Midterm Study

Question 1

Lateral surface area of cylinder

Answer 1

A = pi DL = 2pi RL

• X-rays reflect off side of nearly cylindrical mirror

Question 2

What area of a grazing-incidence X-ray mirror determines its physical reflecting surface?

Answer 2

Lateral Cylindrical area pi DL

Question 3

Projected Area at Grazing Incidence

Answer 3

A eff = A physical sin theta

For small angles sin theta = theta

Question 4

Why is effective collecting area much smaller than physical mirror area?

Answer 4

Photons strike at grazing incidence so only projected area Asintheta collects flux.

Question 5

Degrees to radians

Answer 5

1 degree = pi/180 radians

Question 6

Why must grading angles be converted to radians when using small-angle approximations?

Answer 6

sin theta = theta only works if theta in radians

Question 7

Why can’t X-ray telescopes use normal mirrors like optical telescopes?

Answer 7

X-rays penetrate material unless incident at very small grazing angles.

Question 8

External reflection or grazing incidence reflection

Answer 8

1. X-rays penetrate materials at normal incidence.
2. Reflection occurs at very shallow angles.

Question 9

Grazing Incidence Reflection

Answer 9

1. Reflection occurs when angle is below critical angle.
2. Critical angle decreases as photon energy increases.
3. Soft x-rays reflect more easily than hard x-rays.

Question 10

Why does effective area decrease for harder x-rays?

Answer 10

Because critical grazing angle decreases with increasing photon energy.

Question 11

Nested Mirrors

Answer 11

1. Multiple mirrors increase collecting area without blocking each other.

Called confocal grazing-incidence mirror nest.

Question 12

Why are grazing-incidence mirrors nested?

Answer 12

To increase total collecting area without increasing telescope diameter excessively.

Question 13

Physical Area vs. Effective Area

Answer 13

Physical area is actual reflecting surface and effective area is projected area that intercepts photons—this area depends on grazing angle.

Question 14

What does instrumental uncertainty depends on?

Answer 14

Sensitivity proportional to Aeff

More effective area —> more photons —> better signal-to-noise

Question 15

Why are X-Ray telescopes so long?

Answer 15

To compensate for small grading angles and increase collecting area via mirror.

Question 16

What are trade-offs with X-Ray telescopes design? Purpose?

Answer 16

Smaller grazing angle —> better reflection of harder x-rays —> smaller projected area without blocking
Do design balances reflectivity vs collecting power.

Question 17

Wien’s Law (BBR)

Answer 17

Lambda max T = 0.29 cm

E peak = 2.8 kT

Question 18

How do you estimate temperature from X-Ray spectrum peak?

Answer 18

Use E peak = 2.8kT

X-ray spectra peaking at few keV —> T ~ 10^7 K

Question 19

How do you estimate radius of thermal X-ray source?

Answer 19

Rearrange L = 4piR^2 sigma T^4

Question 20

Blackbody Luminosity

Answer 20

L = 4piR^2 sigma T^4

where sigma = 5.67 x 10^-5 erg/s/cm^2/K^4

Question 21

How can you tell an X-ray spectrum is thermal black body?

Answer 21

It has smooth peak an exponential high-energy cut off.

Question 22

Luminosity-Flux-Distance Relation

Inverse Square Law

How do you compute observed flux from luminosity?

Answer 22

F = L / 4pid^2

Rearrange when needed

Question 23

kpc to cm Conversion

Answer 23

1 kpc = 3.086 x 10^21 cm
10 kpc = 3.1 x 10^22 cm

Question 24

How do you convert energy flux to photon flux?

Answer 24

Energy flux in erg/s/cm^2

Photon Flux = F/E

where E = keV x 1.6 x 10^-9 erg

Question 25

Poisson Noise: The hat is the noise in photon counting?

Answer 25

Total Counts: T = S + B Noise is root (S + B)

Question 26

Signal-to-Noise Ratio & Detection Criterion

Answer 26

SNR = S / root(S + B) S / root(S + B) > 10

Question 27

Counts from Count Rate

Answer 27

Source Rate: Rs —> S = Rst Background Rate: Rb —> B = Rbt Then SNR becomes: SNR = Rs root(t) / root(Rs + Rb)

Question 28

Exposure Time: how does required exposure time scale with SNR?

Answer 28

t = (SNR)^2(Rs + Rb)/ Rs^2

Question 29

Why longer exposure increases SNR?

Answer 29

Because signal proportional to time, noise proportional to root(time) thus SNR proportional to root time.

Question 30

What limits sensitivity?

Answer 30

Background counts, effective area, detector quantum efficiency.

Question 31

Why do X-Ray flux tools (PMMS) matter?

Answer 31

They include effective area vs energy, detector quantum efficiency and galactic absorption

Question 32

Eddington Luminosity

Answer 32

L edd = 2 x 10^38 erg/s for Neutron Stars