Unwrapping the Mystery of Common Envelope Episodes Morgan MacLeod [email protected] Einstein Fellows Symposium Oct 18, 2016 Common envelope interactions transform binary systems Example: formation of merging pairs of neutron stars Pair of massive stars (>8x sun’s mass) Common envelope interactions transform binary systems Example: formation of merging pairs of neutron stars Pair of massive stars (>8x sun’s mass) much closer pair of neutron stars ? draws the binary closer together Common envelope interactions transform binary systems Example: formation of merging pairs of neutron stars Pair of massive stars (>8x sun’s mass) much closer pair of neutron stars ? draws the binary closer together gravitational wave inspiral Orbital transformation is key in formation of compact binaries Common envelope interactions transform binary systems Example: formation of merging pairs of neutron stars Pair of massive stars (>8x sun’s mass) much closer pair of neutron stars Common Envelope Phase Drag on surrounding Orbit stabilizes as gas tightens the orbit envelope is ejected Evolution to contact NS Companion Common envelope interactions transform binary systems envelope is ejected and orbit stabilizes common envelope outcomes: tightened binary or merger Drag on surrounding gas tightens the orbit Evolution to contact envelope is retained and binary merges Many open questions… Challenging problem for “kitchen sink” numerical approach because of the huge range of relevant spatial and temporal scales. ?? Many open questions… Challenging problem for “kitchen sink” numerical approach because of the huge range of relevant spatial and temporal scales. ?? … and infinite combinations of binary properties! Many open questions… Challenging problem for “kitchen sink” numerical approach because of the huge range of relevant spatial and temporal scales. ?? … and infinite combinations of binary properties! But, there are some general questions: • What are the initial conditions of CE episodes? • How is energy/momentum transfer between embedded object and the gas mediated? • What is the timescale of envelope ejection? • How do initial binary parameters map to outcomes? Two strategies for progress • Gas dynamics of common envelope: goal: isolate and understand aspects of the physics of CE flows • Catching common envelope in action: goal: model-to-data comparison to directly constrain long-uncertain theoretical models of CE processes Gas dynamics of common envelope In the frame of the orbiting star: Hoyle & Lyttleton (1939), Flow is gravitationally focussed Bondi & Hoyle (1944) toward the embedded star 2GM R a ⇠ v2 1 (Edgar 2004) …interacts with a “column” of gas with 2 Area = ⇡Ra Gas dynamics of common envelope 405 THE EFFECT OF INTERSTELLAR MATTER ON CLIMATIC VARIATION BY F. HOYLE AND R. A. LYTTLETON The effect of interstellar matter on climaticReceived variation 19 Apri409l 1939 by the sun's gravitational attraction, and the action of collisions in this con- densation can be shown to give the sun an effective capture radius much larger than its ordinary radius. 1. INTRODUCTION There is direc(a) Calculationt astronomica of the capture radiusl evidenc of the sune for the existence of diffuse clouds of matter Imagine the cloud to be streaming past the sun, from right to left in the figure, anind leinterstellat the velocity of anr yspace element o. f itAn relativy esectio to the sunn whe ofn atht greae tMilk distanceys Way containing a large number of bstare v. Consides usuallr the pary t showof the clous dregion that if undeflectes in dwhic by theh su nn woulo stard passs appear, and the extent of these within a distance o~ or less of its centre. It is clear that collisions will occur to thpatchee left of thse suisn becausofteen th elarg attractioe comparen of the latter dwil witl produch eth tweo opposinaveragg e apparent distance between the streamstarss of themselveparticles and thes effec (seet of ,suc foh collisionr examples is to destro, yRussell the angula,r Dugan, and Stewart (2), p. 820). The existence of the so-called cosmical cloud in interstellar space, sharing in the general motion of the galaxy, is now well established, and observational investiga- tion shows that the obscuration referred to above occurs also on a galactic scale. Thus the diffuse obscuring clouds appear as irregularitieHow sthe in thsune genera gravitationallyl cosmical captures cloud. The dimensions of such regions are comparablinterstellare with the distancegas ands betwee how thisn might the stars, and may be very much greater. In some affectinstance solars the systempresence evolutionof such clouds is revealed by their illumination by a star or stars lying in, or near them, so that the matter then can be directly observed. In shape the clouds are very irregular; some appear like long dark lanes, while other tracts are devoid of Fig. 1. any particular