Detector Background

Acquisition and Reduction of BATSE Data

2.6 Detector Background

Minimizing with respect to s, we find that the effective impact parameter is

( B2)

^1/2

beff = C -

4A (2.7)

We can achieve additional accuracy by abandoning the step-function model for the occultation edges and instead calculating the relative atmospheric transmission along the line of sight. We will assume an exponential atmosphere with density

(2.8) where h is the scale height of the atmosphere. The optical depth of the atmosphere along this line of sight is

T

=

2µ

fo

^{00 p(q)ds, (2.9)}

whereµ is the mass attenuation coefficient of air and we have assumed that the spacecraft is well outside the atmosphere. Noting that s = q sin() and making a substitution of variables, we have

r1² [ beff ( 1 )] d() T=2µbeffP(beff)J

0 exp---,; cos0-1 ^cos2()' Assuming beff

»

^h, we can effectively make a small angle approximation,

T

~

2µbeff P(beff)

fo

^{00 exp}

(-b;~()

²

)

^d()

µp( beff) J27rbeff h.

(2.10)

(2.11) (2.12) The occultation transmission function is then given by e-^7, which varies monotonically between zero and one over an occultation step. Typical parameter values are h = 6 km, p(70 km)= 3 x 10-³ g cm-³, andµ= 0.3 cm² g-¹.

100.00

I > Q) _10.00 c1.7±0.1

~

~

I

(/)

~ c:

::l

._::, 0

1.00

~ "iii c:

Q)

"O Q)

"§

~ _c: 0.10

::l

u 0

10 100 1000 10000

Energy (keV)

Figure 2.10: Typical count spectrum of the background as a function of energy for a BATSE LAD. The count spectrum is fairly flat in the 20-40 ke V range and is well-described by an E-i.⁷ power law above 40 keV. This plot can be used to predict the LAD background rate in an arbitrary energy range.

For pulsar studies, we are mainly interested in energies below 100 keV. In this regime, the dominant background component is diffuse cosmic emission. The raw 20-60 keV BATSE LAD count rates for one day of data are shown in Figure 2.11. The quasi- sinusoidal variations with a ~ 93 min period are due to the spacecraft orbital modulation of sky area visible to the detectors. At these energies, the maximum background occurs when the detector is facing away from Earth, and the minimum occurs when the detector is facing toward Earth. The large gaps in the data occur during passages of the spacecraft through a region of extremely high background known as the South Atlantic magnetic anomaly (SAA; see Tascione 1988). Due to the extremely high flux of trapped charged particles in this region, the detector high voltage is turned off to prevent electrical breakdown damage.

Smaller gaps due to brief telemetry errors are also sometimes present.

It is instructive to consider the power spectral properties of the BATSE background in the frequency domain. The mean raw background rate in the 20-60 keV DISCLA data is 1500 counts s-¹. A steady, unmodulated photon background of this strength would be a Poisson process and would have a power spectral density of 1500 counts² s-² Hz-¹,

2500 2000 1500 1000 0

0

Detector 0

20000 40000 60000 80000

Detector 1

20000 40000 60000 80000

Detector 2

r-.. r.· rJ /""'\ ,.... F ^AJ~-

ⁱ

r ; ^{tJ r1,} t- ;" :

\ 1 . \I ~ ~ .

v

ⁱ

I \ .. \ . . . .. '\ . "i /, \I .\ I . \ . ;

