Accretion onto compact objects during common envelope phases
Morgan MacLeod NASA Einstein Fellow Harvard-Smithsonian Center for Astrophysics
collaborators: Andrea Antoni, Aldo Batta, Soumi De, Jonathan Grindlay, Phillip Macias, Gabriela Montes, Ariadna Murguia-Berthier, Eve Ostriker, Enrico Ramirez-Ruiz, James Stone
October 3, 2018 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
Today’s topic: transformation of compact objects during these interactions by accretion
Dense environment implies that accretion is possible.
Accretion and BH spin LIGO measurements of projected spins
(Farr+ 2017)
e↵ (e.g. King & Kolb 1999) Analytic predictions: inspiral and accretion
In the frame of the orbiting object:
Hoyle & Lyttleton (1939), Flow is gravitationally focussed Bondi & Hoyle (1944) toward the compact object
2GM R a ⇠ v2 1
(Edgar 2004)
…interacts with a “column” of gas with 2 Area = ⇡Ra Hoyle-Lyttleton Accretion 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 large attractioe comparen of the latterd wil witl produch eth tweo opposinaveragg e apparent distance between the streamstarss ofthemselve particles 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 fsun 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 thaparalletl 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 Analytic predictions: inspiral and accretion
In the frame of the orbiting star: Hoyle & Lyttleton (1939), Bondi & Hoyle (1944) Flow is gravitationally focussed toward the compact object Mass passing through this region is
2GM M˙ HL = A⇢v Ra 2 ⇠ v 2 1 = ⇡Ra⇢v (mass per time)
… and kinetic energy is
3 …interacts with a “column” of gas with E˙ HL = A⇢v 2 = ⇡R2⇢v3 Area = ⇡Ra a 2 = M˙ HLv
(energy per time) Inspiral and mass accumulation during common envelope
In the frame of the orbiting star: Hoyle & Lyttleton (1939), Bondi & Hoyle (1944)
Mass passing through this region is Captured!
M˙ HL = A⇢v 2 = ⇡Ra⇢v (mass per time)
… and kinetic energy is Dissipated! 3 E˙ HL = A⇢v 2 3 = ⇡Ra⇢v 2 = M˙ HLv
(energy per time) Analytic predictions: inspiral and accretion
• Energy dissipation drives the orbital inspiral. They are directly related in • Mass capture causes the compact obj. to grow. Hoyle-Lyttleton theory: 2 E˙ HL = M˙ HLv
NS Example: Common envelope orbital inspiral implies an accumulated mass:
E E MNS M˙ = ⇡ E˙ v2
MNSMcomp ⇡ MNS + Mcomp This is enough mass to cause a neutron star to collapse to a black hole! & 1M
(Chevalier 1993) Common Envelope Wind Tunnel
3D (AMR) calculation in FLASH Cartesian geometry
stellar limb ~g inject flow with polytropic (HSE) profile
specified by (✏ , ,q) PM + absorbing central BC ⇢ M
-y boundary enforces HSE Common Envelope Wind Tunnel = s =5/3
(MacLeod+, 2017) COMMONCommonENVELOPE WEnvelopeIND TUNNEL Wind Tunnel 13 gle is not constant, but, in fact, widens with increasing dis- placement into the wake. What we observe from the stream- lines in Figure 4 is that material focused onto the wake at larger +x displacements comes from a larger impact param- eter in the -y-direction. Recalling the profiles of Figure 1, this material, originating from deeper within the stellar enve- lope, has higher sound speed. As a result, there is a gradi- ent of upstream Mach number in the y-direction (which can be observed in the lower panels of Figure 2 and 4). The shock opening angle, which depends inversely on this up- stream Mach number, thus broadens as the focussed material
is drawn from deeper in the stellar envelope potential well. mass accretion This effect is observable primarily in cases of steep gradient (near the envelope limb), where the derivatives of and ✏ M ⇢ become large. The equation of state of the stellar envelope gas also plays a role in determining flow structure. The flow in the = s = density gradient 4/3 shown in Figures 4 and 5 is more compressible than the Figure 6. Median mass accretion rates into the sink boundary con- dition defined by Rs =0.05Ra. Shaded regions denote the 5-th to flow in the = s =5/3 shown in Figures 2 and 3. This results 95-th percentile values of the time-variable M˙ . These are compared in higher densities in the immediate wake of the embedded to the =5/3 case result of MacLeod & Ramirez-Ruiz (2015a), object because the pressure does not build up as rapidly upon which adopted = 2 for all simulations (labeled M2015). In all M compression in the focused material. In the steeper-gradient cases, we find that steepening density gradient inhibits accretion, cases of = s =4/3, we see a nested shock outside of an with typical values for large ✏⇢ of