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Annual modulation in IDV of quasar 0917+624 due to Interstellar Scintillation

The quasar 0917+624 has been one of the best studied intraday variable (IDV) radio sources. However, debate continues as to whether the underlying cause is intrinsic or extrinsic. Much previous work has assumed the IDV to be intrinsic and which implies an extraordinarily compact source for the radio emission; in contrast, an extrinsic variation due to interstellar scintillation (ISS) implies a relatively larger source diameter, though at the smaller end of the range expected for relativistic jet models. Kraus et al. (1999) reported a marked slowing of the IDV at 6cm wavelength in September 1998, and suggested a change in the source was responsible. However, here we show that the slowing is consistent with the annual modulation in scintillation time-scale expected for ISS, under the assumption that the scattering medium moves with the local standard of rest (LSR). The ISS time scale is governed by the ISS spatial scale divided by the Earth's velocity relative to the scattering plasma. It happens that in the direction of 0917+624 the transverse velocity of the Earth with respect to the LSR varies widely with a deep minimum in the months of September to November. Hence the slowing of the IDV in September 1998 strongly suggests that ISS, rather than intrinsic variation of the source is the dominant cause of the IDV.


INTRODUCTION
Rapid (faster than a day) variations in the radio flux density of some extra-galactic sources have attracted considerable attention in the years since they were first reported by Heeschen et al. (1987). Via the classic light travel time argument for intrinsic variations, the short variability time scales have been used to infer an extremely small physical size of the radio emitting regions; the associated apparent brightness temperatures are very much higher than expected from relativistic jets from active galactic nuclei (AGNs) emitting Doppler-boosted radio beams (Qian et al., 1991). The canonical jet model successfully explains "superluminal" motion in VLBI observations, invoking Lorentz-factors (bulk jet speeds) in the range of 1-20. In order to also explain the high brightness temperatures infered from IDV one needs very small viewing angles and hence such jets can explain brightness temperatures of up to 10 16 K. An intrinsic view of the most extreme IDV at cm-wavelengths would imply imply brightness temperatures up to 10 21 K (e.g. Kedziora-Chudczer et al. 1997 andde Bruyn, 2000a). This stretches the jet model too far and in both cases the authors proposed ISS rather than intrinsic interpretations. Quirrenbach et al. (1992) presented the results of daily monitoring of a complete sample of flat spectrum sources at 6cm and 11cm. They found a low level of IDV in most of the sources observed, which also had compact VLBI structure. They concluded that this low level of variabilty seen in almost all such sources was ISS. However, in addition they argued that about 25% of flat spectrum sources also showed intrinsic variations that can reach amplitudes as high as 20%. 0917+624 was one of these strongly variable sources, for which intrinsic models have been invoked (Wagner & Witzel, 1995 and references therein).
On the other hand, Rickett et al. (1995) [R95] demonstrated that ISS could successfully account for the IDV in 0917+624 with a source brightness of about 6×10 12 K, by assuming that the path length for the scattering medium was reduced to 200 pc, from the 930 pc predicted from the Taylor & Cordes (1993) model for the distribution of electrons in the Galaxy [TC93]. In R95 no consideration was given to the influence of the change in the Earth's velocity relative to the scattering medium. In this paper we reconsider the accumulated observations of the source at 6cm by the Bonn group and study how the time scale and modulation index (rms normalized by mean flux density) vary over the year and compare with predictions.
The 0917+624 observations of September 1998 showed a remarkably different character -with the flux varying slowly and nearly linearly over the course of the 5-day observing span. This was reported by Kraus et al. (1999) [K99], who suggested that there had been a pronounced change in the emitting properties of the source, which then had recovered by February 1999 to explain the return to its normal IDV behavior observed at that time. We conclude that this anomolous behavior supports the ISS interpretation since it is simply explained by the changing Earth velocity.