form. momentum of the particles about the sun. If after collision the surviving radial component of the velocity is insufficient to enable the particles to escape, such particleSincs will eeventuall the yexistenc be swept intoe th eo sunf suc. Supposeh cloud, for examples appear, that ans to be general in the galaxy it is elemenof importanct of volume of thee clouto d consideA whose initiar l thangulae effectr momentus mtha is vo~t losecouls d be produced if a star passed this momentum through its constituent particles suffering collisions at C; then ththrouge effectiveh radiu onse a ocafn them be calculate. Thd suce frequench that the velocity oy fradiall s u cyh a toccurrence C is s for a particular star would less than the escape velocity at this distance. The element describes a hyperbola whosclearle equationy depen, with thed usua upol notationn th, mae ydistributio be written n of the clouds in space, and the intervals between these event- = s1 +woul e cos 6.d accordingly be irregular. But it is to be observed r Thate directiooncen parallethatl ttho thee initiaintervall asymptots e woulcorrespondd si nto general be of the order of the periods of time 7 8 occurring in galactiecos0+c problemsl = 0, , that is, of the order of 10 or 10 years, the average period of revolution of a star in the galaxy26- bein2 g about 2-5 x 108 years. The density of an obscuring cloud and the velocity that a star would have relative to it are known as far as orders of magnitude are concerned from astronomical considerations, and it is shown in the sequel that these clouds may have a considerable effect upon a star's radiation during the time of passage of the star through the cloud. The importance to terrestrial climate of such an effect upon the sun is at once evident, and it is to this aspect of the process that the present paper is directed, though it would seem that encounters between stars and the diffuse clouds may also have some bearing on questions of a more general astronomical nature. If any appreciable change in the sun's radiative power The effect of interstellar matter on climatic variation 409 by the sun's gravitational attraction, and the action of collisions in this con- densation can be shown to give the sun an effective capture radius much larger than its ordinary radius. theory Hoyle-Lyttleton of scales dimensionless (a) Calculation of the capture radius of the sun Imagine the cloud to be streamin g pas t the sun, from right to left in the figure, and let the velocity of any element of it relativ e to th e sun whenthe a t great distanceof s terms in properties flow typical Express be v. Consider the part of the cloud that if undeflected by the sun would pass within a distance o~ or less of its centre. It is clear that collisions will occur to the left of the sun because the attraction of the latter will produce two opposing streams of particles and the effect of such collisions is to destroy the angular envelope common of dynamics Gas Mach number: number: Mach Fig. 1. momentum of the particles about the sun. If after collision the surviving radial component of the velocity is insufficient to enable the particles to escape, such Time: Time: particles will eventually be swept into the sun. Suppose, for example, that an element of volume of the cloud A whose initial angular momentum is vo~ loses this momentum through its constituent particle? s suffering collisions at C; then the effective radius a can be calculated such that the velocity radially at C is less tha n the escape velocity at this distance. The element describes a hyperbola M whose equation, with the usual notation, may be written - = 1 + e cos 6. r The direction parallel to the initial asymptote corresponds to Length: Length: ecos0+l = 0, R 26-2 a = /v applied to any stellar pair: pair: stellar any to applied v/c Then simulation results can be be can results simulation Then R a s =2 GM/v 2 The effect of interstellar matter on climatic variation 409 by the sun's gravitational attraction, and the action of collisions in this con- densation can be shown to give the sun an effective capture radius much larger than its ordinary radius. theory Hoyle-Lyttleton of scales dimensionless (a) Calculation of the capture radius of the sun Imagine the cloud to be streamin g pas t the sun, from right to left in the figure, and let the velocity of any element of it relativ e to th e sun whenthe a t great distanceof s terms in properties flow typical Express be v. Consider the part of the cloud that if undeflected by the sun would pass within a distance o~ or less of its centre. It is clear that collisions will occur to the left of the sun because the attraction of the latter will produce two opposing streams of particles and the effect of such collisions is to destroy the angular envelope common of dynamics Gas Density gradient: Density Mach number: number: Mach Fig.