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A Binary Progenitor for the Type IIb Supernova 2011dh in M51

We perform binary stellar evolutionary calculations following the simultaneous evolution of both stars in the system to study a potential progenitor system for the Type IIb supernova 2011dh. Pre-explosion photometry as well as light-curve modeling have provided constraints on the physical properties of the progenitor system. Here we present a close binary system that is compatible with such constraints. The system is formed by stars of solar composition with 16 Msun + 10 Msun on a circular orbit with an initial period of 125 days. The primary star ends its evolution as a yellow supergiant with a mass of ~4 Msun, a final hydrogen content of ~3-5E-03 Msun and with an effective temperature and luminosity in agreement with the HST pre-explosion observations of SN 2011dh. These results are nearly insensitive to the adopted accretion efficiency factor beta. At the time of explosion, the companion star has an effective temperature of 22 to 40 thousand Kelvin, depending on the value of beta, and lies near the zero age main sequence. Considering the uncertainties in the HST pre-SN photometry the secondary star is only marginally detectable in the bluest observed band. Close binary systems, as opposed to single stars, provide a natural frame to explain the properties of SN 2011dh.


INTRODUCTION
Core-collapse supernovae (CCSNe) are the explosive end of massive stars with M ZAMS 8M ⊙ . There is a diversity in the spectroscopic and photometric properties of CCSNe which are mainly related to the ability of the progenitor to retain its outermost layers. Type II SNe, with clear H lines in their spectra, represents the case where a thick H envelope is kept before the explosion. Type Ib SNe, with no H lines but with clear He lines, have lost their H envelope but not the He layers. Finally Type Ic SNe, with no H and He lines in the spectra, represent a more extreme case where not only the the H but also the He envelopes are likely lost before the explosion. There are also transitional objects between these different types. One example is that of Type IIb SNe, which show H lines at early times but then the spectrum is transformed into that of typical SNe Ib (see Filippenko 1997, for a classification scheme). Type IIb, Ib and Ic objects are collectively called striped-envelope SNe (Clocchiatti et al. 1996).
Progenitor models of SNe IIb comprising a helium star surrounded by a very thin hydrogen-rich envelope (of 1 M ⊙ ) have been successful to explain the observed light curves (LC) and spectral features (Shigeyama et al. 1994;Woosley et al. 1994;Blinnikov et al. 1998). However, it is not clear which is the mechanism responsible for the removal of the outer envelope before the explosion. One possibility is strong winds that occur in massive stars with M ZAMS 25M ⊙ . Alternatively, in close binary systems (CBS) stars are expected to exchange mass providing an efficient mechanism to allow for the removal of outer layers. Currently, the binary channel is favored particularly for the case of SNe IIb (Eldridge et al. 2008;Claeys et al. 2011;Smith et al. 2011).
Additional support for the binary scenario in SNe IIb comes from the detection of a hot companion for the famous SN IIb 1993J (Maund et al. 2004). This was initially suggested by pre-explosion photometry (Aldering et al. 1994). The LC and evolutionary models of SN 1993J were also in favor of the binary channel (Nomoto et al. 1993;Podsiadlowski et al. 1993;Woosley et al. 1994). Some evidence for a companion was also reported for another SN IIb 2001ig (Ryder et al. 2006).
The Type IIb SN 2011dh was recently discovered in the nearby galaxy M51 attracting the attention of many observers because of its proximity and brightness. It was discovered almost immediately after explosion (Arcavi et al. 2011). It showed early radio and X-ray emission (Soderberg et al. 2012). Using pre-explosion images obtained from the HST archive Maund et al. (2011) and Van Dyk et al. (2011) detected a source at the location of SN 2011dh. They derived similar values of luminosity and effective temperature for pre-SN source. The object was consistent with a yellow supergiant (YSG) star with a radius R ≈ 270 R ⊙ and without any clear evidence of a companion star contributing to the observed spectral energy distribution (SED).
At present there is a controversy in the literature as to whether the YSG is the actual progenitor of SN 2011dh. Some authors have suggested that the exploding star should be more compact (Arcavi et al. 2011;Soderberg et al. 2012;Van Dyk et al. 2011) based on (1) a simple comparison between the early light curve (LC) of SN 2011dh and SN 1993J; (2) a discrepancy between the temperature derived from an early-time spectrum and that predicted by an analytic expressions for an extended progenitor; and (3) the large shock velocity derived from radio observations. Recently, we have performed a detailed hydrodynamical modeling of SN 2011dh using stellar evolutionary progenitors (Bersten et al. 2012). These models indicate that observations are compatible with a helium star progenitor of a mass near 4 M ⊙ surrounded by a thin hydrogen-rich envelope (≈ 0.1 M ⊙ ) with a radius of ≈ 200 R ⊙ (similar to that of the detected YSG star) that underwent an explosion with an energy of 8 × 10 50 erg that synthesized 0.063 M ⊙ of 56 Ni. Such large radius values are needed to reproduce the early light curve of SN 2011dh without contradicting the temperatures derived from the spectra. In addition, our hydrodynamical modeling rules out progenitors with He core masses larger than 8 M ⊙ , which corresponds to M ZAMS 25M ⊙ .
