Spectropolarimetric Observations of the Helium 10830 A˚ Line: a Search for the Signature of Optical Pumping

SPECTROPOLARIMETRIC OBSERVATIONS OF THE HELIUM 10830 A˚ LINE: A SEARCH FOR THE SIGNATURE OF OPTICAL PUMPING

Nathan Goldbaum

University of Colorado at Boulder

Advisor: Jeﬀ Kuhn

University of Hawaii, Institute for Astronomy

ABSTRACT

In order to characterize the center-to-limb and latitudinal variation of the polarization of the He I 10830 A˚ line we observed the limb of the sun at several position angles using the Scatter-Free Observatory for Limb Active Regions and Coronae (SOLARC), an imaging spectropolarimeter located on the summit of Haleakala, Maui. The data were reduced and analyzed to produce proﬁles of the magnitude of the Stokes Q/I and U/I signals as a function of latitude and solar radius. Modeling of the observed proﬁles should allow us to detect whether the observed linear polarization signal is due entirely to scattering polarization or possibly includes absorptively polarized light transmitted through an optically pumped gas.

Subject headings: Sun, Optical Pumping, He I 10830 A,˚ Spectropolarimetry

1. Introduction

Spectropolarimetric observations offer a unique means to measure many properties of the solar atmosphere. Observing the second solar spectrum (Stenflo & Keller 1998) — the term used to describe the sun’s polarized spectrum — makes possible direct measurements of many important aspects of the sun’s atmosphere, particularly with respect to the vector magnetic field. Stokes I, Q, and U spectra can be used to map the photospheric magnetic field through the transverse Zeeman effect (Mickey et al. 1996). These maps are commonly used as the boundary conditions for force-free extrapolation of the chromospheric and coronal magnetic field (Guo et al. 2008). Spectropolarimetric data also enables direct observation of the coronal magnetic field by using both the Hanléand Zeeman effects (Lin et al. 2000, 2004), a necessary ingredient in fully understanding the nature of flares, the coronal heating problem, and many other open issues in solar physics (Judge 2003). The Helium I 10830 A˚ line is particularly attractive for studying structures in the chromosphere and corona due to its sensitivity to the Hanléand Zeeman effects (Centeno et al. 2008). – 2 –

In this work, we examine the linear polarization of the He I 10830 A˚ line using data obtained with SOLARC (Scatter-Free Observatory for Limb Active Regions and Coronae), a half-meter oﬀ- axis imaging spectropolarimeter designed for coronal observations and located on the summit of Haleakala, Maui. First, we discuss the physics of the transition and the mechanisms that could produce the observed linear polarization signal. Next, we describe the instrument and some of its unique properties. This is followed by a discussion of the observations and data reduction. Finally, we discuss the results of our observations and the key features which must be reproduced in any models which attempt to simulate this spectral line.

2. Optical Pumping

While observing the Hα line of a sample of Herbig Ae/Be stars, Harrington & Kuhn (2007) found a small change in the linear polarization signal in the absorptive component of the P-Cygni Hα proﬁles of several of the observed stars. Previous models, based on scattering polarization in the accretion disks surrounding these young and massive stars, predicted a linear polarization signal in the emissive component due to disk scattering but could not account for observed linear polarization observed in the absorptive component.

Kuhn et al. (2007) proposed a model that employed a resonant absorption mechanism to explain the observed Stokes profiles. In this model, an anisotropic radiation field induces population imbalances in the degenerate sublevels of the lower level of an atomic transition. A gas prepared in this way is said to be pumped. If a second beam of light is transmitted through a pumped gas at an angle to the pumping radiation, the emergent light will be linearly polarized. Kuhn et al. (2007) modeled the atomic physics of hydrogen and the performed the radiative transfer calculations necessary to predict the Stokes Q and U Hα profiles. The predictions included a significant polarization signal in the absorptive component of the Hα profiles. If optical pumping is the explanation for the observed line profiles in the Herbig Ae/Be stars, we should be able to see the signature of optical pumping in solar transitions when looking at the limb of the sun where there is a similar geometry.

