Recent IoA Publications

Dual-field interferometric observations with VLTI/GRAVITY sometimes require the use of a "binary calibrator", a binary star whose individual components remain unresolved by the interferometer, with a separation between 400 and 2000 mas for observations with the Units Telescopes (UTs), or 1200 to 3000 mas for the Auxiliary Telescopes (ATs). The separation vector also needs to be predictable to within 10 mas for proper pointing of the instrument. Up until now, no list of properly vetted calibrators was available for dual-field observations with VLTI/GRAVITY on the UTs. Our objective is to compile such a list, and make it available to the community. We identify a list of candidates from the Washington Double Star (WDS) catalogue, all with appropriate separations and brightness, scattered over the Southern sky. We observe them as part of a dedicated calibration programme, and determine whether these objects are true binaries (excluding higher multiplicities resolved interferometrically but unseen by imaging), and extract measurements of the separation vectors. We combine these new measurements with those available in the WDS to determine updated orbital parameters for all our vetted calibrators. We compile a list of 13 vetted binary calibrators for observations with VLTI/GRAVITY on the UTs, and provide orbital estimates and astrometric predictions for each of them. We show that our list guarantees that there are always at least two binary calibrators at airmass

Mildly irradiated mini-Neptunes have densities potentially consistent with them hosting substantial liquid water oceans (`Hycean' planets). The presence of CO2 and simultaneous absence of ammonia (NH3) in their atmospheres has been proposed as a fingerprint of such worlds. JWST observations of K2-18b, the archetypal Hycean, have found the presence of CO2 and the depletion of NH3 to 4um region, where CO2 and CO features dominate: Magma ocean models suggest a systematically lower CO2/CO ratio than estimated from free chemistry retrieval, indicating that deeper observations of this spectral region may be able to distinguish between oceans of liquid water and magma on mini-Neptunes.

Flux excesses in the early time light curves of Type Ia supernovae (SNe\,Ia) are predicted by multiple theoretical models and have been observed in a number of nearby SNe\,Ia over the last decade. However, the astrophysical processes that cause these excesses may affect their use as standardizable candles for cosmological parameter measurements. In this paper, we perform a systematic search for early-time excesses in SNe\,Ia observed by the Zwicky Transient Facility (ZTF) to study whether SNe\,Ia with these excesses yield systematically different Hubble residuals. We analyze two compilations of ZTF SN\,Ia light curves from its first year of operations: 127 high-cadence light curves from \citet{Yao19} and 305 light curves from the ZTF cosmology data release of \citet{Dhawan22}. We detect significant early-time excesses for 17 SNe\,Ia in these samples and find that the excesses have an average $g-r$ color of $0.06\pm0.09$~mag; we do not find a clear preference for blue excesses as predicted by several models. Using the SALT3 model, we measure Hubble residuals for these two samples and find that excess-having SNe\,Ia may have lower Hubble residuals (HR) after correcting for shape, color, and host-galaxy mass, at $\sim$2-3$\sigma$ significance; our baseline result is $\Delta HR = -0.056 \pm 0.026$~mag ($2.2 \sigma$). We compare the host-galaxy masses of excess-having and no-excess SNe\,Ia and find they are consistent, though at marginal significance excess-having SNe\,Ia may prefer lower-mass hosts. Additional discoveries of early excess SNe\,Ia will be a powerful way to understand potential biases in SN\,Ia cosmology and probe the physics of SN\,Ia progenitors.

