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Astron. Astrophys. 358, 793-811 (2000)

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2. Short-term variability in B1600+434-A & B

B1600+434 is a compact ([FORMULA]1 mas at 8.5 GHz; KBXF00) radio source, which has varied strongly at 8.5 GHz since its discovery in 1994 (Jackson et al. 1995). Its flux density decreased from 58 (48) mJy in March 1994 to only 29 (24) mJy in August 1995 for image A (B) (KBJ98). From February to October 1998, another decrease from 27 (24) to 23 (19) mJy was found (KBXF00). In June 1999, the flux densities appear to have stabilized to 23 (17) mJy. Strong variability was also observed at 5 GHz, where a total flux density was measured of 34-37 mJy in 1987 (GB87; Becker, White and Edwards 1991). Observations in March 1995 gave 45 (37) mJy for image A (B) (KBJ98), whereas in June 1999 this had reduced to only 23 (18) mJy. At 1.4 GHz, the integrated WSRT flux density of B1600+434 has decreased from 60-65 mJy in April-July 1996 (KBJ98) to about 50 mJy in June 1999.

Because of this strong variability, B1600+434 was observed from February to October 1998 with the VLA at 8.5 GHz, in order to measure a time delay between the two lensed images. In KBXF00, the VLA 8.5-GHz light curves of the two lensed images were presented, showing short-term variability, as well as a long-term decrease in the flux density of both lensed images, which we assume to be intrinsic source variability similar to that seen in, for example, Q0957+561, in which no apparent external variability has been found thus far (e.g. Lehár et al. 1992; Haarsma et al. 1997).

In Fig. 1, the normalized VLA 8.5-GHz light curves of both lensed images are shown. The curves were created by dividing the light curves by linear fits (KBXF00). The resulting curves show the fractional variability on short time scales (i.e. shorter than the observing period of about 8 months) with respect to the running mean. The 1-[FORMULA] error for each point on the light-curve is 0.7 to 0.8% (KBXF00). We omitted the six strongest outliers from both plots, which show clear systematic problems with the data or calibration (KBXF00). The resulting normalized light curves have modulation indices (i.e. fractional rms variabilities) of 2.8% and 1.6% for images A and B, respectively. We use these values throughout this paper. Lensed images A and B have modulation-indices significantly larger than expected on the basis of the measurement errors only, indicating the clear presence of short-term variability, either intrinsic or external. The structure functions (e.g. Simonetti, Cordes, & Heeschen 1985) of the normalized light curves are shown in Fig. 6 (Sect. 3.2).

[FIGURE] Fig. 1. The normalized light curves of B1600+434 A (upper) and B (lower), corrected for a long-term gradient (Sect. 2). The error on each light-curve epoch is 0.7 to 0.8% (1-[FORMULA]). Day 0 corresponds to 1998 Febr. 13

2.1. Intrinsic or external variability?

To show that most of the short-term variability is of external origin, the linearly-interpolated light curve of image B was subtracted from the light curve of image A, taking a flux-density ratio of 1.212 and a time delay of 47 days into account (KBXF00). The time delay was determined with the minimum-dispersion method from Pelt et al. (1996). Hence, the modulation-index of the normalized difference light curve, shown in Fig. 2, is by definition a lower limit. This is illustrated by the dotted and dashed lines, which show the normalized difference light curves for a time delay of 41 d and 52 d (i.e. the 68% confidence region), respectively. Both curves have larger modulation-indices, as should be expected.

[FIGURE] Fig. 2. The normalized difference light curve between the two lensed images, corrected for both the time-delay and flux density ratio (Sect. 2.1). The shaded region indicates the expected 1-[FORMULA] (1.1%) region if all variability were due to measurement errors. The dashed-dotted lines indicate the observed modulation-index of 2.8%. The dotted and dashed curves indicate the normalized difference curves for a time delay of 41 and 52 days, respectively. Obviously most variations can not be explained by any reasonable error in the time delay. There seems to be no evidence of any change in the typical time scale of variability over 6 months. Day 0 corresponds to 1998 Febr. 13.

