THE ASTROPHYSICAL JOURNAL, 504 : 588È598, 1998 September 1 ( 1998. The American Astronomical Society. All rights reserved. Printed in U.S.A.
SUBMILLIMETER ARRAY POLARIMETRY WITH HERTZ C. DARREN DOWELL,1 ROGER H. HILDEBRAND, DAVID A. SCHLEUNING, AND JOHN E. VAILLANCOURT Department of Astronomy and Astrophysics and Enrico Fermi Institute, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637 ; cdd=oddjob.uchicago.edu, roger=oddjob.uchicago.edu, david=oddjob.uchicago.edu
JESSIE L. DOTSON, GILES NOVAK, AND TOM RENBARGER Department of Physics and Astronomy, Northwestern University, 2131 Sheridan Road, Evanston, IL 60208 ; jdotson=nwu.edu, g-novak=nwu.edu, tom=clark.phys.nwu.edu
AND MARTIN HOUDE Caltech Submillimeter Observatory, 111 Nowelo Street, Hilo, HI 96720 ; houde=poliahu.submm.caltech.edu Received 1997 December 5 ; accepted 1998 April 6
ABSTRACT We describe the characteristics of the 350 km polarimeter Hertz learned from laboratory tests and recent observations at the Caltech Submillimeter Observatory. Hertz contains a pair of 32 element arrays with 18A pixel spacing and 20A resolution. The instrument has been improved since initial observations in 1994 and 1995 ; the detector noise is now below the sky background noise. In excellent weather conditions on Mauna Kea, the noise-equivalent Ñux density (NEFD) for the measurement of polarized Ñux is 3È4 Jy Hz~1@2. The subtraction of correlated sky noise accomplished by the two-array design is crucial for achieving this performance. A method for analysis of our polarization data in the presence of the correlated noise is described. The instrumental polarization of Hertz is less than 0.5% across the detector array. Systematic errors in the measurement of polarization are less than 0.2%. We present a 350 km polarization map of Sgr B2 with 140 detections at greater than 3 p signiÐcance. For our current database of all 350 km polarization measurements, the median polarization is 1.1%. Subject headings : infrared : ISM : continuum È instrumentation : polarimeters È ISM : magnetic Ðelds È polarization 1.
INTRODUCTION
sky noise that is present. Our new analysis procedure takes advantage of the subtraction of the correlated noise that is possible for a polarimeter with two arrays. We test for systematic errors in the polarization measurements. Finally, we present a sample of observations with Hertz.
Polarimetry of the thermal emission from magnetically aligned dust grains reveals the orientation of magnetic Ðelds in dense molecular clouds (e.g., Hildebrand 1988 ; Jones 1996 ; Roberge 1996). The Ðrst far-infrared detection of polarization from a molecular cloud was made by Cudlip et al. (1982). Since then, approximately eight di†erent instruments have had success in detecting polarization at wavelengths from 60 km to 3.4 mm (Dragovan 1986 ; Novak, Predmore, & Goldsmith 1990 ; Platt et al. 1991 ; Flett & Murray 1991 ; Kane et al. 1993 ; Akeson et al. 1996 ; Glenn, Walker, & Young 1996 ; Schleuning et al. 1997 ; Dowell 1997). Of those instruments, only two have had arrays of detectors to allow the measurement of polarization at many points on the sky simultaneously (Stokes : Platt et al. 1991 ; Hertz : Schleuning et al. 1997, hereafter Paper I). Hertz is designed to measure 350 km polarization from the 10 m Caltech Submillimeter Observatory (CSO). Initial observations took place in 1994 and 1995. Those observations and the optical and cryogenic design of the instrument have been reported in Paper I. Following the observations in 1995, Hertz has been upgraded. Since submillimeter polarimetry requires better than 0.5% accuracy to measure e†ects of order 1%, our goals have been to improve the sensitivity while minimizing instrumental polarization and systematic e†ects. The upgraded instrument is described in this paper. Using data from our observations in 1997 April, we evaluate the sensitivity of the polarimeter, taking into account the correlated
2.
STATUS OF THE POLARIMETER HERTZ
The present optical layout of Hertz is the same as is reported in Paper I. The instrument employs two 32 element bolometer arrays, one for each component of linear polarization, covering a
[email protected] ]
[email protected] Ðeld of view. Cold optics form an image of the sky on the arrays of Winston cones, which concentrate the light onto the bolometers. The bolometers are cooled to 0.26 K by a two-stage 3He refrigerator. A freestanding wire polarizer at a 45¡ incidence angle separates the incoming beam into two orthogonal linear polarizations. A rotating quartz half-wave plate modulates the polarization of the astrophysical source. 2.1. Instrument Upgrades Prior to 1996, the sensitivity of Hertz was limited by a combination of thermal phonon noise from the bolometers and electronic noise from the junction Ðeld e†ect transistor (JFET) ampliÐers (Paper I), both a factor of 3È4 larger than the photon noise from the atmosphere. We have taken several steps to improve the sensitivity since that time. The quartz half-wave plate and two quartz lenses have been antireÑection coated with polyethylene Ðlm, which increased the transmission by a factor of 2. The bandpass Ðlter is now large enough that it does not vignette the beam, an increase of 20% in throughput. The JFETs have been replaced with ones that are quieter. We have also installed
