Multiple delays in QSO 0957+561: observational evidence and interpretation (2024)

Article history

Abstract

1 Introduction

The observed optical luminosity of QSOs is probably generated in a source including an accretion disc around a supermassive black hole and a circumnuclear stellar region (e.g. Umemura, f*ckue & Mineshige 1997, and references therein). Therefore, some kind of intrinsic variability could be due to local and violent physical phenomena (flares) taking place in the accretion disc (e.g. hotspots) or in the innermost stellar region (e.g. starbursts). These two standard regions for flares have very different sizes, and thus, if we were able to map several locations of flares within a source QSO, we would measure the size of the region of flares (RF) and determine the environment in which the local and violent variability is originated (Yonehara 1999). A standard accretion disc has a radius of the order of 10⁻² pc, whereas the innermost stellar region may be extended as far as 10²–10³ pc.

In a pioneer work, Yonehara (1999) has suggested a way to map the positions of the intrinsic flares in a gravitationally lensed quasar. For a double-imaged QSO, with optical images A and B, there is a time delay between a given intrinsic event in image A and its twin event (a similar feature) in image B. However, if the optical variability is generated in different points of a source with finite size, it must be not expected a unique time delay for different pairs of twin events. So, the discovery of multiple delays in a double QSO indicates the presence of twin events induced by flares, and the time delay distribution must inform us about the size and nature of the RF. In this paper (Section 2), we searched for multiple delays in the light curves of the lensed quasar Q0957+561A,B. The light curves of both images in this gravitational mirage show variability on very different timescales, but we concentrated on the well-sampled intrinsic events with an amplitude of about 100 mmag and lasting several months (∼100–300 d), which were recently found by Kundić et al. (1995, 1997) and Serra-Ricart et al. (1999).

In Section 3, we interpret the results derived from the careful analysis of the best available optical light curves of Q0957+561A,B. Finally, we summarize our conclusions in Section 4. Scenarios for flares as diverse as accretion disc instabilities, disruption of stars in the gravitational field of a supermassive black hole, stellar collisions or violent stellar evolution are also put in perspective in this last section (see Cid Fernandes, Sodré & Vieira da Silva 2000, and references therein).

2 Time Delay(S) Between the Components A and B of QSO 0957+561

2.1 Historical background and description of the data

The two optical components of QSO 0957+561 have been monitored during about 20 yr (Lloyd 1981; Keel 1982; Florentin-Nielsen 1984; Schild & Cholfin 1986; Vanderriest et al. 1989; Schild 1990; Schild & Thomson 1995; Kundić et al. 1995, 1997; Serra-Ricart et al. 1999; Oscoz et al. 2001; Slavcheva-Mihova, Oknyanskij & Mihov 2001), and the data sets inferred from the observations have been usually analysed from standard techniques, which look for a unique time delay between Q0957+561A and Q0957+561B. However, only if all features come from a common zone in the source (or the emitting points are included within a very small region), we can properly speak of a well-defined time delay. The use of a standard procedure, in general, leads to an effective time delay that will correspond to either the time delay associated with the dominant twin features or the average of several time delays associated with several pairs of twin features in the light curves of the system.

The best available optical light curves, in terms of sampling rate, signal-to-noise ratio and intrinsic character, were obtained by Kundić et al. (1995, 1997) and Serra-Ricart et al. (1999), and these trends could shed light on the existence of a well-defined delay (when there are no discrepancies between time delays for different pairs of twin events or the possible discrepancies cannot be resolved) or the opposite case. Thus, we concentrate our attention on the events with a width of ∼100–300 d and an amplitude of about 100 mmag (sharp features with high signal-to-noise ratio), which are included in the brightness record obtained at the Apache Point Observatory (APO) and the Teide Observatory (TO) for the period 1995–1998. Another large data set compiled by R. Schild shows clear evidences in favour of extrinsic variability (Schild 1996), and therefore, we avoid this data set. We remark that Schmidt & Wambsganss (1998) and Gil-Merino et al. (2001) have not found reliable microlensing imprints in the records of brightness by Kundić et al. (1995, 1997) and Serra-Ricart et al. (1999), respectively, although Schmidt & Wambsganss (1998) showed a difference light curve with an anomaly during the central dates that is directly related to the subject of this paper (a group of data are slightly but coherently above the zero-line and the next group of data are coherently below the zero-line).

