The Effect of the Ionosphere on Ultra-Low-Frequency Radio-Interferometric Observations? F

Home , Low frequency, Ultra Low Frequency, Very Large Array

A&A 615, A179 (2018) Astronomy https://doi.org/10.1051/0004-6361/201833012 & © ESO 2018 Astrophysics

The effect of the ionosphere on ultra-low-frequency radio-interferometric observations? F. de Gasperin1,2, M. Mevius3, D. A. Rafferty2, H. T. Intema1, and R. A. Fallows3

1 Leiden Observatory, Leiden University, PO Box 9513, 2300 RA Leiden, The Netherlands e-mail: [email protected] 2 Hamburger Sternwarte, Universität Hamburg, Gojenbergsweg 112, 21029 Hamburg, Germany 3 ASTRON – the Netherlands Institute for Radio Astronomy, PO Box 2, 7990 AA Dwingeloo, The Netherlands

Received 13 March 2018 / Accepted 19 April 2018

ABSTRACT

Context. The ionosphere is the main driver of a series of systematic effects that limit our ability to explore the low-frequency (<1 GHz) sky with radio interferometers. Its effects become increasingly important towards lower frequencies and are particularly hard to calibrate in the low signal-to-noise ratio (S/N) regime in which low-frequency telescopes operate. Aims. In this paper we characterise and quantify the effect of ionospheric-induced systematic errors on astronomical interferometric radio observations at ultra-low frequencies (<100 MHz). We also provide guidelines for observations and data reduction at these frequencies with the LOw Frequency ARray (LOFAR) and future instruments such as the Square Kilometre Array (SKA). Methods. We derive the expected systematic error induced by the ionosphere. We compare our predictions with data from the Low Band Antenna (LBA) system of LOFAR. Results. We show that we can isolate the ionospheric effect in LOFAR LBA data and that our results are compatible with satellite measurements, providing an independent way to measure the ionospheric total electron content (TEC). We show how the ionosphere also corrupts the correlated amplitudes through scintillations. We report values of the ionospheric structure function in line with the literature. Conclusions. The systematic errors on the phases of LOFAR LBA data can be accurately modelled as a sum of four effects (clock, ionosphere ﬁrst, second, and third order). This greatly reduces the number of required calibration parameters, and therefore enables new efﬁcient calibration strategies. Key words. atmospheric effects – instrumentation: interferometers – methods: observational – techniques: interferometric

1. Introduction during the night; in normal conditions the TEC during daytime hours is ten times higher. When observing radio emission at The ultra-low frequencies (10 100 MHz) are the last poorly − long wavelengths, the ionosphere introduces systematic effects explored window available for ground-based astronomical obser- such as reﬂection, refraction, and propagation delay of the radio vations. Some attempts have been made in the past to cover waves (Mangum & Wallace 2015). For interferometric observa- this frequency range; notably, the 38 MHz 8th Cambridge tion, propagation delay is the main concern (Intema et al. 2009). survey (8C; Rees 1990) and the 74 MHz Very Large Array The effect is caused by a varying refractive index n of the iono- Low-frequency Sky Survey (VLSS; Cohen et al. 2007; Lane spheric plasma along the wave trajectories. The total propagation et al. 2014) pioneered this exploration. More recently, the delay, integrated along the LoS at frequency ν, results in a phase GaLactic and Extragalactic All-sky MWA Survey (GLEAM; rotation given by Hurley-Walker et al. 2017) produced images down to 72 MHz. A major limitation when observing at these frequencies is the presence of the ionosphere, a layer of partially ionised plasma, 2πν Φion = (n 1) dl. (1) surrounding our planet. − c LoS − The ionisation of the ionosphere is driven by the UV and Z X-ray radiation generated by the Sun during the day and is An n constant in time and space would impose a coherent balanced by recombination at night. A lower level of ionisa- phase error that would result in a spatial shift of the observed tion is maintained during the night by the action of cosmic image compared to the true sky. The problem becomes more rays. The peak of the free electron density lies at a height of complicated as n depends strongly on time and position. 300 km but the ionosphere extends, approximately, from 75 Neglecting the frictional force and assuming a cold, colli- to∼ 1000 km. The free electron column density along a line of sionless, magnetised plasma (such as the ionosphere), the refrac- sight (LoS) through the ionosphere is generally referred to as the tive index n can be calculated exactly (Davies 1990). For signals total electron content (TEC). The TEC unit (TECU) is 1016 m 2, − with frequencies ν ν (the plasma frequency, that for the which is the order of magnitude typically observed at zenith p ionosphere is around1 10 MHz), it can be expanded (see e.g. ? The 3 movies are available at http://www.aanda.org. Datta-Barua et al. 2008−) into a third-order Taylor approximation

Article published by EDP Sciences A179, page 1 of 12 A&A 615, A179 (2018)

Table 1. Typical ionospheric phase errors in degrees.

dTEC (TECU) I ord II ord (day/night) I ord II ord (day/night) I ord II ord (day/night) 30 MHz 30 MHz 60 MHz 60 MHz 150 MHz 150 MHz 0.5 (remote st., bad iono.) 8067 294/214 4033 73/50 1613 12/8 0.1 (remote st., good iono.) 1613 126/46 806 31/10 323 5/2 0.03 (across FoV) 404 97/16 242 24/4 96 4/<1 0.01 (core st.) 160 88/8 80 22/2 31 4/<1

4 retaining only terms up to ν− : The paper is outlined as follow: in Sect.2 we introduce the Low Frequency Array and in Sect.3 the data that we 2 3 q ne q neB cos θ used. In Sect.4, we present the effect of the ionosphere on n 1 2 2 3 2 3 ≈ − 8π me0 · ν ± 16π me0 · ν radio-interferometric observations at low-frequency. In Sect.5, q4 n2 q4 n B2(1 + cos2 θ) we show how our observations can be used to infer iono- e e , (2) spheric properties. Conclusions and consideration for future − π4 22 · ν4 − π4 3 · ν4 128 me 0 64 me 0 low-frequency experiments are outlined in Sect.6. where ne is number density of free electrons, B is the magnetic field strength, θ is the angle between the magnetic field B and the 2. The Low Frequency Array electromagnetic wave propagation direction, q is electron charge, me is electron mass, and 0 is electric permittivity in vacuum. In LOw Frequency ARray (LOFAR; van Haarlem et al. 2013) is a red we show the parameters related to ionospheric conditions radio interferometer that operates at low (including ultra-low) and the Earth’s magnetic field. The first term is associated with a frequencies: 10 240 MHz. It has 38 stations (aperture arrays dispersive delay proportional to the TEC along the LoS. This is capable of multi-beam− forming) in the Netherlands, divided into the dominant term; for most radio-astronomical applications at 24 “core stations”, concentrated within 4 km, and 14 “remote sta- frequencies higher than a few hundred megahertz, higher-order tions”, providing baselines up to 120 km1. The six innermost terms can be ignored. The second term is related to Faraday stations are packed within 1 km2 ∼and are collectively called the rotation, the positive sign is associated with left-hand polarised “superterp”. Thirteen “international stations” are spread across signals and the negative sign with right-hand polarised signals. Europe, but they are not considered in this paper. LOFAR uses This term depends on TEC and the Earth’s magnetic field. The two antenna types: High Band Antenna (HBA, used to observe last two terms are usually ignored but can become relevant for in the frequency range 110 240 MHz) and Low Band Antenna observations at frequencies below 40 MHz. Of these last two (LBA, used to observe in the− frequency range 10 90 MHz). In terms, the first is dominant and depends on the spatial distribu- this paper we consider only data from the LBA system,− that is tion of the electrons in the ionosphere (Hoque & Jakowski 2008); the most strongly affected by measurement corruptions induced it becomes larger if electrons are concentrated in thin layers and by the ionosphere. However, most of the results can be extended not uniformly distributed. to higher frequencies. Using Eq. (2) we can give order of magnitude estimates of The LOFAR core is located at 52◦5403200 N, 6◦5200800 E. the expected effects at first and second order (see also Petit & The telescope is marginally affected by ionospheric gradients Luzum 2010, Ch. 9): generated at low latitude by Rayleigh–Taylor instabilities and ν 1 dTEC ionospheric irregularities typical of the auroral regions. At high δΦ = 8067 − [deg]; latitudes, strong refractive index gradients due to field-aligned 1 − 60 MHz 1TECU ! ionisation structures can cause severe scintillation conditions. ν 2 dTEC The ionosphere conditions in the polar regions are regularly δΦ = 105 − 2 ± 60 MHz 1TECU monitored by the Kilpisjärvi Atmospheric Imaging Receiver " ! Array (KAIRA; McKay-Bukowski et al. 2015), a station built TEC dB + [deg]; (3) using LOFAR hardware in arctic Finland (see e.g. Fallows et al. 1TECU · 40 µT ! !# 2016). This said, the ionospheric impact on a specific LOFAR observation is strongly dependent on the global ionospheric con- where we adopt a magnetic field B = 40 µT with θ = 45◦. The total TEC in quiet geomagnetic conditions can vary from 1 ditions at the time of observation combined with the location of to 20 TECU from night to day, respectively, and influences∼ the target in the local sky. the∼ second-order term. Considering a differential TEC (dTEC) of 0.3 TECU, which is a plausible number for baselines of 3. Data 50'km, and observing at 60 MHz, the first-order term produces ∼ phase variations of several times 2π. The Faraday rotation instead For this paper we analysed a set of LOFAR LBA observa- produces an effect of around 30◦/50◦ (with different signs for tions pointed at three calibrators: 3C196, 3C295, and 3C380 ± the two circular polarisations) at night/day assuming dB = 1%. (see Table2). For the detailed analysis of ionospheric system- This effect is not negligible and needs to be corrected (see also atic effects we used a 5.5 hr observation pointed at 3C196 and Table1). The effect quickly becomes relatively more severe at obtained on May 3, 2013 (18:00 23:30 UTC). The observation lower frequencies because of the 1/ν2 dependency. Higher-order was taken covering a large continuous→ bandwidth (22 70 MHz) effects can be mostly ignored at 60 MHz. However, at a fre- − quency of 20 MHz, the third-order effect can produce large 1 An up-to-date outline of LOFAR station positions is available at phase errors.∼ http://astron.nl/lofartools/lofarmap.html.

