Short-period cataclysmic variables (spCVs), with orbital periods below the period gap ($P_{orb}$ < 2 hr), offer insight into the evolutionary models of CVs and can serve as strong emitters of gravitational waves (GWs). To identify new spCV candidates, we crossmatch a catalog of known CVs to sources with robust parallaxes in the Gaia second data release (DR2). We uncover and fit an apparently monotonic relationship between the color--absolute-magnitude diagram (CMD) position and $P_{orb}$ of these CVs, revealed in DR2. To supplement this relation, we develop a method for identifying sources with large photometric variability, a characteristic trait of spCVs. Using all available Gaia light curves, we construct a machine-learned regression model to predict variability metrics for sources in the CMD locus of known spCVs based solely on time-averaged covariates present in DR2. Using this approach we identify 3,253 candidate spCVs, of which $\sim$95% are previously unknown. Inspection of archival SDSS spectra of these candidates suggests that $>$82% are likely to be spCVs: a noticeably higher recovery rate than previous light curve searches, which bias toward active systems. We obtain optical spectra of 9 new systems at Lick Observatory and confirm that all objects are CV systems. We measure $P_{orb}$ for 7 systems using archival Gaia and Palomar Transient Factory light curves, 3 of which do not have previous $P_{orb}$ measurements. We use the CMD-$P_{orb}$ relation to infer the detectability of these systems to the upcoming LISA mission, and find that six sources may be coherent LISA verification binaries, with an estimated SNR > 5 in the 4 yr mission. This paper demonstrates that the time-averaged Gaia catalog is a powerful tool in the methodical discovery and characterization of time-varying objects, making it complementary to missions like ZTF, TESS, and the Vera Rubin LSST.
We have used ATLAS12 to generate hydrogen-deficient stellar atmospheres to allow us to construct synthetic spectra to explore the possibility that the donor stars in some cataclysmic variables (CVs) are hydrogen deficient. We find that four systems, AE Aqr, DX And, EY Cyg, and QZ Ser have significant hydrogen deficits. We confirm that carbon and magnesium deficits, and sodium enhancements, are common among CV donor stars. The three Z Cam systems we observed are found to have solar metallicities and no abundance anomalies. Two of these objects, Z Cam and AH Her, have M-type donor stars; much co…
The majority of cataclysmic variables are predicted to be post-period minimum systems with degenerate donor stars, the period bouncers. Owing to their intrinsic faintness, however, only a handful of these systems have so far been securely identified. We want to study the X-ray properties of two eclipsing period bouncers, OV Bootis and SDSS J103533.02+055158.3, that were selected for this study due to their proximity to Earth. We have obtained XMM-Newton phase-resolved X-ray and ultraviolet observations of the two objects for spectral and timing analysis. Owing to a recent dwarf nova outburst O…
We report the discovery of 1RXH J082623.6-505741, a 10.4 hr orbital period compact binary. Modeling extensive optical photometry and spectroscopy reveals a $\sim 0.4 M_{\odot}$ K-type secondary transferring mass through a low-state accretion disk to a non-magnetic $\sim 0.8 M_{\odot}$ white dwarf. The secondary is overluminous for its mass and dominates the optical spectra at all epochs, and must be evolved to fill its Roche Lobe at this orbital period. The X-ray luminosity $L_X \sim 1$-$2 \times 10^{32}$ erg s$^{-1}$ derived from both new XMM-Newton and archival observations, although high co…
Secondary stars in cataclysmic variables (CVs) follow a well defined period-density relation. Thus, canonical donor stars in CVs are generally low-mass stars of spectral type M. However, several CVs have been observed containing secondary stars which are too hot for their inferred masses. This particular configuration can be explained if the donor stars in these systems underwent significant nuclear evolution before they reached contact. In this paper we present SDSSJ001153.08-064739.2 as an additional example belonging to this peculiar type of CV and discuss in detail its evolutionary history…
Evolution of a long-period Cataclysmic Variable from the viewpoint of the donor star: the case of SDSS J085210.48+783246.6
