Extreme helium stars (EHes) are low-mass hydrogen-deficient stars thought to be the products of double white dwarf mergers. Despite prolonged ground-based observations, there is no consensus on the properties of their photometric variability. In this article, we present an analysis of TESS light curves for all known EHe stars, constituting the first population-level study of EHe photometric variability. We present updated TESS light curves for the two confirmed large-amplitude pulsators, V652 Her and BX Cir, and discuss the potential r-mode pulsators BD+37 442 and BD+37 1977. Notably, we found that the majority of EHe stars exhibit stochastic low-frequency (SLF) variability, or a signal with power increasing smoothly towards low frequencies, rather than peaks in the power spectrum corresponding to oscillation modes. We characterised the SLF variability of EHe stars using Gaussian process regression with a stochastically-driven/damped simple harmonic oscillator kernel and measured the characteristic timescale, low-frequency amplitude, and quality factor for each star. The variability timescales range from approximately 0.5 to 10 d and correlate strongly with stellar parameters, following both the granulation scaling relations established for cool stars and the convective turnover timescales predicted by the Fe opacity subsurface convection zone in one-dimensional EHe stellar models. Two metal-poor EHe stars show no detectable SLF variability, consistent with a metallicity-dependent driving mechanism. Our results suggest that SLF variability in EHe stars may be driven by subsurface convection, though further theoretical work is needed to distinguish between other potential driving mechanisms.

The R Coronae Borealis (RCB) variables are rare, hydrogen-deficient, carbon-rich supergiants known for large, erratic declines in brightness due to dust formation. Recently, the number of known RCB stars in the Milky Way and Magellanic Clouds has increased from $\sim$30 to 162. We use all-sky and targeted photometric surveys to create the longest possible light curves for all known RCB stars and systematically study their declines. Our study, the largest of its kind, includes measurements of decline activity levels, morphologies, and periodicities for nearly all RCB stars. We confirm previous predictions that cool RCB stars exhibit more declines than warm RCBs, supporting a relationship between dust formation and condensation temperatures. We also find evidence for two distinct dust production mechanisms. R CrB and SU Tau show decline onsets consistent with a Poisson process, suggesting their dust production is driven by stochastic processes, such as convection. In contrast, RY Sgr's declines correlate with its pulsation period, suggesting that its dust production is driven by pulsationally induced shocks. Finally, we show that the dust properties of the related class of DY Per variables differ from those of the RCB stars, suggesting differences in their evolutionary status.

Hydrogen-deficient Carbon (HdC) stars are a class of supergiants with anomalous chemical compositions, suggesting that they are remnants of CO–He white dwarf (WD) mergers. This class comprises two spectroscopically similar subclasses—dusty R Coronae Borealis (RCB) and dustless Hydrogen-deficient Carbon (dLHdC) stars. Both subclasses have a stark overabundance of 18 O in their atmospheres, but spectroscopic differences between them remain poorly studied. We present high-resolution ( R ≈ 75,000) K -band spectra of six RCB and six dLHdC stars, including four newly discovered dLHdC stars, making this the largest sample to date. We develop a semi-automated fitting routine to measure 16 O/ 18 O ratios for this sample, tripling the number of dLHdC stars with oxygen isotope ratios measured from high resolution spectra. All six dLHdC stars have 16 O/ 18 O < 1, while the RCB stars have 16 O/ 18 O > 4. Additionally, for the first time, we find a trend of decreasing 16 O/ 18 O ratios with increasing effective temperature for HdC stars, consistent with predictions of theoretical WD merger models. However, we note that current models overpredict the low 16 O/ 18 O ratios of dLHdC stars by two orders of magnitude. We also measure abundances of C, N, O, Fe, S, Si, Mg, Na, and Ca for these stars. We observe a correlation between the abundances of 14 N and 18 O in our sample, suggesting that a fixed fraction of the 14 N is converted to 18 O in these stars via α -capture. Our results affirm the emerging picture that the mass ratio/total mass of the WD binary determine whether an RCB or dLHdC is formed post-merger.