A179, page 2 of 12 F. de Gasperin et al.: The ionosphere at low-frequencies

Table 2. Observation details.

Target name 3C196 3C295 3C380 RA (J2000) 08:13:36.1 14:11:20.3 18:29:31.8 Dec (J2000) +48:13:02 +52:12:10 +48:44:46 Date 03 May 2013 17 Nov 2017 17 Nov 2017 18 Nov 2017 18 Nov 2017 19 Nov 2017 19 Nov 2017 20 Nov 2017 20 Nov 2017 21 Nov 2017 21 Nov 2017 25 Nov 2017 24 Nov 2017 26 Nov 2017 25 Nov 2017 28 Nov 2017 26 Nov 2017 28 Nov 2017 Time range (UTC) 18:00 23:30 (5.5 hr) 07:00 12:04 (5 hr) 12:05 15:07 (3 hr) → 07:00 → 12:04 (5 hr) 12:05 → 15:07 (3 hr) 07:00 → 12:04 (5 hr) 12:05 → 15:07 (3 hr) 07:00 → 12:04 (5 hr) 12:05 → 15:07 (3 hr) 07:00 → 12:04 (5 hr) 12:05 → 14:06 (2 hr) 07:00 → 12:04 (5 hr) 14:00 → 15:00 (1 hr) 07:00 → 12:04 (5 hr) 12:05 → 15:07 (3 hr) 06:00 → 11:04 (5 hr) 12:05 → 15:07 (3 hr) → 11:05 → 14:07 (3 hr) → Time resolution (s) 5 4 4 Frequency range (MHz) 22 70 42 66 42 66 Frequency resolution (kHz) 195.3− (244 channels) 48.8− (122 channels) 48.8− (122 channels) Recorded polarisations XX XY YX YY XX XY YX YY XX XY YX YY so as to evaluate the effect of the ionosphere down to the low- does not allow for these changes to be tracked. Furthermore, est frequencies. Furthermore, the large bandwidth is an essential combining too many frequency channels is also not advisable. As tool for separating the various effects based on their different shown in Fig.1, between the edges of a single LOFAR subband frequency dependencies. The dataset has been calibrated using (1SB 0.195 MHz) centred at 30 MHz, there is a differential ' procedures that will be described in de Gasperin et al. (in prep.). phase of 100◦ (assuming two stations with a differential TEC Here we focus on the outcome of the calibration to describe the value of 0.5 TECU). For compact arrays (baselines shorter than influence of the ionosphere on the signal measured by the anten- a few kilometer, with dTEC . 0.1 TECU), this constraint can nas. For each station pair, radio interferometers record streams be relaxed. To facilitate accurate calibration for all baselines and of data, called visibilities. While ionospheric effects are clearly ionospheric conditions, our calibration has been performed at present in the visibilities, it is easier to analyse them by looking a relatively high time and frequency resolution, as described in at the solutions. Solutions give a station-based representation of Table2. the systematic effects in the form of complex gain factors derived All ionospheric-related systematic effects described in this when observing a point source with a known position and flux paper induce direction dependent errors (DDE). This means that density (i.e. a calibrator). the effects vary appreciably as a function of viewing direc- We also analysed seven 8-hour-long observations obtained tion, even across the field of view (FoV) of the telescope. between November 17 and 28, 2017. These observations were LOFAR LBA is characterised by a full width half maximum taken during the day, pointing the LOFAR beam towards the (FWHM) of 4◦. Errors across the FoV are particularly prob- calibrator sources 3C295 (5 hr each run) and 3C380 (3 hr each lematic to correct∼ as they require either simultaneous estimation run). One observing run of 3C380 failed after two hours and in multiple directions across the FoV (Tasse et al. 2018), or an was combined with an additional hour taken 3 days later. These iterative approach like “peeling” (Noordam 2004; van Weeren observations have a narrower frequency coverage (42 66 MHz), et al. 2016). For this paper, we observed only fields whose total centred around the bandpass peak response of the LBA− dipoles flux density is strongly dominated by a central compact source. ( 58 MHz). Both the frequency and time resolution of these As a consequence, also solutions are dominated by the sys- observations∼ are slightly higher than the one described above; tematic effects from that source direction. Therefore, DDE can however, this does not affect our results. be treated as direction independent errors (DIE) whose values Because of the low antenna sensitivity and the high sky tem- are an approximation of the DDE value in the direction of the perature, the LOFAR LBA system is often in a relatively low dominant source. signal-to-noise ratio (S/N) regime when observing celestial radio sources. A common way to compensate for this is to average data 4. Systematic effects into larger time or frequency intervals when finding solutions. At low frequencies, the optimal solution intervals are a trade-off In Fig.2 we show phase solutions for each station for 5.5 h of between S/N and decorrelation. The ionosphere tends to vary observation of 3C196, in the frequency range 22 70 MHz. All − very quickly and averaging over more than 5 s in time often stations labelled CS are “core stations” – these stations share ∼ A179, page 3 of 12 F. de Gasperin etA&A al.: The 615, ionosphere A179 (2018) at low-frequencies

103 Furthermore,4.1. Ionospheric a strong (dispersive) correlation and instrumental between the delays dTEC as mea- 0.1 dTEC, 10 SB sured by neighbouring stations is also visible. 0.3 dTEC, 10 SB In theThe top initial two panels part of of the Fig. observation3 the clock delayis aﬀected and the by ionospheric large iono- 0.5 dTEC, 10 SB sphericdelay are traveling plotted forwaves. each We station cross-correlated after separation. the dTEC These values values 0.1 dTEC, 1 SB forare RSdifferential 407, RS with 508, respect and RS to 509 CS to 002, estimate and as athe consequence wave direction core 0.3 dTEC, 1 SB stations (not plotted) have very small dTEC and a constant dif- 0.5 dTEC, 1 SB and speed. We obtained a time lag of 137 s (RS 509–RS 508), 102 0.1 dTEC, .5 SB 177ferential s (RS “clock” 509–RS due 407), to and other 47 sinstrumental (RS 508–RS delays. 407). These Conversely, values 1 0.3 dTEC, .5 SB areremote compatible stations with show waves dTEC traveling values at larger200 than m s− 0.3from TECU south- for 0.5 dTEC, .5 SB weststations to north-east, that are around values 50 compatible km away∼ with from previous CS 002. measure- Further- mentsmore, (e.g. a strong Fallows correlation et al. 2016). between The speed the dTEC of these as measuredwaves might by beneighbouring compatible stations with the is propagation also visible. of traveling ionospheric dis- turbancesThe initial (TIDs) part even ofthe if the observation direction of is the affected propagation by large is iono- usu- 101 allyspheric equatorward traveling waves. (Cesaroni We cross-correlatedet al. 2017). In fact, the dTEC TIDs values are asso- for ciatedRS 407, with RS traveling 508, and atmospheric RS 509 to estimate disturbances the wave (TAD) direction originated and

