Galactic Dark Matter Identified?
Robert L. Oldershaw
population of unbound planetary-mass objects in our galaxy, the
following comments are offered.
A huge population of unbound planetary-mass objects was predicted in
the Astrophysical Journal in 1987 [vol. 322(1), pgs. 34-36]. Pulsar-
planets were also later predicted in a published paper.
A discussion of this form of dark matter and its detection via
microlensing was published in:
http://arxiv.org/ftp/astro-ph/papers/0002/0002363.pdf
It is a great pleasure to see this population finally being revealed
to us. The stellar-mass MACHOs and the planetary-mass unbound objects
discovered via microlensing may constitute the galactic dark matter,
and its specific two-peak mass spectrum was predicted almost 25 years
ago. It has been a long wait, but better late than never.
Robert L. Oldershaw
http://www3.amherst.edu/~rloldershaw
Discrete Scale Relativity; Fractal Cosmology
Phillip Helbig---undress to reply
Oldershaw" <rlold...@amherst.edu> writes:
> A huge population of unbound planetary-mass objects was predicted in
> the Astrophysical Journal in 1987 [vol. 322(1), pgs. 34-36]. Pulsar-
> planets were also later predicted in a published paper.
>
> A discussion of this form of dark matter and its detection via
> microlensing was published in:
>
> http://arxiv.org/ftp/astro-ph/papers/0002/0002363.pdf
>
> It is a great pleasure to see this population finally being revealed
> to us. The stellar-mass MACHOs and the planetary-mass unbound objects
> discovered via microlensing may constitute the galactic dark matter,
> and its specific two-peak mass spectrum was predicted almost 25 years
> ago. It has been a long wait, but better late than never.
What is the current lower bound on the amount of galactic dark matter,
and what is the current upper bound on how much of it can be in such
objects? Don't selectively cite publications, but include all relevant
ones, keeping in mind that later publications tend to have tighter
limits, just from the progress of science.
One cannot rule out, on observational grounds, that all of the dark
matter consists of bricks. (There are of course other arguments against
this.) It also might be the case that SOME of the dark matter is in
such objects (almost certainly the case). But you seem to be claiming
that "most" dark matter is in such objects. Can you support that claim?
Can you counter the objections to it?
Robert L. Oldershaw
<hel...@astro.multiCLOTHESvax.de> wrote:
> In article <mt2.0-13166-1305821...@hydra.herts.ac.uk>, "Robert L.
>
> Oldershaw" <rlolders...@amherst.edu> writes:
> > A huge population of unbound planetary-mass objects was predicted in
> > the Astrophysical Journal in 1987 [vol. 322(1), pgs. 34-36]. Pulsar-
> > planets were also later predicted in a published paper.
> this.) It also might be the case that SOME of the dark matter is in
> such objects (almost certainly the case). But you seem to be claiming
> that "most" dark matter is in such objects. Can you support that claim?
> Can you counter the objections to it?
---------------------------------------------------------------------
The actual population statistics for the stellar-mass and planetary-
mass microlenses are still in flux and depend on assumptions that have
not been fully tested.
The authors of the Nature paper admit that the recently observed
planetary-mass population could just be the high-mass tail of a larger
and lower-mass population.
In the case of the stellar-mass population, we are still struggling to
decide exactly how many of the hundreds and hundreds of microlensing
events are due to dark matter, as opposed to "normal" stellar scale
objects.
As scientists we proceed with an open mind that is not clouded by
emotion or fixed assumptions. We let nature guide us and verify/
falsify our assumptions.
In 1987 I definitively predicted that microlensing searches would find
huge populations of stellar-mass and planetary mass objects in numbers
that ruled out "normal" stellar scale objects. The specific mass peaks
at 0.15 and 8 x 10^-5 solar masses are looking pretty good considering
the current uncertainties. Look at the mass peaks of Figs. 7 and 8 in
the Nature paper. The predicted stellar-mass peak is spot-on. The
predicted planetary-mass peak is within the error circles.
I like the cards I am currently holding, and I am very confident about
what nature will reveal to us as a final verdict, based on what nature
has shown us so far.