Hydrogen-deficient Carbon (HdC) stars are rare, low-mass, chemically peculiar, supergiant variables believed to be formed by a double white dwarf (DWD) merger, specifically of a Carbon/Oxygen- (CO-) and a Helium-white dwarf (He-WD). They consist of two subclasses– the dust-producing R Coronae Borealis (RCB) variables and their dustless counterparts the dustless HdCs (dLHdCs). Additionally, there is another, slightly cooler set of potentially related carbon stars, the DY Persei type variables which have some, but not conclusive, evidence of Hydrogen-deficiency. Recent works have begun to explore the relationship between these three classes of stars, theorizing that they share an evolutionary pathway (a DWD merger) but come from different binary populations, specifically different total masses (Mtot) and mass ratios (q). In this work, we use the mesa modelling framework that has previously been used to model RCB stars and vary the merger parameters, Mtot and q, to explore how those parameters affect the abundances, temperatures, and luminosities of the resultant post-merger stars. We find that lower Mtot and larger q’s both decrease the luminosity and temperatures of post-merger models to the region of the Hertzsprung-Russell Diagram populated by the dLHdCs. These lower Mtot and larger q models also have smaller oxygen isotopic ratios (16O/18O) which is consistent with recent observations of dLHdCs compared to RCBs. None of the models generated in this work can explain the existence of the DY Persei type variables, however this may arise from the assumed metallicity of the models.

The ArmazoNes high Dispersion Echelle Spectrograph (ANDES) is the optical and near-infrared high-resolution echelle spectrograph envisioned for the European Extremely Large Telescope (ELT). We present a selection of science cases, supported by new calculations and simulations, where ANDES could enable major advances in the fields of stars and stellar populations. We focus on three key areas, including the physics of stellar atmospheres, structure, and evolution; stars of the Milky Way, Local Group, and beyond; and the star-planet connection. The key features of ANDES are its wide wavelength coverage at high spectral resolution and its access to the large collecting area of the ELT. These features position ANDES to address the most compelling and potentially transformative science questions in stellar astrophysics of the decades ahead, including questions which cannot be anticipated today.

Context. The Gaia DR3 release includes heliocentric radial velocity measurements and velocity variability indices for tens of millions of stars observed over 34 months. Aims. In this study, we utilise these indices to investigate the intrinsic radial velocity variations of Hydrogen-deficient Carbon (HdC) stars and Extreme Helium (EHe) stars across their large ranges of temperature and brightness. Methods. Taking advantage of the newly defined HdC temperature classes, we examine the evolution of the total velocity amplitude with effective temperature. Additionally, we analyse the variation in the dust production rate of R Coronae Borealis (RCB) stars with temperature using two different proxies for the photometric state of RCB stars: one from Gaia and another from the 2MASS survey. Results. Our observations revealed a trend in the evolution of the maximum radial velocity amplitude across each HdC temperature class. Similarly, we also observed a correlation between stellar temperature and the dust production rate. Conclusions. Interestingly, we possibly observed for the first time some variations of the intrinsic radial velocity amplitude and the dust production rate with HdC temperature class. If confirmed, these variations would indicate that the helium shell-burning giant stage starts with strong atmospheric motions that decrease in strength, up to similar to 6000 K, before picking up again as the HdC star atmosphere shrinks further in size and reaches warmer temperatures. Moreover, the dust formation rate appears to be much higher in colder RCB stars compared to warmer ones.

We present results from a systematic infrared (IR) census of R Coronae Borealis (RCB) stars in the Milky Way, using data from the Palomar Gattini IR (PGIR) survey. R Coronae Borealis stars are dusty, erratic variable stars presumably formed from the merger of a He-core and a CO-core white dwarf (WD). PGIR is a 30 cm J-band telescope with a 25 deg(2) camera that surveys 18000 deg(2) of the northern sky (delta>-28(o)) at a cadence of 2 days. Using PGIR J-band lightcurves for similar to 60 million stars together with mid-IR colors from WISE, we selected a sample of 530 candidate RCB stars. We obtained near-IR spectra for these candidates and identified 53 RCB stars in our sample. Accounting for our selection criteria, we find that there are a total of approximate to 350(-100)(+150)RCB stars in the Milky Way. Assuming typical RCB lifetimes, this corresponds to an RCB formation rate of 0.8 - 5 x 10(-3) yr(-1), consistent with observational and theoretical estimates of the He-CO WD merger rate. We searched for quasi-periodic pulsations in the PGIR lightcurves of RCB stars and present pulsation periods for 16 RCB stars. We also examined high-cadenced TESS lightcurves for RCB and the chemically similar, but dustless hydrogen-deficient carbon (dLHdC) stars. We find that dLHdC stars show variations on timescales shorter than RCB stars, suggesting that they may have lower masses than RCB stars. Finally, we identified 3 new spectroscopically confirmed and 12 candidate Galactic DY Per type stars - believed to be colder cousins of RCB stars - doubling the sample of Galactic DY Per type stars.