Universidad Nacional Autónoma de México（墨西哥国立自治大学）；Instituto de Astronomía（天文研究所）；INAF – Osservatorio Astronomico di Brera（INAF-布雷拉天文台）；International Centre of Supernovae (ICESUN)（超新星国际中心（ICESUN））；Yunnan Key Laboratory of Supernova Research（云南省超新星研究重点实验室）；Yunnan Observatories, Chinese Academy of Sciences (CAS)（中国科学院云南天文台）；University of Warwick（华威大学）；Universidad Técnica Federico Santa María（费德里科·圣玛丽亚技术大学）；Università degli Studi di Padova（帕多瓦大学）
We present high-speed, three-colour photometry of the eclipsing dwarf nova PHL 1445, which, with an orbital period of 76.3 min, lies just below the period minimum of ~82 min for cataclysmic variable stars. Averaging four eclipses reveals resolved eclipses of the white dwarf and bright spot. We determined the system parameters by fitting a parameterised eclipse model to the averaged lightcurve. We obtain a mass ratio of q = 0.087 +- 0.006 and inclination i = 85.2 +- 0.9 degrees. The primary and donor masses were found to be Mw = 0.73 +- 0.03 Msun and Md = 0.064 +- 0.005 Msun, respectively. Thro…
Context. We present time-resolved spectroscopy and photometry of HS 0218+3229, a new long-period cataclysmic variable discovered within the Hamburg Quasar Survey. It is one of the few systems that allow a dynamical measurement of the masses of the stellar components. Aims. We combine the analysis of time-resolved optical spectroscopy and R-band photometry with the aim of measuring the mass of the white dwarf and the donor star and the orbital inclination. Methods. Cross-correlation of the spectra with K-type dwarf templates is used to derive the radial velocity curve of the donor star. An opti…
We present measurements of the component masses in 15 Cataclysmic Variables (CVs) - 6 new estimates and 9 improved estimates. We provide new calibrations of the relationship between superhump period excess and mass ratio, and use this relation to estimate donor star masses for 225 superhumping CVs. With an increased sample of donor masses we revisit the implications for CV evolution. We confirm the high mass of white dwarfs in CVs, but find no trend in white dwarf mass with orbital period. We argue for a revision in the location of the orbital period minimum of CVs to $79.6 \pm 0.2$ min, signi…
We reconstruct the evolutionary path followed by cataclysmic variables (CVs) from the observed mass-radius relationship of their donor stars. Along the way, we update the semi-empirical CV donor sequence of Knigge (2006) and present a comprehensive review of the link between CV evolution and donor physics. After calibrating state-of-the art stellar models for use in the CV setting, we fit self-consistent theoretical evolution sequences to the observed donor masses and radii. In the standard model of CV evolution, AML below the period gap is assumed to be driven solely by gravitational radiatio…
The detection of heavy elements at suprasolar abundances in the atmospheres of some accreting white dwarfs in cataclysmic variables, coupled with the high temperatures needed to produce these elements requires explosive thermonuclear burning. The central temperatures of any formerly more massive secondary stars in CVs undergoing hydrostatic CNO burning are far too low to produce these elements. Evidence is presented that at least some cataclysmic variables contain donor secondaries that have been contaminated by repeated novae ejecta and are transferring this material back to the white dwarf. …
We present high-speed, multicolour photometry of the faint, eclipsing cataclysmic variable (CV) SDSS J105754.25+275947.5. The light from this system is dominated by the white dwarf. Nonetheless, averaging many eclipses reveals additional features from the eclipse of the bright spot. This enables the fitting of a parameterised eclipse model to these average light curves, allowing the precise measurement of system parameters. We find a mass ratio of q = 0.0546 $\pm$ 0.0020 and inclination i = 85.74 $\pm$ 0.21$^{\circ}$. The white dwarf and donor masses were found to be M$_{\mathrm{w}}$ = 0.800 $…
We derive metallicities for 41 cataclysmic variables (CVs) from near-infrared spectroscopy. We use synthetic spectra that cover the 0.8 $μ$m $\leq λ\leq$ 2.5 $μ$m bandpass to ascertain the value of [Fe/H] for CVs with K-type donors, while also deriving abundances for other elements. Using calibrations for determining [Fe/H] from the $K$-band spectra of M-dwarfs, we derive more precise values for T$_{\rm eff}$ for the secondaries in the shortest period CVs, and examine whether they have carbon deficits. In general, the donor stars in CVs have sub-solar metallicities. We confirm carbon deficits …
