Received 1995 November 27; accepted 1996 February 13. ABSTRACT. Using data from Hubble Space Telescope observations, we report the first optical ...
THE ASTROPHYSICAL JOURNAL, 461 : L91–L94, 1996 April 20 q 1996. The American Astronomical Society. All rights reserved. Printed in U.S.A.
PARALLAX OBSERVATIONS WITH THE HUBBLE SPACE TELESCOPE YIELD THE DISTANCE TO GEMINGA 1 PATRIZIA A. CARAVEO, 2 GIOVANNI F. BIGNAMI, 2, 3 ROBERTO MIGNANI, 2, 4
AND
LAURENCE G. TAFF 5, 6
Received 1995 November 27; accepted 1996 February 13
ABSTRACT Using data from Hubble Space Telescope observations, we report the first optical measurement of the annual parallax of a neutron star. This is the counterpart of the X-ray/g-ray pulsar Geminga, for which strong proper motion has already been reported. Significant displacement from such motion is detected using WFPC2 observations, taken at the dates of the maximum predicted parallactic factor. The resulting distance value is 157 pc (159, 234), just consistent with the lower end of the wide range derived from X-ray data. This measurement solves the long-standing problem of Geminga’s distance and allows for the first precise determination of a neutron star luminosity from electron volts to giga– electron volts. Moreover, the repeated precise positionings substantially improve our knowledge of its proper motion. Subject headings: astrometry — pulsars: individual (Geminga) — stars: neutron 1. INTRODUCTION
2. THE HST IMAGES AND THEIR ANALYSIS
The story of Geminga is an example of the power of multiwavelength astronomy, coupled with the evolution of ground-based and space-borne instrumentation, over the last 20 years (see Bignami & Caraveo 1996 for a complete review). The faint object, known as G0, was proposed as the optical counterpart of the X-ray/g-ray source Geminga on the basis of its color peculiarities (Bignami et al. 1987; Halpern & Tytler 1988). The discovery of its high proper motion (Bignami, Caraveo, & Mereghetti 1993; Mignani, Caraveo, & Bignami 1994) strongly supported such identification by giving to it the characteristic properties of a neutron star (high velocity, low optical luminosity), and Geminga had meanwhile been shown to be a neutron star through the discovery of X-ray/g-ray pulsation (Halpern & Holt 1992; Bertsch et al. 1992; Bignami & Caraveo 1992). So far, the only information on the source distance was derived from the soft X-ray data (Bignami, Caraveo, & Lamb 1983; Halpern & Ruderman 1993) leading to a wide range of values: from little over 100 pc to about 400 pc. The same upper limit was also derived from the overall energy output requirements in high-energy g-rays (Bertsch et al. 1992; Bignami & Caraveo 1992). Such a distance uncertainty hampered, among other things, the possibility of discriminating between thermal and nonthermal processes in the optical/soft X-ray range, given the neutron star nature of Geminga for which an age, and thus a cooling time, was now known. In the wake of the proper-motion discovery, it was explicitly mentioned (Bignami et al. 1993) that the challenging measurement of Geminga’s annual parallax was within reach. In this Letter, we report on the Hubble Space Telescope (HST) program yielding a positive parallax measurement.
Owing to its near-equinoctial position, close to the ecliptic plane, the expected parallactic factor of G0 is maximum close to the equinoxes, and it is mostly in right ascension, with a declination component of less than 1/30. Of course, any annual parallactic displacement would appear, in the plane of the sky, as superimposed on the observed proper motion of 1170 mas yr 21 in the northeast direction. For objects as faint as G0, ground-based measurements cannot reliably determine a milliarcsecond annual parallax, and the refurbished HST was required. The Geminga field has been observed 3 times by the Planetary Camera on 1994 March 19, 1994 September 23, and 1995 March 18. About 1500 s of useful exposure time are available during each HST orbit for a source at the Geminga coordinates. To allow for the cleaning of the picture from pixels hit by cosmic rays, each orbit was split into two images of 700 and 800 s each. The total exposure time was 3000 s in 1994 March and 4500 s in the subsequent observations. All observations were performed with the filter F555W, roughly equivalent to the classical V filter, where ground-based observations had shown the source to be brightest (Bignami et al. 1987; Halpern & Tytler 1988; Bignami, Caraveo, & Paul 1988). Following careful cosmic-ray cleaning, the individual images of each pointing were summed and smoothed, and the centroid of each object was computed. Particular care was used in this latter step, especially for the computation of the centroids of G0, which appears to be the faintest object in the three image stacks (see Fig. 1 of Bignami et al. 1996 for an image of the PC field). A Gaussian function was used to fit source data yielding the best position and its associated error. To evaluate the real significance of this error, the fitting procedure was repeated for varying areas of surrounding background, up to several hundreds of pixels. It was noted that, while the error is indeed very small for a small background area, it grows and rapidly stabilizes for areas bigger than 200 pixels. This stabilized value is the one used for the errors of the different observations reported in this Letter. Since the average FWHM of the point sources measured in each of the three images is slightly different in x and y, we have used different errors for the two coordinates. The centering errors of the reference objects are between 0.01 and 0.03 pixels, while for G0, which is
1 Based on observations with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by AURA, Inc., under NASA contract NAS 5-26555. 2 Istituto di Fisica Cosmica del CNR, Via Bassini, 15, 20133 Milano, Italy. 3 Dipartimento di Ingegneria Industriale, University of Cassino, Cassino, Italy. 4 Universita ` di Milano, Italy. 5 Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218. 6 Research supported in part by General Observer Grant GO-5484.01-93A.
