Документ взят из кэша поисковой машины. Адрес оригинального документа : http://hea-www.harvard.edu/AstroStat/astro193/HW_feb4.pdf Дата изменения: Thu Feb 5 02:18:48 2015 Дата индексирования: Sun Apr 10 09:08:36 2016 Кодировка:

Astro 193 : HW 3
Due Feb 11


Homework 3.1 : Propagate errors
Compute g assuming that a and b are known.

1. 2.

g = a/b
!

g = ln(a)
!

3. g = ln(a)-ln(b)


Homework 3.2 : G21.5
Tsujimoto et al. (2011, A&A 525, A25) carried out spectral analyses of supernova remnant G21.5-0.9 for data obtained from a variety of observatories. They fit an absorbed powerlaw model to all datasets. These are reported in their Table 2.
!

Calculate the estimate and total variance of both model parameters using multiple imputation (using only those values that are not struck out). Compute the degrees of freedom for both parameters. Is a Gaussian approximation acceptable?
!

Present the results in a figure. In order to display the uncertainty on the estimate, assume that it is Gaussian and show the ±1 error bar.


Homework 3.2 : G21.5
A&A 525, A25 (2011) Table 2. Best-fit parameters and uncertainties in the spectral fitting. Label CS0 CS1 CS2 CS3 CS4 CS5 CS6 CS0­6 IS0 RP0 SI0 SI1 SI3 SP0 SX0 SX1 SX2 SX3 SX0+1 SX2+3 EM1 EM2 EP0 Soft Hard 2. 2. 3. 3. 2. 3. 97 90 05 16 93 10 ( ( ( ( ( ( 2. 3. 3. 3. 3. 3. 3. 3. N
H b a

(1022 cm-2 ) 99 07 04 11 16 00 14 07 ( ( ( ( ( ( ( ( 2. 3. 2. 3. 3. 2. 3. 3. 93­3. 01­3. 98­3. 05­3. 11­3. 95­3. 08­3. 05­3. 04) 12) 09) 16) 22) 06) 20) 09) 1. 1. 1. 1. 1. 1. 1. 1. 83 85 82 84 88 81 88 84

2.99 2.99 3.07 (3.03­3.11) 3.18 (3.14­3.22) 3.07 (3.03­3.11) 2.99 2. 2. 2. 3. 2. 3. 88­3. 83­2. 98­3. 08­3. 87­2. 05­3. 07) 98) 13) 25) 99) 16)

2.09 2.05 1.91 1.92 1.90 2.28 1. 1. 1. 1. 1. 1. 77 77 90 93 77 91

2.90 (2.87­2.94) 2.94 (2.91­2.98) 2.74 (2.72­2.77) 2.99 (2.98­3.00) 2.99

1.78 1.84 1.76 1.84 2.05

(10-11 erg Chandra ACIS-S3 (1.80­1.86) 6.10 (6.05­6.16) (1.83­1.88) 6.09 (6.04­6.13) (1.79­1.84) 6.06 (6.01­6.11) (1.81­1.87) 6.04 (5.99­6.09) (1.85­1.91) 6.10 (6.05­6.15) (1.78­1.84) 6.01 (5.97­6.06) (1.85­1.91) 6.03 (5.98­6.08) (1.83­1.85) 6.06 (6.04­6.08) INTEGRAL IBIS-ISGRI (2.02­2.16) ... RXTE PCA (2.04­2.07) ... Suzaku XIS (1.89­1.92) 5.62 (5.59­5.65) (1.90­1.93) 5.73 (5.70­5.76) (1.88­1.92) 5.66 (5.63­5.69) Suzaku HXD-PIN (2.14­2.42) ... Swift XRT (1.73­1.81) 5.79 (5.72­5.87) (1.74­1.81) 5.48 (5.42­5.54) (1.87­1.94) 5.46 (5.40­5.51) (1.89­1.96) 5.46 (5.40­5.52) (1.75­1.80) 5.61 (5.56­5.65) (1.89­1.94) 5.46 (5.41­5.50) XMM-Newton EPIC (1.77­1.80) 5.47 (5.44­5.50) (1.83­1.86) 5.37 (5.34­5.40) (1.75­1.77) 5.07 (5.06­5.09) Joint fitting (1.84­1.85) 5.69 (2.01­2.09) ...



c

F

X,soft

d

s-

1

FX,har cm-2 ) . . . . . . . . . . . . . . . . . . . . . . . .

d

e

Red-2 /d.o.f.

f

0.93/ 302 0.90/ 326 1.04/ 325 0.89/ 327 1.03/ 330 1.06/ 327 1.07/ 326 0.99/2281 1.43/ 9 0.61/ 51 1.04/ 616 1.06/ 632 0.98/ 624 1.40/ 12 0. 1. 1. 1. 1. 1. 99/ 03/ 07/ 14/ 02/ 11/ 421 479 488 478 903 969

4.17 (4.03­4.31) 5.54 (5.45­5.64) ... ... ... 6.10 (5.79­6.42) . . . . . . . . . . . . . . . . . .

... ... ... ... 4.87

1.05/ 264 1.11/ 260 1.13/ 623 1.07/6217 0.96/ 66

Notes. (a) The parentheses indicate the 1 statistical uncertainty of the best-fit value. The values without an uncertainty were fixed in the fitting. ( b) H-equivalent column density of the interstellar extinction. (c) Power-law index. (d) Flux in the 2.0­8.0 keV range for the soft-band instruments. (e) Flux in the 15­50 keV range for the hard-band instruments. ( f ) The goodness of fit with the reduced 2 (Red-2 )and degrees offreedom (d.o.f.).


Homework 3.3 : R
Install R
!

Plot the Normal and t distributions for the estimated quantities in HW 3.2 using R.