Special Relativity is one of the most abstract courses in the standard curriculum for physics majors, and therefore practical applications or laboratory exercises are particularly valuable for providing real-world experiences with this subject. This course poses a challenge for lab development because relativistic effects manifest themselves only at speeds close to the speed of light. The laboratory described in this paper constitutes a low-cost, low-barrier exercise suitable for students whose only background is the standard mechanics-plus-electromagnetism sequence. The activity uses research-quality astronomical data on SS433—a fascinating Galactic X-ray binary consisting of a compact object (a neutron star or a black hole) and a normal star. A pair of moderately relativistic jets moving with v 0.3 c in opposite directions emanate from the vicinity of the compact object and are clearly detected in optical and radio observations. Following step-by-step instructions, students develop a full kinematic model of a complex real-world source, use the model to fit the observational data, obtain best-fit parameters, and understand the limitations of the model. The observations are in exquisite agreement with the Doppler effect equations of Special Relativity. The complete lab manual, the dataset and the solutions are available in online supplemental materials; this paper presents the scientific and pedagogical background for the exercise.

1.
N. L.
Zakamska
, “
Theory of special relativity
,” preprint arXiv:1511.02121 (
2015
).
2.
J.
Dryzek
,
D.
Singleton
,
T.
Suzuki
, and
R.
Yu
, “
An undergraduate experiment to test relativistic kinematics using in flight positron annihilation
,”
Am. J. Phys.
74
,
49
53
(
2006
).
3.
G.
Pegna
, “
An extraordinary tabletop speed of light apparatus
,”
Am. J. Phys.
85
,
712
720
(
2017
).
4.
F. D.
Seward
,
C. G.
Page
,
M. J. L.
Turner
, and
K. A.
Pounds
, “
X-ray sources in the aquila-serpens-scutum region
,”
Mon. Not. R. Astron. Soc.
175
,
39P
46P
(
1976
).
5.
C. B.
Stephenson
and
N.
Sanduleak
, “
New H-alpha emission stars in the milky way
,”
Astrophys. J. Suppl. Ser.
33
,
459
469
(
1977
).
6.
D.
Crampton
,
A. P.
Cowley
, and
J. B.
Hutchings
, “
The probable binary nature of SS 433
,”
Astrophys. J. Lett.
235
,
L131
L135
(
1980
).
7.
M. C.
Begelman
,
A. R.
King
, and
J. E.
Pringle
, “
The nature of SS433 and the ultraluminous X-ray sources
,”
Mon. Not. R. Astron. Soc.
370
,
399
404
(
2006
).
8.
S.
Fabrika
, “
The jets and supercritical accretion disk in SS433
,”
Astrophys. Space Phys. Rev.
12
,
1
152
(
2004
); availalbe at http://esoads.eso.org/abs/2004ASPRv..12....1F.
9.
S.
D'Odorico
,
T.
Oosterloo
,
T.
Zwitter
, and
M.
Calvani
, “
Evidence that the compact object in SS433 is a neutron star and not a black hole
,”
Nature
353
,
329
331
(
1991
).
10.
V.
Goranskij
, “
Photometric mass estimate for the compact component of SS 433: And yet it is a neutron star
,”
Peremennye Zvezdy (Variable Stars)
31
(
5
) (
2011
); available at http://esoads.eso.org/abs/2011PZ.....31....5G.
11.
T. C.
Hillwig
,
D. R.
Gies
,
W.
Huang
,
M. V.
McSwain
,
M. A.
Stark
,
A.
van der Meer
, and
L.
Kaper
, “
Identification of the mass donor star's spectrum in SS 433
,”
Astrophys. J.
615
,
422
431
(
2004
).
12.
D. R.
Gies
,
M. V.
McSwain
,
R. L.
Riddle
,
Z.
Wang
,
P. J.
Wiita
, and
D. W.
Wingert
, “
The spectral components of SS 433
,”
Astrophys. J.
566
,
1069
1083
(
2002
).
13.
D. R.
Gies
,
W.
Huang