1 Present address : Caltech, Mail Code 320-47, 1200 East California Boulevard, Pasadena, CA 91125.
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SUBMILLIMETER ARRAY POLARIMETRY new bolometers into the Hertz arrays that have improved responsivities and electrical noise-equivalent powers (NEPs). The result is that the major contributor to the noise is now background photon noise. The new JFETs are 2N6451 devices manufactured by InterFET. When the JFETs are operated at D145 K, the combined JFET and preampliÐer noise is approximately 10 nV Hz~1@2 at the signal frequency of 3.1 Hz. A new set of 64 bolometers was installed into Hertz in 1997 March. The thermistor components are 250 km cubes of neutron transmutation doped germanium (Haller 1994) with doping designation 10 (NTD-10 Ge). The bolometer leads are 0.001 inch NbTi. Compared with the previous bolometers in Hertz, the new ones have a lower dynamic thermal conductance G in order to reduce the thermal phonon contribution to the total NEP. We measured G \ 1È3 nW K~1, NEP \ (1È2) ] 10~16 W Hz~1@2, electrical and an average electrical responsivity of 1.5 ] 108 V W~1 for the bolometers, as described in the Appendix. A further improvement to the instrument is that the malfunctioning pixels have been repaired. As of 1997 September, all 32 pixels are functioning. The polarization modulation efficiency has also been improved from 86% to 95% by simply rotating the polarizer by 90¡. In the old conÐguration, the wires were parallel to the plane of incidence of the incoming radiation ; they are now perpendicular to the plane of incidence. 2.2. Quantum Efficiency The interference Ðlter that deÐnes the 350 km bandpass was manufactured by QMC Instruments. The spectral response of the Ðlter, as measured by the manufacturer, is shown in Figure 1. The measurement was made at 300 K, and we assume that the bandpass is not signiÐcantly di†erent at the 4 K operating temperature. The maximum transmission is 78% at a wavelength of 353 km. The transmission drops to 10% of maximum at 320 and 382 km, so we adopt a bandwidth of 62 km (150 GHz) in discussing the quantum
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efficiency. This bandwidth includes greater than 95% of the energy incident on the detector from a blackbody emitter. There are losses in transmission from other elements in the optical path. These are summarized in Table 1. The transmission of the window, half-wave plate, mesh low-pass Ðlter, black polyethylene, and bandpass Ðlter have been measured at room temperature. The transmission of each quartz lens is assumed to be the same as that of the halfwave plate. We estimate the transmission of the array lens and assume perfect reÑection from the mirrors and perfect splitting of the beam by the polarizer. For the 62 km bandpass, the predicted value for the total transmission is 12%. We consider the quantum efficiency for a single detector, and the polarizer is counted as a 50% transmission loss. In order to measure the actual quantum efficiency, we use two methodsÈa DC method and an AC method. In the DC method, a bolometer is exposed to radiation from a 300 K load Ðlling the acceptance angle of the optics. The temperature (resistance) of the bolometer is recorded for a certain bias voltage. Next, the radiation load is removed via an internal 4 K blank-o†. A larger amount of electrical power is applied to the bolometer so that the temperature is the same as before. The change in electrical power is equal to the prior radiation load and is found to be 0.08 nW. For the f-ratio and collector area of Hertz (Paper I) a power of 4.9 nW is expected for perfect quantum efficiency (and no polarizer). Therefore, the total quantum efficiency from the DC method is 1.6%. In the AC method, a chopped 1000 K blackbody source of relatively small angular extent is focused onto Hertz. The AC voltage response of the bolometer is ampliÐed, and its amplitude is recorded. The voltage is converted to a power using the responsivity of 1.5 ] 108 V W~1 (Appendix) and compared with the expected power for perfect quantum efficiency. For the AC method, we derive a total quantum efficiency of 1.8%. We now compare the observed actual quantum efficiency with the expected one. If the Winston cone, integrating cavity, and detector were 100% efficient, we should measure a quantum efficiency of 12%. The observed quantum efficiency is 1.6%È1.8%, a deÐciency of a factor of 7È8. The origin of this loss of signal is not understood. It is hard to imagine that our estimate of the loss through the lenses and Ðlters could be so far o†. Our best guess is that the losses occur in the Winston cone and/or integrating cavity. The problem is probably not inefficient absorption into the TABLE 1 TRANSMISSION OF HERTZ OPTICS
FIG. 1.ÈTransmission of bandpass Ðlter in Hertz at room temperature. We assume that the bandpass when the Ðlter is at D4 K is essentially the same. The peak transmission is 78% at 353 km. The transmission drops to 10% of that at 320 and 382 km. The blocking at longer wavelengths is excellent. Any leaks in the Ðlter at shorter wavelengths are blocked by other low-pass Ðlters in the instrument. Also shown is the zenith atmospheric transmission measured from the CSO during good weather, characterized by approximately 0.8 mm of precipitable water vapor and q B 0.05 (Serabyn et al. 1998). 225 GHz
Element
Transmission (%)
Polyethylene window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Crystal quartz Ðeld lens with AR coating . . . . . . . . . . . . . Two mirrors (aluminum coating) . . . . . . . . . . . . . . . . . . . . . . . Crystal quartz half-wave plate with AR coating . . . . . . Low-pass mesh Ðlter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Black polyethylene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bandpass Ðltera . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Crystal quartz pupil lens with AR coating . . . . . . . . . . . . Mirror (aluminum coating) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Polarizerb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Polyethylene array lens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Total transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
87 96 100 96 84 86 47 96 100 50 92 12
a In 150 GHz bandpass. b Assuming unpolarized light input.
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DOWELL ET AL.
bolometer, despite the fact that the NTD Ge chip Ðlls only 8% of the integrating cavity cross section and does not have an absorbing element. We tested a few composite bolometers Ðlling a larger fraction of the integrating cavity with an absorber, which resulted in no improvement. We also tried blackening a few bolometers with Sty Cast 2850 FT epoxy, again with no improvement. In estimating the quantum efficiency for the combined Hertz/CSO optical system, we assume no loss in transmission from the Ðve telescope mirrors. However, we allow for an imperfect coupling to point sources (° 5.1.1). 3.
OBSERVING METHOD
The standard observing sequence that we use at the CSO is illustrated in Figure 2. We use rapid chopping of the secondary mirror and slow nodding (position switching) of the telescope to subtract the background emission from the source signal. The signals from the bolometers are demodulated by a digital signal processor, using sine waves with frequency and phase synchronized with the chopper. The demodulation is performed for two chopper cycles to form the basic data unit of one ““ frame.ÏÏ An eight-frame ““ integration ÏÏ is accumulated with the telescope in left beam. The telescope is moved to right beam, where two
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integrations are performed. The telescope is then returned to left beam for a Ðnal integration. The left-rightÈright-left observing pattern is called a ““ nodpair ÏÏ and is sufficient for measuring total Ñux. To measure polarized Ñux, we step the half-wave plate between nodpairs. A ““ Ðle ÏÏ consists of six nodpairs at half-wave plate positions 0¡, 30¡, 60¡, 90¡, 120¡, and 150¡. During standard observations, the secondary mirror is chopped at 3.1 Hz with a throw of 2@È8@ in azimuth. The duty cycle of the chopper (time within D6A of stationary positions divided by total time) ranges from 70% to 40%, depending on the chop throw. The telescope is nodded at D0.02 Hz. On account of lost time during nodding and half-wave plate rotation, the observing efficiency (integration time divided by total time) is 45%. A sixnodpair Ðle lasts 5 minutes. We normally observe a Ðxed grid of positions on the sky in order to build up a sufficient signal-to-noise ratio. The grid spacing is equal to the detector spacing (17A. 8 ^ 0A. 5), meaning that the image will be undersampled. For bright sources, the undersampled map can be Ðlled in with observations o†set from the primary grid. To extract the instrumental polarization from the source polarization, we translate the array on the sky by whole
FIG. 2.È““ Strip chart ÏÏ record of the frames accumulated during a single Ðle. The R and T detectors shown here (pixel 14) were centered on the source IRC]10216 (F \ 30 Jy ; Sandell 1994). Each point on a curve is one frame, the fundamental unit of stored data that is accumulated for two cycles of the l chopping secondary (D0.6 s). The T frames have been multiplied by a normalization factor f to bring them to the same scale as the R frames. Correlated sky noise is evident in R and T as well as in their sum. The correlated noise is subtracted away by taking the di†erence (R [ fT ). The organization of the data collection is labeled at the top. Individual integrations in left or right beam and nodpairs are enumerated. The source Ñux is evident as a deÑection in the R and T signals as the telescope is moved from left to right beam, most clearly observed in nodpair 2. Polarized Ñux from the source is not seen since it is weaker than the noise level. The frames were not collected continuously ; time gaps occur during nodding and half-wave plate rotation.
