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Jets in Micro-Quasar SS 433: Analysis involving Acceleration | OMICS International
ISSN: 2329-6542
Journal of Astrophysics & Aerospace Technology
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Jets in Micro-Quasar SS 433: Analysis involving Acceleration

Sanjay M Wagh and Sanjay B Sarwe*

Central India Research Institute, 34, Farmland, Ramdaspeth, Nagpur 440010, India

*Corresponding Author:
Dr. Sanjay B Sarwe
S F S College, Seminary Hill, Nagpur 440006, India
Tel: +91 712 246163
E-mail: [email protected]

Received Date: February 27, 2014; Accepted Date: May 03, 2014; Published Date: June 06, 2014

Citation: Wagh SM, Sarwe SB (2014) Jets in Micro-Quasar SS 433: Analysis involving Acceleration. J Astrophys Aerospace Technol 2:104. doi: 10.4172/2329-6542.1000104

Copyright: © 2014 Wagh SM, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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Abstract

We analyze multi-wavelength observations of the jets of the micro-quasar SS 433 reported by Marshall, vis-à-vis the acceleration dependence of the Doppler Effect as reported by Wagh. Specifically, we are only interpreting the spectral shifts as arising due to the acceleration-dependent Doppler Effect and find the speed of blue-shifted jet to be ~ 0.022c and that of red-shifted jet to be ~ 0.29c. Our results have consequences for the energetics of the prime mover and jets in SS 433.

Keywords

Doppler shift; Velocity and acceleration; Jets in SS 433

Introduction

Micro-quasar SS 433 shows [1-3] emission lines of jets from compact object. Hα Doppler shifts led Margon and Anderson [4] to the kinematic model of SS 433 as a pair of oppositely directed, processing, jets with speed VJ ∼ 0.26. It has, since then, been used in analyzing data on SS 433, although its parameters as well as the model got updated to include nutation with a period of about half the orbital period and small variations in the jet velocity [5]. The distance to SS 433 is argued [5] to be either 5.5 ± 0.2 kpc or somewhat smaller [6] as 4.61 ± 0.35 kpc.

Margon and Anderson [4] determined jet orientation as processing with a 162.5 day period in a cone with half angle of 19.85o about an axis that is at 78.83o to the line of sight to SS 433. The jet lines are Doppler shifted with this period with the extreme red-shift being ~ 0.15 and the extreme blue-shift being ~ - 0.08 as per this analysis.

Marshall et al. [7] report multi-wavelength study of jets of SS 433 using Chandra High Energy Transmission Grating Spectrometer with contemporaneous optical and VLBI observations. It is usual [4] to assume that Doppler shifts arise because of the source velocity, only. Then, assuming furthermore two perfectly oppositely directed jets at an angle θ to the line of sight, the line Doppler shifts of SS 433 are used to estimate [1,4,7,8] the relativistic γ factor and the angular factor μ=COS θ, which are then used to determine the jet velocity and the angle to the line of sight.

To the best of our knowledge, no study is known to have focused on the role of acceleration for the jets in SS 433. It is therefore our aim here to explore it.

In what follows, we then analyze Doppler-shifted lines of SS 433 from Marshall et al. [7] and Marshall et al. [8] vis-à-vis the accelerationdependence of the Doppler Effect [9]. We are only interpreting line shifts using the acceleration-dependence of the Doppler Effect; and are not modeling the jets in SS 433.

Acceleration and Doppler Shift

Recently, Wagh [9] showed that the Doppler shift of a source must include contribution from its acceleration, apart from that due to its velocity, and discussed [10,11] some of its direct implications.

Wagh [12] has also discussed how measurements of velocity and acceleration of the source can be effected from the Doppler shifts of its spectral lines. Cases of constant and temporally (sinusoidal) variable acceleration have, then, been analyzed in Wagh [12].

Jets from a prime mover impinge on external clouds that emit spectral lines. Then, the jet material emitted by the prime mover at a later instant should push material emitted by it at an earlier instant, against the obstruction by cloud. This leads to approximately sinusoidal temporal variability of acceleration, in the manner of a railway engine pushing a train of carriages. Then, jets should show time variable acceleration, in general.

In either case, pushing accelerates and friction decelerates. Sinusoidal variability of acceleration should then be first approximation for the above two situations.

Now, if we were to analyze the situation of jets assuming constant acceleration, we can expect to have overestimated acceleration. It will turn out that this is indeed the case in the analysis of jets in the system of SS433.

