positions of the proðles in Figure 2. Note that the minima are always redshifted and that the line at 8542 A, which is sensitive to higher layers than the one at 8498 A, exhibits larger shifts. Finally, the most remarkable feature of the minimum shifts is its strong correlation with the occurrences of anomalous proðles, as can be seen in Figure 9. Their power spectra are, then, very similar to that shown in Figure 5 (lower panel). The intensity at the line cores is another indicator of the chromospheric oscillation. Figure 10 (upper panel) shows these intensities in both Ca II lines. The units are arbitrary to plot both curves in the same scale. The correlation between both intensities is evident. It can be seen in Figure 10 (lower panel) that the oscillation in the core intensity is also strongly correlated with the oscillation in the shift of the line minimum. FIG. 9.ÈCorrelation between the line minimum shift and the Stokes V asymmetry. The results presented in this section indicate that the chromospheric lines oscillate with two spatially coherent dominant periods of 2.5 and 3.3 minutes (see Fig. 5, lower panel). This oscillation can be seen in the Stokes V proðles FIG. 8.ÈTemporal variation of the Ca II j8498 (upper panel) and j8542 (lower panel) line minimum positions. Positive values indicate redshift. FIG. 10.ÈUpper panel: Line core intensities of Ca II j8498 (solid) and j8542 (dashed) as a function of time. L ower panel: Shift of the line minimum of Ca II j8542 (solid) and its core intensity (dashed).

9 No. 2, 2000 ANOMALOUS STOKES V PROFILES IN SUNSPOT CHROMOSPHERES 1149 asymmetry, the percentage of anomalous proðles in the sunspot umbra at a given time, the shift of the line minima, and the line core intensity. All these quantities are strongly correlated, and their power spectra are very similar, exhibiting two main peaks at 2.5 and 3.3 minutes. In the next section, we present a physical interpretation to the occurrence of anomalous proðles, which is able to explain why all of these quantities are so tightly bond to each other. 5. INTERPRETATION OF THE ANOMALOUS PROFILES In the previous sections we have reported on the observation of strongly asymmetric Stokes V proðles in the umbra of a sunspot. The observational picture that we have sketched sofar can be summarized as follows. The analysis of the time series reveals that normal antisymmetric V pro- Ðles periodically turn into anomalous proðles, returning later to their normal state. This process takes place with a large-scale spatial coherence, which means that the whole umbra is either quiet ÏÏ or producing anomalous proðles at a given moment. The shape of the Stokes I proðles does not show remarkable variations (this sunspot does not exhibit umbral Ñashes), but there is a very strong correlation between the redshift of the line minima, the line core intensities, and the parameter of Stokes V asymmetry. In principle, there are three possibilities to explain, in physical terms, the shape of the proðles: 1. Strong gradients of magnetic Ðeld and line-of-sight velocity in unidimensional models. Gradients in these quantities are known to produce asymmetries on the Stokes V proðles. 2. E ects of atomic orientation (see Trujillo Bueno et al. 1993). When non-lte e ects are important and strong velocity gradients are present in a magnetized plasma, the Zeeman atomic sublevels may not be equally populated. In this situation the red and blue lobes of the V proðle change their relative weights, giving rise to asymmetric proðles. 3. Unresolved components. If more than one atmospheric component coexists within the resolution element, each one producing di erent Doppler-shifted proðles, the result can be strongly asymmetric even if each individual proðle is antisymmetric. Let us now consider each one of these possibilities in some detail Magnetic Field and V elocity Gradients It is well known that, by combining gradients in the magnetic Ðeld and line of sight velocity, one is able to produce asymmetries in the shape of the Stokes V proðles. We therefore tried to invert one of the anomalous proðles using the non-lte inversion code described by Socas-Navarro, Trujillo Bueno, & Ruiz Cobo (2000b) to see if a onedimensional single-component scenario could produce anomalous proðles with a