The Cosmic Dawn marks the first star formations and preceded the Epoch-of-Reionization, when the Universe underwent a fundamental transformation propelled by the radiation from these first stars and galaxies. Interferometric 21-cm experiments aim to probe redshifted neutral hydrogen signals from these periods, constraining the conditions of the early Universe. The SKA-LOW instrument of the Square Kilometre Array telescope is envisaged to be the largest and most sensitive radio telescope at m and cm wavelengths. The latest Aperture Array Verification Systems feature 7m coaxial transmission lines connecting the Low Noise Amplifiers to optical transmitters at the front of the analogue-receiving chain. An impedance mismatch between these components results in a partially reflected electromagnetic signal, which introduces chromatic aberrations in the instrument bandpass. This causes power from the foreground signals to appear at higher delays, potentially contaminating the EoR window, a region at which the 21-cm signal should be detectable. We present an end-to-end simulation pipeline for SKA-LOW using a composite sky model combining radio foregrounds from The GLEAM Survey, Haslam $408$MHz, and a $1.5$cGpc 21-cm brightness temperature cube generated with the 21cmSPACE simulator. Iterating a parametric approach, we derive a model for the scattering parameters of a coaxial transmission line in terms of its specifications and bulk material properties. Assuming identical cables of length $\leq 15.0$m with impedance mismatch $\leq 10\Omega$ confines the reflection to k-modes below the EoR window. However, we demonstrate that even a $0.1$% length tolerance introduces contamination with an RMSE of $\sim 10$% across all accessible k-modes.

HD 142527 A is a young and massive Herbig Ae/Be star surrounded by a highly structured disc. The disc shows numerous morphological structures, such as spiral arms, a horseshoe region of dust emission, a set of shadows cast by an inner disc on the outer disc, and a large cavity extending from $\simeq{}$30 au to $\simeq{}$130 au. HD 142527 A also has a lower mass companion, HD 142527 B (M = 0.13 $\pm$ 0.03 $M_\odot{}$), which is thought to be responsible for most of the structures observed in the surrounding disc. We gathered VLTI/GRAVITY observations of HD 142527, either from our own programmes or from the ESO archive. We used this inhomogeneous set of data to extract a total of seven high-precision measurements of the relative astrometry between HD 142527 A and B, spread from mid-2017 to early 2021. Combined with what is available in the literature, we now have 9 yr of astrometric monitoring on HD 142527. We used orbit fitting tools to determine the orbital parameters of HD 142527 B, and used them as inputs for a 3D hydrodynamical model of the disc to determine whether or not the binary is able to create the structures observed in the disc. Our VLTI/GRAVITY astrometry gives excellent constraints on the orbit of HD 142527 B. We show that the secondary is following an orbit of semi-major axis a = 10.80 $\pm$ 0.22 au, with moderate eccentricity (e = 0.47 $\pm$ 0.01). With such a compact orbit, we show that HD 142527 B can only generate a gap and spiral arms of $\sim$30 au in the disc, which is much smaller than what is revealed by observations. Even from a theoretical standpoint, the observed cavity size of $\sim$100 au far exceeds even the most generous predictions for a companion like HD 142527 B on such a compact orbit. Thus, we conclude that the low-mass companion cannot be solely responsible for the observed morphology of the disc surrounding the system.

Aims. As part of the ongoing GRAVITY+ upgrade of the Very Large Telescope Interferometer infrastructure, we aim to improve the performance of the GRAVITY Fringe-Tracker, and to enable its use by other instruments. Methods. We modify the group delay controller to consistently maintain tracking in the white light fringe, characterised by a minimum group delay. Additionally, we introduce a novel approach in which fringe-tracking is performed in the non-observable Optical Path Length state-space, using a covariance-weighted Kalman filter and an auto-regressive model of the disturbance. We outline this new state-space representation, and the formalism we use to propagate the state-vector and generate the control signal. While our approach is presented specifically in the context of GRAVITY/GRAVITY+, it can easily be adapted to other instruments or interferometric facilities. Results. We successfully demonstrate phase delay tracking within a single fringe, with any spurious phase jumps detected and corrected in less than 100 ms. We also report a significant performance improvement, as evidenced by a reduction of about 30 to 40% in phase residuals, and a much better behaviour under sub-optimal atmospheric conditions. Compared to what was observed in 2019, the median residuals have decreased from 150 nm to 100 nm on the Auxiliary Telescopes and from 250 nm to 150 nm on the Unit Telescopes. Conclusions. The improved phase-delay tracking combined with whit light fringe tracking means that from now-on, the GRAVITY Fringe-Tracker can be used by other instruments operating in different wavebands. The only limitation remains the need for an optical path dispersion adjustment.