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pixel amounts and perform 90¡ rotations of the instrument (Platt et al. 1991). Since the CSO has an altitude-azimuth (alt-az) mount, instrument rotation is also required to follow the apparent rotation of the sky. It is necessary to monitor and Ðne-tune the pointing of the telescope. For sources with distinct peaks, the monitoring is nearly continuous and the pointing is approximately 4A rms. Otherwise, the pointing is checked every 1È2 hours, in which case the pointing errors may increase to 6A rms. 4.
DATA ANALYSIS
4.1. Polarimetry with T wo Detector Arrays Hertz contains a single polarizer at 45¡ incidence to the incoming beam and two identical detector arrays, one observing the reÑected polarization (the R array) and one observing the transmitted polarization (the T array). The arrays are aligned to 3A accuracy on the sky by tilting and translating the polarizer. The adjustment mechanism is operable when the Dewar is cold. The signals from two detectorsÈone in the R array and one in the T arrayÈare used to measure polarization. The polarization signal (Platt et al. 1991) is given by R [ fT h, S \ h (1) h R ] fT h h where h is the half-wave plate angle and f is a normalization factor (the responsivity of R divided by the responsivity of T ). S is expected to have a sinusoidal variation with amplitude hequal to the polarization P, and the phase of S correh sponds to the polarization position angle. Each value of R and T corresponds to one nodpair h composed of 32 individual (left-rightÈright-left hsequence) frames of data. The variations in signal on a frame-by-frame basis can be used to estimate the uncertainties in R and T . h h However, it is important to take into account the observed correlation between the noise in the R frames and the noise in the T frames when calculating the huncertainties (Fig. 2). h The correlated noise is dependent on weather, chopper throw, and chopper rate and is presumably due to sky noise (Ñuctuations in the emission from the sky background). The correlated Ñuctuations cancel in the numerator of the polarization signal (eq. [1]) and add in the denominator. The method we have chosen for the error analysis is as follows. First, the normalization factor f is determined for each pixel pair and for each Ðle (thereby requiring no longterm stability) using both the source Ñux and the correlated noise. We assume that the uncertainty in f is negligible. Second, the frames are reorganized by deÐning two new quantities : PF \ R [ fT , (2) hi hi hi TF \ R ] fT (3) hi hi hi where the index i refers to the frame number. Third, the values and uncertainties of PF (polarized Ñux) and TF h (total Ñux) are calculated and propagated through to theh polarization signal. The noise in PF appears to be random. In order to hi uncertainty, the frames for each intecalculate PF and its h gration (a single left or right) are averaged. For each integration, a standard deviation of the mean is also calculated. The left beam integrations and right beam integrations are di†erenced, and the uncertainties are propagated assuming
591
independence, yielding PF and p(PF ). Bad frames (less h h than 2% of total frames) are discarded using ChauvenetÏs criterion (Taylor 1982). We call this method ““ frame-rate statistics.ÏÏ The Ñuctuations in TF contain signiÐcant power on hi timescales longer than the 5 s integrations (i.e., baseline drifts). Thus, using the frame-rate method to calculate the uncertainty in TF would be an underestimate. This is h evident as statistically signiÐcant ““ detections ÏÏ of positive or negative emission in integrations on the blank sky in the case that frame-rate analysis is used. Our method for calculating the uncertainty in TF is to h disregard the uncertainties from the statistics at the frame level. The values of TF for the six nodpairs in a Ðle are h combined to form a single standard deviation p(TF). This method (““ nodpair-rate statistics ÏÏ) accounts for noise on timescales as long as the duration of a Ðle and is therefore conservative. The polarization signal and its uncertainty are now PF S \ h, (4) h TF h p2(PF ) ] S2 p2(TF) (5) h h . p(S ) \ h TF2 h Following the calculation of S and p(S ), the polarization h analysis is as described by Platthet al. (1991). Submillimeter polarization is typically small (S D 1%). h deterTherefore, it is the uncertainty in PF that usually h mines the sensitivity of polarization measurements. (See eq. [5].) The subtraction of correlated sky noise from PF , h which is accomplished by the two detector arrays, signiÐcantly improves the sensitivity. We can evaluate our choice of error analysis methods by looking at the signal-to-noise ratio (S/N) for measurements of blank sky. For a sample of observations covering the duration of the 1997 April observing run, the median S/N using nodpair-rate analysis of TF , i.e., TF /p(TF), was 0.9. h analysis h of PF , i.e., The median S/N for frame-rate PF /p(PF ), was also 0.9, even though the noise was a hfactor h lower. h The results for both methods are in adequate of D8 agreement with random noise.
S
4.2. Polarization Angle Calibration and Efficiency The o†set in angle of the polarization measurements is determined by installing a polarizer into the beam between the secondary mirror and Cassegrain focus and observing a bright source. The position of the polarizer is known with respect to the altitude/azimuth directions of the telescope to within ^2¡. For the observing runs in 1996 December, 1997 April, and 1997 September we measured the same polarization o†set angle to within 1¡, which was expected since the half-wave plate and instrument alignment were not altered. The angle calibration was conÐrmed to within 5¡ by comparison of our measurements of M42 BN-KL and DR21 Main with results in the literature. From the same experiment, we have also obtained a lower limit to the polarization modulation efficiency of Hertz. The measured polarization efficiency at the CSO was 91%, while the observed polarization efficiency in the lab was 96%. The polarization results have been corrected for a polarization efficiency of 95% because the lab measurement should be more accurate.
