DOCSLIB.ORG

A Calculator for Roche Lobe Properties Denis a Leahy1* and Janet C Leahy2

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
A Calculator for Roche Lobe Properties Denis a Leahy1* and Janet C Leahy2 View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Springer - Publisher Connector Leahy and Leahy Computational Astrophysics and Cosmology (2015)2:4 DOI 10.1186/s40668-015-0008-8 S O F T WA R E Open Access A calculator for Roche lobe properties Denis A Leahy1* and Janet C Leahy2 Abstract Background: The Roche lobe geometry is important to understand and study the properties of the mass-losing component in a semi-detached binary system. However it is not easy to calculate accurately, and existing tables usually do not include the parameters of the binary system under study, nor do they allow for non-synchronous rotation. Results: A calculator for properties of the Roche lobe is presented in two formats. An easy-to-use Java version has a graphic interface, and a Fortran 90 version has a command line interface. The Fortran version allows for easy modifications by the user. Both versions have two basic output options: one provides values of a set of various quantities (such as the Lagrange points along the binary axis, and area and volume of the Roche lobe); the second provides R(θ, φ), the distance from the stellar center to the stellar surface for any specified polar angle. A single set of input parameters can be entered directly or a large set of input parameters can be specified in a text file. The calculator includes the options to have non-synchronous rotation of the star, or to have the star underfill its Roche lobe. It can be used to calculate Roche lobe properties for the case of elliptical orbits, with some restrictions. Conclusions: We present a convenient software tool for quickly and accurately calculating Roche lobe properties for mass ratio in the range 0.01 to 100, for Roche lobe fill-out factor in the range 0.1 to 1.0, and for dimensionless rotation rate of the star in the range 0.1 to 2.0. This will allow anyone working with a binary star system to obtain the Roche lobe or stellar surface geometry for their system. Keywords: stars; binaries 1 Background has the potential equal to the L potential. The Roche lobe The Roche potential is the potential energy per unit test has the property that any material outside this surface is mass which is orbiting the center-of-mass of a binary star unbound from star and will be lost. system at the same rate as the two stars. A circular orbit Many works have studied and calculated properties of is assumed for the binary system. The Roche potential in- the Roche potential and the Roche lobe, starting with the cludes both gravitational and centripetal energy, such that pioneering work of Kopal (). Plavec and Kratochvil its derivative gives the force (and thus acceleration) on the () present tables of distances for several points on the test mass. equipotential surfaces which pass through the L and L The Roche potential has many uses, including finding Lagrange points. This was done for a range of mass ra- the locations in the binary system where the acceleration tios from . to .. Eggleton () calculated volumes, V , is zero- the Lagrange points L, L, L, L and L. In the oftheRochelobeforarangeofmassratiostoobtainthe case of a binary star system where one of the stars (star ) equivalent volume radius Req (defined by V =πReq/). He increases its size, star will reach a limiting surface. This then presented a simple fitting formula for Req as a function surface is called the Roche lobe, which is sketched in Fig- of q,accuratetobetterthan%,whichisoftenusedand ure . The Roche lobe is also defined by the surface that now known as the Eggleton formula. Mochnacki () presented tables of potentials and positions of the L and L Lagrange points as a function of mass ratio. He defined *Correspondence: [email protected] a fill-out factor F in terms of the potential of an equipoten- 1Department of Physics and Astronomy, University of Calgary, 2500 University Dr. NW, Calgary, Canada tial surface relative to the potential of the surfaces through Full list of author information is available at the end of the article the L and L points. F was defined so that F <corre- © 2015 Leahy and Leahy; licensee Springer. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduc- tion in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Leahy and Leahy Computational Astrophysics and Cosmology (2015)2:4 Page 2 of 6 Figure 1 Roche lobe geometry. Illustration of the Roche lobe for star 1, with x, y, z axes and the various Roche radii (RL1, Rbk, Ry, Rz and Req). sponds to surfaces inside the Roche lobe, and < F < tential (r, θ, φ) in the case of synchronous rotation is: corresponds to surfaces between the Roche lobe and the equipotential through the L point. He gave tables of vol- (r, θ, φ)= + q ume radius, area, average gravity and average inverse grav- r –r sin θ cos φ + r ity as a function of mass ratio and F. Pathania and Medupe q + – r sin θ cos φ + r sin θ .() () present series expansions for the radius of Roche equipotential surfaces, and compare various orders of the expansion to numerically calculated values. This is the same form used by Kopal () and Pathania The purpose of the present work is to present an freely and Medupe (). When non-synchronous rotation is available software tool, written in two versions (Java and included Limber (), with p = star/binary is the rate Fortran), which calculates radii of the Roche lobe. It does of stellar rotation divided by the binary rotation rate, the potential becomes: this for any specified direction, and gives some other com- monlyusedquantities(suchastheLagrangepointsand values of the potential). The calculator is designed to be (r, θ, φ)= + q r –r sin θ cos φ + r accurate for any mass ratio q between . and , for di- q + mensionless rotation rates between . and , and fill-out – r sin θ cos φ + pr sin θ .() factors between . and .. The calculator may work for parameters outside these limits but has not been tested for This potential can be further generalized to the case accuracy or errors outside these limits. of elliptical orbits, as discussed in Sepinsky et al. (). The coordinates are Cartesian (x, y, z) and spherical- In the quasi-static approximation, valid for dynamical θ φ polar (r, , ), centred on star (with mass M), with the timescale of the star much less than the tidal timescale, x-axis (θ = π/, φ = ) pointing towards star (with mass theinstantaneousshapeofthestarcanbeapproximated M). The z-axis is perpendicular to the orbital plane. The by the instantaneous surface of constant potential, even mass ratio is defined as q = M/M and the binary separa- though the instantaneous surface is changing with orbital tion is a. phase. As shown by Sepinsky et al. (), the instanta- We use the dimensionless form of the Roche poten- neous potential for an elliptical orbit can be written in the tial (or potential energy per unit mass) obtained by di- same form as equation ()aboveifonereplacesp by the function viding by GM/a,whereG is Newton’s gravitational con- stant, and using distances in units of the binary separa- p( + e) tion a. The equation for the resulting dimensionless po- A(p, e, ν)= () ( + e cos(ν)) Leahy and Leahy Computational Astrophysics and Cosmology (2015)2:4 Page 3 of 6 with e is the eccentricity and ν isthetrueanomalyforthe X), and the values of the potential at the L point (), position of the star in its elliptical orbit. at the L point ()andattheLpoint(). The area, For a physical system, one knows the actual values of the A,andvolume,V ,oftheRochelobearegiven(inunitsof masses M and M. Either one specifies the binary sepa- a and a , respectively), and the equivalent volume radius ration a, or calculates it from the orbital period P,using Req,definedbyV =πReq/ and area radius Ra,definedby π Kepler’s third law, a = G(M + M)P . Dimensionless A =πRa.ForthecaseofF < , i.e. star inside its Roche distances are converted into physical units by multiplying lobe, the values of Rbk , Ry, Rz, A, V , Ra and Req are for the by a. stellar surface. Additionally the front radius, Rfr of the star TheLagrangepointsarethelocationswherethepoten- (along the positive x-axis) is given because it is not equal tial (or dimensionless potential) has a maximum (or min- to RL for F <. imum) or saddle point. There are a total of Lagrange The L, L and L Lagrange points are along the x-axis points (L, L, L, L and L). The L point is the La- (y = z = ). A root-finding routine is used to find the x- grange point located between the two stars. One finds the value where the derivative of (r, θ, φ)alongthex-axisis positions of and the values of the potential at the Lagrange zero. The root is found to an accuracy of part in (Java points by solving version) and part in (Fortran version) using Brent’s method (Brent ). This method combines the bisection ∇(r, θ, φ)=. () method, the secant method and inverse quadratic inter- polation. It has been shown previously that the L and L The Roche lobe (of star ) is the surface surrounding star points lie in the x-y plane, and either of these when taken having the potential equal to the potential of the L point.