Around a million quasars have been catalogued in the Universe by probing deeper and using new methods for discovery. However, the hardest ones to find seem to be the rarest and brightest specimen. In this work, we study the properties of the most luminous of all quasars found so far. It has been overlooked until recently, which demonstrates that modern all-sky surveys have much to reveal. The black hole in this quasar accretes around one solar mass per day onto an existing mass of $\sim$17 billion solar masses. In this process its accretion disc alone releases a radiative energy of $2\times 10^{41}$ Watts. If the quasar is not strongly gravitationally lensed, then its broad line region (BLR) is expected to have the largest physical and angular diameter occurring in the Universe, and will allow the Very Large Telescope Interferometer to image its rotation and measure its black hole mass directly. This will be an important test for BLR size-luminosity relations, whose extrapolation has underpinned common black-hole mass estimates at high redshift.

Upon its release the Gaia DR3 catalogue has led to tremendous progress in multiple fields of astronomy by providing the complete astrometric solution for nearly 1.5 billion sources. We analysed the photometric and astrometric results for Hydrogen-deficient Carbon (HdC), Extreme Helium (EHe), and DYPer type stars to identify any potential biases and thus to select stars suitable for kinematic and spatial distribution studies. We investigated the impact of photometric declines in R Coronae Borealis (RCB) stars on Gaia astrometry using information from the Gaia IPD process cross-matched with light curves. We have reached the conclusion that the astrometric fits for numerous RCB stars are not valid due to the Gaia PSF chromaticity effect in both shape and centroid. The astrometric results of all stars with a significant time-dependent colour variation should be similarly affected. RCB stars might thus be promising sources to correct this effect in future Gaia releases. Furthermore, after validating the Gaia astrometric results for 92 stars, we observed that the majority of HdC and EHe stars are distributed across the three old stellar structures, the thick disk, the bulge and the halo. However, we have also uncovered evidence indicating that some of them exhibit orbits characteristic of the thin disk. This is also particularly true for all DYPer type stars studied. Finally, we have produced a list of star memberships for each Galactic substructure, and provided a list of heliocentric radial velocities and associated errors for targets not observed by Gaia DR3. We are beginning to observe a relationship between kinematics, stellar population, and metallicity in RCB and EHe stars. That relation can be explained, within the double degenerate scenario, by the large range in the delay time distribution expected from population synthesis simulations, particularly through the HybCO merger channel.

Abstract Quasars are supermassive black holes feasting on surrounding matter, which make them outshine their host galaxies. Around a million quasars have been cat- alogued in the Universe by probing deeper and using new methods for discovery. In this work, we study the properties of the most luminous of all quasars found so far. It has been overlooked until recently, which demonstrates that modern all-sky surveys have much to reveal. The black hole in this quasar accretes around one solar mass per day onto an existing mass of 15 billion solar masses. In this process its accretion disc alone releases a radiative energy that is equivalent to the output from between 365 and 640 trillion Suns. The range is mostly due to the unknown viewing angle of the disc, which radiates more intensely near its polar sight lines than at grazing angles to the disc.

Abstract We describe the first results from the All-sky BRIght, Complete Quasar Survey (AllBRICQS), which aims to discover the last remaining optically bright quasars. We present 156 spectroscopically confirmed quasars (140 newly identified) having $|b|>10^{\circ}$ . 152 of the quasars have Gaia DR3 magnitudes brighter than $B_{P}=16.5$ or $R_{P}=16$ mag, while four are slightly fainter. The quasars span a redshift range of $z=0.07-3.93$ . In particular, we highlight the properties of J0529-4351 at $z=3.93$ , which, if unlensed, is one of the most intrinsically luminous quasars in the Universe. The AllBRICQS sources have been selected by combining data from the Gaia and WISE all-sky satellite missions, and we successfully identify quasars not flagged as candidates by Gaia Data Release 3. We expect the completeness to be $\approx$ 96% within our magnitude and latitude limits, while the preliminary results indicate a selection purity of $\approx$ 96%. The optical spectroscopy used for source classification will also enable detailed quasar characterisation, including black hole mass measurements and identification of foreground absorption systems. The AllBRICQS sources will greatly enhance the number of quasars available for high-signal-to-noise follow-up with present and future facilities.

