On the Roche Lobe On the Roche Lobe OverflowOverflow

Reporter: Wang ChenReporter: Wang Chen 12/02/201412/02/2014

Reference: N. Ivanova, 1406.3475v1

outlineoutline IntroductionIntroduction 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 donor’s response and consequences for

the mass transfer stability the mass transfer stability The accretor’s response and consequences The accretor’s response and consequences

for the mass transfer stability for the mass transfer stability How well do we understand stable mass How well do we understand stable mass

transfer transfer

Introduction Introduction

Mass transfer (MT): Roche lobe overflow (Mass transfer (MT): Roche lobe overflow (RLORLOFF))

Introduction Introduction

ClassificationClassification (by the evolutionary (by the evolutionary status of the donor)status of the donor)

Case A – during hydrogen (H) burning in Case A – during hydrogen (H) burning in the core of the donor.the core of the donor.

Case B – after exhaustion of H in the Case B – after exhaustion of H in the center of the donor.center of the donor.

Case C – after exhaustion of central helium Case C – after exhaustion of central helium (He) burning.(He) burning.

IntroductionIntroduction

Blue: radiative envelope

Red: convective envelope

Star: when hydrogen or helium is exhausted in the core

introduction introduction

The specific case of the MT by itself does The specific case of the MT by itself does not imply whether the MT would be stable not imply whether the MT would be stable or not.or not.

It is more important in determining the It is more important in determining the outcome if the initial stability and the outcome if the initial stability and the timescale of the initiated MT are known by timescale of the initiated MT are known by other means.other means.

The structure of the inner layers may The structure of the inner layers may affect the stability of the MT later on.affect the stability of the MT later on.

introductionintroduction

Important for predicting the stability of Important for predicting the stability of thethe MT and the outcomeMT and the outcome

1.1. The evolutionary status of the donor – this The evolutionary status of the donor – this implies its complete internal structure;implies its complete internal structure;

2.2. The structure of the donor’s envelope;The structure of the donor’s envelope;

3.3. The mass ratio of the binary;The mass ratio of the binary;

4.4. The type of the accretor.The type of the accretor.

Stability of the MT: the global Stability of the MT: the global condition condition

(The donor’s response)

(conservative & the angular momentum loss)

Roche Lobe Response 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 Donor’s Response

The star will readjust both the The star will readjust both the hydrostatic and thermal equilibrhydrostatic and thermal equilibriaia when loses mass.when loses mass.

The readjustment of the internal The readjustment of the internal structure results in the star’s radius structure results in the star’s radius evolution and can be described using evolution and can be described using

TimescalesTimescales Hydrostatic readjustment: the initial donor’s response Hydrostatic readjustment: the initial donor’s response

to mass loss can be expected to be almost adiabatic.to mass loss can be expected to be almost adiabatic.

Thermal readjustment: Thermal readjustment:

Superadiabatic readjustment: Superadiabatic readjustment:

Timescales Timescales Dynamical MTDynamical MT TThe lobe-filling star cannot remain within its Roche lobe with he lobe-filling star cannot remain within its Roche lobe with

hydrostatic equilibriumhydrostatic equilibrium.. TThe mass loss rate from the primary is limited only by the sonic he mass loss rate from the primary is limited only by the sonic

expansion rate of its envelopexpansion rate of its envelope.e. Will lead to common envelope evolution or contact.Will lead to common envelope evolution or contact.

Thermal MTThermal MT TThe lobe filling star loses mass, and may remain within its Roche he lobe filling star loses mass, and may remain within its Roche

lobe in hydrostatic, but not thermal equilibrium. It remain just lobe in hydrostatic, but not thermal equilibrium. It remain just filling the Roche lobe, and relaxation toward thermal equilibrium filling the Roche lobe, and relaxation toward thermal equilibrium drives mass on thermal timescale. drives mass on thermal timescale.

Nuclear MTNuclear MT TThe radius of the primary remains constrained to that of its Roche he radius of the primary remains constrained to that of its Roche

lobe, and lobe, and the star remains in thermal equilibrium. the star remains in thermal equilibrium. TThe timescale is dictated by the orbital angular momentum he timescale is dictated by the orbital angular momentum

evolution, or by the nuclear evolution of the donor.evolution, or by the nuclear evolution of the donor.

Envelope’s Structure – adiabatic Envelope’s Structure – adiabatic

responseresponse Convective envelopeConvective envelope: :

forfor non-degenerate & fully ionized ideal gas non-degenerate & fully ionized ideal gas

radiative coreradiative 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 Envelope’s Structure – adiabatic responseresponse

Envelope’s Structure – adiabatic Envelope’s Structure – adiabatic responseresponse

Radiative envelope Radiative envelope

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

Envelope’s Structure – equilibriumEnvelope’s Structure – equilibrium responseresponse

Low-mass giantsLow-mass giants: : the thermal structure is the thermal structure is almost independent from the envelopealmost independent from the envelope, so, so

Main sequence starsMain sequence stars: mass-radius : mass-radius relation, usually positive. E.g., for ZAMS relation, usually positive. E.g., for ZAMS is at least 0.57, and it grows as the donor is at least 0.57, and it grows as the donor approaches the terminal main sequence.approaches the terminal main sequence.

