Under the influence of a spiral gravitational field, there should be differences among the mean motions of different types of objects with different dispersion velocities in a sipral galaxy. The old stars with high dispersion velocity should have essentially no mean motion normal to the galactic rotation. On the other hand, young objects and interstellar gas may be moving relative to the old stars at a velocity of a few kilometer per second in both the radial (galacto-centric), and circular directions, depending on the spiral model adopted. Such a velocity is usually referred as the systematic motion or the streaming motion. The conventionally adopted local standard of rest is indeed co-moving with the young objects of the solar vicinity. Therefore, it has a net systematic motion with respect to the circular motion of an equilibrium galactic model, defined by the old stars

Yuan, C.

English

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Produced by the NASA Center for Aerospace Information (CASI) 
https://ntrs.nasa.gov/search.jsp?R=19830016172 2020-03-21T04:19:13+00:00Z
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	 CSCL 032
V83-24443
C. YUAN
Department of Physics
The City College of the City University of New York
I. Introduction
Under the influence of a spiral gravitational field, there should
be differences among the mean motions of different types of objects
with different dispersion velocities in a spiral galaxy. The old
stars with high dispersion velocity should have essentially no mean
motion normal to the galactic rotation. On the other hand, young
objects and interstellar gas may be moving relative to the old stars
at a velocity of a few kilometer per second in both the radial
(galacto-centric), and circular directions, depending on the spiral
model adopted. Such a velocity is usually referred as the systematic
motion or the streaming motion. In this paper, we shall show that the
conventionally adopted local standard of rest is indeed co-moving with
the young objects of the solar vicinity (also see Lin and Yuan 1974).
Therefore, it has a net systematic motion with respect to the circular
motion of an equilibrium galactic model, defined by the old stars.
Using the spiral p attern consistently adopted by Lin, Yuan and Shu
(1969), the radial component of this motion is found to be about 7
km/sec toward the anticenter direction and the tangential component is
about 5 km/sec in the direction of rotation. The outward motion of
the adopted local standard of rest can be shown in excellent agreement
with the observations. In particular, it resolves the long-standing
problem of the differences between the northern and southern rotation
curves as indicated in HI observations (Kerr 1964). The tangential
component, however, is not well supported by the observations. It may
suggest that the local arm, the Orion spur, is associated with a mass
density which is comparable with a typical spiral arm, and therefore
disturbs the systematic motion near the sun.
The observations are summarized in section 2. The results on the
systematic motion based on the density-wave theory are presented in
section 3. We compare and discuss the results and observations in the
concluding section.
.+k•
 -A.
Table 1:
U
km/sec
Standard -10.4
Peculiar - 9.0
BO - 9.6
0-B5 - 9.8
dKO -10.8
dK5 - 9.5
dMO - 6.1
dM5 - 9.8
H 2CO -10.1
CO:Dark Cloud -11.1
High latitude HI	 -11.9
Molecular Clouds	 - 6.0
1 Delhaye (1965)
2. Frogel and Stothers(1977)
ORIGINAL Peltier IS
OF POOR QUAWY
II. Observations.
The local standard of rest is determined by measuring the solar
motion with respect to the local stars and interstellar gas. Since no
differentiation was expected between the old stars and the young
objects in their mean motions at the time the determinations were
.' made. The adopted local standard of rest rtlies heavily on the data
of young stars, because of their superior observational quality. In
fact, BO stars are given a weight of 6 compared to 0.3 for dM5 stars
(Delhaye 1965). Thus the adopted local standard of rest practically
coincides with the mean motion of the BO stars in solar vicinity
(See Table 1).
Table 1 summarizes the solar motions determined wih respect to
different types of objects in the solar vicinity. The notation
(U,V,W) denotes the three velocity components in the anti-center,
rotational and vertical directions respectively. The table is by no
means complete. However, it gives a fair representation of the
existing observations.
Solar Motion
V W Re f
km/sec km/sec km/sec
14.8 7.s 1
12.0 7.0 1
14.5 6.7 1
17.0 7.5 2
14.9 7.4 1
22.4 5.8 1
14.6 6.9 1
19.3 8.6 1
18.2 10.2 2
19.9 11 6 2
15.7 7.7 3
- - 4
3. Mast and Goldstein (1970)
4. Blitz (1982)
It is clear from table 1 that the U component of the solar motion
changes very little among different types of objects, from very young
to moderately old, or to be more precise, from those with low velocity
dispersion to those with high velocity dispersion. The V component
does display some significant change. But, the situation is
complicated by the effect of the asymmetric drift. Extrapolating the
data of the stars of higher velocity dispersion, Delhaye (1965)
arrived at a conclusion that the true value V after the correction of
the asymmetric drift lies between 10 km/sec to 13 km/sec. He adopted
the value 12 km/sec, which is reflected in the peculiar solar motion
listed in Table 1. If this value is indeed correct, the young objects
such as the BO stars, HI gas, etc are moving at a velocity lower than
the mean motion of the old stars in the rotational direction (2.5
km/sec for BO, 3.7 for HI gas, etc.).
ORIGINAL i• Ig4 r:
OF PWF,, C° ;/%,o_IYI(
Another important piece of observations to be included in
ourdiscussion is the well known result of the difference between the
northern and southern rotation curves determined from the HI data
(Kerr 1964). This result should be given higher weight than those of
the solar motion, in the sense that it deals with the local motion
relative to the Galaxy as a whole, while the solar motion observations
are confined only to the immediate neighborhood of the Sun. If the
adopted local standard of rest has an outward motion um, the
difference between the northern and southern observatins can be
expressed as
vlslnorth - 1v ls1south - 2u,Tcos 1
where vls is the line-of-sight velocity of HI with respect to the
adopted local standard of rest at the tangent points and 1 stands for
+1 for the northern data or -1 for the southern data. Comparing the
HI observational data with this formula, Kerr (1964) suggested a
general expansion of 7 km/sec near the sun. It might be noted that
the tangential component of the net motion of the adopted local
standard of rest has no contribution at all here.
III. Systematic Motion in the Solar Vicinity.
In response to the spiral gravitational field, the stars and the
gas would deviate from the pure circular motion of an equilibrium
model. The amount of deviation will depend on the spiral pattern, the
strength of the spiral gravitational field, the velocity dispersion
and finally the location relative to the spiral arms. Using the
spiral model that we have consistently adopted since 1969, we
calculate the systematic motions of the stars and the gas along the
20
NON-LINEAR Gas
cC.'>7
 - 10 k-,AK	 i
10	 20
50
40
^B0
S
-10
6.0	 9.0	 00.0	 110	 120
20
J 1
({,. ^i . IO tm/S.0
10	
NO
N-LINEAR GAS
Ve	 20
07
.1
 —
.10
e0	 90	 Inn	 un
Figure 1 Radial Systematic Motions 	 Figure 2. Tangeniial Systematic
of the Stars and Gas	 Motions of the stars and the -as
ORIG?e'r°:L
	