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4.3. Instrumental Polarization The instrumental polarization of Hertz at the CSO is modeled by the sum of two componentsÈa constant Hertz component and a rotating telescope component, described from the viewpoint of Hertz. This is also the model that was used for the Stokes polarimeter on the Kuiper Airborne Observatory (KAO) (Platt et al. 1991). Furthermore, since both the CSO and KAO are alt-az telescopes and the bolometer arrays have the same layout, the analyses are essentially identical. The Ðt to the 1997 April data, for which we have achieved the highest S/N to date, yields a reduced s2 of 1.23. The uncertainties in the determination of the instrumental polarization are given below. The antireÑection (AR) coating of the lenses, in addition to improving the transmission, also had the desirable e†ect of reducing the Hertz polarization. The radial polarization pattern seen prior to the AR coatings (Paper I) is no longer visible. The Hertz polarization varies somewhat across the array, ranging from 0.10% to 0.36% ; this amount of polarization is expected from the polyethylene window. The median statistical uncertainty in the determination of the Hertz polarization is 0.02%. The position angle varies by 39¡ across the array. The telescope (rotating) component of the instrumental polarization that we calculate from the multiple regression is 0.12% ^ 0.01%. It is difficult to identify the source of the telescope polarization since it is at approximately the systematic error level (° 5.3) and since we measured a signiÐcantly di†erent angle in 1997 September, although the magnitude is nearly the same. The angle of the Hertz (constant) component was more nearly the same for the two runs, probably due to the fact that it is larger. We have assumed that the telescope polarization is uniform across the bolometer array. We also performed a Ðt of the 1997 April data in which each pixel has a separate telescope component associated with it. The instrumental polarization for this Ðt di†ered from the standard Ðt by as much as 0.11% across the array ; however, the typical disagreement was much less. The inÑuence on the derived source polarization is negligible.
Vol. 504 5.
PERFORMANCE
5.1. Point-Source Response To determine the response of the instrument to a point source, we use observations of the planets Mars, Jupiter, Saturn, and Uranus, which range in size from a fraction of the Hertz beam to a few Hertz beams. 5.1.1. T otal Flux
We mapped the response of the instrument to Mars on 1997 April 20 using a
[email protected] chop throw. The sampling pattern formed a grid with spacing 9A in the center of the map and 18A (the detector spacing) at the edges of the map. The intensity as a function of angular radius is shown in Figure 3. The measured beam FWHM is 24A. After correction for the width of Mars (12A. 5), the point-source response has an FWHM of 20A. Observations of Mars on 1996 December 20, when the diameter was 7A. 3, and of Uranus (3A. 6) on 1997 September 25 conÐrm the beam FWHM of 20A ^ 2A. The beam proÐle has a compact core with extensive wings, presumably due to imperfections in the primary and/or secondary mirrors. There is also an elongation in the direction of the chop. For the 10% contour, the elongation is D25%. The intensity falls more rapidly than h~2 for h Z 75A so that the integrated Ñux will asymptotically approach a Ðnite value. However, since the map extends to only 105A, there are uncertainties in extrapolating to obtain the total Ñux. The encircled Ñux as a function of radius is shown in Figure 4. We approximate that D10% of the total Ñux lies beyond the mapped region. With this approximation, the amount of Ñux from Mars in the central pixel is 18% of the total Ñux. Since Mars is not a true point source, we must make an upward correction to this number for calculation of quantities such as the point-source noise-equivalent Ñux density (NEFD). Based on comparison with the beam map of Mars from 1996 December 20, we Ðnd that 25% of the Ñux from a point source is captured by the central pixel. The four adjacent pixels each receive D5% of the total Ñux. 5.1.2. Polarized Flux
We also made polarization measurements of Mars during 1997 April in order to quantify the polarized Ñux beam of
4.4. Detector Gain Calibration Although Hertz is used primarily to measure polarization, it measures Ñux simultaneously. To generate accurate Ñux maps, we must correct the observed signals for the gain of each detector. Our gain calibration procedure requires no additional observing time as the gains are derived from the polarization observations. During the observations, the array is shifted on the sky by translations and rotations at 5 minute intervals (° 3). Pairs of detectors observe the same positions on the sky, yielding values of r Èthe ratio of the gain of detector i and the gain of detectori, jj. We solve for the detector gains g by minimizing : i S2 \ &(g [ r g )2 , (6) i i, j j with the additional constraint Sg T \ 1.0 . (7) i We calibrated the detector gains for the 1997 April and September data independently. The gains agreed to better than 10% for all pixels, so they are very stable.
FIG. 3.ÈIntensity as a function of angular radius. The source, Mars, had an angular diameter of 12A. 5 at the time of the observations. Each point corresponds to an average of measurements from several pixels. In the center of the map, the grid spacing was 9A. At the edge of the map, the grid spacing was 18A. The intensity has been normalized to 1.0 at the peak. The FWHM of the proÐle is 24A.
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593 5.2. Sensitivity
5.2.1. Atmospheric Optical Depth
The CSO is equipped with a dipping radiometer to measure q (zenith), the atmospheric optical depth 225 GHz toward zenith at 225 GHz. The measurements of this instrument in principle can be used to determine the optical depth at other wavelengths, such as our 350 km bandpass. Due to uncertainties about the absolute calibration of the radiometer, we have compiled several extinction curves to measure the 350 km optical depth. A source is observed as it rises or sets on multiple nights with di†erent atmospheric conditions. The approximate relation of signal to opacity is
FIG. 4.ÈEncircled Ñux as a function of angular radius. The source is Mars. A map is generated with a rectangular grid of spacing 18A (1 pixel). The encircled Ñux is determined by adding the signal values for pixels interior to a given radius. In computing the fraction of total Ñux, we have extrapolated that 10% of the total Ñux lies beyond the edges of the map.
Hertz. In our analysis, we Ðrst subtract the polarization model of ° 4.3 and then examine the residual polarization. Statistically signiÐcant polarization is observed. For the beam centered on Mars, the measured polarization is P \ 0.17% ^ 0.03% with a position angle (maximum electric Ðeld) of 112¡ ^ 5¡ east from north. Interestingly, and perhaps coincidentally, the position angle is within 5¡ of the orientation of the Mars equator. However, the polarization is weak, and conÐrmation is necessary to determine whether Mars is intrinsically polarized. Away from the peak, a radial polarization pattern is evident. For the 13 positions on the sky at which polarization is detected with a greater than 3 p signiÐcance, the median polarization is 0.64%, greater than the instrumental polarization that has been subtracted. At a position one beam away from the peak, the detected polarized Ñux is 0.12% of the peak total Ñux. Elsewhere, the statistically signiÐcant polarized Ñux is no more than 0.05% of the peak total Ñux. The median polarized Ñux across the map, including points with low statistical signiÐcance, is 0.02% of the peak total Ñux. O†-axis polarization e†ects have been noted in other instruments on the KAO (Gonatas et al. 1989) and James Clerk Maxwell Telescope (JCMT) (Holland et al. 1996). For comparison, the o†-axis polarization of Hertz is about 30%È70% of that measured in the JCMT system (Holland et al. 1996). The polarization patterns in Hertz and the JCMT polarimeter are both centrosymmetric ; however, the pattern in the JCMT instrument is azimuthal, while we Ðnd a radial pattern in Hertz. The inÑuence of the o†-axis polarization depends on the intensity distribution of the source. In sources with sharp peaks and faint, weakly polarized extended emission, the e†ect could be signiÐcant. For example, for positions where the intensity is 2% of the intensity of a nearby bright peak, the o†-axis polarization could show up as an observed 1% polarization. In practice, the o†-axis polarization is not signiÐcant for the clouds we have observed to date. The measured polarized Ñux for a majority of positions we observed in 1997 April is at least 10 times the level at which the o†-axis polarization would dominate.