Load more

Recommended publications
  • Eclipsing Binary Pulsars
    Binary Radio Pulsars ASP Conference Series, Vol. 328, 2005 F. A. Rasio and I. H. Stairs Eclipsing Binary Pulsars Paulo C. C. Freire Arecibo Observatory, HC 3 Box 53995, Arecibo, PR 00612, USA Abstract. The ¯rst eclipsing binary pulsar, PSR B1957+20, was discovered in 1987. Since then, 13 other eclipsing low-mass binary pulsars have been found; 12 of these are in globular clusters. In this paper we list the known eclipsing bi- nary pulsars and their properties, with special attention to the eclipsing systems in 47 Tuc. We ¯nd that there are two fundamentally di®erent groups of eclipsing binary pulsars, separated by their companion masses. The less massive systems (M 0:02 M¯) are a product of predictable stellar evolution in binary pulsars. c » The systems with more massive companions (Mc 0:2 M¯) were formed by ex- change encounters in globular clusters, and for that»reason are exclusive to those environments. This class of systems can be used to learn about the neutron star recycling fraction in the globular clusters actively forming pulsars. We suggest that most of these binary systems are undetectable at radio wavelengths. 1. Introduction The ¯rst eclipsing binary pulsar, PSR B1957+12, was discovered in 1987 (Fruchter, Stinebring, & Taylor 1987). Since its discovery, 13 other eclipsing binary pulsars with low-mass companions have been found, these are listed in Table 1, with relevant refer- ences. Of these systems, 12 are found in globular clusters (GCs). To these we add a list of binary systems with companion masses smaller than 0:02 M¯ that are, as we will see, intimately related to a subset of the eclipsing binary systems.
    [Show full text]
  • PSR J2322− 2650–A Low-Luminosity Millisecond Pulsar with a Planetary
    MNRAS 000,1{10 (2017) Preprint 14 December 2017 Compiled using MNRAS LATEX style file v3.0 PSR J2322{2650 { A low-luminosity millisecond pulsar with a planetary-mass companion R. Spiewak,1? M. Bailes,1;2 E. D. Barr,3 N. D. R. Bhat,4 M. Burgay,5 A. D. Cameron,3 D. J. Champion,3 C. M. L. Flynn,1 A. Jameson,1;6 S. Johnston,7 M. J. Keith,8 M. Kramer,3;8 S. R. Kulkarni,9 L. Levin,8 A. G. Lyne,8 V. Morello,8 C. Ng,10 A. Possenti,5 V. Ravi,9 B. W. Stappers,8 W. van Straten,11 C. Tiburzi3;12 1Centre for Astrophysics and Supercomputing, Swinburne University of Technology, PO Box 218, Hawthorn, VIC 3122, Australia 2ARC Centre of Excellence for Gravitational Wave Discovery (OzGrav), Mail H29, Swinburne University of Technology, PO Box 218, Hawthorn, VIC 3122, Australia 3Max-Planck-Institut fur¨ Radioastronomie, Auf dem Hugel¨ 69, D-53121 Bonn, Germany 4International Centre for Radio Astronomy Research, Curtin University, Bentley, WA 6102, Australia 5INAF-Osservatorio Astronomico di Cagliari, via della Scienza 5, I-09047 Selargius, Italy 6ARC Centre of Excellence for All-Sky Astronomy (CAASTRO), Mail H30, Swinburne University of Technology, PO Box 218, Hawthorn, VIC 3122, Australia 7CSIRO Astronomy and Space Science, Australia Telescope National Facility, PO Box 76, Epping, NSW 1710, Australia 8Jodrell Bank Centre for Astrophysics, University of Manchester, Alan Turing Building, Oxford Road, Manchester M13 9PL, UK 9Cahill Center for Astronomy and Astrophysics, MC 249-17, California Institute of Technology, Pasadena, CA 91125, USA 10Department of Physics and Astronomy, University of British Columbia, 6224 Agriculture Road, Vancouver, BC V6T 1Z1, Canada 11Institute for Radio Astronomy & Space Research, Auckland University of Technology, Private Bag 92006, Auckland 1142, New Zealand 12Fakult¨at fur¨ Physik, Universit¨at Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany Accepted XXX.