Hope this helps,
Richard D. Saam
> One cannot rule out, on observational grounds, that all of the dark
> matter consists of bricks. (There are of course other arguments against
> this.) It also might be the case that SOME of the dark matter is in
> such objects (almost certainly the case). But you seem to be claiming
> that "most" dark matter is in such objects. Can you support that claim?
> Can you counter the objections to it?
As an information update:
What are the objections to dark matter as bricks?
1.?
2.?
......?
Richard D. Saam
[Mod. note: not enough baryons -- mjh]
Thomas Smid
wrote:
> Regarding the publication in Nature [5/18/11] of evidence for a huge
> population of unbound planetary-mass objects in our galaxy
Interesting. The question is where do these objects originate from?
Maybe captured from intergalactic space?
Thomas
Eric Gisse
wrote:
> Regarding the publication in Nature [5/18/11] of evidence for a huge
> population of unbound planetary-mass objects in our galaxy, the
> following comments are offered.
>
> A huge population of unbound planetary-mass objects was predicted in
> the Astrophysical Journal in 1987 [vol. 322(1), pgs. 34-36]. Pulsar-
> planets were also later predicted in a published paper.
>
> A discussion of this form of dark matter and its detection via
> microlensing was published in:
>
> http://arxiv.org/ftp/astro-ph/papers/0002/0002363.pdf
Yes, you also asserted that objects on the order of a solar mass would
constitute between a significant and complete fraction of dark matter.
That didn't pan out.
Planetary mass dark matter candidates have been eliminated as a source
for anything other than a minor fraction of the required dark matter
mass budget. Even the publication in nature says roughly 2 Jupiter
massed worlds per star, which isn't even 5% of the _visible_ mass
budget. Which you noted in your paper, and noted by the later
SuperMACHO survey. So that didn't pan out either.
>
> It is a great pleasure to see this population finally being revealed
> to us. The stellar-mass MACHOs and the planetary-mass unbound objects
> discovered via microlensing may constitute the galactic dark matter,
> and its specific two-peak mass spectrum was predicted almost 25 years
> ago. It has been a long wait, but better late than never.
Huh? What stellar mass MACHOs? The non-observation of this aside, this
would require there be more invisible stars than actual shining stars.
The universe is not old enough for that.
As for planetary mass objects, there just aren't enough.
>
> Robert L. Oldershawhttp://www3.amherst.edu/~rloldershaw
Eric Gisse
<hel...@astro.multiCLOTHESvax.de> wrote:
> In article <mt2.0-13166-1305821...@hydra.herts.ac.uk>, "Robert L.
>
> > A huge population of unbound planetary-mass objects was predicted in
> > the Astrophysical Journal in 1987 [vol. 322(1), pgs. 34-36]. Pulsar-
> > planets were also later predicted in a published paper.
>
> > A discussion of this form of dark matter and its detection via
> > microlensing was published in:
>
> >http://arxiv.org/ftp/astro-ph/papers/0002/0002363.pdf
>
> > It is a great pleasure to see this population finally being revealed
> > to us. The stellar-mass MACHOs and the planetary-mass unbound objects
> > discovered via microlensing may constitute the galactic dark matter,
> > and its specific two-peak mass spectrum was predicted almost 25 years
> > ago. It has been a long wait, but better late than never.
>
> What is the current lower bound on the amount of galactic dark matter,
> and what is the current upper bound on how much of it can be in such
> objects? Don't selectively cite publications, but include all relevant
> ones, keeping in mind that later publications tend to have tighter
> limits, just from the progress of science.
http://arxiv.org/abs/astro-ph/0409167
The _upper_ bound from the SuperMACHO survey is 25% of the dark matter
mass budget for the LMC. I see no reason why a similar number would
not apply to the Milky Way.
Robert likes to be selective in his literature, so it is important to
keep this in mind.
