PX158 - H4 - exoplanets

introduction

planets that orbits a star other than the sun
$m a s s < 13 m a s s_{j u p i t e r}$ (nuclear fission begins in core for larger masses)
difficult to detect due to:
- faintness: weak emission and reflection
- very small angular separation from the brighter host star

a star will have a doppler shift if it is orbited by an exoplanet
eg:
$r_{j u p i t e r} = 5.2 A U$
$r_{⊙} = \frac{1}{1000} 5.2 \times 150 \times 10^{6} k m = 780, 000 k m$
$P_{j u p i t e r} = 11.9 y e a r s$
$v = \frac{2 π r_{⊙}}{11.9} = 13 m s^{- 1}$
in $1995$ , $51 P e g b$ was discovered in a very short period orbit: 'hot jupiter' with $T_{e q} \approx 1000 t o 2000 K$
- ' $b$ ' represents an exoplanet, ' $B$ ' represents a binary companion
the earth will only induce a RV signal on the sun at a level oh $\sim 10 c m s^{- 1}$
spectrographs had precision at $\sim 1 m s^{- 1}$
best spectrograph: ESPRESSO on VLT $\sim 10 c m s^{- 1}$
a problem is that the surface of stars are active and dynamic, causing variations in RV measurements
currently, $> 1000$ exoplanets have ben discovered via the RV method, all have mass ( $m \sin i$ , minimum mass)

δ = {(\frac{R_{p}}{R_{s}})}^{2}

for jupiter: $δ_{j u p i t e r} \approx 0.01 \approx 1 %$
WASP project found $100 +$ 'hot jupiters' using transit method
planets must be close to $i = 90 °$
the radius is learned, and if RV is obtained, the mass is learned, which can be used to learn the bulk density
currently, $> 5000$ exoplanets have been discovered by the transit method. some do not have RV measurement
assuming a circular orbit, $D$ is the duration of transit, $α$ is the angle subtended at the centre:

\begin{matrix} D = \frac{α}{2 π} P \\ l = R_{s} + R_{p} \\ \sin (\frac{α}{2}) = \frac{l}{a} = \frac{R_{p} + R_{s}}{a} \\ α = 2 \arcsin (\frac{R_{p} + R_{s}}{a}) \\ D = \frac{P}{π} \arcsin (\frac{R_{p} + R_{s}}{a}) \end{matrix}

θ_{E} = \sqrt{\frac{4 G M}{D c^{2}}}

where, $θ_{E} =$ einstein radius, $D =$ source-lens, lens-earth distance

$D \sim 1000 p c$ , $M = 0.5 M_{⊙}$ , $θ_{E} \sim 1 - 2 A U$
extra lensing due to exoplanet causes a spike in flux-time plot ( $\sim 1 d a y$ )
the amplitude of the spike give information on the mass of the exoplanet

α [^{″}] = \frac{r_{s} [A U]}{d [p c]}

eg: $α = 0.01 \frac{A U}{10 p c} = {0.001}^{^{″}}$
gaia can detect planets this way, but needs to way for ~full period, ie: $\sim 12 y r$ for a jupiter type planet

need to observe very nearby and young stars, ie: $d \sim 10 p c, a g e <\sim 100 M y r$
adaptive optics, large telescopes, and space telescopes are used
currently, $5573$ known exoplanets (confirmed)
radius and period of planets are biased by detection methods