We present a binary evolution study of cataclysmic variables (CVs) and related systems with white dwarf accretors, including for example, AM CVn systems, classical novae, supersoft X-ray sources, and systems with giant donor stars. Our approach intentionally avoids the complications associated with population synthesis algorithms thereby allowing us to present the first truly comprehensive exploration of all of the subsequent binary evolution pathways that ZACVs might follow (assuming fully non-conservative, Roche-lobe overflow onto an accreting WD) using the sophisticated binary stellar evolu…
We present a new sample of $K$-band spectral observations for CVs: non-magnetic and magnetic as well as present day and pre CVs. The purpose of this diverse sample is to address the recent claim that the secondary stars in dwarf novae are carbon deficient, having become so through a far more evolved evolution than the current paradigm predicts. Our new observations, along with previous literature results, span a wide range of orbital period and CV type. In general, dwarf novae in which the secondary star is seen show weak to no CO absorption while polar and pre-CV donor stars appear to have no…
We present LAMOST J0140355+392651 (hereafter J0140), a close ($P_{\rm orb} = 3.81$ hours) binary containing a bloated, low-mass ($M \approx 0.15 M_{\odot}$) proto-white dwarf (WD) and a massive ($M\approx 0.95\,M_{\odot}$) WD companion. The system's optical light curve is dominated by large-amplitude ellipsoidal variability but also exhibits additional scatter, likely driven by pulsations. The proto-WD is cooler ($T_{\rm eff} = 6800\pm 100$ K) and more puffy ($\log\left[g/\left({\rm cm\,s^{-2}}\right)\right]=4.74\pm0.07$) than any known extremely low mass (ELM) WD, but hotter than any known ca…
We model cataclysmic variables (CVs) with solar metallicity donors ($X=0.7,\:Z=0.02$) that evolve to form AM CVn stars through the Evolved CV formation channel using various angular momentum loss mechanisms by magnetic braking ($\mathrm{AML_{MB}}$). We find that the time-scale for $\mathrm{AML_{MB}}$ in our double-dynamo (DD) model is shorter than that of previously used empirical formulae. Owing to the shorter time-scales, a larger parameter space of initial conditions evolves to form AM CVn stars with the DD model than with other models. We perform an analysis of the expected number of AM CV…
I review what we know about the donor stars in cataclysmic variables (CVs), focusing particularly on the close link between these binary components and the overall secular evolution of CVs. I begin with a brief overview of the "standard model" of CV evolution and explain why the key observables this model is designed to explain - the period gap and the period minimum -- are intimately connected to the properties of the secondary stars in these systems. CV donors are expected to be slightly inflated relative to isolated, equal-mass main-sequence (MS) stars, and this "donor bloating" has now bee…
Evolution of cataclysmic variables under different magnetic braking prescriptions
School of Physical Science and Technology, Xinjiang University（新疆大学物理科学与技术学院）；Department of Nuclear Physics and Astronomy, Institute of Engineering Physics, Samarkand State University（撒马尔罕国立大学工程物理学院核物理与天文学系）
We present time-resolved J-band spectroscopy of the short period cataclysmic variable SDSS J143317.78+101123.3. We detect absorption lines from the sub-stellar donor star in this system, which contributes 38 +/- 5% to the J-band light. From the relative strengths of the absorption lines in the J-band, we estimate the spectral type of the donor star to be L2 +/- 1. These data are the first spectroscopic detection of a confirmed sub-stellar donor in a cataclysmic variable, and the spectral type is consistent with that expected from semi-empirical evolutionary models. Using skew mapping, we have …
Using photometric ULTRACAM observations of three new short period cataclysmic variables, we model the primary eclipse lightcurves to extract the orbital separation, masses, and radii of their component stars. We find donor masses of 0.060 +/- 0.008 solar masses, 0.042 +/- 0.001 solar masses, and 0.042 +/- 0.004 solar masses, two being very low-mass sub-stellar donors, and one within 2 sigma of the hydrogen burning limit. All three of the new systems lie close to the modified, "optimal" model evolutionary sequence of Knigge et al. (2011). We briefly re-evaluate the long-standing discrepancy bet…