M˙ M˙ . The =4/3 cases ⌧ HL accretion line, which differs from the much broader fan of show systematically higher M˙ than =5/3, perhaps because pres- material in the ✏⇢ = 2, = s =5/3 simulation. sure gradients provide less resistance to flow convergence and ac- In all cases, the secondary’s gravitational focus lifts some cretion in the more compressible flow. dense material from the stellar interior against the primary star’s gravity. This gravitational force leads some material (with impact parameter R ) to rise and fall in a “tidal We begin by examining the mass accretion rate into the a bulge” trailing the embedded object. In material with im- sink boundary as a function of density gradient in our = =4/3 and = =5/3 simulation suites, shown in Figure pact parameter . Ra, as shown in the streamlines overplot- s s ted on the upper panels of Figures 2 and 4, this gravita- 6. Accretion rates in Figure 6 are normalized to the Hoyle- tional force leads to a slingshot around the embedded ob- Lyttleton accretion rate, ject. Some of this gas leaves the simulation box after be- ˙ 2 MHL = ⇡Ra⇢ v , (29) ing deviated through a large angle then expelled toward the 1 1 lower-density of the primary star’s limb (+y-direction in our which is the flux of material passing through a cross-section simulation setup). 2 of area ⇡Ra assuming a uniform density background. One feature of the accretion rate is that when density gradients are 4.2. Rates of Accretion introduced into the flow, the flow morphology becomes less Our numerical approach replaces the embedded object laminar and variability is introduced into the mass accretion with a sink on the grid, which absorbs convergent flow. The rate. Therefore, we plot the median values (pink and blue sink has a radius of Rs =0.05Ra. We note that this sink could lines) along with the 5-th and 95-th percentile ranges (shaded be of a similar scale to that of a main-sequence star embed- regions) for mass accretion rate, M˙ , as a function of density ded in a typical common envelope (see Table 1 of MacLeod gradient, ✏⇢. & Ramirez-Ruiz 2015a), but is certainly much larger than the As density gradients steepen, the accretion rate into the size of an embedded compact object like a white dwarf, neu- sink drops dramatically and becomes more variable. We see tron star, or black hole. Here we study rates and properties of accretion coefficients (M˙ /M˙ HL) spanning more than an order material accreting through this inner boundary of our compu- of magnitude as density gradient changes across typical val- tational domain, but note that the accretion rate is dependent ues. In all regions, the accretion efficiency is substantially on the size of the sink boundary compared to the accretion ra- lower than accretion from a uniform medium. The impo- dius (for example, MacLeod & Ramirez-Ruiz 2015a, found sition of a density gradient breaks the symmetry of the in- lower accretion rates for Rs =0.01Ra than for Rs =0.05Ra). flowing material (as seen in Figures 2 and 4). As opposed COMMON ENVELOPE WIND TUNNEL 17 COMMONCommonENVELOPE WEnvelopeIND TUNNEL Wind Tunnel 13 the orbital tightening, while flow convergence and mass ac- gle is not constant, but, in fact, widens with increasing dis- cretion might transform the object itself. placement into the wake. What we observe from the stream- There are, of course, caveats associated with the simplifi- lines in Figure 4 is that material focused onto the wake at cations we have made here. We have isolated particular flow larger +x displacements comes from a larger impact param- conditions and measured steady-state rates of drag and accre- eter in the -y-direction. Recalling the profiles of Figure 1, this material, originating from deeper within the stellar enve- tion, but it is worth considering that steady state might not be lope, has higher sound speed. As a result, there is a gradi- realized during the complex and violent flow of a common ent of upstream Mach number in the y-direction (which can envelope interaction. Among the potential concerns with ex- be observed in the lower panels of Figure 2 and 4). The trapolating the results of these simulations is that the geome- shock opening angle, which depends inversely on this up- try of our simulations does not match that of the large-scale common envelope: we have adopted a cartesian geometry, stream Mach number, thus broadens as the focussed material drag force is drawn from deeper in the stellar envelope potential well. where stars are spherical. We similarly disregard the effects This effect is observable primarily in cases of steep gradient of the rotating frame that co-moves with the embedded ob- (near the envelope limb), where the derivatives of and ✏ ject. These simplifications almost certainly affect the exact M ⇢ become large. numerical values derived for our coefficents of drag, particu- The equation of state of the stellar envelope gas also plays larly on scales > Ra, which become similar to the binary sep- aration, a, the scale where curvature becomes very important. a role in determining flow structure. The flow in the = s = density gradient 4/3 shown in Figures 4 and 5 is more compressible than the FigureFigure 10. 