Topic 1 Flashcards
Standard candle
Any type of object whose luminosity is known from its other observable properties, thus allowing its distance to be inferred from the difference between its apparent brightness and its true brightness.
Annual parallax / parallax angle
Half the angle that is subtended by its apparent motion against the background stars over the course of a year. One parsec is the distance at which a star would have a parallax of one arcsecond.
Annual parallax equation (parallax angle)
d (pc) = 1/(ω/arcsecond)
ω=parallax
Parallax uncertainties equation
Δd=Δω/ω^2
ω= parallax
Gaia project
This project is mapping the galaxy measuring propper motion and parallaxes of over one billion stars with an accuracy of 10μas.
RR Lyrae Stars
These are pulsating stars that are used as standard candles within our galaxy and in galaxy’s nearby for distances of up to around 1Mpc.
They are easily recognised by their folded light curves which have periods of around half a day. They have an absolute magnitude of approx 0.75.
Cepheid variables
These are pulsating stars that are used as standard candles for distances of up to tens of Mpc.
They have pulsation periods from a few days to several tens of days, and absolute magnitudes between -1.5 and -6.5.
The relationship between their pulsation and there absolute magnitude can be shown such that
Mv = -2.43 log10(P /day) - 1.62
Type la supernovae
This is also used as a standard candle and is believed to form when a white dwarf exceeds a mass of about 1.4 times that of our sun either through accretion, on the combination of two white dwarfs.
The peak brightness of all type la supernovae reach a similar absolute magnitude of Mb = Mv = -19.6 and are useful of measuring distances of up to 1Gpc.
Hubble-Lemaître law
A relationship between the apparent speed at which a galaxy is moving away from us and its distance away. It is used to calculate distance of very far objects.
v=Hod
v is the apparent speed of recession, d is the distance and Ho is the Hubble constant around 70 / s / Mpc.
Convert arcminutes and arcseconds to degrees
Divide arcminutes by 60 and arcseconds by 3600.
25°21’ 300” = 25 + 21/60 + 300/3600 = 25.4333º
Small angle approximation
For any angle smaller than 0.2 rad
sinθ~θ
Convert right ascension into degrees
First convert the time measurement into decimal hours by dividing the minutes by 60 and the seconds by 3600.
Then multiply your decimal hours by be appropriate number of degrees.
6 h 34 m 45.67s = 6 + 34/60 + 45.67/3600 = 6.579353 h
at the equator 1 hour is equivalent to 15° so multiply the decimal hours by 15
6.579353 x 15 = 98.69029º
Precession definition
The slow movement of the rotation axis of a spinning body the earths axis precesses with a period of around 26000 years.
Angular separation with the same right ascension
θ = the difference between the two declination (δ) values.
θ = δ1 - δ2 = Δδ
Angular separation with the same declination (equation)
θ = different in right ascension (α) multiplied by the cosine of their common declination (δ)
θ = (α1 - α2)cos(δ)
Angular separation with a change in declination and right ascension.
You can use Pythagoras’ theorm to combine both angular separation in both declination (δ) and right ascension (α).
θ^2 = (Δα)^2 (cosδ)^2 + (Δδ)^2
Linear separation
Angular separation is how far objects appear to be from eachother, however linear separation is how far apart the actually are. This is calculated using trigonometry.
The sin of the angular separation (θ) = the linear separation (D) / the distance away (d)
Sin(θ) = D/d
Remember to convert to radians and the small angle approximation.
Proper motion definition
This term is mostly used to refer to the movement of a star relative to the background coordinate system.
Proper motion definition
This term is mostly used to refer to the movement of a star relative to the background coordinate system.
Proper motion in right ascension
This is defined as the difference in a RA measurements divided by the time interval that separates them.
μα = (α2 - α1) / Δt = Δα / Δt
Proper motion in declination
This is defined as the difference between two dec measures divided by the time between them.
μδ = (δ2 - δ1) / Δt = Δδ / Δt
Magnitude of proper motion (equation)
The two components of the magnitude of proper motion (μα and μδ) are at right angles to each other so pythagores’ theorem can be used to calculate their magnitude.
μ^2 = (Δα)^2 (cosδ)^2 + (Δδ)^2
If the cosine factor is already included in the proper motion of RA then it will by written as
μα* = (μα)(cosδ)
So the equation becomes
μ^2 = (μα*)^2 + (μδ)^2
Transverse velocity (equation)
The component of a stars velocity in the plane of the sky i.e. In a direction perpendicular to the line of sight of an observer. Typically measured in km/s.
The sine of the magnitude of proper motion (μ) = the transverse velocity (νt) / the objects distance (d)
Sin(μ) = νt / d
Apparent magnitude (m)
A numerical measure of the apparent brightness of a body. For a star it is a measure of the flux received.
Absolute magnitude (M) (equation)
A numerical measure of the intrinsic brightness of a star equal to the apparent magnitude (m) the star would have if observed from a standard distance of 10 pc. The absolute magnitude (M) provides a measure of a stars luminosity.
M = m - 5log10(d /pc) + 5
Extinction and absolute magnitude
The combined effect of the scattering of electromagnetic radiation by a medium and absorption of such radiation by the medium. Due to extinction the equation for absolute magnitude can be rewritten:
M = m - 5log10(d /pc) + 5 - A
A represents an equivalent number of magnitudes by which a stars brightness is diminished.
Reddening definition
An effect of extinction to cause the observed colour of an astrological object to appear redder than its intrinsic colour.
Astronomical colour
The difference measured in magnitudes, of the brightness of an object in two specified wavebands ( eg in the blue ‘B’ and the red ‘R’ wavebands, in which case the difference is denoted mB-mR or simply B-R). Sometimes referred to as colour index.
A larger B - R value would indicate a redder star, where’s a smaller one would indicate a bluer one.
Apparent colour
The difference between two apparent magnitudes.
Intrinsic colour
The difference between two absolute magnitudes. This is indicated by a subscript 0 on the magnitude difference for example:
MB-MR = (B-R)0
Relationship between apparent magnitude and flux
This can be expressed as
m1 - m2 = 2.5log10(F2 / F1)
Where m1 and m2 are the apparent magnitudes of two objects, while F1 and F2 are their respective fluxes.
This can be rearranged to find the ratio of fluxes given a known difference in magnitude
F2 / F1 = 10^((m1 - m2) / 2.5)
Absolute magnitude and luminosities
This are connected using the equation
M1 - M2 = 2.5log10(L2 / L1)
Where M1 and M2 are absolute magnitudes of 2 objects, and L1 and L2 are their respective luminosities.
The equation can be rearranged to find the ratio of luminosities from known absolute magnitudes.
L2 / L1 = 10^((M1 - M2) / 2.5)
Working an objects maximum size from light time travel
The time interval in which an object changes in brightness can be used to calculate its maximum size. This is because information cannot propagate faster than the speed of light.
So if X-ray emissions double in brightness in a few hours, the size of the x-ray emitting region cannot be larger than the distance traveled by the electro magnetic radiation in that time interval. This interval is known as light travel time.