It has been shown that the rate of angular momentum loss (AML) in cataclysmic variables (CVs) below the period gap is about 2.47 times that caused by gravitational radiation, suggesting extra AML mechanism besides gravitational radiation. Several potential mechanisms have been proposed but none of them has been verified. In this work we examine whether AML caused by friction between the expanding nova envelope and the donor star can account for the required AML rate. By adopting various expanding velocities of the envelope, we have calculated the evolution of CVs with typical initial parameter…
We present high-speed, three-colour photometry of the eclipsing cataclysmic variables CTCV 1300, CTCV 2354 and SDSS 1152. All three systems are below the observed "period gap" for cataclysmic variables. For each system we determine the system parameters by fitting a parameterised model to the observed eclipse light curve by chi-squared minimisation. We also present an updated analysis of all other eclipsing systems previously analysed by our group. New donor masses are generally between 1 and 2 sigma of those originally published, with the exception of SDSS 1502 and DV UMa. We note that the do…
Binary evolution predicts a population of helium core (M < 0.5 Msol) white dwarfs (WDs) that are slowly accreting hydrogen-rich material from low mass main sequence or brown dwarf donors with orbital periods less than four hours. Four binaries are presently known in the Milky Way that will reach such a mass-transferring state in a few Gyr. Despite these predictions and observations of progenitor binaries, there are still no secure cases of helium core WDs among the mass-transferring cataclysmic variables (CVs). This led us to calculate the fate of He WDs once accretion begins at a rate Mdot < …
The NSF's Karl G. Jansky Very Large Array (VLA) is used to observe 122 magnetic cataclysmic variables (MCVs) during three observing semesters (13B, 15A, and 18A). We report radio detections of 33 stars with fluxes in the range 6--8031 uJy. Twenty-eight stars are new radio sources, increasing the number of radio detected MCVs to more that 40. A surprising result is that about three-quarters (24 of 33 stars) of the detections show highly circularly polarized radio emission of short duration, which is characteristic of electron cyclotron maser emission. We argue that this emission originates from…
Cataclysmic Variables (CVs) are a distinct class of X-ray binaries transferring mass from a donor star to a compact star accretor, a white dwarf. They constitute a laboratory for accretion physics, mechanisms and disk theory together with dynamics of outflows and interaction with surrounding medium. Our understanding of the X-ray emission from CVs has shown substantial improvement in the last decade with the instruments on board present X-ray telescopes. We have a better understanding of the boundary layers and the accretion shocks using high sensitivity instruments and/or grating X-ray spectr…
Cataclysmic variable SDSS J143317.78+101123.3 with P=0.054241 d (78.1-min) was suspected to be a possible dwarf nova of WZ Sge type with the sub-stellar donor, but without detected outbursts so far. Checking the newly available data from ATLAS survey has revealed the outburst by at least 6 magnitudes in September 2020, thus confirming the dwarf nova nature of this object with the brown dwarf secondary. Other projects and individual observers have stopped their monitoring of this target several days before the outburst. This finding strengthens the value of observing the twilight zone by the pr…
We present a complete dynamical study of the intermediate polar and dwarf nova cataclysmic variable GK Per (Nova Persei 1901) based on a multi-site optical spectroscopy and $R$-band photometry campaign. The radial velocity curve of the evolved donor star has a semi-amplitude $K_2=126.4 \pm 0.9 \, \mathrm{km}\,\mathrm{s}^{-1}$ and an orbital period $P=1.996872 \pm 0.000009 \, \mathrm{d}$. We refine the projected rotational velocity of the donor star to $v_\mathrm{rot} \sin i = 52 \pm 2 \, \mathrm{km}\,\mathrm{s}^{-1}$ which, together with $K_2$, provides a donor star to white dwarf mass ratio $…
The mass-loss rate of donor stars in cataclysmic variables (CVs) is of paramount importance in the evolution of short-period CVs. Observed donors are oversized in comparison with those of isolated single stars of the same mass, which is thought to be a consequence of the mass loss. Using the empirical mass-radius relation of CVs and the homologous approximation for changes in effective temperature T_2, orbital period P, and luminosity of the donor with the stellar radius, we find the semi-empirical mass-loss rate M2_dot of CVs as a function of P. The derived M2_dot is at ~10^(-9.5)-10^(-10) Ms…
