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Finally. we revisited the GBOS study of cosmic. ray ionization as a mechanism for creating temperature fluctuations in Hu regions. | Finally, we revisited the GB05 study of cosmic ray ionization as a mechanism for creating temperature fluctuations in H regions. |
While this provides a potential mechanism for creating cold tonized plasma in H regions. we show that the values of Z required to produce the ionization. have been overestimated in their treatment. due to the ££? discrepancy discussed above. | While this provides a potential mechanism for creating cold ionized plasma in H regions, we show that the values of $\zeta$ required to produce the ionization have been overestimated in their treatment, due to the $t^2$ discrepancy discussed above. |
Based on the formulae presented here. we re-estimated their model parameters. | Based on the formulae presented here, we re-estimated their model parameters. |
The corrections are apparent. particularly in cases where temperatureof the cold gas component is low. resulting in lower values of Z that agree better with the estimates for the Orion nebula published in the literature. | The corrections are apparent, particularly in cases where temperatureof the cold gas component is low, resulting in lower values of $\zeta$ that agree better with the estimates for the Orion nebula published in the literature. |
range in the C1 solution space. | range in the C1 solution space. |
Otherwise. it is concluded that the inverse Compton losses in Table 4 seem reasonable for a relativistic plasmoid. | Otherwise, it is concluded that the inverse Compton losses in Table 4 seem reasonable for a relativistic plasmoid. |
According to Table 3. the maximum injected energv flux of component Cl is larger than that of component C2. | According to Table 3, the maximum injected energy flux of component C1 is larger than that of component C2. |
Also. the larger minimum bound on the injection energy [Ξ±Ο in Table 3 is for C2. | Also, the larger minimum bound on the injection energy flux in Table 3 is for C2. |
Thus. the maximum injected power during the December 1993 [lare is bounded to the range 4.05xLOβerg/sec<Q(December.1993),6.1410erg/sec. | Thus, the maximum injected power during the December 1993 flare is bounded to the range $4.05 \times 10^{37}\mathrm{erg/sec}<Q(\mathrm{December, \,
1993})_{\mathrm{max}}< 6.14 \times 10^{38}\mathrm{erg/sec}$. |
Assume that there are oppositely directed. plasmoids that are ejected simultaneously. as commonly occurs in other observed flares. | Assume that there are oppositely directed plasmoids that are ejected simultaneously as commonly occurs in other observed flares. |
These components (vpically comprise only e ol the total flix density due to the more intense redshifting when the ejections are directed away [rom the observer (RodriguezancMirabel 2005). | These components typically comprise only $\sim$ of the total flux density due to the more intense redshifting when the ejections are directed away from the observer \citep{rod99,fen99,mil05}. |
. It is noted that the estimates of Q for the components C1 and C2 presented here are slightly high since this extra of the flux appeared in their component flux densities. | It is noted that the estimates of $Q$ for the components C1 and C2 presented here are slightly high since this extra of the flux appeared in their component flux densities. |
The existence of counter-ejecta. would. double the estimate above for (he maximum total injected power from the central engine during the December 1993 (lare. 9.1x10"ere/secβ(December1993)was<1.22xI0" erg/sec. | The existence of counter-ejecta would double the estimate above for the maximum total injected power from the central engine during the December 1993 flare, $9.1 \times 10^{37}\mathrm{erg/sec}<Q(\mathrm{December\,
1993})_{\mathrm{max}}< 1.22 \times 10^{39}\mathrm{erg/sec}$ . |
The central black hole in GRS 1915+105 has a mass estimated at 14 AM. (Greineretal2001). | The central black hole in GRS 1915+105 has a mass estimated at 14 $M_{\odot}$ \citep{gre01}. |