    [Show full text]
  • Arxiv:1901.06939V2 [Astro-Ph.HE] 25 Jan 2019 a Single Object, Possibly Resembling a Thorne-Zytkow Star
    High-Mass X-ray Binaries Proceedings IAU Symposium No. 346, 2019 c 2019 International Astronomical Union L.M. Oskinova, E. Bozzo, T. Bulik, D. Gies, eds. DOI: 00.0000/X000000000000000X High-Mass X-ray Binaries: progenitors of double compact objects Edward P.J. van den Heuvel Anton Pannekoek Institute of Astronomy, University of Amsterdam, Postbus 92429, NL-1090GE, Amsterdam, the Netherlands email: [email protected] Abstract. A summary is given of the present state of our knowledge of High-Mass X-ray Bina- ries (HMXBs), their formation and expected future evolution. Among the HMXB-systems that contain neutron stars, only those that have orbital periods upwards of one year will survive the Common-Envelope (CE) evolution that follows the HMXB phase. These systems may produce close double neutron stars with eccentric orbits. The HMXBs that contain black holes do not necessarily evolve into a CE phase. Systems with relatively short orbital periods will evolve by stable Roche-lobe overflow to short-period Wolf-Rayet (WR) X-ray binaries containing a black hole. Two other ways for the formation of WR X-ray binaries with black holes are identified: CE-evolution of wide HMXBs and homogeneous evolution of very close systems. In all three cases, the final product of the WR X-ray binary will be a double black hole or a black hole neutron star binary. Keywords. Common Envelope Evolution, neutron star, black hole, double neutron star, double black hole, Wolf-Rayet X-ray Binary, formation, evolution 1. Introduction My emphasis in this review is on evolution: on what we think to know about how High Mass X-ray Binaries (HMXBs) were formed and how they may evolve further to form binaries consisting of two compact objects: double neutron stars, double black holes and neutron star-black hole binaries.
    [Show full text]
  • Neutron Star Planets: Atmospheric Processes and Irradiation A
    A&A 608, A147 (2017) Astronomy DOI: 10.1051/0004-6361/201731102 & c ESO 2017 Astrophysics Neutron star planets: Atmospheric processes and irradiation A. Patruno1; 2 and M. Kama3; 1 1 Leiden Observatory, Leiden University, Neils Bohrweg 2, 2333 CA Leiden, The Netherlands e-mail: [email protected] 2 ASTRON, the Netherlands Institute for Radio Astronomy, Postbus 2, 7900 AA Dwingeloo, The Netherlands 3 Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK Received 4 May 2017 / Accepted 14 August 2017 ABSTRACT Of the roughly 3000 neutron stars known, only a handful have sub-stellar companions. The most famous of these are the low-mass planets around the millisecond pulsar B1257+12. New evidence indicates that observational biases could still hide a wide variety of planetary systems around most neutron stars. We consider the environment and physical processes relevant to neutron star planets, in particular the effect of X-ray irradiation and the relativistic pulsar wind on the planetary atmosphere. We discuss the survival time of planet atmospheres and the planetary surface conditions around different classes of neutron stars, and define a neutron star habitable zone based on the presence of liquid water and retention of an atmosphere. Depending on as-yet poorly constrained aspects of the pulsar wind, both Super-Earths around B1257+12 could lie within its habitable zone. Key words. astrobiology – planets and satellites: atmospheres – stars: neutron – pulsars: individual: PSR B1257+12 1. Introduction been found to host sub-stellar companions. The “diamond- planet” system PSR J1719–1438 is a millisecond pulsar sur- Neutron stars are created in supernova explosions and begin their rounded by a Jupiter-mass companion thought to have formed lives surrounded by a fallback disk with a mass of order 0:1 to via ablation of its donor star (Bailes et al.
