10.3 Practical: Find the Zero Point and Transformations
155
Second-Order Extinction and the Zero Point
In the context of a V filter observation, we can rearrange (10.4) to
V = v − k
v X + T v (CI ) + ZP v .
(10.6)
As the second-order fields are all imaged at the same air mass we can safely ignore
the first-order part of (10.6), reducing it to
V − v = T v (CI ) + ZP v .
(10.7)
You should be able to see that (10.7) is the equation of a straight line with T v (CI )
the gradient of the line and ZP v the intercept.
You need to find the mean values for your v band and r band instrumental magnitudes (v and r respectively) for each standard star in the field. Plotting V − −v
against V − R and fitting a straight line to this plot yields the V band colour transform T v as the gradient and the V band zero point ZP v . Performing the same plot
with R − −r against V − R produces the colour transform and the zero point for the
R band.
Once this is done, you need to find the hidden transformations. These are effectively adjustments from your instrumental setup’s colour index to the standard one.
They are hidden because they do not appear in (10.4). They are found by plotting
V − R against v − −r and fitting a straight line to give T vr as the gradient and ZP vr
as the intercept. Undertaking the same process for R − V against r − −v gives T rv
as the gradient and ZP rv as the intercept.
First-Order Extinction
We now move on to our first-order field. We know that the colour transformation and
the zero point are air mass independent and that they are constant during a night’s
observation. So, if we vary the air mass at which we observe calibration stars, the
change in instrumental magnitude when adjusted for colour transformation and zero
point is due to the change in X . Hence, we can find the extinction coefficient.
In order to determine K
v , we need to plot the adjusted mean instrumental magnitude v adj against air mass: v adj and r adj are found by applying
v adj = V − v − (T v × V − R).
(10.8)
Plotting v adj against X and fitting a straight line gives the first-order extinction
coefficient k
v as the gradient, which should always be positive. It should also always
be greater than or equal to k
r . The interception point should be very close to the zero
point of the filter in question.
155
Second-Order Extinction and the Zero Point
In the context of a V filter observation, we can rearrange (10.4) to
V = v − k
v X + T v (CI ) + ZP v .
(10.6)
As the second-order fields are all imaged at the same air mass we can safely ignore
the first-order part of (10.6), reducing it to
V − v = T v (CI ) + ZP v .
(10.7)
You should be able to see that (10.7) is the equation of a straight line with T v (CI )
the gradient of the line and ZP v the intercept.
You need to find the mean values for your v band and r band instrumental magnitudes (v and r respectively) for each standard star in the field. Plotting V − −v
against V − R and fitting a straight line to this plot yields the V band colour transform T v as the gradient and the V band zero point ZP v . Performing the same plot
with R − −r against V − R produces the colour transform and the zero point for the
R band.
Once this is done, you need to find the hidden transformations. These are effectively adjustments from your instrumental setup’s colour index to the standard one.
They are hidden because they do not appear in (10.4). They are found by plotting
V − R against v − −r and fitting a straight line to give T vr as the gradient and ZP vr
as the intercept. Undertaking the same process for R − V against r − −v gives T rv
as the gradient and ZP rv as the intercept.
First-Order Extinction
We now move on to our first-order field. We know that the colour transformation and
the zero point are air mass independent and that they are constant during a night’s
observation. So, if we vary the air mass at which we observe calibration stars, the
change in instrumental magnitude when adjusted for colour transformation and zero
point is due to the change in X . Hence, we can find the extinction coefficient.
In order to determine K
v , we need to plot the adjusted mean instrumental magnitude v adj against air mass: v adj and r adj are found by applying
v adj = V − v − (T v × V − R).
(10.8)
Plotting v adj against X and fitting a straight line gives the first-order extinction
coefficient k
v as the gradient, which should always be positive. It should also always
be greater than or equal to k
r . The interception point should be very close to the zero
point of the filter in question.