Planetary systems can survive stellar evolution, as is clear from the atmospheric metal pollution and circumstellar dusty disks of single white dwarfs1,2. Recent observations show that 1−4% of single white dwarfs are accompanied by dusty disks3,4,5,6, while the occurrence rate of metal pollution is about 25–50%1,7,8. Dusty disks and metal pollution have been associated with accretion of remanent planetary systems around white dwarfs1,9, yet the relationship between these two phenomena is still unclear. Here, we suggest an evolutionary scenario to link the dusty disk and metal pollution. By analysing a sample of metal-polluted white dwarfs, we find that the mass accretion rate onto the white dwarf generally follows a broken power-law decay, which matches well with the theoretical prediction, assuming that dust accretion is primarily driven by Poynting–Robertson drag10 and the dust source is primarily delivered via dynamically falling asteroids perturbed by a Jovian planet11,12. The presence of disks is mainly at the early stage (tcool ~ 0.1−0.7 Gyr) of the whole process of metal pollution, which is detectable until ~8 Gyr, naturally explaining the fraction (~2–16%) of metal-polluted white dwarfs with dusty disks. The success of this scenario also implies that the configuration of an asteroid belt with an outer gas giant might be common around stars of several solar masses.
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Koester, D., Gänsicke, B. T. & Farihi, J. The frequency of planetary debris around young white dwarfs. Astron. Astrophys. 566, A34 (2014).
Farihi, J. Circumstellar debris and pollution at white dwarf stars. New Astron. Rev. 71, 9–34 (2016).
Mullally, F. et al. A Spitzer white dwarf infrared survey. Astrophys. J. Suppl. 171, 206–218 (2007).
Farihi, J., Jura, M. & Zuckerman, B. Infrared signatures of disrupted minor planets at white dwarfs. Astrophys. J. 694, 805–819 (2009).
Debes, J. H. et al. The WIRED Survey II: infrared excesses in the SDSS DR7 White Dwarf Catalog. Astrophys. J. Suppl. 197, 38 (2011).
Barber, S. D., Kilic, M., Brown, W. R. & Gianninas, A. Dusty WDs in the WISE All Sky Survey ∩ SDSS. Astrophys. J. 786, 77 (2014).
Zuckerman, B., Koester, D., Reid, I. N. & Hünsh, M. Metal lines in DA white dwarfs. Astrophys. J. 596, 477–495 (2003).
Zuckerman, B., Melis, C., Klein, B., Koester, D. & Jura, M. Ancient planetary systems are orbiting a large fraction of white dwarf stars. Astrophys. J. 722, 725–736 (2010).
Bonsor, A., Farihi, J., Wyatt, M. C. & van Lieshout, R. Infrared observations of white dwarfs and the implications for the accretion of dusty planetary material. Mon. Not. R. Astron. Soc. 468, 154–164 (2017).
Rafikov, R. R. Metal accretion onto white dwarfs caused by Poynting–Robertson drag on their debris disks. Astrophys. J. 732, L3 (2011).
Jura, M. A tidally disrupted asteroid around the white dwarf G29-38. Astrophys. J. 584, L91–L94 (2003).
Frewen, S. F. N. & Hansen, B. M. S. Eccentric planets and stellar evolution as a cause of polluted white dwarfs. Mon. Not. R. Astron. Soc. 439, 2442–2458 (2014).
Dufour, P. et al. The Montreal White Dwarf Database: a tool for the community. In 20th European White Dwarf Workshop 509, 3 (2017).
Rafikov, R. R. Runaway accretion of metals from compact discs of debris on to white dwarfs. Mon. Not. R. Astron. Soc. 416, L55–L59 (2011).
Bonsor, A., Mustill, A. J. & Wyatt, M. C. Dynamical effects of stellar mass-loss on a Kuiper-like belt. Mon. Not. R. Astron. Soc. 414, 930–939 (2011).
Bonsor, A. S. & Veras, D. A wide binary trigger for white dwarf pollution. Mon. Not. R. Astron. Soc. 454, 53–63 (2015).
Hamers, A. S., Perets, H. B. & Portegies Zwart, S. F. A triple origin for the lack of tight coplanar circumbinary planets around short-period binaries. Mon. Not. R. Astron. Soc. 455, 3180–3200 (2016).
