«VLBA Measurement of Nine Pulsar Parallaxes Walter F. Brisken National Radio Astronomy Observatory PO Box O, Socorro, NM 87801 John M. Benson National ...»
VLBA Measurement of Nine Pulsar Parallaxes
Walter F. Brisken
National Radio Astronomy Observatory
PO Box O, Socorro, NM 87801
John M. Benson
National Radio Astronomy Observatory
PO Box O, Socorro, NM 87801
W. M. Goss
National Radio Astronomy Observatory
PO Box O, Socorro, NM 87801
S. E. Thorsett
Department of Astronomy and Astrophysics, University of California
Santa Cruz, CA 95064
We determined the distances to nine pulsars by parallax measurements using
the NRAO Very Long Baseline Array, doubling the number of pulsars with accurate distance measurements. Broadband phase modeling was used to calibrate the varying dispersive eﬀects of the ionosphere and remove the resulting phase errors from the phase-referenced VLBI data. The resulting parallaxes have a typical accuracy of 100 microarcseconds or better, yielding distances measurements as accurate as 2%. We also report new proper motion measurements of these pulsars, accurate to 400 µas yr−1 or better.
Subject headings: astrometry — techniques: interferometric — pulsars –2–
1. Introduction Accurate pulsar distance measurements are useful for many reasons. Combined with dispersion measures, they probe the electron content along diﬀerent lines of sight through the local Galaxy. Combined with proper motions, they constrain the pulsar velocity distribution and hence the symmetry of supernova explosions. Combined with radio, optical, x ray, and UV ﬂux measurements, they determine the absolute luminosities and radiation eﬃciencies of pulsars. For a thermally emitting neutron star, they even promise the possibility of directly constraining the neutron star radius and hence the nuclear equation of state at high densities. There are many diﬀerent ways of estimating pulsar distances, including association with supernova remnants or globular clusters at known distance, or the use of a model of the electron distribution in the Galaxy together with dispersion measurements.
But the most fundamental method—indeed, the only model-independent method—remains the measurement of parallaxes.
Pulsar parallax measurements are diﬃcult. Even the closest pulsars are 100 pc or more distant; thus parallax leads to an apparent annual motion of 10 mas or (typically) much less. With their steep spectra, pulsars are usually observable only in the low-frequency radio band, where the ionosphere introduces substantial temporally- and geographically-variable shifts in the phase of the signal, making precision interferometry particularly challenging.
Before the completion of the Very Long Baseline Array (VLBA), only six interferometric pulsar parallaxes were published (Table 1). It is important to understand the very great diﬃculties these observers faced. First, in many cases they were limited to rather short baselines ( 500 km) and decimeter and longer wavelengths (λ 10 cm). The ionosphere and the small array size limited the potential accuracy to about 1 milliarcsecond (mas), unless a very nearby calibrator source was used. Some serendipitous measurements were possible. For example, the measurement of the parallax of pulsar B1451−68 was about ten times more precise than the ionosphere would ordinarily have allowed with the available array because of the fortuitous presence of a calibrator only 6 from the pulsar, within the same primary telescope beam.
A second problem for early observers was the limited number of telescopes available in early, ad hoc VLBI networks. With only three or fewer stations, it is very diﬃcult to fully resolve “phase-wrap” ambiguities to determine which of a family of possible positions on the sky is actually occupied by the source. As shown in Brisken et al. (2000), an incorrect choice of phase wraps could lead to parallax errors much larger than the formal measurement errors. (By the time the last measurement in Table 1 was made—the parallax of B2021+51—a number of VLBA stations was available. Although the observations used a diﬀerent set of telescopes at each observing epoch, and large baseline errors in the telescope –3– positions had still not been resolved, it is notable that this early result is within 2σ of our new measurement.) It is probably not coincidental that every repeated pulsar parallax measurement has yielded a smaller parallax (and greater pulsar distance). We suspect that the expectation of larger results in early experiments probably contributed to incorrect lobe choices. With the ten-station VLBA this is no longer a problem.