When the source S is moving (towards observer O in Figure 1 with velocity v making an angle θ with the line SO and with acceleration a, we can write:

astrophysics-aerospace-technology-Doppler-Effect

Figure 1: Doppler Effect: source moving.

astrophysics-aerospace-technology

Where (SP) is the distance covered by the source in time T’, c is the speed of light (in vacuum), T is the period of the wave emitted by the source, and T’ is the measured period, all in the frame of observer.

We evaluate (SP) as follows. Let the temporal rate of acceleration be given by

astrophysics-aerospace-technology

Then, on integration and assuming that the frequency ω is appropriately small, we obtain

astrophysics-aerospace-technology

Where k1, k2, k3 are integration constants.

Substituting this in eq. (1), we then obtain after suitable manipulations:

astrophysics-aerospace-technology

Where νo=1/T’ is the observed frequency, νe=1/T is the emitted frequency, f(β,θ) is as defined below with k2=β c, and we have retained only first order terms in acceleration. We set k1=0 and k3=0. (We recover the case of constant acceleration when k1≠ 0 and a0=0.)

The function

astrophysics-aerospace-technology

has the following characteristics. See Figure 2

astrophysics-aerospace-technology-function

Figure 2: β as a function of θ for values of f(β,θ).

For angular ranges ~ [0,110°] and ~ [240°,360°], we have astrophysics-aerospace-technology and within the angular range ~ [110°,240°], we have 2 ≥ f(β,θ) > 1. (That f>1 does not necessarily mean relativistic velocity. These ranges also overlap: for [90°,110°] and [250°,270°], f>1 and f<1 both.) When f(β,θ)≠1, there exists a non-zero lower bound, βmin, for velocity β. For, βmin=0, as β =0 for all values of angle θ. (Note that for f<1, βmin =1-f and for f>1, βmin = f-1). Importantly, for f(β,θ) ≈1, velocity can be nonrelativistic over quite large angular range, we may also note here.

Let source emit two spectral lines of rest frequencies astrophysics-aerospace-technology and astrophysics-aerospace-technology with corresponding observed frequencies being astrophysics-aerospace-technology and astrophysics-aerospace-technology respectively.

Now, let astrophysics-aerospace-technology,

astrophysics-aerospace-technology

astrophysics-aerospace-technology

Then, from eq. (4), we have

astrophysics-aerospace-technology

where we have set astrophysics-aerospace-technology.

Equation (6) is, evidently, linear in astrophysics-aerospace-technology and astrophysics-aerospace-technology

From the observational data astrophysics-aerospace-technologyor, equivalently, astrophysics-aerospace-technologywhere λ are the corresponding wavelengths, we can then obtain astrophysics-aerospace-technology and astrophysics-aerospace-technologyby linear regression. The acceleration, astrophysics-aerospace-technology of the emitter can then be estimated from the observational data.

Velocity astrophysics-aerospace-technology, corresponding to above astrophysics-aerospace-technology, gives us the minimum speed at which matter emitting frequency astrophysics-aerospace-technology could be moving with.For the mean jet speed, astrophysics-aerospace-technologywe may select average astrophysics-aerospace-technology of astrophysics-aerospace-technology or maximum of astrophysics-aerospace-technology.But, angle to the line of sight will be zero for any astrophysics-aerospace-technology as the velocity of the line emitting material.

Therefore, the selected value astrophysics-aerospace-technology , or max (βmin), is added to each astrophysics-aerospace-technology to obtain line-speeds astrophysics-aerospace-technology Then, angle θ can be obtained from the f-value of each line using:

astrophysics-aerospace-technology

The jet speed is then the average of these line speeds astrophysics-aerospace-technology We therefore obtain observational values of kinematical parameters of the material of the jet.

We then note that, for astrophysics-aerospace-technology the Left Hand Side of eq. (6) directly yields astrophysics-aerospace-technology,as astrophysics-aerospace-technology. The value of acceleration k1, which is constant, is then to be obtained from eq. (4) with k1≠0 replacing astrophysics-aerospace-technology in its last term. This value is unreasonable for the jet in SS 433 as it implies that jet material halts instantaneously. See later.

