A fallback accretion model for the unusual type II-P supernova iPTF14hls
The Intermediate Palomar Transient Factory reported the discovery of an unusual type II-P supernova iPTF14hls. Instead of a 100-day plateau as observed for ordinary type II-P supernovae (SNe), the light curve of iPTF14hls has at least five distinct peaks. The effective temperature of iPTF14hls is roughly constant at 5000-. The very slow evolution of the optical spectra, combined with the duration of one individual peak in the light curve, implies a massive ejecta. In this paper we propose that the multi-peaked light curve of iPTF14hls is a result of intermittent fallback accretion. Detailed modeling indicates that the total fallback mass is , with an ejecta mass . We find the third peak of the light curve cannot be well fit by the fallback model, indicating that there could be some extra rapid energy injection. We suggest that this extra energy injection may be a result of a magnetic outburst if the central object is a neutron star. It is found that this burst lasted for days with a total burst energy . The above results indicate that the progenitor of iPTF14hls could be a massive red supergiant.
Recently, the discovery of an unusual supernova (SN), iPTF14hls, was reported by Arcavi et al. (2017). iPTF14hls was first discovered in band on September 22, 2014 UT (Arcavi et al., 2017). Before its discovery, the position of iPTF14hls was not monitored for approximately 100 days. At beginning, astronomers did not pay much attention to iPTF14hls during its decline in brightness. Only when iPTF14hls began to rebrighten after about 100 days since its discovery were intense multiband observations deployed. iPTF14hls is at a redshift of .
Although identified as a type II-P SN according to its spectroscopic features, iPTF14hls is very unique among currently discovered SNe. The light curve of iPTF14hls lasts for more than 600 days and has at least five distinct peaks, while an ordinary type II-P SN has a 100-day plateau in brightness. The spectral evolution of iPTF14hls is 10 times slower than typical SNe II-P (Arcavi et al., 2017). The photospheric velocities measured by Fe ii 5169 stay at a constant value of .
Arcavi et al. (2017) analyzed several possible theoretical models and found that none of these model can account for the exotic light-curve behavior. However, Dessart (2018) proposed that the magnetar model can fit the light curve, while Soker & Gilkis (2018) explained iPTF14hls as a common-envelope jets SN. Chugai (2018) and Woosley (2018) discussed the models that might explain the light curve and spectral features.
Here we suggest that the multiple peaks in the light curve of iPTF14hls could be powered by intermittent fallback accretion of the SN ejecta. In a successful SN, the material remaining bound could fallback and eventually accrete onto the central object. Accretions onto compact objects (black holes or neutron stars) are usually accompanied by powerful outflows (Mirabel & Rodríguez, 1998; Fender et al., 2004), which can carry away about 10% of the gravitational binding energy of the fallback material. Such powerful outflows can aid the explosion of the SN, and on the other hand, a fraction of this energy would be thermalized to power a bright light curve (Dexter & Kasen, 2013).
2 The fallback accretion model
To account for the multiple peaks in the light curve of iPTF14hls, we propose that the accretion is episodic. Such episodes are not rare in astrophysics. For example, episodic accretion may be caused by instabilities of disks around protostars (Sakurai et al., 2016; Küffmeier et al., 2018), or by knotty jets in young protostellar disks (Vorobyov et al., 2018).
The material accreted at early times comes from the slowly moving inner ejecta. This phase is quickly followed by the long-term accretion (Dexter & Kasen, 2013). Because the early rising phase is missing in the light curve of iPTF14hls, we will model the light curve only by the law.
The outflow energy is , where is the mass accretion rate at the fallback radius, while (Dexter & Kasen, 2013). It should be stressed that is not the mass accretion rate onto the compact object because a large fraction of the accretion flow is channeled as an outflow. The net accretion rate is usually only of . Apart from thermalizing the SN ejecta, the outflow can also accelerate the ejecta.
We use the method outlined in Wang et al. (2016) to calculate the light curve and the evolution of the photospheric velocities. In our model the photospheric radius is at the position outside of which the optical depth is equal to (Wang et al., 2016). The acceleration of the ejecta by the energy injection has also been taken into account by this model. The energy input is
where takes the following expression
Here is the mass fallback rate at time when the th fallback episode begins.