Observations and Data Analysis
We have collected together all of the observations of 0917+624 at 6cm since 1989 made at Effelsberg and at the VLA in flux density monitoring campaigns lasting more than 24 hours. We choose 6cm as the wavelength most commonly observed (since it has good signal-to-noise ratio).
We have used a structure function analysis on each time series to estimate the characteristic time scale and the rms amplitude, as used by R95. The sampling interval for the flux measurements was typically somewhat variable, so the structure function was binned into uniform intervals (δτ ) in time lag about equal to the average time between samples (typical values were 0.05 to 0.1 day). The maximum time lag computed is about half the duration of each data set. The structure function D(τ ) is first corrected for the noise level, which is estimated as D at the smallest time lag and subtracted from D(τ ) at each lag. A region in time lag is then identified where D(τ ) saturates. However, it should be noted that, since D is estimated from a finite sample of a stochastic variation, it will fluctuate about a saturation value rather than tending to an asymptote. The flux variance is estimated as half of the average of D over the saturation region; the time scale is estimated as the lag where D crosses half the saturation level. Table 1 shows the results for each observation with estimated rms errors, which are dominated by the estimation error from the modest number of independent samples in each series.
The procedure works well provided that the structure function does indeed start to saturate before the maximum lag, as is seen for nearly all of the obser-  (K99); so here we set a lower bound on the time scale and on the flux variance by treating D at the maximum lag as if it were saturated. We consider this data set as if it were a sample of a stochastic variation with a time scale longer than its duration and obtain a substantially longer time scale than from the rest of the observations.

Annual Modulation in ISS Parameters
The time scale for ISS is determined by the ratio of two quantities -the spatial scale of the scintillation pattern and the relative speed of the Earth through the pattern. The pattern scale depends on the lineof-sight distribution and the wavenumber spectrum of the scattering material and also on the angular structure of the compact component in the radio source. The ISS theory and model used by R95 assumed the source to be circularly symmetric and sufficiently extended to partially quench the scintillations, in which case the same theory can be applied for both weak and strong refractive scintillation; further it assumes the scattering plasma to be isotropic and to be in a thick layer with a Gaussian profile. The natural scale height to choose is that of the ionized disk component in the TC93 model, which gives a characteristic path length of 930 pc for the density variance at the latitude of 0917+624. However, as noted above a smaller path length (200 pc) was found necessary by R95 to fit the observations with a speed that was (arbitrarily) assumed to be 50 km/s. In this section we use the same R95 model for the spatial scale and calculate the Earth's transverse velocity explicitly versus day of year, under the assumption that the entire scattering medium moves with the LSR and then compare the observed and predicted time scales. This assumption is consistent with ISS observations of the pulsar B0809+74 by Rickett, Coles and Markkanen (2000), who concluded that the velocity of the scattering medium is within 10 km/s of the LSR. Figure 1 shows the Earth's velocity relative to the LSR projected perpendicular to the line of sight to 0917+624 versus day of year. The velocity due to the Earth's orbital motion around the Sun happens to nearly cancel the projected velocity of the Sun relative to the LSR near day number 285. Thus the predicted ISS speed shows a large annual modulation from a maximum of 40 km/s to a minimum of 4 km/s. In Figure 2a we overplot the observed and predicted time scales against the day of year, including as thin lines the bounds derived from predictions for a range of offsets in plasma velocity relative to the LSR covering ±5 km/s in the right ascension direction and ±5 km/s in the declination direction.
The striking feature of the predicted time scale is that it should remain fairly constant over much of the year and exhibit a substantial increase over days 250-330 (September-November). Even though there have been 13 independent observations of the 6cm IDV, it happens that only one of them lies in this period of predicted slow ISS. Thus the apparent constancy of IDV behavior is readily understood as is the one anomolous observation. Overall we find a general agreement between the observations and the predictions for the time scale.
Turning to the scintillation (or modulation) index, there is a question of what should be the normalizing flux, since the source may has some of its flux in components of too large a diameter to scintillate (> 1 mas). The VLBI maps of Standke et al. (1996) and new unpublished maps (Krichbaum, priv. comm.) show that the source exhibits a core jet structure composed out of a number of unresolved (< 1 mas) and partially resolved (> 1 mas) components. However, in considering any annual change in scintillation index this normalizing uncertainty is unimportant. What matters is whether there should be any annual change in the ISS variance. Since the ISS variance is given by the integral of the intensity power spectrum over two-dimensional wavenumber space (Little & Hewish, 1966), the result is independent of the orientation of the velocity vector, even if the wavenumber spectrum is non-circular due to any anisotropy in the irregularity spectrum and/or anisotropy in the source visibility function. Thus there should be no annual change in the scintillation index. Figure 2b shows this as the observed scintillation index versus day of year. The fact that the observations do not show an obvious annual variation is consistent with this model, and though there are some discrepant values they do not appear to be statistically significant.
It has been argued that the interstellar plasma irregularities are commonly anisotropic (e.g. Desai et al. 1994). The orientation of the velocity relative to the major axis of such anisotropy will vary during a year, as the direction of the Earth's motion changes. In such a case the spatial scale of the ISS pattern will show a variation over six months, which can combine with the changing Earth velocity to create a variety in the predicted annual time scale curves. If in addition the source structure is not circular its angular orientation would also affect the spatial scale and so will contribute to the annual modulation. (Dennett- de Bruyn, 2000a and2000b).