Nevertheless, we note the following. The order of the term astrophysics-aerospace-technology is unity and so is that of astrophysics-aerospace-technology. Then, as the order of astrophysics-aerospace-technology is 108c, the order of astrophysics-aerospace-technology is 10-8c-1. Thus, the acceleration astrophysics-aerospace-technology is of order 10-8ω2, which yields reasonable value. (The last term of eq. (4) will then be negligible). The time-scale of change in velocity is, now, of the order of

astrophysics-aerospace-technology

Temporally (sinusoidal) variable acceleration thence allows, in general, reasonable value(s) for the magnitude of acceleration in the jet system.

The aforementioned summarizes the role of acceleration in Doppler shift(s) of spectral lines from a source. As will be seen in the next section, the function f(β,θ) clearly identifies (by way of f being greater than 1 for such lines) certain blue-shifted lines of SS 433 as being emitted by the material beyond angle of 90° to the line of sight.

The role of acceleration-dependence of Doppler Effect is therefore an important one for the analysis not only of astronomical jet situations but in general, also.

In what follows, we adopt the above strategy to analyze data on Doppler-shifted spectral lines of jets in SS 433 from Marshall et al. [7] and Marshall et al. [8].

Jets in SS433

Consider therefore Table 4 of Marshall et al. [7] reporting various blue-shifted spectral lines from the micro-quasar SS 433 with their observed and rest wavelengths. (The rest wavelengths have been computed for blends by applying weights equal to the fractional flux contribution to the blend, according to the multi-temperature plasma model). We use these data in the following analysis performed as per the details outlined in Section 2.

Identity astrophysics-aerospace-technology astrophysics-aerospace-technology astrophysics-aerospace-technology astrophysics-aerospace-technology astrophysics-aerospace-technology astrophysics-aerospace-technology astrophysics-aerospace-technology
FeXXV-1s2p-1s2 1.855 2.147±0.001 0.05983618 0.823078 0.353844 250 -0.17393410
FeXXVI-Lyα 1.780 2.057±0.005 0.05116418 0.829972 0.346950 250 -0.15218493
NiXXVII-1s2p-1s2 1.592 1.836±0.003 0.03968798 0.837108 0.339814 251 -0.12111256
FeXXIV 7.986 9.214±0.006 0.03436392 0.841166 0.335755 251 -0.10650083
SiXIII-1s2p-1s2 6.675 7.747±0.018 -0.02797551 0.888690 0.288232 256 0.11138681
SiXIV-Lyα 6.182 7.133±0.004 -0.07025553 0.917810 0.259112 259 0.36507672

Table 4: Parameters of red-shifted lines of the jet of SS433 for βJ ˜0.32. Average angle is 253°.

Firstly, of significance is the value of acceleration that we get, namely, astrophysics-aerospace-technology , when assuming constant acceleration and analyzing data in Table 4 of Marshall et al. [7] as per the corresponding discussion in Wagh [12]. If the material of the jet were free-streaming with velocity astrophysics-aerospace-technology and encountering this deceleration, then it would be brought to rest almost instantaneously in time astrophysics-aerospace-technology! This is a certain indication that the material of the jet is also being pushed through the obstructing matter as it propagates through. That is to say, the material of the jet emitting blue-shifted lines cannot be freestreaming, and the mechanism of its acceleration is operating within the emission regions of these lines.

For these above reasons, we question the assumption of the constancy of acceleration, also. This issue was discussed in Section 2. We therefore also obtain justification for the procedure outlined in Section 2, then.

Results of our analysis (following Section 2, now) of the data on SS 433 in Table 4 of Marshall et al. [7] are given in Table 1 for jet speed astrophysics-aerospace-technology and in Table 2 for jet speed astrophysics-aerospace-technology.Notice that every spectral line with astrophysics-aerospace-technology has astrophysics-aerospace-technology

