A MULTI-INSTRUMENT ANALYSIS OF SUNSPOT UMBRAE

Two instruments are used to obtain continuum and magnetogram data for sunspots. The first of these is the Michelson Doppler Imager (MDI; Scherrer et al. 1995) which was launched in 1995 on board the Solar and Heliospheric Observatory (SOHO). MDI was capable of producing intensitygrams at a 6 hr cadence and magnetograms at a 96 minute cadence with 4.0 arcsec spatial resolution and did so until 2010 when a similar instrument was launched on the Solar Dynamics Observatory (SDO) spacecraft.

The Helioseismic and Magnetic Imager (HMI; Scherrer et al. 2012) was launched on board SDO in 2010 and is capable of the same measurements as MDI but at an improved spatial and temporal resolution as well as being able to more accurately measure the magnetic field on the Sun. Intensitygrams and magnetograms are available with 45 s cadence and at 1.0 arcsec spatial resolution.

The ground-based observations used in this study are the collection of infrared sunspot umbrae measurements taken with the Baboquivari detector (BABO) at the National Solar Observatory McMath–Pierce Solar Telescope from 1999–2013. The spectrum of the Fe i line at 1564.8 nm is recorded and the Zeeman splitting of the line is directly measured to give the magnetic field strength in the darkest part of sunspot umbrae. The wavelength splitting is completely independent of viewing angle and is fully resolved for magnetic fields greater than around 1100 G. This is described in more detail in Penn & Livingston (2006) and Livingston et al. (2012).

Both the space and ground-based data sets come with advantages and disadvantages for this type of study. The MDI and HMI data benefit from near-complete temporal coverage during their missions. As such, there is data available for almost every day in the period 1995–2013 (excluding some time in 1998 when SOHO was essentially lost for four months). In comparison, the infrared measurements at the McMath–Pierce Solar Telescope are less regular, depending on the amount of observation time allocated as well as weather conditions. For most of the period of interest, this amounts to 5–7 days per month. As such, the space record is a more complete temporal picture of the sunspot population.

The method of measuring the magnetic field used by MDI and HMI is to take a number of points along the spectral line profile and fit them to a model. In doing so, the line-of-sight magnetic field can be inferred. However, the infrared measurements show the whole spectrum from 1564.4–1565.6 nm and allows the true continuum as well as the magnetic field at the source to be directly measured.

A major disadvantage of the MDI measurements is that only the line-of-sight magnetic field strength is obtained. As we measure the darkest part of sunspot umbrae, we expect this to have the strongest magnetic field within the sunspot and correct the line-of-sight field assuming that the field is normal to the photosphere.

The HMI magnetogram data used are Stokes profile inversions using the Milne–Eddington model of stellar atmospheres, which are now one of the standard data products produced by the HMI team. Details of the method used are explained in detail in Borrero et al. (2007) and Borrero et al. (2011). As a result, we expect the HMI magnetic fields to be more reliable than those from MDI where it is assumed that the magnetic field in the darkest part of the sunspot umbra is normal to the photosphere and a simple cosine correction is applied for line of sight effects.

Different methods are used to choose sunspots from each of the data sets. The MDI and HMI data is analyzed using the STARA code (Watson et al. 2009) which is an automated detection algorithm that allows sunspot properties to be extracted from large data sets. The infrared catalog is comprised of the visible sunspots on the disk when observing time was available, and as mentioned previously, this is around 5–7 days per month. For all data sets, when data is available one measurement per umbra is made per day. The MDI, HMI and infrared catalogs contain 17379, 9542 and 3949 entries respectively. It should be noted that these are not all individual sunspots, but individual detections. If a sunspot persists for 12 days, it will have 12 entries in each catalog, assuming data was available.

Sunspots have been observed to appear on the disk as part of the solar activity cycle and have been shown to correlate with various different indices of solar activity (see Hathaway 2010 and references therein). As such, this section will examine the evolution of umbral properties over the 1996–2013 period, covering all of solar cycle 23 as well as the rise phase of cycle 24.

In Figure 4, the solar latitude of sunspots is shown as a function of time, commonly referred to as a "butterfly diagram." It shows the expected pattern of sunspots appearing at preferentially higher latitudes at the beginning of a solar cycle and migrating, on average, toward the equator as the cycle progresses. Both MDI and HMI sunspot locations are included with the dashed lines showing the period for which each instrument provides data.