TEC induced error [deg] atspeed. auroral We latitude obtained by a Joule time heating lag of 137 (Hunsucker s (RS 509–RS 1982). 508), Traveling 177 s ionospheric(RS 509–RS disturbances 407), and 47 can s (RS have 508–RS periods 407). of minutes These values to hours are 1 (Hockecompatible & Schlegel with waves 1996). traveling In the at second200 halfm s− offrom the observation south-west ∼ theto north-east, ionosphere values becomes compatible less ordered with and previous likely more measurements dominated 100 by(e.g. turbulent Fallows motions. et al. 2016 Large). The variations speed ofin the these dTEC waves are might not nec- be LBA HBA essarilycompatible an indicationwith the propagation of a dataset of that traveling is diffi ionosphericcult to calibrate. distur- Anbances ionosphere (TIDs) even that is if very the direction active, but of relativelythe propagation coherent is usually across 10 30 90 110 190 240 theequatorward FoV and with (Cesaroni relatively et al. slow 2017 variation). In fact, in time TIDs (the are first associ- half Frequency [MHz] ofated the with test traveling dataset) is atmospheric easier to calibrate disturbances than an (TAD) ionosphere originated that at auroral latitude by Joule heating (Hunsucker 1982). Traveling Fig. 1. Ionospheric-induced phase variations between the begin- is highly direction dependent with fast scintillations (the second Figure 1: Ionospheric-induced phase variations between the be- halfionospheric of the test disturbances dataset). can have periods of minutes to hours ning and the end of a band of 1/2,/ 1 and 10 LOFAR sub bands (ginning1SB 0 and.195 theMHz). end Theof a banddTEC of is 1 assumed2, 1 and to 10 be LOFAR 0.1, 0.3, sub and bands 0.5 (HockeTo demonstrate & Schlegel the1996 spatial). In the coherence second ofhalf the of dTEC the observation solutions, (1SB' 0.195 MHz). The dTEC is assumed to be 0.1, 0.3 and the ionosphere becomes less ordered and likely more dominated TECU.' These are typical values for distances of a few tens of kilometres. we construct spatial screens of the dTEC variations across the A0.5 phase TECU. variation These larger are typical than 100 values◦ creates for distances strong decorrelation. of a few tens This of array.by turbulent One screen motions. is made Large for variations each time in the slot dTEC solved are for not in nec- the kilometres. A phase variation∼ larger than 100◦ creates strong essarily an indication of a dataset that is difficult to calibrate. plot can be used to estimate the maximum amount∼ of averaging (or the calibration, fitting to the projected locations (pierce points) of maximumdecorrelation. band usable This plot to find can a single be used solution) to estimate before decorrelating the maximum the 3C196An ionosphere onto a thin that plane is very located active, at buta height relatively of 200 coherent km above across the signal.amount Coloured of averaging bands (orare the frequency maximum ranges band observed usable to by find LOFAR. a sin- ground.the FoV Generally, and with relatively there is one slow pierce variation point per in time station, (the per first direc- half gle solution) before decorrelating the signal. Coloured bands are tion,of the per test time dataset) slot. In is the easier case to of calibrate the fits discussed than an ionosphere here, we use that a the frequency ranges observed by LOFAR. singleis highly direction direction (that dependent of 3C196); with therefore fast scintillations we can have (the up second to 38 half of the test dataset). the same clock and are close together. Stations labelled RS are pierce points per screen (some of which are flagged; see Fig. 2). To demonstrate the spatial coherence of the dTEC solutions, “remote stations” and each of them has an independent clock. We adopt the same method as Intema et al. (2009) which uses we construct spatial screens of the dTEC variations across the Clocks are not perfectly synchronised and may drift in time with Karhunen-Loeve` (KL) base functions to model the spatial varia- two effects (clock errors and ionospheric dispersive delay) to dis- array. One screen is made for each time slot solved for in the respect to one another. This imprints a time-variable system- tions of the dTEC values. During the fitting, we adopt a power- entangle their contribution to the phase solutions. This process is calibration, fitting to the projected locations (pierce points) of atic error on the phases of remote stations which is linear in law dependence for the phase structure function (see Sect. 5.1), known as clock/TEC separation and is performed by the LOFAR 3C196 onto a thin plane located at a height of 200 km above frequency ( ν). This2 effect dominates the phase error in the with a power-law index, β = 5/3. Lastly, we fix the number of Solution Tool (LoSoTo ). The outcome is time-streams of values the ground. Generally, there is one pierce point per station, per closest remote∝ stations such as RS 106 that in fact shows a rather KL base vectors fit per screen to five, resulting in five free model representing the various systematic effects that we want to dis- direction, per time slot. In the case of the fits discussed here, uniform phase wrapping across the sampled bandwidth. In the parameters per screen. entangle. It is important to note that the clock/TEC separation we use a single direction (that of 3C196); therefore we can have most distant remote stations (such as RS 508 or RS 509) the iono- We plot the screen fits at two times in Fig. 4. The spatial procedure does not impose any time coherency in the expected up to 38 pierce points per screen (some of which are flagged; spheric dispersive delay ( 1/ν) dominates the error budget, and coherence of the dTEC values at each time is clearly visible in systematic effects; each time stamp is treated separately. The see Fig.2). We adopt the same method as Intema et al.(2009) as a consequence phases∝ wrap differently at different frequen- these plots. Therefore, it should be possible to interpolate spa- fact that the outcome looks well-correlated in time is an indica- which uses Karhunen–Loève (KL) base functions to model the cies. We can use the different frequency dependency of the two tially between pierce points using the dTEC screens to obtain tor that the procedure works as expected. As a final verification spatial variations of the dTEC values. During the fitting, we effects (clock errors and ionospheric dispersive delay) to disen- dTEC values in directions other than that of 3C196. The screens we also subtracted the derived phase effect of all the systematic adopt a power-law dependence for the phase structure function tangle their contribution to the phase solutions. This process is can also be used during fitting as constraints that enforce spa- effects combined from the original solutions, this produced the (see Sect. 5.1), with a power-law index, β = 5/3. Lastly, we fix known as clock/TEC separation and is performed by the LOFAR tial coherence of the dTEC solutions, thus reducing the number second panel of Fig. 3 which shows rather uniform residuals, the number of KL base vectors fit per screen to five, resulting in Solution Tool (LoSoTo2). The outcome is time-streams of values of free parameters solved for during the calibration. We are cur- meaning that the vast majority of the LOFAR phase systematic five free model parameters per screen. representing the various systematic effects that we want to dis- rently investigating the use of screens in this way. effect can be described with a simple model of clock delays and We plot the screen fits at two times in Fig.4. The spatial entangle. It is important to note that the clock/TEC separation ionospheric effects. coherence of the dTEC values at each time is clearly visible in procedure does not impose any time coherency in the expected 4.2.these Higher-order plots. Therefore, terms it should be possible to interpolate spa- systematic effects; each time stamp is treated separately. The tially between pierce points using the dTEC screens to obtain fact4.1. that Ionospheric the outcome (dispersive) looks well-correlated and instrumental in time delays is an indica- With this dataset we were able to measure the second-order iono- dTEC values in directions other than that of 3C196. The screens tor that the procedure works as expected. As a final verification spheric effect due to Faraday rotation and the third-order disper- can also be used during fitting as constraints that enforce spa- weIn the also top subtracted two panels the derived of Fig. phase3 the clockeffect delayof all the and systematic the iono- sive delay effect. Faraday rotation is not easily obtainable from tial coherence of the dTEC solutions, thus reducing the number effectsspheric combined delay are plotted from the for original each station solutions, after thisseparation. produced These the the XX and YY phase solutions. Instead, we took advantage of ff of free parameters solved for during the calibration. We are secondvalues are panel di oferential Fig.3 withwhich respect shows to rather CS 002, uniform and as residuals, a conse- its different sign in the right and left polarisations (see Eq. 2). currently investigating the use of screens in this way. meaningquence core that stations the vast (not majority plotted) of the have LOFAR very small phase dTEC systematic and a This required a conversion of the dataset from linear to circu- ff effectconstant can di beerential described “clock” with a due simple to other model instrumental of clock delays delays. and lar polarisation and the extraction of the RR-LL phase solutions ionosphericConversely, effects. remote stations show dTEC values larger than 0.3 (see4.2. Higher-orderFig. 5). Since terms clock delay and ionospheric first and third TECU for stations that are around 50 km away from CS 002. terms are scalar, their effect is the same for the RR and LL po- With this dataset we were able to measure the second-order 2 larisation and they cancel out if we subtract one from the other. 2https://github.com/revoltek/losotohttps://github.com/revoltek/losoto Ationospheric this point, effect one can due now to Faraday easily fit rotation the second-order and the third-order term as a