Identity astrophysics-aerospace-technology astrophysics-aerospace-technology astrophysics-aerospace-technology astrophysics-aerospace-technology astrophysics-aerospace-technology astrophysics-aerospace-technology astrophysics-aerospace-technology
Ni-XXVIII 1.532 1.526 ± 0.005 0.08903135 0.935532 0.075639 33 -0.10583205
Ni-XXVII 1.592 1.590 ± 0.002 0.08267751 0.939096 0.072075 34 -0.09912994
Fe-XXVI 1.780 1.786 ± 0.001 0.05108051 0.960209 0.050963 40 -0.06630088
Fe-XXV 1.855 1.860 ± 0.001 0.03133152 0.975514 0.035657 47 -0.04627725
Fe-XXIII 8.815 8.851 ± 0.010 0.02612262 0.988381 0.022791 60 -0.05211100
Ni-XIX 12.435 12.426 ± 0.010 0.01795082 0.989686 0.021485 62 -0.03805716
Si-XIIIr 6.648 6.652 ± 0.002 0.00838549 0.991826 0.019346 66 -0.02022888
Ar-XVII (S-XVI) 3.962 3.970 ± 0.004 0.00938674 0.992918 0.018253 68 -0.02469117
Ar-XVIII 3.733 3.740 ± 0.003 0.00871313 0.993540 0.017632 69 -0.02428936
Ni-XXVI 9.075 9.080 ± 0.004 0.00971661 0.993659 0.017513 69 -0.02741428
Ne-X 12.134 12.146 ± 0.006 0.01102429 0.994347 0.016825 71 -0.03355997
Ca-XX 3.020 3.025 ± 0.005 0.00643031 0.994555 0.016616 71 -0.02008114
S-XVI 4.729 4.735 ± 0.001 0.00438256 0.995105 0.016067 73 -0.01473865
Ca-XIX 3.187 3.191 ± 0.004 0.00445602 0.996212 0.014959 76 -0.01810022
Fe-VIII 15.014 15.021 ± 0.029 0.00639499 0.996579 0.014592 77 -0.02810862
Si-XIV 6.182 6.186 ± 0.001 0.00296826 0.996812 0.014359 78 -0.01379550
Si-XIV 5.217 5.224 ± 0.006 0.00661529 0.997036 0.014135 78 -0.03260272
Ni-XXIII 9.529 9.538 ± 0.006 0.00431469 0.997556 0.013615 80 -0.02495843
Ni-XXVI 9.745  9.737 ± 0.007   -0.00096485 0.998554 0.012618 84 0.00890177
Si-XIIIf 6.740 6.735 ± 0.004 -0.00369856 0.998642 0.012530 84 0.03618465
O-VIII 16.006 16.022 ± 0.013 0.00091487 0.999368 0.011804 87 -0.01919415
Fe-XXIII(XXII) 11.753 11.778 ± 0.008 0.00016857 1.000772 0.011944 94 0.00238848
Ni-XXVI(XXV) 9.372 9.371 ± 0.005 -0.00353610 1.000885 0.012057 95 -0.04453187
Ni-XXVI 9.970 9.973 ± 0.003 -0.00636519 1.002949 0.014121 102 -0.02952588
Fe-XXIII(XXIV) 7.457 7.459 ± 0.006 -0.00617159 1.003787 0.014959 105 -0.02372392
Ni-XIX 14.060 14.109 ± 0.024 -0.00577074 1.004039 0.015210 106 -0.02117257
Fe-XXIV 10.634 10.633 ± 0.005 -0.00955665 1.004169 0.015341 106 -0.03427216
S-XV 5.055 5.050 ± 0.002 -0.01080625 1.006229 0.017400 111 -0.02956479
Fe-XXIV 7.989 7.984 ± 0.004 -0.01365020 1.006965 0.018136 113 -0.03484912
Fe-XXIV(XXIII) 11.026 11.025 ± 0.007 -0.02092979 1.010153 0.021324 119 -0.04321873
Fe-XXIV 11.432 11.465 ± 0.017 -0.01904846 1.011509 0.022681 121 -0.03693196
Mg-XII 8.421 8.425 ± 0.002 -0.01857007 1.011780 0.022952 121 -0.03560158
Fe-XXIV 11.176 11.182 ± 0.004 -0.02442425 1.012483 0.023654 122 -0.04555587
Al-XIII 7.173 7.172 ± 0.004 -0.01942630 1.013844 0.025016 124 -0.03456750
Fe-XXIV 8.316 8.309 ± 0.004 -0.02675849 1.015154 0.026325 126 -0.04579591
Mg-XII (Ni-XXVI) 7.101 7.083 ± 0.003 -0.03774527 1.022585 0.033756 133 -0.05565784

Table 1: Parameters of blue-shifted lines of the jet of SS 433 for βJ ̴ 0.022. Average angle is 86°.

