ESA’s “PRoject for On-Board Autonomy” Belgian microsatellite in Sun-synchronous orbit 725 km altitude Launched 02 Nov 2009 Nominal operations since March 2010 Technology and science mission 4 innovative instruments and 17 technological experiments for in-orbit demonstration Among them the EUV imager SWAP and the radiometer LYRA

Correlation between sunspot numbers and EUV irradianceas observed by LYRA on PROBA2

Ingolf E. Dammasch & Laure Lefevre, Royal Observatory of Belgium

Abstract: The solar radiometer LYRA on board the ESA micro-satellite PROBA2 has observed the Sun continuously since January 2010 in various spectral band passes. Two of the LYRA channels cover the irradiance between soft X-ray and extreme ultraviolet. The variation of the sunspot number appears to show a strong similarity with the variation of these channels, when their long-range development is taken into account. We will try to give some explanation, and complement the findings with other instruments’ results. References: Chatfield, C., Collins, A.J.: 1990, Introduction to multivariate Analysis, Chapman & Hall, London Hochedez, J.-F., et al.: 2006, LYRA, a solar UV radiometer on PROBA2, Adv Space Res 37, 2, 303-312

Golub, G.H., Van Loan, C.F.: 2000, Matrix Computations, Johns Hopkins Press, Baltimore Dominique, M., et al.: 2012, The LYRA instrument onboard PROBA2, Solar Physics Special Issue, submPreminger & Walton: 2007, Solar Physics, 240, 17P BenMoussa, A., et al.: 2009, Pre-flight calibration of LYRA, Astron & Astrophys 508, 1085-1094

“Large-Yield RAdiometer” 3 instrument units (redundancy) 4 spectral channels per head 3 types of detectors, Silicon + 2 types of diamond detectors (MSM, PIN): - radiation resistant - insensitive to visible light compared to Si detectors High cadence up to 100 Hz

Redundancy with different types of detectors::

Channel 1 (Lyman-alpha) 120-123nm Channel 2 (Herzberg) 190-222nm Channel 3 (Aluminium) 17-80nm + <5nm Channel 4 (Zirconium) 6-20nm + <2nm

To represent the long-term, non-flaring solar development, one daily value had to be chosen from LYRA channel 3, LYRA channel 4, and GOES data, each. Since there are many possible instrument artifacts (data gaps, satellite rotations, occultations by Earth atmosphere, off-pointings, temperature variations, etc.), which are not yet all corrected , the significant minimum was manually selected per day. - In addition, one must take into account the spectral degradation of some LYRA channels; channel 3 of nominal unit 2 - the unit that has been used practically all the time since First Light on 06 Jan 2010 - has, e.g., lost approximately 90% of its response, most of it probably above 19nm.

(left) Nominal spectral response of LYRA channels 3 and 4 of unit 2, compared to spectral range of GOES.

(right) Time series of GOES, the two LYRA channels, and the scaled daily sunspot number.

We examine here the solar irradiance measurements emitted from different layers of the solar atmosphere. The time series we use are presented here in approximate order of the solar layer: starting from the soft X-rays of the GOES data (0.1-0.8 nm) to the radio flux at 10.7cm (corona-transition zone), the CaIIK index (high chromosphere), the LYRA data for channels 4 and 3, and then the photosphere with the facular area (still seen at higher temperatures), the sunspot area and the sunspot number. We also use the Total Solar Irradiance (Virgo composite, ftp.pmodwrc.ch), which covers all wavelengths. The sunspot areas, facular areas and CaIIK index were graciously provided by A. Cookson from the San Fernando Observatory (www.csun.edu/sfo/). Because of different temporal coverage for the different series we cover about 900 days from 06 Jan 2010 until 04 Jul 2012. The LYRA curves were up to date and the analysis was done also on the larger datasets (without including the TSI for example) and results are equivalent.

As method, we used the Principal Component Analysis (PCA: Chatfield and Collins, 1990), or Singular Value Decomposition (SVD: Golub and Van Loan, 2000) as it can help understanding the linear relations between solar parameters throughmultidimensional scaling. The 2-D similarity maps shown here were obtained by applying SVD to the mentioned time series, such as the International Sunspot Number (SN) and the flux at 10.7cm (F10.7). All the series were first normalized with respect to time and then subjected to SVD/PCA. In this mapping, all included parameters are projected on two axes, which maximize the variance among them. The remaining fraction of the total variance is small and contained in the other non-mapped dimensions. The axes themselves or their units do not match any physical dimension, but the mapping is such that the relative distance between the different parameters is inversely proportional to the correlation between their corresponding data series. Another interesting property of SVD/PCA is the fact that linear combinations of different quantities will be connected by a straight line.

Figure 1 shows that the correlations between these time-series are very consistent with the physical processes that are at play in the different layers of the Sun. It also shows that the Facular areas and the Sunspot number are very consistent with processes that happen close to the corona, where the temperatures have nothing in common with the photosphere from which they originate. Also note that, on the contrary, the sunspot areas do not correlate well with any of these quantities on the overall timescales. This lower correlation with the sunspot area can be seen for example if we cross-correlate LYRA channel 3 with the Sunspot areas, compared to the Sunspot Number and the facular areas. What can also be seen in Figure 2, is that the effect of the sunspots and faculae on the LYRA EUV curves is a delayed effect. The cross-correlations do not show clear peaks, but rather “plateaus” that start one to two days before the actual event in the LYRA channel 3 curve. This would indicate that the sunspot parameters have an influence on the spectral irradiance that is not a direct effect but rather a specific impulse response function (Preminger & Walton, 2007)

Now we decompose the time-series into two different timescales (above 81 days, and below 81 days) by smoothing with a time window. We obtain two time-series that we can submit to the same SVD/PCA analysis (Figures 3 and 4) . We can immediately see that the longer timescale is very similar to the complete time-series. This means that the time-series are dominated by an intermediate scale component. We do not say “long” scale, because we have to keep in mind that this data set is only two and half years and thus we cannot talk about the longer timescales (solar cycles). We are bound to timescales shorter than 900 days. - The shorter timescales, on the other hand, show a very different picture. First, you see that, indeed, at shorter timescales, the TSI can be reconstructed by a combination on facular and sunspot areas. You can see it by the nice straight line that goes through all three of the time-series. And it is not true at larger timescales. Second, you see that, at these scales, the Flux at 10.7cm and the Sunspot number correlate better with LYRA 4 and 3 than with GOES. So at short scales, the Sunspot number represents better variations in the EUV in the chromosphere, while at larger (intermediate) scales, it represents better the X-ray flux, thus the corona.

Figure 1:SVD/PCA of the time series at all timescales (no treatment applied).

Figure 2: Cross-correlation of the channel 3 of LYRA with the Sunspot number, the Sunpot area and the Facular area on the same period.

Figure 3: SVD/PCA of the time series at short timescales (< 81 days).

Figure 4: SVD/PCA of the time series at intermediate timescales (81< T< 900 days).