. Thus. the maximum impulsive power required to initiate the plasmoids is 0.05iqq<Qua0.68Ljq in terms of the Eddineton luminosity. Lia. | Thus, the maximum impulsive power required to initiate the plasmoids is $0.05 L_{\mathrm{Edd}}< Q_{\mathrm{max}} < 0.68 L_{\mathrm{Edd}}$ in terms of the Eddington luminosity, $L_{\mathrm{Edd}}$. |
In this paper. a major flare from December 1993 from the miero-quasar GRS 19154-105 was analvzed in order to address four major unknowns [rom historical estimates of flare energv flux. | In this paper, a major flare from December 1993 from the micro-quasar GRS 1915+105 was analyzed in order to address four major unknowns from historical estimates of flare energy flux. |
These major uncertainties Chat were discussed in the Introduction are listed again here with the corresponding resolution implied by Che detailed modeling described in | These major uncertainties that were discussed in the Introduction are listed again here with the corresponding resolution implied by the detailed modeling described in |
radius in that case is ~2xLOM em and the final Lorentz factor is ro75. | radius in that case is $\sim 2 \times 10^{13}$ cm and the final Lorentz factor is $\g_{f,0}\approx 5$. |
The SN associated with GRB 031203. SN 2003Iw. is similar in ejected mass and slightly more energetic than SN 1998bw (MazzaliΞ΅αΌ°al... | The SN associated with GRB 031203, SN 2003lw, is similar in ejected mass and slightly more energetic than SN 1998bw \citep{Mazzali06}. . |
2006).. Setting Β£2,~2x10M and M;=15M. in equation 26. we find that an explosion energv of Ezz10?! produces a breakout with the observed properties ol GRB 031203. | Setting $R_* \sim 2 \times 10^{13}$ and $M_{ej}=15 M_\odot$ in equation \ref{eq g0b0} we find that an explosion energy of $E \approx 10^{54}$ produces a breakout with the observed properties of GRB 031203. |
Again this value is larger by about an order of magnitude compared to the one observe in the associated SN, | Again this value is larger by about an order of magnitude compared to the one observe in the associated SN. |
The breakout radii that we find for GRBs 980425 and 031203 are larger than (hose βtypical Woll-Bavet stus. the probable progenitors of GRB-SNe. | The breakout radii that we find for GRBs 980425 and 031203 are larger than those of typical Wolf-Rayet stars, the probable progenitors of GRB-SNe. |
This implies that either je. breakout is not from the edge of the progenitor star (e.g.. from a wind) or that GRB progenitors are larger (han commonly thought. (which may help chockine the velativislic jet). | This implies that either the breakout is not from the edge of the progenitor star (e.g., from a wind) or that low-luminosity GRB progenitors are larger than commonly thought (which may help chocking the relativistic jet). |
Finally. a prediction of relativistic shock breakouts is a significant X-ray Mwission. Chat can be comparable in energy (o that of the breakout 7?-rav Mare. | Finally, a prediction of relativistic shock breakouts is a significant X-ray emission, that can be comparable in energy to that of the breakout $\g$ -ray flare. |
The A-ravs are emitted during the spherical phase. over time scale (hat is significantly longer (than that βthe breakout emission. | The X-rays are emitted during the spherical phase, over time scale that is significantly longer than that of the breakout emission. |
GRD 031203 has shown a bright signal of dust scattered: XN-ravs. which indicates on ~2 keV emission with enerev comparable tothat of the gamma-rays. during the first 1000 s after the burst (Vaughanefaf2004:Feng&Fox2010). | GRB 031203 has shown a bright signal of dust scattered X-rays, which indicates on $\sim 2$ keV emission with energy comparable tothat of the gamma-rays, during the first $1000$ s after the burst \citep{Vaughan04,FengFox10}. |
. These values fit (he predictions of a breakout model. | These values fit the predictions of a breakout model. |
