Apparent motion of extragalactic radio sources V.E.Zharov, V.N.Sementsov, M.V.Sazhin, K.V.Kuimov, O.S.Sazhina, E.A.Rastorgueva Sternberg Astronomical Institute of Moscow State University, Moscow, Russia From Quantum to Cosmos – III: Fundamental Physics in Space for the Next Decade Airlie Center, July 6-10, 2008

ICRS The International Celestial Reference System (ICRS) is based on a kinematical definition. It is postulated that the coordinate axis of this system fixed with respect to the distant objects of the Universe. It means that the ICRS is the inertial system. So the ICRS is the basis for solution of all modern problems in astrometry and navigation.

What is the International Celestial Reference Frame? A realization of the ICRF consists of a set of precise coordinates of extragalactic radio sources: quasars, BL Lac type objects, active galactic nuclei (AGN). These sources are so far away that their expected proper motions should be negligibly small. It means that the ICRF is almost inertial.

The first catalog The first realization of the ICRF (catalog) was constructed in 1995 by a reanalysis of all VLBI observations (Ma et al. 1998). It contains coordinates of 608 sources. The objects are divided in three subsets: “defining”, “candidate” and “other”. 212 of these are “defining” sources. They are a core of the ICRF. 294 “candidate” sources. 102 ‘other’ sources. Two extensions have been announced since 1995 covering observations at 1994 through 2002 (Fey et al. 2001, 2004). Positions for 109 new radio sources were added to the list of the initial ICRF catalogue.

The source subsets The defining sources should have a large number of observations over long data span and show position stability; they maintain the axes of the ICRS. Sources with an insufficient number of observations or an observing time span are designated as the candidates; they could be potential defining sources in future realizations of the ICRF. The category of other sources includes objects with poorly determined positions, but they are useful to link the ICRF with other reference frames.

ICRF

Toward the ICRF-2 The necessity of maintaining the reference axes fixed and the continuing improvement in the sources coordinates requires regular maintenance of the frame. The XXVI-th General Assembly of IAU formed a working group for a purpose to oversee the generation of the second realization of the ICRF from VLBI observations of extragalactic radio sources. One of the primary goals is the selection of defining sources and the mitigation of source position variations to improve the stability of the ICRF.

First step to the ICRF-2 The problem of stable radio source selection is now one of the key problems for ICRF improvement (MacMillan and Ma 2007, Tornatore and Charlot 2007). Feissel-Vernier (2003) developed a detailed scheme for the selection of stable radio sources using time series of the position estimates during 1979–2002 produced by the US Naval Observatory.

Methods of selection (1) A set of stable sources is selected in a two-step process. 1.Continuity criteria for one-year weighted average coordinates. (a) Length of observation period longer than five years. (b) Not less than two observations of the source in a given session. (c) One-year average coordinates based on at least three observations. (d) Not more than three successive years with no observations, conditions (b) and (c) being met. (e) At least half of the one-year averages available over the source observation time span. This first screening keeps 362 sources. These include 141 defining sources, 130 candidates, 87 other and 4 new sources.

Methods of selection (2) 2. The time series of yearly values of  cos  and  are then analyzed in order to derive: (a) the linear drift (least squares estimation); (b) the Allan standard deviation for a one-year sampling time. Based on these statistics, partial indices are defined. Sources with stability indices 1 and 2 are considered as stable. Original list contains 199 ‘stable’ sources. Feissel-Vernier et al. (2006) made another selection, using new information about drift and proposed updated list of sources. The original set was reduced to 181.

Are the defining sources necessary? Stability of the defining (or “stable”) source positions guarantees the constancy of the vector w in space or the frame stability.

In our work we analyze the time series of values of  cos  and  that were derived by different centers (USNO, GSFC, IAA, SAI, MAO) that analyzed the VLBI observations in order to derive the parameters of motion of the radio sources. We found that all of them show one of the types of motion listed below.

Method: best regression fit It is necessary to find the best subset regressions for a regression problem  are the regression coefficients, and the  i ’s are independently distributed normal errors each with mean zero and variance   We suggest that motion can be curvilinear We test of all possible regressions and maximize value of Fisher coefficient is the weighted mean, is the fitting function

Motion of (OQ208) - 1

Motion of (OQ208) - 2

Model of source

Types of motion (1) Proper motion of source (linear motion, constant flux) Z = 1, V = 100 km/s   0.01  as/y (defining) z=1.150, scale = kpc/” |  |  (0.043±0.002)mas/y, V T  1.2c (apparent)

Types of motion (2) Precession motion of steady jet (curvilinear motion, small flux variation) Jet precession period: years

Types of motion (2a) Example (defining and stable) curvilinear apparent path constant velocity module z=2.384, scale = kpc/” |  |  0.077mas/yr, V T  2.1c

Types of motion (3) Motion of dense condensations (clouds) accelerated by a jet (Blandford, Konigl, 1979) (linear motion, variable velocity, significant flux variation) (defining, small linear drift on  but cubic polynomial on  z=3.408, scale=7.521 kpc/”  0.024mas/yr, V T  0.6c

Types of motion (4) Weak microlensing (circular motion) Not found in ICRF Theory (Sazhin,Zharov, 1998) (HP23106) – is not observed (HP59803) – small variation J (Jupiter) (Fomalont, Kopeikin, 2003)

Statistics of motion Total of 196 ICRF sources are processed using best-fit polynomials (standard IMSL routine). The statistics are as follows: So, there are 15% of objects move with constant velocity, 23% of objects move along a straight-line with variable velocity, 25% of objects move along conic cross-sections. The remaining objects show more complex motion that is not yet classified.

Short-term motion of the “stable” source Precession motion of steady jet + dense condensations (clouds) accelerated by the jet

Difference from other selection schemes (1) Feissel Zharov (excluded from stable sources by Feissel)

Difference from other selection schemes (2) In our model  t   and  t  depend on time, so w=w(t) depends on time too. In modern level of accuracy all extragalactic radio sources became non-stable. This instability is significant for modern astrometry task.

Conclusions Our recommendation: to calculate vector w astronomers have to use all sources without dividing on “defining”, “candidate” and “other” through 1 (or 3, or 5) years Catalog of sources must contain both positions and coefficients of the best polynomials The ICRF is non-inertial frame due to non-predictable motions of radio sources and due to non-stationary gravity field of Galaxy (weak microlensing effect) on microarcsecond level of accuracy. Radio Reference Frame Image Database (RRFID) of the United States Naval Observatory (USNO) was used in this research