The normalized difference light curve has a modulation-index of 2.8%. This is significantly larger than the modulation-index of 1.0-1.1% (i.e. the shaded region in Fig. 2), which one would expect on the basis of the measurement errors only. Most of the short-term variability present in the light-curves must therefore be of external origin. A [FORMULA]-value of 377 was determined from the 58 points composing the difference light curve. This is inconsistent with a flat difference light curve at the 14.6-[FORMULA] confidence level.

If the short-term variability of the two lensed images is uncorrelated, the expected modulation-index in the normalized difference curve should be [FORMULA][FORMULA]3.2%, which is slightly larger than the observed value of 2.8%. It remains hard to assess whether individual features in the light curves might be of intrinsic origin. In this paper we will therefore assume that all short-term variability in both lensed images is of external origin.

2.2. WSRT 1.4 & 5-GHz monitoring

Before proceeding with the analysis of the VLA 8.5-GHz light curves, we first present multi-frequency WSRT total-flux-density data of B1600+434 obtained in 1998/9 at 1.4 and 5 GHz. This data will play an essential role in distinguishing between the different physical mechanisms causing the external variability observed in the VLA 8.5-GHz lensed-image light curves, as we will see in Sect. 7.

Starting in August 1998 the WSRT was outfitted with a series of new multi-frequency front-ends (MFFE's) that can operate at frequencies from 0.3 to 8.5 GHz. When the WSRT observations of B1600+434 were begun in August 1998 only 6 front-ends were available at 1.4 GHz. The available number of telescopes with MFFE's increased at a rate of about 1 per month until the full array was outfitted in February 1999. Towards the end of 1998 the monitoring was extended to include 5 GHz. In the spring of 1999 we also included 8.5-GHz observations. However, the analysis of the 8.5-GHz data is still encountering some problems and we therefore do not report on the results of the 8.5-GHz observations here.

Each run consisted of two sets of observations (at up to 3 frequencies) on B1600+434 and the nearby reference source B1558+439. The latter is a strong steep spectrum double radio source (0.8-arcsec size) about 40 arcmin north-east of B1600+434. In each run we also observed two primary calibration sources (3C286, 3C343 and CTD93). Although we changed the details of the observing sequence during the year the basic structure did not change.

The resolution of the WSRT is about 12[FORMULA]18 arcsec (1.4 GHz) and 3.5[FORMULA]5 arcsec (5 GHz). B1600+434 is therefore always unresolved at 1.4 GHz. At 5 GHz the source, however, shows slight hour-angle dependent resolution effects [the WSRT is an east-west synthesis array, hence the instantaneous synthesized response is a fan beam rotating clockwise on the sky]. Because the observations were scheduled at random hour angles the resolution effect is therefore variable from session to session. We minimized the magnitude of this effect by determining the flux density using only baselines up to 1300 meter; the residual effect on the flux density is below the thermal noise error.

The amplitude and flux calibration was performed in NEWSTAR using standard procedures starting with a selfcalibration on the primary reference source. The complex telescope gains were then transferred to the target and reference source. The flux densities of B1600+434 and B1558+439 were then determined using a uv-plane fitting algorithm in the program NMODEL . Selfcal phase solutions on the reference source B1558+439 usually showed only very slight decorrelation effects due to slow instrumental/atmospheric phase-drifts. Because these would be very similar for B1600+434 and the reference source we decided not to apply a phase selfcal solution.

The flux density of the reference source B1558+439 was found to show a scatter of about 1-2% around 700 mJy at 1.4 GHz and about 1.0% around 204 mJy at 5 GHz. This scatter is still larger than the noise error on the flux density. We believe these can be attributed to small changes in atmospheric opacity and small instrumental gain drifts (e.g. due to pointing). Normalizing the amplitudes of B1600+434 by those of the reference source should eliminate them. We therefore expect that the final errors on the flux density of B1600+434 are determined by the thermal noise only. Still, to be on the safe side we adopted as a final error on the flux density of B1600+434 the quadrature sum of the thermal noise level and a 1% scale error. This amounts to a typical error of 1.0% and 1.3% at 1.4 and 5 GHz, respectively.