, and
M. V.
McSwain
, “
The spectrum of the mass donor star in SS 433
,”
Astrophys. J. Lett.
578
,
L67
L70
(
2002
).
14.
G. O.
Abell
and
B.
Margon
, “
A kinematic model for SS433
,”
Nature
279
,
701
703
(
1979
).
15.
M. G.
Watson
,
G. C.
Stewart
,
A. R.
King
, and
W.
Brinkmann
, “
Doppler-shifted X-ray line emission from SS433
,”
Mon. Not. R. Astron. Soc.
222
,
261
271
(
1986
).
16.
R. C.
Lamb
,
J. C.
Ling
,
W. A.
Mahoney
,
G. R.
Riegler
,
W. A.
Wheaton
, and
A. S.
Jacobson
, “
Gamma-ray line emission from SS433
,”
Nature
305
,
37
39
(
1983
).
17.
B. J.
Geldzahler
and
H. A.
Geller
, “
Search for gamma-ray emission lines from SS433: 2: 1980–1989
,”
Astrophys. J.
420
(2),
655
660
(
1994
).
18.
S.
Migliari
,
R.
Fender
, and
M.
Méndez
, “
Iron emission lines from extended x-ray jets in SS 433: Reheating of atomic nuclei
,”
Science
297
,
1673
1676
(
2002
).
19.
M.
Díaz Trigo
,
J. C. A.
Miller-Jones
,
S.
Migliari
,
J. W.
Broderick
, and
T.
Tzioumis
, “
Baryons in the relativistic jets of the stellar-mass black-hole candidate 4U1630-47
,”
Nature
504
,
260
262
(
2013
).
20.
A cartoon of the binary system SS433 defining some of the key terminology is available at http://www.aoc.nrao.edu/∼mrupen/XRT/SS433/ss433.shtml.
21.
S. S.
Eikenberry
,
P. B.
Cameron
,
B. W.
Fierce
,
D. M.
Kull
,
D. H.
Dror
,
J. R.
Houck
, and
B.
Margon
, “
Twenty years of timing SS 433
,”
Astrophys. J.
561
,
1027
1033
(
2001
).
22.
B.
Margon
and
S. F.
Anderson
, “
Ten years of SS 433 kinematics
,”
Astrophys. J.
347
,
448
454
(
1989
).
23.
B.
Margon
,
H. C.
Ford
,
J. I.
Katz
,
K. B.
Kwitter
,
R. K.
Ulrich
,
R. P. S.
Stone
, and
A.
Klemola
, “
The bizarre spectrum of SS 433
,”
Astrophys. J. Lett.
230
,
L41
L45
(
1979
).
24.
Observations of the precessing radio jet in SS433 assembled into a movie are available at http://www.aoc.nrao.edu/∼mrupen/XRT/SS433/ss433jimovie.gif.
25.
K. M.
Blundell
and
M. G.
Bowler
, “
Symmetry in the changing jets of SS 433 and its true distance from us
,”
Astrophys. J. Lett.
616
,
L159
L162
(
2004
).
26.
B.
Margon
, “
The bizarre spectrum of SS 433
,”
Sci. Am.
243
,
54
65
(
1980
).
27.
J. I.
Katz
,
S. F.
Anderson
,
S. A.
Grandi
, and
B.
Margon
, “
Nodding motions of accretion rings and disks—A short-term period in SS 433
,”
Astrophys. J.
260
,
780
793
(
1982
).
28.
B.
Margon
, “
Observations of SS 433
,”
Annu. Rev. Astron. Astrophys.
22
,
507
536
(
1984
).
29.
P. R.
Maloney
,
M. C.
Begelman
, and
J. E.
Pringle
, “
Radiation-driven warping: The origin of WARPS and precession in accretion disks
,”
Astrophys. J.
472
,
582
587
(
1996
).
30.
See supplementary material at https://doi.org/10.1119/1.5022796 for the lab instructions, the redshift data files and the lab solutions.
31.
H. L.
Marshall
,
C. R.
Canizares
,
T.
Hillwig
,
A.
Mioduszewski
,
M.
Rupen
,
N. S.
Schulz
,
M.
Nowak
, and
S.
Heinz
, “
Multiwavelength observations of the SS 433 jets
,”
Astrophys. J.
775
,
75
89
(
2013
).
32.
H. L.
Marshall
,
C. R.
Canizares
, and
N. S.
Schulz
, “
The high-resolution x-ray spectrum of SS 433 using the Chandra HETGS
,”
Astrophys. J.
564
,
941
952
(
2002
).
33.
Derivation of the apparent superluminal motion observed in some relativistic jets is available at https://en.wikipedia.org/wiki/Superluminal_motion.
34.
S. H.
Russell
,
M. P.
Hancock
, and
J.
McCullough
, “
Benefits of undergraduate research experiences
,”
Science
316
,
548
549
(
2007
).

Supplementary Material

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