6. MedianDynamical mass friction accretion drag rates forces into the plotted sink versus boundary density con- Similarly, by fixing the gas compressibility, , and studying gradientdition defined for two by integrationRs =0.05 radii,Ra. Shaded 1.06Ra and regions 1.6R denotea. The coefficientthe 5-th to flow in the = s =5/3 shown in Figures 2 and 3. This results two representative values of 4/3 and 5/3, we ignore thermo- 95-th percentile values of the time-variable M˙ . These are compared / in higher densities in the immediate wake of the embedded of drag is systematically higher in the more compressible =4 3 dynamic transitions that might result from the gas’s passage simulationsto the =5 because/3 case a result higher of densityMacLeod wake & trails Ramirez-Ruiz the embedded(2015a ob-), through shocks and compression as it passes near the embed- object because the pressure does not build up as rapidly upon ject.which In adopted all cases, the= drag 2 for coefficient all simulations increases (labeled with M2015). density gradi- In all M ded object. compression in the focused material. In the steeper-gradient ent,cases, because we find dense that material steepening offset density from thegradient object’s inhibits position accretion, in the Our coefficients of accretion have dependence on the cases of = s =4/3, we see a nested shock outside of an -withy-direction typical (toward values for the large primary-star✏⇢ of M˙ center)M˙ HL. is The focussed =4/ into3 cases the ⌧ accretion line, which differs from the much broader fan of wake.show systematically higher M˙ than =5/3, perhaps because pres- size of the sink boundary, as documented in MacLeod & material in the ✏⇢ = 2, = s =5/3 simulation. sure gradients provide less resistance to flow convergence and ac- Ramirez-Ruiz (2015a). These rates should thus be treated In all cases, the secondary’s gravitational focus lifts some cretion in the more compressible flow. as rates of flow convergence through a boundary of a par- dense material from the stellar interior against the primary allows pressure to partially resist the density asymmetry of ticular size: if we are considering an embedded compact star’s gravity. This gravitational force leads some material the wake. Ostriker (1999) discusses this effect extensively, object, which might be orders of magnitude smaller, it is (with impact parameter R ) to rise and fall in a “tidal andWe shows begin that by the examining drag should the behave mass accretionln 1 + rate-2 intoin the the not obvious that all of the converging material will reach the a / M bulge” trailing the embedded object. In material with im- supersonicsink boundary limit, as thus a function decreasing of steeply density as gradient1 in (equation our = embedded object’s surface. Secondly, not all objects are ther- =4/3 and = =5/3 simulation suites,M shown! in Figure pact parameter . Ra, as shown in the streamlines overplot- 15s in Ostriker 1999).s The lowest Mach number simulation in modynamically able to accrete from the common envelope ted on the upper panels of Figures 2 and 4, this gravita- our6. Accretion = =4 rates/3 suite in Figure has 6 =1are. normalized35, so we do to not the Hoyle- expect gas. Accretion onto white dwarfs or main-sequence stars s M tional force leads to a slingshot around the embedded ob- (orLyttleton see) as accretion dramatic rate, of a correction due to low flow Mach has no obvious cooling channel (photons will be trapped in ject. Some of this gas leaves the simulation box after be- number. the very dense flow) and therefore we probably should not ˙ 2 MHL = ⇡Ra⇢ v , (29) ing deviated through a large angle then expelled toward the We note here that the coefficients1 of1 drag and their depen- expect mass accumulation on these objects despite flow con- lower-density of the primary star’s limb (+y-direction in our dence on ✏ derived here