For example. if the breakout is [rom a stellar surface at R,=2x107 and M;=15.M.. then equations 30-32. predict a release of ~LO50 erg ad ~2 keV within the first hour alter the burst. | For example, if the breakout is from a stellar surface at $R_* = 2 \times 10^{13}$ and $M_{ej}=15
M_\odot$, then equations \ref{eq tNW}- \ref{eq E10tNW} predict a release of $\sim 10^{50}$ erg at $\sim 2$ keV within the first hour after the burst. |
To conclude. we find that (he energy. temperature. ancl lime scales of all four GRBs are explained very well by shock breakout emission and that all of them salisly the relativistic breakout relation between ΟΟ. 7j, and !obsbo (equation 18)). | To conclude, we find that the energy, temperature, and time scales of all four low-luminosity GRBs are explained very well by shock breakout emission and that all of them satisfy the relativistic breakout relation between $E_{bo}$, $T_{bo}$ and $t_{bo}^{obs}$ (equation \ref{eq tbo test}) ). |
These observables are largely independent of the pre-shocked density profile aud are therefore applicable also for a breakout [rom a shell of mass ejected by the progenitor prior to the explosion aud possibly to a breakout from a wind. | These observables are largely independent of the pre-shocked density profile and are therefore applicable also for a breakout from a shell of mass ejected by the progenitor prior to the explosion and possibly to a breakout from a wind. |
Breakout emission can also explain many other observed properties. such as the smooth light curve. the afterglow radio emission. the small fraction of the explosion energy. carried by (he prompt high energy. emission. and the delaved bright X-ray. emission seen in GRB 031203. | Breakout emission can also explain many other observed properties, such as the smooth light curve, the afterglow radio emission, the small fraction of the explosion energy carried by the prompt high energy emission, and the delayed bright X-ray emission seen in GRB 031203. |
We therefore find it to be verv likely that indeed all low-Inminosity. GRBs are relativistic shock breakouts. | We therefore find it to be very likely that indeed all low-luminosity GRBs are relativistic shock breakouts. |
GRB 1012254 is a peculiar explosion showing an ~hour long smooth burst of and X-ravs Followed by a peculiar IR-UV afterglow. which is consistent with a blackbodyemission. | GRB 101225A is a peculiar explosion showing an $\sim$ hour long smooth burst of gamma-rays and X-rays followed by a peculiar IR-UV afterglow, which is consistent with a blackbodyemission. |
Its origin is unclear. | Its origin is unclear. |
Thoneefaf(2011) arene for a cosmological origin and estimate its redshift to be zz 0.3. while Levan&Tanvir(2011) argue that its origin is local. | \cite{Thone11} argue for a cosmological origin and estimate its redshift to be $\approx 0.3$ , while \cite{Levan11}
argue that its origin is local. |
top-heavy IMF (Nakamura&Umeninura2001) aid zeroanetallicity massive star vields [rom Chieffi&Limongi(2002) and Umeda&Nomoto(2002). | top-heavy IMF \citep{nakamura01} and zero-metallicity massive star yields from \citet{chieffi02} and \citet{umeda02}. |
. During the second stage. we assume that the GC stars form in 10* vears [rom this low- gas*.. | During the second stage, we assume that the GC stars form in $^{7}$ years from this low-metallicity . |
In Fenneretal.(2004).. the Ixroupaetal.(1993) IMF was adopted and it was assumed that the GC retained ejecta [rom stars with m.<6.5\L.: here we change to a standard Salpeter-like IMFE (Salpeter1955) and test the effect of different power-law slopes (see refsecimf)). | In \citet{fenner04}, the \citet{kroupa93} IMF was adopted and it was assumed that the GC retained ejecta from stars with $m \le 6.5\Msun$ ; here we change to a standard Salpeter-like IMF \citep{salpeter} and test the effect of different power-law slopes (see \\ref{sec:imf}) ). |
Furthermore we also run separate simulations using the AGB vields [rom [or helium and the CNO isotopes. | Furthermore we also run separate simulations using the AGB yields from \citet{ventura02} for helium and the CNO isotopes. |