It is very difficult for a single star to reach these pre-SN conditions. The existence of a strong wind capable of removing most of the envelope requires a massive star of ≈ 25 M ⊙ or more (Heger et al. 2003;Georgy et al. 2009), which is in contradiction with the LC models. Moreover, in order to retain a thin hydrogen-rich layer, the mass loss rate would have to be on a very narrow interval. These facts strongly suggests that the progenitor of SN 2011dh should be a component of a binary system. However, a recent work by Georgy (2012) proposed that single YSG stars such as the one detected at the location of SN 2011dh are plausible SN progenitors. This is based on stellar evolution calculations of stars with main sequence masses of 12-15 M ⊙ under the assumption of an increased mass-loss rate several times above the standard values. However, no physical explanation is given for such an increase. Also note that a recent paper by Mauron & Josselin (2011) found a good agreement between modern determinations of mass-loss for RSGs and the standard mass-loss prescription (de Jager et al. 1988). Although, other mass-loss formulation as proposed by van Loon et al. (2005) point towards higher mass-loss rates but this prescription seems to be applicable only to dusty stars and gives a overestimates of the mass-loss rates for Galactic RSGs.
The aim of this work is to show the plausibility that the progenitor of SN 2011dh was part of a close binary system (CBS) with properties compatible with the pre-SN observations and the results of LC modeling. The observational properties of the remaining companion star are discussed in anticipation of future detections. Although we do not perform a complete exploration of the parameter space (stellar masses, initial orbital period, and mass-transfer efficiency β), we show that our results are robust if we consider moderate changes of the initial conditions.
The remainder of this paper is organized as follows. In Section 2 we present a brief description of our binary stellar evolution code paying special attention to the characteristics that enabled us to compute pre-SN models. In Section 3 we present the main results of this paper regarding the adopted binary configuration ( § 3.1), evolutionary calculations ( § 3.2) as well as the spectra of the components at the moment of the explosion ( § 3.3). In Section 4 we present a discussion of our results and finally, in Section 5 we provide some concluding remarks.

THE STELLAR CODE
In order to compute the evolution of the CBSs quoted above we shall employ a code similar to that described in Benvenuto & De Vito (2003), adapted for the case of massive stars. Briefly, this is a Henyey code that when the star reaches Roche Lobe Over Flow (hereafter RLOF) conditions it solves implicitly not only the whole structure of the donor star but also the Mass Transfer Rate (hereafter MTR)Ṁ 1 in a simultaneous, fully implicit way. Such a procedure has been found to largely improve numerical stability as compared to algorithms that compute the MTR explicitly (Büning & Ritter 2006), enabling us to reach pre-SN condition meanwhile the donor star is losing mass at an appreciable rate with a detailed, continuous and convergent sequence of stellar models. In detached conditions, the code works as a standard Henyey scheme.
In order to adapt the code to the case of massive stars we have incorporated several nuclear reactions from the compilation of Caughlan & Fowler (1988) and rewritten the difference equations to largely improve numerical stability. Also, we incorporated semiconvection following the diffusive approach presented in Langer et al. (1983) and first applied to massive stars by Langer et al. (1985). This formulation of diffusive semiconvection depends on an efficiency parameter α SC for which we assumed α SC = 1 as in Yoon et al. (2010). In this paper we shall ignore the effects due to overshooting and rotation.
In semidetached conditions we computeṀ 1 following the prescription given by Ritter (1988) where R 1 is the radius of the donor star; R L , the radius of a sphere with a volume equal to the corresponding Roche lobe is computed following Eggleton (1983); M 0 > 0 is a smooth function of M 1 and M 2 whereas H p = −dr/d ln p (where r and p are the radial coordinate and pressure respectively) is the photospheric pressure scale height. For further details see Ritter (1988). In detached conditions we consider stellar wind following de Jager et al. (1988). As we shall discuss in § 3, we consider different accretion efficiencies, β, of the material transferred by the donor to the secondary, i.e.Ṁ 2 = −βṀ 1 , and evolve the orbit as described in Benvenuto & De Vito (2003).
After computing the evolution of the donor star, we evolve the companion star taking into account the accretion rate it receives from the donor as described in Neo et al. (1977). We do not consider mass loss from the accreting star. As we ignore any effect of the secondary star on the donor one other than imposing a limit on its volume, this is an usual assumption in this type of problems.