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the faintest object detected in the field, the uncertainties range between 0.05 and 0.07 pixels, depending on the background conditions. The values of all the centroids were corrected for the instrument geometrical distortion, following the procedure outlined by the WFPC2 team (Holtzman et al. 1995). The three observations cannot be immediately superimposed since they have been obtained with different roll angles as well as with slightly different pointing directions. Thus, precise alignment of the three images is crucial for our analysis. The traditional astrometric approach would be to perform a linear transformation (called the plate model) from one image, or plate, to another, with one observation arbitrarily chosen as the reference image. In this process, one would allow for at least four plate constants, i.e., two independent translations in the two orthogonal directions, a change in plate scale, and a rotation between images. We have not followed this procedure since the limited number of stars present in our field of view would have hampered the overall accuracy. In fact, because of slightly different pointing directions in the different observations, only four stars (namely stars D, A, G, and B of Fig. 1 of Bignami et al. 1996) are found to be present in all the images. They are sufficiently bright, but none of them is saturated. Other potential objects could not be used either because they are not present in all observations, because they are located too close to the field edges, or because of their possibile extended nature. Fortunately, the mapping of the geometrical distortion of the PC is so accurate (Holtzman et al. 1995) that the standard PC value of 0"0455 pixel 21 can be used as plate scale for all corrected frames. To account for the rotation, we have used the known telescope roll angles, ending up with x-axis aligned with increasing right ascension and y-axis aligned with increasing declination. Thus, all the statistical weight of the common stars in our PC frames was used in establishing the translation factors, which are determined to better than 0.01 pixel. Note that the above procedure is carried out in the PC reference frame, and this renders our points totally free from any systematic uncertainty induced on the absolute star position by the HST Guide Star Catalog (Taff et al. 1990). 3. THE RELATIVE ASTROMETRY
First, we checked the internal accuracy of our multistep analysis. To evaluate empirically the errors introduced, after centering, by the procedure described above, we compare the coordinates of our stars in the three images. In the absence of significant proper motions or parallaxes, they should be the same, within errors, i.e., their residuals should cluster around zero. For Geminga we expect a different behavior. Its known proper motion should show up immediately in the images taken at 6 month intervals. In the absence of a parallactic displacement, the segment of trajectory travelled in the two identical periods should be identical, within errors. Any parallax should alter the displacements in right ascension, lengthening the March-to-September one and shortening the September-to-March one. This is due to the right ascension component of the parallax (in fact twice its actual value) being added to the proper motion in the first case and subtracted in the second. The displacements in declination will be essentially unchanged.
Vol. 461 TABLE 1 DIFFERENCES
BETWEEN
OBJECT POSITIONS
Star
Pair a
Dx
D. . . . . . . . . . . . . . . . . . .
1 2 3
20.11 H 0.03 20.03 H 0.03 20.14 H 0.03
0.29 H 0.03 0.05 H 0.03 0.37 H 0.03
Dy
A. . . . . . . . . . . . . . . . . . .
1 2 3
0.05 H 0.02 20.01 H 0.02 0.02 H 0.02
20.11 H 0.02 0.02 H 0.02 0.04 H 0.02
G. . . . . . . . . . . . . . . . . . .
1 2 3
20.02 H 0.03 0.11 H 0.02 0.09 H 0.02
20.01 H 0.03 20.06 H 0.02 20.09 H 0.02
B...................
1 2 3
0.02 H 0.03 20.07 H 0.03 20.05 H 0.03
20.01 H 0.03 0.06 H 0.03 20.07 H 0.03
H. . . . . . . . . . . . . . . . . . .
1 2 3
··· 0.03 H 0.07 ···
··· 20.06 H 0.07 ···
L ...................
1 2 3
··· 20.004 H 0.12 ···
··· 0.06 H 0.12 ···
M ..................
1 2 3
··· 20.07 H 0.10 ···
··· 20.03 H 0.10 ···
N. . . . . . . . . . . . . . . . . . .
1 2 3
··· 0.06 H 0.05 ···
··· 0.04 H 0.04 ···
Geminga . . . . . . . . . . .