A179, page 4 of 12 4 F. de Gasperin et al.: The ionosphere at low-frequencies F. de Gasperin et al.: The ionosphere at low-frequencies

Fig.Figure 2. Gain 2: Gain phase phase solutions solutions (from + (fromπ: blue+ toπ:π blue: red) to for theπ: XXred) polarisation for the XX referenced polarisation to station referenced CS 002 (located to station in the CS superterp 002 (located centre). in Each the panelsuperterp is one centre). station. WhiteEach panel pixels isrepresents one station. bad− data White that pixels− were removed. represents Stations bad data CS 013, that CS were 026, removed. CS 031, CS Stations 101, and CS RS 013, 310 were CS 026, fully CSremoved 031, dueCS to101 hardware and RS issues 310 were or strong fully radio removed frequency due interference to hardware (RFI) issues contamination. or strong radio In the frequency bottom image interference we show the (RFI) residuals contamination. after subtracting In the all thebottom effects image shown we inshow Fig.3. the residuals after subtracting all the eﬀects shown in Fig. 3.

A179, page 5 of 12 5 A&A 615, A179 (2018) F. de Gasperin et al.: The ionosphere at low-frequencies

Fig.Figure 3. From 3: From top-left top-left to bottom-right to bottom-right:: instrumental instrumental clock delay clock (in s). delay Total (in electron s). Total content electron variation content along the variation observation along (in the TECU). observation Faraday 2 2 3 3 rotation(in TECU). (in rad Faraday m− ). Ionospheric rotation (in third-order rad m− effect). Ionospheric (in rad m− third-order). All values e areffect differential (in rad mbetween− ). All CS values 001 (assumed are diff constanterential at between 0) and all CS remote 001 stations (from blue to red in alphabetical order). (assumed constant at 0) and all remote stationsF. de Gasperin (from blue et al.: to The red ionosphere in alphabetical at low-frequencies order). differential delay between the two polarisations with a 1/ν2 de- fit. As a consequence, imperfect separation in the parameter dependency. In the third panel of Fig. 3 we show the result in terms termination generates small noise-like perturbations in the other of rotation measure (RM). estimated parameters. The second-order term is not affected by this problem as its estimation is done with different methods as 2πν q3 1 described above. Φ = RM λ2 = n B cos θ dl . (4) c · 16π3m2 · ν3 e e 0 LoS ! Z 4.3. Amplitude scintillations The term in parentheses comes from the second term of Eq. 2. Again we observe that nearby stations have a similar be- Scintillations are caused by electromagnetic waves scattered in haviour and that there is a correlation between the dTEC and the a non-uniform medium with small changes in the refractive in- dRM. This is a consequence of the presence of ne in both the first dex, such as the ionosphere. A plane wave that enters such a and second terms of Eq. 2. The measured RM of 0.03 rad pro- medium with a spatially uniform phase exits the medium with a duces 45◦ phase error, which is compatible with expectations spatially irregular phase. After propagation to a station, the irreg- ∼ given a measured dTEC of 0.3 TECU. ular phases may combine either constructively or destructively In certain observations, such as the one used in this example, (see Kintner et al. 2007). As a consequence, the wave amplitude when the ionospheric variation is strong enough, the third-order is increased or decreased and the gain amplitude solutions of the term can also be extracted by fitting a 1/ν3 term together with station compensate for the effect by producing an exact opposite the clock delay and the ionospheric first-order dispersive delay trend. To some degree, at frequencies below 100 MHz, we ob- at the clock/TEC separation time. The third-order term becomes serve that scintillations are always present in LOFAR amplitude relevant only below 40 MHz but it can rarely be ignored at fre- solutions. ∼ quencies close to the plasma frequency (< 20 MHz). In the last An example of this is visible in Fig. 6, where an “amplitude panel of Fig. 3 we show the estimated third-order effect using: wave” crosses the core area (4 km) in 1 minute, therefore travelling at a velocity of 240 km/h. Projecting the linear size of ∼ 2πν q4 1 these coherent structures to the height of 300 km, we can esti- Φ = TEC λ3 n2 dl . (5) 3 4 2 2 4 e mate an angular size over which amplitude corrections can be ≈ c · 128π me · ν LoS  0 Z  considered fairly uniform, which is 200. Scintillations there-   ∼ As the first- and third-order terms both depend on the num- fore create a strongly direction-dependent amplitude error across Fig.Figure 4. Two 4: Two examples examples of TEC-screen of TEC-screen fits from fits the from observation the observation shown in shown Fig.3. Values in Fig. are 3. in Values differential are in TECU differential with respect TECU to with station respect CS 002. to ber of free electrons, ne, not surprisingly they trace each other. the FoV. Eachstation circle CS represents 002. Each a circleLOFAR represents station; colour a LOFAR coded withinstation; the colour circle codedis the dTEC within value the for circle that is station the dTEC (we note value that for the that markers station are filled (we note with theInthe colour initial corresponding part of the to theobservation, measured dTEC). the eff Theect isbackground stronger colour due is theInterestingly, TEC screen fitted wave-like across the structures array as described are a recurrent in the text. Stationspattern crossedtothat the the large with markers andTEC X are are and thefilled possibly samewith excluded other the colour from ionospheric Fig. corresponding2. The characteristics full movie to the is available measuredacross in the thedTEC). onlinecore The stations material. background in the second colour half is the of TEC our test screen observa- fitted (e.g.across athe thin array dominant as described layer). Inin the text. second Stations part of crossed the observa- with an Xtion are (see the same the online excluded material). from Fig. On 2. the The other full movie hand,is in available the first tion,in the the online third-order material. term becomes less prominent and harder to part of the observation that is dominated by large waves, am- A179, page 6 of 12 6plitude scintillations seem to be quasi-simultaneous across the We fit this function to the data to obtain an estimation of β entire array (including remote stations). The amplitude of the (expected to be 5/3 = 1.67 for pure Kolmogorov turbulence) scintillations is around 10% during both halves of the observa- and of rdiff, the spatial scale over which the phase variance is 1 tion; therefore, it does± not seem to depend strongly on the size rad2, referred to as the diffractive scale (Narayan 1992). Since of the wave phenomena. Although scintillations with timescales the phase errors of the core stations are dominated by iono- larger than a few seconds are highly unlikely to be due to the spheric errors, we did not use those phases directly, instead interplanetary medium, the possibility cannot be entirely ruled first converting to dTEC. This gives a fast rough estimate of out: Kaplan et al. (2015) demonstrated that interplanetary scin- the diffractive scales and thus of the ionospheric quality dur- tillation (IPS) was still visible in observations taken with the ing an observation. The air mass factor was not corrected for, Murchison Widefield Array (MWA, Tingay et al. (2013)) with resulting in a slightly larger variance depending on the ele- a time resolution of 2s, and Fallows et al. (2016) demonstrated vation angle. We obtained β = 1.88, 1.88, 1.92, 1.94, 1.88 and that IPS appears near-simultaneous across the Dutch stations of rdiff@150MHz = 7, 8, 16, 16, 22 km, for time chunks 1 to 5, respec- LOFAR. Furthermore, dedicated observations of IPS taken with tively (see Fig. 7). These values for β are larger than expected for LOFAR show good IPS signal for the radio sources observed Kolmogorov turbulence (β = 5/3), and are probably due to the here, with both 3C295 and 3C380 used in an IPS observing cam- effect of large-scale waves, which were not filtered. The base- paign run during October 2016 and 3C196 used in spring and lines that were used for Fig. 7 are much smaller than the typical summertime observations. wavelength of such waves ( 100 200 km), therefore the effect closely resembles that of a∼ linear− gradient over these baselines, which would correspond to β = 2.0 in the phase structure func- 5. The ionosphere as sensed by LOFAR tion. The results are similar to those reported in Mevius et al. (2016). The smaller diffractive scales correspond to the first half 5.1. Structure function of the observation, where the magnitude of the dTEC variations We divided the observations into five time chunks of 1 hr is larger. ∼ each and calculated the ionosphere phase structure function as After removing the large ionospheric gradient (e.g. with a described in Mevius et al. (2016). For Kolmogorov turbulence, direction-independent calibration), higher orders of the refrac- the phase structure function is a power-law of the form: tive index expansion in Eq. 2 are small, and are assumed to be uniform across the LOFAR beam. To test this assumption we β r can use the structure function. The LOFAR primary beam size D(r) = . (6) r is 4◦, that corresponds to 20 km at a 300 km-high ionospheric diff ! ∼