These values are applicable only for the start of the mass transfer

Envelope’s Structure – superadiabatic Envelope’s Structure – superadiabatic responseresponse

This is the response of the donor on the This is the response of the donor on the mass loss that proceeds on a timescale mass loss that proceeds on a timescale longer than longer than a a but shorter than .but shorter than .

Arguably this is the most important Arguably this is the most important response for determining the mass transfer response for determining the mass transfer stabilitystability

Consider here the superadiabatic response Consider here the superadiabatic response for confor convectivevective donors only. donors only.

Envelope’s Structure – Envelope’s Structure – superadiabatic responsesuperadiabatic response

If mass is removed from this entropy profile in an If mass is removed from this entropy profile in an adiabatic regime, the envelope is momentarily adiabatic regime, the envelope is momentarily expanding by a large fraction of its radius.expanding by a large fraction of its radius.

The dramatic expansion finds a very different The dramatic expansion finds a very different hydrostatic equilibrium than a normal giant of hydrostatic equilibrium than a normal giant of almost the same mass.almost the same mass.

Woods & Ivanova found that if the superadiabatic Woods & Ivanova found that if the superadiabatic layer is resolved, the MT could be stable in layer is resolved, the MT could be stable in systems with larger mass radio than would be systems with larger mass radio than would be predicted by the adiabatic approximation . They predicted by the adiabatic approximation . They found that real giants will often contract.found that real giants will often contract.

Sudden change of the donor’s Sudden change of the donor’s response – delayed dynamical response – delayed dynamical

instability (DDI)instability (DDI) A case of a dynamical instability that A case of a dynamical instability that

follows a period of a stable MT.follows a period of a stable MT. suddenly drops during the MT, and suddenly drops during the MT, and

become smaller than become smaller than .. It usually takes place in initially It usually takes place in initially

radiative donorsradiative donors.. It requires detailed stellar modeling.It requires detailed stellar modeling. qqcritcrit

The donor’s response and The donor’s response and consequences for the MT consequences for the MT

stability stability

Initial stability: fully conservative MTInitial stability: fully conservative MT

non-conservative MTnon-conservative MT Stability of the ensuing MT Stability of the ensuing MT

Initial stability Initial stability

Fully conservative MTFully conservative MT:: if q>1, >0.46if q>1, >0.46 for confor convectivevective envelopes < dynamical unstable. 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 increase, and the stability of the MT is

increasing.increasing.

Stability of the ensuing MTStability of the ensuing MT

Stability must be satisfied not only at the Stability must be satisfied not only at the start of the MT, but during the whole duration start of the MT, but during the whole duration of the MT.of the MT.

In population synthesis studies, the instability In population synthesis studies, the instability is evaluated only is evaluated only at the start of the MTat the start of the MT..

is decreasing as the mass transfer is decreasing as the mass transfer proceeds , hence the proceeds , hence the stabilitystability of the MT is of the MT is expected to only expected to only increaseincrease after it started after it started

Exception: DDI (unstable) Exception: DDI (unstable) convective giants (stable)convective giants (stable)

The accretor’s response and The accretor’s response and consequence for MT stability consequence for MT stability

During the RLOF, the During the RLOF, the donor’s donor’s materialmaterial will form a stream, and the will form a stream, and the stream’s angular momentum and stream’s angular momentum and entropy may affect the stability of entropy may affect the stability of the ongoing mass transfer.the ongoing mass transfer.

The stream’s angular The stream’s angular momentummomentum

Form an accretion disc or hit the accretor.Form an accretion disc or hit the accretor.1. If an accretion disc is formed: 1. If an accretion disc is formed:

the accretor is not necessary gaining angular the accretor is not necessary gaining angular momentum.momentum.

2. Direct impact: 2. Direct impact:

the accretor spun up the accretor spun up

critical rotationcritical rotation

get rid of the angular momentumget rid of the angular momentum

the stream is deflectedthe stream is deflected

stabilizes the mass transferstabilizes the mass transfer

The accretor’s responseThe accretor’s response

For as long as the mass of the donor remains For as long as the mass of the donor remains larger than the mass of the accretor, the larger than the mass of the accretor, the accretor’s thermal timescale is longer than accretor’s thermal timescale is longer than that of the donor. that of the donor. Thus, the accretor will be Thus, the accretor will be brought out of its thermal equilibrium.brought out of its thermal equilibrium.

This accretor’s response on a timescale This accretor’s response on a timescale shorter than its thermal timescale can be shorter than its thermal timescale can be considered as the considered as the reverse on fast rapid mass reverse on fast rapid mass loss from the donorloss from the donor (adiabatic response): for (adiabatic response): for radiative envelope, the accretor will expand radiative envelope, the accretor will expand and may overfill its Roche lobe, forming a and may overfill its Roche lobe, forming a contact binary contact binary

How well do we understand stable How well do we understand stable MTMT

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 How well do we understand stable MTstable MT

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