THE FIRST VERY LONG BASELINE INTERFEROMETRIC SETI EXPERIMENT

VLBI allows, by the combination (via a correlator) of signals from multiple radio telescopes, the emulation of a telescope of the size of the maximum telescope separation, which is generally hundreds to thousands of kilometers. The outputs of the correlator are four-dimensional (baseline, time, frequency, polarization) data sets consisting of multiple spectral channels and time averages over ∼1 s. The primary characteristic of VLBI is its very high angular resolution, which falls in the milliarcsecond regime, the highest resolution in astronomy. This high resolution makes VLBI ideally suited for high-precision astrometry (see Thompson et al. 2001, chap. 12), and observation of high energetic compact objects.

Existing VLBI instruments are able to monitor a wide range of frequencies, from 10 MHz (the Low Frequency Array, LOFAR; Stappers et al. 2011) to 230 GHz (The Event Horizon Telescope; Broderick et al. 2011). In addition, current VLBI systems such as the LBA and the European VLBI network (EVN) include some of the most sensitive radio telescopes in the world.

To date there has been little or no use of VLBI in SETI investigations. The SETI project SETI-Italia (Montebugnoli et al. 2001) uses data commensally from the 32 m VLBI Medicina telescope. SETI-Korea (Rhee et al. 2010) has proposed the use of existing and new telescopes from the Korean VLBI Network (KVN) for SETI. In addition, Slysh (1991) proposed to use VLBI or space-VLBI satellites to measure the angular size of suspected SETI radio sources. Pseudo-interferometric observations were conducted by the SETI Institute, using both the Arecibo Telescope and the Lovell Telescope, Jodrell Bank Observatory between 1200 and 1750 MHz (Backus & The Project Phoenix Team 2002). The survey searched for signals from nearby stars with appropriate frequency drift and offset caused by the rotation of the Earth.

Radio frequency interference (RFI) is human-made, unwanted radio emission within the telescope's field of view. Potential sources include mobile phones, radars, television signals, FM-radio, satellites, etc. Separating RFI from a real SETI signal is one of the most challenging problems faced by SETI projects. Thousands of hours of computing time are spent identifying and removing RFI from the data sets, before one can search for SETI signals. Since its inception, the SETI@home project has detected over 4.2 billion potential signals. While essentially all these potential signals are RFI, it is possible that therein lies a true extra-terrestrial signal (Korpela et al. 2010). VLBI offers several ways of discriminating RFI signals from SETI signals not applicable to single dish or even short baseline radio interferometers.

First, VLBI uses N telescopes separated by hundreds to thousands of kilometers giving N(N − 1)/2 baselines, once the data from independent pairs of telescopes are correlated together. This aspect of VLBI is important, as RFI that is not present at both telescopes involved in a baseline does not correlate. An astronomical or SETI compact radio source within the interferometer field of view will be detected on all baselines. This is also true for RFI if it is detectable by both telescopes in a baseline. However, even correlated RFI can be easily identified with VLBI, as it produces distinct phase variations in both frequency and time in the correlated output as discussed below.

The correlated signals from an interferometer are complex quantities (known as visibilities), with amplitude and phase as the fundamental observables. The amplitudes are proportional to the correlated power of the source, while the phase, ϕ, represents the residual time delay that results from the wave front of the radio emission arriving at one antenna before the other. At the center of the field of view (also known as the phase center), the delay (and hence the phase) is set to zero, via application of an a priori time delay, τ, at the correlator. This time delay accounts for many different effects, but primarily simple geometry. The phase ϕ of a radio point-source offset from the phase center can then be related to its position relative to the phase center and is given by Equation (1) from Morgan et al. (2011),

$$\begin{equation} \phi = \frac{2\pi \nu }{c}(lu + mv), \end{equation} \tag{ 1 }$$

where ν is the observing frequency, l and m are the coordinates of the source in the plane of the sky, relative to the phase center, and u and v are coordinates that describe the instantaneous geometry of the projected baseline, with respect to the phase center. The reader is referred to Thompson et al. (2001) and Taylor et al. (1999) for details. For a finite observational bandwidth, and for the duration of the observation, the radio source in Equation (1) will display a phase change with frequency and time given by,

$$\begin{equation} \frac{d\phi }{d\nu } = \frac{2\pi }{c}(lu + mv), \end{equation} \tag{ 2 }$$

$$\begin{equation} \frac{d\phi }{dt}= \frac{2\pi \nu }{c}\left(l\frac{du}{dt} + m\frac{dv}{dt}\right). \end{equation} \tag{ 3 }$$