It is well known that in CBSs like those we are interested in here, the material accreted by the secondary star may have a mean molecular weight higher than the corresponding to its outer layers. This may lead to an unstable situation that induces the so -called thermohaline mixing (Kippenhahn et al. 1980). In the present version of our code we have not included thermohaline mixing yet. In any case, it is worth to remark that Stancliffe & Eldridge (2009) have shown that ignoring thermohaline mixing has a minor effect on the evolutionary track of secondary stars of CBSs similar to those studied here. Therefore, we expect that the main conclusions of this work not to be affected by neglecting this phenomenon.

THE BINARY MODELS FOR SN 2011DH
3.1. The initial configuration The broad-band HST pre-explosion photometry of the SN 2011dh (Maund et al. 2011;Van Dyk et al. 2011) and the light curve modeling (Bersten et al. 2012) impose strong constraints about our election of the binary parameters, mass of the primary, of the secondary and the initial period. Here we briefly discuss the motivations of our election of these parameters before we present our results.
If the object detected in the pre-explosion image is indeed the progenitor of SN 2011dh and it belongs to a binary system, the primary (donor) star needs to have a luminosity (L) compatible with the value derived by Maund et al. (2011) andVan Dyk et al. (2011) for the progenitor candidate, i.e. log L/L ⊙ = 4.92 ± 0.2. This luminosity is an indication of the He core mass at the moment of the explosion which in turn is related with the mass of the star on the main sequence (M ZAMS ). Maund et al. (2011) derived M ZAMS = 13 ± 3 M ⊙ comparing the luminosity with the end points of the evolutionary tracks of single stars. Note that they did not use the color information of the progenitor to derive this mass because uncertainties are expected in the color due to unknown mass-loss history. Meanwhile Van Dyk et al. Here we adopt an initial mass of 16 M ⊙ for the donor star that is well within the ranges provided in previous studies.
After assuming a mass value for the donor star, we still have to consider the mass of the secondary star as well the orbital period of the binary. Our choice should be guided by the fact that pre-explosion observations indicate that the observed portion of the spectrum is compatible with a single source. Obviously, the secondary has to be less massive than the donor star but we have to distinguish between two cases: i) the mass ratio is close to one and ii) the mass ratio appreciably differs from one.
Let us consider the case i): If the masses of the stars differ in (say) few tents of solar mass, the secondary star would be able to exhaust core hydrogen before explosion. This object would receive material coming from the donor star when it is on the Hertzsprung gap where the shell nuclear burning around the core takes place. Calculations available in the literature as well as our own test (see § 4) indicate that, after accretion, such object appears as an overluminous B supergiant with a T eff in between that of the observed YSG and that of the ZAMS (see, e.g., Fig. 5 of Claeys, et al. 2011 and our Fig. 15). In this case some evidence of the secondary should have been detected in the HST pre-explosion photometry as in the case of SN 1993J.
Case ii) results more natural. If the secondary star has a mass appreciably lower than that of the donor, it will be still undergoing core hydrogen burning at the moment of the explosion of the primary star. Therefore, at the moment of the explosion and in the HRD, we expect the secondary to be close to the ZAMS. The object will remain hot and will emit most of the flux in the UV. As it is well known the more massive the object the greater its luminosity on the ZAMS and therefore the greater its effect on the pre-explosion photometry. Thus, the mass value chosen for the secondary star should be low enough to have remained almost undetected. Note, however, that if the mass of the secondary is much lower than 10 M ⊙ , the Kelvin-Helmholtz timescale increases appreciably and it is very likely that the system reaches common envelope conditions. Therefore, we adopt a mass of 10 M ⊙ for the secondary.
Even with a mass of 10 M ⊙ if the secondary object were able to undergo a conservative mass transfer and the primary star ends its evolution with a mass of ≈ 4 M ⊙ as required by LC modeling, the secondary would end its evolution with ≈ 22 M ⊙ on the ZAMS. This would produce a very bright object that may not be compatible with the pre-SN observations. One possibility that we will explore in the next section is that the secondary captures a fraction β of the material transferred, therefore its final mass will be of ≈ 10 + 12 β M ⊙ . Note that the accretion efficiency, β, is one of the most uncertain parameters in binary stellar evolution. Another parameter usually employed in the treatment of orbital evolution in binaries is the specific angular momentum α of the material lost by the system in units of the angular momentum of the primary star. We shall assume α = 1 throughout this paper.
