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Enhanced Mass Transfer in U Geminorum During Its Outbursts and Superoutburst

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Enhanced Mass Transfer in U Geminorum During Its Outbursts and Superoutburst ACTA ASTRONOMICA Vol. 55 (2005) pp. 315–320 Enhanced Mass Transfer in U Geminorum during its Outbursts and Superoutburst by J. Smak N. Copernicus Astronomical Center, Polish Academy of Sciences, ul. Bartycka 18, 00-716 Warsaw, Poland e-mail: [email protected] Received August 24, 2005 ABSTRACT The mass transfer rate in U Gem at quiescence, estimated to be M˙ ≈ 1.3−2.0×1016 g/s, is used to calculate the amount of mass ∆Mtr transfered to the disk during quiescence. Light curves of U Gem are used to estimate the amounts of mass ∆Maccr accreted during its three types of outbursts. In the case of wide outbursts and the 1985 superoutburst ∆Maccr are much larger than ∆Mtr , indicating significant enhancement in the mass transfer by a factor of f ≈ 20−50. There is no evidence for comparable enhancement during narrow outbursts. Key words: Accretion, accretion disks – navae, cataclysmic variables – Stars: dwarf novae – Stars: individual: U Gem 1. Introduction U Gem is a classicaldwarf nova with well determined system parameters (Smak 2001) and a well covered light curve (Mattei et al. 1987, 1991, 1996). It appears therefore to be a perfect case for detecting and studying the effects of the enhanced mass transfer during outbursts. Our analysis, which is essentially similar to that applied earlier to the case of SU UMa stars (Smak 2004), consists of the following steps. The observational data for the narrow and wide outbursts of U Gem, as well as for its 1985 superoutburst, collected in Section 2, are used in Section 3 to determine the amount of mass ac- creted onto the white dwarf during three different types of outbursts. In Section 4 we use the observed luminosity of the hot spot to determine the lower limit to the mass transfer rate at quiescence. These data are then used (Section 5) to estimate the mass transfer rates during outbursts. Results are discussed in Section 6. 316 A. A. 2. Observational Data Our analysis will be based on AAVSO light curves of 10 narrow and 10 wide outbursts of U Gem taken from Mattei et al. (1987, 1991, 1996). They were chosen in an essentially random way, the only condition being their good observational coverage. For each outburst we determine the magnitude at maximum Vmax , the width of outburst W1 at a level one magnitude below maximum, and the length of cycle ∆t (counted from the previous outburst). These parameters are listed in Table 1, where the first column gives the approximate JD for the mid-rise. Listed in the last row are data for the 1985 superoutburst (Smak and Waagen 2004). The unusually long duration of the preceding cycle (∆t = 290 d) is simply the time interval between the last recorded normal outburst and the superoutburst. In fact, however, it is highly probable that another outburst could have occurred somewhere during the interval JD 2446215-300 not covered by observations. If so, ∆t would be much closer to mean value of 110 days. 3. Mass Accreted during Outbursts The amount of mass accreted onto the white dwarf during outburst (or super- outburst) is calculated as ∆M = M˙ (Mv) dt (1) accr Z W1 where the M˙ = f (Mv) relation is obtained using system parameters of U Gem (including inclination) and assuming stationary accretion (for details see Smak 2002b). This requires three comments. First, that when calculating Mv = f (M˙ ) we assume that the radius of the disk during outburst is equal to the tidal radius: rd = rtid = 0.85rRoche . Secondly, that the assumption of stationary accretion may not be applicable to the situation during outbursts (particularly the narrow ones). To check this point we apply Eq. (1) to model light curves and find that values result- ing from Eq. (1) are actually lower limits to ∆Maccr . Thirdly, that our M˙ = f (Mv) relation includes the contribution from the spot. Therefore, in a situation with no enhancement in the mass transfer rate during outburst, this relation will give lower limits to M˙ and ∆Maccr . The resulting values of ∆Maccr are listed in the fifth column of Table 1. 