These vields cover (he mass range 5.5: we extrapolate these vields to 3.581. and G.5\L. ancl substitute in vields from Fenneretal.(2004). for im<2.5M.. | These yields cover the mass range $3 \le m (\Msun) \le 5.5$ ; we extrapolate these yields to $\Msun$ and $\Msun$ and substitute in yields from \citet{fenner04} for $m < 2.5\Msun$ . |
We underline here that (his extrapolation to hieher mass renders uncertain (he results obtained in terms of the masxinnun Y expected after 50 β LOO Myr when using the Venturaetal.(2002) vields. | We underline here that this extrapolation to higher mass renders uncertain the results obtained in terms of the maximum $Y$ expected after 50 $-$ 100 Myr when using the \citet{ventura02} yields. |
Although. in this case the extrapolation should be fairly reasonable given that the yields are monotonic wilh mass. | Although, in this case the extrapolation should be fairly reasonable given that the yields are monotonic with mass. |
No contribution from Type Ia SNe was included due to the observed uniform |Fe/II]. | No contribution from Type Ia SNe was included due to the observed uniform [Fe/H]. |
We favor a scenario in which the next (third) generation of stars is assunied to out of this polluted eas rather than tliis gas acereting onto their surfaces. | We favor a scenario in which the next (third) generation of stars is assumed to out of this polluted gas rather than this gas accreting onto their surfaces. |
This is because observational evidence shows that there is no dilution of the surface abundances when stars move (through the first dredge-up. | This is because observational evidence shows that there is no dilution of the surface abundances when stars move through the first dredge-up. |
The first dredge-up would mix the polluted envelope material wilh primordial material. vet no changes to ΞΏ. Na. Mg or Al abundances are observed at (his stage 2001). | The first dredge-up would mix the polluted envelope material with primordial material, yet no changes to O, Na, Mg or Al abundances are observed at this stage \citep{gratton01}. |
. In ihe GCCE model we simply track (he composition of the cluster gas as a function of time. | In the GCCE model we simply track the composition of the cluster gas as a function of time. |
Ilence the abundance of the gas reflects the continuous addition of AGB material as stars of decreasing mass evolve and lose their envelopes via winds. | Hence the abundance of the gas reflects the continuous addition of AGB material as stars of decreasing mass evolve and lose their envelopes via winds. |
We do not model the formation of the third stellar generation but we can speculate that star formation will lock up some of this gas in new stars al a rate (and efficiency) Chat does not use up all of the gas from the G.5A\L. stars before the GAL. stars have added new material (~20 Myr). | We do not model the formation of the third stellar generation but we can speculate that star formation will lock up some of this gas in new stars at a rate (and efficiency) that does not use up all of the gas from the $\Msun$ stars before the $\Msun$ stars have added new material $\sim 20$ Myr). |
This is eoing on star formation timescalesfor low-mass stars. which can be anything from 1 Myr during theproto-star phase to 105 Mvr to reach the zero-aged main sequence ).. | This is going on star formation timescalesfor low-mass stars, which can be anything from $\sim 1$ Myr during theproto-star phase to $\sim 10^{8}$ Myr to reach the zero-aged main sequence \citep{siess00,white04}. . |
This loss term. Β£. represents the AlfvΓ©n--wave damping mechanisms; we consider both non-linear Landau damping (in the hot. intercloud medium) as derived by ?:: (where wehave substituted cai=Ava with k~+β¬ J, and ion-neutral friction Ceaseafrom?):: where v; is the ion thermal speed (which we set to δαΟΟ) throughout this work). 6B is the amplitude of the -wave perturbation to the large-scale magnetic field (B). and p, is the mass density of neutral atoms. | This loss term, $\mathcal{L}$, represents the -wave damping mechanisms; we consider both non-linear Landau damping (in the hot, intercloud medium) as derived by \citet{Kulsrud2005}: (where wehave substituted $\omega_{\rm Alfven} = k\vA$ with $k \sim
