Non-circular Motions in the Outer Perseus Spiral Arm
Nobuyuki Sakai Mark J. Reid Karl M. Menten Andreas Brunthaler Thomas M. Dame
 
 


 



 
 
Nobuyuki Sakai 
nobuyuki.sakai@nao.ac.jp
nsakai@kasi.re.kr
 
0000-0002-0786-7307]Nobuyuki Sakai 
National Astronomical Observatory of Japan, 2-21-1 Osawa,
Mitaka, Tokyo 181-8588, Japan                                          
 Korea Astronomy & Space Science Institute, 776, Daedeokdae-ro, 
Yuseong-gu, Daejeon 34055, Korea                                          

 
Center for Astrophysics | Harvard & Smithsonian, 
60 Garden Street, Cambridge, MA 02138, USA                  
 

 
 
Max-Planck-Institut für Radioastronomie Auf dem
Hügel 69, D-53121 Bonn, Germany                                    

 
 

Max-Planck-Institut für Radioastronomie Auf dem
Hügel 69, D-53121 Bonn, Germany                                    

 
 


Center for Astrophysics | Harvard & Smithsonian, 
60 Garden Street, Cambridge, MA 02138, USA                  

 

 
 
We report measurements of parallax and proper motion for five 6.7-GHz 
methanol maser sources in the outer regions of the Perseus arm as part of the BeSSeL
Survey of the Galaxy. By combining our results with previous astrometric
results, we determine an average spiral arm pitch angle of 9.2±1.5 deg 
and an arm width of 0.39 kpc for this spiral arm.   
For sources in the interior side of the Perseus arm, 
we find on average a radial inward motion in the Galaxy of 13.3±5.4 km s^-1 
and counter to Galactic rotation of 6.2±3.2 km s^-1. 
These characteristics are consistent with models for spiral arm formation that involve 
gas entering an arm to be shocked and then forming stars.  However, similar data for
other spiral arms do not show similar characteristics. 
 
 
 



                                                         
 
 














 




§ INTRODUCTION
  

While spiral patterns can be prominent in disk galaxies, their
formation mechanism and the dynamical evolution of spiral arms remain
under discussion.  Two general mechanisms for spiral arm formation have
dominated the discussion in the literature: 
1) density-wave theories <cit.> and 
2) dynamic theories <cit.>.  
In density-wave theories, spiral structures are long-lived and rotate 
nearly uniformly, while stars and gas rotate differentially and pass through 
the arms.
In dynamic theories, arms are short-lived and reform as open structures.
They are seen in N-body simulations of multi-arm spirals (e.g.,
),
unbarred grand-design spirals (), and barred spirals (e.g.,
).                                  
 
Comparing the spatial distributions of stars and gas in a spiral arm
may help to distinguish between the two mechanisms 
(e.g., ).
Density-wave theories predict a 
spatial offset between the gravitational potential minimum of a spiral 
arm (traced by the distribution of old stars) and the peak of gas density 
(). On the other hand, dynamic (non-stationary) spiral-arm models
predict that both star and gas accumulate into a minimum in the
spiral potential and hence are not separated 
(e.g., ). 
In the future one could test these theories by comparing the 3-dimensional (3-d) positions of 
older stars measured by Gaia with that of masers from newly 
formed stars measured by Very Long Baseline Interferometry (VLBI).

If gas entering a spiral arm is shocked prior to the formation of stars, 
the resulting stars should display the kinematic signature of that shock.  
By measuring 3-d velocity fields, one could therefore determine if such 
shocks occur and how strong they are. Such as the 
Bar and Spiral Structure Legacy (BeSSeL) Survey and VLBI Exploration of Radio Astrometry
(VERA) have yielded precise distances and 3-d velocity fields for
high-mass star-forming regions (HMSFRs) associated with spiral arms 
(e.g., ). 
Optical astrometric results from Gaia DR2 typically have parallax uncertainties 
larger than 20 μas (e.g. see Fig. 7 in ) and are starting 
to become significant for this type of study.