7 F. de Gasperin et al.: The ionosphere at low-frequencies F. de Gasperin et al.: The ionosphere at low-frequencies

Fig.Figure 5. As 5: Asin Fig. in2 Fig., but 2, here but we here show we the show differential the diff phaseerential solutions phase in solutions circular polarisation in circular (RR polarisation – LL). The (RR plot – isolates LL). The theplot effect isolates of Faraday the 2 rotation.effect of Since Faraday it depends rotation. on dTEC Since and it d dependsB, the effect on isdTEC stronger and on d stationsB, the e furtherffect is away stronger from the on reference stations (CS further 002). away By fitting from a 1 the/ν referencedispersive delay(CS 002). we can By recover fitting the a 1 rotation/ν2 dispersive measure delay displayed we incan the recover third panel the ofrotation Fig.3. measure displayed in the third panel of Fig. 3. dispersiveT1 delay effect. Faraday T2 rotation is not easily T3 obtain- at the clock/TEC T4 separation time. The third-order T5 term becomes able from the XX and YY phase solutions. Instead, we took relevant only below 40 MHz but it can rarely be ignored at advantage of its different sign in the right and left polarisations frequencies close to the∼ plasma frequency (<20 MHz). In the last (see Eq. (2)). This required a conversion of the dataset from panel of Fig.3 we show the estimated third-order effect using: linear to circular polarisation and the extraction of the RR–LL 4 phase solutions (see Fig.5). Since clock delay and ionospheric 3 2πν q 1 2 Φ = TEC3 λ n dl . (5) first and third terms are scalar, their effect is the same for the RR ≈ c · 128π4m22 · ν4 e  e 0 ZLoS  and LL polarisation and they cancel out if we subtract one from   the other. At this point, one can now easily fit the second-order As the first- and third-order terms both depend on the num- term as a differential delay between the two polarisations with a ber of free electrons, ne, not surprisingly they trace each other. 1Figure/ν2 dependency. 6: Left to right: In the time third evolution panel of Fig.of amplitude3 we show solutions the result for LOFARIn the initial core stations part of theforthe observation, observation the shown effect in is Fig.stronger 3. Each due inplot terms is separated of rotation from measure the next (RM by). 10 seconds. Each point representsto a the core large station dTEC and and each possibly is positioned other ionospheric in the plot according characteristics to its geographical location. Colour (blue to red) and size (small to large)(e.g. are related a thin dominant to the value layer). of the Inamplitude the second correction part of the (from observation,10% 2πν q3 1 the third-order term becomes less prominent and harder− to fit. Φto =+10%).λ2 A= wave travelling south-north is visible.θ Similar. structures were also reported with single-station observations. The full RM 3 2 3 neB cos dl (4) As a consequence, imperfect separation in the parameter deter- movie is availablec in· the16π onlinem 0 material.· ν e ZLoS ! mination generates small noise-like perturbations in the other The term in parentheses comes from the second term of estimated parameters. The second-order term is not affected by Eq.layer. (2 With). Again a di weffractive observe scale that of nearby 10 km andstations assuming have aβ similar= 1.7, 5.2.this problem Multi-epoch as its observations estimation is done with different methods as behaviourEq. 6 gives and a phase that there variance is a correlationof 3 rad2 betweenat 150 MHz. the dTEC This cor- and described above. ∼ theresponds dRM. to This a dTEC is a consequenceof about 0.03 of TECU. the presence Consequently, of ne in even both at In November 2017, we performed a series of eight observations the60 MHz, first and only second the first-order terms of term Eq. varies (2). substantially The measured across RM the of pointed4.3. Amplitude at the calibrators scintillations 3C295 and 3C380. The observations 0.03 rad produces 45 phase error, which is compatible with FoV, while other terms∼ ◦ can be considered constant. This finding were carried out during daytime hours. We extracted the dTEC expectationscan be used givento simplify a measured the calibration dTEC of 0.3 strategies TECU. on the target andScintillations dFR measurements are caused for by electromagneticall of them (see wavesFigs. 9 scattered and 10). in A a fields.In certain observations, such as the one used in this example, basicnon-uniform expectation medium of ionospheric with small models changes is in the the presence refractive of index,an in- when the ionospheric variation is strong enough, the third-order such as the ionosphere. A plane wave that enters such a medium 3 creasing north-south TEC gradient; in all observations, the dTEC term can also be extracted by fitting a 1/ν term together with valueswith a show spatially its presence uniform (red phase lines exits are stations the medium in the with North, a blue spa- the clock delay and the ionospheric first-order dispersive delay linestially are irregular stations phase. in the After South, propagation all referenced to a station, to station the CS irregular 002 in A179, page 7 of 12 8 F. de Gasperin et al.: The ionosphere at low-frequencies

Figure 5: As in Fig. 2, but here we show the differential phase solutions in circular polarisation (RR – LL). The plot isolates the effect of Faraday rotation. Since it depends on dTEC and dB, the effect is stronger on stations further away from the reference (CS 002). By fitting a 1/ν2 dispersive delay we can recoverA&A the 615, rotation A179 (2018) measure displayed in the third panel of Fig. 3.