Nicolaas Vroom
I think this is the article Robert uses:
http://www.nature.com/nature/journal/v473/n7347/full/nature10092.html
Also: http://www.bbc.co.uk/news/science-environment-13416431
In the book Galactic Dynamics paragraph 10.1.6 (Dark Matter/
Rotation Curves of Galaxies) is written:
"By now there are over seventy spiral galaxies with reliable rotation
curves out to large radii. In almost all of them the rotation curve
is flat or slowly rising out to the last measured point. Very few galaxies
show falling rotation curves etc.
The simplest interpretation of these results is that other spiral galaxies,
like our own, possess massive dark halos that extend to larger radii than
the optical disks etc."
IMO this simple interpretation can only be considered if you completely
have ruled out that there is not enough invisible visible matter within
this last measured point and outside the optical disk to simulate
a galaxy rotation curve. (No halo)
My simulations show that relative small amounts of matter outside
the optical disk, show an increase in speed of the curve within
the last measured point.
The first issue is how much matter is required that the two curves
match. (i.e. the simulated/calculated versus the observed)
The second issue is can that amount of matter be explained
by Jupiter sized planets (invisible visible matter)
Nicolaas Vroom
http://users.pandora.be/nicvroom/
Goto section 11 Dark Matter.
Robert L. Oldershaw
>
> Robert likes to be selective in his literature, so it is important to
> keep this in mind.
Eric likes to assume that current, and incompletely tested
assumptions, are absolutely correct and fixed for all times. It is
important to keep this in mind.
Robert L. Oldershaw
http://www3.amherst.edu/~rloldershaw
Discrete Scale Relativity; Fractal Cosmology
[Mod. note: I've allowed this as right of reply, but please, if you
would like to make remarks about some other poster rather than about
the scientific content of the discussion, take it to private e-mail.
-- mjh]
Robert L. Oldershaw
>
> Huh? What stellar mass MACHOs? The non-observation of this aside, this
> would require there be more invisible stars than actual shining stars.
> The universe is not old enough for that.
>
> As for planetary mass objects, there just aren't enough.
You can choose to ignore the published evidence for at least 20% of
the dark matter being in the form of stellar-mass ultracompacts, and
instead claim that the DM is in the form of "sterile neutrinos". Good
luck with that. The evidence for MACHOs in very large numbers is
there. It's just that you do not want that to be the DM answer. I'll
let nature render a more meaningful and less biased verdict.
You are correct that planetary-mass ultracomacts could not make up the
majority of the mass of the DM. I NEVER said they did. In terms of
numbers, I have predicted that their abundance is about the same as
the stellar-mass ultracompacts. However, because they are a factor of
1836 times lighter, they contribute only a small fraction of the DM
mass.
Are we clear on these issues, or do we have to keep correcting your
misleading and erroneous comments eternally?
Robert L. Oldershaw
Eric Flesch
>In the book Galactic Dynamics paragraph 10.1.6 is written:
>The simplest interpretation of these results is that other spiral galaxies,
>like our own, possess massive dark halos that extend to larger radii than
>the optical disks etc."
>IMO this simple interpretation can only be considered if you completely
>have ruled out that there is not enough invisible visible matter within
>this last measured point and outside the optical disk to simulate
The point of the halo explanation is not how much extra matter there
is, but where it must be to flatten the galaxy rotation profile. The
observational problem with the large halo theory is that neutral
hydrogen (HI) profiles show only a small halo, beyond which the gas
departs the galaxy as with tidal tails.
A geometric explanation is available where matter gravitationally
depresses GR-like into an additional large dimension. The resultant
"gravitational scalar" (i.e. surface tension of the additional
dimension) reduces the inverse square law within complex matter
structures, and adds a gravitational "lip" onto the outside edge of
those structures. Handy for globular star clusters and elliptical
galaxies.
Eric Flesch
Thomas Smid
> I think this is the article Robert uses:http://www.nature.com/nature/journal/v473/n7347/full/nature10092.html
> Also:http://www.bbc.co.uk/news/science-environment-13416431
Actually, you can get the full original article for free from
http://arxiv.org/abs/1105.3544 (no need to pay Nature for access).
What I find a remarkable result here is that the distribution function
for the planetary masses has a peak at 1 Jupiter mass, and tails off
not only towards higher masses (which is familiar from stellar mass
functions) but also for lower masses. Is there any explanation for
this fact as yet (I couldn't find anything in this respect in the
paper, and neither elsewhere)?