Recently, <cit.>, <cit.> and <cit.> showed evidence for 
systematic (radially) inward motion for HMSFRs in the Perseus arm.         
Here, we report new astrometric results obtained with the National Radio Astronomy
Observatory (NRAO)[NRAO official HP: 
 <https://public.nrao.edu/>]
 Very Long Baseline Array (VLBA), which more clearly 
reveal the structure and kinematics of the Perseus arm. 
In section 2, we describe our VLBA observations.
In section 3, we outline the data reduction. In section 4,
we show new astrometric results for five 6.7-GHz CH_3OH masers. 
In section 5, we discuss the structure
and kinematics of the Perseus arm, based on our new results and Gaia
DR2 results for OB-type stars (taken from ) and compare
those with spiral arm models. In section 6, we summarize the paper.    
 
 


§ OBSERVATION
  
 
We observed a total of six methanol masers 
(ie, the CH_3OH (J_K = 5_1 - 6_0A^+) transition
at a rest frequency of 6.668519 GHz) under VLBA programs
BR149S, T and U (see Table <ref> in the appendix)[Please
also see the BeSSeL survey HP: 
 <http://bessel.vlbi-astrometry.org/observations>].  
Each set of observations was optimized to sample the peaks of the sinusoidal 
parallax signature in right ascension over one year, as described for previous
BeSSeL Survey observations (e.g., ). 
Each maser source, listed in Table <ref>, was observed with three or 
four background quasars (QSOs).  A single observation involved  
(i) four half-hour “geodetic blocks” spaced by about 2 hours for clock and atmospheric 
delay calibration, (ii) “manual phase-calibration” scans of a bright quasar (QSO) every 2 hours,
iii) fast switching between a target maser and each QSO, used for relative position determination.
 
Observational data was recorded on the Mark5A system at 512 Mbps. 
Geodetic block data was taken in left circular polarization with
four 16 MHz bands spanning 496 MHz centered at both 4.3 and 7.3 GHz
(8 IFs in total).   Fast switching data was taken
in dual circular polarization with four adjacent 16-MHz bands spanning
64 MHz. The data were correlated with the DiFX software correlator
<cit.> in Socorro, NM.                                           
The fast switching data were correlated in two passes:
for the maser (line) data the central
8 MHz of the third IF band was correlated with 1000 channels, giving
a frequency (velocity) spacing of 8 kHz (0.36 km s^-1) at the
rest frequency.  The continuum data for all IFs were correlated
with 32 spectral channels. 
 
 
 


§ DATA REDUCTION
  

The VLBA data reduction was conducted with the NRAO Astronomical Image
Processing System (AIPS) and a ParselTongue pipeline described in
previous BeSSeL Survey papers (e.g., ). Details of
the techniques employed to determine parallax and proper motion for
6.7-GHz CH_3OH masers are described in <cit.>. Here, we
briefly outline the data reduction.
 
The largest source of relative position error for 6.7 GHz astrometric data is 
uncertainty in the ionospheric delay calibration. For the
ionospheric delay calibration, we firstly applied the Global Ionospheric
Maps obtained from NASA's ftp server[<ftp://cddis.gsfc.nasa.gov/gps/products/ionex/>].
However, at our observing frequency of 6.7 GHz, tropospheric and ionospheric
delay residuals can still be significant, with residual path-delays of
∼5 cm for both components.   Using the geodetic-block observations,
tropospheric (non-dispersive) delays were estimated by differencing delays 
at 4.3 and 7.3 GHz and subtracting these from the total delays.  These
were modeled as owing to a zenith delay for each observations block.
To better calibrate the ionospheric delay residual, the delay differences
between 4.3 and 7.3 GHz bands were scaled to the 6.7 GHz CH_3OH band
and a residual zenith dispersive delay could also be determined. 
 
After applying the geodetic-block calibrations to the phase-reference
data, we used a bright maser spot as the phase reference for the 
associated QSOs.  In cases where the maser displayed significant
structure, we self-calibrated the maser data and applied these
solutions to both maser and QSO data.  All sources were imaged
and the positions of compact components were determined by fitting
elliptical Gaussian brightness distributions.   The variations the
positions of maser spots relative to background QSOs were then modeled
as owing to parallax and proper motion components.

