Can angular momentum loss cause the period change of NN Ser?

NN Ser is a non mass-transferring pre-cataclysmic variable containing a white dwarf with a mass of $\sim 0.5 M_{\odot}$ and an M dwarf secondary star with a mass of $\sim 0.2 M_{\odot}$. Based on the data detected by the high-speed CCD camera ULTRACAM, it was observed that the orbital period of NN Ser is decreasing, which may be caused by a genuine angular momentum loss or the presence of a third body. However, neither gravitational radiation and magnetic braking can ideally account for the period change of NN Ser. In this Letter, we attempt to examine a feasible mechanism which can drain the angular momentum from NN Ser. We propose that a fossil circumbinary disk (CB disk) around the binary may have been established at the end of the common envelope phase, and the tidal torques caused by the gravitational interaction between the disk and the binary can efficiently extract the orbital angular momentum from the system. We find that only if M dwarf has an ultra-high wind loss rates of $\sim 10^{-10} M_{\odot} \rm yr^{-1}$, and a large fraction ($\delta\sim 10 %$) of wind loss is fed into the CB disk, the loss rates of angular momentum via the CB disk can interpret the period change observed in NN Ser. Such a wind loss rate and $\delta$-value seem to be incredible. Hence it seems that the presence of a third body in a long orbit around the binary might account for the changing period of NN Ser.

💡 Research Summary

The paper investigates the observed decrease in the orbital period of the pre‑cataclysmic variable NN Ser, a detached binary composed of a ∼0.5 M⊙ white dwarf and a ∼0.2 M⊙ M‑type secondary. High‑speed photometry obtained with ULTRACAM over more than a decade shows a secular period derivative of roughly (\dot{P}\simeq-4\times10^{-11},\mathrm{s,s^{-1}}). The authors first assess the two conventional angular‑momentum‑loss (AML) mechanisms that operate in close binaries: gravitational radiation (GR) and magnetic braking (MB). Using the measured component masses and orbital separation, the GR contribution to (\dot{P}) is found to be an order of magnitude smaller than observed, while MB, modeled with the standard Skumanich‑type prescription, is strongly suppressed because the M‑dwarf is expected to be tidally locked to the orbit. Consequently, neither GR nor MB can account for the measured period change.

To explain the discrepancy, the authors propose that a fossil circumbinary (CB) disk, formed from residual common‑envelope material, extracts orbital angular momentum through tidal torques. The torque is expressed as (\tau = -\frac{3}{2}\alpha\Sigma\Omega r^{2}), where (\alpha) is the viscous parameter, (\Sigma) the surface density, (\Omega) the Keplerian angular velocity at radius (r). The disk is assumed to be fed by the stellar wind of the M‑dwarf: a fraction (\delta) of the wind mass‑loss rate (\dot{M}{\rm wind}) is captured by the disk ((\dot{M}{\rm disk}= \delta\dot{M}{\rm wind})). By relating the observed (\dot{P}) to the required angular‑momentum loss (\dot{J}{\rm orb}) via (\dot{P}/P = 3\dot{J}{\rm orb}/J{\rm orb}), the authors back‑calculate the necessary (\dot{J}{\rm CB}). Their algebra shows that reproducing the observed period derivative demands an implausibly high wind loss rate, (\dot{M}{\rm wind}\sim10^{-10},M_{\odot},\mathrm{yr^{-1}}), and a capture efficiency (\delta\sim0.1). Empirical studies of low‑mass M dwarfs typically find wind rates in the range (10^{-14})–(10^{-12},M_{\odot},\mathrm{yr^{-1}}), several orders of magnitude lower. Moreover, a 10 % capture efficiency would require the wind to be dramatically slowed and redirected toward the binary’s orbital plane, contrary to the expectation that most of the wind escapes at high velocity.

The authors also discuss the longevity of such a CB disk. Viscous spreading and radiative cooling would cause the disk to dissipate on timescales of a few hundred Myr unless a continuous mass supply is maintained. Since the required wind rate is already unrealistic, sustaining the disk over the ∼1 Gyr age of NN Ser appears untenable. Therefore, the CB‑disk hypothesis, while theoretically capable of extracting sufficient angular momentum, relies on parameters that are inconsistent with current observations of M‑dwarf winds and disk physics.

Given these difficulties, the paper turns to the alternative explanation of a third body in a wide orbit. A low‑mass companion (planetary or brown‑dwarf mass) on a long‑period orbit can produce an apparent period change via the light‑travel‑time (LTT) effect. The observed O–C diagram does not show a clear sinusoidal modulation, but a companion with a period of several decades and a mass of a few Jupiter masses could generate a secular trend that mimics the measured (\dot{P}). This scenario does not require any exotic wind properties and is testable: continued high‑precision eclipse timing will eventually reveal a periodic component if a third body is present, and radial‑velocity monitoring could directly detect its gravitational influence.

In conclusion, the study demonstrates that the conventional AML mechanisms fall short of explaining NN Ser’s period decrease, and that a CB disk would need an unrealistically high stellar wind and capture efficiency to do so. The more plausible explanation is the presence of a distant third body, whose LTT effect can naturally account for the observed timing variations. The authors recommend long‑term timing campaigns and spectroscopic follow‑up to confirm or refute the third‑body hypothesis.