    [Show full text]
  • Tidal Decay and Stable Roche-Lobe Overflow of Short-Period Gaseous Exoplanets Brian Jackson Boise State University
    Boise State University ScholarWorks Physics Faculty Publications and Presentations Department of Physics 11-1-2016 Tidal Decay and Stable Roche-Lobe Overflow of Short-Period Gaseous Exoplanets Brian Jackson Boise State University Emily Jensen Boise State University Sarah Peacock University of Arizona Phil Arras University of Virginia Kaloyan Penev Princeton University This is an author-produced, peer-reviewed version of this article. The final, definitive version of this document can be found online at Celestial Mechanics and Dynamical Astronomy, published by Springer. Copyright restrictions may apply. The final publication is available at doi: 10.1007/ s10569-016-9704-1 This is an author-produced, peer-reviewed version of this article. The final, definitive version of this document can be found online at Celestial Mechanics and Dynamical Astronomy, published by Springer. Copyright restrictions may apply. doi: 10.1007/s10569-016-9704-1 Celestial Mechanics and Dynamical Astronomy manuscript No. (will be inserted by the editor) Tidal Decay and Stable Roche-Lobe Overflow of Short-Period Gaseous Exoplanets Brian Jackson · Emily Jensen · Sarah Peacock · Phil Arras · Kaloyan Penev Received: date / Accepted: date Abstract Many gaseous exoplanets in short-period orbits are on the verge or are in the process of Roche-lobe overflow (RLO). Moreover, orbital stability analysis shows tides can drive many hot Jupiters to spiral inevitably toward their host stars. Thus, the coupled processes of orbital evolution and RLO likely shape the observed distribution of close-in exoplanets and may even be responsible for producing some of the short-period rocky plan- ets. However, the exact outcome for an overflowing planet depends on its internal response to mass loss, and the accompanying orbital evolution can act to enhance or inhibit RLO.
    [Show full text]
  • Evolutionary History of Four Binary Blue Stragglers from the Globular Clusters Ω Cen, M 55, 47 Tuc, and NGC 6752 K
    A&A 597, A87 (2017) Astronomy DOI: 10.1051/0004-6361/201629511 & c ESO 2017 Astrophysics Evolutionary history of four binary blue stragglers from the globular clusters ! Cen, M 55, 47 Tuc, and NGC 6752 K. Ste¸pien´1, A. A. Pamyatnykh2, and M. Rozyczka2 1 Warsaw University Observatory, Al. Ujazdowskie 4, 00-478 Warsaw, Poland e-mail: [email protected] 2 Nicolaus Copernicus Astronomical Center, Bartycka 18, 00-716 Warsaw, Poland e-mail: [alosza; mnr]@camk.edu.pl Received 10 August 2016 / Accepted 30 September 2016 ABSTRACT Context. Origin and evolution of blue stragglers in globular clusters is still a matter of debate. Aims. The aim of the present investigation is to reproduce the evolutionary history of four binary blue stragglers in four different clusters, for which precise values of global parameters are known. Methods. Using the model for cool close binary evolution that we developed, progenitors of all investigated binaries were found and their parameters evolved into the presently observed values. Results. The results show that the progenitors of the binary blue stragglers are cool close binaries with period of a few days, which transform into stragglers by rejuvenation of the initially less massive component as a result of mass transfer from its more massive companion overflowing the inner critical Roche surface. The parameters of V209 from ! Cen indicate that the binary is substantially enriched in helium. This is an independent and strong evidence of the existence of the helium rich subpopulation in this cluster. Key words. stars: evolution – binaries: close – globular clusters: general – blue stragglers 1.