2.2 First evidence for multiple delays

The observations carried out at TO from 1996 through 1998 (in the R band) were used to compare the light curves of images A and B and obtain effective time delays using pairs of seasons (Serra-Ricart et al. 1999). In principle, two comparisons are possible: 1996(A)–97(B) seasons and 1997(A)–98(B) seasons, but the signal-to-noise ratio in the first pair was very small, and only the two twin features seen in the last pair (with an amplitude of 120 mmag and a duration of about 300 d; see Serra-Ricart et al. 1999; Gil-Merino et al. 2001) can be seriously considered to measure an accurate time delay. Using the data included in this last pair of seasons and the δ²-test, Serra-Ricart et al. (1999) derived a reliable delay of 425 ± 4 days (1σ). As they basically compared two twin events, we do not consider their detection as an effective delay but the time delay between the quoted prominent features. So, taking into account the TO events with S/N∼ 2.5 (we define the signal-to-noise ratio as the ratio between the semi-amplitude of the events and the mean photometric error), it is inferred an optimal delay of 425 d. We remark that brightness records with S/N∼ 1 are not suitable for measuring time delays, because the techniques fail in this situation. With regard to this issue, the Section 3 of Pijpers (1997) is very instructive. In order to infer reliable delays, it seems reasonable to work with signals characterized by S/N > 2.

On the other hand, CCD images of Q0957+561A,B were taken with the APO 3.5-m telescope in the g and r bands, during the 1995 and 1996 seasons (Kundić et al. 1995, 1997). The light curve of the image A in the first season (A95) exhibited a significant variability. In particular, A95 included a sharp drop of about 100 mmag in 1994 December (data in A95 encompass 6 months of observations between 1994 December 2 and 1995 May 31), which represents the second half of a whole event. The twin event of this feature in A95 was observed in the light curve of the image B during the 1996 season (B96). In the g band, the twin event is characterized by an amplitude and a width of 130 mmag and about 100 d, respectively. Just after these two APO main events in A95 and B96, we can find other two sharp twin features. The APO secondary events have a duration slightly less than the main ones and an amplitude of 50–70 mmag in the g band. Fig. 1 shows the main event (top panel) and the secondary event (bottom panel) in B96. The data in the g band (light filled squares) and in the r band (dark filled squares) are depicted. We note the high signal-to-noise ratios in the g band: S/N∼ 6.5 in the main event and S/N∼ 3 in the secondary one. The (S/N)_g–band value in the secondary events is similar to the (S/N)_r–band value in the main features. The secondary events in the r band are very noisy. Using A95 and B96 in the g band, and three different techniques to infer the effective time delay (linear interpolation, optimal reconstruction and dispersion spectrum), Kundić et al. (1997) derived a best value of 417 d. Fig. 2 displays together A95 (open circles) and B96 (filled squares) in the g band. A95 was shifted by a time delay of 417 d, while B96 was shifted by an optimal magnitude offset of 118 mmag (see Kundić et al. 1997). Only the main overlapping region of A95 and B96 is showed, i.e. that one including the two pairs of twin features, and to guide the eye, a line joins the data for the A component. One sees in Fig. 2 an excellent agreement between the APO main twin features (from day 1100 to day 1150) as well as an anomaly with regard the two APO secondary events. The secondary event in the flux of image A is not aligned with the secondary one in the flux of image B, or in other words, the secondary event in the time-shifted (417 d) A95 seems still delayed with respect to its twin event in B96. As an additional problem, the best solution for the delay from TO data (425 d) is out of the 95 per cent confidence interval claimed by Kundić et al. (1997): 417 ± 3 d. From another point of view, the solution of 417 d is in clear disagreement with the TO photometry (see Fig. 16 in Serra-Ricart et al. 1999).