Discussion and Conclusions
It is clear from Figure 2 that ISS governs the time scale of the IDV, unless there was a transient slowing of intrinsic variability that coincidentally echoed the behaviour expected for ISS. Hence we conclude that the IDV of 0917+624 at 6cm is predominantly caused by scintillation in the interstellar medium. If simultaneous intrinsic variations faster than 6 hours are also present their rms amplitude must be less than 1% (obtained from the structure function analysis of the data from September 1998).
This confirms the work of R95 and also opens up the possibility of using these seasonal ISS effects to explore anisotropy in both the source and the scattering plasma. Our conclusion does not at all reduce the importance of intrinsic variations in explaining source variations on times of months to years, as particularly evident in VLBI maps and longer term flux changes. Indeed both phenomena are needed for a full understanding of AGN behaviour.
As discussed by R95 the time scale observations jointly constrain the scattering distance and source diameter in a fashion that depends on the distribution of the scattering plasma. The sense of this constraint is that a large distance implies a smaller source diameter and vice versa. In the R95 model the scattering distance was about 200 pc, in preference over the 930 pc expected under the TC93 model. The accompanying source diameter at 6cm was about 0.07 mas. Models with a larger scale height required a smaller source size and vice versa. R95 assumed that the velocity was fixed at 50 km/s. Now with a better model for the velocity over the course of a year we can re-examine the distance/diameter constraint. The best estimate of the ISS time scale comes from the 25day observations from February 1990 (Quirrenbach et al. 2000). Since the LSR velocity was 42 km/s at that time (see Figure 1), the nominal 200 pc medium thickness is only reduced by the ratio 42/50 to 170 pc. In a related paper (Rickett and Lyne, in preparation, 2000) we consider this constraint in the light of diffractive ISS observations of pulsar B0917+63, which at a nominal distance of 760 pc probes the same path through the Galaxy.
The agreement in time-scale with the prediction based on assuming that the medium is stationary in the LSR allows us to put an upper bound on the range of velocities that contribute to the scattering. If the distribution of speeds in the scattering medium is a Gaussian function, its standard deviation must be no more than the slowest effective ISS speed, (defined by the spatial scale in the model divided by the observed time scale). This bounds the standard deviation in speed at about 8 km/s. In comparison transverse differential Galactic rotation amounts to about 1km/s at 200 pc along this line of sight. Though there is no distinction possible between a spread of velocities due to shear or due to turbulence in the medium, this result puts an upper limit of 8 km/s for any turbulent velocities in the scattering plasma. This is one of the few formal constraints on turbulent plasma velocities that have been extracted from three decades of ISS work. Future observations sampling the full annual cycle of ISS will help determine the velocity distribution in the ISM, though the influence of anisotropic scattering will also have to be modelled.
Evidently, there is a strong incentive to verify the annual variation and to study whether similar phenomena exist for other IDV sources, several of which are in directions for which a substantial annual modulation should be expected. Preliminary examination for IDV sources 0716+714 and 0954+658 do not show the predicted annual modulation in IDV time scale. Thus the present result for 0917+624 does not rule out the existence of intrinsic IDV in these sources. A program of IDV observations of 0917+624 has been started in September 2000 and is continuing in order to verify the slow ISS phenomenon for 0917+624. During the final preparation of this paper, we have received a draft of a paper by Jauncey & Macquart, in which they independently report the same annual modulation and its ISS interpretation, derived from 0917+624 data in the literature.