    [Show full text]
  • Young Blue Straggler Stars in the Galactic Field Gemunu Ekanayake Manhattanville College
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by University of Kentucky University of Kentucky UKnowledge Physics and Astronomy Faculty Publications Physics and Astronomy 6-19-2018 Young Blue Straggler Stars in the Galactic Field Gemunu Ekanayake Manhattanville College Ronald Wilhelm University of Kentucky, [email protected] Right click to open a feedback form in a new tab to let us know how this document benefits oy u. Follow this and additional works at: https://uknowledge.uky.edu/physastron_facpub Part of the Astrophysics and Astronomy Commons, and the Physics Commons Repository Citation Ekanayake, Gemunu and Wilhelm, Ronald, "Young Blue Straggler Stars in the Galactic Field" (2018). Physics and Astronomy Faculty Publications. 641. https://uknowledge.uky.edu/physastron_facpub/641 This Article is brought to you for free and open access by the Physics and Astronomy at UKnowledge. It has been accepted for inclusion in Physics and Astronomy Faculty Publications by an authorized administrator of UKnowledge. For more information, please contact [email protected]. Young Blue Straggler Stars in the Galactic Field Notes/Citation Information Published in Monthly Notices of the Royal Astronomical Society, v. 479, issue 2, p. 2623-2629. This article has been accepted for publication in Monthly Notices of the Royal Astronomical Society ©: 2018 The Author(s). Published by Oxford University Press on behalf of the Royal Astronomical Society. All rights reserved. The opc yright holders have granted the
    [Show full text]
  • Binaries and Stellar Evolution
    Chapter 6 Binaries and stellar evolution In the next few chapters we will consider evolutionary processes that occur in binary stars. In particular we will address the following questions: (1) Which kinds of interaction processes take place in binaries, and how do these affect their evolution as compared to that of single stars? (2) How do observed types of binary systems fit into the binary evolution scenario? One type of interaction process was already treated in Chapter 5,1 namely the dissipative effect of tides which can lead to spin-orbit coupling and to long-term evolution of the orbit (semi-major axis a and eccentricity e). Tidal interaction does not directly affect the evolution of the stars themselves, except possibly through its effect on stellar rotation. In particular it does not change the masses of the stars. However, when in the course of its evolution one of the stars fills its critical equipotential surface, the Roche lobe (Sect. 3.4), mass transfer may occur to the companion, which strongly affects both the masses and evolution of the stars as well as the orbit. Before treating mass transfer in more detail, in this chapter we briefly introduce the concept of Roche-lobe overflow, and give an overview of the aspects of single-star evolution that are relevant for binaries. 6.1 Roche-lobe overflow The concept of Roche-lobe overflow (RLOF) has proven very powerful in the description of binary evo- lution. The critical equipotential surface in the Roche potential, passing through the inner Lagrangian point L1, define two Roche lobes surrounding each star (Sect.
    [Show full text]
  • 23 Accretion
    23.Accretion 23Accretion 23.1 Useful references • Murray & Dermott, Ch.3 • Choudhuri, Secs.4.5.1,5.6 • Hansen, Kawaler, and Trimble, Sec.2.13 Much of our empirical knowledge of neutron stars and black holes comes from accretion: theflow of material from some object (usually a star) onto another. Accretion is a ubiquitous process in astrophysics, 3 contributing to the formation and growth of planets (< 10− M ), stars � ( M ), stellar remnants such as white dwarfs, neutron stars and black ∼ � holes (� 40M ), and even the supermassive black holes that lie at the � centers of galaxies (106 109 M ). − � 23.2 Lagrange Points and Equilibrium Ourfirst goal is to identify the points of equilibrium in a two-body bi- nary system with orbital periodP. Imagine a test particle (e.g., an atom of potentially accretable gas) near the binary: what forces act on it? To answer this we examine the system in a frame co-rotating with the bi- nary, as sketched in Fig. 53. We have two objects with massesm 1 > m2, Figure 53: Schematic view of a coordinate frame co-rotating with a binary. “CoM” indicates the center of mass. 180 23.2.LagrangePoints andEquilibrium total massM, mass ratioq = m1/m2, and a systemic angular velocity (588) 2π Ω� = zˆ P (589) GM 1/2 = zˆ a3 � � We expect tofind a zone of influence near each body in the binary, such that our test particle will remain near that body. Any material inside this zone will stay on or near its dominating body; any material outside the zone will not be bound and could accrete onto the other object.