3 The results
We use the bolometric luminosity data provided by Arcavi et al. (2017). For the observational data during which bolometric luminosity cannot be constructed because of the missing of multiband data, we adopt a bolometric correction closest in time to the data where bolometric data are available. In Figure 1 we show the bolometric data obtained by integrating multiband in dark cyan, while those obtained by applying a bolometric correction in green.
We neglect the possible contribution of Ni and Co to the light curve of iPTF14hls. The SN explosion would have surely synthesized some amount of Ni. However, because of the finite lifetimes of Ni () and Co (), such contribution is only limited to the first since explosion, which were largely missed by the observation. Because iPTF14hls is hydrogen-rich, we take the electron Thomson scattering opacity (e.g., Moriya et al., 2011; Chatzopoulos et al., 2012), which is suitable for fully ionized material with solar metallicity.
The fitting results, including the light curve and photospheric velocity evolution, are shown in Figure 1, with fitting parameters listed in Table 1. To give a decent fit to the light curve, seven episodes are needed. In Figure 1 we mark as vertical blue ticks. The explosion date is before the first observational data point.
Notes. is in units of . The accretion rates at fallback radius are in units of , while are in units of since SN explosion. In this fit we fixed . Because of the lack of observational data between the third and fourth peaks, cannot be accurately constrained, so is because of the missing of observational data around the first peak.
Figure 1 shows that the fallback accretion model gives a reasonably good fit to both the light curve and velocity evolution of iPTF14hls. However, the third peak in the light curve cannot be fitted. Such a steep peak require a very rapid energy release rate. This may suggest some activity in the central compact object. At such late times () since explosion, the energy may be released by a magnetic outburst (Gavriil et al., 2002; Rea et al., 2009, 2012) if the central object is a neutron star. Indeed, stellar evolution model predicts that a single star with initial masses between and will explode as an SN II-P, leaving behind a neutron star remnant (Heger et al., 2003).
To quantify the outburst power, we assume a power-law injection
followed by a rapid shutoff of the outburst
Here and are the times at which the outburst begins and ends, respectively; and are the durations for the rise and fall of the outburst, respectively. Obviously, . We set in Equation during the fitting. This power exponent does not result from the fitting constraints but was appropriately selected. To give a good fit to the light curve, we found . The fitting parameters for the outburst are listed in Table 2, with the resulting light curve depicted in Figure 1 as dashed lines. It can be seen that the model including a magnetic outburst can fit the light curve very closely.
From Table 2 we see that the outburst lasted for , and released in total. This is in accordance with observations, which show that some X-ray pulsars may experience sporadic giant X-ray outbursts lasting weeks to years followed by a long-term quiescence (Gavriil et al., 2002; Kaspi et al., 2003; Rea et al., 2012; Cusumano et al., 2016).
4 Discussion and conclusions
To date, many SNe were found to be double-peaked (Arnett et al., 1989; Richmond et al., 1994; Mazzali et al., 2008; Nicholl et al., 2015; Nicholl & Smartt, 2016), in which case the first short-lived peak has been attributed to shock cooling (Piro, 2015; Vreeswijk et al., 2017; Wang et al., 2017b), although sometimes the cooling peak could merge with the second main peak (Wang et al., 2017a). The first peak in the light curve of iPTF14hls is unlikely the result of shock cooling because that would require a very massive and extended envelope.
Because of the lack of observational data between the third and fourth peaks of the light curve, and also the missing of observational data around the first peak, and in Table 1 cannot be accurately constrained. As a demonstration of this uncertainty, in Figure 1 we choose different for the solid and dashed curves. However, as can be seen from Figure 1, an earlier , as depicted by the dashed curve, is preferred because of the light-curve decline rate between and . For the dashed line, we choose and .
The most likely progenitor of iPTF14hls is a red supergiant (RSG) since observations have demonstrated that the progenitors of several type II-P SNe are RSGs (e.g., Smartt 2009; Davies 2017; Van Dyk 2017; Huang et al. 2018). This is consistent with the fact that the total fallback mass is about , as expected for a RSG progenitor (Dexter & Kasen, 2013). The ejecta mass, , is also consistent with a RSG (Davies & Beasor, 2018), though at the high end of the distribution of the SNe II-P ejecta masses.
