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Astron. Astrophys. 327, 1023-1038 (1997)

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5. The reconstruction results

The UBVRI light curves of four successive nights were used to create the eclipse maps of the system IP Peg on decline from an outburst. Normally the fit is done with a [FORMULA] - value of 1. This means that the fit deviates from data by roughly what is expected from observational errors. But due to flickering in the light curve we had to relax the data constraints by increasing the target value of [FORMULA].

The disk radius used for the reconstructions was determined from the geometric system parameters and the duration of the disk eclipse. For details see Sulkanen et al. (1981). The disk was assumed to be geometrically thin and of concave shape with an disk opening angle [FORMULA] of [FORMULA] for total opening (i.e. [FORMULA] up and down) because of our considerations in the previous section. Simulations showed that an error in the disk opening angle affects mainly the outer rim, but not the global steepness of the temperature profile. This effect can be estimated to be below 10 percent for the pixels with the greatest radius if the angle changes by a factor of two. The main reason is that (as long as small angles are concerned) a change in opening angle causes only a slight change in the projected area for pixels on the disk, but a dramatic change of the effective area for pixels on the ribbon. The system parameters of IP Peg were taken from Wolf et al. (1993). Reconstructions were done with MONA-default images, because these are best in conserving the radial profiles of the disk (see appendix A and B for details concerning our reconstruction method, MONA-images, geometry and our choice of the default-image).

5.1. The reconstructions

Fig. 4 presents our phase-folded eclipse light curves on each night in all colours in the upper four panels. The solid lines represent the fitted model light curves. The intensity maps in colour V are presented in Fig. 4 in the lower four panels. The inner Lagrangian point in these plots is centered in the middle of the bottom right edge of the three dimensional grid. The brightness temperature profiles are shown in Figs. 5 and 6. In this two figures the profiles of all nights are plotted in the individual colours seperately. So the time resolved evolution of the disk on the decline from outburst is visible in each colour separately. Here only the colours UBVR are plotted. In colour I the obtained maps are all structureless and flat, decreasing only slightly in temperature from night to night; furthermore these reconstructions were suspected to be not very reliable, because of the strong influence of the secondary which is affecting this light curve, so they are omitted here.

[FIGURE] Fig. 4. Upper four panels: The IP Peg outburst data and the fits (solid lines) are shown for each night as UBVRI-Plots (phase-folded). Also the residuals are plotted around the zero line. Lower four panels: The corresponding reconstructed intensity maps in 3-dimensional representation of colour V. (For clarity the ribbon is not plotted here)
[FIGURE] Fig. 5. log-T/log-R plots of colours U and B. For each colour all nights are plotted in one panel. [FORMULA] -signs and the solid line belong to the night of 19.7.90. [FORMULA] -signs and the dashed line belong to the night of 20.7.90. [FORMULA] -signs and the dash-dot line belong to the night of 21.7.90. [FORMULA] -signs and the dotted line belong to the night of 22.7.90. The three inclined solid lines correspond to theoretical effective temperature profiles of stationary disks, depending on mass transfer rates of [FORMULA], [FORMULA] and [FORMULA] per year.

5.2. Discussion

In the intensity plots in Fig. 4a clear change in the shape of the intensity distribution can be seen. Especially the comparison between the first and last night shows that the intensity decreases first in the outer regions of the disk.

The brightness temperature distribution (especially in V and R) in the log-T/log-R plots (Fig. 6) of the first night ([FORMULA] -signs and solid line) shows a steep [FORMULA] profile from the outer edge inward to about 0.45 [FORMULA] radius. Inside 0.45 [FORMULA] the disk seems to be flat in temperature. In the last night ([FORMULA] -signs and dotted line) the interface between the flat and declining temperature zone has "travelled" inward and covers the disk between 0.3 and 0.1 [FORMULA], leaving the disk about 2500 Kelvin colder and flat outside. If this structure is interpreted in terms of some kind of cooling front this front would have travelled about 0.35 [FORMULA] in three days.