1 2 3
1.81 H 0.07 1.21 H 0.10 3.02 H 0.09
0.98 H 0.07 1.16 H 0.10 2.14 H 0.09
a Pairs of images are defined as follows: (1) 1994 September vs. 1994 March; (2) 1995 March vs. 1994 September; (3) 1995 March vs. 1994 March. Thus, pair 3 gives the displacement totalled in 1 yr (i.e., the proper motion), while pairs 1 and 2 give the semiannual displacements to be used for the parallax computation.
Finding a significant difference in the right ascension displacements in the two 6 month intervals will be the signature of a measurable parallax. To obtain accurate cross-comparisons between field stars and Geminga, we worked with three pairs of images: Pair 1: 1994 September versus 1994 March; Pair 2: 1995 March versus 1994 September; and Pair 3: 1995 March versus 1994 March. Since only four common field stars are present in the 1994 March observation, comparisons 1 and 3 are restricted to these objects, while comparison 2 uses all the eight field stars present in 1994 September and 1995 March. Table 1 summarizes the results of the centroid crosscomparisons for the x- and y-coordinates. The first column contains the field star identification, following the lettering used in Figure 1 of Bignami et al. (1996). Next, for each star, three rows are given: comparisons 1, 2, and 3. For each line, D x, in pixels, represents the displacement of the star centroid, together with its error, along the x-axis, aligned in right ascension, and similarly for the y-axis, aligned in declination. While the errors are just the combination of the original star centering uncertainties (plus translation accuracy), the actual values of the displacements provide a measure of the precision achieved in the image superposition.
No. 2, 1996
DISTANCE TO GEMINGA
All field stars show residuals comfortably close to zero, averaging absolute displacements of 0.06 pixels in R. A. and 0.09 pixels in decl. This gives us confidence in the overall correctness and accuracy of our procedure and also yields an empirical evaluation of our global final uncertainty. The behavior of G0 is quite different. It shows the presence of both proper motion and parallactic displacement. Comparison 3 is a direct measure of its proper motion, since it gives the displacement totalled in exactly 1 yr, between two positions with identical parallactic factors. Geminga has moved 3.02 H 0.09 pixels in R. A. and 2.14 H 0.09 in decl. Comparisons 1 and 2, on the other hand, show the right ascension displacements to be markedly different for the two semesters. For a March-to-September displacement of 1.8 H 0.07 pixels, we find a September-to-March one of 1.2 H 0.1 pixels, to be compared with an expected ‘‘pure proper motion’’ of 1.51 H 0.06. Thus, each measurement deviates in the expected direction from the pure proper motion. To get the overall statistical significance of the effect, we can compare directly the two right ascension displacements. From Table 1, we find that they are different at the 5 s level. On the other hand, the displacements in declination are the same within errors, again as expected. To compute the observed parallactic displacement, let G be the geocentric right ascension of Geminga (actually the quantity we measure), and let H be its heliocentric right ascension. At any time t, the two differ by the parallactic displacement in the form G~t! 2 H~t! 5 p P a ~t!,
H~t! 5 a 3/94 1 m~t 2 t 3/94 ! 5 a 3/94 1 mt, where t is the time in years since 1994 March and a 3/94 is Geminga’s heliocentric right ascension at the time. Assuming, for simplicity, that the HST points were taken at the extreme values of the parallax factor P a , which for Geminga are approximately H1, and that the images are exactly one-half year apart, we have three equations relating the three HST PC measures: because t 5 0 and P a 5 21,
G(9/94) 5 a 3/94 1 m/2 1 p
(1a)
because t 5 11/2 and P a 5 11,
G(3/95) 5 a 3/94 1 m 2 p
FIG. 1.—Geminga’s real trajectory (dotted line) as inferred by the measurement of the parallactic displacement superimposed to the proper motion, computed from only the ST data (solid line). The three PC relative positions are also shown.