The He I 10830 A˚ line has been well studied in the context of solar spectropolarimetric observations and atmospheric diagnostics (Trujillo Bueno et al. 2002; Trujillo Bueno & Asensio Ramos 3 2007; Centeno et al. 2008). This spectral line arises as a transition between the 2 P0,1,2 (Ju = 0, 1, 2) 3 3 state and the 2 S1 (Jl = 1) state of the neutral helium atom. The 2 S1 state is the metastable ground level of orthohelium and can only be populated through collisional excitation from the 1 ground level 1 S1 parahelium state. The 10830 A˚ line is a triplet, but it is observed as a doublet in the solar spectrum since the transitions with Ju=2,1 appear thermally blended at plasma tem- peratures (Trujillo Bueno et al. 2002). The observations presented here do not resolve the ‘blue’ component, a common occurrence in observations of the quiet sun He I 10830 A˚ line (Sanz-Forcada

& Dupree 2008). This transition is susceptible to optical pumping since the lower level has Jl = 1, which means there are three degenerate substates corresponding to mJ = ±1,0. If we consider the – 3 –

transition with Ju=0 and Jl = 1, as in Figure 1, the upper level will have only one substate and the lower level will have three substates. Resonant polarized absorption in this particular quantum system can be explained using an interesting semiclassical model.

Consider a pumping beam traveling in the z direction, incident on an isotropic gas that is susceptible to a transition with Ju=0 and Jl = 1. We assume the pumping beam has been tuned to excite this transition and that all of the degenerate lower level sublevels are equally populated. Since the pumping beam cannot excite oscillations along the beam’s direction of propagation, those transitions that correspond to oscillations in z, with ∆mJ =0, are not allowed. Transitions with ∆mJ = ± 1 may proceed, however. The pumping beam will induce any electrons in the levels with |mJ | = 1 — corresponding to induced oscillations in the x and y directions — to quickly jump to the upper level. After a short time in the upper level, the electrons undergo a spontaneous de-excitation with an equal probability for the electron to end up in any of the degenerate sublevels (mj=0 or ±1). Electrons in the state with mJ = 0 will only transition to a higher level due to collisions or through some other ‘forbidden’ mechanism. Over time the system will reach an equilibrium in which most of the electrons are in the state with mJ = 0 (Kuhn et al. 2007). The optical pumping mechanism can also operate on the states in which Ju = 2,1 (Trujillo Bueno 2002). If another unpolarized beam is incident on the gas in the y direction, the pumped gas absorbs and scatters the component of the unpolarized beam that is polarized along the z direction. The emergent beam will be polarized in the x direction due to resonant polarized absorption in an optically pumped gas. The observations considered here were of regions at the limb of the sun. In this geometry the pumping ﬁeld originates at the photosphere directly below the atmospheric helium. The transmitted absorptively polarized light, which we observe as linearly polarized light aligned with the limb, originates on the disk at the extreme limb. The radiation ﬁeld is anisotropic due both to the geometry and the limb darkening. It also bears mentioning that we will be observing polarized photons that originate in classical scattering events as well as ones which were polarized by passing through a pumped gas. Only modeling of the relevant atomic physics and radiative transfer will determine whether an optical pumping mechanism is in operation in our data.

3. SOLARC

SOLARC (Kuhn et al. 2003) is a 45 cm off-axis Gregorian telescope (Figure 3). The 11◦ off-axis angle places the primary focus out of the telescope’s line of sight, removing the secondary mirror and support structures from the field of view. This minimizes scattered light, allowing longer integration times that are critical for photon-limited observations. The telescope is fitted with a liquid-crystal-based fixed retarder system (Figure 4) that modulates the polarization state of the incoming light so that one Stokes parameter is sure to be transmitted through a linearly polarized analyzer and the orthogonal (negative) Stokes parameter is sure to be blocked. This allows a fixed linearly polarized analyzer to block, say, +Q polarized light but allow -Q, along with the unpolarized, U, and V polarized components of the beam. The modulated beam is focused – 4 – onto a fiber bundle array. The fiber array is made up of 128 fibers arranged in a 16×8 rectangular pattern. A lenslet on each fiber focuses light into the fiber core, minimizing lost photons due to thick fiber claddings. Each fiber images a 22-arcsecond field of view in the current configuration. The fibers pipe the light to an optical bench where the OFIS spectrograph (Figure 5) is located. At the fiber bundle exit the fibers have been rearranged into a 2×64 array, using the mapping scheme illustrated in Figure 2. The light exits the fiber bundle, passes through a collimating lens, and then is dispersed by an echelle grating ruled to 79 lines/mm with a blaze angle of 63.5◦. Another lens focuses the dispersed beam that passes through a blocking filter with a bandpass centered on the spectral region of interest. Finally, the beam is imaged on a 256 X 256 pixel Rockwell NICMOS near infrared array cooled to 77 K. The fiber bundle exit is aligned so that one spectrum falls in between two rows of the array — minimizing cross-talk between spectra from different fibers. Since the detector only has 256 rows and the spectrum from one fiber falls on two rows of the detector, each of the 128 spectra is imaged on two rows of the array.