    [Show full text]
  • Cataclysmic Variables
    Cataclysmic variables Robert Connon Smith Department of Physics and Astronomy, University of Sussex, Falmer, Brighton BN1 9QH, UK E-mail: [email protected] Abstract. Cataclysmic variables are binary stars in which a relatively normal star is transferring mass to its compact companion. This interaction gives rise to a rich range of behaviour, of which the most noticeable are the outbursts that give the class its name. Novae belong to the class, as do the less well known dwarf novae and magnetic systems. Novae draw their energy from nuclear reactions, while dwarf novae rely on gravity to power their smaller eruptions. All the different classes of cataclysmic variable can be accommodated within a single framework and this article will describe the framework, review the properties of the main types of system and discuss models of the outbursts and of the long-term evolution. Cataclysmic variables 2 1. Introduction Variable stars have a great variety of behaviours on many different timescales, enabling astronomers to make key tests of the structure and evolution of stars. A subset of variable stars turns out to be in double star systems, and Cataclysmic Variables (CVs)‡ form a particularly interesting part of this subset, with orbital periods typically of less than half a day. The canonical model of these systems (figure 1) consists of a white dwarf star that is accreting material from a lower mass red dwarf star; the separation between the two stars is normally less than a few solar radii, so the interaction between the components is extreme and the red dwarf is tidally and rotationally distorted into a tear-drop shape known as a Roche lobe (Section 3).
    [Show full text]
  • Post-Main-Sequence Planetary System Evolution Rsos.Royalsocietypublishing.Org Dimitri Veras
    Post-main-sequence planetary system evolution rsos.royalsocietypublishing.org Dimitri Veras Department of Physics, University of Warwick, Coventry CV4 7AL, UK Review The fates of planetary systems provide unassailable insights Cite this article: Veras D. 2016 into their formation and represent rich cross-disciplinary Post-main-sequence planetary system dynamical laboratories. Mounting observations of post-main- evolution. R. Soc. open sci. 3: 150571. sequence planetary systems necessitate a complementary level http://dx.doi.org/10.1098/rsos.150571 of theoretical scrutiny. Here, I review the diverse dynamical processes which affect planets, asteroids, comets and pebbles as their parent stars evolve into giant branch, white dwarf and neutron stars. This reference provides a foundation for the Received: 23 October 2015 interpretation and modelling of currently known systems and Accepted: 20 January 2016 upcoming discoveries. 1. Introduction Subject Category: Decades of unsuccessful attempts to find planets around other Astronomy Sun-like stars preceded the unexpected 1992 discovery of planetary bodies orbiting a pulsar [1,2]. The three planets around Subject Areas: the millisecond pulsar PSR B1257+12 were the first confidently extrasolar planets/astrophysics/solar system reported extrasolar planets to withstand enduring scrutiny due to their well-constrained masses and orbits. However, a retrospective Keywords: historical analysis reveals even more surprises. We now know that dynamics, white dwarfs, giant branch stars, the eponymous celestial body that Adriaan van Maanen observed pulsars, asteroids, formation in the late 1910s [3,4]isanisolatedwhitedwarf(WD)witha metal-enriched atmosphere: direct evidence for the accretion of planetary remnants. These pioneering discoveries of planetary material around Author for correspondence: or in post-main-sequence (post-MS) stars, although exciting, Dimitri Veras represented a poor harbinger for how the field of exoplanetary e-mail: [email protected] science has since matured.
    [Show full text]
  • X-Ray Astronomy
    X-Ray · Astron Introduction problem of which is to understand the source of the energy released in X-ray sources, supernovae, The discovery in the last two decades of the radio galaxies, quasars, etc., and the processes by large amounts of energy released in supernovae, which the high energy particles, responsible for of radio galaxies and quasars, of the microwave the radiation from these objects, are produced. background radiation and more recently of X-ray The resolution of these problems constitutes one sources and pulsars, has demonstrated that high of the most important and fascinating tasks in al1 energy processes playa major, possibly decisive, of physics. role in our universe. 'In these processes, the energy released per gram Since production of high energy photons is ex­ is much greater than for normal stellar matter. For pected wherever high energy particles exist, it was instance, gravitational forces, weak in our norma] anticipated that observations in the X-ray and experience, become all-important in the late phases gamma-ray range of the electromagnetic spectrum of stellar evolution. Matter is crushed to incon­ would become important as soon as the means to ceivably high densities and the stars can release carry them out became available. enormous amounts of energy, of the order of 10 During the last two decades, space observatories to 40% of their total mass energy as compared to have allowed us for the first time in man's history less than 1 % liberated by nuclear burning during to observe the sky unimpeded by the atmospheric their entire previous lives.
    [Show full text]