In anticipation of the Euclid Wide and Deep Surveys, we present optical emission-line predictions at intermediate redshifts from 0.4 to 2.5. Our approach combines a mock light cone from the GAEA semi-analytic model to self-consistently model nebular emission from HII regions, narrow-line regions of active galactic nuclei (AGN), and evolved stellar populations. Our analysis focuses on seven optical emission lines: H$\alpha$, H$\beta$, [SII]$\lambda\lambda 6717, 6731$, [NII]$\lambda 6584$, [OI]$\lambda 6300$, [OIII]$\lambda 5007$, and [OII]$\lambda\lambda 3727, 3729$. We find that Euclid will predominantly observe massive, star-forming, and metal-rich line-emitters. Interstellar dust, modelled using a Calzetti law with mass-dependent scaling, may decrease observable percentages by a further 20-30% with respect to our underlying emission-line populations from GAEA. We predict Euclid to observe around 30-70% of H$\alpha$-, [NII]-, [SII]-, and [OIII]-emitting galaxies at redshift below 1 and under 10% at higher redshift. Observability of H$\beta$-, [OII]-, and [OI]- emission is limited to below 5%. For the Euclid-observable sample, we find that BPT diagrams can effectively distinguish between different galaxy types up to around redshift 1.8, attributed to the bias toward metal-rich systems. Moreover, we show that the relationships of H$\alpha$ and [OIII]+H$\beta$ to the star-formation rate, and the [OIII]-AGN luminosity relation, exhibit minimal changes with increasing redshift. Based on line ratios [NII]/H$\alpha$, [NII]/[OII], and [NII]/[SII], we further propose novel z-invariant tracers for the black hole accretion rate-to-star formation rate ratio. Lastly, we find that commonly used metallicity estimators display gradual shifts in normalisations with increasing redshift, while maintaining the overall shape of local calibrations. This is in tentative agreement with recent JWST data.

The emergence of the disc in our Galaxy and the relation of the thick and thin disc formation and evolution is still a matter of debate. The chemo-dynamical characterization of disc stars is key to resolve this question, in particular at parameter regimes where both disc components overlap, such as the region around [Fe/H] $\sim$ $-0.7$ corresponding to the thin disc metal-poor end. In this paper we re-assess the recent detection of a metal-poor extension of stars moving with thin-disc-like rotational velocities between -2 20,000) spectroscopic surveys available, the GALAH DR3 and the APOGEE DR17. We confirm that there are high angular-momentum stars moving in thin-disc-like orbits, i.e., with high angular momentum $\rm L_{z}/J_{tot}$ > 0.95, and close to the Galactic plane, $\rm |Z_{max}|$

The unprecedented medium-resolution (R~1500-3500) near- and mid-infrared (1-18um) spectrum provided by JWST for the young (140+/-20Myr) low-mass (12-20MJup) L-T transition (L7) companion VHS1256b gives access to a catalogue of molecular absorptions. In this study, we present a comprehensive analysis of this dataset utilizing a forward modelling approach, applying our Bayesian framework, ForMoSA. We explore five distinct atmospheric models to assess their performance in estimating key atmospheric parameters: Teff, log(g), [M/H], C/O, gamma, fsed, and R. Our findings reveal that each parameter's estimate is significantly influenced by factors such as the wavelength range considered and the model chosen for the fit. This is attributed to systematic errors in the models and their challenges in accurately replicating the complex atmospheric structure of VHS1256b, notably the complexity of its clouds and dust distribution. To propagate the impact of these systematic uncertainties on our atmospheric property estimates, we introduce innovative fitting methodologies based on independent fits performed on different spectral windows. We finally derived a Teff consistent with the spectral type of the target, considering its young age, which is confirmed by our estimate of log(g). Despite the exceptional data quality, attaining robust estimates for chemical abundances [M/H] and C/O, often employed as indicators of formation history, remains challenging. Nevertheless, the pioneering case of JWST's data for VHS1256b has paved the way for future acquisitions of substellar spectra that will be systematically analyzed to directly compare the properties of these objects and correct the systematics in the models.

