- Zero point of the P-L relation.
The Zero point of the fiducial P-L relation is tied to the
distance modulus of the LMC. Unfortunately, the current range of
this distance modulus ranges from 18.1-18.7 mag! There doesn't
seem to be a particularly good method (with small systematic
error) for determining the distance to the LMC. For example, if
the Key Project changed their distance modulus to the LMC from
18.5 to 18.3 mag, there would be a 10% (positive) change in
H0 to 79 km/s/Mpc.
The Zero point of the fiducial P-L relation is tied to the distance modulus of the LMC. Unfortunately, the current range of this distance modulus ranges from 18.1-18.7 mag! There doesn't seem to be a particularly good method (with small systematic error) for determining the distance to the LMC. For example, if the Key Project changed their distance modulus to the LMC from 18.5 to 18.3 mag, there would be a 10% (positive) change in H0 to 79 km/s/Mpc.
- NGC 4258 and it's H2O masers
One really neat development over the past decade is the detection
of strong water masers in the nearly edge-on active galactic
nucleus (AGN) galaxy NGC 4258 (Herrnstein
et al. 1999, Newman
et al. 2001, Caputo
et al. 2002).
These masers have very high brightness temperatures
(>1012K), small sizes
(1014cm), and very narrow line
widths (a few km/s). These features conspire to make them ideal
probes of galactic structure and dynamics.
I will leave it to the viewer to get the details from Binney and
Merrifield (Galatic Astronomy) §7.2.4... basically,
we can measure the masers positions relative to the center of the
disk as well as their accelerations by tracking the features in
the spectrum. The spots which appear to be close to the center
of the disk have a measured acceleration of 9.3 ±0.3
km/s/yr. Assuming circular orbits and that newtonian mechanics
is valid, we can use a = v2/r to
get the physical extent of the maser from the center of the
galaxy. Then it's just a matter of taking the physical extent
and your angular distance and getting the physical distance to
the Galaxy (of course, the Herrnstein paper is way more
sophisticated than this).
The result is the best known distance in extragalactic
astronomy... 7.2 ±0.3 Mpc. The Cepheid P-L relation is
calibrated against this now.
- NGC 4258 and it's H2O masers
One really neat development over the past decade is the detection of strong water masers in the nearly edge-on active galactic nucleus (AGN) galaxy NGC 4258 (Herrnstein et al. 1999, Newman et al. 2001, Caputo et al. 2002).
These masers have very high brightness temperatures (>1012K), small sizes (1014cm), and very narrow line widths (a few km/s). These features conspire to make them ideal probes of galactic structure and dynamics.
I will leave it to the viewer to get the details from Binney and Merrifield (Galatic Astronomy) §7.2.4... basically, we can measure the masers positions relative to the center of the disk as well as their accelerations by tracking the features in the spectrum. The spots which appear to be close to the center of the disk have a measured acceleration of 9.3 ±0.3 km/s/yr. Assuming circular orbits and that newtonian mechanics is valid, we can use a = v2/r to get the physical extent of the maser from the center of the galaxy. Then it's just a matter of taking the physical extent and your angular distance and getting the physical distance to the Galaxy (of course, the Herrnstein paper is way more sophisticated than this).
The result is the best known distance in extragalactic astronomy... 7.2 ±0.3 Mpc. The Cepheid P-L relation is calibrated against this now.
- Reddening.
Reddening is relatively boring and well-understood. I point you
to Freedman
1988 and the Galactic extinction law. This is a small source
of systematic error (±1%)
- Metallicity effects.
This is a lot more interesting. Earlier on it was suggested that
there could be a significant metallicity effect to the Cepheid
P-L relation. That is, if there were relatively metal-poor
Cepheids in a given sample their periods could be longer (not as
much opacity). Traditionally, the small scatter that is present
in the P-L relation has been attributed to metallicity
effects. In the past decade there has been a concerted effort to
try and nail down the metallicity dependence of the P-L zero
point but it has proved very difficult. There is a good listing
and summary of experimental and theoretical efforts in the HST
Key Project final results paper (Freedman
et al. 2001)
and they adopt a value that is uncertain by 100% in their work
(-0.2 ±0.2 mag/dex) which is in the midrange of current
values. This issue could use a whole lot of observational and
theoretical work. This is a large source of error (±4%)
- Completeness bias, crowding effects and contamination from
companions.