Each spectrum corresponds to a different spatial point in the sky. In this way, we sample both spatially and spectrally simultaneously. A single observation consists of four separate exposures. A computer controls the peak-to-peak voltage of two AC signals which in turn modulate the birefringence of a liquid crystal inside each of the liquid crystal variable retarders (LCVRs). The first LCVR in the light path is aligned with the axis of the beamsplitter, which we use to analyze the beam’s polarization state. The second LCVR is permanently rotated 45◦ with respect to the analyzer. The light beam is made up of unpolarized, linearly polarized, and circularly polarized components. The polarization state of each component is modulated by passing through the retarders since the LCVRs have different indices of refraction along the vertical and horizontal axes. Both retarders together transform the polarization states we are not interested in into states that will cancel out when we calculate difference frames. For example, if we are trying to measure Stokes Q, one image (I+Q) will record the components that are unpolarized, polarized in U and V, and the +Q polarized component of the beam, but not the component that is -Q polarized. The next image (I−Q) will include −Q polarized component but not the +Q component. A Stokes Q image is the pixel-by-pixel difference between the I+Q frame and I−Q frame. Most counts will cancel out — corresponding to counts from the unpolarized, U, and V components of the incoming beams — but the component of the beam that is actually +Q polarized will not be present in the I−Q frame and will not be canceled out in the difference frame (and vice versa for the −Q component).

The system is very sensitive to vertical motions of the fiber bundle. Optimally, the spectrum from one fiber is centered between two rows of the array. In this way light from a single fiber falls more or less evenly on two rows of the detector. However, if the fiber exit drifts only by a few microns, the spectrum will tend to fall mostly on one row of the array with significant residual bleed on the rows directly above and below. If we are unaware of the drift, and a spectrum is calculated by adding together the counts from two adjacent rows of the array, the calculated spectrum will show double lines. This is because we have naively included the bleed rows that have counts originating from two fibers that are diagonally offset at the spectrograph entrance. These neighbor fibers that – 5 – sample completely different spatial points in the sky. We cannot correct for this bleed without knowing the signal we are measuring at the outset. Care must be taken to align the fiber exit periodically throughout an observing run. If data are taken in a misaligned configuration, then bleed rows must be discarded. The data are carefully inspected during reduction for this effect. There is no way to completely eliminate the cross-talk since the point spread function goes to zero over a distance of several pixels. However, the systematic error it produces is small — around 5% if the fibers are correctly aligned. This is small compared to the other systematic effects we must account for (e.g., the fringing discussed in Section 5).

