On the Roche Lobe Overflow Reporter: Wang Chen 12/02/2014 Reference: N. Ivanova, v1

outline Introduction Introduction Stability of the mass transfer Stability of the mass transfer Different mass transfer timescales Different mass transfer timescales Roche Lobe response Roche Lobe response The donor ’ s response and consequences for the mass transfer stability The donor ’ s response and consequences for the mass transfer stability The accretor ’ s response and consequences for the mass transfer stability The accretor ’ s response and consequences for the mass transfer stability How well do we understand stable mass transfer How well do we understand stable mass transfer

Introduction Mass transfer (MT): Roche lobe overflow (RLOF) Mass transfer (MT): Roche lobe overflow (RLOF)

Introduction Classification (by the evolutionary status of the donor) Classification (by the evolutionary status of the donor) Case A – during hydrogen (H) burning in the core of the donor. Case A – during hydrogen (H) burning in the core of the donor. Case B – after exhaustion of H in the center of the donor. Case B – after exhaustion of H in the center of the donor. Case C – after exhaustion of central helium (He) burning. Case C – after exhaustion of central helium (He) burning.

Introduction Blue: radiative envelope Red: convective envelope Star: when hydrogen or helium is exhausted in the core

introduction The specific case of the MT by itself does not imply whether the MT would be stable or not. The specific case of the MT by itself does not imply whether the MT would be stable or not. It is more important in determining the outcome if the initial stability and the timescale of the initiated MT are known by other means. It is more important in determining the outcome if the initial stability and the timescale of the initiated MT are known by other means. The structure of the inner layers may affect the stability of the MT later on. The structure of the inner layers may affect the stability of the MT later on.

introduction Important for predicting the stability of the MT and the outcome Important for predicting the stability of the MT and the outcome 1. The evolutionary status of the donor – this implies its complete internal structure; 2. The structure of the donor’s envelope; 3. The mass ratio of the binary; 4. The type of the accretor.

Stability of the MT: the global condition (The donor ’ s response) (conservative & the angular momentum loss)

Roche Lobe Response Conservative MT: Conservative MT: None-conservative MT (liberal): None-conservative MT (liberal): Non-conservative MT is stable than conservative MT

Donor ’ s Response The star will readjust both the hydrostatic and thermal equilibria when loses mass. The star will readjust both the hydrostatic and thermal equilibria when loses mass. The readjustment of the internal structure results in the star ’ s radius evolution and can be described using The readjustment of the internal structure results in the star ’ s radius evolution and can be described using

Timescales Hydrostatic readjustment: the initial donor ’ s response to mass loss can be expected to be almost adiabatic. Hydrostatic readjustment: the initial donor ’ s response to mass loss can be expected to be almost adiabatic. Thermal readjustment: Thermal readjustment: Superadiabatic readjustment: Superadiabatic readjustment:

Timescales Dynamical MT Dynamical MT The lobe-filling star cannot remain within its Roche lobe with hydrostatic equilibrium. The lobe-filling star cannot remain within its Roche lobe with hydrostatic equilibrium. The mass loss rate from the primary is limited only by the sonic expansion rate of its envelope. The mass loss rate from the primary is limited only by the sonic expansion rate of its envelope. Will lead to common envelope evolution or contact. Will lead to common envelope evolution or contact. Thermal MT Thermal MT The lobe filling star loses mass, and may remain within its Roche lobe in hydrostatic, but not thermal equilibrium. It remain just filling the Roche lobe, and relaxation toward thermal equilibrium drives mass on thermal timescale. The lobe filling star loses mass, and may remain within its Roche lobe in hydrostatic, but not thermal equilibrium. It remain just filling the Roche lobe, and relaxation toward thermal equilibrium drives mass on thermal timescale. Nuclear MT Nuclear MT The radius of the primary remains constrained to that of its Roche lobe, and the star remains in thermal equilibrium. The radius of the primary remains constrained to that of its Roche lobe, and the star remains in thermal equilibrium. The timescale is dictated by the orbital angular momentum evolution, or by the nuclear evolution of the donor. The timescale is dictated by the orbital angular momentum evolution, or by the nuclear evolution of the donor.

Envelope ’ s Structure – adiabatic response Convective envelope: Convective envelope: for non-degenerate & fully ionized ideal gas for non-degenerate & fully ionized ideal gas radiative core radiative core for giants with a radiative core and convective envelopes: for giants with a radiative core and convective envelopes: Is positive when m>=0.2. The stability of the MT increases as the star evolves on the red giant branch

Envelope ’ s Structure – adiabatic response

Radiative envelope Radiative envelope The entropy is growing towards the surface. If some mass is removed, then a layer with a a lower entropy is exposed. In an adiabatic case, this implies that if a star attains hydrostatic equilibrium and regains the same surface pressure, the density of the outer layers will be larger than previously, and the donor shrinks. The entropy is growing towards the surface. If some mass is removed, then a layer with a a lower entropy is exposed. In an adiabatic case, this implies that if a star attains hydrostatic equilibrium and regains the same surface pressure, the density of the outer layers will be larger than previously, and the donor shrinks.