Verifying the fully kinematic nature of the cosmic microwave background (CMB) dipole is of fundamental importance in cosmology. In the standard cosmological model with the Friedman-Lemaitre-Robertson-Walker (FLRW) metric from the inflationary expansion the CMB dipole should be entirely kinematic. Any non-kinematic CMB dipole component would thus reflect the preinflationary structure of spacetime probing the extent of the FLRW applicability. Cosmic backgrounds from galaxies after the matter-radiation decoupling, should have kinematic dipole component identical in velocity with the CMB kinematic dipole. Comparing the two can lead to isolating the CMB non-kinematic dipole. It was recently proposed that such measurement can be done using the near-IR cosmic infrared background (CIB) measured with the currently operating Euclid telescope, and later with Roman. The proposed method reconstructs the resolved CIB, the Integrated Galaxy Light (IGL), from Euclid's Wide Survey and probes its dipole, with a kinematic component amplified over that of the CMB by the Compton-Getting effect. The amplification coupled with the extensive galaxy samples forming the IGL would determine the CIB dipole with an overwhelming signal/noise, isolating its direction to sub-degree accuracy. We develop details of the method for Euclid's Wide Survey in 4 bands spanning 0.6 to 2 mic. We isolate the systematic and other uncertainties and present methodologies to minimize them, after confining the sample to the magnitude range with negligible IGL/CIB dipole from galaxy clustering. These include the required star-galaxy separation, accounting for the extinction correction dipole using the method newly developed here achieving total separation, accounting for the Earth's orbital motion and other systematic effects. (Abridged)

Blue Horizontal Branch (BHB) stars, excellent distant tracers for probing the Milky Way's halo density profile, are distinguished in the $(g-r)_0$ vs $(i-z)_0$ color space from another class of stars, blue straggler stars (BSs). We develop a Bayesian mixture model to classify BHB stars using high-precision photometry data from the Dark Energy Survey Data Release 2 (DES DR2). We select $\sim2100$ highly-probable BHBs based on their $griz$ photometry and the associated uncertainties, and use these stars to map the stellar halo over the Galactocentric radial range $20 \lesssim R \lesssim 70$ kpc. After excluding known stellar overdensities, we find that the number density $n_\star$ of BHBs can be represented by a power law density profile $n_\star \propto R^{-\alpha}$ with an index of $\alpha=4.28_{-0.12}^{+0.13}$, consistent with existing literature values. In addition, we examine the impact of systematic errors and the spatial inhomogeneity on the fitted density profile. Our work demonstrates the effectiveness of high-precision $griz$ photometry in selecting BHB stars. The upcoming photometric survey from the Rubin Observatory, expected to reach depths 2-3 magnitudes greater than DES during its 10-year mission, will enable us to investigate the density profile of the Milky Way's halo out to the virial radius, unravelling the complex processes of formation and evolution in our Galaxy.

The INSPIRE project has built the largest sample of ultra-compact massive galaxies (UCMGs) at 0.1<z<0.4 and obtained their star formation histories (SFHs). Due to their preserved very old stellar populations, relics are the perfect systems to constrain the earliest epochs of mass assembly in the Universe and the formation of massive early-type galaxies. The goal of this work is to investigate whether a correlation exists between the degree of relicness (DoR), quantifying the fraction of stellar mass formed at z>2, and the other stellar population parameters.We use the Full-Index-Fitting method to fit the INSPIRE spectra to single stellar population (SSP) models. This allows us to measure, for the first time, the low-mass end slope of the IMF, as well as stellar metallicity [M/H], [Mg/Fe], [Ti/Fe] and [Na/Fe] ratios, and study correlations between them and the DoR. Similarly to normal-sized galaxies, UCMGs with larger stellar masses have overall higher metallicities. We found a correlation between the low-mass end of the IMF slope and the DoR, that, however, breaks down for systems with a more extended SFH. An even stronger dependency is found between the IMF and the fraction of mass formed at high-z. At equal velocity dispersion and metallicity, galaxies with a higher DoR have a dwarf-richer IMF than that of low-DoR counterparts. This might indicate that the cosmic epoch and formation mechanisms influence the fragmentation of the star formation cloud and hence might be the explanation for IMF variations detected in massive ETGs.