Delay residuals at 6.7 GHz are generally dominated by the ionospheric 
miscalibration and can cause a systematic position shift across the sky 
(so called ionospheric wedges).  We used our multiple QSO data to
account for these effects.  As discussed in <cit.>, one can
generate an “artificial QSO” at the position of the target maser
to remove most of the effects of the ionospheric wedges.  In this
paper we incorporated an improved procedure that solved for the
wedge effects at each epoch, while at the same time estimating the
parallax and proper motion components as described in <cit.>.

 


§ RESULTS
  
 
  

We estimated trigonometric parallaxes and proper motions for five of the
six sources we observed. For G098.03+1.44 
the brightest maser spot was too faint (<0.5 Jy) to use as a phase reference.
In order to estimate a single proper motion for each source, we 
averaged the values for all spots.  We adopted these values for
the proper motion of the central star, but added ±5 km s^-1
in quadrature to the fitted error estimates for each motion coordinate in 
order to allow for uncertainty in this step.   Note that class II CH_3OH masers 
generally have internal motions of about 5 km s^-1 (e.g., ).
The parallax and proper motions results are summarized in Table <ref> (see also Fig. <ref>).

Some sources have published parallax and proper 
motions for 22-GHz water or 12.2-GHz methanol masers as discussed below.   
When combining parallaxes, we used variance weighting.   However, for
combined proper motion estimates of 6.7-GHz methanol and 22-GHz water masers motions, 
we adopted the methanol values, since water masers typically form in outflows 
of tens of km s^-1, and transferring the maser motions to that of the central star 
is less certain than from methanol masers.


We now briefly discuss some individual sources.
 
 


 §.§ G094.60-1.79

 
All background QSOs were northward of the maser, rather than
surrounding it.  When accounting for the effects of ionospheric wedges, this
requires extrapolation of the fitted planar position tilt instead of interpolation,
and we expect increased parallax uncertainty.  To allow for this, 
we added ±0.05 mas per degree of offset times the offset of the nearest QSO in
quadrature with the formal parallax uncertainty.
This parallax gradient error source is a rough estimate based on
BeSSeL Survey experience fitting for 6.7 GHz data for many sources.  

<cit.> used the VERA array and estimated a parallax of 
0.326±0.031 mas based on three 22-GHz water maser spots.  
In order to be conservative, we have inflated their uncertainty by
√(3) to ±0.054 mas in order to allow for correlated systematic errors caused 
by similar differential atmospheric delay differences between maser spots and 
a background QSO. Generally, residual atmospheric delay errors dominate cm-wave VLBI parallax uncertainty. Another result for this source comes from <cit.>, 
who obtained a 22-GHz parallax of 0.253±0.024 mas using the VLBA.
In order to assess if the three parallax results are statistically consistent 
we calculated parallax differences of 0.147±0.072, 0.074±0.054, and 0.073±0.059 mas.
Only the first difference is marginally statistically significant, while the other two 
are statistically insignificant.  We conclude that these could reasonably have come from random
differences and combine all three by variance-weighting to give a best parallax for 
G094.60-1.79 of 0.250±0.020 mas.
 


 §.§ G111.25-0.76
 

<cit.> derived a parallax of 0.299±0.022 mas for water masers and
the difference between this and our result is not statistically significant (0.035±0.030 mas). 
Thus we variance-weighted them to obtain a best parallax of 0.280±0.015 mas.




 §.§ G136.84+1.16
 

All background QSOs were northward of the maser, and, as discussed above for G094.60-1.70, 
we inflated the parallax uncertainty to account for a likely ±0.05 (mas/degree) parallax 
gradient.  However, since the maser's structure was fairly extended, the final parallax 
uncertainty is quite large (±0.123 mas).