In Fig. 3, we have shown the calibrated WSRT 1.4-GHz (L-band) and 5-GHz (C-band) light curves, together with the total-flux-density VLA 8.5-GHz (X-band) light curve (KBXF00). We note the following properties: (i) All light curves are dominated by systematic trends with decreasing intensity at 8.5 and 1.4 GHz, but increasing at 5 GHz. We believe these changes to be due to intrinsic variations. (ii) If the VLA 8.5-GHz and WSRT 5-GHz long-term intrinsic flux-density variations are correlated, there has been a clear trend-break in the gradient of the light curves around day 300 (Fig. 3). The WSRT 1.4-GHz light curve still shows a similar gradient as the VLA 8.5-GHz light curves in 1998, hence there appears to be a time-lag of at least 200 days between long-term intrinsic source variability at 8.5 and 1.4 GHz. This trend-break is supported by the first results from the 1999 VLA campaign (Koopmans et al. in prep.). (iii) At those epochs where the light curves overlap, the higher-frequency light curves show a larger short-term modulation-index around the long-term linear gradient.

[FIGURE] Fig. 3. The integrated flux-density light curves of B1600+434 (sum of lensed images A and B) in X-band (VLA 8.5 GHZ), C-band (WSRT 5 GHz) and L-band (WSRT 1.4 GHz). The two vertical dashed lines indicate the time-span, where the WSRT 1.4 and 5-GHz observations overlap. Day 0 corresponds to 1998 Febr. 13

An important statistical property of the light curves is their modulation-index on short time scales (i.e. time scales shorter than the length of the light curves), as function of frequency. To calculate the modulation-indices, we divide the light curves through a linear fit (see Sect. 2) in order to remove most of the presumably intrinsic source variability. The results are normalized light curves, similar to the normalized VLA 8.5-GHz light curves shown in Fig. 1. We only calculate the 1.4 and 5-GHz modulation indices ([FORMULA]) for those epochs, where we have both 1.4 and 5-GHz WSRT flux-density measurements. The normalized light curves of these epochs are shown in Fig. 4. The resulting modulation-indices are listed in Table 1. Because the modulation-index at 1.4 GHz is very close to the estimated flux-density error, we regard it as an upper limit.

[FIGURE] Fig. 4. The normalized WSRT 1.4 and 5-GHz flux-density light curves of B1600+434. Only those epochs of the WSRT light curves are shown that have both a 1.4 and 5-GHz measurement (Fig. 3). The light curves were created similar to the VLA 8.5-GHz light curves shown in Fig. 1. One notices a clear increase in the modulation-index from 21 to 6 cm by a factor [FORMULA]3


Table 1. The short-term total flux-density modulation-indices of B1600+434, as function of frequency

The total flux-density modulation-indices in Table 1 are a combination of the individual modulation-indices of images A and B. If we assume that the ratio of modulation-indices are equal to those at 8.5 GHz (i.e. [FORMULA][FORMULA]2.8/1.6=1.75) for each wavelength, we only make a slight error ([FORMULA]15%) compared to the assumption that image B does not vary at all on short time scales. Because we will only use modulation-index ratios (see Sect. 7), which are independent from these assumptions in first order, this is of negligible importance.

2.3. Possible origins of the external variability

What can be the origin of the external variability seen in the VLA 8.5-GHZ light curves, why does the modulation-index differ between the two image light curves and what causes the short-term variability in the WSRT 1.4 and 5-GHz light curves? Below we have listed different physical mechanisms which can introduce external variability in the flux density of compact radio sources:

  1. Scintillation

    • Weak scattering (Sect. 3.1)

    • Refractive scattering (Sect. 3.2)

    • Diffractive scattering (Sect. 3.3)

  2. Microlensing (Sect. 4-5)

In the next three sections, we will investigate in detail whether one or more of these can explain the external variability seen in the VLA 8.5-GHz light curves of B1600+434-A & B. In Sect. 7, we will combine the conclusions from Sect. 3-5 with the results from the WSRT 1.4 and 5-GHz observations to further constrain the scintillation and microlensing hypotheses.

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© European Southern Observatory (ESO) 2000

Online publication: June 20, 2000