The three methods used by Kundić et al. (1997) to infer an optimal effective time delay of 417 d, seem very sensitive to the two main features. In a manner of speaking, these classical methods forget the rest of data, and we need to find some discrete technique to compare all information in both brightness records. The discrete cross-correlation method has several variants which may be sensitive to the whole light curves, and we choose the δ²-test (e.g. Serra-Ricart et al. 1999), in which the shifted discrete autocorrelation function (DAC) is matched to the discrete cross-correlation function (DCC). From the δ²-test we infer optimal effective time delays of 424 d (using bins with size of 5 d) and 422 d (using bins with size of 15 d), both in agreement with the measurement from TO data. We note that the TO data were studied with a relatively poor time resolution (bins with size of 40 d), while we analysed the APO data with a good time resolution: smoothing size of 5–15 d. In Fig. 3 (top panel) the DAC for the A component shifted by 424 d (open circles) and the DCC (filled circles) are presented. In this DAC versus DCC comparison we used bins with size of 5 d (results with the best time resolution). Using bins with size of 5 d (solid line) and 15 d (dashed line), possible values of the effective time delay (θ) versus the associated δ²(θ) values, normalized by its minimum value δ²(θ₀), have been also plotted in Fig. 3 (bottom panel). As it was already mentioned, the new optimal values close to 425 d are in good agreement with the measurement made by the IAC group. However, is there a good alignment between twin features? To answer this question we have redrawn in Fig. 4 the combined photometry of Q0957+561A,B for the 1995–96 seasons in the g band, but shifting A95 by a time delay of 424 d. We conclude that an effective delay of 424 d is not able to align neither the APO main events nor the APO secondary events, although this larger value can be considered as the estimate of an average time delay. The 424 d solution leads to some discrepancies whose imprints can be seen in the top panel of Fig. 3 (e.g. there is a clear lag between the ‘humps’ to the right of the central peaks). Only the existence of two different delays can lead to the alignment of both pairs of twin events.

2.3 Detection of multiple delays

Our last task must be to obtain, in a consistent way, the time delay between the APO main events and the time delay between the APO secondary events. From the data included in the sharp drop of the main events, we make a first δ² function. Moreover, using the data corresponding to the secondary events, we do a second δ²-test. The two new δ² functions together with the δ² function inferred from all data (see bottom panel of Fig. 3) are showed in Fig. 5. When we only take data corresponding to the main events, we obtain a narrow peak in δ² and recover the expected result of a delay of 417 d, whereas if only data in the secondary events are used, then another narrow peak centred on 432 d is derived. In Fig. 6, we draw our best solution for the 1995–96 seasons in the g band: the first part of A95 is shifted by 417 d (main drop) and the second part is shifted by +432 d (secondary event). Finally, to sum up, a time delay of 425 ± 4 d explains the signal recorded at Teide Observatory in the R band (two twin events with a relatively long time-scale of about 300 d), while a unique time delay does not align the two pairs of twin events detected at Apache Point Observatory in the g band. From the APO light curves, a double time delay of 417.0 ± 0.6 d (for the main features) and 432.0 ± 1.9 d (for the secondary events) is favoured, and thus, three different delays are detected from APO/TO data (the APO/Main-APO/Secondary difference delay is of −15.0 ± 2.0 d, the APO/Main-TO difference delay is of −8.0 ± 4.0 d and the APO/Secondary-TO difference delay is of +7.0 ± 4.4 d; see Table 1).

We computed 1σ uncertainties (68.3 per cent confidence limits) for the time delays inferred from the δ²-test. Each 1σ confidence interval was derived through intensive simulations: we made 10⁵ possible underlying signals which are consistent with the observed light curve of the image A, and 10⁵ possible underlying brightness trends of the image B (in agreement with the photometric behaviour of this image). From the 10⁵ pairs of possible underlying signals, we can estimate 10⁵ time delays (using the δ²-test), and therefore, the distribution of delays and the standard confidence interval. The whole procedure is similar to the methodology used by Serra-Ricart et al. (1999). By means of intensive simulations, other studies are also interesting and viable. For example, from the APO main twin events, we found that 99.9 per cent of the delays are included in the range 417 ± 2 d. On the other hand, from the APO secondary twin events, the delay distribution is broader. However, a delay ≥425 d has a probability higher than 99 per cent. So, we unambiguously found two different time delays in the APO light curves.

