1. Radio Astrometry of Young Stars
Luis F. Rodríguez
Centro de Radioastronomía y Astrofísica, UNAM, Campus Morelia
Interferometric radio observations of the emission from young stars in our Galaxy can allow the determination of masses and distances and in some cases a much deeper understanding of the origin, age and evolution of the source studied.
Most of the proper motions discussed here are obtained from continuum (thermal and nonthermal) observations of stars and their envelopes.

2. Collaborators:
L. Loinard, L. Gómez, M. Rodríguez, & P. D’Alessio (CRyA, UNAM, Morelia)
S. Curiel, J. Cantó, & A. C. Raga (IAUNAM, México City)
J. M. Torrelles (IEEC, Spain), J. M. Girart (U. Barcelona, Spain)
David J. Wilner (CfA, USA) &
Paul T. P. Ho (CfA, USA & ASIAA, Taiwan)

3. The radial velocity of a source can be obtained from a single measurement and the application of the Doppler effect. In contrast, the plane-of-the-sky velocity requires of at least two measurements, as separated in time as possible.

4. The effect is usually very small…
A body moving at the respectable speed of 1,000 km/s in the pane of the sky, and located at the center of the Milky Way (at 8.5 kpc), will take 40 years to move one arc second.

5. Definition of proper motion

6. STELLAR MASSES
Most of the information on stellar masses comes from the study of orbital motions in binary systems, using Kepler´s third law:

7. BACKGROUND
Most information on stellar masses comes from studies of orbital motions
Work at optical band toward visible stars has been going on for 200 years
In the last decade, near-IR speckle and adaptive optics has been used to investigate T Tauri binaries
What about heavily obscured protostars, not detectable even at near-IR wavelengths?

8. STELLAR MASSES
That is, if we know a, the semimajor axis of the orbit, and P, the orbital period, we can find m+M, the sum of the masses of the two stars. But, how can we study very young stars that form inside clouds with high obscuration and that cannot be studied with the usual optical and infrared techniques?
Fortunately, some young stars have radio emission that allows this type of studies.

9. RADIO OBSERVATIONS
Remarkably, protostars can be tracked at radio wavelengths due to three processes:
Free-free emission from ionized outflows
Thermal emission from circumstellar disks
Gyrosynchrotron from active stellar magnetosphere
No extinction. Processes (1) and (2) produce extended sources, suitable for VLA. Process (3) very compact, suitable for VLBA. These emissions may or may not be present.

10. Very Large Array
Angular resolution of 0.1” at 2 cm Positional accuracy of order 0.01”

11. HEAVILY OBSCURED SOURCES:
L1551 IRS5
YLW 15
L1527 (= IRAS )
IRAS
VLA observations; all low mass forming stars

12. L1551 IRS5 Ha
[SII]
Cont.
Reipurth & Bally 2001
ESO NTT

13. L1551 IRS VLA-A 2 cm

15. Proper Motions
The large, lineal motions are due to the relative motion between the Sun and the object and they coincide with what is expected (Jones & Herbig 1979).
However, there is also relative motion between the two components, suggesting orbital motions.

16. Total proper motions

17. “Relative” proper motions

18. From the observations and making the following (reasonable) assumptions:
Plane of orbit near plane of the sky.
Circular orbit.
=> M+m = 1.2 Msun; P = 260 years
If in the main sequence, the luminosity of this system should be like 1 solar luminosty, but it actually has like 30 solar luminosity.
This confirms that, as expected, forming stars have a large luminosity excess, most probably as a result of accretion.

19. Lim & Takakuwa (2006) have obtained new data and made detailed analysis to obtain a more accurate estimate:
M + m = Msun
P = yr

20. YLW VLA-A cm

22. YLW 15

23. YLW 15
Relative velocity in the plane of the sky of km/s, implying:
M > 1.7 Msun
Assuming observed separation is close to true separation, P < 360 yr
Lbol = 13 Lsun

24. L VLA-A mm

25. Relative Velocity in Plane of the Sky = 4+-2 km/s
M > 0.1 Msun, most likely 0.5 Msun
Lbol about 2.5 Lsun

26. Up to now, binary systems, what about multiples (i. e. triples)?
IRAS

27. IRAS 16293-2422, VLA-A, 3.5 cm, average proper motion subtracted

28. IRAS
Relative velocity of about 15 km/s and separation of about 30 AU between components A1 and A2, implies relatively large mass of about 4 Msun
However, A1 has been proposed in the past to be a shock with ambient medium
Loinard et al. (2007) has new paper on the region, but no news about proper motions.

29. CONCLUSIONS OF ORBITAL MOTIONS
Orbital motions in protostars will provide important constraints on the early phases of stellar evolution
We are getting reasonable results, but must follow “strange” cases such as IRAS

30. T Tauri: Prototype of its class. VLA observations:

32. T Tauri is triple (Koresko 2000) Data from Dûchene et al. (2002):

33. Dûchene et al. (2002)
V = 20 km/s => M > 4 Msun

34. What are we seeing in the radio?
Comparison between radio and near-IR, as well as circular polarization characteristics of southern source indicates that in the radio we are always seeing T Tau Sb
Even when in the radio we do not see component Sa, it is possible, combining radio and near-IR to obtain orbit of Sb relative to Sa
This relative orbit comes from detailed astrometric measurements and tries to correct for relative motion of Sa with respect to N

35. Johnston et al. (2003)

36. T Tau: Use VLBA to improve on VLA.
Measure not only orbital motions, but also geometric parallax.

37. VLBA

38. Very Long Baseline Interferometry
You can get amazing positional precision, ” and better.
Not always can be applied, the source has to be very compact and relatively intense (implying nonthermal processes).
With VLBI you can measure the subtle effect of the geometric parallax, that can provide accurate distances.

39. Stellar parallax
As the Earth moves in its orbit around the Sun, the nearby stars seem to change their position with respect to the remote, “fixed” stars.
d = 1 / p
d = distance to star in parsecs
p = parallax angle of the star in arc seconds.

40. You detect the combination of the elliptical motion of the parallax plus the lineal proper motion due to relative motion.

41. You detect the combination of the elliptical motion of the parallax plus the lineal proper motion due to relative motion.

42. T Tauri: as seen with the VLBA.

43. Distance = parsec, the best precision achieved for this type of stars (Loinard et al. 2007).

44. Duchene et al. (2006), from infrared observations:

45. Loinard et al. (2007) VLBA

46. Hipparcos
Why can we do better than astrometric satellites for this type of stars?

47. Young stars are highly obscured in the optical and infrared or, if detected, they are associated with nebulosity that difficults the astrometry.

48. Conclusions
As a result of great improvements in angular resolution and positional accuracy, astrometry is undergoing a renaissance.
Approach that takes advantage of old archival data that can be compared with more recent observations.
Addresses key parameters in astronomy such as mass, distance, and kinematics.