Regarding the initial period, this has been evaluated in order for the pre-SN donor star to fall inside the error box given by the L and T eff estimated for the progenitor candidate of SN 2011dh. Suppose that the donor star is losing mass by RLOF at the moment of the explosion, i.e. that the the size of the Roche Lobe is approximately equal to the radius of the donor star. This radius can be determined using log L/L ⊙ = 4.92 ± 0.2 and log T eff = 3.78 ± 0.02 (Maund et al. 2011;Van Dyk et al. 2011) leading to values of ≈ 270 R ⊙ . If the initial masses are 16 + 10 M ⊙ and the final masses are 4 + 12 M ⊙ , the final orbital semiaxis is ≈ 900 R ⊙ and the final period at the moment of the explosion can be estimated to be ≈ 800 days. Finally, the initial period can be calculated using Eqs. 6-8 of Podsiadlowski et al. (2002) which relates the initial and final orbital semiaxes as a function of the initial and final masses of the system. This leads to initial periods of ≈ 120 days. Note that if the luminosity is due to the internal structure of the star, then at pre-SN conditions a given orbital period will correspond to a given effective temperature: the larger the period the lower the effective temperature. In the next section we analyze in detail a system with an initial period of 125 days consistent with this first approximation. Other values are discussed in section 5. with an initial period of 125 days assuming fully non -conservative mass transfer (β = 0.00). Solid black line represents the evolutionary track of the donor star. Dots along it indicate the mass of the star during the RLOFs. The corresponding labels are in solar mass units. The star ends its evolution with a mass of 4.034 M ⊙ with an effective temperature and luminosity compatible with the data observed for the object at the position of the supernova SN2011dh. Meanwhile the donor star evolves from the ZAMS to pre-SN conditions, the companion star suffers a much slower evolution. Its evolutionary track is depicted with a solid blue line and ends with a dot representing the conditions attained at the moment of the explosion of the primary. For comparison, the ZAMS corresponding to objects of the same composition is shown in dashed line.

Evolutionary Results
In the previous section we discussed our election of the binary parameters adopted to study a possible progenitor for SN 2011dh. Here we present our results for a CBS of solar-composition stars with masses of 16 M ⊙ + 10 M ⊙ on a circular orbit with an initial period of 125 days. As stated in § 3.1, we analyzed different values of the masstransfer efficiency, β = 0.00, 0.25, 0.50, 0.75, and 1.00. We computed the evolution of both stars starting with ZAMS models up to core oxygen exhaustion. The main results of these calculations are presented in Figures 1 to 12. Notice that the evolutionary tracks corresponding specifically to the cases β = 0.25 and 0.75 are provided only in the electronic edition.
As an extreme case, we show in Fig. 1 the evolution of the donor and companion stars assuming β = 0.00 (fully non -conservative mass transfer). This CBS undergoes class B mass transfer: the donor star fills its Roche lobe with a mass of 15.54 M ⊙ well after core helium ignition (the central abundance of helium at the onset of the first RLOF is X He = 0.32). With respect to the stellar mass, this is the main RLOF because the donor star detaches from its lobe when has only 4.54 M ⊙ . Remarkably, the RLOF takes only 7.6 × 10 4 y, which implies a mean MTR Ṁ of Ṁ = 1.44 × 10 −4 M ⊙ /y. However the maximum mass transfer rateṀ max is of M max = 1.90 × 10 −3 M ⊙ /y (see below for further details on MTRs). At detaching from its Roche lobe, the donor star is still undergoing core helium burning and has increased its central abundance due to semiconvective mixing (X He = 0.39). The physical agent that sets the end of the RLOF is the outer layers hydrogen abundance X H S that fallen down from its initial value of X H S = 0.70 to X H S = 0.49. Thus the stellar envelope is no longer able to support its very large radius (192 R ⊙ ), and starts a fast contraction performing a blue-wards loop on the HR diagram. During this loop core helium is exhausted. Soon, due to semiconvective mixing and nuclear shell burning the star undergoes a second and very brief RLOF followed by another (smaller as compared to the previous) blue-wards loop. Finally, the star swells and again goes through a RLOF up to its final explosion. During this RLOF the star undergoes carbon, neon, oxygen and silicon core burning (we did not computed the silicon burning stage). During this final RLOF the mass transferred from the donor is a relatively small amount of 0.27 M ⊙ on 3.57×10 4 y ( Ṁ = 7.95×10 −6 M ⊙ /y anḋ M max = 2.92 × 10 −5 M ⊙ /y). Notice that these MTRs are far lower than the corresponding to the initial RLOF.
The evolution of the central point of the donor star in the temperature-density plane is presented in Fig 2. There, it can be clearly noticed the nuclear activity present in the central part of the star during each RLOF. It is remarkable that during the first RLOF central density and temperature remain almost constant.  In this case of β = 0, the secondary star does not accrete any material and evolves as it were an isolated object. As the main sequence lifetime of a 10 M ⊙ star is far longer than that corresponding to the donor star, the companion star suffers from a very small excursion in the HRD up the moment of explosion (see Fig. 1). Let us here mention that the characteristic lifetime of isolated stars of 10 M ⊙ and 16 M ⊙ is of 23.018 Myr and 12.284 Myr respectively.