are different (though similar or- vergence. On the other hand, for high enough accretion rates which is the⇢ flux of material passing through a cross-section simulation setup). der of magnitude) from those in MacLeod & Ramirez-Ruiz neutrinos can likely mediate the accretion luminosity of ac- of area ⇡R2 assuming a uniform density background. One (2015a, Figurea 13), both because of our updated formalism cretion onto neutron stars (Houck & Chevalier 1991; Cheva- feature of the accretion rate is that when density gradients are and different flow parameters (section 2), and because of our lier 1993; Fryer et al. 1996; Brown et al. 2000; MacLeod 4.2. Rates of Accretion introduced into the flow, the flow morphology becomes less corrected dynamical friction diagnostics described in section & Ramirez-Ruiz 2015b), and, lacking a surface, black holes Our numerical approach replaces the embedded object laminar and variability is introduced into the mass accretion 3.2. These updates represent a significant improvement in will certainly accrete material passing through their horizons. with a sink on the grid, which absorbs convergent flow. The rate. Therefore, we plot the median values (pink and blue our ability to correctly asses the dynamical friction acting on Despite the remaining uncertainties, the coefficients of sink has a radius of Rs =0.05Ra. We note that this sink could lines) along with the 5-th and 95-th percentile ranges (shaded the embedded object, and the difference of our new results drag and accretion derived here carry lessons for the dynam- be of a similar scale to that of a main-sequence star embed- regions) for mass accretion rate, M˙ , as a function of density reflects these changes. ics of common envelope episodes. In MacLeod & Ramirez- ded in a typical common envelope (see Table 1 of MacLeod gradient, ✏⇢. Ruiz (2015a,b) we argued that the ratio of drag coefficient & Ramirez-Ruiz 2015a), but is certainly much larger than the As density gradients steepen, the accretion rate into the size of an embedded compact object like a white dwarf, neu- sink5. dropsIMPLICATIONS dramatically and FOR becomes COMMON more ENVELOPE variable. We see to accretion coefficient that arises from asymmetric flows in thecommon envelope implies that objects grow by at most a tron star, or black hole. Here we study rates and properties of accretion coefficients (M˙ /INSPIRALM˙ HL) spanning more than an order few percent during their inspiral. This qualitative conclusion material accreting through this inner boundary of our compu- ofWe magnitude have used as density idealized gradient numerical changes simulations across typical to study val- remains unchanged despite our improved derivations of drag tational domain, but note that the accretion rate is dependent flowues. morphologies, In all regions, as the well accretion as coefficients efficiency of drag is substantially and accre- and accretion coefficients. on the size of the sink boundary compared to the accretion ra- tionlower for than objects accretion embedded from in a the uniform common medium. envelope. The These impo- In Figures 11 and 12, we illustrate the effect of includ- dius (for example, MacLeod & Ramirez-Ruiz 2015a, found quantitiessition of adescribe density the gradient transformation breaks the of symmetry an object and of the its or- in- ing a coefficient of drag that varies with the flow parame- lower accretion rates for Rs =0.01Ra than for Rs =0.05Ra). bitflowing through material the common (as seen envelope in Figures episode.2 and Drag4). forces As opposed drive Common Envelope Wind Tunnel COMMON ENVELOPE WIND TUNNEL 13 gle is not constant, but, in fact, widens with increasing dis- placement into the wake. What we observe from the stream- lines in Figure 4 is that material focused onto the wake at larger +x displacements comes from a larger impact param- eter in the -y-direction. Recalling the profiles of Figure 1, this material, originating from deeper within the stellar enve- lope, has higher sound speed. As a result, there is a gradi- ent of upstream Mach number in the y-direction (which can be observed in the lower panels of Figure 2 and 4). The dM dEorb shock opening angle, which depends inversely on this up- ˙ ˙ stream Mach number, thus broadens as the focussed material = C M = C F v is drawn from deeper in the stellar envelope potential well. m HL d HL This effect is observable primarily in cases of steep gradient dt dt (near the envelope limb), where the derivatives of and ✏ M ⇢ become large. The equation