Stellar spectral classification has been highly useful in the study of stars. While there is a currently accepted spectral classification system for carbon stars, the subset of Hydrogen-deficient Carbon (HdC) stars has not been well described by such a system, due predominantly to their rarity and their variability. Here we present the first system for the classification of HdCs based on their spectra, which is made wholly on their observable appearance. We use a combination of dimensionality reduction and clustering algorithms with human classification to create such a system with eight total classes corresponding to temperature, and an additional second axis corresponding to the carbon molecular band strength. We classify over half of the known sample of HdC stars using this, and roughly calibrate the temperatures of each class using their colors. Additionally, we express trends in the occurrence of certain spectral peculiarities such as the presence of Hydrogen and Lithium lines. We also present three previously unpublished spectra, report the discovery of two new Galactic dustless HdC (dLHdC) stars and additionally discuss one especially unique star that appears to border between the hottest HdCs and the coolest Extreme Helium (EHe) stars.

Decades after their discovery, only four hydrogen-deficient carbon (HdC) stars were known to have no circumstellar dust shell. This is in complete contrast to the $\sim$130 known Galactic HdC stars that are notorious for being heavy dust producers, i.e. the R Coronae Borealis (RCB) stars. Together they form a rare class of supergiant stars that are thought to originate from the merger of CO/He white dwarf binary systems, otherwise known as the double-degenerate scenario. We searched for new dustless HdC (dLHdC) stars. We used primarily the 2MASS and GAIA eDR3 catalogues to select candidates that were followed-up spectroscopically. We discovered 27 new dLHdC stars, one new RCB star and two new EHe stars. Surprisingly, 20 of the new dLHdC stars share a characteristic of the known dLHdC star HD 148839, having lower atmospheric hydrogen deficiencies. The uncovered population of dLHdC stars exhibit a Bulge-like distribution, like the RCB stars, but show multiple differences from those that indicate they are a different population of HdC stars following its own evolutionary sequence with a fainter luminosity and also a narrow range of effective temperature. We found indication of a current low dust production activity for four of the new dLHdC stars which could be typical RCB stars passing through a transition time. We have evidence for the first time of a large range of absolute magnitudes in the overall population of HdC stars, spanning over 3 mag. In the favoured formation framework, this is explained by a large range in the initial total WD binary mass which leads to a series of evolutionary sequences with distinct maximum brightness and initial temperature. The cold Galactic RCB stars are also noticeably fainter than the Magellanic ones, possibly due to a difference in metallicity resulting in different WD mass ratio. In our Galaxy, there could be as many dLHdC stars as RCB stars.

ABSTRACT We search for ultraluminous Quasi-Stellar Objects (QSOs) at high redshift using photometry from the SkyMapper Southern Survey Data Release 3 (DR3), in combination with 2MASS, VHS DR6, VIKING DR5, AllWISE, and CatWISE2020, as well as parallaxes and proper motions from Gaia DR2 and eDR3. We report 142 newly discovered Southern QSOs at 3.8 < z < 5.5, of which 126 have M145 < −27 AB mag and are found in a search area of 14 486 deg2. This Southern sample, utilizing the Gaia astrometry to offset wider photometric colour criteria, achieves unprecedented completeness for an ultraluminous QSO search at high redshift. In combination with already known QSOs, we construct a sample that is >80 per cent complete for M145 < −27.33 AB mag at z = 4.7 and for M145 < −27.73 AB mag at z = 5.4. We derive the bright end of the QSO luminosity function at rest frame 145 nm for z = 4.7–5.4 and measure its slope to be β = −3.60 ± 0.37 and β = −3.38 ± 0.32 for two different estimates of the faint-end QSO density adopted from the literature. We also present the first z ∼ 5 QSO luminosity function at rest frame 300 nm.