The evolution of the components of the CBS for the cases of β = 0.25, 0.50, 0.75, and 1.00 is shown in Figs. 3-6 respectively (Figs. 3 and 5, corresponding to the cases of β = 0.25 and 0.75 respectively, are available in the electronic version of this paper). An inspection of these figures is sufficient to realize that the evolution of the donor star is almost independent of the value of β while the secondary is strongly dependent on it. In Fig. 7 we show the evolutionary tracks of the donor star corresponding to the five values of β considered in this paper. They are remarkably similar. This behavior resembles the results found in the case of low mass CBSs (De Vito & Benvenuto 2012).
In Fig. 8 we show the evolutionary tracks of the companion, accreting star as a function of β. There, for comparison, we also show the ZAMS corresponding to the initial composition of these stars. For the cases of β > 0 the final position in the HRD for the accreting star is somewhat hotter and overluminous than objects of the same mass on the ZAMS. This is partially due to the fact that we have neglected thermohaline mixing in our calculations. Note that in all considered cases, the companion star does not fill its Roche lobe and no contact configuration is found. Thus, the CBSs studied here do not undergo any common envelope episode.
The evolution of the central point of the accreting star  is shown in Fig. 9. Notice that the excursion of these objects in the density -temperature plane is by far smaller than the one corresponding to the donor stars. Accreting stars are not able to exhaust central hydrogen in the time spent by the donor star to reach pre-SN conditions The evolution of the MTR from the donor star is pre-   In sharp contrast with the case of the donor star, the evolution of the secondary star is strongly dependent on the value of β. We show the ZAMS with dashed line on which we have indicated some values of mass (in solar units). For the cases of β > 0 the final position in the HRD for the accreting star is somewhat hotter and overluminous than objects of the same mass on the ZAMS. sented in Fig. 10. The only difference in the MTR evolution as a function of β is in the time spent by the star from the end of the first RLOF to the onset of the second one which is minimum for β = 0.50. All the cases predict a third mass-transfer episode that lasts until the end of the evolution and whose MTR differs markedly from constant. Therefore any inference on the mass of the envelope of the donor star at the time of the explosion should take into account the appropriate mass loss in this phase.
By analyzing the evolution of the MTR it is possible to understand the evolution of the companion star. During the first RLOF, MTR reaches very high values (Ṁ 10 −3 M ⊙ /y). If the secondary star is able to efficiently accrete (β > 0.1) the material coming from the donor star, it may swell appreciably, reaching low effective temperatures (see Figs. 3-6). For the range of initial periods considered here (≈ 125 d) this happens during the core helium burning of the donor star. Near the end of the first RLOF, the MTR falls down and the secondary star evolves (in the HRD) towards the ZAMS being overluminous. Thus, it has to evolve to lower luminosities, compatible with its internal nuclear energy release, keeping close to the ZAMS.
Later on, the donor star undergoes two further RLOF episodes, reaching pre-SN conditions on the last of them. While the MTR during the first RLOF is large enough to force the secondary star to swell, our calculations indicate that this is not the case in the second and third RLOFs. During these RLOFs, MTR is about two orders of magnitude lower compared to the case of the first Fig. 9.-The evolution of the central temperature as a function of the central density for the secondary, accreting star. This is the equivalent to Fig. 2 which corresponds to the central evolution of the donor star but, in any case we should remark that the scale is completely different because the secondary star is still burning hydrogen during its evolution up to the explosion of the donor star.
RLOF. So, the secondary star remains close to the ZAMS until the explosion of the donor star.
The evolution of the orbital period is not very sensitive to the value of β, as can be seen in Fig. 11 (see also Table 1). This is not surprising, since Podsiadlowski et al. (2002) showed that the evolution of the orbital period of CBS depends only slightly on the accretion efficiency. Their analytic prediction for the evolution of the period as a function of the initial and final masses and the β parameter fit almost perfectly with our numerical results.
An important result of our calculations is that despite of the fact that the system is in semi -detached conditions at the moment of explosion, the donor star retains an appreciable amount of hydrogen in its outermost layers as it is shown in Fig. 12. The total hydrogen content is again almost independent of the value of β and enough to account for the H lines observed in the spectra of SN 2011dh (Dessart et al. 2011). While a full exploration of the total hydrogen content of donor stars at pre-SN conditions for CBSs in general is beyond the scope of the present paper, this result strongly indicates that the total hydrogen content should be a function of the initial orbital period: the larger the period the larger the hydrogen content. In this sense, the progenitor of SN 2011dh may be considered as a transition object.
For completeness, we present in Table 2 the main characteristics of the pre-SN object and in Table 3 those properties corresponding to the accreting, secondary star.