Envelope ’ s Structure – equilibrium response Low-mass giants: the thermal structure is almost independent from the envelope, so Low-mass giants: the thermal structure is almost independent from the envelope, so Main sequence stars: mass-radius relation, usually positive. E.g., for ZAMS is at least 0.57, and it grows as the donor approaches the terminal main sequence. Main sequence stars: mass-radius relation, usually positive. E.g., for ZAMS is at least 0.57, and it grows as the donor approaches the terminal main sequence. These values are applicable only for the start of the mass transfer

Envelope ’ s Structure – superadiabatic response This is the response of the donor on the mass loss that proceeds on a timescale longer than a but shorter than. This is the response of the donor on the mass loss that proceeds on a timescale longer than a but shorter than. Arguably this is the most important response for determining the mass transfer stability Arguably this is the most important response for determining the mass transfer stability Consider here the superadiabatic response for convective donors only. Consider here the superadiabatic response for convective donors only.

Envelope ’ s Structure – superadiabatic response If mass is removed from this entropy profile in an adiabatic regime, the envelope is momentarily expanding by a large fraction of its radius. If mass is removed from this entropy profile in an adiabatic regime, the envelope is momentarily expanding by a large fraction of its radius. The dramatic expansion finds a very different hydrostatic equilibrium than a normal giant of almost the same mass. The dramatic expansion finds a very different hydrostatic equilibrium than a normal giant of almost the same mass. Woods & Ivanova found that if the superadiabatic layer is resolved, the MT could be stable in systems with larger mass radio than would be predicted by the adiabatic approximation. They found that real giants will often contract. Woods & Ivanova found that if the superadiabatic layer is resolved, the MT could be stable in systems with larger mass radio than would be predicted by the adiabatic approximation. They found that real giants will often contract.

Sudden change of the donor ’ s response – delayed dynamical instability (DDI) A case of a dynamical instability that follows a period of a stable MT. A case of a dynamical instability that follows a period of a stable MT. suddenly drops during the MT, and become smaller than. suddenly drops during the MT, and become smaller than. It usually takes place in initially radiative donors. It usually takes place in initially radiative donors. It requires detailed stellar modeling. It requires detailed stellar modeling. q crit q crit

The donor ’ s response and consequences for the MT stability Initial stability: fully conservative MT Initial stability: fully conservative MT non-conservative MT non-conservative MT Stability of the ensuing MT Stability of the ensuing MT

Initial stability Fully conservative MT : Fully conservative MT : if q>1, >0.46 if q>1, >0.46 for convective envelopes < dynamical unstable. for convective envelopes < dynamical unstable. for radiative envelopes >>0 dynamical stable for radiative envelopes >>0 dynamical stable Non-conservative MT: Non-conservative MT: the stability of the mass transfer is increasing the stability of the mass transfer is increasing Mass loss prior to RLOF: Mass loss prior to RLOF: increase, and the stability of the MT is increasing. increase, and the stability of the MT is increasing.

Stability of the ensuing MT Stability must be satisfied not only at the start of the MT, but during the whole duration of the MT. Stability must be satisfied not only at the start of the MT, but during the whole duration of the MT. In population synthesis studies, the instability is evaluated only at the start of the MT. In population synthesis studies, the instability is evaluated only at the start of the MT. is decreasing as the mass transfer proceeds, hence the stability of the MT is expected to only increase after it started is decreasing as the mass transfer proceeds, hence the stability of the MT is expected to only increase after it started Exception: DDI (unstable) Exception: DDI (unstable) convective giants (stable) convective giants (stable)

The accretor ’ s response and consequence for MT stability During the RLOF, the donor ’ s material will form a stream, and the stream ’ s angular momentum and entropy may affect the stability of the ongoing mass transfer. During the RLOF, the donor ’ s material will form a stream, and the stream ’ s angular momentum and entropy may affect the stability of the ongoing mass transfer.

The stream ’ s angular momentum Form an accretion disc or hit the accretor. Form an accretion disc or hit the accretor. 1. If an accretion disc is formed: the accretor is not necessary gaining angular momentum. the accretor is not necessary gaining angular momentum. 2. Direct impact: the accretor spun up the accretor spun up critical rotation critical rotation get rid of the angular momentum get rid of the angular momentum the stream is deflected the stream is deflected stabilizes the mass transfer stabilizes the mass transfer

The accretor ’ s response For as long as the mass of the donor remains larger than the mass of the accretor, the accretor ’ s thermal timescale is longer than that of the donor. Thus, the accretor will be brought out of its thermal equilibrium. For as long as the mass of the donor remains larger than the mass of the accretor, the accretor ’ s thermal timescale is longer than that of the donor. Thus, the accretor will be brought out of its thermal equilibrium. This accretor ’ s response on a timescale shorter than its thermal timescale can be considered as the reverse on fast rapid mass loss from the donor (adiabatic response): for radiative envelope, the accretor will expand and may overfill its Roche lobe, forming a contact binary This accretor ’ s response on a timescale shorter than its thermal timescale can be considered as the reverse on fast rapid mass loss from the donor (adiabatic response): for radiative envelope, the accretor will expand and may overfill its Roche lobe, forming a contact binary

How well do we understand stable MT The observed low-mass X-ray binaries have usually much higher MT rate than the theoretically obtained MT rate Most of the ultra-compact X-ray binaries do match very well the theoretically obtained MT rate

How well do we understand stable MT It can be stated that the theory of the stable MT in systems with a well known mechanism of angular momentum loss and a well understood simple donor’s response agrees with observations very well. It can be stated that the theory of the stable MT in systems with a well known mechanism of angular momentum loss and a well understood simple donor’s response agrees with observations very well.