\frac{1}{r_{\rm g}} \sim \frac{c}{3}\frac{1}{\omega_{\rm c,i}}$ ), and ion-neutral friction \citep[`case a' from][]{dePontieuEtAl2001}: where $v_i$ is the ion thermal speed (which we set to $\sqrt{8 k_B
T/(\pi m_P)}$ throughout this work), $\delta B$ is the amplitude of the -wave perturbation to the large-scale magnetic field $B$ ), and $\rho_n$ is the mass density of neutral atoms. |
This equation applies for ion-neutral friction between protons and hydrogen atoms: lower eross-sections are necessary for the collision of carbon ions with hydrogen atoms. for instance. in much cooler clouds. | This equation applies for ion-neutral friction between protons and hydrogen atoms; lower cross-sections are necessary for the collision of carbon ions with hydrogen atoms, for instance, in much cooler clouds. |
Cosmic-ray protons themselves are subject to energy loses due to pion production. ionization. and Coulomb collisions ?):: these losses are required in Equation 4.. and are represented there with the term Q. | Cosmic-ray protons themselves are subject to energy loses due to pion production, ionization, and Coulomb collisions \citep[e.g.,][]{SkillingStrong1976}; these losses are required in Equation \ref{crPressureEq}, and are represented there with the term $Q$. |
To model these effects as a function of cosmic-ray-proton energy. we utilize a modified version of the the energy loss function given in 2. as his Equation (5.3.58): In this equation. 7 1s the kinetic energy per proton. H[...| is the Heaviside step function. x is the ionization fraction. and αΌΟΞ½ΞΏ. | To model these effects as a function of cosmic-ray-proton energy, we utilize a modified version of the the energy loss function given in \citet{Schlickeiser2002} as his Equation (5.3.58): In this equation, $T$ is the kinetic energy per proton, $H[...]$ is the Heaviside step function, $x$ is the ionization fraction, and $\beta \equiv v/c$. |
In this expression. the first term describes pion production. the second gives Coulomb losses (normally negligible). and the third term characterizes losses due to ionization. | In this expression, the first term describes pion production, the second gives Coulomb losses (normally negligible), and the third term characterizes losses due to ionization. |
The exact form of this equation in ?. made some assumptions valid in the high-energy regime. but which could be problematic at lower energies. so Equation 17. 1s our modified version of the result from ?.. | The exact form of this equation in \citet{Schlickeiser2002} made some assumptions valid in the high-energy regime, but which could be problematic at lower energies, so Equation \ref{protonLossEqn} is our modified version of the result from \citet{Schlickeiser2002}. |
In particular. the derivation of the pion-production loss term in 2. assumed 57Β» 1. and is undefined below =1.3. but we are interested in the regime 5~2. | In particular, the derivation of the pion-production loss term in \citet{Schlickeiser2002} assumed $\gamma \gg 1$ , and is undefined below $\gamma = 1.3$, but we are interested in the regime $\gamma \sim
2$. |
Equation 17. also more explicitly includes the dependencies on ayy. ayy and ny, from earlier expressions in 2.. | Equation \ref{protonLossEqn} also more explicitly includes the dependencies on $n_{HI}$, $n_{HII}$ and $n_{H_2}$ from earlier expressions in \citet{Schlickeiser2002}. |
Because we are especially interested in the cosmic-ray spectrum nearGeV..where the majority of cosmic-ray momentum is. we will start by considering only the energy-loss rate near GeV.. but will examine the impact of the variation in energy-loss rate in Section ??.. | Because we are especially interested in the cosmic-ray spectrum near,where the majority of cosmic-ray momentum is, we will start by considering only the energy-loss rate near , but will examine the impact of the variation in energy-loss rate in Section \ref{SensitivityToInitialConditions}. . |