We have searched for long duration microlensing events originating from intermediate mass Black Holes (BH) in the halo of the Milky Way, using archival data from EROS-2 and MACHO photometric surveys towards the Large Magellanic Cloud. We combined data from these two surveys to create a common database of light curves for 14.1 million objects in LMC, covering a total duration of 10.6 years, with flux series measured through 4 wide band filters. We have carried out a microlensing search on these light curves, complemented by 22.7 million light curves, observed by EROS-2 only or MACHO only over about 7 years, with flux series measured through only 2 filters. A likelihood analysis, taking into account LMC self lensing and Milky Way disk contributions allows us to conclude that compact objects with masses in the range 10 − 100M cannot make up more than ∼ 15% of a standard halo total mass (at 95% confidence level). Our analysis sensitivity weakens for heavier objects, although we still exclude that ∼ 50% of the halo be made of ∼ 1000M BHs. Combined with previous EROS results, an upper limit of ∼ 15% of the total halo mass can be obtained for the contribution of compact halo objects in the mass range 10−6 − 102 M .

We searched for long-duration microlensing events originating from intermediate-mass black holes (BH) in the halo of the Milky Way, using archival data from the EROS-2 and MACHO photometric surveys towards the Large Magellanic Cloud (LMC). We combined data from these two surveys to create a common database of light curves for 14.1 million objects in the LMC, covering a total duration of 10.6 years, with flux series measured in four wide passbands. We carried out a microlensing search on these light curves, complemented by the light curves of 22.7 million objects, observed only by EROS-2 or only by MACHO, over about 7 years, with flux series measured in only two passbands. A likelihood analysis, taking into account the LMC self-lensing and Milky Way disk contributions, allows us to conclude that compact objects with masses in the range 10 − 100 M⊙ cannot make up more than ∼15% of a standard halo total mass (at a 95% confidence level). Our analysis sensitivity weakens for heavier objects, although we still rule out the possibility of ∼50% of the halo being made of ∼1000 M⊙ BHs. Combined with previous EROS results, an upper limit of ∼15% of the total halo mass can be obtained for the contribution of compact halo objects in the mass range 10−6 − 102 M⊙.

Context. R Coronae Borealis (RCB) variables and their non-variable counterparts, the dustless Hydrogen-deficient Carbon (dLHdC) stars have been known to exhibit enhanced s-processed material on their surfaces, especially Sr, Y, and Ba. No comprehensive work has been done to explore the s-process in these types of stars, however one particular RCB star, U Aqr, has been under scrutiny for its extraordinary Sr enhancement. Aims. We aim to identify RCB and dLHdC stars that have significantly enhanced Sr abundances, such as U Aqr, and use stellar evolution models to begin to estimate the type of neutron exposure that occurs in a typical HdC star. Methods. We compared the strength of the Sr II 4077 Å spectral line to Ca II H to identify the new subclass of Sr-rich HdCs. We additionally used the structural and abundance information from existing RCB MESA models to calculate the neutron exposure parameter, τ. Results. We identified six stars in the Sr-rich class. Two are RCBs, and four are dLHdCs. We additionally found that the preferred RCB MESA model has a neutron exposure τ ≃ 0.1 mb−1, which is lower than the estimated τ between 0.15 and 0.6 mb−1 for the Sr-rich star U Aqr found in the literature. We found trends in the neutron exposure corresponding to He-burning shell temperature, metallicity, and assumed s-processing site. Conclusions. We have found a sub-class of six HdCs known as the Sr-rich class, which tend to lie in the halo, outside the typical distribution of RCBs and dLHdCs. We found that dLHdC stars are more likely to be Sr-rich than RCBs, with an occurrence rate of ~13% for dLHdCs and ~2% for RCBs. This is one of the first potential spectroscopic differences between RCBs and dLHdCs, along with dLHdCs having stronger surface abundances of 18O. We additionally found neutron exposure trends in our RCB models that will aide in understanding the interplay between model parameters and surface s-process elements.