 §.§ G188.94+0.88
 

<cit.> using VERA obtained a parallax of 0.569±0.068 mas for water masers, 
while <cit.> using the VLBA found a value of 0.476±0.006 mas based on 
12-GHz methanol masers.  The differences among the three parallax measurements
are not statistically significant (0.104±0.080, 0.011±0.042, and
0.093±0.068 mas), and we variance weighted them to obtain a best parallax of
0.476±0.006 mas. 
For a combined proper motion, we use our 6.7-GHz and the published
12-GHz methanol maser result, yielding (μ_αcosδ,
μ_δ) = (-0.30±0.60, -1.95±0.51) mas yr^-1,
where we have added in quadrature ±5 km s^-1 for each component uncertainty.

 
 
 




§ DISCUSSION
 
 



 §.§ Pitch angle and arm width of the Perseus arm
   
Using the five astrometric results discussed above, along with 
other sources in the literature, we now evaluate the pitch angle and width 
of the Perseus arm based on 27 sources.       
Following <cit.>, we fitted a logarithmic spiral-arm model to the 
locations of the Perseus arm sources using the following equation:                       
 

    ln(R/R_ref)=-(β-β_ref)tanψ,


where R_ ref and β_ ref are a Galactocentric
radius (kpc) at a reference azimuth (radians).  Azimuth (β) is defined as zero
toward the Sun as viewed from the Galactic center and increases with
Galactic longitude, and ψ is the spiral pitch angle.  β_ ref = 13.2 degrees
was chosen to be  near the midpoint of the azimuth values.
Our best fitting values are R_ ref =  9.93 ± 0.09 kpc and 
ψ = 9.2 ± 1.5 degrees.   These results are consistent with those in 
<cit.> within errors.  The arm's width, defined 
as the 1σ scatter in the sources perpendicular to the
fitted arm, is 0.39 kpc.      
 
 


 §.§ Non-circular motion in the Perseus arm
 

We now assess the three-dimensional non-circular (peculiar) motions of Perseus arm sources, 
based on the parallaxes, proper motions and LSR velocities. The LSR velocity of the central star is estimated 
from the masers and from observations of thermal line emission (e.g., CO) from the parent cloud. Peculiar motions are 
referenced to a model Galactic rotation curve, using Galactic parameters (R_0 and Θ_0), 
and solar motion (U_⊙, V_⊙, W_⊙). 
Note that U values are positive directed toward the Galactic center, V is in the 
direction of the Galactic rotation, and W is toward the north Galactic pole.                    
In the following, we use 24 of the 27 sources available, removing three outliers
(G043.16+0.01, owing to its large motion uncertainty of >20 km s^-1, and 
G108.20+0.58 and G229.57+0.15 owing to their large deviation of >2.2σ 
from the spiral arm fit).


 
 





Figure <ref> shows the non-circular motions of Perseus-arm
sources with uncertainties less than 20 km s^-1. 
The solid curve in Fig. <ref> represents a logarithmic 
spiral-arm fit and the dashed lines indicate (±1σ) width (see section <ref>). 
Figure <ref> plots the non-circular motions as a function of distance perpendicular 
to the arm, ρ_⊥, defined positive outward from the arm.
Interestingly, we see a significant velocity gradient of -25±8 km s^-1 kpc^-1 
in U vs. ρ_⊥.  Note that excluding the two high points with U>25 km s^-1 
and ρ_⊥<-0.2 kpc as potential outliers still yields a significant gradient of 
-16±7 km s^-1 kpc^-1.  The other peculiar motion components (V,W) do not show a 
statistically significant gradient across the spiral arm.
 
As an alternative approach to examining systematics in the peculiar motions,
Table <ref> presents unweighted means of (<U>, <V>, <W>) 
in three ρ_⊥ bins:  
the interior given by 
-3σ_Per/2≦ρ_⊥(kpc) < -σ_Per/2),
the middle given by 
(-σ_Per/2 ≦ρ_⊥ (kpc) < σ_Per/2),
and the exterior given by 
(σ_Per/2≦ρ_⊥(kpc) < 3σ_Per/2).
In the above, σ_Per is a Gaussian 1σ width for the arm, which
we estimate to be 0.39 kpc.  For uncertainties, we adopt the standard error of the mean, 
because the scatter evident in Figures <ref>(Left) is much larger than 
would be suggested by the measurement uncertainties, indicating there is significant 
“astrophysical” noise. 