This energy loss rate gives the expression for Q in the equation for the cosmic-ray pressure (Eq. 4)). | This energy loss rate gives the expression for $Q$ in the equation for the cosmic-ray pressure (Eq. \ref{crPressureEq}) ). |
To investigate cosmic rays penetrating diffuse clouds using Equations 4+ and 14. (with definitions from Eqs. 3.. 6.. 7.. 15.. 16.. | To investigate cosmic rays penetrating diffuse clouds using Equations \ref{crPressureEq} and \ref{dPwEquation} (with definitions from Eqs. \ref{wavePressureEq}, \ref{BPressureEq}, \ref{kappaCRDefinition}, \ref{landauDampingEq}, \ref{ionNeutralDampingEq}, |
and 17)). we set up a simple interface between a highly-10nized plasma and a cool. neutral cloud. | and \ref{protonLossEqn}) ), we set up a simple interface between a highly-ionized plasma and a cool, neutral cloud. |
Our first use of this setup will be to check that the code reproduces an analytical result: if there is no cosmic-ray diffusivity (the cosmic rays are perfectly locked to waves). the cosmic-ray pressure and speed change together to conserve the adiabatic constant Pv5" (2).. | Our first use of this setup will be to check that the code reproduces an analytical result: if there is no cosmic-ray diffusivity (the cosmic rays are perfectly locked to waves), the cosmic-ray pressure and speed change together to conserve the adiabatic constant $P_{\rm cr} v_{\rm A}^{\gamma_{\rm cr}}$ \citep{BreitschwerdtEtAl1991}. |
To test this. we define the density contrast between the ionized and neutral phases with a simple profile (the same profile we will use for all of our calculations in this paper): ββββ£βββββββΎββ£βͺβββ΄βββΎβ
ββ―β£ββ΄βββββββ
ββ§βΎβΆβ³β³β£βββ³β£βββ£ββ½βββΆββ€β°β£ββ£βββ
β
βββββ£βββββ΄ββΆβββ£ββ½βββΆβ©βββ€β£ββ£βββΆβββ£ββ£βββ£ββ―βΏββββ£β³βΏβββββ£βββ―βͺββββΎ βΎββββ΄β―βͺββ£ββ£ββ£ββ
ββ§β£βΎβββ£β»β―ββΆβ£β―β£β΄βββ―ββ³βββ―βΏβ£β»β£β―ββ£βΆβ―β―β£β΄βββ―ββ³βββββ£β½βββ£β―βββΎβββ£βββ£βββββββ΄β£βͺββββββΎββ£βΎβ£β΄β£βͺβββΆββΊβ£β―ββΎβ
β
ββ§β―ββΊββ§ββββ£βͺββ―βββββββ₯β£ββββΎββ£βͺββ―ββ΄β―βͺβ | To test this, we define the density contrast between the ionized and neutral phases with a simple profile (the same profile we will use for all of our calculations in this paper): with the center of the $\tanh$ function at $z_{\rm
cloud~edge}=0.5$ pc, a width of$\Delta z_{\rm edge}=0.05$ pc; the initial and final densities are set to (for this initial test) $\rho_{\rm init} = 1$ $m_{\rm p}$ $^{-3}$ and $\rho_{\rm final} =
10$ $m_{\rm p}$ $^{-3}$ . |
βββ―ββββ£βͺββββββ₯ββββͺβΎβ£ββββββ£ββΎβββββ£ββ£βββββΎββ
β³ββΆββ
ββββββ―βΎββΆββΊβ£βͺββΎββββ£ββββ³β£ββββͺββ±β°ββ΄β―βͺβ β£β£β±ββ β£βΆβ | We also set the ionization fraction to $1$ throughout, and have removed all loss terms for thecosmic rays. |
null | It is not possible to simply set $\kappa_{\rm cr} \equiv 0$, so we integrate only Equation \ref{crPressureEqSimplified} for $dP_{\rm
cr}/dz$ . |
βββ£β½βββββ£βββ£ββ₯βββΎβ£β΄ββββ―βββ£βͺββββ£ββ£βͺββββ―βͺββΎβͺβ―ββ£ββββ£βͺβΆββΎββββ―βββ
β
ββ§β―βΏβ£ββΎββΆββΎβ£βͺββΎββΎβ£β΄βββ³β£ββββͺββββ΄β―βͺβββββββ£βͺββββ
ββ§β―βΏββββββββ£ββ£βͺββββ―βͺββ£ββΎβ | Wethen initialize thecosmic-ray pressure to $10^{-12}$ $^{-3}$ , and integrate the equations for cosmic-ray and wave pressure into |
High-frequency qasi-periodic oscillations (HFQPO) have been observed in quite a number of X-ray binaries containing a compact object. Le. neutron stars or black holes. | High-frequency qasi-periodic oscillations (HFQPO) have been observed in quite a number of X-ray binaries containing a compact object, i.e. neutron stars or black holes. |
HFQPOs are considered to originate in the accretion disk around the compact object. | HFQPOs are considered to originate in the accretion disk around the compact object. |
A special group is obviously set up by the galactic microquasars GRO J1655-40. XTE J1550-564 and GRS 19154105. | A special group is obviously set up by the galactic microquasars GRO J1655-40, XTE J1550-564 and GRS 1915+105. |
They are special because they do not show just one frequency but twin frequencies at a fixed ratio of 3:2 (Abramowiez Kluznniak. 2001. Remillard et al.. | They are special because they do not show just one frequency but twin frequencies at a fixed ratio of 3:2 (Abramowicz KluΕΊnniak, 2001, Remillard et al., |
