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Astron. Astrophys. 332, L13-L16 (1998)

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3. Discussion

To place the IRAM detection in the context of other observations in the millimetre, optical and centimetre range, we plot a compilation of the reported fluxes and 3 [FORMULA] upper limits during May 1997 in Fig. 1.

[FIGURE] Fig. 1. Evolution of the flux of GRB 970508 in the a  millimetre, b  optical and c  centimetre range, and d  of the spectral index [FORMULA]. References are: IRAM (this article, Table 1), BIMA: Gruendl et al. (1997), OVRO: Shepherd et al. (1997), Palomar: Djorgovski et al. (1997), Loiano: Mignoli et al. (1997), NOT: Pedersen et al. (1998), WHT: Galama et al. (1997b), SAO-RAS: Sokolov et al. (1997), HST: Fruchter et al. (1997), VLA: Frail et al. (1997b), VLBI: Taylor et al. (1997), CAHA: Castro-Tirado et al. (1998). Spectral indices: [FORMULA] from Frail et al. (1997b), others from Table 2. Optical data are corrected with [FORMULA] (Djorgovski et al. 1997). Palomar and Loiano Gunn-r data were converted to Cousins R with Fukugita et al. (1995)

Gruendl et al. (1997) observed the source with the BIMA at 85 GHz, and the OVRO was used by Shepherd et al. (1997) at 86.8 GHz. First upper limits by BIMA ([FORMULA]  mJy on May 10.2) and OVRO ([FORMULA]  mJy on May 11.1) are outside the range of the uppermost plot but constrain the early development of the source. A tentative detection on May 15 by BIMA was reported by Smith and Gruendl (1997), but was not confirmed by a deeper analysis of the data (Gruendl et al. 1997). Optical observations were selected with emphasis on days 5-25 after the burst, calibrating [FORMULA] as 3080 Jy (Bessell 1979).

Fluxes at centimetre wavelengths are at 8.46 GHz from the VLA by Frail et al. (1997b) and 8.41 GHz from VLBI by Taylor et al. (1997). The VLA has observed GRB 970508 at 4.86 GHz and 1.43 GHz, too, but less frequently, which is the reason why only the 8.46 GHz data are plotted here.

Pooley and Green (1997) detected the source at the MRAO on May 16.5 ([FORMULA]  mJy) and on May 17-22 ([FORMULA]  mJy). From the available fluxes from VLA, VLBI, MRAO and IRAM, one can derive a finer record of the spectral development than previously possible.


[TABLE]

Table 2. Spectral index [FORMULA] from observations which closely match in time. Data are from: (1) this article, (2) Frail et al. (1997b), (3) Taylor et al. (1997), (4) Pooley and Green (1997). Columns are UT day in May, frequency, flux and reference for both observations, the mean UT day, and the spectral index [FORMULA] assuming a power law [FORMULA] between frequency pairs


The time dependence of the [FORMULA], x-ray and optical fluxes of GRB 970508 agrees with a power law fading for a given band of the form [FORMULA] which was at least once interrupted by a flare (Piro et al. 1997b).

Compared to this, the radio data at 8.46 and 4.84 GHz (Frail et al. 1997b) show approximately constant average fluxes, with many superimposed flares that occur independently at the two frequencies. About 30 days after the burst, these flares calm down, and the fluxes vary in a more similar way. The variations could be either extrinsic or intrinsic to the source: In the first case, one assumes a constant source-intrinsic flux that is modified by interstellar scintillation (IS) in our galaxy. As the source expands, the scintillation characteristics pass from the strong diffractive to the weak refractive regime (Goodman 1997, Frail et al. 1997b). The intrinsic case demands shock induced coherent/collective plasma emission as in intra-day variable QSO's (see e.g. Standke et al. 1996). Both effects can produce strong narrow-band variations in the cm range while not influencing the optical light curve.

We will now discuss how the mm observations reported here fit in this context. They are not consistent with a constant flux, because the fading after May 22 is highly significant (the non-detection on May 28 has nearly the same r.m.s. as the [FORMULA] detection on May 17-22). Also, they do not fit well the high energy power law above.

An important point to be verified is the possibility of external flux modification, i.e. if an intrinsically weak, constant mm source could have been boosted on three occasions above the detection limit by IS. We argue that this is highly improbable, as flux modulations close to 100% can only be produced by strong diffractive IS, whose maximum frequency [FORMULA] at the GRB's galactic latitude of [FORMULA] reaches [FORMULA]  GHz for typical galactic scattering measures (Goodman 1997). The weak refractive type of IS has no such limiting frequency, but the r.m.s. of its amplitude modulation scales with [FORMULA], so that any variation at 8.46 GHz is reduced by a factor of [FORMULA]. Also, for [FORMULA], timescales for weak diffractive and refractive IS scale with the Fresnel length [FORMULA] (Goodman 1997) which would be some hours at 86.2 GHz. No significant flux variation has been seen on this timescale (Sect. 2).

For the intrinsic light curves of GRB 970508, two mechanisms seem to dominate: self-similar forms with power-law fading, which pass in time from high to low energies (interpreted as non-thermal emission from a decelerating relativistic fireball, e.g. Vietri 1997, Waxman 1997, Wijers et al. 1997), and closely correlated broad-band flares (Piro et al. 1997b). Fig. 1a,b show that optical flares were absent during our mm detections. Near 8.4 GHz (Fig 1c), the situation on May 21-23 is less clear, as flares from intrinsic and extrinsic origins could be present in the cm records. The closest fluctuation at 8.4 GHz is a strongly double-peaked feature, which is difficult to associate with the constant mm flux levels during the May 21,22 detections. For our May 19 observation, the closest VLA observation from May 18.85 shows a quiescent source at 8.46 GHz. This makes broad-band flaring an unlikely mechanism for the millimetre light curve.

A power-law fading form would require to place the time of maximum 86.2 GHz flux between the optical maximum ([FORMULA] May 11) and an 8.4 GHz peak (e.g. the May 21-23 flare). For this, the May 17 upper limit must receive a low weight, and one would have expected a "barely missed" detection on May 28 from the [FORMULA] law, which is not the case (Table 1). Such a fading cannot be ruled out, but it is not a good fit (Fig. 1a).

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Online publication: March 10, 1998
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