I \ I exp [[k ] airmass ] q (zenith)] . (8) 0 225 GHz A sample extinction curve from 1997 April is shown in Figure 5. The slope of the line, giving the relation between q and q , is k \ 26.9. The mean slope of this 350 km 225 GHz and two other extinction curves from 1997 April is k \ 25.1 ^ 1.0, so we assume hereafter that q \ 25q . (9) 350 km 225 GHz The q refers to an average over the bandpass, across km atmospheric transmission varies signiÐcantly which350 the (Fig. 1 ; Serabyn et al. 1998). The slope that we Ðnd is slightly higher than the value of 22.6 derived by Stevens & Robson (1994) for the 350 km bandpass of the UKT14 photometer at the JCMT during 1992È1993, reÑecting either a change in the radiometer calibration or di†erences in the bandpasses. 5.2.2. T heoretical Sensitivity
We now calculate the NEFD expected for photon noise, using the formula of Mather (1982). We start by calculating the electrical NEP, since its dependence on the atmospheric opacity is slight for q [ 1. We use the following km characteristics for the 350 instrument, telescope, and atmosphere : j \ 353 km, *j/j \ 0.18, quantum efficiency Q \ fa \ 1.7% (° 2.2), ) \ 7.8 ] 10~9 sr, A \ 79 m2, and T \ 270 K. For bad weather (q ? 1) NEP \ s ] 10~16 W Hz~1@2. For 350 3.3 thekm very best electrical weather
FIG. 5.ÈExtinction curve of G34.3 from observations in 1997 April. The signal, observed with a single pixel centered on the source, is plotted vs. the atmospheric optical depth at 225 GHz measured by the CSO radiometer. Each point corresponds to an average signal during a 5 minute Ðle. The signal has been normalized to 1.0 at q \ 0. The linear Ðt shown has a slope of [26.9.
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(q \ 0.8) NEP \ 2.4 ] 10~16 W Hz~1@2. In 350 km electrical both cases, the particle term (proportional to Q1@2) dominates the wave term (proportional to Q1) in the expression for the NEP. To convert the electrical NEP to an NEFD, we use the following formula : NEFD \
C exp (q ) 350 km NEP , electrical gA(*l)Q
(10)
where C is a numerical factor having to do with the method of deriving the source signal and g is the fraction of Ñux from a point source in the central detector (° 5.1.1). Several factors go into the computation of C. First, the signal is a di†erence of the source and reference beams, each with a nominal duration of half the chopper period, contributing a factor of 2 to C. Second, the source is actually in the beam for less than half of the chopper period due to the inertia of the secondary (° 3) ; we estimate a typical enlargement of C by 1.3 from this. Third, the polarized Ñux and total Ñux are calculated from a di†erence or sum of two detectors (R and T), contributing a factor of 2~1@2 to C. Therefore, we estimate C \ 1.8 .
(11)
Assuming g \ 0.25 (° 5.1.1), we expect the NEFD in exceptional weather (q \ 0.8) to be 1.9 Jy Hz~1@2. The 350 kmin bad weather (e.g., q expected performance \ 5) is 2 km orders of magnitude worseÈNEFD \ 170 Jy350 Hz~1@2. 5.2.3. Measured Sensitivity
We now compare the theoretical NEFD with the observed NEFD. For the measurement of the total Ñux, the quantity of interest is TF \ R ] T (° 4.1). For the measurement of the polarized Ñux, we are concerned with the quantity PF \ R[T . Therefore, there are several ways to deÐne the instrumental noise for computation of the NEFD. In the polarimetry data analysis, frame-rate statistics is used for the calculation of the uncertainty in PF , while nodpair-rate h statistics is used to compute the uncertainty in TF . (See ° 4.1.) We also compare the frame-rate statistics ofh TF , h although it is not used in the polarimetry analysis. To summarize, the NEFD computations are as follows : NEFD \ p(PF )t1@2, PF,framevrate h frame-rate statistics ;
(12)
NEFD \ p(TF)t1@2, TF,nodpairvrate nodpair-rate statistics ;
(13)
NEFD \ p(TF )t1@2, TF,framevrate h frame-rate statistics ;
(14)
where t is the integration time not including the time for nodding and rotation of the half-wave plate. The NEFD as a function of optical depth during observations of G34.3 is shown in Figure 6. Because of the correlated noise present, the uncertainties in TF are consistently h smallest values higher than the uncertainties in PF . At the h of q , the nodpair-rate noise in TF is a factor of 10 350than km the frame-rate noise in PF . h higher h The excess noise in TF above background-limited perh formance can have at least three componentsÈ transmission noise (Ñuctuations in source signal due to changes in atmospheric transmission), pointing noise
FIG. 6.ÈSensitivity measurements on G34.3 from 1997 April. Each point represents the result of a several minute integration and shows the median noise across the array. The noise is Ñux calibrated vs. the signal measured in the detector centered on G34.3, assuming 1125 Jy for the source (Sandell 1994). The integration time includes the time spent o† the source during chopping but does not include the time required to nod the telescope and rotate the half-wave plate. Three methods are used to measure the noise (° 4.1) : frame-rate statistics of the total Ñux TF, framerate statistics of the polarized Ñux PF, and nodpair-rate statistics of TF. The theoretical sky-backgroundÈlimited NEFD (° 5.2.2) is shown with the dashed line. The chopper throw was 6@È8@.