Context. R Coronae Borealis (RCB) and dustless Hydrogen-deficient Carbon (dLHdC) stars are believed to be remnants of low mass white dwarf mergers. These supergiant stars have peculiar hydrogen-deficient carbon-rich chemistries and stark overabundances of O-18. RCB stars undergo dust formation episodes resulting in large-amplitude photometric variations that are not seen in dLHdC stars. Recently, the sample of known dLHdC stars in the Milky Way has more than quintupled with the discovery of 27 new dLHdC stars. Aims. It has been suggested that dLHdC stars have lower O-16/O-18 than RCB stars. We aim to compare the O-16/O-18 ratios for a large sample of dLHdC and RCB stars to examine this claim. Methods. We present medium resolution (R approximate to 3000) near-infrared spectra of 20 newly discovered dLHdC stars. We also present medium resolution (R approximate to 3000 - 8000) K-band spectra for 49 RCB stars. Due to the several free parameters and assumptions in our fitting strategy, we provide wide range estimates on the O-16/O-18 ratios of seven dLHdC and 33 RCB stars that show (CO)-C-12-O-16 and (CO)-C-12-O-18 absorption bands, and present the largest sample of such O-16/O-18 wide-range values for dLHdC and RCB stars to date. Results. We find that six of the seven dLHdC stars have O-16/O-18 < 0.5, while 28 of the 33 RCB stars have O-16/O-18 > 1. We also confirm that unlike RCB stars, dLHdC stars do not show strong blueshifted (>200 km s(-1)) He I 10 833 angstrom absorption, suggesting the absence of strong, dust-driven winds around them. Conclusions. Although we only can place wide range estimates on the O-16/O-18 and these are more uncertain in cool RCBs, our medium resolution spectra suggest that most dLHdC stars have lower O-16/O-18 than most RCB stars. This confirms one of the first, long-suspected spectroscopic differences between RCB and dLHdC stars. The different oxygen isotope ratios rule out the existing picture that RCB stars represent an evolved stage of dLHdC stars. Instead, we suggest that whether the white dwarf merger remnant is a dLHdC or RCB star depends on the mass ratios, masses and compositions of the merging white dwarfs. Future high resolution spectroscopic observations will help confirm and more precisely quantify the difference between the oxygen isotope ratios of the two classes.

We report the discovery of a bright (g = 14.5 mag (AB), K = 11.9 mag (Vega)) quasar at redshift z = 0.83 -- the optically brightest (unbeamed) quasar at z > 0.4. SMSS J114447.77-430859.3, at a Galactic latitude of b = +18.1deg, was identified by its optical colours from the SkyMapper Southern Survey (SMSS) during a search for symbiotic binary stars. Optical and near-infrared spectroscopy reveals broad MgII, H-beta, H-alpha, and Pa-beta emission lines, from which we measure a black hole mass of log10(M_BH/M_Sun) = 9.4 +/- 0.5. With its high luminosity, L_bol = (4.7 +/- 1.0) * 10^47 erg/s or M_i(z=2) = -29.74 mag (AB), we estimate an Eddington ratio of ~1.4. As the most luminous quasar known over the last ~9 Gyr of cosmic history, having a luminosity 8 times greater than 3C 273, the source offers a range of potential follow-up opportunities.

Since July 2014, the Gaia mission has been engaged in a high-spatial-resolution, time-resolved, precise, accurate astrometric, and photometric survey of the entire sky. Aims: We present the Gaia Science Alerts project, which has been in operation since 1 June 2016. We describe the system which has been developed to enable the discovery and publication of transient photometric events as seen by Gaia. Methods: We outline the data handling, timings, and performances, and we describe the transient detection algorithms and filtering procedures needed to manage the high false alarm rate. We identify two classes of events: (1) sources which are new to Gaia and (2) Gaia sources which have undergone a significant brightening or fading. Validation of the Gaia transit astrometry and photometry was performed, followed by testing of the source environment to minimise contamination from Solar System objects, bright stars, and fainter near-neighbours. Results: We show that the Gaia Science Alerts project suffers from very low contamination, that is there are very few false-positives. We find that the external completeness for supernovae, C_E=0.46, is dominated by the Gaia scanning law and the requirement of detections from both fields-of-view. Where we have two or more scans the internal completeness is C_I=0.79 at 3 arcsec or larger from the centres of galaxies, but it drops closer in, especially within 1 arcsec. Conclusions: The per-transit photometry for Gaia transients is precise to 1 per cent at G=13, and 3 per cent at G=19. The per-transit astrometry is accurate to 55 milliarcseconds when compared to Gaia DR2. The Gaia Science Alerts project is one of the most homogeneous and productive transient surveys in operation, and it is the only survey which covers the whole sky at high spatial resolution (subarcsecond), including the Galactic plane and bulge.