In summary, we have shown that a system with 16 M ⊙ + 10 M ⊙ and an initial period of 125 days, independently of the adopted value of β, predicts that the primary star ends its evolution within the region of the H-R diagram    Note.
-Form left to right we tabulate the value of β; the orbital semiaxis and the orbital period at the moment of explosion. For all these cases the initial period is of 125 d and the orbital semiaxis is of 311.5 R ⊙ .
compatible with the pre-SN photometry of SN 2011dh (Maund et al. 2011;Van Dyk et al. 2011). Furthermore, at the end of the evolution the primary star has a mass of ≈ 4 M ⊙ and a hydrogen content of 3 − 4 × 10 −3 M ⊙ , which is consistent with the LC modeling (Bersten et al. 2012) and the SN IIb classification of SN 2011dh.

Pre-Supernova Spectral Energy Distribution
Our model calculations predict that the primary star ends its evolution with properties (L and T eff ) compatible with those inferred for the pre-explosion object located at the SN position (Maund et al. 2011; Van Dyk et al. Note. -Form left to right we tabulate the value of β; the mass; effective temperature; luminosity; radius, total amount of hydrogen; and the age of the pre-SN. 2011). At the same time, the secondary star has a luminosity that, depending on the value of β, could be comparable with that of the primary star and therefore produce a detectable effect on the pre-SN spectral energy distribution (SED). In all cases the secondary star is found to be significantly hotter than the donor star. Indeed, for high enough effective temperatures, the effect of the secondary would only be appreciable in the bluest available photometric band.
We thus study here the effect of the secondary on the SED of the system for different values of β, and compare this with the HST pre-explosion photometry. To calculate the SED for each star of the binary system as well as the composed SED we used atmospheric models for solar composition provided by Kurucz (1993). The model spectrum of each star was obtained by linearly interpolating at the values of T eff and surface gravity (g) given in Tables 2 and 3. The observed fluxes were computed by multiplying the models by (R/d) 2 where d is the distance to M51 assumed to be 7.1 Mpc (Takáts & Vinkó 2006). The sum of the SEDs was used to compute synthetic photometry through the HST transmission filters 1 Fig. 13 shows the resulting SED of each star and their sum for β = 0 and 1. Mean synthetic and observed fluxes are compared for all bands. Observed fluxes were obtained from the tabulated magnitudes given by Van Dyk et al. (2011) and zero points in the Vega system calculated using the Alpha Lyrae SED provided by Bohlin (2007). Note that the contribution of the secondary star is significant only for the bluest observed band, F336W. The increase in the F336W flux due to the presence of the secondary is of 16%, 22%, 32%, 45%, and 62% for the cases of β = 0.00, 0.25, 0.50, 0.75, and 1.00 respectively.
For the rest of the observed HST bands the contribution of the secondary is < 6%, i.e. for wavelengths λ ≥ 4000Å the spectra is completely dominated by the light coming from the donor, pre-SN star. In this wavelength range the available observations on four photometric bands pose no constraint on the properties of the accreting star. On the contrary, the bluest filter, with a maximum transmittance at λ ≈ 3400Å partially detects the red tail of the spectrum of the accreting star.
For the filters with transmittance at λ ≥ 4000Å the agreement between calculations and observations is very good, especially considering that we have not adjusted Note.
-Form left to right we tabulate the value of β; the mass; effective temperature; luminosity; radius; and the central values of density, temperature, and hydrogen abundance at the moment of explosion. Fig. 13.-The spectra of the donor and accreting stars (shown with red an cyan lines respectively). Gray line represents the addition of both spectra which, in turn, should represent the observed one. We show the results corresponding to fully-non conservative and conservative cases (β= 0 and 1 respectively). The mean synthetic (black squares) and observed fluxes (red squares) in each bandpass are included in the figure. The secondary star is significantly bluer than the primary at the time of explosion. Its contribution to the total flux is non-negligible only for the bluest observed band, F336W. See § 3.3 for further discussion. any parameter. For the case of the bluest filter, F336W, the contribution of the secondary to the total flux is not negligible. If we consider the measurement uncertainty in this band we find that the secondary is detectable only at the 2-σ level in the most extreme case (β = 1). The contribution is further decreased to the 0.6-σ level when completely non-conservative mass accretion (β = 0) is considered.
Remarkably, irrespective of the value of β, at the moment of the explosion, the secondary star is so hot that its light has been barely detected. Thus, quite unfortunately, the characteristics of the secondary star are very poorly constrained by the presently available data.

DISCUSSION
In the previous section we have shown that a properly chosen binary configuration can explain very well the proposed YSG progenitor of SN 2011dh. Our models also predict that the total and hydrogen masses of the donor star at the moment of the explosion are consistent with the results of LC modeling and the SN IIb classification.