Although we will not further discuss non-radio measurements here, for completeness we note that the high-energy pulsar Geminga (J0633+1746) has a three-epoch parallax measured by HST of π = 6 ± 2 mas (Caraveo et al., 1996), and the radio quiet neutron star J185635−3754 has an HST-derived parallax of 16.5 ± 2.3 mas (Walter, 2001).
Our successful measurement (Brisken et al. 2000) of the parallax of PSR B0950+08, using a new calibration technique to remove the disruptive eﬀects of the ionosphere from the interferometry data, prompted us to expand our program of parallax measurements to a larger sample. We had two primary goals. One was the immediate desire to increase the number of pulsars with well-measured distances. But a second goal was to improve our understanding of the new calibration technique, to test its limitations, and to measure the level of residual systematic errors. For this reason, our target selection was not yet optimized solely to produce an unbiased pulsar sample for statistical work on pulsar distances. Instead, we chose nine pulsars at a variety of declinations, of varying ﬂux densities, and with varying pulsar-calibrator angular separations. We also continued our observations of PSR B0950+08, to produce an extremely over-constrained data set for studies of our errors.
An important constraint on target selection was the need for a high ﬂux density at 1400 MHz. Based on our experience with B0950+08, we expected that we would be able to successfully do an ionospheric correction for pulsars with ﬂux densities above about 10 mJy at 1400 MHz. We also preferentially targeted pulsars with estimated distances (from the dispersion model) of less than about 2 kpc. For this experiment, we only considered candidate pulsars whose nearest VLBA calibrator source was no more than 5◦ from the pulsar.
Larger separations lead to larger diﬀerential ionospheric and tropospheric eﬀects, and will be more diﬃcult to calibrate. The 5◦ limit was set after experiments in which we attempted to calibrate PSR B0950+08 against the International Celestial Reference Frame calibrator source 1004+141, at a separation of 6.9◦. At this separation the diﬀerential propagation eﬀects were too large to correct using the new calibration technique. We also rejected pulsars at declinations below −10◦, where high elevation ( 20◦ ) observations cannot be made simultaneously at all VLBA stations. The pulsars observed are listed in Table 2, together with their dispersion measures and ﬂux densities from the Princeton pulsar catalog (Taylor et al., 1993).
Five epochs of observations for each pulsar were planned over the course of one year, enough to redundantly determine the proper motion and parallax even with a failed epoch.
To maximize our sensitivity to the angular signature of parallax, the measurements were scheduled at times when the parallactic displacement was at a maximum or minimum. Observations hence occurred at roughly three month intervals, although the exact dates varied with telescope scheduling. Pulsar J2145−0750 was not detected in either of its ﬁrst two epochs. This non-detection is most likely because of the extreme, long-term scintillation modulation that aﬀects the signal from this pulsar. It was dropped from the program, and the time allotted to other pulsars was increased slightly. About ninety minutes of on-source integration was obtained for each pulsar at each epoch.
In order to make relative position measurements, each pulsar observation was interleaved with observations of a VLBA calibrator source with position known to better than 15 mas.
The antennas nodded back and forth between the pulsar and calibrator with a cycle time of about ﬁve minutes. This interval is long enough to detect calibrator fringes yet short enough to allow unambiguous phase connection between calibrator observations. In the case of B1237+25 two calibrators were observed in a cycle, integrating for 100 seconds on the pulsar and 60 seconds on each calibrator.
All observations were made with the ten-station NRAO VLBA. The 20 cm band (1400 to 1740 MHz) was chosen as a compromise between falling ﬂux densities and increasing resolution as frequency increases. This band also oﬀers the wide fractional bandwidths needed for the ionosphere calibration. The 338 MHz wide band available from the receivers was Nyquist sampled in eight 8 MHz spectral windows beginning at 1404, 1414, 1434, 1474, 1634, 1694, 1724 and 1734 MHz. Pulsar gating was employed to increase the signal-to-noise of the pulsar measurements by disabling correlation during oﬀ-pulse. The gate gain listed in Table 2 is the expected signal-to-noise increase factor based on the pulse proﬁles measured at 1400 MHz. The timing data needed to construct the pulse arrival time ephemerides was collected by Andrew Lyne at Jodrell Bank.