The remnant of a RSG explosion is believed to be a neutron star. This is also partially supported by the need to fit the third peak of the light curve by a magnetic outburst. Inspection of Table 1 shows that the mass fallback rates decrease monotonically, as expected. However, is much larger than . This is in sharp contrast to the mass fallback rates that follow. could be reduced if there is some contribution from the energy injection of the neutron star. We have neglected the contribution of Ni and Co because their contribution is short-lived, but the contribution of a neutron star (or magnetar) could be long-lived (Kasen & Bildsten, 2010; Woosley, 2010; Inserra et al., 2013; Nicholl et al., 2014; Wang et al., 2015; Dai et al., 2016; Liu et al., 2017b).
To examine the properties (dipole magnetic field , and initial spin period ) of the neutron star, we set (somewhat arbitrarily) and found , . With these parameters, the first peak can be closely fitted while the remaining peaks are affected neglibly by the contribution of the magnetar. We will not show the fitting results by this model because the resulting light curve closely follows the curves presented in Figure 1. It is found that cannot be too large, say , because in that case the magnetar would contribute too much at late times so that the late-time light curve deviates from the law. We note that the above constraints on and should not be taken seriously because they are degenerated with .
We propose that the third, brightest peak is mainly powered by a magnetic outburst. Such outburst is usually accompanied by X-ray emission, which is however not detected (Arcavi et al., 2017). The nondetection of X-ray emission can be understood by considering the optical depth of the ejecta in the X-ray band
where the values of X-ray opacity , SN expansion velocity , and the time since explosion have been substituted. We see that at the time the third peak was observed, the ejecta are still opaque to X-rays. In the above estimate, is taken to be the same as , that is, the electron Thomson scattering opacity. This should be a lower limit to the true X-ray opacity because other heavier elements could make a significant contribution to .
Observations indicate that the photospheric radius of iPTF14hls is quite different from the line-forming region. Arcavi et al. (2017) estimate the latter at position of , where is the SN expansion velocity. It is well known that the photospheric radius of an SN recedes as the SN expands and inner material is observed. The discrepancy of these two radii might be linked to the existence of persistent Balmer series P Cygni lines observed in the spectra of iPTF14hls (Arcavi et al., 2017). The presence of P-Cygni profiles betrays the existence of a stellar wind, as observed in Wolf-Rayet stars (Willis, 1982) and luminous blue variables (Israelian & de Groot, 1999). We suggest that this wind is far above the photosphere and is responsible for the spectral lines.
The rarity of iPTF14hls among SNe II-P may be understood because of its extreme ejecta mass. This large ejecta mass may also account for the reason why so much mass fallbacks so as to give a multi-peak light curve.
In summary, iPTF14hls can be explained by the episodic fallback accretion model.111Alternatively, the circumstellar medium (CSM) interaction is also a plausible model. Liu et al. (2017a) propose a multiple ejecta-CSM interaction model and employed it to model a multi-peak SN iPTF15esb. The fitting parameters suggest a RSG as the progenitor. Although the central object cannot be identified, the rapid third peak might indicate the formation of a neutron star that experienced a magnetic outburst lasting for with a total burst energy .