G(9/94) 2 G(3/94) 5 m/2 1 2p
where p is the annual parallax we want to compute and P a is the parallax factor. Since the displacement in declination is expected to be a factor of 30 less, we shall concentrate on right ascension observations. The full formula for the heliocentric right ascension H at any time t includes the right ascension at some epoch (e.g., t 5 t 0 ), the proper motion component in right ascension m, and the time from the reference epoch t 0 . Let us take the standard epoch to be that of the first PC observation (i.e., 1994 mid-March or 3/94), so we can write
G(3/94) 5 a 3/94 2 p
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(1b)
because t 5 11 and P a 5 21. (1c)
By forming pairs of differences, we obtain, in addition to the complete cancellation of the right ascension at the reference epoch (and an increase in statistical weight of p and m at the expense of knowing a 3/94 ), the two half-year equations
(2a)
i.e., line 1 for Geminga (see Table 1) and G(3/95) 2 G(9/94) 5 m/2 2 2p
(2b)
i.e., line 2 for Geminga (see Table 1). Thus, the difference in right ascension displacement in alternate half-years is 4 times the value of the annual parallax. In other words, the difference between comparisons 1 and 2 in Table 1, multiplied by the cosine of the declination, is 4 times the parallax of Geminga. Redoing this work, but with the actual numerical values of the time differences and the correct parallax factors, the end result is
p 5 0.140 H 0.038 pixel, where the error is that obtained by subtracting equation (2b) from equation (2a) performing a standard error propagation. As an independent check on the error evaluation, we applied the parallax computing procedure described above to the four reference field stars present in all observations, the displacements of which are given in Table 1. The resulting values are all smaller than the uncertainty quoted above, ranging from 20.032 pixel to 10.022 pixel. Thus, our procedure is free of systematics, and the error quoted is realistic or even conservative. Since the PC plate scale is 0"0455 per pixel,
p 5 0"00636 H 0"00174, i.e., the distance to Geminga is 157 (159, 234) pc. The positive measurement of an annual parallax for Gem-
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inga can also be pictorially represented in Figure 1. The three relative positions for the three epochs, 1994 March, 1994 September, and 1995 March, are given in the plane of the sky. The September point is obviously displaced from an ideal ‘‘zero parallax’’ line joining the two March points. As expected, it is displaced in the sense of increasing right ascension. Also as expected, the segment of trajectory joining the two 1994 points is longer than the 1994 September–1995 March one. The source proper motion from the PC data given in Figure 1 is
m a 5 138 H 4 mas yr 21 and
m d 5 97 H 4 mas yr 21 , corresponding to a total of 170 H 6 mas yr 21 . These values are identical to, but much more accurate than, the ground-based one, despite the much shorter time base. 4. CONCLUSIONS
Some immediate astrophysical consequences can be inferred from the measurement of the distance to Geminga. First, the thermal emission. Using EUVE data in conjunction with the now known distance, Bignami et al. (1996) obtain an excellent global fit with a standard neutron star radius of 10 km, an N H value of 0.5–1 3 10 20 , and a temperature in the range 2–3 3 10 5 K. This is consistent with the lower limit of the temperature range allowed by ROSAT data (Halpern & Ruderman 1993; Meyer, Pavlov, & Me´sza´ros 1994), although more work is needed to reconcile EUVE and ROSAT data. The bolometric luminosity under the single eV-to-keV Planckian is 12 3 10 31 ergs s 21 . For the high-energy gamma rays, where the vast majority of the Geminga power is emitted, the distance value determines the efficiency of the neutron star in transforming its rotational ˙ 1 3.5 3 10 34 ergs s 21 ) into g-rays. In the energy loss (IVV
absence of beaming, the isotropic g-ray luminosity for E . 100 MeV is 11.5 3 10 34 ergs s 21 , or about half of its mechanical energy loss. Beaming, however, is obviously at work and appears similar, for example, to that of the Vela pulsar. Thus, a comparison between the two objects is possible (see also Goldoni et al. 1995), yielding evidence that Geminga is a far more efficient g-ray machine than the Vela pulsar. With the much more precise proper motion of Figure 1, one can now reassess the work done so far in trying to locate the most probable place of origin of this neutron star for its canonical age of 3.4 3 10 5 yr. Gehrels & Cheng (1993), propagating backward the data of Bignami et al. (1993), obtained a starting position of a 5 5 h 40 m , d 5 88249, or l 5 1978, b 5 211$7, and proposed that the supernova event generating the neutron star could also be responsible for the so-called Local Bubble. A more general approach was used by Frisch (1993) who analyzed the problem from the statistical point of view. The general Orion region was found to be a more likely place of origin than the Local Bubble. Smith, Cunha, & Plez (1994) went one step further and pointed out that the backward extrapolation of the Geminga position falls almost exactly on the l Ori association, at a distance of 400 H 40 pc in the direction l 5 195$26 and b 5 211$62. The newly measured value of the distance translates immediately into a tranverse velocity of 122 km s 21 , while the more precise knowledge of the proper motion shrinks significantly, in the plane of the sky, the region of origin. The star l Ori continues to be inside it. Cuhna & Smith (1996) have suggested that the expanding ring of gas surrounding this star could be due to a supernova explosion that occurred 300,000 – 370,000 yr ago, in good agreement with the dynamical age of Geminga. However, the radial velocity required in this case would be 2700 km s 21 , not unheard of in the pulsar family, but rather high compared to the tangential one. A radial velocity with the opposite sign would allow Geminga to have travelled 250 pc, starting from coordinates l 5 108, b 5 2128, diametrically opposed to the current ones.
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