(Ñuctuations in signal due to pointing drifts), and sky noise (changes in the relative emission from the atmosphere in the source and reference beams). In principle, one should be able to distinguish the three by observing sources with different brightnesses and Ñux distributions. Without performing a detailed investigation, we speculate that the transmission noise and pointing noise are signiÐcant for extraordinarily bright sources such as G34.3 (F B 1000 Jy) l Jy, where but are insigniÐcant for sources fainter than D100 sky noise dominates. The observed sensitivity is essentially the same as the calculated background limit for the polarized Ñux (PF) measurements over the range of q . The good agreekm uncertainty in the ment is somewhat fortuitous, since350 the theoretical NEFD could be as much as 30%È50%. We give the time required in good weather to measure the polarization of a point source with low polarization, assuming an NEFD of 4 Jy Hz~1@2, as observed for low q , and an observing efficiency of 45% : 350 km 50 Jy 2 0.3% 2 . (15) t \ 0.9 hour F p l P The use of two arrays in Hertz is vital for measurement of the polarization from faint sources given the atmospheric conditions. With only a single array, the correlated sky noise would not be subtracted cleanly, and the observing time required to achieve a certain p could be increased by P an order of magnitude or more.
A BA B
5.3. Other T ests of Systematic Errors in Measuring Polarization In this section, we make an attempt to quantify the systematic errors in polarization measured by Hertz. Up to now, we have identiÐed three systematic errorsÈa system-
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atic uncertainty in polarization angles of ^2¡ (° 4.2), a ¹0.11% uncertainty in the model for the instrumental polarization (° 4.3), and an o†-axis polarization surrounding point sources (° 5.1.2). There is also an uncertainty of several percent in the polarization efficiency, which a†ects only data with very high S/N in polarization. A systematic error that has possibly appeared in another polarimeter is the presence of a background polarized Ñux that corrupts measurements of faint sources (Glenn 1997). We can put a limit on any such systematic error in Hertz from observations of essentially blank sky. During the 1997 April observations we integrated for approximately 4 hours on the faint point source IRC]10216 (F \ 30 Jy ; Sandell l 1994) during good to moderate conditions. We did not detect polarization at the 2 p level for any position on the sky. For the beam centered on IRC]10216, the measured polarized Ñux was 0.075 ^ 0.120 Jy. (The polarized Ñux is calculated as P ] Ñux, and the error in polarized Ñux is calculated as p(P) ] Ñux.) For the 24 positions on the sky located more than one beam away from the source and observed at least half of the time, the maximum value in the polarized Ñux was 0.107 ^ 0.116 Jy. When analyzed in terms of Stokes parameters Q and U, the polarized Ñux distribution across the map is sufficiently random. The absolute values of the mean Q and mean U are less than 0.020 Jy, and the standard deviation of each distribution is less than 0.040 Jy. Erring toward the conservative side, we put a limit of 0.050 Jy on any polarized background Ñux. Thus for sources brighter than 25 Jy, the inÑuence on the measured polarization is less than 0.2%. Our method to test for further systematic errors is to divide the 1997 April data into bins and to compare the source polarization results for the separate bins. Some possible sources of systematic errors that we keep in mind are inadequate subtraction of instrumental polarization, Ñux in the reference beams (Paper I), and a change in the instrumental polarization with elevation due to Ñexure of the telescope. The Ðrst test was to perform independent polarization Ðts for partial segments of the detector array. In the Ðrst case, we considered each quadrant of the array separately. In the second case, we divided the data into the central 16 pixels and the outer 16 pixels. Since the array is translated and rotated on the sky during the observations, positions are observed with more than one segment of the array. We can thus compare the observed source polarizations for several independent data sets. The quantities we considered were dq, the median di†erence in the Stokes parameter q, and the similarly deÐned du. For both binning cases, (dq2 ] du2)1@2 was less than 0.12%. The second test was to divide the data into telescope elevation ranges. By limiting the range of telescope elevation, we are also limiting the range of chopping direction on the sky for each object since the secondary is always chopped in azimuth, and we are also limiting the range of instrument rotation with respect to the telescope since the instrument rotation usually follows the sky rotation. We investigated two elevation cuts, one at 50¡ and the other at 40¡. When we compared the source polarization results for elevations of 50¡È72¡ to the results for elevations of 24¡È50¡, we found (dq2 ] du2)1@2 \ 0.23%. However, the median differences depend signiÐcantly on which source is being considered. For M17, a source known to be extended larger than our chopper throw, (dq2 ] du2)1@2 was 0.32%. For
595
G34.3, a more compact source with a brighter peak, (dq2 ] du2)1@2 was only 0.16%. We thus attribute a large part of the systematic variations in source polarization with elevation to the inÑuence of polarized Ñux in the reference beams, which changes as the sky rotates. For the central region of M17, Dotson (1996) estimated systematic errors due to a reference beam Ñux of 0.1%È0.3% in a 100 km polarization map. We can expect larger errors for the 350 km map since the chopper throw is 20%È30% smaller and not rotatable with respect to the telescope. When the elevation cut was placed at 40¡, a similar trend was observed. For a source in the Sgr A region with the lowest ratio of sourceÈtoÈreference beam Ñux, the polarization varied by as much as 0.5% as the source passed across the sky. For the Sgr B2 core, which is much brighter compared with the reference beams, (dq2 ] du2)1@2 was 0.18%. It is difficult to disentangle the e†ects of reference beam Ñux from other possible causes of systematic errors because of the large extent of many of the sources in our data set. Systematic errors intrinsic to the instrument do not seem to be greater than dP \ 0.18%, and they could be signiÐcantly less. 5.4. Polarization Results Our goal with Hertz is to map magnetic Ðeld structure in molecular clouds. For bright clouds, we can obtain independent measurements for a dozen to a hundred positions. An example polarization map is shown in Figure 7 for the source Sgr B2. The vectors shown in the map are detected with greater than 3 p signiÐcance. The polarization ranges from 2.8% in the southernmost part of the map to under 1.0% for much of the core region. Toward the Main and North sources, the polarization is less than 0.4%, and the
FIG. 7.ÈPolarization of Sgr B2 at 350 km, measured with Hertz. The vectors show the orientation of the maximum electric Ðeld. If we assume polarization by emission, the implied magnetic Ðeld is perpendicular to the vectors. The vector length is proportional to the polarization. All of the vectors shown were detected with greater than 3 p signiÐcance. The contours show the distribution of total Ñux measured simultaneously with Hertz. The contour levels are 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, and 0.9 times the peak Ñux of 3960 Jy in a 20A beam at Sgr B2 Main (Goldsmith et al. 1990). The second peak approximately 50A to the north of Main is Sgr B2 North.
596
DOWELL ET AL. TABLE 2 HERTZ 350 km POLARIZATION DATABASE Source
Date
M42 . . . . . . . . . . . . . . . . . . . . . . G34.3 . . . . . . . . . . . . . . . . . . . . . IRAS 16293[2422 . . . . . . M17 . . . . . . . . . . . . . . . . . . . . . . NGC 2264 . . . . . . . . . . . . . . . o Oph A . . . . . . . . . . . . . . . . . Sgr A . . . . . . . . . . . . . . . . . . . . . Sgr B2 . . . . . . . . . . . . . . . . . . . . DR 21 . . . . . . . . . . . . . . . . . . . . NGC 2024 . . . . . . . . . . . . . . . W3 . . . . . . . . . . . . . . . . . . . . . . . . W51 . . . . . . . . . . . . . . . . . . . . . . W75N . . . . . . . . . . . . . . . . . . . .