A complete exploration of the parameter space of initial stellar masses and orbital periods is not the scope of this paper. Nevertheless, we briefly test that our results are robust if we consider moderate changes of the initial parameters. For example, Fig. 14 shows the sensitivity of the evolutionary track of the primary star on small variations of the initial period, P i between 100 and 200 days, for the same configuration presented in the previous section, i.e. 16 + 10 M ⊙ , and β = 0.5. Within such range of initial periods the donor star ends its evolution as a YSG close to the region of the HRD allowed by the pre-SN photometry. The evolutionary track of the secondary is not shown in Fig. 14 because it is not sensitive to the initial period in the range under study.
The effect of changes in the mass of the secondary star on the binary evolution is shown in Fig. 15. Three values were considered, M 2 = 15, 15.25 and 15.50 M ⊙ . In all the cases, we assumed a value of β = 0.5 and a mass of the primary star of 16 M ⊙ as in our previous models. The initial period was modified to make the endpoint of the donor star match the region allowed by the pre-SN photometry. Following the criteria described in section 3.1, the adopted initial period for this test was of 50 days. From the figure, it is clear that only for the case of M 2 = 15.5 M ⊙ , where the mass ratio is closest to one, the secondary star moves appreciably away from the ZAMS at the moment of the explosion of the primary. This is because the secondary has exhausted its hydrogen core before the beginning of the first RLOF. Consequently, the secondary ends with a redder color than that of lower-mass stars and it is expected to contribute significantly to the observed pre-SN photometry. Indeed, the flux of the secondary in the bluest observed band, F336W, is 2.5 times larger than that of the primary star, which would lead to a 8.5 σ detection. For the rest of the HST bands the contribution of the secondary is within 6-30%. While not compatible with the case of SN 2011dh, this configuration may be applicable to SN 1993J whose pre-SN observations showed evidence of a companion star (Stancliffe & Eldridge 2009).
Secondary stars of slightly lower initial masses (15 and 15.25 M ⊙ ) remain near the ZAMS and end as hot stars of similar luminosity to the primary. Stars of masses between 10 and 15 will also remain as blue objects near the ZAMS. Because of the high effective temperature most of the flux from the secondary is emitted in the UV, away from the bandpasses of the pre-explosion imaging. However, if the luminosity is high enough, the secondary may produce a detectable effect in the optical range. For instance, with masses of 15 and 15.25 M ⊙ , the flux of the secondary in the F336W band would be comparable to that of the primary star. The level of detection of the secondary in these cases would be close to 3.5 σ. The final luminosity of the secondary also depends on the assumed value of β. Lower initial masses could result in similarly high luminosities with values of β close to unity. However, if the secondary star has an initial mass of 15.50 M ⊙ , at the supernova event it will have at much lower effective temperature. This is not compatible with the available observations of the progenitor of SN 2011dh. Unfortunately, it is not possible to break such degeneracy based solely on the available pre-explosion photometry. Future observations of the possible secondary star after the SN fades from sight can shed light on this matter.
The initial mass of 16 M ⊙ for the primary star leads to a progenitor with the right characteristics as derived from pre-explosion photometry, LC modeling and spectral classification. Therefore, our choice of initial masses and orbital period is by no means unique but it allows to prove that a CBS is a plausible progenitor for SN 2011dh and other SNe IIb. Moreover, the right progenitor properties are achieved in a self-consistent manner and independently of the detailed initial conditions.
In the past few years, some progenitors of SNe II have been associated with YSG stars, e.g. Type IIP SN 2008cn (Elias-Rosa et al. 2009), Type IIL SN 2009kr (Fraser et al. 2010;Elias-Rosa et al. 2010), and the SN studied here. The explosion of a YSG is not compatible with the theoretical prediction of single stellar evolution. Motivated by this apparent discrepancy and the lack of evidence of a companion for SN 2011dh, Georgy (2012) studied the effect of an increased mass-loss rate on the final properties of stars with initial masses of 12-15 M ⊙ . Assuming rates several times higher than the standard values, they found that it was possible to explain the explosion of single stars of relatively low mass in the yellow area of the HRD. In particular, the proposed scenario could explain the progenitor of SN 2011dh. However, no physical explanation was given for such an increased mass-loss process.
