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specifically for X-ray astronomy like for making outflow, accretion disc etc.
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Draw.io is a good choice for the diagrams, but may be too general.
Also, I use GeoGebra for illustrating ideas in a geometrical sense.
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It may be a binary black hole accretion disk or an AGN.
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Their study shows that B is around for 33 G for V404 Cygni
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I noted that ultraluminous X-ray Source (ULX) luminosity is usually determined by calculation from flux and host galaxy's distance measurement. I want to know the idea of determining ULX membership to a particular host galaxy, since there maybe no counterpart observation in other bands.
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ULXs are compact, off-nuclear, X-ray sources with X-ray luminosity > 10^39 erg/s. If there is no counterpart detected in other wavelength (lets say Optical), we can possibly rule out the association of foreground stars or background AGNs to ULXs (unless they are very faint or highly obscured). Since these objects (stars/AGNs) were dominantly emit in visible wavelength and can be easily identified in the optical observations. The flux ratio (X-ray-to-optical) of these objects will have specific range, which can be used to differentiate the background/foreground objects from ULXs.
(See Stocke et al 1991, Lotz et al. 2004, Jithesh et al 2011) 
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In the literature we find that relativistic e- - e+ jets are not possible. For truly relativistic jests, we need to have e- - p pairs.
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The ionization state of the jet material varies considerably within the jet due to the presence of dust which can scatter the harder radiation.  Nonetheless, many heavy ions are also present in these jets.   The jets in AGNs are physically different than those in X-ray binaries.  X-ray binaries are basically accretion flows with some collimation, where as AGN jets are much more energetic and more highly collimated and are not accretion flows, but rather ejected collimatted  and highly ionized matter.
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 Ex-AGN, Particularly Gamma Ray Study, GRB, QUASARS & Jet's
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Agreeing with the previous answers, I would add that different wavebands have different strengths. Gamma ray detectors are sensitive to the most extremely energetic events such as GRBs, but are very bad at localising the source; for this you need to match the event to detections at other wavelengths. X-ray telescopes are useful for following up GRBs as well as studying accreting black holes such as those in AGN. But for distant sources the angular resolution is still poor, and optical imaging is needed to identify the host. The optical benefits from the best resolution and sensitivity, but the problem in the optical and infrared is separating the emission of an AGN from that of the host galaxy, and to understand this one needs to model the broadband spectrum or multi-wavelength SED (spectral energy distribution). The radio spectrum is also useful for the study of high-energy sources since it includes synchrotron radiation from relativistic electrons that are accelerated by high-energy processes such as jets and shocks associated with SNe and AGN.
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Why does the outward increase of angular momentum in an accretion disk make the disk Rayleigh stable? Since the density profile in an accretion disk increases inward in the case of constant accretion rate, there should not be an instability in between consecutive rings. Is that the reason why they are Rayleigh stable?
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The Rayleigh criterion, relies on fluid elements retaining their angular momenta.
Following Rayleigh, suppose we interchange the fluid in two rings, of equal masses, at radii r1 and r2 . So the fluid initially at r1 is moved to r2 , conserving its angular momentum L1 . Similarly the fluid initially at r2 is moved to r1 , conserving its angular momentum L2 . Then,
change in KE ∼ (L2^2 − L1^2 )(r1^-2 - r2^-2)
Now a system always wants to go to the lowest energy state. If angular momentum is a increasing function of r, then the swapping of fluid parcels is going to cost the system to increase its energy, so the system will not try to do it and the system is stable to this perturbation.
However in case when angular momentum is a decreasing function of r, then the system can release its energy by swapping of fluid parcels and the system will try to do so, so the system is unstable to this perturbation.
So we can say that when the angular momentum is a increasing function of r in an accretion disk, the disk is Rayleigh stable.
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How does the mass accretion rate affect these transitions? Further can the hardening or softening of the spectrum in the accretion be related to the changes in the shock properties in accretion flows, the shock strength and compression ratio for instance?
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This is still very much an open question.
Recent ideas include:
Turbulence in a magnetic field -
Begelman, M. \& Armitage, P. 2014
arXiv:1401.5475
The tearing off of rings from the accretion disk -
Nixon, C. \& Salvesen G. 2014,
MNRAS 437,3994
An older idea is that of magnetically arrested disks (MAD). Here, material initially builds up against a magnetic barrier while in the hard state. When it breaks through, significant mass accumulates close to the black hole, heats up and emits a soft spectrum which outshines the harder power-law component.
e.g. Narayan, Igumenschev & Abramowicz PASJ: Publ. Astron. Soc. Japan 55, L69-L72, 2003
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What will be the statistical properties of the error present in the signal?
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It depends on how "raw" your raw data is. The number of triggers received in a given time period will be Poisson distributed. This is true for most kinds of cuts you have on your data; for example, an energy threshold. If you have downstream non-linear data processing or electronics effects, you can push this off Poisson, but it's pretty robust. Now, the measured energy is a different beast, which will be entirely detector dependent. If you have a measured energy dispersion function (ideally but rarely measured by shooting a known monoenergetic beam into the detector, and measuring the distribution of the reported energy) your on-orbit data will be the true energy spectrum convolved with your energy dispersion function.
See Gregory and Loredo, ApJ 398, 146, 1992, or Feigelson and Babu, "Promise of Bayesian Inference for Astrophysics" (a book of articles), or WF Tompkins, "Applications of LIkelihood Analysis in Gamma-Ray Astrophysics," a PhD thesis from Stanford -- pretty sure it's on arXiv.
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Also, in the accretion disks dominated by magnetic pressure what is the order of this magnetic pressure in cgs units? Also what is the order of the magentic field in Gauss?
And finally are the magnetic fields in any way important in the collapsar model as well?
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Answer by Indrani Banerjee, IISC Bangalore. I am just posting her comments from her e-mail.
There is no fixed magnitude of gas or radiation pressure for a particular disk. Both the pressues vary with distance from the black hole.
The gas pressure in collapsar accretion disks is given by P_gas = rho k_B
T/m_N, and the radiation pressure P_rad =(1/3) a T^4, where rho is the
density, k_B is Boltzmann's constant, T is temperature, m_N is mass of
nucleon, and a is radiation density constant. You have to know the
temperature and the density profile in order to estimate their magnitude.
You can find the temperature and density profile of collapsar I accretion
disk in Chen & Beloborodov 2007 (ApJ 657, 383) and collapsar II accretion
disk in our RAA paper.
As far as 'The Standard Disk' (Shakura-Sunyaev disk) is concerned the
outer and the middle region of the disk is dominated by gas pressure, i.e,
the total pressure is almost equal to the gas pressure while the inner
disk is radiation pressure dominated. The expressions for gas and
radiation pressure are same as above. The temperature and density profiles
for Shakura-Sunyaev/Novikov-Thorne disk is given in Abramowicz & Fragile
2013 (Living Review in Relativity, 16,1). So, once you know the
temperature and density profiles you can easily estimate the magnitudes of
the gas and radiation pressures.
Moving on to your last question, magnetic fields are important in
collapsar accretion disks as they often help in driving jets and outflows
from the disk.