Study of Magnetized Accretion
Flow With Relativistic Equation
of State
Kuldeep Singh
Working with
Indranil Chattopadhyay
Aryabhatta Research Institute of Observational Sciences
(ARIES), Nainital
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Outline Of Talk
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Introduction
Basic equations and relativistic equation of
state
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Parameter space
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Accretion solutions
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Conclusions
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Introduction
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Accretion is a process in which a
massive object gravitationally attacts
surrounding gaseous matter. It forms an
accretion disc if initially matter has nonzero angular momentum.
But if central object has very high
magnetic field (e.g. neutron star), then
matter is chanelled through the magnetic
field lines.
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*http://astrobites.org/ http://iopscience.iop.org/article/10.1086/304774/fulltext/36030.text.html
Basic Equations and Assumptions
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We assume that star has dipole like magnetic
field and stream function is,
We also assume that the magnetic field
energy density is larger than the matter
kinetic energies,
There are conserved quantities along the
field lines which are labeled by flux function
or stream function,
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*”Funnel flows from discs to magnetized stars” Koldoba et. al. 2002
Basic Equations and Assumptions
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we can derive the expression for ω and Bφ,
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Because,
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If field lines are frozen into the star‘s surface,
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Thus, the Bernoulli constant along this field line is,
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Cooling term,
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Equation of motion,
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Shock conditions,
*Koldoba et. al. 2002
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*Wu, K., Chanmugam, G., & Shaviv, G. 1994, ApJ, 426, 664
Relativistics EoS
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The EoS for multi-species flow (e-, e+, p+)
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Where,
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The enthalpy (h), adiabatic index
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and sound speed is given by,
By using 1st law of thermodynamics and continuity equation, we
can obtain adiabatic equation of state and entropy accretion rate,
where,
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*Chattopadhyay 2008; Chattopadhyay & Ryu 2009, Kumar et al.2013
Parameter Space
Pmin = 0.16s
P = 1s
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Topology of Solutions
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Accretion solutions
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Accretion solutions
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Accretion solutions
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Accretion solutions
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Accretion solutions
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Conclusions
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We study the parameter space and magnetized shock accretion
solutions with different compositions with and without the
presence of cooling mechanisms.
We find that there is a certain value rotation period (P min) below
which multiple critical points are not possible.
Accretion solutions with cooling which connects the flow from
the disc to the star's surface through shock.
Adiabatic index varies from ~ 1.66 far away to ~ 1.40 before
shock and after shock it again approaches ~ 1.66.
Only with cooling mechanisms we find the consistent accretion
solutions and these solutions can explain the accretion process
in case of the neutron star and radiation emission.
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Thank You
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Accretion solutions (White Dwarf)
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Bremsstrahlung and Cyclotron
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Bremsstrahlung and Cyclotron
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Magnetic Field
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Cross-sectional area
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