Identity astrophysics-aerospace-technology astrophysics-aerospace-technology astrophysics-aerospace-technology astrophysics-aerospace-technology astrophysics-aerospace-technology astrophysics-aerospace-technology astrophysics-aerospace-technology
FeXXV-1s2p-1s2       1.855 2.147±0.001 0.05983618     0.823078    0.320618    245    -0.14255121
FeXXVI-Lyα       1.780 2.057±0.005 0.05116418     0.829972    0.313723    246    -0.12427799
NiXXVII-1s2p-1s2       1.592 1.836±0.003 0.03968798     0.837108    0.306588    246    -0.09850676
FeXXIV       7.986 9.214±0.006 0.03436392     0.841166    0.302529    247    -0.08641189
SiXIII-1s2p-1s2       6.675 7.747±0.018  -0.02797551     0.888690    0.255005    251      0.08681686
SiXIV-Lyα       6.182 7.133±0.004  -0.07025553     0.917810    0.225886    255      0.27182612

Table 2: Parameters of red-shifted lines of the jet of SS433 for βJ ̴ 0.29. Average angle is 248°.

Figure 3 then compares angular plots of line-velocities β for astrophysics-aerospace-technology and astrophysics-aerospace-technology.Data points are fitted with cubic spline curves.

astrophysics-aerospace-technology-Angular-plots

Figure 3: Angular plots for line velocities.

We then find the blue-shifted jet of SS 433 to be angularly limited within astrophysics-aerospace-technology (with average angle of inclination to the line of sight being 86°) for astrophysics-aerospace-technology , and within astrophysics-aerospace-technology (with average angle of inclination to the line of sight being 90°) for astrophysics-aerospace-technology

Evidently, the jet is narrower for higher jet velocity. Furthermore, apart from the distribution expected on the basis of Figure 2, there exist variations in line-velocities at various angular ranges. These variations get enhanced at the higher jet speed, we note.

Variations within angular ranges are also seen in the lineacceleration parameter, astrophysics-aerospace-technology, as shown in Figures 4 and 5. Data are fitted with cubic spline curves. (We are not using acceleration, astrophysics-aerospace-technology as we have not fixed ω, the frequency of temporal variations of acceleration).

astrophysics-aerospace-technology-angle-Table

Figure 4: Variation of a0 ⁄w3 with angle from Table 1.

astrophysics-aerospace-technology-Angular-variation

Figure 5:Angular variation of a0 ⁄w3 from Table 2.

Variation of line-velocity β with parameter astrophysics-aerospace-technology is then depicted in Figure 6 for astrophysics-aerospace-technology and in Figure 7 for astrophysics-aerospace-technology Data are also fitted with cubic spline curves to indicate these variations.

astrophysics-aerospace-technology-Velocity-versus

Figure 6: Velocity versus a0 ⁄w3 from Table 1.

astrophysics-aerospace-technology-Velocity-versus

Figure 7: Velocity versus a0 ⁄w3 from Table 3.

Of interest to modeling of jets and considerations of their prime mover is angular distribution of elements emitting observed spectral lines. We therefore provide the angular distribution of elements in Figure 8 for astrophysics-aerospace-technology and in Figure 9 for astrophysics-aerospace-technology.

astrophysics-aerospace-technology-Angular-plot

Figure 8: Angular plot for elements from Table 1.

astrophysics-aerospace-technology-Angular-plot

Figure 9: Angular plot for elements from Table 3.

Tables 2 and 4 then provide the results of analysis, following Section 2, for data on the red-shifted jet as in Marshall et al. [8].

Figure 10 then shows the angular variation of line velocities for astrophysics-aerospace-technology (Table 2) for astrophysics-aerospace-technology (Table 4). Notice here that the jet velocity is substantially larger for the red-shifted jet than that for the blue-shifted jet of SS 433. Figure 11 now shows the angular variation of the line-acceleration parameter astrophysics-aerospace-technology for astrophysics-aerospace-technology(Table 2) and for astrophysics-aerospace-technology (Table 4).

astrophysics-aerospace-technology-Angular-variation

Figure 10: Angular variation of line-velocity for red-shifted jet.

astrophysics-aerospace-technology-Angular-variation

Figure 11: Angular variation of line-acceleration for red-shifted jet.

Discussion

Acceleration dependence of Doppler Effect has an important consequence: the spectral shift is not dependent on only the velocity of the source. Acceleration also contributes to the spectral shift, as in eq. (4), in a significant manner.

In our analysis of the micro-quasar SS 433, we then find that acceleration plays one important role. Lines of the blue-shifted jet with f>1 then correspond to angles larger than 90° to the line of sight. (For the red-shifted jet, f>1 would imply angles greater than 270°, we note. However, we do not find such lines in the data on SS 433 for the redshifted jet. However, see later, also.) This kind of identification of angle is not possible without the acceleration dependence of the Doppler shift.