T1 T2 T3 T4 T5

Fig.Figure 6. Left 6: Left to right to right:: timetime evolution evolution of amplitude of amplitude solutions solutions for LOFAR for core LOFAR stations core for stations the observation for the shown observation in Fig.3 shown. Each plot in Fig. is separated 3. Each fromplotis the separated next by 10 from s. Each the point next represents by 10 seconds. a core station Each point and each represents is positioned a core in stationthe plotand according each is to positioned its geographical in the location. plot according Colour (blue to its to red)geographical and size (small location. to large) Colour are related (blue to to red)the value and sizeof the (small amplitude to large) correction are related (from to10% theto value+10% of). the A wave amplitude travelling correction south–north (from is visible.10% Similar structures were also reported with single-station observations. The full movie is− available in the online material. − to +10%). A wave travelling south-north is visible. Similar structures were also reported with single-stationF. deobservations. Gasperin et al.: The The full ionosphere at low-frequencies movie is available in the online material. phases may combine either constructively or destructively (see 11 Kintner et al. 2007). As a consequence, the wave amplitude is layer. With a diffractive scale of 10 km and assuming β = 1.7, 5.2. Multi-epoch observations 10 increased or decreased and the gain amplitude2 solutions of the stationEq. 6 gives compensate a phase forvariance the effect of by3 rad producingat 150 MHz. an exact This oppo- cor- ∼ 9 siteresponds trend. to To a dTEC some of degree, about 0.03 at frequencies TECU. Consequently, below 100 even MHz, at In November 2017, we performed a series of eight observations 60 MHz, only the first-order term varies substantially across the we observe that scintillations are always present in LOFAR pointed at the calibrators 3C295 and 3C380. The observations 8 amplitudeFoV, while solutions. other terms can be considered constant. This finding were carried out during daytime hours. We extracted the dTEC canAn be example used to simplify of this is the visible calibration in Fig.6 strategies, where an on “amplitude the target and dFR measurements for all of them (see Figs. 9 and 10). A 7 wave”fields. crosses the core area (4 km) in 1 min, therefore travelling basic expectation of ionospheric models is the presence of an in- 1 creasing north-south TEC gradient; in all observations, the dTEC 6 at a velocity of 240 km h . Projecting the linear size of these vTEC (TECU) ∼ − coherent structures to the height of 300 km, we can estimate an values show its presence (red lines are stations in the North, blue 5 angular size over which amplitude corrections can be considered lines are stations in the South, all referenced to station CS 002 in fairly uniform, which is 200. Scintillations therefore create a 4 codg strong direction-dependent∼ amplitude error across the FoV. uqrg 8 3 igsg Interestingly, wave-like structures are a recurrent pattern LOFAR LBA across the core stations in the second half of our test observation 2 (see the online material). On the other hand, in the first part of 0 1 2 3 4 5 the observation that is dominated by large waves, amplitude scin- Time (since start of observation, hr) tillations seem to be quasi-simultaneous across the entire array FigureFig. 7. 7:Phase Phase structure structure function function divided divided into fiveinto time five chunks time chunks for the (including remote stations). The amplitude of the scintillations observation of Fig.3. The initial part of the observations is visibly more Figure 8: Absolute TEC derived from World Magnetic Model, foraffected the observation by ionospheric of disturbances Fig. 3. The also initial in Fig. part3. The of phase the observa- variance is around 10% during both halves of the observation; there- tions is visibly more affected by ionospheric disturbances also in dTEC and dRM of the first observation in Fig. 10 compared to fore, it does± not seem to depend strongly on the size of the wave is converted to the expected value at 150 MHz to compare it with other three different interpolated IGS model datasets. Fig.experiments 3. The phase such as variance LOFAR HBAis converted and MWA. to the expected value at phenomena. Although scintillations with timescales larger than 150 MHz to compare it with other experiments such as LOFAR a few seconds are highly unlikely to be due to the interplane- HBA and MWA. tary medium, the possibility cannot be entirely ruled out: Kaplan and of rdiff, the spatial scale over which the phase variance is 5.3. Absolute TEC and satellite comparison 1 rad2, referred to as the diffractive scale (Narayan 1992). Since et al.(2015) demonstrated that interplanetary scintillation (IPS) An interesting application is the possibility to estimate the ab- was still visible in observations taken with the Murchison Wide- the phase errors of the core stations are dominated by ionospheric errors, we did not use those phases directly, instead solute TEC from the differential TEC and differential Faraday field Array (MWA; Tingay et al. 2013) with a time resolution of rotation. We make the following approximation: 2 s, and Fallows et al.(2016) demonstrated that IPS appears near- first converting to dTEC. This gives a fast rough estimate of the diffractive scales and thus of the ionospheric quality dur- simultaneous across the Dutch stations of LOFAR. Furthermore, dRM12 c B 1 TEC1 c B 2 TEC2, (7) dedicated observations of IPS taken with LOFAR show good IPS theing superterp). an observation. The wave-like The air mass behaviour factor of was the not ionospheric corrected sys- for, ≈ · || · − · || · tematic effects are clear, although during some time intervals, signal for the radio sources observed here, with both 3C295 and resulting in a slightly larger variance depending on the ele- with dRM12 differential Faraday rotation between stations 1 and waves appear more structured and on larger scales than at other 3C380 used in an IPS observing campaign run during October vation angle. We obtained β = 1.88, 1.88, 1.92, 1.94, 1.88 and 2, B 1,2, the parallel magnetic field, and TEC1,2, the integrated ff || 2016 and 3C196 used in spring and summertime observations. timesrdiff@150 (as MHz seen= 7 with, 8, 16 di, 16erent, 22 km, techniques for time with chunks MWA 1 to Loi 5, respec- et al. electron content along the LoS for stations 1 and 2, respectively. 2015b,a).tively (see Fig.7). These values for β are larger than expected for We approximate the integral in Eq. 1 with the thin-layer ap- KolmogorovIonospheric turbulence conditions (β are= 5/ driven3), and by are a probably number of due factors to the proach. This can be rewritten in terms of absolute TEC at station 5. The ionosphere as sensed by LOFAR (e.g.effect season, of large-scale solar activity, waves, and which latitude). were not The filtered. dominant The factor base- 1: 5.1. Structure function islines the that day-night were used cycle. for During Fig.7 are the much night, smaller the ionospheric than the typical TEC TEC1 dB 12 = C dRM12 B 2 dTEC12, (8) wavelength of such waves ( 100 200 km), therefore the effect · || · − || · is reduced; this has an impact∼ on− the magnitude of the second- with dB being the differential parallel magnetic field and We divided the observations into five time chunks of 1 h closely resembles that of a linear gradient over these baselines, 12 order term of Eq. 2, which is expected to be smaller. However, dTEC ||the differential integrated electron content between sta- each and calculated the ionosphere phase structure function∼ as which would correspond to β = 2.0 in the phase structure func- 12 single-station observations taken under an ionospheric scintil- tions 1 and 2. We used the World Magnetic Model (Chulliat described in Mevius et al.(2016). For Kolmogorov turbulence, tion. The results are similar to those reported in Mevius et al. lation monitoring project demonstrate that scintillation is of- et al. 2014) and the measurements of dRM and dTEC to esti- the phase structure function is a power-law of the form: ten(2016 much). The stronger smaller at diffractive night, particularly scales correspond prior to midnight.to the first Wehalf of the observation, where the magnitude of the dTEC variations mate the absolute vertical TEC for the first observation in Fig. β report a large fraction of data loss due to intense scintillation 10 in this way. The thin layer model places a single ionospheric r eventsis larger. during night-time observations. During these events we D(r) = . (6) After removing the large ionospheric gradient (e.g. with layer at an altitude of 450 km. Slant TEC to vertical TEC con- rdiff were not able to disentangle the various phase effects, and ampli- ! a direction-independent calibration), higher orders of the versions are done assuming a spherical ionosphere at the same tude solutions show clear signs of decorrelation. Along a seven- altitude. The resulting vertical TEC at the position of CS 001 We fit this function to the data to obtain an estimation of nightrefractive campaign index that expansion we carried in Eq. out ( in2) February are small, and and March are assumed 2015, β (expected to be 5/3 = 1.67 for pure Kolmogorov turbulence) to be uniform across the LOFAR beam. To test this assumption as a function of time is shown in Fig. 8. The error bars reflect around 30% of our observations had to be discarded for this the spread of the measurements using all different station com- reason. Conversely, in 14 days of daytime observations taken A179, page 8 of 12 binations. In the same plot, we show the interpolated vertical in 2017 (7 of which are presented in this paper), only a small TEC values from three different TEC maps created using the percentage of our data were affected by strong scintillations. Global Navigation Satellite System (GNSS) and provided by the Since the observations were taken far apart in time, it is difficult International GNSS service (IGS). In particular, CODE, UPC to derive strong conclusions. A downside of daytime observa- and combined final products have been used (Schaer 1999; Orus´ tions is the (unavoidable) presence of the Sun, combined with et al. 2005; Hernandez-Pajares et al. 2009). The B field param- the relatively poor side-lobe suppression of a phased array like eters and satellite-based TEC values were determined using the LOFAR compared to dish-based radio interferometers. However, RMextract package3. The measured absolute TEC values are the low-frequency radio spectrum of the (quiet) Sun is strongly within 10% and following the trend of the GNSS based products inverted, with S ν3, and as a consequence, at 50 MHz, the ν ∝ from IGS. The time resolution is 10 s, two orders of magnitude Sun flux density is expected to be a few thousand janskies, which better than that of the IGS models which is 2 hours for codg is comparable to the flux density of some other sources present and igsg and 15 minutes for uqsg. The main uncertainty in the at night. Moreover, solar emission is extended on scales of sev- LOFAR measurement comes from the value of dB , which can eral arc-minutes; therefore, it is resolved out on moderately long || baselines. 3 https://github.com/lofar-astron/RMextract.