3 Interpretation of the Results

We assume that the observed optical luminosity of QSO 0957+561 is due to a standard hybrid source (accretion disc and circumnuclear stellar region), and consequently, exotic sources are not taken into account in this paper (e.g. two accretion discs around two close supermassive black holes). The total luminosity is the superposition of a dominant non-variable ‘background’ component and a variable part, where the background luminosity is mainly originated in either the full accretion disc or the full stellar environment, and the QSO variability can be made by flares or another kind of activity. In this scenario, the APO/TO events must be caused by flares in the source QSO.

4 Conclusions and Discussion

Using the best available optical light curves of Q0957+561A,B, which contain three pairs of twin events with significant signal-to-noise ratio (S/N≥ 2.5), we found a clear evidence for three different time delays. As far as we know, this is the first detection of multiple delays in a double-imaged QSO. Our analysis based on data of a lens system sampled during many years could be extended to other lens systems in a near future.

We concentrated on relatively violent events with an amplitude of ∼100 mmag (a fluctuation of Δm∼ 0.1 mag represents a relative fluctuation in flux of ΔF/F_back∼ 10 per cent) and a duration of ∼100–300 d. If these events are originated inside a standard hybrid source (accretion disc and circumnuclear stellar region), the observed time delay multiplicity suggests that they do not come from a common zone in the source (Yonehara 1999). So, the studied events may be related to violent and local physical phenomena (flares). Accepting the hypothesis of events caused by flares in a standard hybrid source, in Section 3 we discussed on the size and nature of the region of flares. In particular, it is showed that two of the three flares must be generated at distances (from the central black hole) larger than 90 pc. Therefore, taking into account that the radius of a typical accretion disc is of 10⁻² pc, accretion disc instabilities or collisions of stars with the black hole + hot disc complex (e.g. Haardt, Maraschi & Ghisellini 1994; Kawaguchi et al. 1998; Ayal, Livio & Piran 2000) can be discarded as candidates to these two flares far away from the black hole. However, in principle, the observed flux variability may be due to either stellar collisions in dense clusters separated from the centre (e.g. Courvoisier, Paltani & Walter 1996) or the violent evolution of stars in the circumnuclear stellar region (e.g. Aretxaga, Cid Fernandes & Terlevich 1997). A more complex scenario, involving star–gas encounters in a extended gaseous disc or bar, is also possible.

We can roughly estimate the rest-frame B-band energy released in the flare related to the main events in the g-band APO data, and compare it with the rest-frame B-band energy released in a typical event occurring in a given stellar scenario. To do the estimation/comparison we followed several steps. First, from the light curve of the image A in the first season (A95), we deduced a g-band background of m_back(g) = 17.08 mag. We transformed this g-band background component to a B-band background contribution using the g−r colour and the equations of Kent (1985). The B magnitude can be then converted to a monochromatic flux (4400 Å) using standard laws (e.g. Allen 1973; Henden & Kaitchuck 1990; Léna, Lebrun & Mignard 1998). The relevant flux, F[λ4400(1 +z_s)], may be found by multiplying the monochromatic flux F(λ4400) by the k-correction (1 +z_s)^0.5 (e.g. Schmidt & Green 1983). Thus, F_back[λ4400(1 +z_s)]≈ 10⁻¹⁵ erg cm⁻² s⁻¹Å⁻¹. Secondly, using the luminosity distance D_L, one obtains: τ_backL_back(λ4400) = 4πD_L²F_back[λ4400(1 +z_s)], where L_back(λ4400) is the background intrinsic luminosity (at 4400 Å) and τ_back is the extinction-magnification factor. This last factor is due to both the magnification of the light from image A by the lens, and the extinction by dust in the lens galaxy, the Milky Way and so on. The magnification can be easily obtained, whereas it is difficult to estimate the total extinction. In a cosmology with Ω_Λ= 0, Ω_M= 1 and H= 100 h km s⁻¹ Mpc⁻¹, we inferred h²τ_backL_back(λ4400) ≈ 3 10⁴² erg s⁻¹Å⁻¹. Thirdly, the observed event has a duration of Δt= 100 d and an effective (top hat) amplitude of Δm(g) =−0.07 mag. We assumed that Δm(B)≈−0.07 mag and found an intrinsic luminosity of the associated flare given by h²τ_flareL_flare(λ4400) ≈ 2 10⁴¹ erg s⁻¹Å⁻¹. Taking h²τ_flare∼ 1, a time scale of Δt_flare=Δt/(1 +z_s) ≈ 40 d, and a filter bandpass width of 1000 Å, the rest-frame B-band energy released in the flare will be E_flare(B) ∼ 10⁵¹ erg. Finally, we compared the result on E_flare(B) with the energy released in a supernova explosion and in a head-on stellar collision. The mean rest-frame B-band energy released in a SN explosion is of E_SN(B) ≈ 0.5 10⁵¹ erg (Aretxaga et al. 1997). On the other hand, the energy released in a collision of two solar-mass stars with a velocity parameter β=v/c will be of E_COL(B) < E_COL≈ M_⊙c²β²≈ 10⁵⁴β² erg (Courvoisier et al. 1996). Therefore, the value of E_flare(B) agrees with the energy released in a supernova explosion and in a relativistic stellar collision (β≈ 0.1), and a stellar collision at moderate velocities (β≈ 10⁻³−10⁻²) cannot produce so high energy in the rest-frame B band.

