On the idempotent semirings such that D∙\mathcal{D}^\bullet is the least distributive lattice congruence

Here we describe the least distributive lattice congruence $\eta$ on an idempotent semiring in general and characterize the varieties $D^\bullet, L^\bullet$ and $R^\bullet$ of all idempotent semirings such that $\eta=\mathcal{D}^\bullet, \mathcal{L}^\bullet$ and $\mathcal{R}^\bullet$, respectively. If $S \in D^\bullet [L^\bullet, R^\bullet]$, then the multiplicative reduct $(S, \cdot)$ is a [left, right] normal band. Every semiring $S \in D^\bullet$ is a spined product of a semiring in $L^\bullet$ and a semiring in $R^\bullet$ with respect to a distributive lattice.Comment: arXiv admin note: text overlap with arXiv:1706.0267

Properties of the propagating oscillatory shock wave in the accretion flows around few transient black hole candidates during their outbursts

In our study of the timing properties of few Galactic black hole candidates evolutions of the low and intermediate frequency quasi-periodic oscillations (LIFQPOs) are observed. In 2005, for explaining evolution of QPO frequency during rising phase of 2005 GRO J1655-40 outburst, Chakrabarti and his students introduced a new model, namely propagating oscillatory shock (POS) model. Here we present the results obtained from the same POS model fitted QPO evolutions during both the rising and declining phases of the outbursts of 2005 GRO J165540, 2010-11 GX 339-4, and 2010 & 2011 H 1743-322.Comment: 3 pages, 3 figures, Thirteenth Marcel Grossmann (MG13) Conference Proceedin

On band orthorings

A semiring $S$ which is a union of rings is called completely regular, if moreover, it is orthodox then $S$ is called an orthoring. Here we study the orthorings $S$ such that $E^+(S)$ is a band semiring. Every band semiring is a spined product of a left band semiring and a right band semiring with respect to a distributive lattice. A similar spined product decomposition for the band orthorings have been proved. The interval $[\mathbf{Ri}, \mathbf{BOR}]$ is lattice isomorphic to the lattice $\mathcal{L}(\mathbf{BI})$ of all varieties of band semirings, where $\mathbf{Ri}$ and $\mathbf{BOR}$ are the varieties of all rings and band orthorings, respectively

Inference on accretion flow dynamics using TCAF solution from the analysis of spectral evolution of H 1743-322 during 2010 outburst

We study accretion flow dynamics of Galactic transient black hole candidate (BHC) H 1743-322 during its 2010 outburst by analyzing spectral data using Two Component (Keplerian and sub-Keplerian) Advective Flow (TCAF) solution, after its inclusion in XSPEC as a local model. We compare our TCAF solution fitted results with combined disk black body and power-law model fitted results and find a similar smooth variation of thermal (Keplerian or disk black body) and non-thermal (power-law or sub-Keplerian) fluxes/rates in two types of model fits. For a spectral analysis, 2.5-25 keV spectral data from RXTE PCA instrument are used. From the TCAF solution fit, accretion flow parameters, such as Keplerian rate, sub-Keplerian rate, location of centrifugal pressure supported shock and strength of the shock are extracted, thus providing a deeper understanding of accretion process and properties of accretion disks around BHC H 1743-322 during its X-ray outburst. Based on the halo to disk accretion rate ratio (ARR), shock properties, accretion rates and nature of quasi-periodic oscillations (QPOs, if observed) entire outburst is classified into four different spectral states, such as, hard, hard-intermediate, soft-intermediate, and soft. From time variation of intrinsic flow parameters it appears that their evolutions in decline phase do not retrace path of rising phase. Since our current model does not include magnetic fields, spectral turnover at energies beyond 500-600 keV cannot be explained.Comment: 7 pages, 4 figures, 1 table; accepted for publication in Ap

Delayed Outburst of H 1743--322 in 2003 and relation with its other outbursts

The Galactic transient black hole candidate H 1743--322 exhibited a long duration outburst in 2003 after more than two and a half decades of inactivity. The 2003 event was extensively studied in multi-wavelength bands by many groups. The striking feature is that the total energy released is extremely high as compared to that in tens of outbursts which followed. In this paper, we look at this event and study both the spectral and temporal properties of the source using two component advective flow (TCAF) paradigm. We extract accretion flow parameters for each observation from spectral properties of the decay phase and determine the mass of the black hole. We computed the energy released during all the known outbursts since 2003 and showed that on an average, the energy release in an outburst is proportional to the duration of the quiescent state just prior to it, with the exception of the 2004 outburst. A constant rate of supply of matter from the companion cannot explain the energy release in 2004 outburst. However, if the energy release of 2003 is incomplete and the leftover is released in 2004, then the companion's rate of matter supply can be constant since 1977 till date. We believe that erratic behaviour of viscosity at the accumulation radius $X_p$ of matter as well as location the $X_p$ itself, rather than the random variation of mass transfer rate from the companion, could be responsible for non-uniformity in outburst pattern. We discuss several factors on which the waiting time and duration of the next outburst could depend.Comment: 29 pages, 6 figures, 3 tables (accepted for publication in "Advances in Space Research"

A comparative study of the timing and the spectral properties during two recent outbursts (2010 & 2011) of H 1743-322