Institute of Astronomy and National Astronomical Observatory, Bulgarian Academy of Sciences（保加利亚科学院天文学研究所和国家天文台）；Department of Physics and Astronomy, Shumen University ”Episkop Konstantin Preslavski”（舒门大学“埃皮斯科普·康斯坦丁·普雷斯拉夫斯基”物理与天文学系）
V1082 Sgr is a cataclysmic variable with accretion luminosity above $10^{34}$erg s$^{-1}$, indicating a mass transfer rate above $10^{-9}M_{\odot}$yr$^{-1}$. However, its K type companion was suggested to be under-filling its Roche lobe (RL), making the high mass transfer rate a mystery. In this work we propose a possible model to explain this discrepancy. The system is proposed to be an intermediate polar, with its K type companion filling its RL. The mass of the white dwarf star is evaluated to be $0.77\pm0.11M_{\odot}$ from both X-ray continuum fitting and Fe line flux ratio measurements. W…
The Long-Period Radio Transient and Cataclysmic Variable ASKAP J1745-5051: Evidence for a 15,000 K White Dwarf and a Sub-Stellar Donor
School of Physics and Astronomy, University of Southampton（南安普顿大学物理与天文学院）；Centre for Extragalactic Astronomy, Department of Physics, Durham University（杜伦大学物理系河外天文中心）；INAF-Capodimonte Astronomical Observatory（意大利国家天体物理研究所卡波迪蒙特天文台）；Department of Physics, University of Warwick（华威大学物理系）；Institute of Space Sciences (ICE, CSIC)（空间科学研究所（西班牙高等科学研究委员会））；Institut d’Estudis Espacials de Catalunya (IEEC)（加泰罗尼亚太空研究学院）
According to standard evolutionary theory for cataclysmic variables (CVs), angular momentum loss drives CVs to initially evolve from longer to shorter orbital periods until a minimum period is reached (\approx 80 min). At roughly this stage, the donors becomes degenerate, expand in size, and the systems move towards longer Porb. Theory predicts that 70% of all CVs should have passed their minimum period and have sub-stellar donors, but until recently, no such systems were known. I present one CV showing evidence of harbouring a sub-dwarf donor, SDSS J1507+52. Due to the system's unusually shor…
Purely photometric models can be used to determine the binary parameters of eclipsing cataclysmic variables with a high degree of precision. However, the photometric method relies on a number of assumptions, and to date there have been very few independent checks of this method in the literature. We present time-resolved spectroscopy of the P=90.9 min eclipsing cataclysmic variable OY Carinae obtained with X-shooter on the VLT, in which we detect the donor star from K I lines in the J-band. We measure the radial velocity amplitude of the donor star K2 = 470.0 +/- 2.7 km/s, consistent with pred…
Classifying optical (out)bursts in cataclysmic variables: the distinct observational characteristics of dwarf novae, micronovae, stellar flares and magnetic gating
The orbital periods of most eclipsing cataclysmic binaries are not undergoing linear secular decreases of order a few parts per billion as expected from simple theory. Instead, they show several parts per million increases and decreases on timescales of years to decades, ascribed to magnetic effects in their donors, triple companions, or both. To directly test the triple companion hypothesis, we carried out a speckle imaging survey of six of the nearest and brightest cataclysmic variables. We found no main sequence companions earlier than spectral types M4V in the separation range 0.02" - 1.2"…
We present a systematic survey for mass-transferring and recently-detached cataclysmic variables (CVs) with evolved secondaries, which are progenitors of extremely low-mass white dwarfs (ELM WDs), AM CVn systems, and detached ultracompact binaries. We select targets below the main sequence in the Gaia color-magnitude diagram with ZTF light curves showing large-amplitude ellipsoidal variability and orbital period $P_{\rm orb} < 6$ hr. This yields 51 candidates brighter than G=18, of which we have obtained many-epoch spectra for 21. We confirm all 21 to be completely -- or nearly -- Roche lobe f…
While highly evolved cataclysmic variables (CVs) with brown dwarf donors, often called "period bouncers", are predicted to make up $\simeq40-70$ % of the Galactic CV population, only a handful of such systems are currently known. The identification and characterization of additional period bouncers is therefore important to probe this poorly understood phase of CV evolution. We investigate the evolution of the CV QZ Lib following its 2004 super-outburst using multi-epoch spectroscopy. From time-resolved spectroscopic observations we measure the orbital period of the system, $P_\mathrm{orb}= 0.…