2002). which are 450. 300 Hz (Strohmayer 2001a. Remillard et al.. | 2002), which are 450, 300 Hz (Strohmayer 2001a, Remillard et al., |
1999), 276. 184 Hz (Remillard et al.. | 1999), 276, 184 Hz (Remillard et al., |
2002) and 168. 113 Hz (Remillard et al.. | 2002) and 168, 113 Hz (Remillard et al., |
2003. McClintock Remillard. 2004). respectively. | 2003, McClintock Remillard, 2004), respectively. |
Out of those three objects XTE J1550-564 might have an additional power spectral density peak at 92 Hz. the significance. of which is modest. however (Remillard et Ξ±αΌ±. | Out of those three objects XTE J1550-564 might have an additional power spectral density peak at 92 Hz, the significance of which is modest, however (Remillard et al., |
2002). | 2002). |
Around the time the discoveries were made. it was suggested independently that some resonance effect in the accretion disk could give rise to such a 3:2. frequency behaviour (Kluznniak Abramowiez. 2001a. b). | Around the time the discoveries were made, it was suggested independently that some resonance effect in the accretion disk could give rise to such a 3:2 frequency behaviour (KluΕΊnniak Abramowicz, 2001a, b). |
There are three fundamental oscillation modes for a test particle orbiting Γ black hole. which produce the orbital or azimuthal (Kepler) frequency. the radial (in the orbital plane) epicyclic frequency and the vertical or polar (perpendicular to the orbital plane) epicyclic frequency. | There are three fundamental oscillation modes for a test particle orbiting a black hole, which produce the orbital or azimuthal (Kepler) frequency, the radial (in the orbital plane) epicyclic frequency and the vertical or polar (perpendicular to the orbital plane) epicyclic frequency. |
Initially it has been suggested that the 3:2 frequency ratio is due to a coupling of orbital and radial frequency (Abramowiez Kluznniak. 2001. Schnittman Bertschinger. 2004). | Initially it has been suggested that the 3:2 frequency ratio is due to a coupling of orbital and radial frequency (Abramowicz KluΕΊnniak, 2001, Schnittman Bertschinger, 2004). |
However. the proponents of the resonance theory then concentrated on a parametric 3:2 resonance between the polar and the radial epicyelic modes (Kluznniak Abramowiez 2002. Abramowiez et al. | However, the proponents of the resonance theory then concentrated on a parametric 3:2 resonance between the polar and the radial epicyclic modes (KluΕΊnniak Abramowicz 2002, Abramowicz et al. |
2002. 2003. Abramowiez Kluznniak 2003. Kluznniak Abramowiez 2003. Rebusco. 2004). and Remillard et al. ( | 2002, 2003, Abramowicz KluΕΊnniak 2003, KluΕΊnniak Abramowicz 2003, Rebusco, 2004), and Remillard et al. ( |
2002) found solutions for a 3:2 frequency ratio for each of the three possible couplings. re. orbital/radial. orbital/polar and radial/polar. | 2002) found solutions for a 3:2 frequency ratio for each of the three possible couplings, i.e. orbital/radial, orbital/polar and radial/polar. |
The method of associating a frequency to one specific oscillation mode has in principle the benefit that from frequency measurements the mass M. the angular momentum Β« (the Kerr parameter) of the black hole and the radial position of the orbiting test particle in the accretion disk can be determined. | The method of associating a frequency to one specific oscillation mode has in principle the benefit that from frequency measurements the mass ${M}$, the angular momentum ${a}$ (the Kerr parameter) of the black hole and the radial position of the orbiting test particle in the accretion disk can be determined. |
But with the measurement of even several frequencies the relevant equations remain underdetermined and more information is needed. | But with the measurement of even several frequencies the relevant equations remain underdetermined and more information is needed. |