where σH2 O is the column density of water in the atmosphere. Only the diﬀerential phase shifts at two antennas enter into the visibility phases. After phase-referencing, only the diﬀerence in visibility phase shifts due to propagation between the pulsar and calibrator remain. While the absolute phase shifts may be several thousand degrees, only the doublediﬀerences of their values are relevant to the position measurements. For the troposphere, we ﬁnd that this amount is typically less than 45◦ of phase for calibrator-target separations of up to 5◦ at 20 cm. In contrast, the diﬀerential ionosphere can be up to 1200◦ on long baselines.
In addition to the unwanted phase shifts due to propagation eﬀects, the geometric phase associated with the position of the pulsar (the quantity that is to be determined) also contributes to the pulsar’s visibility phase. The point-like nature of pulsars simpliﬁes the geometric phase to ν φGeom = ( u + mv), (3) ν c where (, m) are the pulsar’s oﬀset from the correlation center in radians, c is the speed of light, and (u, v) are the components of the projected baseline perpendicular to the direction to the pulsar. The phase delays due to geometry and the troposphere are both independent of frequency (non-dispersive), making their disentanglement impossible for a given visibility.
Visibility measurements spanning a large range of elevations can be used to separate out the troposphere, but this was not done due to the limited elevation ranges that we used. Fortunately, it is possible to measure the diﬀerential ionosphere strength with multi-frequency – 10 – data since the ionosphere’s phase delay is frequency dependent (dispersive). The visibility phase on a single baseline can be expressed as B φVis = Aν + + 2πn. (4) ν ν where A incorporates all of the non-dispersive components (the geometry and the troposphere), B is the strength of the diﬀerential ionosphere, and the integer n is the number of additional phase wraps. Once B is known, the distorting eﬀects due to the ionosphere can be removed from the visibility.
Station-based ionosphere solutions were determined by ﬁtting station-based phases to Eqn 4. The station-based phases at each frequency band were determined by ﬁtting the measured phases to a point source model representing the pulsar with solution intervals shorter than the amount of time that the ionospheric phase shift changes by about 30◦ (about 20 or 30 seconds at 20 cm). Solution intervals of 10 seconds or less were used on the brightest pulsars. Since all phases are relative, one station was chosen to be the reference antenna and was assigned zero phase.
Unknown phase wraps complicate the ﬁtting for A and B. This is because certain combinations of the A and B parameters closely mimic an additional undetectable phase wrap due to the limited spanned bandwidth as is shown in Figure 1. The ﬁtting was performed ﬁrst on the Southwestern Antennas (Fort Davis, TX, Kitt Peak, AZ, Los Alamos, NM, and Pie Town, NM) where baselines are shorter and thus the geometric phases are smaller and the diﬀerential propagation eﬀects are also less. An image was made without any ionosphere calibration to determine the pulsar’s position to better than 10 mas. The pulsar’s approximate position was used to reduce the unknown non-dispersive phase to less than 90◦.
Since the tropospheric phase is usually less than 45◦, the number of phase shifts, n, can be determined and the ionosphere can be calibrated away for the Southwestern antennas.
The phase shifts associated with the ﬁtted B parameters were removed from the visibility data. An image made with the ionosphere calibrated Southwestern antennas yielded pulsar positions to better than 1 mas, allowing ionosphere solutions to be found at and applied to the remaining stations.
– 11 – Fig. 1.— The source of phase-wrap ambiguity. For certain ionosphere solutions, A∗ =
2.0 rad/GHz and B ∗ = 4.9 rad·GHz, the resultant phase across the observed band is almost indistinguishable from 2π. Since 2π can be added to the visibility phases without observable consequences, an entire family of ionosphere solutions is consistent with the data. The eight 8 MHz bands observed are shown as short vertical bars. The RMS deviation from 2π at these frequencies is only 0.6◦.