of state of the stellar envelope gas also plays a role in determining flow structure. The flow in the = s = COMMON ENVELOPE WIND TUNNEL 17 4/3 shown in Figures 4 and 5 is more compressible than the Figure 6. Median mass accretion rates into the sink boundary con- dition defined by Rs =0.05Ra. Shaded regions denote the 5-th to flow in the = s =5/3 shown in Figures 2 and 3. This results the orbital tightening, while flow convergence and mass ac- 95-th percentile values of the time-variable M˙ . These are compared in higher densities in the immediate wake of the embedded cretion might transform the object itself. to the =5/3 case result of MacLeod & Ramirez-Ruiz (2015a), ( C ,C ) are coefficients of There are, of course, caveats associated with the simplifi- d m object because the pressure does not build up as rapidly upon which adopted = 2 for all simulations (labeled M2015). In all M compression in the focused material. In the steeper-gradient cases, we find that steepening density gradient inhibits accretion, cations we have made here. We have isolated particular flow cases of = s =4/3, we see a nested shock outside of an with typical values for large ✏⇢ of M˙ M˙ . The =4/3 cases conditions and measured steady-state rates of drag and accre- ⌧ HL drag and mass accretion accretion line, which differs from the much broader fan of show systematically higher M˙ than =5/3, perhaps because pres- tion, but it is worth considering that steady state might not be material in the ✏⇢ = 2, = s =5/3 simulation. sure gradients provide less resistance to flow convergence and ac- realized during the complex and violent flow of a common In all cases, the secondary’s gravitational focus lifts some cretion in the more compressible flow. envelope interaction. Among the potential concerns with ex- dense material from the stellar interior against the primary trapolating the results of these simulations is that the geome- AC EOD ET AL star’s gravity. This gravitational force leads some material try of our simulations does18 not match that of the large-scale M L . (with impact parameter R ) to rise and fall in a “tidal We begin by examining the mass accretion rate into the common envelope: we have adopted a cartesian geometry, a bulge” trailing the embedded object. In material with im- sink boundary as a function of density gradient in our = where stars are spherical. We similarly disregard the effects =4/3 and = =5/3 simulation suites, shown in Figure pact parameter . Ra, as shown in the streamlines overplot- s s of the rotating frame that co-moves with the embedded ob- ted on the upper panels of Figures 2 and 4, this gravita- 6. Accretion rates in Figure 6 are normalized to the Hoyle- ject. These simplifications almost certainly affect the exact A priori, we might imagine that the initial inspiral of com- tional force leads to a slingshot around the embedded ob- Lyttleton accretion rate, numerical values derived for our coefficents of drag, particu- ject. Some of this gas leaves the simulation box after be- larly on scales > Ra, which become similar to the binary sep- ˙ 2 MHL = ⇡Ra⇢ v , (29) aration, a, the scale where curvature becomes very important. mon envelope episodes is slow, taking many orbits while the ing deviated through a large angle then expelled toward the 1 1 lower-density of the primary star’s limb (+y-direction in our Figure 10. Dynamical friction drag forces plotted versus density Similarly, by fixing the gas compressibility, , and studying which is the flux of material passing through a cross-section simulation setup). gradient for two integration radii, 1.06Ra and 1.6Ra. The coefficient two representative values of 4/3 and 5/3, we ignore thermo- 2 secondary passes through the low-density atmosphere of the ofof drag area is⇡ systematicallyRa assuming higher a uniform in the density more compressible background. =4 One/3 dynamic transitions that might result from the gas’s passage simulationsfeature of the because accretion a higher rate density is that wake when trails density the embedded gradients ob- are through shocks and compression as it passes near the embed- 4.2. Rates of Accretion ject. In all cases, the drag coefficient increases with density gradi- introduced into the flow, the flow morphology becomes less ded object. primary’s envelope. Instead, with the realistic coefficients, Our numerical approach replaces the embedded object ent,laminar because and dense variability material is offset introduced from the into object’s the mass position accretion in the -y-direction (toward the primary-star center) is focussed into the Our coefficients of accretion have dependence on the with a sink on the grid, which absorbs convergent flow. The rate. Therefore, we plot the median values (pink and blue withwake. simulation coefficients:size of the sink boundary, as documented in MacLeod & sink has a radius of Rs =0.05Ra. We note that this sink could lines) along with the 5-th and 95-th percentile ranges (shaded Ramirez-Ruiz (2015a). These rates should thus be treated the initial common envelope inspiral is substantially more ˙ be of a similar scale to that of a main-sequence star embed- regions) for mass accretion rate, M, as a function of density as rates of flow convergence through a boundary of a par- ded in a typical common envelope (see Table 1 of MacLeod allowsgradient, pressure✏⇢. to partially resist the density asymmetry of ticular size: if we are considering an embedded compact rapid than with the Hoyle-Lyttleton force alone. In the late & Ramirez-Ruiz 2015a), but is certainly much larger than the As density< gradients few steepen, the accretion% ratemass into the object, which might be orders of magnitude smaller, it is the wake. Ostriker (1999) discusses this effect extensively, size of an embedded compact object like a white dwarf, neu- andsink shows drops that dramatically the drag should and becomes behave moreln variable.1 + -2 Wein the see not obvious that all of the converging material will reach the ˙ ˙ / M tron star, or black hole. Here we study rates and properties of supersonicaccretion coefficients limit, thus decreasing (M/MHL) spanning steeply as more than1 (equation an order embedded object’s surface. Secondly, not all objects are ther- inspiral, the drag force drops, and the orbits wrap tighter. M ! material accreting through this inner boundary of our compu- 15of inmagnitudeOstriker 1999 as density). The gradient lowest Mach changes number across simulation typical val- in modynamically able to accrete from the common envelope tational domain, but note that the accretion rate is dependent ues. In all regions, theincrease accretion efficiency is substantially our = =4/3 suite has =1.35, so we do not expect gas. Accretion onto white dwarfs or main-sequence stars s M This result can be qualitatively understood in the context of on the size of the sink boundary compared to the accretion ra- (orlower see) than as dramatic accretion of from a correction a uniform due medium. to low flow The Mach impo- has no obvious cooling channel (photons will be trapped in dius (for example, MacLeod & Ramirez-Ruiz 2015a, found number.sition of a density gradient breaks the symmetry of the in- the very dense flow) and therefore we probably should not lower accretion rates for Rs =0.01Ra than for Rs =0.05Ra). flowingWe note material here that (as the seen coefficients in Figures of2 dragand and4). their As opposed depen- expect mass accumulation on these objects despite flow con- our simulations: when an embedded object lies along a steep dence on ✏⇢ derived here are different (though similar or- vergence. On the other hand, for high enough accretion rates der of(MacLeod+, magnitude) from those in MacLeod 2015ab,2017, & Ramirez-Ruiz neutrinos can likely mediate the accretion luminosity of ac- density gradient (where the scale height is small compared to (2015a, Figure 13), both because of our updated formalism cretion onto neutron stars (Houck & Chevalier 1991; Cheva- and different flow parameters (section 2), and because of our lier 1993; Fryer et al. 1996; Brown et al. 2000; MacLeod corrected dynamical friction De+ diagnostics describedin prep) in section & Ramirez-Ruiz 2015b), and, lacking a surface, black holes Ra), the object gravitationally focusses dense material from 3.2. These updates represent a significant improvement in will certainly accrete material passing through their horizons. our ability to correctly asses the dynamical friction acting on Despite the remaining uncertainties, the coefficients of deeper in the stellar interior into its wake. This denser ma- the embedded object, and the difference of our new results drag and accretion derivedFigure here carry lessons 11. for the dynam-Inspiral of a 0.3M secondary through a 3M , 31R reflects these changes. ics of common envelope episodes. In MacLeod & Ramirez- Ruiz (2015a,b) we arguedprimary that the ratio of drag star’s coefficient envelope. The two examples show a drag force ap- terial (compared to the density at the secondary’s position 5. IMPLICATIONS FOR COMMON ENVELOPE to