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To compare with the results in the articles mentioned in Section 1, the STARA sunspot catalog was used to find the darkest pixel in each detected umbra. The corresponding magnetogram pixel was then used to determine the magnetic field in the darkest part of the sunspot umbra. The HMI team has made Milne–Eddington inversions of the magnetic field available and they are used whenever possible. In order to make a more direct comparison, the HMI and MDI data has been treated in the same manner as the BABO data set. The average of all measurements for a given year is plotted and the error is the standard error of the mean (equivalent to 1σ). The data show that before around 2005, the space data did not agree well with the infrared data measured on the ground but since 2005 there is a much better agreement. Figure 5 shows these results as well as the latest measurements from Livingston's BABO detector.

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The BABO data set does not track sunspots from day to day and so the data include many instances of the same sunspot being measured. As large sunspots tend to have stronger magnetic fields and exist for longer, this could introduce a bias into the results. To test this, MDI results were compared allowing for multiple measurements of the same sunspot on consecutive days, and single measurements of sunspots. To do this, only sunspots in a longitude band of −7.5 deg to +7.5 deg were taken. As the Sun appears to rotate about 15 deg day⁻¹ from our point of view, this 15 deg window ensured that sunspots were only measured once. The result of this comparison is shown in Figure 6. The results are similar enough to justify making the comparison between BABO and MDI data using the full data set.

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From 1998–2003, there is poor agreement in the MDI and BABO data sets other than the presence of a small downward trend after around 2000. The MDI data is around 2σ from the BABO results over this time period. Considering the data the other way around, the BABO data is over 10σ from the MDI results. As such, we conclude that the two sets of data do not agree with one another over the 1998–2003 time period. Also, the decrease in umbral fields measured by BABO from 1999–2003 are eight times larger than the corresponding decrease measured by MDI (BABO falls from 2900 G to 2250 G whereas MDI falls from 2425 G to 2350 G). After the two data sets converge sometime in the year 2006 there is far better agreement, and this continues with HMI data. This raises the question of why the two data sets should be different early on and then agree later.

The major differences between the MDI and BABO data sets are, as described in Section 2.3, what is being measured and how often the measurements are taken. The BABO data is derived from a direct measurement of the Zeeman splitting of the Fe i 1546.8 nm spectral line whereas MDI magnetograms involve taking points along a spectral line and fitting them to a model. The result of this is that the individual BABO measurements are a more accurate representation of the magnetic field. It measures the total field compared to the MDI magnetogram measurement of the line-of-sight field (which is corrected assuming a field normal to the photosphere). However, the plots in Figure 5 are annual averages and so the frequency and completeness of measurements are also factors.

To examine this, Table 1 contains the number of umbral detections for each year from both the STARA catalog and the BABO catalog. Also in the table are the number of days each year where at least one umbra was successfully detected and observed. With these values it is possible to calculate the average number of umbrae per day on days where at least one umbra was present.

It should be noted here that the number of days each year that yielded a successful umbral measurement is not the same as the number of observing days per year, particularly during times of low solar activity. This would be an unfair metric to use when comparing the data sets as MDI and HMI are taking measurements many times per day whereas the BABO data set relies on the availability of both the telescope and the observer to make the observation. In addition to this, the fact that BABO was used less often than MDI or HMI does not mean that it is not able to measure a sample that is representative of the full sunspot population. That is what will be addressed in this section.

Table 1 shows that the number of days that BABO observed sunspot umbrae was very low from 1998 until the end of 2000 and so this could explain why the data sets disagree over this time period. From the beginning of 2001, more frequent observations were taken with BABO at the McMath–Pierce Solar Telescope starting with 14 days in the year 2000 and even reaching 66 separate successful observation days in 2012 (equivalent to a 5 or 6 day observation run each month although some days are lost due to weather).

As both data sets did not have the same observing cadence, it is beneficial to look at the number of umbrae observed per successful observing day which is shown in Figure 7. This is calculated by taking the total number of umbrae detected in a given year and dividing by the number of days when at least one umbra was detected. It should eliminate effects from the different observation cadences.

