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 On 4 November 2003, the largest solar flare ever recorded saturated the GOES X-ray detectors; from these a magnitude of X28 (2.8 mW/m2) has been extrapolated (http://sec.noaa.gov/weekly/pdf/prf1471.pdf). However, using the Earth's ionosphere as a giant X-ray detector, we show the magnitude of this flare is consistent with X45 ± 5 (4.5 ± 0.5 mW/m2), or more than twice that of the two previously recorded largest flares, both about X20. This flare magnitude is determined by using the large observed phase changes recorded at Dunedin, New Zealand, on long VLF radio paths across the Pacific from transmitters in the continental USA and Hawaii. The enhanced X-ray flux caused a dramatic lowering of the height of the D-region of the ionosphere, allowing the flare to be measured relative to the GOES observations.
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 During solar flares the X-ray flux received at the Earth increases dramatically, often within a few minutes, and then typically decays again over periods ranging from a few tens of minutes to several hours (http://sec.noaa.gov/Data/goes.html). These X-ray fluxes have major effects in the Earth's upper atmosphere but are absorbed before they reach the ground. Since 1976 they have been measured above the atmosphere by the geostationary GOES satellites.
Figure 1 shows the GOES measured X-ray fluxes provided by NOAA Space Environment Center (NOAA-SEC) (http://sec.noaa.gov/Data/goes.html) as a function of time for the great flare of 4 November 2003, in the two wavelength bands: (1) ‘short’ or XS, 0.05–0.4 nm and (2) ‘long’ or XL, 0.1–0.8 nm. The detectors went into clear saturation near the peak of the flare. The 3-second resolution data shown in the figure have been scaled to match the 1-minute data on the NOAA-SEC web site, and thus the standard (C,M,X) X-ray flare magnitudes (http://sec.noaa.gov/weekly/Usr_guide.pdf).
 Even though the GOES X-ray detectors work over a dynamic range of at least 104–105, the range of X-ray flux magnitudes can be even greater, and so a compromise has had to be made in setting the effective gain which has been set high enough to get the quiet time detail, but leaving a risk of a large flare overloading the detectors near the peak of the flare. This overloading, or saturation, occurred (at X17.4) for about 13 minutes during the peak of the great flare of 4 November 2003 from about 1943 to 1956 UT. NOAA's estimate of the peak at X28 thus had to be made by extrapolation (http://sec.noaa.gov/weekly/pdf/prf1471.pdf).
 An increase in the X-ray flux to a level of only 1 μW/m2 in the long wave band, termed a C1 flare, has a just detectable effect on the D-region of the ionosphere as observed by VLF radio propagation [e.g., McRae and Thomson, 2004]. Similarly the terms C2–C9 are associated with fluxes of 2–9 μW/m2, M1–M9 with 10–90 μW/m2, and X1, X2, X20, etc. with long wave fluxes of 0.1 mW/m2, 0.2 mW/m2 and 2.0 mW/m2 etc., respectively. Although flares are typically labeled according to their fluxes in this long wave band, the short wave band fluxes, even though smaller, normally have the greatest effect at the lower edge of the D-region where VLF radio waves reflect. During periods of enhanced solar activity, particularly during flares, the solar X-ray flux hardens. As can be seen in Figure 1, the ratio of the long wave flux to the short wave flux is ∼40 at the C1 level dropping to around 2–3 at the highest flare levels (X10+).
 The lowest region of the Earth's ionosphere, the D-region, is maintained by day mainly by Lyman-α radiation (121.6 nm) from the Sun ionizing the minor neutral constituent, nitric oxide [e.g., Banks and Kockarts, 1973]. However, when a solar flare occurs the X-ray flux (∼0.1–0.2 nm) ionizes the dominant particles, N2 and O2, and lowers the effective height of the D-region for flares greater than about C1–C2.
 VLF (Very Low Frequency) radio waves (say 10–30 kHz) typically propagate with good signal-to-noise ratio over ranges up to 10–15 Mm or more in the Earth-ionosphere waveguide, bounded above by the D-region and below by the Earth's surface [e.g., Watt, 1967]. Powerful transmitters (up to about 1 MW) are run by the US Navy with very stable frequencies, and phases controlled by cesium beam atomic clocks. By day the propagation paths are largely stable and the received phases are reproducible, in quiet conditions away from dawn and dusk, to a very few microseconds or better than about 10 degrees [e.g., Watt, 1967; McRae and Thomson, 2000, 2004].