From our analysis, presented in Table 1 and Table 3, we find that the speed of the blue-shifted jet is non-relativistic, that is, astrophysics-aerospace-technology or astrophysics-aerospace-technology.But, the red-shifted jet is mildly relativistic astrophysics-aerospace-technology or astrophysics-aerospace-technology.

Identity astrophysics-aerospace-technology astrophysics-aerospace-technology astrophysics-aerospace-technology astrophysics-aerospace-technology astrophysics-aerospace-technology astrophysics-aerospace-technology astrophysics-aerospace-technology
Ni-XXVIII 1.532 1.526±0.005 0.08903135 0.935532 0.128936 63 -0.19850916
Ni-XXVII 1.592 1.590±0.002 0.08267751 0.939096 0.125371 64 -0.19008134
Fe-XXVI 1.780 1.786±0.001 0.05108051 0.960209 0.104259 70 -0.15230057
Fe-XXV 1.855 1.860±0.001 0.03133152 0.975514 0.088954 77 -0.13435166
Fe-XXIII 8.815 8.851±0.010 0.02612262 0.988381 0.076087 83 -0.22681902
Ni-XIX 12.435 12.426±0.010 0.01795082 0.989686 0.074781 84 -0.17789672
Si-XIIIr 6.648 6.652±0.002 0.00838549 0.991826 0.072642 86 -0.10972645
Ar-XVII (S-XVI) 3.962 3.970±0.004 0.00938674 0.992918 0.071550 86 -0.14818177
Ar-XVIII 3.733 3.740±0.003 0.00871313 0.993540 0.070928 87 -0.15634897
Ni-XXVI 9.075 9.080±0.004 0.00971661 0.993659 0.070809 87 -0.17909405
Ne-X 12.134 12.146±0.006 0.01102429 0.994347 0.070121 87 -0.24159577
Ca-XX 3.020 3.025±0.005 0.00643031 0.994555 0.069913 88 -0.14958766
S-XVI 4.729 4.735±0.001 0.00438256 0.995105 0.069363 88 -0.12195564
Ca-XIX 3.187 3.191±0.004 0.00445602 0.996212 0.068256 89 -0.20838703
Fe-VIII 15.014 15.021±0.029 0.00639499 0.996579 0.067889 89 -0.38865587
Si-XIV 6.182 6.186±0.001 0.00296826 0.996812 0.067656 89 -0.22321473
Si-XIV 5.217 5.224±0.006 0.00661529 0.997036 0.067432 89 -0.64584070
Ni-XXIII 9.529 9.538±0.006 0.00431469 0.997556 0.066912 90 -1.40762246
Ni-XXVI 9.745 9.737±0.007 -0.00096485 0.998554 0.065914 91 -0.08763031
Si-XIIIf 6.740 6.735±0.004 -0.00369856 0.998642 0.065826 91 -0.30135897
O-VIII 16.006 16.022±0.013 0.00091487 0.999368 0.065100 91 0.04008418
Fe-XXIII(XXII) 11.753 11.778±0.008 0.00016857 1.000772 0.065240 93 0.00379753
Ni-XXVI(XXV) 9.372 9.371±0.005 -0.00353610 1.000885 0.065353 93 -0.07661996
Ni-XXVI 9.970 9.973±0.003 -0.00636519 1.002949 0.067417 94 -0.08239460
Fe-XXIII(XXIV) 7.457 7.459±0.006 -0.00617159 1.003787 0.068255 95 -0.06908094
Ni-XIX 14.060 14.109±0.024 -0.00577074 1.004039 0.068506 95 -0.06211102
Fe-XXIV 10.634 10.633±0.005 -0.00955665 1.004169 0.068637 95 -0.10085846
S-XV 5.055 5.050±0.002 -0.01080625 1.006229 0.070697 97 -0.08791105
Fe-XXIV 7.989 7.984±0.004 -0.01365020 1.006965 0.071432 98 -0.10295231
Fe-XXIV(XXIII) 11.026 11.025±0.007 -0.02092979 1.010153 0.074621 100 -0.12149952
Fe-XXIV 11.432 11.465±0.017 -0.01904846 1.011509 0.075977 101 -0.10125270
Mg-XII 8.421 8.425±0.002 -0.01857007 1.011780 0.076248 101 -0.09711047
Fe-XXIV 11.176 11.182±0.004 -0.02442425 1.012483 0.076950 102 -0.12263362
Al-XIII 7.173 7.172±0.004 -0.01942630 1.013844 0.078312 102 -0.09071594
Fe-XXIV 8.316 8.309±0.004 -0.02675849 1.015154 0.079621 103 -0.11733112
Mg-XII (Ni-XXVI) 7.101 7.083±0.003 -0.03774527 1.022585 0.087052 107 -0.12620914