By measuring the phase change with time and frequency for a given source, its location with respect to the phase center can be determined using the above equations. Additionally, if the source's position is known, maximum values for both dϕ/dν and dϕ/dt can be determined, using maximum values of u or v and du/dt or dv/dt.

3.3.1. Determining the Phase Variations with Fourier Transforms

An estimate of dϕ/dt or dϕ/dν for a radio source can be determined by the discrete Fourier transform (DFT) of the complex visibilities. For narrowband (persistent or intermittent in time) and broadband signals, DFTs can be applied to the complex visibilities as a function of time to determine dϕ/dt and frequency to determine dϕ/dν, respectively.

This method is illustrated in Figure 1. The upper panel shows the phase of a narrowband test signal as a function of time, with a sample time of 5 minutes per point over a 40 minute observation. The lower panel displays the corresponding discrete power spectrum obtained by applying DFTs to the complex visibilities.

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A signal with little or no phase change in time or frequency (implying a source close to the phase center) will appear in bin zero. However, a signal with high phase change with time (as the test signal in Figure 1) is indicative of a source far from the phase center, probably RFI, and will appear in a different bin. The height of the DFT amplitude of bin zero compared with the others gives an indication of the signal to noise of any signal which comes from the phase center.

There are, however, ambiguities in signals with dϕ/dt greater than the Nyquist frequency. The component of the test signal located in the −3 bin can be generalized as dϕ/dt = −135 ± 180N° per data point, where N is a wide range of positive and negative integers. The dϕ/dt of the Nyquist bin due to ambiguities is ±180° per data point.³

Gl581 was observed on 2007 June 19, for 8 hr in the 20 cm wavelength band by three stations of the Long Baseline Array (LBA): Mopra (Mp), Parkes (Pa), and the Australia Telescope Compact Array (At) in phased array mode. The observation was conducted in three frequency pairs of 64 MHz bandwidth centered on: 1262,1312; 1362,1412; 1462,1512 MHz, in dual-polarization mode. The uv coverage is shown in Figure 2. This configuration gives a maximum resolution of 127 mas. The observations of Gl581 were phase referenced to the ICRF2 source 1510−089 (J1512−0905, R.A. = $15^{{\rm h}}12^{{\rm m}}50\mbox{$.\!\!^{\mathrm s}$}532925$; decl. = −09°05'5982961, J2000), a calibrator located 214 from Gl581 (Fey et al. 2004). 1510−089 shows an unresolved core with extended structure to the northeast of the core at 2.3 GHz (Fey & Charlot 1997) and 327 MHz (Rampadarath et al. 2009) on the longest baselines of the Very Long Baseline Array (VLBA). The longest baseline of our observation (At–Pa) is a factor of 9 less than the longest VLBA baseline, hence, 1510−089 is expected to be unresolved in our observations.

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A phase-referencing cycle of 5 minutes (2 minutes on calibrator, 3 minutes on Gl581) was employed. A single observation block consisted of 8 × 5 minute phase-referencing cycles. The entire observation comprised 12 × 40 minute observational blocks switching between the three frequency pairs (Table 1).

The data were correlated using the DiFX software correlator (Deller et al. 2007, 2011), with a frequency resolution of 1.95 kHz per spectral channel, and converted to the standard FITS-IDI format. The lowest and highest 5 MHz (2500 channels) were discarded from each band due to band edge drop-off in sensitivity. The data files were then sub-divided into five data sets of 4000 channels each and one data set of 1268 channels at each center frequency.