We present the discovery and characterization of two warm mini-Neptunes transiting the K3V star TOI-815 in a K-M binary system. Analysis of the spectra and rotation period reveal it to be a young star with an age of $200^{+400}_{-200}$Myr. TOI-815b has a 11.2-day period and a radius of 2.94$\pm$0.05$\it{R_{\rm\mathrm{\oplus}}}$ with transits observed by TESS, CHEOPS, ASTEP, and LCOGT. The outer planet, TOI-815c, has a radius of 2.62$\pm$0.10$\it{R_{\rm\mathrm{\oplus}}}$, based on observations of three non-consecutive transits with TESS, while targeted CHEOPS photometry and radial velocity follow-up with ESPRESSO were required to confirm the 35-day period. ESPRESSO confirmed the planetary nature of both planets and measured masses of 7.6$\pm$1.5 $\it{M_{\rm \mathrm{\oplus}}}$ ($\rho_\mathrm{P}$=1.64$^{+0.33}_{-0.31}$gcm$^{-3}$) and 23.5$\pm$2.4$\it{M_{\rm\mathrm{\oplus}}}$ ($\rho_\mathrm{P}$=7.2$^{+1.1}_{-1.0}$gcm$^{-3}$) respectively. Thus, the planets have very different masses, unlike the usual similarity of masses in compact multi-planet systems. Moreover, our statistical analysis of mini-Neptunes orbiting FGK stars suggests that weakly irradiated planets tend to have higher bulk densities compared to those suffering strong irradiation. This could be ascribed to their cooler atmospheres, which are more compressed and denser. Internal structure modeling of TOI-815b suggests it likely has a H-He atmosphere constituting a few percent of the total planet mass, or higher if the planet is assumed to have no water. In contrast, the measured mass and radius of TOI-815c can be explained without invoking any atmosphere, challenging planetary formation theories. Finally, we infer from our measurements that the star is viewed close to pole-on, which implies a spin-orbit misalignment at the 3$\sigma$ level.

Tight relationships exist in the local universe between the central stellar properties of galaxies and the mass of their supermassive black hole. These suggest galaxies and black holes co-evolve, with the main regulation mechanism being energetic feedback from accretion onto the black hole during its quasar phase. A crucial question is how the relationship between black holes and galaxies evolves with time; a key epoch to probe this relationship is at the peaks of star formation and black hole growth 8-12 billion years ago (redshifts 1-3). Here we report a dynamical measurement of the mass of the black hole in a luminous quasar at a redshift of 2, with a look back time of 11 billion years, by spatially resolving the broad line region. We detect a 40 micro-arcsecond (0.31 pc) spatial offset between the red and blue photocenters of the H$\alpha$ line that traces the velocity gradient of a rotating broad line region. The flux and differential phase spectra are well reproduced by a thick, moderately inclined disk of gas clouds within the sphere of influence of a central black hole with a mass of 3.2x10$^{8}$ solar masses. Molecular gas data reveal a dynamical mass for the host galaxy of 6x10$^{11}$ solar masses, which indicates an under-massive black hole accreting at a super-Eddington rate. This suggests a host galaxy that grew faster than the supermassive black hole, indicating a delay between galaxy and black hole formation for some systems.