Table 3: Parameters of blue-shifted lines of the jet of SS433 for βJ ˜ 0.076. Average angle is 90°.

As discussed in Section 2, values astrophysics-aerospace-technology and astrophysics-aerospace-technology have been obtained by adding average astrophysics-aerospace-technology of the line-values of astrophysics-aerospace-technology; while the values of astrophysics-aerospace-technology and astrophysics-aerospace-technology have been obtained by adding maximum of the line-values of astrophysics-aerospace-technology. We, of course, suggest the addition of the average astrophysics-aerospace-technology of the line-values of astrophysics-aerospace-technology to each of them. Maximum of astrophysics-aerospace-technology corresponds, from the analogy of a train; to maximum effect of the push material receives. We have therefore used it only to compare the jet characteristics at astrophysics-aerospace-technologywith those at any higher value for astrophysics-aerospace-technology

We therefore measure astrophysics-aerospace-technology for the blue-shifted jet and astrophysics-aerospace-technology for the red-shifted jet as our observed values. We also find variations in line velocities in both these jets of SS 433.

We have not provided errors of various quantities here, as we find that errors do not change the main conclusions of our analysis in any significant manner. That the speed of the blue-shifted jet is substantially non-relativistic, that the speed of the blue-shifted jet is different than that of the red-shifted jet, that there are interesting variations of linevelocity, etc. hold.

The bulk flow speed of the material 0.26c of the blue-shifted jet is, in particular, substantially smaller than obtained [7] from the standard analysis with no acceleration dependence of the Doppler shift. Nevertheless, the bulk flow speed, astrophysics-aerospace-technologythe red-shifted jet is close to this value, we then note.

We therefore find blue-shifted and red-shifted jets to be possessing different speeds in the system of SS 433. Then, any model assuming the same speed for the two oppositely directed jets appears to be in difficulty here.

But, we could be viewing an early (meaning “closer” to the prime mover) part of the receding jet (for which the speed is higher) and the later (meaning “away from” the prime mover) part of the approaching jet (for which the speed is lower as a result of its passage through matter), perhaps. This could then be a possible reason for difference in speeds of the (blue-shifted) approaching and (red-shifted) receding jets.

Angular dependence of the line-acceleration parameter astrophysics-aerospace-technology of Figure 4 and the dependence of line-velocity βL on the line-acceleration parameter of Figure 6 are of definite significance, now.

In this context, we note that variations of astrophysics-aerospace-technology correspond directly with those of astrophysics-aerospace-technology , the line-acceleration. We can, consequently, interpret these variations as providing us the angular distribution of the clouds causing deceleration of the jet material.

We emphasize then that the multi-epoch monitoring of these variations will provide us valuable information on the jet advance and the parameters of these jet-obstructing clouds. Furthermore, such monitoring will also provide us information about temporal character of the activity of the prime mover of these jets, we emphasize.

Now, just the line Doppler shifts do not provide us any information on the radial distance of the jet material from its prime mover. Nevertheless, the angular distribution of elements in Figure 8 is of definite significance for it shows us the shell encountered by the jet.

Lastly, Marshall et al. [7] have also observed aperiodic variability of Doppler shifts (of blue-shifted jet) over timescale much shorter than any of the known periodicities in the system, like that of precession, orbit, and nutation. We then only note here that aperiodic variability could come from the material of jet experiencing aperiodic changes of deceleration. Any aperiodic variability of acceleration could then be related to the mechanisms of the jet acceleration and deceleration, both.

In summary, we find that analysis of data on Doppler-shifted lines of SS 433, specifically X-ray emission lines seen using Chandra HETGS, implies non-relativistic speed of the material of the jet causing their emission. Our results have consequences for the energetics of the prime mover as well as for the model of the jets in SS 433.

Detailed model of the jets in SS 433 consistent with the aforementioned results of observational nature is a subject of our separate considerations.

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