Impact of mass transfer on the orbital evolution of a white dwarf close to an intermediate-mass black hole

TL;DR

We address WD EMRIs around spinning IMBHs and show that phase-dependent MT, resolved with a perturbed Kepler approach plus PN corrections, can compete with GW-driven inspiral. MT can increase orbital period and eccentricity, potentially preventing complete tidal disruption and producing detectable GW phase shifts of order $1$ rad over multi-year observations; it may also explain QPE variability or disappearance. By deriving MT accelerations from angular-momentum considerations and incorporating GR corrections to Roche geometry, the work demonstrates the necessity of jointly modeling relativistic dynamics and MT for WD–IMBH systems and highlights observable GW signatures that accompany mass transfer. The results have direct implications for multi-messenger astronomy and the interpretation of QPEs, emphasizing that MT feedback can significantly alter EMRI evolution and GW waveforms.

Abstract

Extreme mass ratio inspirals (EMRIs) of low-mass white dwarfs (WDs, 0.1 - 0.3 Msun) around spinning intermediate-mass black holes (IMBHs, 10^3 - 10^5 Msun) offer unique opportunities for multi-messenger astronomy, emitting both gravitational waves (GWs) and electromagnetic (EM) signals. Yet, despite their astrophysical relevance, theoretical models often omit key interactions between relativistic dynamics and phase-dependent mass transfer (MT). In this study, we integrate a perturbed Keplerian formalism with post-Newtonian (PN) corrections to simulate the relativistic orbit of a WD around a rotating IMBH, explicitly resolving the narrow phase near pericentre where Roche-lobe overflow initiates MT. We find that GW emission and MT exert competing influences on the orbit: MT episodes can increase both orbital period and eccentricity, potentially enabling the WD to avoid complete tidal disruption and even escape. We further quantify the GW phase evolution induced by MT, identifying parameter regimes in which GW detectors could observe a one-radian phase shift over observational timescales. Finally, we propose that the orbital expansion driven by MT may lead to the disappearance of quasi-periodic eruptions (QPEs). Our results underscore the necessity of jointly modeling relativistic effects and dynamic mass transfer in WD-IMBH systems.

Figures (12)

• Figure 1: Simulation result of semi-major axis in high eccentricity WD-IMBH system. The mass of the WD is $0.15\text{M}_{\sun}$ and the mass of the IMBH is $4\times 10^5\text{M}_{\sun}$, the initial eccentricity is $0.99$. A more detailed diagram can be seen in Figure \ref{['5.2 Variation of the semi-major axis, eccentricity, WD period']}.
• Figure 2: Definition of the ralative coordinate and the angle parameters. The origin of the relative coordinate system is placed at mass $m_2$, while mass $m_1$ follows an orbit defined by $\boldsymbol{r}$$=$$r^{X}\boldsymbol{e}_{X}$$+$$r^{Y}\boldsymbol{e}_{Y}$$+$$r^{Z}\boldsymbol{e}_{Z}$. For a quasi-Keplerian orbit, the system has pericenter and an ascending node, where the ascending node is the point of intersection of the orbit with the $OXY$ plane. The parameters are as follows: $\iota$ is the inclination of the orbital plane relative to the $OXY$ plane; $\Omega$ is the longitude of the ascending node, the angle between the ascending node and the positive X-axis; $\omega$ is the argument of pericenter, the angle between the ascending node and the pericenter; $f$ is the phase angle of $m_1$ relative to the pericenter. The angle $\phi$ is defined as $\phi$$=$$\omega+f$. The basis vectors $\boldsymbol{e}_{X}$, $\boldsymbol{e}_{Y}$, $\boldsymbol{e}_{Z}$ define the Cartesian coordinate system with coordinates $(X,Y,Z)$.
• Figure 3: The top view of the instantaneous orbital plane. The directions of $x$, $y$, $z$ are determined by the line connecting the center-of-mass and the rotation axis of WD. The donor (WD) has mass $m_1$, and the accretor (IMBH) has mass $m_2$. The parameters are as follows: $R_{\mathrm{WD}}$ is the radius of WD, $R_{\mathrm{L}}$ is the Roche-lobe radius. $\tilde{Z}$ is the depth beneath the donor surface, $\tilde{X}=R_{\mathrm{WD}}-\tilde{Z}$ is the distance from the center-of-mass (CM) of the donor to the mass element, $D$ is the distance from the CM of the donor to the accretor, $\Omega _{1}$ is the spin angular velocity of the donor. The Schwarzschild radius of the IMBH is much larger than the WD radius, so it is not drawn to scale.
• Figure 4: The pericenter distance $r_{\text{p}}$ for Roche-lobe overflow given by $r_{\text{p}}$$=$$\lambda R_{\mathrm{WD}}(M_{\mathrm{WD}})/f(A,q)$, is shown as a function of $M_{\mathrm{WD}}$ for fixed values of $M_{\mathrm{IMBH}}/10^{5} \text{M}_{\sun}$$=$$0.5$, $1$, $4$. Here, $\lambda$$\le$$1$ ensures $R_{\text{L}}$$\le$$R_{\mathrm{WD}}$ at pericenter. The three black lines represent different distances: ISCO is the innermost stable circular orbit of a Schwarzschild black hole, $r_{\mathrm{ISCO}}$$=$$6 GM_{\text{IMBH}}/c^2$; MBO is the marginally bound orbit, $r_{\mathrm{MBO}}$$=$$4 GM_{\text{IMBH}}/c^2$; R$_{\text{s}}$ is the Schwarzschild radius, R$_{\text{s}}$$=$$2 GM_{\text{IMBH}}/c^2$.
• Figure 5: The evolution of the radial eccentricity $e_{\mathrm{r}}$ with and without MT. In each panel, the higher curve represents the evolution of $e_{\mathrm{r}}^{\mathrm{MT}}$ with MT, and the low one represents the evolution of $e_{\mathrm{r}}^{*}$ without MT. Different line colors correspond to the same initial latitude $\psi_0$, and different line styles denote the same IMBH spin parameters $\chi_2$.