As anticipated by the negative gradient of U vs ρ_⊥<0,
the results in Table <ref> show that sources 
toward the interior side of the arm are moving radially inward with 
<U> = 13.3±5.4 km s^-1 (2.5σ for 9 masers), while
sources exterior to the arm show a small average U motion of
=2.7±7.6 km s^-1 (for 5 masers). 
Regarding the <V> component of peculiar motion, the result in 
Table <ref> provides marginally significant evidence for a small
average motion counter to Galactic rotation of 
<V> =-6.2±3.2 km s^-1 (1.9σ for 10 maser)
in the middle region of the Perseus arm. 
We investigated the sensitivity of the above results to the value of the
value of the pitch angle used to define the trace of the Perseus arm.
Changing the pitch angle by ±2σ and recalculated the 
average peculiar motions on the interior, middle and exterior of the
arm yielded no significant changes.                                    

We now compare our observational results with basic predictions from
various models for spiral arm formation.




  §.§.§ Density wave model without shock
 
 
Linear density-wave theories which rely purely on gravity have difficulty 
explaining the radially inward motion at the interior side of the Perseus spiral arm as 
observed in the VLBI astrometric data.  This is because gas entering an overdense arm 
is accelerated gravitationally and should show radially outward motion at the interior
side of the arm as shown in Fig. 10 of <cit.>. 

 

 





  §.§.§ Density wave model with a shock
 
lcrrrrrr

Non-circular motion for Perseus, Local and Sagittarius arms.
0pt

Spiral    Type    2cInterior side     #    2cExterior    # 

Arm 	      2c-3σ/2≦ρ_⊥(kpc) < -σ/2      2cσ/2≦ρ_⊥(kpc) < 3σ/2   

       <U>    <V> 	       <U>    <V> 	

       (km s^-1)	    (km s^-1)       (km s^-1)	   (km s^-1) 

Perseus   Masers   13.3±5.4		   -2.5±2.8	   9   2.7±7.6	   3.4±2.8			   5

Local   Masers    2.3±2.8		   -5.1±1.0	   4   -4.4±4.1		   -6.1±2.1		   6	

   OB stars   2.7±0.9			   0.9±1.6		   119    5.3±3.9		   4.9±2.6	   50	

Sagittarius   Masers   3.1±4.6	   2.6±3.5	   3   11.1±6.8		   15.5±4.6	   3		

   OB stars    		   		   0   1.1±3.5		   7.2±1.3	   32	

Columns 1-2 indicates the spiral arm and type of observational data. Columns 3-4 show unweighted means of the non-circular
  motion components (U, V) for sources at -3σ/2≦ρ_⊥(kpc) < -σ/2, where σ is the
  arm width and ρ_⊥ is perpendicular distance for each spiral arm (taken from ). Note that positive
  ρ_⊥ value means exterior of each arm as viewed from the Galactic center. An error in each mean shows the standard error of the
  mean. A number with the bold font indicates a statistical significance greater than 2σ. Column 5 represents the number of the sources.
  Columns 6-8 are the same as the Columns 3-5, but for sources at σ/2≦ρ_⊥(kpc) < 3σ/2.


Our finding of a large positive <U> value, corresponding to radially inward 
motion, for the interior side of the Perseus arm is consistent with 
density wave theories which include a shock as gas in circular Galactic
orbits encounters slower rotating spiral arms <cit.>
triggering the formation of stars. 
The hydrodynamic shock model of <cit.> with a pitch angle, ψ, of 12^∘,
a pattern speed, Ω_ p, of 12.5 km s^-1 kpc^-1, a gaseous dispersion speed, a, of
8 km s^-1, and a spiral potential with an enhancement, F, of 7.5% compared to
the axisymmetric potential, predicts a velocity jump in front of the gravitational 
potential minimum as shown by Fig. 1 of <cit.>.