Due to its proximity to Earth, the exact coordinates of Gl581 at the time of observation must be calculated taking into account parallax and proper motion. An accurate position was computed via a python script (J. Miller-Jones (ICRAR) 2011, private communication), using a reference position of Gl581 (R.A. and decl.) and the barycentric coordinates of the Earth (in AU) at the time of the observation (obtained from NASA's Jet Propulsion Laboratory HORIZONS online solar system data and ephemeris computation service⁴).

The reference position for Gl581 was taken from the Hipparcos catalog (Perryman et al. 1997). Gl581 was observed on 1991 March 1, by the Hipparcos satellite, and a position of R.A.(J2000) = $15^{{\rm h}}19^{{\rm m}}26\mbox{$.\!\!^{\mathrm s}$}825$; decl.(J2000) = −07°43'20210 was recorded with positional errors: e_R.A. = 1.99 mas and e_decl. = 1.34 mas. Additionally, a parallax of 159.52 ± 2.27 mas was measured by Hipparcos. A proper motion of R.A. = −1227.67 ± 3.54 mas yr⁻¹; decl. = −97.78 ± 2.43 mas yr⁻¹ was also taken from the Hipparcos catalog. The position calculated for Gl581 at the VLBI observation date is R.A.(J2000) = $15^{{\rm h}}19^{{\rm m}}26\mbox{$.\!\!^{\mathrm s}$}206$; decl.(J2000) = −07°43'17555. This calculation has a positional uncertainty of 53 mas, largely due to the cumulative effect of the uncertainty in the proper motion measured by the Hipparcos 1991 observation.

The data reduction and calibration was performed using the National Radio Astronomical Observatory (NRAO) software package AIPS.⁵ Prior to calibration and data analysis, the phase center of the calibrator was shifted, via the AIPS task UVFIX, to match the calculated positional difference. Flagging and phase-only calibration (fringe-fitting and self-calibration) were carried out on the phase center shifted calibrator. The phase solutions were transferred and applied to the Gl581 data sets. After calibration, further analysis was carried out using the ParselTongue scripting language (Kettenis et al. 2006) and the numerical python package, numpy.⁶ The flagging, phase calibrations, and transfer of solutions were implemented separately for the frequency pairs listed in Table 1.

The uncertainty in the position of Gl581 (53 mas) and the semi-major axes of the planets (Gl581d = 40 mas and Gl581g = 23 mas) produces a quadratic error of 66 mas and 57 mas on the positions of Gl581d and Gl581g, respectively. The positional uncertainty places upper limits on the dϕ/dν and dϕ/dt expected for a SETI signal from Gl581. From Equations (2) and (3) the upper limits are (dϕ/dν)_max = (1.2 × 10⁻¹⁰)° per spectral channel⁷ and (dϕ/dt)_max = (2 × 10⁻⁴)° per second (or (6 × 10⁻²)° per data point, after averaging each scan).

4.5.1. Search for Candidate SETI Signals

4.5.2. Broadband Signals

4.5.3. Narrowband Signals

4.5.4. Frequency Distribution of the Candidate Signals

Figure 3 shows the frequency distribution of the SETI candidate signals (1525–1534 MHz), with the 200 narrowband (gray) and the 22 broadband (black) candidate signals. Australian Space to Earth geostationary satellites, Optus' Mobilesat and the INMARSAT⁸ based systems, marketed in Australia by Telstra are known to operate at frequencies in the range 1525–1559 MHz (Symons 1998). The close match between the transmission frequencies of the satellites and our candidate signals suggests that many or all of our detected signals may be RFI coming from these satellites.

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4.5.5. Phase Variation of Broadband Candidate SETI Signals

Recall from Section 3.3, dϕ/dν is dependant on the location of the signal with respect to the phase center. To obtain dϕ/dν for the 22 broadband SETI candidates, DFTs were applied to the complex visibilities as a function of frequency, as described in Section 3.3.1. The maximum expected dϕ/dν for a radio signal from the planets is (1.2 × 10⁻¹⁰)° per spectral channel (Section 4.4). This phase variation is effectively zero at the level of frequency sampling in the observations.