9 F. de Gasperin et al.: The ionosphere at low-frequencies we can use the structure function. The LOFAR primary beam respectively. We approximate the integral in Eq. (1) with the size is 4◦, that corresponds to 20 km at a 300 km-high iono- thin-layer approach. This can be rewritten in terms of absolute spheric∼ layer. With a diffractive scale of 10 km and assuming TEC at station 1: β = 1.7, Eq. (6) gives a phase variance of 3 rad2 at 150 MHz. ∼ This corresponds to a dTEC of about 0.03 TECU. Consequently, TEC1 dB 12 = C dRM12 B 2 dTEC12, (8) even at 60 MHz, only the first-order term varies substantially · || · − || · across the FoV, while other terms can be considered constant. with dB being the differential parallel magnetic field and ||12 This finding can be used to simplify the calibration strategies on dTEC12 the differential integrated electron content between sta- the target fields. tions 1 and 2. We used the World Magnetic Model (Chulliat et al. 2014) and the measurements of dRM and dTEC to esti- 5.2. Multi-epoch observations mate the absolute vertical TEC for the first observation in Fig.9 in this way. The thin layer model places a single ionospheric In November 2017, we performed a series of eight observations layer at an altitude of 450 km. Slant TEC to vertical TEC con- pointed at the calibrators 3C295 and 3C380. The observations versions are done assuming a spherical ionosphere at the same were carried out during daytime hours. We extracted the dTEC altitude. The resulting vertical TEC at the position of CS 001 as and dFR measurements for all of them (see Figs.8 and9). A a function of time is shown in Fig. 10. The error bars reflect basic expectation of ionospheric models is the presence of an the spread of the measurements using all different station com- increasing north–south TEC gradient; in all observations, the binations. In the same plot, we show the interpolated vertical dTEC values show its presence (red lines are stations in the TEC values from three different TEC maps created using the North, blue lines are stations in the South, all referenced to sta- Global Navigation Satellite System (GNSS) and provided by the tion CS 002 in the superterp). The wave-like behaviour of the International GNSS service (IGS). In particular, CODE, UPC, ionospheric systematic effects are clear, although during some and combined final products have been used (Schaer 1999; Orús time intervals, waves appear more structured and on larger scales et al. 2005; Hernandez-Pajares et al. 2009). The B field param- than at other times (as seen with different techniques with MWA; eters and satellite-based TEC values were determined using the Loi et al. 2015a,b). RMextract package3. The measured absolute TEC values are Ionospheric conditions are driven by a number of factors within 10% and following the trend of the GNSS based products (e.g. season, solar activity, and latitude). The dominant factor from IGS. The time resolution is 10 s, two orders of magnitude is the day–night cycle. During the night, the ionospheric TEC better than that of the IGS models which is 2 hr for codg and is reduced; this has an impact on the magnitude of the second- igsg and 15 min for uqsg. The main uncertainty in the LOFAR order term of Eq. (2), which is expected to be smaller. However, measurement comes from the value of dB , which can be very single-station observations taken under an ionospheric scintil- small. A small unmodelled perturbation of||dB could artificially lation monitoring project demonstrate that scintillation is often enhance the amplitude of the waves as observed|| in Fig. 10. Here much stronger at night, particularly prior to midnight. We report we merely illustrate the main concept. A further discussion of a large fraction of data loss due to intense scintillation events systematic uncertainties of this method will be the subject of a during night-time observations. During these events we were subsequent publication (Mevius et al. in prep.). not able to disentangle the various phase effects, and amplitude solutions show clear signs of decorrelation. Along a seven-night campaign that we carried out in February and March 2015, 6. Conclusions around 30% of our observations had to be discarded for this reason. Conversely, in 14 days of daytime observations taken The ionosphere is the main limiting factor of the quality of low- in 2017 (7 of which are presented in this paper), only a small frequency radio-interferometric observations. The time/space percentage of our data were affected by strong scintillations. variable refractive index of the ionospheric plasma generates Since the observations were taken far apart in time, it is difficult highly direction-dependent dispersive delays that affect phases to derive strong conclusions. A downside of daytime observa- recorded by the interferometer. At ultra-low frequencies, differ- tions is the (unavoidable) presence of the Sun, combined with ential Faraday rotation and higher-order terms (in frequency) the relatively poor side-lobe suppression of a phased array like also become prominent. The most important results of this paper LOFAR compared to dish-based radio interferometers. However, are as follows. the low-frequency radio spectrum of the (quiet) Sun is strongly – We show that LOFAR station-based gain phase can be 3 inverted, with S ν ν , and as a consequence, at 50 MHz, the decomposed into a small number of systematic effects: clock Sun flux density is∝ expected to be a few thousand janskies, which delays, ionospheric effects of first, second (Faraday rotation), is comparable to the flux density of some other sources present and third order. The third-order effect is only important for observations below 40 MHz. at night. Moreover, solar emission is extended on scales of sev- ∼ eral arc-minutes; therefore, it is resolved out on moderately long – We show that the ionospheric parameters we derived with baselines. our decomposition are consistent with expectation (e.g. they are time and spatially coherent) and with independent mea- 5.3. Absolute TEC and satellite comparison surements from satellites. This procedure also demonstrates that LOFAR can be used to obtain independent measure- An interesting application is the possibility to estimate the abso- ments of the absolute TEC. lute TEC from the differential TEC and differential Faraday – We show that visibility amplitudes are affected by scintilla- rotation. We make the following approximation: tions and that at ultra-low frequencies (<100 MHz) they are dRM12 c B 1 TEC1 c B 2 TEC2, (7) always present. We show that amplitude scintillations also ≈ · || · − · || · follow patterns both in time and space and in certain periods with dRM12 differential Faraday rotation between stations 1 behave like travelling waves across the array. and 2, B 1,2, the parallel magnetic field, and TEC1,2, the integrated electron|| content along the LoS for stations 1 and 2, 3 https://github.com/lofar-astron/RMextract

A179, page 9 of 12 F. de Gasperin et al.: The ionosphere at low-frequencies

A&A 615, A179 (2018) erential Faraday rotation between the LOFAR core and all remote stations. ff erential TEC and di ff ects quantified by variation of di ff

Fig. 8. First- and second-order ionospheric effects quantiﬁed by variation of differential TEC and differential Faraday rotation between the LOFAR core and all remote stations. Each panel is a separate observation towards 3C380. The gaps between observations are: 21, 21, 21, 21, 72, 21, 21, and Each panel is a separateThe observation similarity towards between 3C380. the The top gaps between and observations bottom are: panels 21, is 21, due 21, to 21, the 72, TEC 21, dependency 21, of and Faraday 44 rotation. hours. Stations are colour-coded in alphabetical order. 44 hr. Stations are colour-coded in alphabetical order. The similarity between the top and bottom panels is due to the TEC dependency of FaradayFigure 9: First- and second-order ionospheric e rotation. 11

A179, page 10 of 12 F. de Gasperin et al.: The ionosphere at low-frequencies

F. de Gasperin et al.: The ionosphere at low-frequencies Figure 10: As in Fig. 9 but for 3C295. Gaps between observations are: 19, 19, 19, 19, 91, 19, and 42 hours.

Fig. 9. As in Fig.8 but for 3C295. Gaps between observations are: 19, 19, 19, 19, 91, 19, and 42 hr.

A179, page 11 of 12 F. de Gasperin et al.: The ionosphere at low-frequencies A&A 615, A179 (2018)

11 – In sight of the large data volume produced by SKA, an auto- matic pipeline to reduce calibrator data could assess the 10 quality of the observation in a short time period and provide 9 a quantitative ﬁgure of merit to decide whether to archive the data or to re-schedule the observation (e.g. through plots 8 similar to Fig.3).