Payne, M. J., Veras, D., Holman, M. J. & Gänsicke, B. T. Liberating exomoons in white dwarf planetary systems. Mon. Not. R. Astron. Soc. 457, 217–231 (2016).
Lai, Y.-C., Grebogi, C., Blümel, R. & Ding, M. Algebraic decay and phase-space metamorphoses in microwave ionization of hydrogen Rydberg atoms. Phys. Rev. A 45, 8284–8287 (1992).
Liu, J. & Sun, Y. S. Chaotic motions of comets in near-parabolic orbits: mapping approaches. Celest. Mech. Dynam. Astron. 60, 3–28 (1994).
Zhou, J. L., Sun, Y. S., Zhen, J. Q. & Valtonen, M. J. The transfer of comets from near-parabolic to short-period orbits: map approach. Astron. Astrophys. 364, 887–893 (2000).
Zhou, J. L., Sun, Y. S. & Zhou, L. Y. Evidence for Lévy random walks in the evolution of comets from the Oort Cloud. Celest. Mech. Dynam. Astron. 84, 409–427 (2002).
Wright, J. T. et al. The Exoplanet Orbit Database. Publ. Astron. Soc. Pacif. 123, 412–422 (2011).
Chen, C. H. & Jura, M. A possible massive asteroid belt around Leporis. Astrophys. J. 560, L171–L174 (2001).
Farihi, J., Hippel, T. V. & Pringle, J. E. Magnetospherically-trapped dust and a possible model for the unusual transits at WD 1145+017. Mon. Not. R. Astron. Soc. 471, L145–L149 (2017).
Debes, J. H. & Sigurdsson, S. Are there unstable planetary systems around white dwarfs? Astrophys. J. 572, 556–565 (2002).
Veras, D., Mustill, A. J., Bonsor, A. & Wyatt, M. C. Simulations of two-planet systems through all phases of stellar evolution: implications for the instability boundary and white dwarf pollution. Mon. Not. R. Astron. Soc. 431, 1686–1708 (2013).
Bochkarev, K. V. & Rafikov, R. R. Global modeling of radiatively driven accretion of metals from compact debris disks onto white dwarfs. Astrophys. J. 741, 36 (2011).
Farihi, J., Parsons, S. G. & Gänsicke, B. T. A circumbinary debris disk in a polluted white dwarf system. Nat. Astron. 1, 0032 (2017).
Hollands, M. A., Koester, D., Alekseev, V., Herbert, E. L. & Gänsicke, B. T. Cool DZ white dwarfs I. Identification and spectral analysis. Mon. Not. R. Astron. Soc. 467, 4970–5000 (2017).
Farihi, J., Jura, M., Lee, J. E. & Zuckerman, B. Strengthening the case for asteroidal accretion: evidence for subtle and diverse disks at white dwarfs. Astrophys. J. 714, 1386–1397 (2010).
Xu, S. & Jura, M. Spitzer observations of white dwarfs: the missing planetary debris around DZ stars. Astrophys. J. 745, 88 (2012).
Girven, J. et al. Constraints on the lifetimes of disks resulting from tidally destroyed rocky planetary bodies. Astrophys. J. 749, 154 (2012).
Bergfors, C., Farihi, J., Dufour, P. & Rocchetto, M. Signs of a faint disc population at polluted white dwarfs. Mon. Not. R. Astron. Soc. 444, 2147–2156 (2014).
Dufour, P. et al. On the spectral evolution of cool, helium-atmosphere white dwarfs: detailed spectroscopic and photometric analysis of DZ stars. Astrophys. J. 663, 1291–1308 (2007).
Limoges, M. M., Bergeron, P. & Lépine, S. Physical properties of the current census of northern white dwarfs within 40 Pc of the Sun. Astrophys. J. Suppl. 219, 19 (2015).
Koester, D. & Kepler, S. O. DB white dwarfs in the Sloan Digital Sky Survey Data Release 10 and 12. Astron. Astrophys. 583, A86 (2015).
Kepler, S. O. et al. New white dwarf stars in the Sloan Digital Sky Survey Data Release 10. Mon. Not. R. Astron. Soc. 446, 4078–4087 (2015).