The Galactic black hole candidate (BHC) H~1743-322 recently exhibited two outbursts in X-rays in August 2010 & April 2011. The nature (outburst profile, evolution of quasi-periodic oscillation (QPO) frequency and spectral states, etc.) of these two successive outbursts, which continued for around two months each, are very similar. We present the results obtained from a comparative study on the temporal and the spectral properties of the source during these two outbursts. The evolutions of QPOs observed in both the outbursts were well fitted with propagating oscillatory shock (POS) model. During both the outbursts, the observed spectral states (i.e, hard, hard-intermediate, soft-intermediate and soft) follow the `standard' type of hysteresis-loop, which could be explained with two component advective flow (TCAF) model.Comment: 2 pages, 2 figures, Thirteenth Marcel Grossmann (MG13) Conference Proceedin

Spectral signatures of dissipative standing shocks and mass outflow in presence of Comptonization around a black hole

Accretion flows having positive specific energy are known to produce outflows and winds which escape to a large distance. According to Two Component Advective Flow (TCAF) model, centrifugal pressure dominated region of the flow just outside the black hole horizon, with or without shocks, acts as the base of this outflow. Electrons from this region are depleted due to the wind and consequently, energy transfer rate due to inverse Comptonization of low energy photons are affected. Specifically, it becomes easier to cool this region and emerging spectrum is softened. Our main goal is to show spectral softening due to mass outflow in presence of Compton cooling. To achieve this, we modify Rankine-Hugoniot relationships at the shock front when post-shock region suffers mass loss due to winds and energy loss due to inverse Comptonization. We solve two-temperature equations governing an accretion flow around a black hole which include Coulomb exchange between protons and electrons and other major radiative processes such as bremsstrahlung and thermal Comptonization. We then compute emitted spectrum from this post-shock flow. We also show how location of standing shock which forms outer boundary of centrifugal barrier changes with cooling. With an increase in disc accretion rate $(\dot{m_d})$, cooling is enhanced and we find that the shock moves in towards the black hole. With cooling, thermal pressure is reduced, and as a result, outflow rate is decreased. We thus directly correlate outflow rate with spectral state of the disc.Comment: 10 pages, 6 figures, Accepted for publication in Astrophysics and Space Scienc

Properties of X-ray Flux of Jets During 2005 Outburst of Swift J1753.5-0127 Using TCAF Solution

Galactic black hole candidate Swift~J1753.5-0127 was discovered on 2005 June 30 by the Swift Burst Alert Telescope. We study the accretion flow properties during its very first outburst through careful analysis of the evolution of the spectral and the temporal properties using the two-component advective flow (TCAF) paradigm. RXTE proportional counter array spectra in $2.5-25$ keV are fitted with the current version of the TCAF model fits file to estimate physical flow parameters, such as two component (Keplerian disk and sub-Keplerian halo) accretion rates, properties of the Compton cloud, probable mass of the source, etc. The source is found to be in harder (hard and hard-intermediate) spectral states during the entire phase of the outburst with very significant jet activity. Since in TCAF solution, the model normalization is constant for any particular source, any requirement of significantly different normalization to have a better fit on certain days would point to X-ray contribution from components not taken into account in the current TCAF model fits file. By subtracting the contribution using actual normalization, we derive the contribution of X-rays from the jets and outflows. We study its properties, such as its magnitude and spectra. We find that on some days, up to about 32\% X-ray flux is emitted from the base of the jet itself.Comment: 11 pages, 4 figures, 1 table (accepted for publication in ApJ

Spectral study of GX 339-4 with TCAF using Swift/XRT and NuSTAR Observation

We fit spectra of galactic transient source GX~339-4 during its 2013 outburst using Two Component Advective Flow (TCAF) solution. For the first time, we are fitting combined NuSTAR and Swift observation with TCAF. We use TCAF to fit 0.8-9.0~keV Swift and 4-79 keV NuSTAR spectra along with the LAOR model. To fit the data we use disk accretion rate, halo accretion rate, size of the Compton cloud and the density jump of advective flows at this cloud boundary as model parameters. From TCAF fitted flow parameters, and energy spectral index we conclude that the source was in the hard state throughout this particular outburst. The present analysis also gives some idea about the broadening of Fe $K_{\alpha}$ with the accretion rate. Since TCAF does not include Fe line yet, we make use of the `LAOR model' as a phenomenological model and find an estimate of the Kerr parameter to be $\sim 0.99$ for this candidate.Comment: 10 pages, 4 figures, 1 table, Accepted for Publication in Astrophysics and Space Scienc

Characterization of GX 339-4 outburst of 2010-11: analysis by xspec using two component advective flow model

We study spectral properties of GX 339-4 during its 2010-11 outburst with Two Component Advective Flow (TCAF) model after its inclusion in XSPEC as a table model. We compare results fitted by TCAF model with combined disk black body and power-law model. For a spectral fit, we use 2.5-25 keV spectral data of the PCA instrument onboard RXTE satellite. From our fit, accretion flow parameters such as Keplerian (disk) rate, sub-Keplerian (halo) rate, location and strength of shock are extracted. We quantify how the disk and the halo rates vary during the entire outburst. We study how the halo to disk accretion rate ratio (ARR), quasi-periodic oscillations (QPOs), shock locations and its strength vary when the system passes through hard, hard-intermediate, soft-intermediate, and soft states. We find pieces of evidence of monotonically increasing and decreasing nature of QPO frequencies depending on the variation of ARR during rising and declining phases. Interestingly, on days of transition from hard state to hard-intermediate spectral state (during the rising phase) or vice-versa (during decline phase), ARR is observed to be locally maximum. Non-constancy of ARR while obtaining reasonable fits points to the presence of two independent components in the flow.Comment: 12 Pages, 4 Figures, 1 Table, and 1 Appendix (Table