If we assume the full jump velocity is in the line-of-sight direction, the line-of-sight 
vector of <cit.> model can be decomposed into U (and V) jumps by subtracting the
rotation curve model of <cit.>. This assumption is reasonable for the Perseus arm at
the Galactic longitude range l = 110-140 (deg) since the non-circular motion vectors in Fig. <ref>
are aligned in the line-of-sight direction at the section. The U jumps with amplitudes of 20-30 km s^-1,
shown by cyan and green curves in Fig. <ref>, indicate large positive <U> values for the interior side of the Perseus arm and no significant <U> values for the
exterior of the arm, which are consistent with the observational results. 
We also investigated the shock model of <cit.> with ψ = 8^∘ and 
F = 5% (taken from his Figures 7 and 8) and found similar characteristics, but with 
shock velocities decreased to 10-20 km s^-1 and the shock locations shifted by < 150 pc. 



  §.§.§ Dynamic spiral arm formation
 
 
We now compare the observational results with a dynamic spiral-arm model
proposed by <cit.>. The dynamic spiral-arm model is a barred spiral galaxy
generated from N-body/hydrodynamics simulations, and amplitudes, pitch angles,
and pattern speeds of spiral arms change within a few hundred million years. <cit.>
picked spiral arms in growth and disruption phases, respectively, from the model. 
The growth phase has negative <U> value for the interior side of an arm and
thus is inconsistent with our observational results.  While the disruption phase has
positive <U> for the interior side of the arm, it has negative values for the exterior 
of the arm, and thus also does not agree with our observational results.
  


 §.§ Universality of non-circular arm motions


We confirm that the shock model of <cit.> can explain the 
observed radially inward motions in the interior side of the Perseus arm. 
In order to investigate the universality of these motions, we examine the 
non-circular motions for other spiral arms using the same procedure
applied to the Perseus arm and the VLBI astrometric results compiled
in <cit.>.  We also examine Gaia DR2 results for OB-type stars 
taken from Fig. 2(a) of <cit.>.
Table <ref> displays the non-circular motion components (<U>, <V>) for the 
interior and exterior of the spiral arms.   While there are some statistically significant
average motions, no clear trend is evident for these spiral arms, suggesting a more complex 
picture than expected from the basic models discussed above.





§ SUMMARY

We presented parallaxes and proper motions for five 6.7-GHz methanol masers associated with 
HMSFRs in the outer portion of the Perseus spiral arm as part of the BeSSeL Survey of the Galaxy 
(see Figure <ref> and Table <ref>). Combining these new and previous VLBI results, we determined a spiral-arm pitch angle 
of 9.2 ± 1.5 deg  and an arm width of 0.39 kpc (see Section <ref>). 

We divided the sources into interior, middle and exterior regions of the Perseus arm 
and averaged the non-circular motion components (<U>, <V>, <W>) for each region. For nine sources 
in the interior of the arm, we found a radially inward motion of <U> = 13.3 ± 5.4 km s^-1; 
for 10 sources in the middle of the arm, we obtained a marginal detection of motion slower than Galactic rotation 
of <V> = -6.2 ± 3.2 km s^-1; and for 5 sources in the exterior of the arm, we found no statistically
significant non-circular motion (see Section <ref> and Table <ref>). These characteristics are
consistent with predictions of models for spiral arm formation that involve gas entering an arm to be shocked 
and then forming stars as shown by Fig. <ref>.

We performed a similar analysis on previous VLBI astrometric data, as well
as on Gaia DR2 results for OB-type stars, for stars in other spiral arms.  While some statistically 
significant non-circular motions are found in other arms, no clear pattern among arms was found
(see Table <ref>). This suggests a more complex picture than expected from basic spiral-arm models.




 

We acknowledge anonymous referee for valuable comments, which improved the manuscript.



 

 
 

VLBA. 


  

  
   
    
 








apj


 


§ APPENDIX
 
 
Here, we show supplemental materials to further document observations 
(Table <ref>) and detailed maser maps for (Fig. <ref>).                               
  
 
 
 
 
 
 
 














 



 





 






 



 