1995 1997 1997 1997 1997 1997 1997 1997 1997 1997 1997 1997 1997
Total Measurements
Detections at 3 p
76 53 43 143 45 55 136 177 209 100 73 72 45
45 43 1 114 4 19 106 140 81 31 23 12 3
Oct Apr Apr Apr Apr Apr Apr Apr Sep Sep Sep Sep Sep
measured polarization angles could be inÑuenced by systematic errors. The polarization from Sgr B2 has also been mapped at 60 and 115 km with coarser resolution (Dowell 1997 ; Novak et al. 1997a). The authors concluded that the far-infrared polarization from the Sgr B2 core is due to absorption by cold, aligned grains at the front of the cloud. The e†ects of absorption should diminish at longer wavelengths, however, as the optical depths become smaller and as emission from the cold component becomes more signiÐcant. Indeed, the 350 km polarization from the Main and North sources is as much as a factor of 20 lower than the 60 km polarization. While the 60 and 115 km polarization maps are ““ unusual,ÏÏ with the polarization greatest at the intensity maxima, the 350 km map is ““ normal,ÏÏ with the polarization increasing away from the center. We hypothesize that the 350 km polarization over most of the Sgr B2 map is due to emission from aligned grains. Thus, the polarization vectors are orthogonal to the inferred magnetic Ðeld direction. Our database of 350 km polarization results accumulated through 1997 September is outlined in Table 2. Of this sample, the median polarization is 1.1%, which is a factor of 3.5 above the median statistical uncertainty of 0.3% and a factor of 6 above our estimated systematic error level. The polarization from M42 has been analyzed in detail (Schleuning 1998). The Sgr A results have been reported by Novak et al. (1998). The polarization results for the remaining sources will be published elsewhere. 6.
CONCLUSIONS
We have improved the sensitivity of the 350 km polarimeter Hertz. While the increased sensitivity widens the
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range of objects for which we can measure polarization, it also enhances the inÑuence of the sky noise that is correlated among the detectors. We describe a method of data analysis that takes into account the correlated noise. The noise cancels when taking the di†erence R[T of the signals from the two arrays, i.e., in the measurement of polarized Ñux. The sensitivity for the measurement of polarized Ñux agrees with the theoretical limit calculated for no correlated noise. In good weather, the NEFD for polarimetry is 3È4 Jy Hz~1@2. For many Galactic clouds, it is now possible to map the polarization at dozens of independent positions with 20A resolution. The angular resolution, instrumental polarization (\0.5%), and systematic error level intrinsic to the instrument (¹0.18%) are better than what was achieved on the KAO with the polarimeter Stokes (Platt et al. 1991). Measurable polarization at 350 km appears to be widespread, as is the case at 100 km (Hildebrand et al. 1995), although the two wavelengths often sample di†erent physical components of clouds. The median polarization among the points we have measured to date is 1.1%. The 350 km polarization from the core of Sgr B2 is much lower than that measured at shorter wavelengths. This is consistent with the hypothesis that the 60 and 115 km polarization is due to absorption by aligned grains (Dowell 1997). The polarization mechanism over our 350 km map is predominantly emission. The quantum efficiency of Hertz is low (1.7%) compared with what might be achieved (10%È20%), most likely because of an inefficient design of the Winston concentrators at the focal plane. Improving the quantum efficiency is a medium-range goal for Hertz, since the NEFD per pixel could be lowered by a factor of 3. During such an upgrade we also wish to take advantage of emerging technology in the fabrication of large monolithic arrays of detectors (Bock et al. 1997 ; Wang et al. 1996). We are grateful for the support of the CSO sta† during our observations. We appreciate the advice of J. Ruhl and M. Dragovan regarding JFETs and bolometers. E. Haller and J. Beeman kindly provided the NTD Ge thermistors in a timely manner. We thank S. Meyer for helpful discussions of electrical nonlinearity in bolometers. We thank D. A. Harper for sharing the data acquisition electronics, S. Platt for work on the acquisition software, and D. Cole for the software to do the initial analysis of the data Ðles. The CSO is funded by the NSF through contract AST 96-15025. The authors were supported by NSF grants AST 96-19186 and 97-32326 ; NASA grants NAG 2-1081, NGT-252210, and NGT-51311 ; and NSF Faculty Early Career Development Award OPP-9618319 to G. N.
APPENDIX A BOLOMETER CHARACTERIZATION The thermistor component in the Hertz bolometers is NTD-10 Ge (Haller 1994). The approximate size is (250 km)3. The bolometers are assembled by soldering weakly conducting metal leads to gold contacts on the Ge thermistors with indium. The ends of the leads are soldered with indium to pads on a printed circuit (PC) board located behind the Winston concentrators. The PC board and 20 M) load resistors are cooled to 0.26 K by the two-stage 3He refrigerator. The leads are constructed from 0.001 inch copper-clad NbTi wire. NbTi has a low thermal conductivity at subkelvin temperatures because of its superconducting electrons and anomalously high phonon scattering (Ikebe et al. 1977). A section of the copper jacket near the thermistor is etched away to leave a weak thermal link to the cold bath (Ruhl 1993). The length
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597
FIG. 8.ÈLoad curves for two Hertz bolometers. The bolometer T13 is representative of the ones in the tops of the arrays with higher G (about 3 nW K~1), and T28 is representative of the ones in the bottoms of the arrays with lower G (about 1 nW K~1). The bolometers were exposed to a 300 K radiation load just outside the Dewar window.