accretion coefficient that arises from asymmetric flows in INSPIRAL thecommon envelope implies that objects grow by at most a 2 2 within the primary star) leads to a more massive wake, and few percent during their inspiral.plied This qualitative with conclusionF = Cd⇡Ra ⇢v , where we adopt the Hoyle-Lyttleton value We have used idealized numerical simulations to study remains unchanged despite our improved derivations of drag flow morphologies, as well as coefficients of drag and accre- and accretion coefficients. / a higher dynamical friction drag force. In terms of the flow tion for objects embedded in the common envelope. These of Cd = 1 and a coefficient interpolated from our =5 3 simulation In Figures 11 and 12, we illustrate the effect of includ- quantities describe the transformation of an object and its or- ing a coefficient of drag that varies with the flow parame- bit through the common envelope episode. Drag forces drive results of Figure 10, for an integration radius of 1.6Ra. With simu- streamlines shown in Figures 2 and 4, the envelope gas con- lation coefficients applied, the initial orbital inspiral is much more tributing to the wake comes largely from dense material with rapid, while the late inspiral slows and wraps tighter than in the impact parameters in the -y-direction in simulation coordi- C = 1 case. d nates – toward the primary-star interior. One potential impact of the increased rapidity of early in- spiral is on transients from the onset of a common envelope. The emergent class of luminous red novae transients has been associated with mass ejection in stellar merger and common envelope encounters (see, e.g. Tylenda et al. 2011; Ivanova et al. 2013a; Williams et al. 2015; Kurtenkov et al. 2015; Blagorodnova et al. 2017; Smith et al. 2016; MacLeod et al. 2016, for recent examples). A rapid early inspiral would match the rapid lightcurve rise of some of these transients. For example, the M31 LRN 2015 outburst rose from detec- tion to peak brightness in a timescale of order one binary orbital period. With a 3 - 5M , 35R progenitor giant, ⇠ ⇠ this system had a primary star broadly similar to that shown in Figure 11 (Williams et al. 2015; MacLeod et al. 2016). This is a surprisingly rapid timescale when we compare to Figure 12. Same as Figure 11 for an 8M secondary object and the slow early inspiral predicted by Hoyle-Lyttleton drag co- an 80M , 720R primary star. Numerical coefficients of drag are efficients (Cd = 1), but it is perhaps more consistent with our interpolated from our =4/3 simulation suite in this calculation. numerically derived coefficients, which show substantial in- spiral in a single orbit. There remains much work to be done, though, to establish the mappings between orbit evolution, ters of the material that it is passing through. We use the mass ejection, and light-curve generation in these events. primary-star profiles of Figure 1, and (as elsewhere in this The q =0.1 inspirals of Figure 11 and 12 differ qualita- paper), take a mass ratio q =0.1. We assume the primary tively between the 3.0M primary and the 80M primary star is initially non-rotating. We integrate the equation of in the number of orbits elapsed during the inspiral. For the motion of the secondary star relative to the enclosed mass 3.0M primary, the secondary spirals to a =0.1R1 in 4 or- of the primary, and add a drag force, F = C ⇡R2⇢v2, where ⇠ d d a bits, while in the 80M case, the plunge takes 13 orbits 2 2 Cd = Fdf/⇡Ra⇢ v is the coefficient of drag. We illustrate ⇠ 1 (with the interpolated drag coefficients). This difference re- the influence of two1 choices: C = 1, a Hoyle-Lyttleton drag d flects the difference in primary-star envelope structure. The force, and a numerically-derived C from our simulations d density of the 80M red supergiant envelope is very low, be- (which comes from Figure 10; here we take the force gen- cause radiation pressure (and the fact that the star is nearly at erated from r < 1.6R , and use the = =5/3 case for the a s the Eddington limit) inflates the envelope (e.g. Sanyal et al. 3M primary and the = s =4/3 case for the 80M pri- 2017). One consequence of this difference might be that the mary). Our example inspirals are initialized at a =0.95R 1 embedded star orbits through material that it has disturbed (or and are integrated until a =0.1R1. Common envelope interactions transform binary systems
Today’s topic: transformation of compact objects during these interactions by accretion
Dense environment implies that accretion is possible.