For Seyfert nuclei, the isolated SN events have a characteristic time-scale of ≈300 d. However, the evolution of SNs in QSOs can be very much faster, with time-scales of ≈10 d (see Aretxaga et al. 1997). So, the time-scale and the energy corresponding to the g-band flares agree with the expected ones in a starburst scenario. On the other hand, for QSO 0957+561, a picture including only a starburst nucleus or ring has one difficulty. Kawaguchi et al. (1998) claimed that the measured slope of the first-order structure function is in clear disagreement with the pure starburst model. However, as it was remarked by Kawaguchi et al. (1998), the assumption of either a realistic shape of each SN event or a hybrid scenario could conciliate the existence of supernova explosions and the observed structure function. Moreover, the observational sampling was not taken into account in the simulations, and the observed structure function included observational noise, which was absent in model calculations.

Very recently, Collier (2001) found evidence for accretion disc reprocessing in QSO 0957+561. He compared the two events depicted in the top panel of Fig. 1 (the g-band APO main event and the r-band APO main event in B96) and obtained that the event in the r band lags the event in the g band by ∼1 d. This non-zero chromatic lag seems to support a reverberation within an accretion disc, and therefore, flares originated at points very close to the black hole. The result disagrees with our suggestion about the origin of the flare related to the APO main events in the g band, but with regard to this discrepancy, we must do a remark. The detection of a non-zero lag is only based in an interpolated cross-correlation method. Another discrete technique (ZDCF) led to an 1σ interval including a lag equal to zero. In any case, we can conciliate the claim by Collier (2001) and the measured delays in a simple way. The g-band APO main events could come from a flare in the hot disc, with the other two flares (which generated the g-band APO secondary events and the R-band TO events) having a stellar origin and typical time delay differences of +8 and +15 d. In this new scheme, the projected (on a direction joining both images of the QSO) relative positions of the two stellar flares are δy=+140 pc and δy=+263 pc. However, the solution to the possible conflict is not very comfortable. As the direction defined by the vector θ_A−θ_B is not a privileged one in relation to the physics of the source (obviously, it is a privileged direction of the gravitational mirage), there is an apparent bias in the 2D distribution of stellar flares: the two flares are produced in the semicircle defined by θ_A−θ_B. Of course the statistic is very poor with only a few flares, and we must analyse new monitoring campaigns to find more flares and a reliable estimate of the time delay associated with hypothetical signals from the centre of the source.

Acknowledgments

I am grateful to Atsunori Yonehara and Joachim Wambsganss for interesting discussions during the GLITP Workshop held at the Instituto de Astrofisica de Canarias (IAC). I also acknowledge the anonymous referee for criticisms that helped improve the paper. This work was supported by Universidad de Cantabria funds, the DGESIC (Spain) grant PB97-0220-C02 and the Spanish Department of Science and Technology grant AYA2001-1647-C02.

References

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