 However, when a solar flare occurs (on a sunlit path), the extra ionization generated by the X-rays lowers the effective reflection height of the ionosphere and advances the phase at the receiver by an amount that depends on the intensity of the X-ray flux [e.g., Mitra, 1974]. Similar changes (but in the night ionosphere) have also been used to detect and quantify a γ burst from a distant magnetar [Inan et al., 1999]. For daytime solar flares, both the height lowering and the phase advance (at least for path lengths greater than a few Mm) are found to be nearly proportional to the logarithm of the X-ray flux [McRae and Thomson, 2004]. As an example an X5 flare lowers the effective reflection height from about 70 km (mid-day) to about 58 km [McRae and Thomson, 2004]. In this paper we use such VLF phase observations to determine the size of the great flare of 4 November 2003.
2. Flare Magnitude From the Ionospheric Response
2.1. Experimental Setup
Figure 2 shows the VLF radio paths across the Pacific Ocean to Dunedin, New Zealand from the US Navy transmitters, NLK (24.8 kHz, near Seattle, 12.3 Mm path), NPM (21.4 kHz, Hawaii, 8.1 Mm) and NDK (25.2 kHz, North Dakota, 13.5 Mm). The phases were recorded with AbsPAL receivers which are similar to OmniPAL VLF data loggers [Dowden et al., 1998] but modified so that they lock to GPS 1-second pulses [Bahr et al., 2000].
2.2. VLF Phase Shifts on NLK due to the Great Flare
 In Figure 3 the phase of NLK received at Dunedin is shown as a function of time for the flare on 4 November 2003. (The brief negative spike at ∼2104 UT is due to a ∼1-min power cut in our VLF telemetry.)
 Also shown in Figure 3 are the X-ray fluxes (from Figure 1) with their logarithms linearly scaled to fit the VLF phase curve from NLK. Immediately prior to the start of this flare (left hand side of the plot) the X-ray flux level was fairly constant at 4.2 μW/m2. This is higher than the normal background, which is usually well below 1 μW/m2, but not uncommon when there are very active regions on the Sun. What this means is that the solar X-ray flux was the dominant source of D-region ionization both before and during the flare here, and so it is not surprising that the linearly scaled logarithms of the X-ray fluxes match rather well with the VLF phase perturbations.
 Thus, from the relatively good fits in Figure 3, the VLF phase can be seen to be a realistic means of extrapolating the X-ray fluxes beyond detector saturation. This is reinforced by an earlier finding that, at least up to about X5, the sizes of the phase shifts at the peaks of the VLF perturbations fit rather linearly with the peaks of the logarithms of the (long) solar X-ray fluxes for a good range of flare magnitudes [McRae and Thomson, 2004]. From Figure 3, particularly from the enlargement in the lower panel, it can be seen, that if we assume that the 0.1–0.8 nm (XL) X-ray flux continued to follow the phase of NLK at Dunedin to the peak, then the peak X-ray flux was about 4.5 mW/m2 and the flare thus had magnitude X45, peaking at 1945–1946 UT.
 A close up look at the fluxes and phases shown in the lower panel of Figure 3, particularly their slopes near where the X-ray detectors come out of saturation, indicates why extrapolation of the GOES X-ray data alone can give the significantly lower value of X28 rather than the higher value of X45 obtained here from the ionospheric response to the X-rays via the observed NLK phase changes.
2.3. Additional VLF Phase Shifts due to the Great Flare
 To check against the possibility that there might have been something unusual about the NLK transmitter's phase or path, we also examined the recorded phase changes at Dunedin from NPM, Hawaii, and NDK, North Dakota. For these, similar plots to that for NLK are shown in Figure 4.
 Extrapolation of the NPM phase, as shown in the upper panel, to give the peak X-ray flux results in a flare magnitude of about X44. If the X-ray flux fit to the phase were adjusted to optimize the fit in the descending period, 20.5–23.5 UT, at the expense of the good fit shown just before the flare start (i.e., just before 19.5 UT) then the resulting magnitude would become about X46. This difference probably arises because the NPM path, being the most westerly, has the lowest solar zenith angles early in the observation period. Reality is probably somewhere in between: i.e., a flare magnitude of X45 as for NLK.
 The flux extrapolation via the NDK phase gives a slightly higher magnitude, about X47, but the fitting for NDK was degraded by the transmitter being off-air until about a minute before the X-ray detectors saturated. This meant that the scaling of the X-ray fluxes to NDK's phase had to rely on the decaying part of the flare only. All the VLF phases reported here (NLK, NPM, NDK) were recorded on two separate versions of AbsPAL receiver, one running at 20-s resolution and the other at 0.2-s resolution later averaged to 10-s resolution. The phase shifts measured by each of these were essentially identical, apart from a period of slightly lower stability for the NDK phase a few minutes after NDK power-up. The NDK phase in Figure 4 used the 20-s resolution data (as opposed to the 10-s data displayed for NLK and NPM); the 10-s resolution data for NDK suggest the possibility of a slightly higher magnitude of X48 or X49. Although the two AbsPAL receivers phase tracked and recorded independently, they used the same VLF preamplifiers and the same GPS receiver (frequently checked against another independent GPS receiver).