--p f
OF POOR QUALITY
line connecting the galactic center and the sun from 8 kpc to 12 kpc.
The results of the calculations are plotted in Figures 1 and 2. The
response in scars is calculated by the linear density-wave while the
response in the gas, by the non-linear theory. One of the underlying
assumptions of these calculations is that the stars and the gas are in
a quasi-stationary state. This is certainly true for the moderately
old stars, or stars with higher dispersion velocities as well as the
gas. But, it is not true for the very young stars whose have just
been formed out of gas clouds, and their initial conditions at birth
probably still play a dominant role in their present motions. Figures
1 and 2, therefore are applicable to the gas in general and to the
stars of dispersion velocity at least higher than 20 km/sec.
For stars with low dispersion velocities, their mean motion should
be determined by the method of star migration calculations (Yuan and
Grosbol 1982). Unfortunately, due to our choice of the spiral model,
the very young stars, say 0-B5, whose ages are within 60 x 10 6 years
(Stothers 1980) would not have enough time to migrate to the solar
vicinity after their birth in the Sagittarius Arm and the Perseus
Arm. The sun is situated between these two major arms in our model
(See Figure 3). Those young stars near the sun are likely formed by
mechanisms other the shock-driven star formation proposed by Roberts
(1969) or simply delayed in formation after the galactic shock by some
reasons. Being so young, they probably still move with the same
velocity of the nearby gas clouds out of which they were formed.
Therefore, the present purpose, oe shall use the results of the
non-linear gas motion for the young stars as a rule. In order to get
some feeling about the star migration calculations, the mean velocity
for B5 stars, with age ranges 55-70 x 10 6 (Stothers 1980) is vw = 10
km/sec and vp - 0 km/sec, although the number density for those
stars formed in the Sagittarius Arm and the Perseus Arm and having
migrated to the solar vicinity is too small to be considered seriously.
The theoretical results are summarized in Table 2 in which (u,,, ,ue )
is the systematic motion for the gas and (v m ,ve ), for the stars.
Table 2	 Systematic Motions at the position of
the Sun (in km/sec).
Non-linear gas ^,, um = 6.5 u0 = 5.0
Stars with (c n	 =20 km/sec v m = 9.5 V,:,= 0
Stars with	 of 	 " vIT = 5.0 vE - 0
Stars with	 it 	 " v = 3.0 v, = 0
Star Migration for B5 stars vm = 10.0 v©= 0
IV. Discussion
We first examine the radial motion of the stars and the
gas in the solar vicinity. Let us recall that the adopted local
standard of rest is practically comoving with the BO stars, and
^p
^ 1
OF POUR QUALITY
tnere seems no significant difference among various types of object in
their radial velocity components. Furthermore, as suggested by the
difference of the northern and southern rotation curves, the adopted
local standard of rest seems to have a net motion of 7 km/sec in the
anti-center direction. The theoretical results for the radial
systematic motion listed in Table 2 are in perfect agreement with
these obvservations. The young objects, such as BO stars as well as
the HI gas are indeed expected to have a systematic motion towards the
anti-center direction with a magnitude equal to about 7 km/sec. For
the moderately old stars whose dispersion velocites are around '10
km/sec, the outgoing motion is only slightly reduced to 5 km/sec.
Only when the velocity dispersion reaches 40 km/sc or more, does the
motion of the star drop below 3 km/sec. The observational data for
the disk sta.,s with velocity dispersion greater than 40 km/sec are
scarce. With u = 6.5 km/sec the northern and the southern rotation
curves based on the 1965 Schmidt model are shown in Figure 4.
180,
G.G
tGO[
	 NORTHERN SKY
t50
SOUTHERN SKY
?40
?30t-
210
S	 G b kee
Figure 3. The adopted spiral
pattern and the gas streamlines
in the neighborhood the sun.
The darklines are the potential
minima and the thick lines are the
location of the shocks.
Figure 4. The northern and the
southern rotation curves based
on the 1965 Schmidt model and
an outgoing motion of 6.5
km/sec for the local standard
of rest.
The situation for the tangential component, however, is far from
ideal. First, there is the asymmetric drift. After its effect
carefully removed, the young objects would still move slightly faster
than the old stars in the rotational direction. The trend is
difficult to reverse even though we would like to press harder for
more correction. The result therefore is at variance with the
observation, in which the young stars and the gas lag behind the old
stars by about 3 km/sec.
A possible explanation of this discrepancy may lie on the fact
of the presence of the local arm. In our view, the local arm is not a
ORIO,f':9 ", ;- -. 	 r.,
OF POOR QUALITY
major arm of the basic two-arm pattern, but an inter-ann spur (Lin,
Yuan and Shu 1969). The spur is comoving with the local material and
it may be associated with a certain mass concentration. Using the
linear analysis of the gas response, we may be able to bi. , e a
order-of-magnitude estimate of the mass density required for the
systematic motiin of the gas to reverse its direction	 The fo nnula is
given as follows:
=	 Ql/cra:u-Tn
	