4. Observations

The observing run considered here was conducted on June 28, 2008, over the course of approximately three hours, starting at 20:19 UTC. An illustration of the pointing and solar conditions at the time of the observations is given in Figure 6. NOAA active region 988, one of the last solar cycle 23 sunspots, was decaying and going over the western limb near the equator at position angle 265◦ (with respect to the earth’s reference frame). The data consist of nine 20-minute integrations along the western limb of the sun, where each 20-minute integration yielded two minutes of exposure time. Since a single observation consists of four images and the final Stokes Q and U images are differences of two raw frames, each Stokes image is really the result of one minute of exposure time. The exposures are spaced out at 20◦ intervals in position angle, starting at 85◦ S latitude and ending at 80◦ N. A summary of the observations is given in Table 1. Although SOLARC has a 45 cm mirror, disk observations required either a smaller collecting surface or shorter exposure time. Since the camera control software required a minimum 50 ms exposure time, we opted to use a 1 cm ‘pinhole’ aperture, effectively turning SOLARC into a 1 cm telescope. Since SOLARC is a fast optical system, this collimated beam configuration leads to fringes in the final polarized spectra caused by internal reflections in the LCVRs. These must be removed using Fourier filtering, discussed in Section 5. In the future, we will use a 35 cm annular aperture that will take advantage of the telescope’s fast optics and eliminate fringing in the final spectra. This should improve the signal-to-noise ratio for the Stokes Q signal we are attempting to measure and decrease the sizes of the error bars in Figures 10 and 11.

5. Reduction

A raw data frame from one of the exposures is presented in Figure 7. The two dark, zigzagging bands correspond to individual sets of Si I absorption lines that appear in each spectrum. The zigzagging is a product of the fiber mapping diagrammed in Figure 2. The two data rows that each absorption line falls on is a single spectrum. The data consist of 128 of these spectra aligned vertically in an image, each sampling a different point on the sun. Our ultimate goal is a flux and wavelength-calbrated data-cube — the relative intensity at every wavelength we sample for each x – 6 – and y position in the field of view.

The first step in the processing is flat-fielding. Raw images are flat-fielded using frames obtained by pointing 2.5 solar radii from the north limb of the sun. Sky-flats taken in this manner do have strong wavelength dependence due to scattered photospheric and atmospheric absorption lines. However, the scattered spectrum does not show any features at 10830 A,˚ so we expect the flat- fielding to be correct in the regions where the He I line we are trying to measure falls on the detector.

Next, the individual rows in the images are rearranged so as to separate spectra that came from the left-hand and right-hand column of ﬁbers. This allows us to check for spatial cross-talk, which would show up here as double-lines in the descrambled spectra. One set of descrambled spectra are shifted by 6 pixels to align them to the same wavelength scale. This shift is only good to an accuracy of 1 pixel, or ∼ .2 A,˚ about a ﬁfth of the separation between the two components of the He I 10830 A˚ line. Once this is done, it is straightforward to invert the mapping given in Figure 2 to produce a data cube. We step through each spectrum and wavelength-calibrate using the known wavelengths of the two photospheric silicon features. Using only two lines can lead to errors since this method cannot account for nonlinear dispersion. In practice, shifts are small, and our measurement is not sensitive to the precise wavelength calibration. A better approach would be to calibrate the wavelength scale using several more lines present in the spectra.

Finally, differences are calculated to produce full Stokes I, Q, and U data cubes. As men- tioned earlier, Stokes Q and U spectra exhibit significant fringing effects that considerably reduce the signal-to-noise ratio. Conveniently, when the raw spectra are Fourier transformed the peak corresponding to the fringing had a more or less constant central frequency and had a relatively narrow bandpass. This kind of oscillatory noise is amenable to Fourier filtering. The Fourier transform of each spectrum is found and then multiplied by a Gaussian band pass filter centered at approximately 60 pixels−1. The inverse Fourier transform is calculated and this is taken to be the fringe-corrected spectrum. This procedure is shown in Figure 8.

6. Analysis and Discussion

In order to interpret our observations, it is necessary to determine the pointing of the telescope in order to infer the position on the sun that the spectra are sampling. Unfortunately, the tracking software used on SOLARC can only determine the pointing to an accuracy of about 40 arcseconds. In order to correct the pointings to 1-pixel accuracy, we first had to invert an image of the field of view sampled by the fiber bundle during the observation. This fiber bundle illumination image is just the sum of a data-cube along the spectral direction. If we align these spatial images to a disk with a diameter equal to the solar angular diameter on the date of observations, we can correct the pointing to a 1-pixel accuracy (± 22 arcseconds). This procedure is described in Figure 6. Using our corrected pointings, we can derive the solar radius and position angle of each pixel and thus of – 7 – each observed spectrum.