Thomas
Eric Gisse
wrote:
> On May 21, 5:01 am, Eric Gisse <jowr...@gmail.com> wrote:
>
> > Huh? What stellar mass MACHOs? The non-observation of this aside, this
> > would require there be more invisible stars than actual shining stars.
> > The universe is not old enough for that.
>
> > As for planetary mass objects, there just aren't enough.
>
> --------------------------------------------------------------------------------
>
> You can choose to ignore the published evidence for at least 20% of
> the dark matter being in the form of stellar-mass ultracompacts, and
> instead claim that the DM is in the form of "sterile neutrinos". Good
> luck with that. The evidence for MACHOs in very large numbers is
> there. It's just that you do not want that to be the DM answer. I'll
> let nature render a more meaningful and less biased verdict.
Woah there, partner. Not so fast. Where's the evidence that at least
20% of dark matter is solar mass ultracompacts?
As for sterile neutrinos, at least that guess is buttressed by the
WMAP estimates of neutrino species number. I'm not married to it, it
just happened to be the best shot at this moment.
And yes, I see that there is evidence for 'large numbers' of MACHOs.
Which first off, we both know that is an extrapolation which you have
been saying - this whole time - is possibly not representative of
reality. Plus, number is irrelevant! There are uncountably many
neutrinos out there, but they have insufficient mass to be relevant.
>
> You are correct that planetary-mass ultracomacts could not make up the
> majority of the mass of the DM. I NEVER said they did. In terms of
> numbers, I have predicted that their abundance is about the same as
> the stellar-mass ultracompacts. However, because they are a factor of
> 1836 times lighter, they contribute only a small fraction of the DM
> mass.
And where is the evidence all these stellar mass ultracompacts exist,
and are 1836 times heavier? Note: I said EVIDENCE, not "A theory-only
paper I wrote."
Why have these stellar mass ultracompacts evaded microlensing surveys?
Perhaps I am missing the results of a survey in my previous literature
searches.
>
> Are we clear on these issues, or do we have to keep correcting your
> misleading and erroneous comments eternally?
>
> Robert L. Oldershawhttp://www3.amherst.edu/~rloldershaw
Robert L. Oldershaw
>
> What I find a remarkable result here is that the distribution function
> for the planetary masses has a peak at 1 Jupiter mass, and tails off
> not only towards higher masses (which is familiar from stellar mass
> functions) but also for lower masses. Is there any explanation for
> this fact as yet (I couldn't find anything in this respect in the
> paper, and neither elsewhere)?
In order to go from the obeserved temporal durations of the lensing
events to the average mass of the microlenses involves some major
assumptions and some statistical reasoning.
Therefore, there are uncertainties involved. It is a complex subject
and one would have to go to published reviews of microlensing research
to get a full understanding.
Some difficulties occur in estimating the distance to the lenses,
their average velocities, blending of multiple sources, detection
efficiencies that are a function of the lens mass, etc. Not for the
faint of heart; takes sustained effort.
RLO
Robert L. Oldershaw
>
> Why have these stellar mass ultracompacts evaded microlensing surveys?
> Perhaps I am missing the results of a survey in my previous literature
> searches.
The stellar-mass objects have not evaded microlensing surveys. There
is published physical evidence for up to an estimated trillion MACHOs.
Perhaps your literature search is constrained by your assumptions?
I am sure you have a very clear understanding that the search for
"WIMPs" is difficult and that one should not expect immediate and
complete results.
So why do you not take the same approach with MACHOs and PLANCHOs?
Robert L. Oldershaw
Thomas Smid
> to us. The stellar-mass MACHOs and the planetary-mass unbound objects
> discovered via microlensing may constitute the galactic dark matter,
> and its specific two-peak mass spectrum was predicted almost 25 years
> ago. It has been a long wait, but better late than never.