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The MDI and HMI data show a cyclic trend in the average number of umbrae observed per day and even show the double peaked structure of solar cycle 23 with highs in 2000 and 2002 (when binned annually). The BABO data shows a noisy cyclic trend with a rise from 2000–2003 then falling to a minimum in 2007–2009. This leads to the conclusion that the STARA sunspot umbra detections from the MDI data set can be thought of as a good representation of the global sunspot population due to the fact that the number of sunspot umbrae detected correlates with the sunspot number from other sources. The BABO data appears to follow the sunspot number from 2003 onward but they are not in agreement before that time. In 2011 and 2012, very large numbers of umbrae were detected per day in the BABO set, far more than at any point during the previous cycle. This is strange as the sunspot number in 2011 and 2012 has been comparable to that in 2003. It is also shown that the HMI number of umbrae observed per day in 2011 is comparable to the MDI value in 2002 when the sunspot number is different. This is likely because the increased spatial resolution of HMI allows smaller umbrae to be detected and so more are observed on average. The BABO number of umbrae observed per day are systematically higher than the automated MDI and HMI values. This is a result of the automated nature of those detections. To ensure the lowest number of false sunspot detections possible, very small sunspots are not included in the detections. This is not the case with the manual BABO data set and so more umbrae are observed per day. Due to the method of measurement, the extra spots in the BABO data are considered very small.

The data in Table 1 along with Figure 7 seem to show an issue in the sampling of the sunspot population with the BABO data set. As mentioned previously, the BABO detector can provide more accurate magnetic field strength measurements than MDI or HMI. However, the apparent change in the BABO population sample over time makes extrapolating long-term trends difficult. By examining a property that is independent of the magnetic field, in this case the observation frequency and the number of umbrae detected, it appears that the number of umbrae measured in the BABO data set is not correlated with the sunspot number until sometime in the 2003–2005 period after which a trend can be seen. This implies that the BABO data set is not a representative sample of the full sunspot umbrae population before 2003 and provides an explanation for the difference between the umbral magnetic fields measured by BABO and by MDI and HMI. This is reinforced by Figure 5 which shows that from 2005 onward, the annual umbral magnetic field strengths measured by all instruments are in agreement.

It has been previously shown that the solar activity levels in the north and south hemispheres of the Sun are out of sync (see Howard & Gilman 1986 and Durrant & Wilson 2003), particularly during polar reversals. We show the magnetic field values of MDI and HMI in Figure 8 but this time, split by hemisphere. This shows that the drop in sunspot magnetic fields during the minimum between cycles 23 and 24 was larger in the northern hemisphere than in the southern. In addition, the lowest value of the maximum field in the northern hemisphere occurred 6–12 months before the equivalent value in the southern hemisphere indicating a delay as reported by previous studies. Including the BABO data in these plots was not possible as the location of the sunspot on the disk was not listed in the catalog.

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Besides examining the magnetic field strengths, it is also possible to look at how the intensity of sunspot umbrae change over time. Figure 1 has already shown a correlation between umbral intensity and magnetic field and so we would expect this to be reflected in the long term measurements of intensities. The intensities of sunspots and sunspot umbrae have been the subject of many studies including Albregtsen et al. (1984), Maltby et al. (1986), Norton & Gilman (2004), Penn & Livingston (2006), Mathew et al. (2007), Livingston et al. (2012) and Rezaei et al. (2012) (see Norton et al. 2013 for a comparison of some of these studies). Even more recently, de Toma et al. (2013) have used images from the San Fernando Observatory to examine the intensities of spots and umbrae. The variation in the sample size used in these studies is detailed in Table 2 and ranges from 22 umbrae to almost 27,000. The intensities of all umbrae in the STARA catalog along with an annual mean are shown in Figure 9.

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The plot shows that there is a fundamental difference in the intensity ratio numbers between MDI and HMI. The MDI data is mostly in the 0.60–0.05 range whereas HMI data is found in the 0.50–0.05 range. In addition to this, the running mean is fairly flat from 1996–2010 which contains all of the MDI data but after switching to HMI observations, the running mean drops from 0.43 to 0.33 almost immediately. This indicates that there is either an issue with the method used to measure the intensity ratio (which is the same for both instruments) or that there is a difference in the data. The latter explanation is most likely as these instruments observe in different spectral lines (MDI in 676.8 nm and HMI in 617.3 nm). The calculated intensity is a linear combination of filtergrams taken at various points in the spectral line profile and there is no reason why the combination should be the same for two different spectral lines. However if each data set is examined independently then the intensity ratio is, on average, mostly constant over time.