Kepler, S. O. et al. New white dwarf and subdwarf stars in the Sloan Digital Sky Survey Data Release 12. Mon. Not. R. Astron. Soc. 455, 3413–3423 (2016).
Kepler, S. O. et al. White dwarf mass distribution in the SDSS. Mon. Not. R. Astron. Soc. 375, 1315–1324 (2007).
Cavanaugh, J. E. Unifying the derivations for the Akaike and corrected Akaike information criteria. Stat. Prob. Lett. 33, 201–208 (1997).
Veras, D., Leinhardt, Z. M., Bonsor, A. & Gänsicke, B. T. Formation of planetary debris discs around white dwarfs I. Tidal disruption of an extremely eccentric asteroid. Mon. Not. R. Astron. Soc. 445, 2244–2255 (2014).
Shapiro, S. L. & Teukolsky, S. A. Black Holes, White Dwarfs and Neutron Stars: The Physics of Compact Objects 663 (Wiley, New York, 1983).
Livio, M., Pringle, J. E. & Wood, K. Disks and planets around massive white dwarfs. Astrophys. J. 632, L37–L39 (2005).
Catalán, S., Isern, J., García-Berro, E. & Ribas, I. The initial–final mass relationship of white dwarfs revisited: effect on the luminosity function and mass distribution. Mon. Not. R. Astron. Soc. 387, 1693–1706 (2008).
Veras, D. et al. Full-lifetime simulations of multiple unequal-mass planets across all phases of stellar evolution. Mon. Not. R. Astron. Soc. 458, 3942–3967 (2016).
Mustill, A. J. & Villaver, E. Foretellings of Ragnarök: world-engulfing asymptotic giants and the inheritance of white dwarfs. Astrophys. J. 761, 121 (2012).
Duncan, M. J., Quinn, T. & Tremaine, S. The long-term evolution of orbits in the Solar System: a mapping approach. Icarus 82, 402–418 (1989).
Chambers, J. E. A hybrid symplectic integrator that permits close encounters between massive bodies. Mon. Not. R. Astron. Soc. 304, 793–799 (1999).
Press, W. H., Teukolsky, S. A., Vetterling, W. T. & Flannery, B. P. Numerical Recipes in FORTRAN. The Art of Scientific Computing (Cambridge Univ. Press, New York, 1992).
Krasinsky, G. A., Pitjeva, E. V., Vasilyev, M. V. & Yagudina, E. I. Hidden mass in the asteroid belt. Icarus 158, 98–105 (2002).
Debes, J. H., Walsh, K. J. & Stark, C. The link between planetary systems, dusty white dwarfs, and metal-polluted white dwarfs. Astrophys. J. 747, 148 (2012).
Morrison, S. & Malhotra, R. Planetary chaotic zone clearing: destinations and timescales. Astrophys. J. 799, 41 (2015).
Mustill, A. J., Veras, D. & Villaver, E. Long-term evolution of three-planet systems to the post-main sequence and beyond. Mon. Not. R. Astron. Soc. 437, 1404–1419 (2014).
Koester, D. & Wilken, D. The accretion–diffusion scenario for metals in cool white dwarfs. Astron. Astrophys. 453, 1051–1057 (2006).
Dupius, J., Fontaine, G. & Wesemael, F. A study of metal abundance patterns in cool white dwarfs. III—comparison of the predictions of the two-phase accretion model with the observations. Astrophys. J. Suppl. 87, 345–365 (1993).
The authors thank S.-Y. Xu and D. Koester for discussions and suggestions. They also thank the MWDD for useful data and evolutionary models of white dwarfs. This research is supported by the National Natural Science Foundation of China (numbers 11333002, 11661161014, 11503009 and 11673011). J.-W. X. acknowledges the Foundation for the Author of National Excellent Doctoral Dissertation of the People’s Republic of China (number 10284201426) and the LAMOST Fellowship. The LAMOST Fellowship is supported by Special Funding for Advanced Users, budgeted and administrated by the Center for Astronomical Mega-Science, Chinese Academy of Sciences.
The authors declare no competing interests.
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Chen, DC., Zhou, JL., Xie, JW. et al. A power-law decay evolution scenario for polluted single white dwarfs. Nat Astron 3, 69–75 (2019). https://doi.org/10.1038/s41550-018-0609-7
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