combination of strong gradients in the atmospheric variables. Several attempts with di erent proðles, using up to six nodes for the velocity and the magnetic Ðeld vector (a larger number of nodes results in serious convergence problems), have proved unsuccessful. Note that six equispaced nodes, placed within a range of log (q ) between 1 and [7, should allow for the recovery of fairly 500 steep gradients. However, we could not Ðt the anomalous proðles or even obtain qualitative similarities with this approach. Clearly, there have to be other physical ingredients to take into account to produce proðles like those described in this paper Atomic Orientation E ects Atomic orientation is the name given to the situation where the Zeeman sublevels (pertaining to a given atomic level) with magnetic quantum numbers M \]m and M \[m are not equally populated (see Landi DeglÏInnocenti 1985). This situation may be produced in transitions formed under non-lte conditions in the presence of magnetic Ðelds and macroscopic velocity gradients. In non-lte, the atomic level populations are strongly coupled with the radiation Ðeld, which is Doppler-shifted by the velocity Ðeld, as illustrated in Figure 11. The di erent illumination seen by the Zeeman sublevels with di erent magnetic quantum number leads to the atomic orientation. When the populations are equipartitioned among the sublevels pertaining to each atomic level, the emergent pro- Ðles are straightforwardly computed from the vector radiative transfer equation (see, e.g., Rees, Murphy, & Durrant 1989). In the absence of atomic polarization (i.e., when all of the sublevels are equally populated), the circular polarization proðle is given by n + n 0 n - / V \ 1 2 (/ r [ / b ) cos c, (16) which is proportional to the di erence between the redshifted (/ ) and the blueshifted (/ ) p components and the r b cosine of the inclination angle c. In the case that atomic orientation is present, it can be shown (Trujillo Bueno 2000) for a normal Zeeman triplet with J \ 0 and J \ 1 that the above formalism is still low up valid if the / and / proðles are scaled by an amount that b r accounts for the atomic orientation: / r a.o. \ (1 ] a)/ r, (17) / b a.o. \ (1 [ a)/ b, (18) where a is a parameter that measures the di erence in the populations of the sublevels with M \]1 and M \[1 (n` and n~, respectively): n` [ n~ a \ n` ] n~. (19) In a general case where the lower and upper levels are Zeeman multiples, each pair of levels with opposite values for M has its own parameter a, which describes the atomic orientation in those particular sublevels. Besides, one may n + n 0 n - FIG. 11.ÈSchematic illustration of the physical process that originates the atomic orientation. In the absence of velocity Ðelds, the atomic populations n` and n~ are the same (left). When the radiation Ðeld is Dopplershifted by an amount comparable to the line width, the sublevels are not equally illuminated (right) and we have atomic orientation.

10 1150 SOCAS-NAVARRO, TRUJILLO BUENO, & RUIZ COBO Vol. 544 have atomic orientation either in the lower level (which a ects the absorption matrix) or in the upper level (which, neglecting stimulated emission, a ects only the emission vector) of the transition, or in both levels simultaneously. Thus, for a given transition, the absorption matrix has the proðles / and / scaled with an a@ that accounts for the lower level b atomic r orientation, while the emission vector has them scaled with an a that accounts for the upper level atomic orientation. With these ingredients we are now in a position to study what the observational signatures of the atomic orientation on the Stokes V proðles are. To this aim, we carry out a number of ad hoc simulations in the following way. Using the sunspot umbra model of Socas-Navarro et al. (2000b), the non-lte problem is solved with the Ðeld-free approximation. The departure coefficients obtained in this manner are then used to synthesize the Stokes vector but scaling the proðles / and /, as in equations (17) and (18), with an arbitrary orientation b r parameter a that we can vary at will to simulate a stronger or weaker atomic orientation e ect. Figure 12 shows an example of such simulations for the Mg I b line, which is a triplet transition with J \ 0 and 4 low J \ 1, using