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Astron. Astrophys. 361, 952-958 (2000)

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2. Deriving the mass-transfer history

In order to derive the mass-transfer history of the secondary star in AM Her, we must first derive the mass-accretion history from the available observations at many times and wavelengths. The bulk of the gravitational energy released in an accreting polar is emitted in the X-ray regime, partly as optically thick quasi-blackbody radiation from the heated white dwarf atmosphere in regions of high local mass-flow densities, partly as optically thin bremsstrahlung from the stand-off shock in regions of relatively low accretion densities. In addition to the bremsstrahlung, the hot post-shock plasma emits cyclotron radiation in the visual/IR. Only about half of the bremsstrahlung/cyclotron emission is radiated away directly, the other half is intercepted by the white dwarf surface and either reflected or reprocessed into the UV range, as evidenced by a large heated spot around the main accretion region (Gänsicke et al. 1995,1998). At low accretion rates, one sees the photospheric flux of the (heated) white dwarf. Finally, the accretion stream can be a source of largely optically thin emission in the visual/UV wavelength range.

It is clear that a dense sampling of multi-wavelength observations of AM Her would be desirable to determine the temporal variation of all individual accretion flux components. However, the prime observational parameter which is available is the brightness at optical wavelengths. The intense visual monitoring of AM Her by the observers of the AAVSO resulted in more than 10 000 individual brightness estimates for the last 20 years. Fig. 1 shows the AAVSO data binned in 10 day intervals. [FORMULA] can - in principle - be derived from Fig. 1 if the time-dependent accretion flux [FORMULA] can be expressed as a function of V. In a first approximation, we neglect the emission from the accretion stream and write


where [FORMULA], [FORMULA], and [FORMULA] are the observed soft X-ray, thermal bremsstrahlung, and cyclotron fluxes, respectively. [FORMULA] is the flux of the reprocessed emission from the heated pole cap. Gänsicke et al. (1995) have shown that in AM Her [FORMULA], [FORMULA], and [FORMULA] are of the same order of magnitude both during the high state and during the low state. Thus, it is possible to estimate


from X-ray observations alone. The main uncertainty in our estimates of [FORMULA] is not the approximation involved in the second term but the systematic uncertainties in the parameters of the dominant first term in Eq. 2, the bolometric value of the soft X-ray flux.

We have compiled values for [FORMULA] from the literature based on observations with ROSAT (Gänsicke et al. 1995), BeppoSAX (de Martino et al. 1998), and EXOSAT (Paerels et al. 1994). Fig. 2 shows [FORMULA] as function of the visual magnitude V, where the values of V for the individual X-ray observations were obtained from the AAVSO data. [FORMULA] varies smoothly over a wide range in [FORMULA]. For [FORMULA], [FORMULA] drops steeply as the emission of AM Her approaches that of the underlying stellar components, indicating that accretion nearly ceases. We approximated the [FORMULA] distribution with two separate linear fits to the ranges [FORMULA] and [FORMULA].

[FIGURE] Fig. 2. Correlation between the visual magnitude and the accretion flux in AM Her. Plotted as dashed lines are two linear fits for [FORMULA] and [FORMULA].

With [FORMULA] known, we compute the accretion luminosity


with [FORMULA] pc the distance of AM Her (Gänsicke et al. 1995). The assumption of isotropic emission may overestimate the accretion luminosity somewhat. As all values of [FORMULA] are orbital mean values, this uncertainty does, however, not exceed a factor of 2, and is probably less as we neglected the emission of the accretion stream.

From [FORMULA], we finally compute


with [FORMULA] cm the adopted white dwarf radius, [FORMULA] the adopted white dwarf mass, and G the gravitational constant. [FORMULA] is shown in Fig. 3 (contiguous 10 day bins are connected by lines). The average value of [FORMULA] is [FORMULA], or [FORMULA].

[FIGURE] Fig. 3. The mass transfer rate in AM Her as a function of time (see Fig. 1). The dashed line indicates a reasonable value for the maximum quasi-stationary mass-transfer rate: [FORMULA] (i.e. [FORMULA]).

Hereafter, we will use [FORMULA] to denote either the instantaneous mass-transfer or mass-accretion rate, on the assumption that they are effectively the same for our purposes.

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© European Southern Observatory (ESO) 2000

Online publication: October 10, 2000