4. The Mass Transfer Rate at Quiescence Needed in our further analysis will be the mass transfer rate in U Gem dur- ing quiescence. It was estimated earlier by several authors (e.g.,by Paczynski´ and Schwarzenberg-Czerny 1980). Using new data we redetermine it as follows. The Vol. 55 317 Table1 U Gem Outburst Parameters JD Vmax W1 ∆t ∆Maccr ∆Mtr hM˙ enhi 2400000+ days days /1023g /1023g /1017g/s Narrow outbursts 40657 9.4 3.5 81 1.29 0.88 1.36 42837 9.2 3.5 131 1.93 1.43 1.68 43563 9.3 5.0 129 2.58 1.40 2.72 43795 9.1 3.5 123 2.39 1.34 3.47 44238 9.6 4.5 97 1.38 1.06 0.84 44637 9.2 3.5 116 2.32 1.26 3.51 45043 9.3 3.0 99 1.47 1.08 1.49 45712 9.3 3.5 105 1.98 1.14 2.76 45952 9.5 3.5 103 1.22 1.12 0.31 47594 9.4 3.5 93 1.41 1.01 1.30 mean 9.3 3.7 108 1.80 1.17 1.95 Wide outbursts 39212 9.1 9.5 103 6.05 1.12 6.01 39579 9.1 10.5 111 6.56 1.21 5.90 42447 9.2 10.0 100 5.85 1.09 5.51 43170 9.2 9.5 115 5.09 1.25 4.68 43435 8.9 12.5 141 8.20 1.53 6.17 43956 9.0 12.5 161 8.60 1.75 6.34 44706 9.3 9.5 69 4.73 0.75 4.85 44944 9.0 10.5 89 8.85 0.97 8.68 45393 9.1 12.0 115 7.28 1.25 5.82 46056 9.2 10.0 105 5.71 1.14 5.28 mean 9.1 10.6 111 6.69 1.21 5.96 1985 Superoutbursts 46345 9.0 37.0 290 16.40 3.16 4.14 bolometric luminosity of the hot spot can be written as π 2 1 2 1 2 2 A Ls = η ∆V M˙ = η ∆v M˙ (2) 2 2 P where ∆V is the “impact velocity”, i.e.,the velocity of the stream relative to the outer parts of the disk; accordingly 1/2 ∆V 2 is the energy dissipation per 1 gram 2 of the stream material and ∆v = f (µ,r/rRoche) – its dimensionless equivalent (see Appendix in Smak 2002a); P is the orbital period and A – the radius of the or- bit. To calculate Ls as a function of M˙ we adopt system parameters of U Gem 2 (Smak 2001). In particular, for ∆v we adopt rd = 0.7rRoche , i.e.,a value which corresponds to the quiescence. 318 A. A. Included in Eq. (2) is the “efficiency” factor η ≤ 1 which represents the fraction of the available energy responsible for the luminosity of the spot. This factor ac- counts, in particular, for the effects of stream overflow (cf. Smak 2001). Adopting η = 1 we obtain an upper limit to Ls . The bolometric luminosity of the spot can be written also as σ 4 Ls = S Ts (3) where S is the surface of the hot spot and Ts – its effective temperature. The 2 spot’s surface is calculated as S = πsasbA , where sa = 0.04 and sb = 0.009 are the horizontal and vertical dimensions of the spot as determined from its eclipses (Smak 2001). With Ls = f (M˙ ) from Eq. (2) we now also have Ts = f (M˙ ). Using it, together with fluxes from Kurucz (1993) model atmospheres, we can calculate the luminosity of the spot in the V -band. Radiation from the hot spot is strongly non-isotropic. Using formulae given by Paczynski´ and Schwarzenberg-Czerny (1980) we have for the spot luminosity corresponding to the “hot spot hump” observed at inclination i 12 L (i,max) = (1 − u + usini)sinihL i (4) s 3 − u s where hLsi is the mean luminosity (discussed above) and u is the coefficient of limb darkening. In the case of U Gem with i=69◦ (Smak 2001) and u=0.6 Eq. (4) reduces to Ls(i,max) = 4.48hLsi. Using results obtained above we now calculate the absolute visual magnitude corresponding to the “hot spot hump” Mv(i,max) = f (M˙ ). Paczynski´ and Schwarzenberg-Czerny (1980), using photometric data from Paczynski´ (1965), obtained for the spot: V(i,max) = 14.76. With distance modu- lus (m − M) = 4.91 (Smak 2001) this gives Mv(i,max) = 9.85. Using this value and our theoretical relation Mv(i,max) = f (M˙ ) we obtain for the mass transfer rate: M˙ = 1.26 × 1016 g/s. We also obtain the effective temperature of the spot Ts ≈ 12000 K, i.e.,a value which looks quite reasonable. In further analysis we are going to use the value of M˙ given above but we must keep in mind that it was obtained with η = 1 and that – consequently – it is actually a lower limit to the mass transfer rate during quiescence. 5. Enhanced Mass Transfer during Outbursts The values of ∆Maccr obtained in Section 3, together with the mass transfer rate during quiescence (Section 4) can now be used to estimate the mass transfer rates during outbursts. Assuming that all material accumulated in the disk during quiescence ∆Mtr = M˙ ∆t is accreted onto the white dwarf we have: ∆Maccr = M˙ ∆t + hM˙ enhiW1 (5) Vol.
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