of the etch determines G. For the bolometers in the upper half of the Hertz array, the etch length is 0.01 inches, leading to G \ 3 nW K~1. The etch for the bolometers in the lower half of the array is 0.04 inches, yielding G \ 1 nW K~1. The thermal phonon noise of these detectors is NEP \ (1È2) ] 10~16 W Hz~1@2, below the expected background photon noise of electrical NEP \ (2È3) ] 10~16 W Hz~1@2 (° 5.2.2). electrical load curves for the Hertz bolometers are shown in Figure 8. The thermistors have a resistance of D1600 M) at Example the standard cold bath temperature of 0.26 K for a small applied voltage. The resistance when the bolometers are optimally voltage biased is 15È25 M). The NTD-10 Ge thermistors exhibit nonthermal nonlinearity in the load curves caused by the bias electric Ðeld (Kenny et al. 1989). Using a bolometer with very high thermal conductance, we quantiÐed the electric Ðeld e†ect, yielding a functional relationship between the thermistor resistance, its temperature, and the bias voltage. The results for the bolometer thermal conductance, responsivity, and DC quantum efficiency (° 2.2) take the nonthermal behavior into account. Had we ignored the nonthermal e†ects, the results would have di†ered by D30%. The electrical responsivity of the bolometers was calculated from the load curves and the high-frequency bolometer impedance (Mather 1984). The average responsivity is 1.5 ] 108 V W~1, although there is variation by as much as a factor of 3 across the array due to inconsistency in the lead etch length. The bolometers in the bottom of the array have a median responsivity that is 30% less than the bolometers in the top of the array. Given the responsivity of 1.5 ] 108 V W~1, the expected voltage noise caused by background photons (D40 nV Hz~1@2) is a factor of 4 above the ampliÐer noise. The Johnson noise from the 20 M) load resistor (¹5 nV Hz~1@2) is not signiÐcant since the dynamic impedance Z of the bolometer is small. The Johnson noise from the bolometer (D12 nV Hz~1@2) is well below the background photon noise. There is no signiÐcant di†erence in S/N between the top and bottom of the array.
FIG. 9.ÈBolometer electrical circuit. Shown is the signal path for a single detector. The bolometer forms a voltage divider with the 20 M) load resistor. For the bolometers in the top of the array (higher G), the bias voltage is 0.11 V. For the bolometers in the bottom of the array (lower G), the bias voltage is 0.055 V. A JFET voltage follower located in a 145 K box inside the Dewar lowers the impedance of the bolometer signal. The AC-coupled preampliÐer stage is normally operated with a gain of 10,000, and the voltage is digitized with a 16 bit analog-to-digital (A/D) converter. The preampliÐer box bolts onto the outside of the Dewar, and the A/D box is located nearby. The digitized signals are transmitted serially over a Ðber-optic cable to a digital signal processor in the data acquisition computer, located in the observatory control room. The A/D and digital signal processor hardware were designed at NASA Goddard Space Flight Center.
598
DOWELL ET AL.
The bolometers form a voltage divider with the load resistors (Fig. 9). The impedance of the bolometer signal is lowered with a JFET follower and then ampliÐed by the preampliÐer. The electrical time constants of the bolometers average 17 (higher G) and 48 ms (lower G), which is sufficiently fast given the 3.1 Hz modulation frequency. REFERENCES Akeson, R. L., Carlstrom, J. E., Phillips, J. A., & Woody, D. P. 1996, ApJ, Kane, B. D., Clemens, D. P., Barvainis, R., & Leach, R. W. 1993, ApJ, 411, 456, L45 708 Bock, J. J., LeDuc, H. G., Lange, A. E., & Zmuidzinas, J. 1997, in The Far Kenny, T. W., Richards, P. L., Park, I. S., Haller, E. E., & Beeman, J. W. Infrared and Submillimetre Universe (ESA SP-401), ed. A. Wilson 1989, Phys. Rev. B, 39, 8476 (Noordwijk : ESA-ESTEC), 349 Mather, J. C. 1982, Appl. Opt., 21, 1125 Cudlip, W., Furniss, I., King, K. J., & Jennings, R. E. 1982, MNRAS, 200, ÈÈÈ. 1984, Appl. Opt., 23, 3181 1169 Novak, G., Dotson, J. L., Dowell, C. D., Goldsmith, P. F., Hildebrand, Dotson, J. L. 1996, ApJ, 470, 566 R. H., Platt, S. R., & Schleuning, D. A. 1997a, ApJ, 487, 320 Dowell, C. D. 1997, ApJ, 487, 237 Novak, G., Dotson, J. L., Dowell, C. D., Hildebrand, R. H., Renbarger, T., Dragovan, M. 1986, ApJ, 308, 270 & Schleuning, D. A. 1998, ApJ, submitted Flett, A. M., & Murray, A. G. 1991, MNRAS, 249, 4P Novak, G., Predmore, C. R., & Goldsmith, P. F. 1990, ApJ, 355, 166 Glenn, J. 1997, Ph. D. thesis, Univ. Arizona Platt, S. R., Hildebrand, R. H., Pernic, R. J., Davidson, J. A., & Novak, G. Glenn, J., Walker, C. K., & Young, E. T. 1996, Int. J. Infrared Millimeter 1991, PASP, 103, 1193 Waves, 18, 285 Roberge, W. G. 1996, in ASP Conf. Ser. 97, Polarimetry of the Interstellar Goldsmith, P. F., Lis, D. C., Hills, R., & Lasenby, J. 1990, ApJ, 350, 186 Medium, ed. W. G. Roberge & D. C. B. Whittet (San Francisco : ASP), Gonatas, D. P., Wu, X. D., Novak, G., & Hildebrand, R. H. 1989, Appl. 401 Opt., 28, 1000 Ruhl, J. E. 1993, Ph. D. thesis, Princeton Univ. Haller, E. E. 1994, Infrared Phys. Technol., 35, 127 Sandell, G. 1994, MNRAS, 271, 75 Hildebrand, R. H. 1988, QJRAS, 29, 327 Schleuning, D. A. 1998, ApJ, 493, 811 Hildebrand, R. H., Dotson, J. L., Dowell, C. D., Platt, S. R., Schleuning, D., Schleuning, D. A., Dowell, C. D., Hildebrand, R. H., Platt, S. R., & Novak, Davidson, J. A., & Novak, G. 1995, in Proc. ASP 73, Airborne G. 1997, PASP, 109, 307 (Paper I) Astronomy Symp. on the Galactic Ecosystem : From Gas to Stars to Serabyn, E., Weisstein, E. W., Lis, D. C., & Pardo, J. R. 1998, Appl. Opt., Dust, ed. M. R. Haas, J. A. Davidson, & E. F. Erickson (San Francisco : 37, 2185 ASP), 97 Stevens, J. A., & Robson, E. I. 1994, MNRAS, 270, L75 Holland, W. S., Greaves, J. S., Ward-Thompson, D., & Andre, P. 1996, Taylor, J. R. 1982, An Introduction to Error Analysis (Oxford : Oxford A&A, 309, 267 Univ. Press), 142 Ikebe, M., Nakagawa, S., Hiraga, K., & Muto, Y. 1977, Solid State Wang, N., et al. 1996, Appl. Opt., 35, 6629 Commun., 23, 189 Jones, T. J. 1996, in ASP Conf. Ser. 97, Polarimetry of the Interstellar Medium, ed. W. G. Roberge & D. C. B. Whittet (San Francisco : ASP), 381