. . , . . · , · ·V· .v .. \J ·\;·· ·" \i

500~~~~~~~~~~~~~~~~~~~~~~~~~~~~

0 20000 40000 60000 80000

Detector 3

~

I rn

..., c

:J

u 0

0 20000 40000 60000 80000

Detector 4

0 20000 40000 60000 80000

Detector 5

2500 .

~~~~~v

_{1 000 500}

\J

_{. .}

\J'

_{. . . .}

\v/

_{. .}

\j

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\J~\

_{' . . . .}

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^;1L\

_. . v . . .

~J ~J~ ~

_{. .} .v . _{. . .} 'v _. \i

\

_.. "

2500 2000 1500 1000

0 20000 40000 60000 80000

Detector 6

500~~~~~~~~~~~~--'-~~~~~~~~~~~~-'-~~

0 20000 40000 60000 80000

Detector 7

0 20000 40000 60000 80000

Time since MJD 49505.0 (s)

Figure 2.11: Raw DISCLA channel 1 (20-60 keV) count rates from the 8 BATSE LADs on 1994 June 2 (MJD 49505). The data shown are averaged at 50 s intervals. The large off-scale events (e.g., near t = 15000 s) occur at the edges of passages through the South Atlantic magnetic anomaly.

94.0

93.5

"'

2 93.0

:J c

l

"O 0

":ii 92.5

Q_

:s ~

0

~ 92.0

('.)

91.5

91.0~~~~~~~~~~~

8000 8500 9000 9500 1 0000

Julian Date 2,440,000.5

-;;;-

"'

.:::, 0

53

" 52

"O 0 c

"'

c 'O c

"

g

0

~ 51

('.)

"O

·c 0

"

Q_

c

0

"iii 50

"'

"

<.>

a.. ~

49~~~~~~~~~~~

8000 8500 9000 9500 1 0000

Julian Date - 2,440,000.5

Figure 2.12: Decay of the Compton spacecraft orbit. (Left panel:} Evolution of the Comp- ton orbital period. {Right panel:) Evolution of the precession period of Compton's ascend- ing node. The discontinuity of both plots near day MJD 49300 is due to the reboost of the Compton spacecraft during that interval.

independent of frequency. However, as is evident in Figure 2.11, the BATSE background is by no means steady and unmodulated. The strong 93 min orbital modulation results in a large excess of power at frequencies near llGRO ~ 2 x 10-⁴ Hz. In addition, the complicated time structure of the SAA gaps and the sharp occultation edges caused by bright astrophysical sources are also modulated at the orbital period, introducing significant power at higher harmonics of llGRO· There are also power contributions at beat frequencies of llGRO and its harmonics with the Earth's daily rotation period. For analysis of long time series of BATSE data, power contributions at harmonics of the precession frequency of the spacecraft orbit, as well as at beats with these frequencies, are also important. Periodic and secular variations in the spacecraft orbital parameters caused by the tidal perturbations and atmospheric drag (see Figure 2.12) result in a modulation of the relevant families of low-frequency noise peaks in the power spectrum.

The complex low-frequency noise contributions to the BATSE background result in a significant departure from Poisson statistics in the raw data, especially at long time scales (top curve of Figure 2.13). We can improve our sensitivity to pulsed signals by attempting

Pulse period (s)

810000 1000 100 10

10

107

~ _I Raw

N I

N 106

I U1 N~

c

::J 105

.:=, 0

·u; 2';-c Physical model 104

Q)

u

L Q)

;;:

0

Cl. 103 ^{- - -.} - - - -. - - - - Poisson noise level

102

0.0001 0.0010 0.0100 0.1000 1.0000

Pulse frequency (Hz)

Figure 2.13: Typical pulse frequency dependence of the BATSE LAD background in the 20-60 ke V range. The top curve is for the unprocessed raw data. The middle curve is for the raw data after subtraction of an ad hoc background model. The bottom curve is for the raw data after subtraction of the Rubin et al. (1996) physical background model.

The dotted line shows the Poisson noise level expected for the raw count rates. For both versions of the background subtraction, the background fluctuations are consistent with the Poisson level on time scales ;S 100 s. The data shown are for DISCLA channel 1 (20-60 keV) from LAD 0 on 1994 June 2 (MJD 49505). A peak near 0.28 Hz due to the pulsar 4U 0115+63 is visible in the background-subtracted data.

to remove the background contributions. There are two basic approaches to this task:

• Ad hoc background model. We can construct an ad hoc model for the background by removing impulsive spikes and interpolating over gaps in the raw data and then smoothing. The resulting time series is a good approximation to the orbital background variation, which can be subtracted from the raw data. Any sort of smoothing or averaging will affect low-frequency signals as well as background. To keep track of this explicitly, we perform the smoothing in the frequency domain by multiplying the Fourier transform of the interpolated raw time series by a frequency-dependent (low pass) filter function

R(v) = {

~ (i+cosn;,)

^{for v < vo}

for Vo < ^v < ^VNyq

(2.13)

where v₀ is the cutoff frequency of the low-pass filter and ^ZINyq is the Nyquist frequency of the time series. (For all of the analysis presented in this thesis, vo

=

1.6 x 10-³ Hz). We then use the inverse Fourier transform of this product as an approximate background model, which we subtract from the raw time series. After this subtraction, we discard the interpolated segments by reintroducing the original gap structure into the background-subtracted time series. The power spectrum of a time series with the ad hoc background model subtracted is shown in the middle curve of Figure 2.13.

Most of the noise reduction is from the elimination of broadband "ringing" harmonics introduced by spikes and gaps. We emphasize the explicit side effect of this technique, that real signals with periods ~ 1/vo ::::::; 640 s are attenuated along with the noise background.

• Physical background model. Both the BATSE instrument team (Rubin et al.

1996) and investigators at JPL (Skelton et al. 1993) have developed semi-empirical physical models for the known sources of background in the BATSE data. The Rubin et al. (1996) model includes the diffuse cosmic gamma-ray background, the atmospheric gamma-ray background caused by cosmic ray interactions, the prompt background due to cosmic ray interactions with material on the spacecraft, the delayed internal background caused by activation of spacecraft material by cosmic rays and trapped particles in the SAA, and occultation edges due to bright astrophysical sources. This technique assumes the presence of periodic behavior at harmonics of the orbital period, so some attenuation of low frequency signal as well is inevitable in the fitting process.

For both methods of background subtraction, the noise power is consistent with the Poisson level on time scales ;:; 80 s. However, at longer time scales, a strong noise red-noise compo- nent is still present, although at a substantially reduced level compared to the original time series. The physical background model performs somewhat better than the ad hoc model at long time scales, yielding a factor of ,..., 3 reduction in the noise power (corresponding to a factor of ,...,

J3

improvement in sensitivity at these pulse frequencies).