an orientation parameter a \ The up intensity proðle remains almost una ected, and the changes are only visible on the polarization proðle. This is to be expected, because the polarization is weak (see Sa nchez Almeida & Trujillo Bueno 1999). The symmetric contribution to the Stokes V proðle introduced by the atomic orientation does not yield proðles like the observed anomalous proðles. The clearest signature of the atomic orientation is a net shift of the polarization signals in the wings. Figure 12 shows that, while the proðle without orientation has its wings more or less symmetrically situated above and below the zero level, the proðle with a \ 0.05 has both wings above the zero level (although, of course, the polarization signal vanishes in the continuum). This signature is not observed in our data, where the polarization in the chromospheric lines has di erent sign at the red and blue wings (see Fig. 4). Atomic orientation, therefore, does not seem to be under the physical origin of the anomalous proðles. Since the Ca II lines are sensitive to the radiation Ðeld in the atmosphere and the Doppler shift of the proðles is more important in the infrared, one might be tempted to conclude that the absence of atomic orientation e ects on the observed proðles implies that there cannot exist large velocity Ðelds in the atmosphere. However, it must be kept in mind that in non-lte all the level populations are coupled together. In this particular case, the upper level populations of the Ca II infrared transitions are dominated by the strong ultraviolet resonance lines H and K. In the ultraviolet, the Zeeman splitting is much smaller, because *j is proportional to j2. The H and K lines are so broad, and the Zeeman splitting is so small, that the di erential illumination of the Zeeman sublevels with opposite M is negligible. Another important e ect, which smooths out the atomic orientation, is that even in the presence of a di erential illumination, there exist elastic collisions in the medium. These are the same collisions that originate the collisional broadening of the line wings, and their presence contributes to redistribute the atomic populations among the various Zeeman sublevels Multicomponent Atmospheres A clear hint on the nature of the anomalous Stokes V proðles described in this paper shows up when one subtracts a normal antisymmetric proðle from an anomalous proðle. Figure 13 (upper panel) shows two successive proðles in the time series (the Ðrst one being normal and the second FIG. 12.ÈSynthetic Stokes I and V proðles of the Mg I line in the absence of atomic orientation (solid lines) and with an orientation parameter a \ 0.05 b 4 (dashed lines).

11 No. 2, 2000 ANOMALOUS STOKES V PROFILES IN SUNSPOT CHROMOSPHERES 1151 FIG. 13.ÈTop: Anomalous (solid lines) and normal (dashed lines) Stokes V proðles. The di erence between them (dotted lines) is rather antisymmetric. Bottom: Corresponding Stokes I proðles and their di erence. anomalous) and their di erence. A number of conclusions can be drawn from this Ðgure, that we now proceed to discuss. It turns out that the anomalous proðles can be constructed from a normal proðle, like the one observed 36 s before, plus another contribution (dotted line) with the following properties. The additional contribution seems to be another, rather antisymmetric, Stokes V signal. This signal can be interpreted as being produced by an unresolved second component. In this qualitative discussion

12 1152 SOCAS-NAVARRO, TRUJILLO BUENO, & RUIZ COBO Vol. 544 FIG. 14.ÈL eft: Stokes I and V proðles of an umbral Ñash in S-B, averaged with the surrounding umbra to simulate an unresolved Ñash. Right: Stokes I and V proðles corresponding to an instant of anomalous proðles in S-A. The ordinate scale in the bottom left panel has been inverted to allow for an easy comparison with the bottom right panel, because both sunspots have opposite polarities. we have not taken into account that the contributions coming from both components are weighted by appropriate Ðlling factors. Our only aim, for the moment, is to show that a combination of two normal ÏÏ Stokes V proðles leads straightforwardly to the observed anomalous proðles. In this scenario we would have a quiet ÏÏ sunspot chromosphere producing the normal proðles in Figure 4; every 2.5 minutes, a second atmospheric component shows up. The emergent proðles from this second component (which we will denote as active ÏÏ component and active proðles) are also antisymmetric Stokes V proðles. However, when they are combined with the proðles from the quiet component, the result is one of the observed strongly asymmetric anomalous proðles. A close examination of the active proðle in Figure 13 (upper panel) shows two noteworthy features. First, the zero-crossing wavelength is blueshifted with respect to the quiet proðle by about 5 km s~1, which suggests important