Note that the evolutionary tracks of isolated stars are strongly dependent upon the details of mass loss. In this sense, explaining the position of the progenitor of SN 2011dh in the HRD would require some degree of fine tuning. The binary scenario instead provides a selfconsistent picture that naturally explains why the star remains as YSG for long periods of time and until the explosion. In the case of CBS evolution we find that, irrespective of the mass transfer efficiency, the donor star undergoes a final RLOF before igniting carbon and so it is still transferring mass to the companion at the moment of explosion. During the final RLOF, the donor star transfers a small amount of material. So, the orbit and its Roche lobe enlarge very little meanwhile the donor star tends to swell as a consequence of nuclear shell burning. This precludes the donor star to attain lower effective temperatures and makes it evolve to higher luminosities in a way equivalent to the evolution of giant stars with extended outer convective zones. In any case, the observed effective temperature of the proposed progenitor of SN 2011dh strongly indicates the initial orbital period, but no other parameter has to be adjusted for the pre-SN object to fall inside the observational error box. The YSG nature of the progenitor is thus a direct consequence of close binary evolution.
Recently Chevalier & Soderberg (2010) suggested a division of SNe IIb into compact (cIIb; R ∼ 10 11 cm) and extended (eIIb; R ∼ 10 13 cm) subtypes essentially based on radio LC properties. Compact objects were proposed to have smaller hydrogen masses, roughly below 0.1 M ⊙ . Claeys et al. (2011) used this criterion and their own CBS evolutionary code to analyze the range of periods (for P i > 1000 days) and initial masses needed to produce extended SNe IIb. However, our calculations show that it is possible to have an extended progenitor (R ≈ 250 R ⊙ ) with a H mass of < 0.1 M ⊙ . Therefore, if the cIIb and eIIb subtypes correspond to physically distinct progenitors, the division criterion may need to be revised. In addition, Yoon et al. (2010) also analyzed the space of parameters in CBSs to produce Type Ib/Ic SNe using very different initial periods of 8 days, as compared with the ones adopted here. They found that some of their models predict a thin hydrogen layer of 0.01 M ⊙ with a compact structure. This channel of production of SNe IIb is different from the one we have presented and leads to explosions far away from the YSG regime.

CONCLUSIONS
With the aim of providing a description of the progenitor of SN 2011dh, we have studied the evolution of close binary systems of solar composition stars with masses of 16 M ⊙ + 10 M ⊙ . We considered an initial period of 125 days and different efficiencies (β) of the mass transfer process. We followed the simultaneous evolution of the donor and accreting stars from the zero age main sequence up to the oxygen core exhaustion of the donor. We found that the donor star, independently of β, ends its evolution with effective temperature and lu-minosity consistent with the YSG object detected in the HST pre-SN photometry. The exploding star has a mass M ≈ 4 M ⊙ , a radius R ≈ 250 R ⊙ and an outermost layer containing 3−5×10 −3 M ⊙ of hydrogen. This is generally consistent with the type IIb classification and the results of LC modeling of SN 2011dh by Bersten et al. (2012). These results are a natural consequence of the close binary evolution and require no external adjustment of any physical condition.
Regarding the accretion efficiency, β, we found that (1) the evolution of the donor star is almost independent of β while the secondary strongly depends on it, and (2) the evolution of the orbital period, the MTR and the total hydrogen content are almost independent of the value of β.
Our calculations indicate that the donor star is lossing mass at the moment of the explosion with rates that differ markedly from constant. Inferences on the mass of the donor star at the time of the explosion should take into account the appropriate mass loss in this phase. We also found some indication that the total hydrogen content may be a function of the initial orbital period with larger period producing a larger the hydrogen content. A more detailed study of this point is left for future work.
Note that the structure of the donor star at the moment of the explosion is consistent with an extended SN IIb but with very little H mass (< 0.1 M ⊙ ).
We analyzed the effect of the secondary star on the observed HST pre-explosion photometry. For all the values of β, at the moment of the explosion of the donor, the secondary star is still near the ZAMS. This is a direct consequence of our assumption that the object has a mass appreciably lower than that of the donor. The effective temperature of the companion is far higher than that of the donor with values within of 22 to 40 thousand Kelvin. Thus, the largest contribution to the flux of the system from the secondary is in the bluest observed band, F336W, producing a marginal detection of 0.6-2σ level depending of the value of β. Unfortunately, the available HST pre-SN observations are not very suitable to constrain the properties of the secondary.
The ultimate proof of the binary nature of SN 2011dh must come from the possible detection of a very hot star once the SN light fades enough. This situation would be similar to what occurred with SN 1993J but with different properties of the companion. In any case, we should remark that detecting the companion star of SN 2011dh would provide valuable information on the efficiency of the mass transfer process and evolution of massive CBSs in general.
OGB wants to thank Prof. Juan Carlos Forte for his help in getting funds that enabled him to visit the IPMU. The funds were provided by a PIP 712 of the Comisión de Investigaciones Científicas y Técnicas (CONICET), Argentina. This research has been supported in part by the Grant-in-Aid for Scientific Research of MEXT (22012003 and 23105705) and JSPS (23540262) and by World Premier International Research Center Initiative, MEXT, Japan.