So. in general the mass. which has been determined from the dynamies of the binary orbit for each of the three microquasars. has been made use of and a value of a could be determined. which. however. is different for each of the three coupling possibilities. | So, in general the mass, which has been determined from the dynamics of the binary orbit for each of the three microquasars, has been made use of and a value of ${a}$ could be determined, which, however, is different for each of the three coupling possibilities. |
Furthermore. as Remillard et al. ( | Furthermore, as Remillard et al. ( |
2002) have pointed out on their findings on XTE 564 that the frequency ratio might not be just 3:2 but that 3:1 is another possibility. one ends up with a choice for o of one out of six. still adopting 1 from dynamical measurements. | 2002) have pointed out on their findings on XTE J1550-564 that the frequency ratio might not be just 3:2 but that 3:1 is another possibility, one ends up with a choice for ${a}$ of one out of six, still adopting ${M}$ from dynamical measurements. |
There may be a possibility to resolve this ambiguity by introducing another constraint in the resonance model. | There may be a possibility to resolve this ambiguity by introducing another constraint in the resonance model. |
I| have investigated whether both a 3:2 and a 3:1 parametric resonance between the vertical and radial epicyclie frequencies would exist. of course at two different orbits. but that these two orbits are commensurable orbits. | I have investigated whether both a 3:2 and a 3:1 parametric resonance between the vertical and radial epicyclic frequencies would exist, of course at two different orbits, but that these two orbits are commensurable orbits. |
The commensurability is meant in the traditional sense that the Kepler frequencies of the two orbits come in ratios of natural numbers. | The commensurability is meant in the traditional sense that the Kepler frequencies of the two orbits come in ratios of natural numbers. |
Actually. there exists such a configuration and there is only one solution. so that the Kepler frequency of the inner orbit is three times the Kepler frequency of the outer orbit. | Actually, there exists such a configuration and there is only one solution, so that the Kepler frequency of the inner orbit is three times the Kepler frequency of the outer orbit. |
Furthermore. this solution allows only one value for the angular momentum. which ts a=0.99616. | Furthermore, this solution allows only one value for the angular momentum, which is ${a~=~0.99616}$. |
The mass of the black hole AZ is uniquely determined after a choice for one of the two possible orbits has been made. | The mass of the black hole ${M}$ is uniquely determined after a choice for one of the two possible orbits has been made. |
It is likely that the discriminator between the orbits is the mass accretion rate. | It is likely that the discriminator between the orbits is the mass accretion rate. |
In any case the two possible values for A/ differ by a factor of 1.5 only. | In any case the two possible values for ${M}$ differ by a factor of 1.5 only. |
The masses of the three black holes in GRO J1655-40. XTE J1550-564 and GRS 19154105. predicted by this model on the basis of their measured HFQPOs. agree in each case with the dynamically determined masses within their measurement uncertainty range. | The masses of the three black holes in GRO J1655-40, XTE J1550-564 and GRS 1915+105, predicted by this model on the basis of their measured HFQPOs, agree in each case with the dynamically determined masses within their measurement uncertainty range. |
[| have applied this model also to the Galactic Center black hole. AA*. making use of the one quasi-period recently published by Genzel et al. ( | I have applied this model also to the Galactic Center black hole, A*, making use of the one quasi-period recently published by Genzel et al. ( |
2003) and the quasi-periods published by Aschenbach et al. ( | 2003) and the quasi-periods published by Aschenbach et al. ( |
2004). | 2004). |
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