Due to the geometry of limb observations and the nature of the optical pumping eﬀect and scattering polarization, we expect the polarization signal to be aligned with the limb. The instrument Q frame is aligned so that −Q polarization is tangential to the sun at a position angle of 270◦ (5◦ S lattitude). Since we would like to coadd and compare spectra from diﬀerent position angles, we must perform a rotation of the instrument Q/U frame, independently for each set of Q and U spectra. This is accomplished by multiplying the observed Stokes vector at each wavelength and position by a Mueller rotation matrix of the form:

 I0   1 0 0 0   I   Q0   0 cos θ sin θ 0   Q    =     (1)  0       U   0 − sin θ cos θ 0   U  V 0 0 0 0 1 V where θ is the position angle of the observation. Once this is done spectra from the same radius and approximately the same position angle in a single exposure are coadded, increasing the signal to noise by adding several equivalent spectra together.

In Figure 9, we present the I and Q coadded limb spectra in a 10 A˚ window around 10830 A,˚ where we have coadded the spectra from the ﬁbers that were pointed closest to the limb at all position angles. In the ﬁgure, we can clearly see the deep photospheric Si I absorption line visually apparent in the raw data as well as fainter Na, Ca, and atmospheric water lines. We can also see the weak He I 10830 Aline˚ in the I spectrum. In Q, this spectral line shows up as strongly −Q. The corresponding plot for Stokes U shows no features. The averages plotted in Figure 9 discard all of the spatial dependence of the strength of the He I Stokes Q signal.

In order to measure both the latitudinal dependence and the center-to-limb variation (CLV) of the stokes Q signal, we find the minimum value within a smoothed spectral region centered on the line and take this number as the magnitude of the Stokes Q He 10830 A˚ signal. The errors in our measurement are determined by taking the standard deviation of the Stokes Q signal in a 10 A˚ window that exhibited no significant spectral features. In Figure 10, we have plotted the center-to-limb variation of the Stokes Q and U signals for two position angles along the western limb. An active region was moving over the limb during the observations at the position angle of the top set of Q and U CLV curves and may have influenced the magnetic field environment for the data points closest to the limb. The second set of plots samples similar equatorial regions where no limb active region was present. We see that the magnitude of the Stokes Q signal increases as a function of radius, while the Stokes U signal remains zero within the measurement error. We also see an increase in the magnitude of the Stokes Q signal above the active region and a decrease in the magnitude of the signal away from the active region.

In Figure 11 we have plotted the magnitude of the Stokes Q signal as a function of position angle for two different radii, one near the limb and one on the limb. In the near-limb plot we see how – 8 – the magnitude of the Stokes Q signal remains constant at all latitudes within measurement error. In the on-limb plot, we see how the Stokes Q signal above the active region is significantly stronger compared to the other position angles at the same radius, indicating that in the environment above the active region some other mechanism for producing polarized light in this transition was at work in the strong-field region above the active region.

7. Conclusion

In this paper we presented observations of the center-to-limb variation and latitudinal dependence of the magnitude of the Stokes Q polarization signal of the He 10830 A˚ line. In the future we would like to model these curves using atomic data and a radiative transfer code. This will allow us to link the observed linear polarization signal to check whether we have observed an optically pumped sample of He I or simply a polarization signal entirely due to scattering polarization.

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This preprint was prepared with the AAS LATEX macros v5.2. – 10 –

Fig. 1.— A schematic depiction of a transition with Ju=0 and Jl=1. An anisotropic radiation ﬁeld can only induce transitions with ∆MJ = ±1, so no transitions are allowed out of the MJ =0 state. This leads to a population imbalance between the lower state’s degenerate sublevels. – 11 –

Fig. 2.— The fiber bundle images a 5.86 X 2.93 arcminute region on the sky with 128 fiber pixels. Each pixel is dispersed in the spectrograph and each spectrum is imaged. To maximize detector efficiency, the fibers are rearranged into 2 vertically offset columns of 64 fibers each. Errors of only a few tens of microns can skew the vertical alignment, which must be accounted for in the data reduction. – 12 –

Fig. 3.— The SOLARC dome and telescope. – 13 –

Fig. 4.— The liquid crystal polarimeter. The liquid crystal variable retarders (at top) modulate the polarization state of an incident beam so that a cubical polarizing beamsplitter (center) can analyze the polarization signal, in eﬀect converting it into an intensity signal. The component polarized beam is focused onto the ﬁber bundle (bottom). – 14 –