AE Aqr was until recently the only known magnetic cataclysmic variable (MCV) containing a rapidly spinning (33.08 s) white dwarf (WD). Its radio emission is believed to be a superposition of synchrotron emitting plasmoids, because it has a positive spectral index spanning three orders of magnitude (~2-2000 GHz) and is unpolarized. Both characteristics are unusual for MCVs. Recently, Thorstensen has suggested that the cataclysmic variable LAMOST J024048.51+195226.9 (henceforth, J0240+19) is a twin of AE Aqr based on its optical spectra. Optical photometry shows the star to be a high-inclination…
We present a study of the orbital light curves of the recurrent nova IM Normae since its 2002 outburst. The broad "eclipses" recur with a 2.46 hour period, which increases on a timescale of 1.28(16)x10^6 years. Under the assumption of conservative mass-transfer, this suggests a rate near 10^-7 M_sol/year, and this agrees with the estimated /accretion/ rate of the postnova, based on our estimate of luminosity. IM Nor appears to be a close match to the famous recurrent nova T Pyxidis. Both stars appear to have very high accretion rates, sufficient to drive the recurrent-nova events. Both have qu…
We have carried out an extensive population synthesis study of the ensemble properties of the present-day population of cataclysmic variables (PDCVs) that takes into account the nuclear evolution of high-mass donors close to the bifurcation and dynamical instability limits. Assuming the interrupted magnetic braking paradigm, we confirm many of the general features associated with the observed CV population and find enormous diversity in their secular properties. We predict that nearly half of the non-magnetic CVs with Porb > 6 hours are at least mildly evolved (i.e., greater than one-half of t…
We present high time-resolution spectroscopy of the eclipsing cataclysmic variable SDSSJ143317.78+101123.3 obtained with QUCAM2, a high-speed/low-noise electron-multiplying CCD camera. Littlefair et al. measured the mass of the secondary star in SDSSJ143317.78+101123.3 using a light-curve fitting technique and obtained a value of M2=0.060+/-0.003 Msun, making it one of the three first bona-fide detections of a brown-dwarf mass donor in a cataclysmic variable. In this paper we present a dynamical measurement supporting this important result. We measured the radial-velocity semi-amplitude of the…
We present time-series spectroscopy of two short period cataclysmic variables, CC Scl and V2051 Oph, to test the efficiency of Doppler tomography-based methods in constraining orbital parameters of evolved cataclysmic variables. We find that the Ca~II triplet lines offer superior diagnostics, revealing emission components from the mass donors and sharp images of the accretion discs. Furthermore, we use Monte-Carlo methods to estimate the uncertainties from ensembles of Doppler maps. We compare our new methods against traditional radial velocity methods and show that they offer a valid route to…
We used the light curve code XRBinary to model the quiescent K2 light curves of three low-inclination cataclysmic variables (CVs): 1RXS\,J0632+2536 (J0632+2536), RZ\,Leo, TW\,Vir and the pre-CV WD\,1144+011. Optimized light curve models were obtained using a nonlinear fitting code NMfit and visualized by Phoebe 2.0. The disk model of J0632+2536 shows that one hotspot at the edge of the disk is enough to describe its light curve, while the other two dwarf nova (DN): RZ\,Leo and TW\,Vir require two hotspots. A typical pre-CV model with a weak irradiation effect for WD\,1144+011 can explain its s…
Photometric masses for long period CVs: the case study of CSS131106
University of Ferrara（费拉拉大学）；University of Sheffield（谢菲尔德大学）；Instituto de Astrofísica de Canarias（加那利群岛天体物理研究所）；University of Hamburg（汉堡大学）；Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma（俄克拉荷马大学霍默·L·多德物理与天文系）；JILA, University of Colorado and National Institute of Standards and Technology（科罗拉多大学与美国国家标准与技术研究院联合JILA实验室）
The predicted and observed space density of cataclysmic variables (CVs) have been for a long time discrepant by at least an order of magnitude. The standard model of CV evolution predicts that the vast majority of CVs should be period bouncers, whose space density has been recently measured to be $ρ\lesssim 2 \times 10^{-5}$ pc$^{-3}$. We performed population synthesis of CVs using an updated version of the Binary Stellar Evolution (BSE) code for single and binary star evolution. We find that the recently suggested empirical prescription of consequential angular momentum loss (CAML) brings int…