As is the case with any flux-limited observation (read image),
there can be a loss of dimmer Cepheids that biases the moduli to
smaller distances. This type of bias is referred to as a
completeness bias (or Malquist bias). The Key project folks have
attempted to circumvent this by imposing a low-end period cutoff
for all the galaxies that they measure Cepheids in. This amounts
to ±1% in error.
There also exists the possibility that a Cepheid you measure is
actually coincident with another star. This can be a real pain
in the butt because it is nearly impossible to correct for. It
is possible to quantify the magnitude of such an effect by
inserting artificial stars into real fields at random and then
test how much your distance moduli are off by. Unfortunately it
can be significant... +5%, -0% is what has been determined by Ferrarese
et al 2000... (note that it is -0% because your field won't
have stars in it that take away the light from a co-incident
star)
Another pain in the old rump is the fact that Cepheids in the LMC
and the Galaxy have been found in binary systems. Fortunately,
Cepheids are hella massive and the binary distribution is heavily
peaked towards small masses. This will be negligible (in terms
of relative distances) unless the frequency of binaries in
massive systems varies from galaxy to galaxy.
- Local velocities and the Hubble flow.
Does a local measurement of H0 have anything to do
with the value at larger scales? Our local velocities can affect
the expansion rate we measure. Fortunately, the fact that the
Hubble diagram (distance v. redshift) is linear out to 30,000
km/s proves that this can only enter in at the few percent level
(±5%)... but that still needs to be factored into the
systematic error that is reported. For more on this, see Wang
et al. (1998) who find an upper limit on deviations from the
local 1e4 km/s sphere of 10.5% with 95% confidence.
Next
Home
Reddening is relatively boring and well-understood. I point you to Freedman 1988 and the Galactic extinction law. This is a small source of systematic error (±1%)
This is a lot more interesting. Earlier on it was suggested that there could be a significant metallicity effect to the Cepheid P-L relation. That is, if there were relatively metal-poor Cepheids in a given sample their periods could be longer (not as much opacity). Traditionally, the small scatter that is present in the P-L relation has been attributed to metallicity effects. In the past decade there has been a concerted effort to try and nail down the metallicity dependence of the P-L zero point but it has proved very difficult. There is a good listing and summary of experimental and theoretical efforts in the HST Key Project final results paper (Freedman et al. 2001) and they adopt a value that is uncertain by 100% in their work (-0.2 ±0.2 mag/dex) which is in the midrange of current values. This issue could use a whole lot of observational and theoretical work. This is a large source of error (±4%)
As is the case with any flux-limited observation (read image), there can be a loss of dimmer Cepheids that biases the moduli to smaller distances. This type of bias is referred to as a completeness bias (or Malquist bias). The Key project folks have attempted to circumvent this by imposing a low-end period cutoff for all the galaxies that they measure Cepheids in. This amounts to ±1% in error.
There also exists the possibility that a Cepheid you measure is actually coincident with another star. This can be a real pain in the butt because it is nearly impossible to correct for. It is possible to quantify the magnitude of such an effect by inserting artificial stars into real fields at random and then test how much your distance moduli are off by. Unfortunately it can be significant... +5%, -0% is what has been determined by Ferrarese et al 2000... (note that it is -0% because your field won't have stars in it that take away the light from a co-incident star)
Another pain in the old rump is the fact that Cepheids in the LMC and the Galaxy have been found in binary systems. Fortunately, Cepheids are hella massive and the binary distribution is heavily peaked towards small masses. This will be negligible (in terms of relative distances) unless the frequency of binaries in massive systems varies from galaxy to galaxy.
Does a local measurement of H0 have anything to do with the value at larger scales? Our local velocities can affect the expansion rate we measure. Fortunately, the fact that the Hubble diagram (distance v. redshift) is linear out to 30,000 km/s proves that this can only enter in at the few percent level (±5%)... but that still needs to be factored into the systematic error that is reported. For more on this, see Wang et al. (1998) who find an upper limit on deviations from the local 1e4 km/s sphere of 10.5% with 95% confidence.