Figure 4 shows the dϕ/dν for the 22 broadband SETI candidates. The horizontal dashed lines indicate the dϕ/dν range expected for a radio signal from the Gl581 system. Any signal with a dϕ/dν range that crosses the horizontal dashed lines on all three baselines is considered as possibly originating from the Gl581 system and merits further investigation. None of the 22 broadband signals has satisfied this criteria and are thus rejected as originating from the Gl581 planets.

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A large percentage of the signals are clustered around dϕ/dν = 45° per spectral channel on the shortest baseline (At–Mp) in Figure 4. Using Equation (2), and assuming a north–south baseline of projected length, v = 0.5 Mλ (see Figure 2), this phase variation implies a minimum distance of ∼10° from the phase center (cf. declination of Gl581 ≃ −7°, geostationary satellite declination ≃+5°). This effect is less clear on the longer baselines since the rapidly rotating phase of the complex visibilities along both the frequency and time axes leads to averaging losses (smearing).

4.5.6. Phase Variation of Narrowband Candidate SETI Signals

4.5.7. Hypothesis Testing and Monte Carlo Simulations

For Gaussian-distributed noise in the complex visibilities, the amplitudes of the DFT bins are Rician-distributed. The two hypotheses are as follows. (1) The alternative hypothesis, $\mathcal {H}_{1}$: signal-present—a source located at the phase center has most of the power concentrated in bin zero, yielding a Rice distribution of amplitudes with parameters (amplitude and variance) determined by the data S/N and noise level. (2) The null hypothesis, $\mathcal {H}_{0}$: signal-absent—a source located away from the phase center, yielding power in a bin other than bin zero, with the same Rician parameters. The ratio of the likelihoods for bin zero to the next highest bin is the test statistic.

The test statistic is compared to a threshold to determine our level of confidence that the signal is real. To determine the threshold, we simulate 10⁶ signal-present and 10⁶ signal-absent sources, with the non-phase center signals distributed randomly in the field, and for S/Ns that reflect our data set. In addition, given that we expect the primary signals in the data to be RFI, rather than true signals, we also simulate zero-mean Gaussian noise with random RFI spikes located at a single time point in the visibilities. Figure 5 plots the log-scale distribution of the test statistics for both the signal-present (upper plot) and the signal-absent case (lower plot). The thresholds were chosen so as to minimize the chance of false positives, i.e., Type I error (Kay 1998, chap. 3). From Figure 5 the thresholds range from the maximum log of the test statistic for the signal-absent case (=2) to the minimum log of the test statistic for the signal-present case (=35).

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The method was then applied to the 200 narrowband signals, where the overall test statistic, T(x), was taken as the product of the test statistics of the individual baselines. Ten narrowband signals were found to have ln [T(x)] > 2 of which only two are beyond ln [T(x)] = 35 (Table 2). The data are expected to be consistent with no signal present at the phase center (i.e., consistent with the null hypothesis). The significance level of rejecting the null hypothesis (the p-value) for the 200 signals was found by integrating the probability distribution of the signal-absent test statistic, obtained from the simulations. A small p-value (p ⩽ 0.01) corresponds to a signal that may not be consistent with the null hypothesis and warrants further investigation. Figure 6 shows the p-values of the 200 signals. Most of the 200 signals were found to have a p-value greater than 0.01, with ten signals having a p-value of <0.01.

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Table 2. The Ten Signals with ln [T(x)] > 2

Frequency	UT	ln [T(x)]	Baseline Specific log of the Test Statistic
(MHz)			At–Mp	At–Pa	Pa–Mp
1531.69080115	13:10:00–13:50:00	2.39	1.92	−0.30	0.77
1533.6297203	09:10:00–09:50:00	3.11	6.12	−1.36	−1.65
1533.80206867	13:10:00–13:50:00	3.50	2.19	0.66	0.66
1527.85017443	09:10:00–09:50:00	4.21	4.89	1.40	−2.07
1527.50351919	11:10:00–11:50:00	6.51	16.91	−4.95	−5.45
1527.56227431	11:10:00–11:50:00	7.25	11.04	−0.27	−3.52
1525.18856723	09:10:00–09:50:00	14.84	30.53	−15.32	−0.37
1527.50156068	09:10:00–09:50:00	26.19	17.86	2.87	5.47
1532.03158088	09:10:00-09:50:00	86.19	88.270	0.03	−2.10
1527.56423282	09:10:00–09:50:00	242.77	1782.83	−1305.76	−234.30

Notes. Column 1: the center frequency; Column 2: the observed (UT) time period; Column 3: the sum of the log of the test statistics of the individual baselines, which is taken as the final test statistic; Columns 4–6: the log of the test statistics of the individual baselines.

