Study of shocks in relativistic viscous accretion flow around Kerr black hole. (arXiv:1903.02856v1 [astro-ph.HE])
<a href="http://arxiv.org/find/astro-ph/1/au:+Dihingia_I/0/1/0/all/0/1">I. Dihingia</a> (IITG), <a href="http://arxiv.org/find/astro-ph/1/au:+Das_S/0/1/0/all/0/1">Santabrata Das</a> (IITG), <a href="http://arxiv.org/find/astro-ph/1/au:+Maity_D/0/1/0/all/0/1">Debaprasad Maity</a> (IITG), <a href="http://arxiv.org/find/astro-ph/1/au:+Nandi_A/0/1/0/all/0/1">Anuj Nandi</a> (URSC, ISRO)
We study the relativistic viscous accretion flows around the Kerr black
holes. We present governing equations that describe the flow motion in full
general relativity and solve them to obtain the complete set of global
transonic solutions in terms of the flow parameters, namely energy (${cal
E}$), angular momentum (${cal L}$) and viscosity ($alpha$). We obtain a new
type of accretion solution which was not reported earlier. Further, to the best
of our knowledge, we show for the first time that viscous accretion solutions
may contain shock waves particularly when flow simultaneously passes through
both inner critical point ($r_{rm in}$) and outer critical point ($r_{rm
out}$) before entering to the Kerr black hole. We examine the shock properties,
namely shock location ($r_s$) and compression ratio ($R$, measure of density
compression across the shock front) and show that shock can form for a large
region of parameter space in ${cal L}-{cal E}$ plane. We study the effect of
viscous dissipation on the shock parameter space and find that parameter space
shrinks as $alpha$ is increased. We also calculate the critical viscosity
parameter ($alpha^{rm cri}$) beyond which standing shock solutions disappear
and examine the correlation between the black hole spin ($a_k$) and
$alpha^{rm cri}$. Finally, the relevance of our work is conferred where using
$r_s$ and $R$, we empirically estimate the oscillation frequency of the shock
front ($nu_{QPO}$) when it exhibits quasi-periodic (QP) variations. The
obtained results indicate that the present formalism seems to be potentially
viable to account for the QPO frequency in the range starting from milli-Hz to
kilo-Hz as $0.386~{rm Hz}le nu_{QPO} left(frac{10M_odot}{M_{BH}} right)
le 1312$ Hz for $a_k=0.99$, where $M_{BH}$ stands for black hole mass.
We study the relativistic viscous accretion flows around the Kerr black
holes. We present governing equations that describe the flow motion in full
general relativity and solve them to obtain the complete set of global
transonic solutions in terms of the flow parameters, namely energy (${cal
E}$), angular momentum (${cal L}$) and viscosity ($alpha$). We obtain a new
type of accretion solution which was not reported earlier. Further, to the best
of our knowledge, we show for the first time that viscous accretion solutions
may contain shock waves particularly when flow simultaneously passes through
both inner critical point ($r_{rm in}$) and outer critical point ($r_{rm
out}$) before entering to the Kerr black hole. We examine the shock properties,
namely shock location ($r_s$) and compression ratio ($R$, measure of density
compression across the shock front) and show that shock can form for a large
region of parameter space in ${cal L}-{cal E}$ plane. We study the effect of
viscous dissipation on the shock parameter space and find that parameter space
shrinks as $alpha$ is increased. We also calculate the critical viscosity
parameter ($alpha^{rm cri}$) beyond which standing shock solutions disappear
and examine the correlation between the black hole spin ($a_k$) and
$alpha^{rm cri}$. Finally, the relevance of our work is conferred where using
$r_s$ and $R$, we empirically estimate the oscillation frequency of the shock
front ($nu_{QPO}$) when it exhibits quasi-periodic (QP) variations. The
obtained results indicate that the present formalism seems to be potentially
viable to account for the QPO frequency in the range starting from milli-Hz to
kilo-Hz as $0.386~{rm Hz}le nu_{QPO} left(frac{10M_odot}{M_{BH}} right)
le 1312$ Hz for $a_k=0.99$, where $M_{BH}$ stands for black hole mass.
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