Episodic accretion is one of the competing models to explain the observed luminosity spread in young stellar clusters. These short-lived high accretion events could also have a strong impact on planet formation. Observations of high-amplitude variability in young stellar objects (YSOs) due to large changes in the accretion rate provide direct observational evidence for episodic accretion. However, there are still uncertainties in the frequency of these events and if episodic accretion is universal among YSOs. To determine the frequency of outbursts in Class I YSOs, we built a large and robust sample of objects at this evolutionary stage, and searched for high-amplitude near-infrared ($\Delta K_{\rm S}>2$~mag) variability in the VIRAC2 database of the Vista Variables in the Via Lactea (VVV) survey. By complementing with near-IR (2MASS and DENIS) and mid-IR (WISE/Neo-WISE) data, we find that from $\sim$ 7000 Class I YSOs, 97 objects can be classified as eruptive variable YSOs. The duration of the outbursts vary from a few months to longer than 9 years, and cover a similar range of amplitudes. Values of $\Delta K_{\rm S}>5$~mag, however, are only observed in outbursts with duration longer than 9 years. When considering different effects of completeness and contamination we estimate that the incidence of episodic accretion in Class I YSOs is between 2\% and 3\%. Finally, we determine a recurrence timescale of long-term outbursts (a.k.a FUors) of $\tau=1.75^{+1.12}_{-0.87}$~kyr. The latter value agrees with previous estimates and is in line with the expectations of higher frequency of FUor outbursts during younger stages of evolution.

We have performed a comprehensive search of a VISTA Variables in the Via Lactea (VVV) database of 9.5 yr light curves for variable sources with $\Delta K_s \ge 4$ mag, aiming to provide a large sample of high amplitude eruptive young stellar objects (YSOs) and detect unusual or new types of infrared variable source. We find 222 variable or transient sources in the Galactic bulge and disc, most of which are new discoveries. The sample mainly comprises novae, YSOs, microlensing events, Long Period Variable stars (LPVs) and a few rare or unclassified sources. Additionally, we report the discovery of a significant population of aperiodic late-type giant stars suffering deep extinction events, strongly clustered in the Nuclear Disc of the Milky Way. We suggest that these are metal-rich stars in which radiatively driven mass loss has been enhanced by super-solar metallicity. Among the YSOs, 32/40 appear to be undergoing episodic accretion. Long-lasting YSO eruptions have a typical rise time of $\sim$2 yr, somewhat slower than the 6-12 month timescale seen in the few historical events observed on the rise. The outburst durations are usually at least 5 yr, somewhat longer than many lower amplitude VVV events detected previously. The light curves are diverse in nature, suggesting that multiple types of disc instability may occur. Eight long-duration extinction events are seen wherein the YSO dims for a year or more, attributable to inner disc structure. One binary YSO in NGC 6530 displays periodic extinction events (P=59 days) similar to KH 15D.

During the pre-main-sequence evolution, Young Stellar Objects (YSOs) assemble most of their mass during the episodic accretion process. The rarely seen FUOr-type events (FUOrs) are valuable laboratories to investigate the outbursting nature of YSOs. Here, we present multi-wavelength detection of a high-amplitude eruptive source in the young open cluster VdBH 221 with an ongoing outburst, including optical to mid-infrared time series and near-infrared spectra. The initial outburst has an exceptional amplitude of $>$6.3 mag in Gaia and 4.6 mag in $K_s$, with a peak luminosity up to 16 $L_{\odot}$ and a peak mass accretion rate of 1.4 $\times$ 10$^{-5}$ $M_\odot$ yr$^{-1}$. The optical to infrared spectral energy distribution (SED) of this object is consistent with a low-mass star (0.2$M_\odot$) with a modest extinction ($A_V < 2$ mag). A 100-d delay between optical and infrared rising stages is detected, suggesting an outside-in origin of the instability. The spectroscopic features of this object reveal a self-luminous accretion disc, very similar to FU Orionis, with a low line-of-sight extinction. Most recently, there has been a gradual increase in brightness throughout the wavelength range, possibly suggesting an enhancement of the mass accretion rate.