u/,rn: 
9
Aun = (-k tit) ( 1 -flp/0) rc 2/2Rz
where Q1/0, 0 is the ratio of the perturbed - irface density to the mean
density of the gas,(u.,„ u 6 ) are the amplitudes of the velocity
components, k is the radial wave number, S2 is the local angular
speed, t2^? the pattern speed, % is the epicyclic frequency, and
is the galacto-centric distance. Since the interarm spur is a
material arm,Qp = Q . Thus, no radial velocity component is caused by
its presence, which is an excellent feature of this approach. If we
take the wavelength for the Orion spur to be 2.5 kpc, or k = 2.13
kpc-1 and u3 =8 km/sec we obtain a ratio Q1/Q o equal to 0.8. This
is somewhat greater than the mass density of a spiral arm. A
concentration like this in a spiral galaxy is not uncommon. We can
also check this by pla-ing a point mass 300 pc away in the ant'.-.enter
direction of the sun. The mass required for u 0, = -8 km/sec is of the
order of 10710.
In conclusion, we believe that the conventionally adopted local
standard of rest is comoving with the young objects which has a net
outward motion of about 7 km/sec and a net motion of 5 km/sec in the
direction of the galactic rotation. Ibis outward motion of the young
object is due to the presence of the spiral density wave_:. The fact
that the tangential motion is not observed implies that the local arm
may have a mass densit y like those in the regular spiral arm.
Acknowledgement. I wish to thank Professor C.C. Lin for the
early collaboration on this research and for many valuable suggestions
afterwards. The work is supported in part by NASA grant NGC-2348 and
PSC-CUNY Research Award Program.
References
Blitz, L.: 1982, private communication
Delhaye, J. : 1965, in Galactic Structure, Stars and Stellar Systems
Vol V, ed. Blaauw, A. and Schmidt, M., Univ. of Chicago Press,
Chicago, pp. 61-84.
Frogel, J.A. and Stothers, R.: 1977, A.J., 82, 890.
Kerr, F.J.: 1964, I A.U. - U.R.S.I. Symp. 20, 81
Lin, C.C. and Yuan, C.: 1975, B.A.A.S., 7, 344
Lin, C.C., Yuan, C. and Roberts, W.W.: 1978, A. A., 69, 181.
Lin, C.C., Yuan, C. and Shu, F.H.: 1969, Ap.J., 155, 721.
Roberts, W.W.: 1969, Ap.J., 158, 123
Stothers, R.: 1980, private communication
Yuan, C. and Grosbol, P.: 1981, Ap.J. , 243, 432.


On the local standard of rest

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