7 Acknowledgements. The authors want to thank Claudio Cesaroni for the many discussions and suggestions. FdG is supported by the VENI research programme 6 with project number 639.041.542, which is financed by the Netherlands Organi- vTEC (TECU) sation for Scientific Research (NWO). M.M. acknowledges support from the ERC 5 (grant 339743, LOFARCORE). This paper is based on data obtained with the International LOFAR Telescope (ILT) under project code LC9_016. LOFAR is 4 codg the Low Frequency Array designed and constructed by ASTRON. It has observ- uqrg ing, data processing, and data storage facilities in several countries, that are 3 igsg owned by various parties (each with their own funding sources), and that are LOFAR LBA collectively operated by the ILT foundation under a joint scientific policy. The 2 ILT resources have benefitted from the following recent major funding sources: 0 1 2 3 4 5 CNRS-INSU, Observatoire de Paris and Université d’Orléans, France; BMBF, Time (since start of observation, hr) MIWF-NRW, MPG, Germany; Science Foundation Ireland (SFI), Department of Business, Enterprise and Innovation (DBEI), Ireland; NWO, The Netherlands; Figure 7: Phase structure function divided into five time chunks Fig. 10. The Science and Technology Facilities Council, UK; Ministry of Science and Figure 8:Absolute Absolute TEC TEC derived derived from from World World Magnetic Magnetic Model, Model, dTEC for the observation of Fig. 3. The initial part of the observa- and dRM of the first observation in Fig.9 compared to three different Higher Education, Poland. This work had made use of the Lofar Solution Tool tions is visibly more affected by ionospheric disturbances also in interpolateddTEC anddRM IGS model of the datasets. first observation in Fig. 10 compared to (LoSoTo), developed by F. de Gasperin. Fig. 3. The phase variance is converted to the expected value at three different interpolated IGS model datasets. 150 MHz to compare it with other experiments such as LOFAR References HBA and MWA. – We showed that scintillations at night can result in a data 5.3. Absolute TEC and satellite comparison loss of 30% and that this phenomenon is reduced dur- Cesaroni, C., Alfonsi, L., Pezzopane, M., et al. 2017, J. Geophys. Res. Sp. Phys., ∼ 122, 794 An interestinging the day. application Based on is these the possibilityresults weto would estimate recommend the ab- Chulliat, A., Macmillan, S., Alken, P., et al. 2014, The US/UK World Magnetic soluteobservation TEC from during the di daytimefferential hours. TEC However, and differential the origin Faraday of the Model for 2015 (Boulder, CO: NOAA National Geophysical Data Center) rotation.scintillations We make (interplanetary the following or approximation: ionospheric) needs to be clar- Cohen, A. S., Lane, W. M., Cotton, W. D., et al. 2007, Astron. J., 134, 1245 ified and more statistics need to be gathered for a definitive Datta-Barua, S., Walter, T., Blanch, J., & Enge, P. 2008, Radio Sci., 43, RS5010 Davies, K. 1990, Ionospheric Radio, IEEE edn., (London, UK: Peter Pergrinus answer.dRM12 c B 1 TEC1 c B 2 TEC2, (7) the superterp). The wave-like behaviour of the ionospheric sys- ≈ · || · − · || · Ltd.), 36 We also gather here some considerations for future low- tematic effects are clear, although during some time intervals, with dRM differential Faraday rotation between stations 1 and Fallows, R. A., Bisi, M. M., Forte, B., et al. 2016, Astrophys. J., 828, L7 frequency12 experiments: waves appear more structured and on larger scales than at other 2, B , the parallel magnetic field, and TEC , the integrated Hernandez-Pajares, M., Juan, J. M., Sanz, J., et al. 2009, J. Geod., 83, 263 – Low-frequency1,2 telescopes operate in a regime1,2 of low S/N Hocke, K., & Schlegel, K. 1996, Ann. Geophys., 14, 917 times (as seen with different techniques with MWA Loi et al. electron|| content along the LoS for stations 1 and 2, respectively. due to the high sky temperature. The ionosphere itself con- Hoque, M. M., & Jakowski, N. 2008, Radio Sci., 43 2015b,a). We approximate the integral in Eq. 1 with the thin-layer ap- Hunsucker, R. D. 1982, Atmospheric Gravity Waves Generated in the High tributes with one or more parameters to be estimated every proach. This can be rewritten in terms of absolute TEC at station Latitude Ionosphere: a Review (Fairbanks, AL: Alaska University) Ionospheric conditions are driven by a number of factors second. It is important that no further degrees of freedom are 1: Hurley-Walker, N., Callingham, J. R., Hancock, P. J., et al. 2017, MNRAS, 464, (e.g. season, solar activity, and latitude). The dominant factor added to the solving process (e.g. by using different clocks 1146 TEC dB = C dRM B dTEC , (8) is the day-night cycle. During the night, the ionospheric TEC in different1 stations).· ||12 · 12 − ||2 · 12 Intema, H. T., van der Tol, S., Cotton, W. D., et al. 2009, A&A, 501, 1185 is reduced; this has an impact on the magnitude of the second- Kaplan, D. L., Tingay, S. J., Manoharan, P. K., et al. 2015, Astrophys. J. Lett., with– Again, dB 12 tobeing maximise the diff theerential S/N,parallel modernmagnetic solvers need field to and be order term of Eq. 2, which is expected to be smaller. However, || 809 dTECconceived12 the diff inerential order to integrated exploit all electron known content coherent between structures sta- Kintner, P. M., Ledvina, B. M., & De Paula, E. R. 2007, Sp. Weather, 5, S09003 single-station observations taken under an ionospheric scintil- tionsof 1 the and ionosphere, 2. We used including the World spatial, Magnetic time, Model and frequency (Chulliat Lane, W. M., Cotton, W. D., van Velzen, S., et al. 2014, MNRAS, 440, 327 lation monitoring project demonstrate that scintillation is of- et al.coherency. 2014) and In the this measurements paper, time-coherency of dRM and has dTEC never to been esti- Loi, S. T., Murphy, T., Cairns, I. H., et al. 2015a, Geophys. Res. Lett., 42, 3707 ten much stronger at night, particularly prior to midnight. We mateimposed, the absolute although vertical this TEC has already for the been first consideredobservation in in some Fig. Loi, S. T., Trott, C. M., Murphy, T., et al. 2015b, Radio Sci., 50, 574 Mangum, J. G., & Wallace, P. 2015, Publ. Astron. Soc. Pacific, 127, 74 report a large fraction of data loss due to intense scintillation 10 inmodern this way. algorithms The thin (e.g. layer Tasse model 2014 places). a single ionospheric events during night-time observations. During these events we McKay-Bukowski, D., Vierinen, J., Virtanen, I. I., et al. 2015, KAIRA: The layer– Several at an altitude regimes of are 450 identifiable km. Slant based TEC on to vertical the observing TEC con- fre- Kilpisjärvi Atmospheric Imaging Receiver Array – System Overview and were not able to disentangle the various phase effects, and ampli- versionsquency are and done the assuming maximum a baseline spherical length ionosphere (see Table at the1). same The First Results, 53, 1440 tude solutions show clear signs of decorrelation. Along a seven- altitude.adopted The calibration resulting verticalstrategy TEC must atvary the accordingly, position of by CS iden- 001 Mevius, M., van der Tol, S., Pandey, V. N., et al. 2016, Radio Sci., 51, 927 night campaign that we carried out in February and March 2015, as atifying, function given of time the desired is shown dynamic in Fig. range, 8. The which error of bars the effects reflect Narayan, R. 1992, Phil. Trans. R. Soc. A Math. Phys. Eng. Sci., 341, 151 around 30% of our observations had to be discarded for this Noordam, J. E. 2004, Proc. SPIE, 5489, 817 the spreadare relevant of the and measurements which have direction-dependent using all different station properties. com- Orús, R., Hernández-Pajares, M., Juan, J. M., & Sanz, J. 2005, J. Atmos. Sol. reason. Conversely, in 14 days of daytime observations taken binations.– The multi-beam In the same capability plot, we of show modern the phased-array interpolated interfer- vertical Terr. Phys., 67, 1598 in 2017 (7 of which are presented in this paper), only a small TECometers values needsfrom three to be di testedfferent extensively TEC maps to created see how using large the a Petit, G., & Luzum, B. 2010, IERS Conventions (2010), ed. Frankfurt am Main: percentage of our data were affected by strong scintillations. Globalreliable Navigation TEC screen Satellite can System be. Furthermore, (GNSS) and this provided capability by can the Verlag des Bundesamts für Kartographie und Geodäsie, IERS Technical Note 36 Since the observations were taken far apart in time, it is difficult Internationalbe used to GNSS develop service novel techniques (IGS). In particular, to transfer time-variableCODE, UPC to derive strong conclusions. A downside of daytime observa- Rees, N. 1990, MNRAS, 244, 233 andinstrumental combined final errors products fromhave the calibrator been used to (Schaer the target 1999; fields. Orus´ Schaer, S. 1999, Mapping and Predicting the Earth’s Ionosphere Using the tions is the (unavoidable) presence of the Sun, combined with et–al. So 2005; far, GNSS Hernandez-Pajares data have been et al. marginally 2009). The usedB field to calibrate param- Global Positioning System, 59 the relatively poor side-lobe suppression of a phased array like etersradio and satellite-based interferometric TEC observations. values were However, determined it would using the be Tasse, C. 2014, A&A, 566, A127 LOFAR compared to dish-based radio interferometers. However, RMextractimportant to check3 those data in real time to assess the Tasse, C., Hugo, B., Mirmont, M., et al. 2018, A&A, 611, A87 package . The measured absolute TEC values are Tingay, S. J., Goeke, R., Bowman, J. D., et al. 2013, Publ. Astron. Soc. Aust., 30 the low-frequency radio spectrum of the (quiet) Sun is strongly withinionospheric 10% andfollowing state and thereforethe trend of decide the GNSS whether based to scheduleproducts inverted, with S ν3, and as a consequence, at 50 MHz, the van Haarlem, M. P., Wise, M. W., Gunst, A. W., et al. 2013, A&A, 556, A2 ν ∝ fromultra-low-frequency IGS. The time resolution observations is 10 s, two(or orders any interferometric of magnitude van Weeren, R. J., Williams, W. L., Hardcastle, M. J., et al. 2016, ApJs, Sun flux density is expected to be a few thousand janskies, which betterobservation than that at of all). the IGS models which is 2 hours for codg 223, 2 is comparable to the flux density of some other sources present and igsg and 15 minutes for uqsg. The main uncertainty in the at night. Moreover, solar emission is extended on scales of sev- LOFAR measurement comes from the value of dB , which can eral arc-minutes; therefore, it is resolved out on moderately long || baselines. 3 https://github.com/lofar-astron/RMextract.

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