Accretion and BH spin LIGO measurements of projected spins
(Farr+ 2017)
e↵ (e.g. King & Kolb 1999) Open question: feedback from accretion?
Any accretion that occurs is highly super-Eddington and 4 L´opez-C´amara et al. may be accompanied by mechanical feedback
Murguia-Bertier+ 2017: Under what conditions do disks form y x around objects during CE? z
Murguia-Berthier and CEWT team, 2017
Lopez-Camara+ 2018: If the accretion flow launches jets, how do these impinge upon the surroundings.
(See also Chamandy+ 2018)
Figure 2. Same as Figure 1 but for model NS0.05. An animation of the 3D figure is available in the online journal.
Figure 3. Density volume rendering and velocity stream lines for model BH0.05 at t =2.42 105 s(left)andt =2.50 105 s(right). ⇥ ⇥ 9 3 The density volume palette covers values from 10 gcm 8 3 (green) to 10 gcm (red). In order to better visualize the stream lines, the dominion is limited to: x [ 2, 2], z [10, 12], 2 2 y [0, 2]. The axis units are the same as in Figure 1. 2 Figure 1. Left panels: xz, xy,andyz density map slices showing the 3D time evolution of the CO-self regulated jet-wind evolution (2.36 105 s, 2.42 105 s, and 2.50 105 sformodelBH0.05). ⇥ ⇥ ⇥ exerted by the BHL bulge onto the jets of the NS models is Right panels: zoom of the density and velocity maps of the xy, small 5 . and yz slices. The orange, green, blue, and white isocontour lines ⇠ 6 7 8 9 3 An interesting feature of the self-regulated jets is that correspond to densities 10 ,10 ,10 ,and10 gcm ,re- spectively. The axis are in units of 1012 cm. An animation of the the fast component shows large scale variability in both po- 3D figure is available in the online journal. sition and size, see for e.g. the white contour in Figure 1 and Figure 2 where the size of the fast component of the jet drastically varies in a two hour time lapse. In order to models is smaller than that from the BH models (as the understand such structure and orientation modification, in mass of the CO is lower, and hence so is the gravitational Figure 3 we show the density volume render and velocity pull of the NS), the global morphology and evolution of the stream lines showing the fast and slow components of the NS models is akin to that for the BH models. Figure 2 the jet for model BH0.05. Panel a) of Figure 3 corresponds to shows density map slices and velocity field slices of the NS the time where the fast component of the jet from model model with ⌘ =0.05 (model NS0.05). By t =2.50 105 s BH0.05 has disappeared in Figure 1. Comparing both fig- ⇥ the jet from model NS0.05 is able to drill through the BHL ures, it is clear how the jet has substantially decreased, and bulge and forms a quasi-spherical cocoon composed with low has started to tilt towards the nucleus of the RG. Panel b) of 9 6 3 density, turbulent material ( 10 10 gcm ). The jet Figure 3 shows how the jet has an amorphous and complex ⇠ is present in both the xy and zy planes and is also composed configuration that has increased its size and is changed its by the fast and slow components. An interesting e↵ect is that alignment from the xy plane to mostly the zy plane. The due to the reduced gravitational pull of the NS (compared variability of the self-regulated jet is a consequence of the to the BH models), the formed BHL bulge is less dense and NJF which in turn depends solely on the accretion rate onto smaller than that of the BH models, hence, the forward push the CO and which will be further discussed in Section 4.
MNRAS 000, 1–10 (2018) Common envelope interactions transform binary systems
Common envelope interactions play a key role in the assembly of compact binaries. In the dense, gaseous environment objects can grow via accretion while dynamical friction tightens the orbit.
Strong density gradients provide an angular momentum barrier, making accretion inefficient relative to predictions of Bondi-Hoyle-Lyttleton accretion rates.
potentially-low accreted mass implies low accreted spin, with implications for the observable properties of merging GW sources.