13 No. 2, 2000 ANOMALOUS STOKES V PROFILES IN SUNSPOT CHROMOSPHERES 1153 upward motions within the active component. And second, the proðle polarity is reversed. The polarity reversal does not necessarily imply a change in the magnetic Ðeld polarity (which would be very difficult to understand). An emission feature in the core of a spectral line yields Stokes V signals exhibiting a reversed polarity with respect to the case of pure absorption. Figure 13 (lower panel) shows the corresponding Stokes I proðles. Note that even though there are no clear emission features visible in the observations, the proðle plotted in solid line can be constructed by adding a blueshifted emission to the one in dashed line, thus supporting the idea that the polarity reversal of the active Stokes V proðle is due to the presence of an emission feature. So far we have seen that the anomalous proðles, which are observed at regular time intervals in S-A, cannot be explained by gradients of magnetic Ðeld and velocities or by atomic orientation e ects. A plausible explanation arises in a natural way if one considers that a second active ÏÏ component develops periodically within the resolution element, everywhere in the umbra. This second component produces Stokes I proðles with blueshifted emission cores and the corresponding Stokes V proðles with reversed polarities. The combination of the quiet and active proðles explains the observed anomalous Stokes V proðles. In this manner, one is also able to understand the tight correlation observed among the di erent parameters of the chromospheric umbral oscillation (see Figs. 9 and 10). In 4.2 we showed that the position of the line minimum, the line core intensity, and the occurrence of anomalous proðles were in perfect synchronization. It is now obvious that when the active component develops, the line core intensities are enhanced by the emission and the Stokes V proðles become anomalous. The redshift of the line minimum would not correspond to a real velocity-induced Doppler shift but is rather a consequence of the blueshifted emission core. All of the above-summarized properties of the active proðle resemble the observed properties of the UFs. The question that immediately arises is whether we are observing the same physical process that leads to the emission of UFs but at either weaker energies or smaller scales. This is an interesting question because if this is the case, there are two important considerations to bear in mind. First, the potential value of the polarization proðle as a diagnostic of weak ÏÏ UFs would be beyond question, allowing one to detect them as anomalous V proðles. And second, because it would suggest that the answer to the question of why UFs occur in some sunspots and not in the others could be that they are present in all of them at di erent scales or with di erent strengths, being only detectable in some cases as emissions in the core of Stokes I. As mentioned in 2, we detected some UFs (deðned following Beckers & Tallant 1969, as emission reversals in the Ca II line cores) in the time series for S-B. In Figure 14 (left) we have depicted the Stokes I and V proðles of an UF in S-B averaged with the surrounding umbra, in order to see what an unresolved UF would look like. The FWHM of the UF is D2A, and it was averaged with D4A of umbra along the slit direction. The left-hand side of Figure 14 shows, then, what an unresolved UF with a Ðlling factor of 30% looks like. Compare it to Figure 14 (right), where we have plotted the Stokes I and V proðles for an instant with anomalous proðles in the time series of S-A. Even though these Ðgures correspond to data from di erent sunspots, the similarities between them are striking. 