Fig. 5.— The OFIS spectrograph. A lens collimates light from the ﬁber bundle (bottom right). A grating (top) disperses the collimated beam and the resulting spectrum is focused on to the IR array, which is inside a dewar (bottom left). – 15 –

Fig. 6.— The nine individual fiber illumination images (see Section ??) are overlaid on a co- temportal SOHO EIT 195 image. An image like this is used to correct the recorded pointing to 1-pixel accuracy by aligning fiber illumination images to the Sun’s limb. The telescope was pointed at nine different positions along the western limb. Integration time was 20 minutes for all exposures. One of the equatorial exposures (fifth from the bottom) was centered on a limb active region. – 16 –

Fig. 7.— From left to right, raw SOLARC I, Q, and U images. One can clearly see the two deep double absorption lines in the I frame These appear doubled due to the placement of the ﬁbers in the spectrograph entrance. Fringing is plainly visible in the Q and U images. The He 10830 A˚ polarization signal is just barely visible in the Stokes Q image, near the center, between the leftmost and middle absorption lines in the I spectrum. – 17 –

Fig. 8.— A polarized spectrum from a single fiber is Fourier transformed producing a power spectrum (e.g., bottom of the plot above). A gaussian band-stop filter is constructed (middle) and then the power spectrum is multiplied by it (top), and then inverse Fourier transformed to produce a fringe-corrected spectrum. Little power from the image itsself is contained in the peak we are filtering, as we can see by comparing the filtered spectra to coronal data that do not have the fringes. At bottom, a filtered Stokes Q image; compare to Figure 7. – 18 –

Fig. 9.— The coadded limb I and Q spectra between 10825 A˚ and 10835 A.˚ The water lines are telluric absorption lines, while the rest are photospheric lines. In Stokes Q there is a significant -Q signal at the same wavelength as the He I signal. We also see two small lines due to instrument cross-talk induced by the high contrast in the silicon lines with respect to the continuum. We can be confident that a similar effect is not at work in the observed Helium stokes Q signal since the Stokes I profile has a small contrast around the 10830 A˚ line. – 19 –

Fig. 10.— The center-to-limb variation of the He I 10830AQ˚ and U signal at position angle 265◦ and 285◦. The U polarization is approximately zero at both position angles. The Q signal increases in magnitude closer to the limb at both position angles. At position angle 285◦, the Q signal decreases in magnitude at the limb. At position angle 265◦, the Q polarization signal increases at the limb. The active region going over the limb at position angle 265◦ may have activated a mechanism for polarizing light in this transition. – 20 –

Fig. 11.— The average maximum of the Stokes Q and U limb polarization as a function of position angle. The ﬁrst two plots are the Stokes Q and U spectra at R/R = .95. The second set of plots are the Stokes Q and U spectra at R/R = .99. Note how in the bottom two plots that sample closer to the limb (R/R = .99) there is an increase in the magnitude of the Stokes Q signal at a position angle of 265◦ (above the limb active region). This increase is not present at any other position angle and is not present farther away from the limb. This could possibly be due to a polarization mechanism activated by the presence of the active region. – 21 –

Table 1. Summary of Observations

Position Angle Radius Start Time Stop Time Exposure Time Notes Degrees R/R s

185.1 ± .3 .88 ± .06 21:48:33 22:06:29 117.6 205.1 ± .3 .88 ± .06 21:26:14 21:46:27 141.6 225.1 ± .3 .88 ± .06 21:03:44 21:23:51 140.8 245.1 ± .3 .88 ± .06 20:41:26 21:01:30 140.4 265.1 ± .3 .88 ± .06 20:19:51 20:39:54 140.4 Active Region 285.1 ± .3 .88 ± .06 22:07:09 22:28:01 146.4 305.1 ± .3 .88 ± .06 22:29:58 22:49:10 134.4 325.1 ± .3 .88 ± .06 22:50:14 23:10:00 138.4 345.1 ± .3 .88 ± .06 23:11:29 23:31:13 138.0