[FIGURE] Fig. 6. log-T/log-R plots of colours V and R. For each colour all nights are plotted in one panel. [FORMULA] -signs and the solid line belong to the night of 19.7.90. [FORMULA] -signs and the dashed line belong to the night of 20.7.90. [FORMULA] -signs and the dash-dot line belong to the night of 21.7.90. [FORMULA] -signs and the dotted line belong to the night of 22.7.90. The three inclined solid lines correspond to theoretical effective temperature profiles of stationary disks, depending on mass transfer rates of [FORMULA], [FORMULA] and [FORMULA] per year.

If we look back to our simulations in Sect. 4 and compare it with our reconstructions, the "steady-state-like" part of the temperature profile could be the smeared-out front (see temperature profiles in Fig. 2).

With the assumption that [FORMULA] of IP Peg is about 0.8 solar radii (Marsh 1988 ), it would have a speed of about 800 m/s. This is in agreement with simulations done by Ludwig et al. (1994) (see Fig. 6 in his article). After one day it should have travelled inward about 0.12 [FORMULA]. That is in agreement with the shape of the disk belonging to the second night ([FORMULA] -signs and dashed line) and also to the fourth night ([FORMULA] -signs and dotted line).

This behavior can not clearly be confirmed by the reconstruction of the third night ([FORMULA] -signs and dash-dot line). However it should be mentioned here that the third night caused lots of troubles during the reconstructions, regardless of reconstruction method and preparation of the data. A value of 15 was needed for [FORMULA] in order to get convergence! For the other three nights we used [FORMULA] values between one and three, depending on the amount of flickering. This high [FORMULA] value of the third night might be due to out-of-eclipse variations which are unreconstructable by the adopted geometry of the disk, i.e. variations due to the secondary's surface. Therefore the reconstruction of this night may be not very significant.

So in contrast to the disk instability model of accretion disk outbursts, the temperature profiles of the disk show no quasi stationary profiles, they have flat temperature profiles in the disk inside the front!

Haswell et al. 1994 , have made spectrally resolved eclipse maps of the accretion disk in the dwarf nova IP Peg covering one eclipse during the 1993 May outburst and also got radial temperature profiles from these maps. The temperature profiles obtained were also flat and quite similar to those observed in quiescent dwarf novae, with temperatures ranging from 4000 K to 6500 K.

Possible solutions for this problem could be for example a flared disk (Rutten 1995, private communication), energy dissipation due to magnetic fields, material over the disk and shading the inner regions (Doppler Tomography made by Kaitchuck et al. 1994 , showed strong absorption in the central regions of IP Peg's disk), a hole in the disk, a high disk rim which obscures the inner hot parts of the disk or an optically-thick wind sphere. The last three possibilities will be discussed in the next section.

A rough estimate for the viscosity parameter [FORMULA] can be obtained by assuming that the front velocity [FORMULA] is determined by the sound speed [FORMULA] and the viscosity parameter [FORMULA] (Meyer 1984):

[EQUATION]

where the sound speed is given by

[EQUATION]

([FORMULA]: mean molecular weight, [FORMULA]: gas constant, T : mid-plane temperature of the disk). If we take between 5000 K and 100000 K respectively for the mid-plane temperature and 800 m/s for [FORMULA], then we get values for [FORMULA] which are listed in Table 2.

[TABLE]

Table 2.Values of viscosity parameter [FORMULA] for different midplane temperatures.

However, it is worth mentioning that [FORMULA] is not properly defined within the front: two [FORMULA] 's are required, one [FORMULA] for the hot (stationary) part and one [FORMULA] for the cool part of the disk. The [FORMULA] value derived here may be a mixture of [FORMULA] and [FORMULA].

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© European Southern Observatory (ESO) 1997

Online publication: April 6, 1998
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