6. CONCLUSIONS In this paper we have described in detail novel observations that give information on the time-dependent behavior of the circular polarization proðles in sunspot umbrae. The lines observed are the chromospheric Ca II lines at 8498 and 8542 A and the photospheric Fe I line at 8497 A. These observations have unveiled a so far unknown behavior of Stokes V in the chromospheric lines, with a periodic oscillation between a normal antisymmetric proðle and an anomalous, strongly asymmetric proðle. The occurrence of the anomalous proðles is global over the whole umbra and is strongly correlated with the line minimum shift and their core intensities. These spectropolarimetric observations should be considered as a reference for future radiation magnetohydrodynamic simulations of sunspot chromospheres. We have taken into account three possible mechanisms to interpret in physical terms the anomalous Stokes V pro- Ðles, namely, strong gradients in velocity and magnetic Ðeld e ects of atomic orientation and unresolved atmospheric components. We explored each one of these possibilities and found arguments to discard the former two so that we are Ðnally left only with the latter. A careful examination of the proðles leads to the conclusion that they are probably caused by the periodical development of an active component within the resolution element, whose proðles are characterized by a blueshifted emission feature which is not directly visible in the observations because it is masked within the quiet proðle. A comparison with a di erent set of data from another sunspot reveals that this active component is probably the same that produces UFs in other sunspots. There are two important consequences of this fact. First, the Stokes V proðle proves to be an important diagnostic tool for such weak ÏÏ Ñashes that cannot be detected otherwise. Second, the physical process that leads to the occurrence of UFs might be present in all the sunspots and not only in some of them. In some cases the Ðlling factor of the active component is large enough to make the Ñash detectable as line core emissions; in some others, the Ðlling factor is small and the UFs are not resolved in the umbra, thus remaining undetected. Partial support from the Spanish DGES through project PB is gratefully acknowledged. We are grateful to Franz Kneer and Jorge Sa nchez Almeida for their advice in relation with the observations and the data analysis. This work is part of a continuing EC-TMR European Solar Magnetometry Network. REFERENCES Athay, R. G. 1970, Sol. Phys., 11, 347 Beckers, J. M., & Tallant, P. E. 1969, Sol. Phys., 7, 351 Kneer, F., Mattig, W., & von Uexku ll, M. 1981, A&A, 102, 147 Lites, B. W. 1993, in Sunspots: Theory and Observations, ed. J. H. Thomas & N. O. Weiss (NATO ASI Ser., 375; Dordrecht: Kluwer), 261 Moore, R. L. 1981, in The Physics of Sunspots, ed. L. E. Cram & J. H. Landi DeglÏInnocenti, E. 1985, in Theoretical Problems in High Thomas (Sunspot: Sacramento Peak Obs.), 259 Resolution Solar Physics, ed. H. U. Schmidt (Mu nchen: Max-Planck- Inst. fu r Astrophysik), 162 Moore, R., & Rabin, D. 1985, ARA&A, 23, 239 Neckel, H., & Labs, D. 1984, Sol. Phys., 90, 205

14 1154 SOCAS-NAVARRO, TRUJILLO BUENO, & RUIZ COBO Rees, E. E., Murphy, G. A., & Durrant, C. J. 1989, ApJ, 339, 1093 Sa nchez Almeida, J. 1988, Ph.D. thesis, Univ. La Laguna Sa nchez Almeida, J., & Mart nez Pillet, V. 1994, ApJ, 424, 1014 Sa nchez Almeida, J., Mart nez Pillet, V., & Wittmann, A. D. 1991, Sol. Phys., 134, 1 Sa nchez Almeida, J., & Trujillo Bueno, J. 1999, ApJ, 526, 1013 Schro ter, E. H., Soltau, D., & Wiehr, E. 1985, Vistas Astron., 28, 519 Semel, M. 1980, A&A, 91, 369 Socas-Navarro, H., Trujillo Bueno, J., & Ruiz Cobo, B. 2000a, Science, 288, 1396 ÈÈÈ. 2000b, ApJ, 530, 977 Thomas, J. H. 1981, in The Physics of Sunspots, ed. L. E. Cram & J. H. Thomas (Sunspot: Sacramento Peak Obs.), 345 ÈÈÈ. 1984, A&A, 135, 188 ÈÈÈ. 1985, Australian J. Phys., 38, 811 Trujillo Bueno, J. 2000, in preparation Trujillo Bueno, J., Mart nez Pillet, V., Sa nchez Almeida, J., & Landi DeglÏInnocenti, E. 1993, in ASP Conf. Ser. 46, The Magnetic and Velocity Fields of Solar Active Regions, ed. H. Zirin, G. Ai, & H. Wang (San Francisco: ASP), 526 Wittmann, A. 1969, Sol. Phys., 7, 366