This would appear to contradict the earlier results given in this article. We have shown in Figure 1 that the umbral intensity is related to the umbral magnetic field strength. Then, in Figure 5, we show that the average magnetic field in the darkest part of sunspot umbrae has decreased by around 325 G from 1998–2010 as measured by MDI. If both these results are true, it seems counterintuitive that the umbral intensity from 1998–2010 is almost constant. This can be explained by considering the range of possible magnetic field measurements for a single umbral intensity. The mean umbral intensity from 1998–2010 is around 0.43 from Figure 9. Looking back at Figure 1, we can see that for an umbral intensity ratio of 0.43, the range of possible magnetic field strengths measured by MDI is over 1000 G, and with the improved HMI instrument that range drops to around 650 G. This leads to the conclusion that the umbral magnetic field could change by the measured 375 G without a significant change in umbral intensity. And so, the lack of changing intensity shown here is consistent with the results shown earlier in this article. Physically, this intensity change in a sunspot with a given maximum magnetic field may be related to the twist of the magnetic field geometry as discussed in Martinez Pillet & Vazquez (1993).

To allow the MDI and HMI intensity data to be compared with other data, the two most "complete" studies from Table 2 are used, with complete meaning the most observations over the longest timescale. This leads to the Livingston et al. (2012) and de Toma et al. (2013) studies.

Figure 2 in the Livingston et al. (2012) article shows the raw intensity ratio data along with annual averages measured with the BABO detector. It shows a clear upward trend over the 1998–2012 range plotted and also shows some sunspot umbrae measured in 2011 and 2012 with intensities well above 0.95. The upward trend starts at a value of around 0.60 in 1998 and rises to around 0.85 in 2012. This is in agreement with the magnetic field trend also reported in that article as an increase in sunspot umbral intensity would imply a decrease in umbral magnetic fields. However, earlier in this article a possible explanation for differences in magnetic field strength between data sets was low sampling rates in the BABO data set before 2005. If this caveat is applied here there is still a small upward trend in the BABO data although it is now from around 0.70 in 2005 to 0.85 in 2012. This range of 0.15 is approximately equivalent to the range seen in the MDI running mean intensity in Figure 9. Note that it is the trends that are more important here as the different spectral lines used make direct intensity comparisons difficult.

Figure 2 in the de Toma et al. (2013) article also shows sunspot umbral intensities but this time using the Cartesian Full Disk Telescope 1 (CFDT1) at a wavelength of 672.3 nm at San Fernando Observatory. This wavelength is different to those probed by MDI, HMI and BABO. A primary advantage of this data set is that it covers the period of 1986–2012, substantially longer than any data set used in this article. The umbral intensity data given spans a very large range, from 0.90 down to 0.15 but the trend is similar to that seen in the MDI and HMI data. Very little variation is seen in the average umbral intensity over time.

Although ground observations contain more scattered light from outside the instrument due to the atmosphere, these results show that even comparing ground-based telescopes does not provide the same result. A similar study by Schad (2014) shows the same result of sunspot umbral intensities being almost constant using observations from Hinode. All of the visible light studies agree with the visible light MDI and HMI results presented in the article. It would then appear that there is a possible difference between instruments measuring visible light and infrared light.

An article by Harvey et al. (2012) shows that instrumental stray light varies as 1/λ² and using the values for MDI and BABO, this means that the stray light within the instrument is around 5.3 times bigger for MDI than for BABO. This equation assumes reflective optics and the transmissive optics in MDI will make this value worse. In addition to this, the sunspot contrast is greater in visible light than in infra-red light. This means that observations in visible light are more susceptible to scatter from outside the umbra than infra-red observations. In all of the MDI and HMI intensity measurements, there is a large amount of scatter that could be masking a trend in intensity. As such, it is possible that the BABO observations are seeing a trend that either cannot be seen in visible light due to scattered light effects, or that only exists in infra-red emission. To check further, it would be advantageous to have similar infra-red observations from another observatory.