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Eight signals lie between both distributions (2 < ln [T(x)] < 35). These signals are strictly inconsistent with both hypotheses and reflect the limitations of our simple analysis, namely, the simulation of data with either pure signals at the phase center or a single RFI peak in the visibility, and the need for the overall test statistic to have a value in excess of the threshold rather than those for the individual baselines.

Table 2 lists ln [T(x)] along with the test statistic for the individual baselines for all 10 events with ln [T(x)] > 2. For all but one of the 10 events, ln [T(x)] < 2 if the shortest baseline is excluded. For all 10 events the test statistic is far greater for the shorter baseline than for the other baselines. This is not consistent with a source at the phase center. It is, however, consistent with RFI distant from the phase center. We can therefore easily exclude these signals as being from the GL581 system.

Since this was a proof-of-concept observation, two differences between this experiment and a typical VLBI observation should be noted. First, the baseline lengths in this experiment were short by VLBI standards. Baselines one or even two orders of magnitude longer would significantly reduce the amount of correlated RFI. Second, most VLBI observations are carried out using more than three telescopes. Increasing the number of baselines to four or more constrains both the phase and amplitude closure relations,¹⁰ drastically increasing the quality of calibration. This would also provide the opportunity for image plane searching. However, it would likely be computationally expensive as a technique for searching over very wide frequency ranges. Relaxing the single baseline five times median limit could enhance the sensitivity beyond that of the weakest baseline.

We should also note that the width of the DFT bin is not a fundamental limit on the determination of the phase variation. A least-squares fit would allow the delay and delay rate to be determined more accurately. Essentially, the error on these parameters is limited by the signal to noise. Certainly, the LBA has been used for astrometry at the submilliarcsecond level (Deller et al. 2009b, 2009a). Observations of spacecraft have proven VLBI astrometry techniques for very weak narrowband sources (Avruch et al. 2006) and suggest that VLBI might even allow the detection of the orbital motion of SETI signals.

While the techniques discussed in this paper are ideal for targeted SETI, we also note the possibility of carrying out SETI commensally with normal VLBI operations. SETI target stars (Turnbull & Tarter 2003) would be expected to be present in the field of view of the antennas for VLBI observations reasonably regularly. Using the techniques discussed in Deller et al. (2011) and Morgan et al. (2011) it would be possible to produce visibility data sets for any target star in the primary beam. Additionally, direct analysis of the voltages (the baseband data) although computationally expensive could also be implemented at the correlator in an efficient manner to search for signals from extra-terrestrial intelligence. A possible model for this is the VFASTR transient search currently running at the VLBA operations center (Wayth et al. 2011; Thompson et al. 2011).

A sensitive and advanced radio telescope, the SKA is currently being planned for the coming decades.¹¹

At 1400 MHz, the long baselines of the SKA will provide an astrometric precision of ∼10 μas (Fomalont & Reid 2004). In addition, the SKA is expected to achieve sub-μJy sensitivities (Carilli & Rawlings 2004). At ∼20 ly the SKA would probe an isotropic luminosity of a few $\mathrm{k}\mathrm{W}\mathrm{\mathrm{Hz}}^{\mathrm{-1}}$, far below the power output of radars and telecommunication satellites (Tarter 2004). The fields of view will be ∼1 deg² at the maximum baselines and ∼30 deg² for the shorter baselines (Carilli & Rawlings 2004). These capabilities will make the SKA the fastest, most sensitive, and widest field of view survey instrument in astronomy. However, for the SKA to be used for SETI, suitable targets are required. Such targets are currently being provided by the Kepler mission (Borucki et al. 2011; Batalha et al. 2012).