- Arcavi et al. (2017) Arcavi, I., Howell1, D. A., Kasen, D., et al. 2017, Natur, 551, 210
- Arnett et al. (1989) Arnett, W. D., Bahcall, J. N., Kirshner, R. P., & Woosley, S. E. 1989, ARA&A, 27, 629
- Chatzopoulos et al. (2012) Chatzopoulos, E., Wheeler, J. C., & Vinko, J. 2012, ApJ, 746, 121
- Chugai (2018) Chugai, N. N. 2018, Astronomy Letters, in press (arXiv:1802.03241)
- Cusumano et al. (2016) Cusumano, G., La Parola, V., D’Aì, A., et al. 2016, MNRAS, 460, L99
- Dai et al. (2016) Dai, Z. G., Wang, S. Q., Wang, J. S., Wang, L. J., Yu, Y. W. 2016, ApJ, 817, 132
- Davies (2017) Davies, B. 2017, RSPTA, 375, 20160270
- Davies & Beasor (2018) Davies, B., & Beasor, E. R. 2018, MNRAS, 474, 2116
- Dessart (2018) Dessart, L. 2018, A&A, in press (arXiv:1801.05340)
- Dexter & Kasen (2013) Dexter, J., & Kasen, D. 2013, ApJ, 772, 30
- Fender et al. (2004) Fender, R., Wu, K., Johnston, H., et al. 2004, Natur, 427, 222
- Gavriil et al. (2002) Gavriil, F. P., Kaspi, V. M., & Woods, P. M. 2002, Natur, 419, 142
- Heger et al. (2003) Heger, A., Fryer, C. L., Woosley, S. E., et al. 2003, ApJ, 591, 288
- Huang et al. (2018) Huang, F., Wang, X.-F., Hosseinzadeh, G., et al. 2018, MNRAS, in press (arXiv:1801.03167)
- Inserra et al. (2013) Inserra, C., Smartt, S. J., Jerkstrand, A., et al. 2013, ApJ, 770, 128
- Israelian & de Groot (1999) Israelian, G., & de Groot, M. 1999, SSRv, 90, 493
- Kasen & Bildsten (2010) Kasen, D., & Bildsten, L. 2010, ApJ, 717, 245
- Kaspi et al. (2003) Kaspi, V. M., Gavriil, F. P., Woods, P. M., et al. 2003, ApJL, 588, L93
- Küffmeier et al. (2018) Küffmeier, M., Frimann, S., Jensen, S. S., & Haugbølle, T. 2018, MNRAS, in press (arXiv:1710.00931)
- Liu et al. (2017a) Liu, L. D., Wang, L. J., Wang, S. Q., Dai, Z. G. 2017a, ApJ, submitted (arXiv:1706.01783)
- Liu et al. (2017b) Liu, L. D., Wang, S. Q., Wang, L. J., et al. 2017b, ApJ, 842, 26
- Mazzali et al. (2008) Mazzali, P. A., Valenti, S., Della Valle, M., et al. 2008, Sci, 321, 1185
- Mirabel & Rodríguez (1998) Mirabel, I. F., & Rodríguez, L. F. 1998, Natur, 392, 673
- Moriya et al. (2011) Moriya, T., Tominaga, N., Blinnikov, S. I., Baklanov, P. V., & Sorokina, E. I. 2011, MNRAS, 415, 199
- Nicholl & Smartt (2016) Nicholl, M., & Smartt, S. J. 2016, MNRAS, 457, L79
- Nicholl et al. (2014) Nicholl, M., Smartt, S. J., Jerkstrand, A., et al. 2014, MNRAS, 444, 2096
- Nicholl et al. (2015) Nicholl, M., Smartt, S. J., Jerkstrand, A., et al. 2015, ApJL, 807, L18
- Piro (2015) Piro, A. L. 2015, ApJL, 808, L51
- Rea et al. (2012) Rea, N., Israel, G. L., Esposito, P., et al. 2012, ApJ, 754, 27
- Rea et al. (2009) Rea, N., Israel, G. L., Turolla, R., et al. 2009, MNRAS, 396, 2419
- Richmond et al. (1994) Richmond, M. W., Treffers, R. R., Filippenko, A. V., et al. 1994, AJ, 107, 1022
- Sakurai et al. (2016) Sakurai, Y., Vorobyov, E. I., Hosokawa, T., et al. 2016, MNRAS, 459, 1137
- Smartt (2009) Smartt, S. J. 2009, ARA&A, 47, 63
- Soker & Gilkis (2018) Soker, N., & Gilkis, A. 2018, MNRAS, 475, 1198
- Van Dyk (2017) Van Dyk, S. D. 2017, RSPTA, 375, 20160277
- Vorobyov et al. (2018) Vorobyov, E., Elbakyan, V., Plunkett, A., et al. 2018, A&A, in press (arXiv:1801.06707)
- Vreeswijk et al. (2017) Vreeswijk, P. M., Leloudas, G., Gal-Yam, A., et al. 2017, ApJ, 835, 58
- Wang et al. (2016) Wang, L. J., Wang, S. Q., Dai, Z. G., et al. 2016, ApJ, 821, 22
- Wang et al. (2017a) Wang, L. J., Wang, X. F., Cano, Z., et al. 2017a (arXiv:1712.07359)
- Wang et al. (2017b) Wang, S. Q., Cano, Z., Wang, L. J., et al. 2017b, ApJ, 850, 148
- Wang et al. (2015) Wang, S. Q., Wang, L. J., Dai, Z. G., & Wu, X. F. 2015, ApJ, 799, 107
- Willis (1982) Willis, A. J. 1982, MNRAS, 198, 897
- Woosley (2010) Woosley, S. E. 2010, ApJL, 719, L204
- Woosley (2018) Woosley, S. E. 2018, ApJ, submitted (arXiv:1801.08666)