During the pre-main-sequence (pre-MS) evolution stage of a star, significant amounts of stellar mass are accreted during episodic accretion events, such as multi-decade FUor-type outbursts. Here, we present a near-infrared spectroscopic follow-up study of 33 high-amplitude (most with $\Delta K_s$ > 4 mag) variable sources discovered by the Vista Variables in the Via Lactea (VVV) survey. Based on the spectral features, 25 sources are classified as eruptive young stellar objects (YSOs), including 15 newly identified FUors, six with long-lasting but EXor-like bursts of magnetospheric accretion and four displaying outflow-dominated spectra. By examining the photometric behaviours of eruptive YSOs, we found most FUor-type outbursts have higher amplitudes ($\Delta K_s$ and $\Delta W2$), faster eruptive timescales and bluer infrared colours than the other outburst types. In addition, we identified seven post-main sequence variables apparently associated with deep dipping events and an eruptive star with deep AlO absorption bands resembling those seen in the V838 Mon stellar merger.

Period bouncers are cataclysmic variables (CVs) that have evolved past their orbital period minimum. The strong disagreement between theory and observations of the relative fraction of period bouncers is a severe shortcoming in the understanding of CV evolution. We test the implications of the hypothesis that magnetic braking (MB), which is suggested to be an additional angular momentum loss (AML) mechanism for CVs below the period gap ($P_\mathrm{orb}\lesssim 120$ min), weakens around their period minimum. We compute the evolution of CV donors below the period gap using the MESA code, assuming that the evolution of the system is driven by AML by gravitational wave radiation (GWR) and MB. We parametrize the MB strength as $\mathrm{AML_{MB}}=\kappa\mathrm{AML_{GWR}}$. We compute two qualitatively different sets of models, one where $\kappa$ is a constant and the other where $\kappa$ depends on stellar parameters. We find that in the latter set of models, $\kappa$ decreases as the CV approaches the period minimum ($P_\mathrm{orb}\approx80\,$ min), beyond which $\kappa\approx0$. This stalls their evolution so that they spend a long time in the observed period minimum spike ($80\lesssim P_\mathrm{orb}/\,\mathrm{min}\lesssim 86$). Here they become difficult to distinguish from pre-bounce systems in the spike. A strong decrease in mass-transfer rate makes them virtually undetectable as they evolve further. We also discuss the physical processes, such as dynamo action, white dwarf magnetism and dead zones, that may cause such a weakening of MB at short orbital periods. The weakening magnetic braking formalism solves the problem of the lack of period bouncers in CV observational surveys.

We develop a rapid algorithm for the evolution of stable, circular, circumbinary discs suitable for parameter estimation and population synthesis modelling. Our model includes disc mass and angular momentum changes, accretion on to the binary stars, and binary orbital eccentricity pumping. We fit our model to the post-asymptotic giant branch (post-AGB) circumbinary disc around IRAS 08544-4431, finding reasonable agreement despite the simplicity of our model. Our best-fitting disc has a mass of about $0.01\, \mathrm{M}_{\odot }$ and angular momentum $2.7\times 10^{52}\, \mathrm{g}\, \mathrm{cm}^{2}\, \mathrm{s}^{-1}\simeq 9 \,\mathrm{M}_{\odot }\, \mathrm{km}\, \mathrm{s}^{-1}\, \mathrm{au}$, corresponding to 0.0079 and 0.16 of the common-envelope mass and angular momentum, respectively. The best-fitting disc viscosity is $\alpha _\mathrm{disc} = 5 \times 10^{-3}$ and our tidal torque algorithm can be constrained such that the inner edge of the disc $R_{\mathrm{in}}\sim 2a$. The inner binary eccentricity reaches about 0.13 in our best-fitting model of IRAS 08544-4431, short of the observed 0.22. The circumbinary disc evaporates quickly when the post-AGB star reaches a temperature of $\sim \! 6\times 10^4\, \mathrm{K}$, suggesting that planetismals must form in the disc in about $10^{4}\, \mathrm{yr}$ if secondary planet formation is to occur, while accretion from the disc on to the stars at about 10 times the inner-edge viscous rate can double the disc lifetime.