2.4. Comparisons With the X10 Flare of 29 October 2003
 Although the VLF phases follow the (scaled) X-ray fluxes rather well on either side of the flare peaks in Figures 3 and 4, it is desirable to be a little more confident that they would also have tracked the X-ray fluxes as well at and around the peak itself if the X-ray detectors had not saturated. We have examined some smaller flares (for which there is no GOES saturation) and the tracking is normally good. Flares nearly as large as the great flare of 4 November 2003 are not common and, of these, most are not suitably timed for our VLF paths: the Sun should preferably be well above the horizon for all of the path. However, just 6 days earlier, in the same period of intense solar activity, there was a similarly timed X10 flare. In Figure 5 we show a similar superposition of NLK phase and the X-ray fluxes for this X10 flare as was done for the great flare in Figure 3. The tracking can be seen to be generally good including the peak itself. There is one slightly unusual feature of this X10 flare; the fall in the long wavelength X-ray flux (XL: 0.1–0.8 nm) is somewhat delayed with respect to the short wavelength flux (XS: 0.05–0.4 nm). Our examination of other flares suggests that this XL delay just happens to be appreciably larger than normal for this particular flare. Of course, no two flares are exactly the same.
3. Discussion and Conclusions
McRae and Thomson  have shown experimentally that VLF phase is a nearly linear monitor of the effective D-region reflection height and a nearly linear measure of the logarithm of the solar X-ray flux. The latter finding is reinforced here by the rather good tracking of the VLF phase with the logarithm of the solar X-ray flux right up to the peak of the X10 flare in Figure 5, and also by the good tracking up to GOES saturation at X17.4 for the great flare in Figures 3 and 4. Because the X-rays ionize the dominant atmospheric constituents (N2 and O2) and because the atmospheric composition and scale height vary only rather slowly with height, the flare phase changes are likely to mirror the X-ray flux changes up to very much higher levels than have so far been tested. In contrast, as McRae and Thomson  also showed, the relationship between long path VLF amplitude and X-ray flux is more complicated, generally less sensitive and hence less useful here.
 The possible effect of VLF phase variation with local time on the paths needs to be considered. The sub-solar point at the time of the flare peak (1945 UT) is shown in Figure 2 and from this the maximum solar zenith angle along the paths is found to be about 65°. From McRae and Thomson , the NLK to Dunedin phase, in unperturbed conditions (low solar activity), would vary by only about 25° over the flare interval 19–23 UT, and by only about 5° over the rise time of the flare, 1930–1945 UT. This 5° would represent an error of ∼1% in the ∼500° phase perturbation from flare start to saturation. Thus the scaling from saturation at X17.4 to the peak at X45 would change by only about 1%, which is near negligible. Also, McRae and Thomson  have reported that the VLF phase is less sensitive to solar zenith angle when X-rays dominate over Lyman-α which is always the case here (even before the flare onset) and so the local time or solar zenith angle effects should be even smaller.
 We conclude that the great flare of 4 November 2003 peaked between 1945 and 1946 UT, and that its magnitude was about X45, more than twice the size of any other solar flare since at least 1976. An examination of the quality of the VLF phase fits suggests a reasonable uncertainty range of X40–X50. This flare occurred on the limb of the Sun just before it rotated out of sight; while this may not have degraded the resulting X-ray flux near the Earth, it certainly resulted in very much lower particle and magnetic effects at the Earth than would have been expected if the flare had been near the center of the solar disk. This raises the real likelihood that some day such a flare (or an even larger one) will occur nearer the center of the Earth side of the Sun and produce more dramatic effects at the Earth, including the possibility of even larger GICs (geomagnetically induced currents) disrupting mains power supplies than occurred in Quebec in 1989. Indeed the ‘extreme’ magnetic storm of nearly 150 years ago, in 1859, [Tsurutani et al., 2003] may well have been preceded by such a flare.
 We are very grateful to NOAA's Space Environment Center, particularly to Dr. Rodney Viereck, for their help and for providing not only the 1-min but also the 3-s GOES X-ray data, which made possible the (flux) calibration of our VLF phase data. We would also like to thank Mr. Dave Hardisty of our institution for the design and implementation of the digital MSK multi-channel modulator/demodulator which carries our VLF signals live from our field station.