Actually, after having a closer look at the paper in question (
http://arxiv.org/abs/1105.3544 ), I don't think there is a strong case
for a planetary population at all. The error bars in the plot for the
distribution function of the event time scales (Fig.2 in the paper)
are just standard error bars, and thus a non-overlap of the latter
with the theoretical stellar distribution is statistically not
significant (see http://www.graphpad.com/articles/errorbars.htm ).
I have extended the error bars for time scales below 2 days to 2-sigma
error bars (indicated by the green delimiters) and now practically all
of them cut the theoretical stellar curve (see
http://www.plasmaphysics.org.uk/imgs/planet_microlensing.gif ), so
there is no conclusive evidence for a planetary population.
So it seems just like another case of the authors having jumped the
starting gun in order to be the first to have discovered something.
Thomas
Eric Gisse
wrote:
> On May 23, 3:43 am, Eric Gisse <jowr...@gmail.com> wrote:
>
> > Why have these stellar mass ultracompacts evaded microlensing surveys?
> > Perhaps I am missing the results of a survey in my previous literature
> > searches.
>
> --------------------------------------------------------------------------------
>
> The stellar-mass objects have not evaded microlensing surveys. There
> is published physical evidence for up to an estimated trillion MACHOs.
> Perhaps your literature search is constrained by your assumptions?
Then you can provide the references rather than being coy.
>
> I am sure you have a very clear understanding that the search for
> "WIMPs" is difficult and that one should not expect immediate and
> complete results.
Regardless, lots of candidate theories have been excluded via non-
detection in regimes where they should be detected, eg axions.
>
> So why do you not take the same approach with MACHOs and PLANCHOs?
Because microlensing surveys, eg SuperMACHO which you are yet to
directly address, haven't found stellar mass candidates.
What am I to believe? References I have actually seen, replicated
across several groups, which say such things do not exist? Or
references, kept hidden, that say they do?
>
> Robert L. Oldershawhttp://www3.amherst.edu/~rloldershaw
Steve Willner
> > population of unbound planetary-mass objects in our galaxy
In article <mt2.0-20371...@hydra.herts.ac.uk>,
Thomas Smid <thoma...@gmail.com> writes:
> Interesting. The question is where do these objects originate from?
Why not from star formation regions, where they are expelled
gravitationally from (youngish) planetary systems?
> Maybe captured from intergalactic space?
That doesn't answer how they formed. And wouldn't the velocities be
too high to match observations?
--
Help keep our newsgroup healthy; please don't feed the trolls.
Steve Willner Phone 617-495-7123 swil...@cfa.harvard.edu
Cambridge, MA 02138 USA
Jonathan Thornburg [remove -animal to reply]
> Actually, after having a closer look at the paper in question (
> http://arxiv.org/abs/1105.3544 ), I don't think there is a strong case
> for a planetary population at all. The error bars in the plot for the
> distribution function of the event time scales (Fig.2 in the paper)
> are just standard error bars, and thus a non-overlap of the latter
> with the theoretical stellar distribution is statistically not
> significant (see http://www.graphpad.com/articles/errorbars.htm ).
> I have extended the error bars for time scales below 2 days to 2-sigma
> error bars (indicated by the green delimiters) and now practically all
> of them cut the theoretical stellar curve (see
> http://www.plasmaphysics.org.uk/imgs/planet_microlensing.gif ), so
> there is no conclusive evidence for a planetary population.
The authors claim that their quantitative statistical analysis refutes
the above interpretation. Quoting from page 3 of the arxiv version of
the paper:
| We have evaluated the likelihood distributions for these mass
| functions both with and without the $t_E < 2$ events, but the inclusion
| of the events with $t_E < 2$ days makes little difference. The results
| are shown in Supplementary Table 3 and Supplementary Figs 6 and 7.
| Fig. 2 indicates that both models match the data well for $t_E \ge 2$
| days, but at $t_E < 2$ days, the ten observed events are well above
| the model predictions. The power-law and log-normal models predict
| 1.5 and 2.5 events with $t_E < 2$ days, respectively, and the corresponding
| Poisson probabilities for the ten observed events are $4 \times 10^{-6}$
| and $3 \times $10^{-4}$. Thus, we feel confident in adding a new
| planetary-mass population.
Those Poisson probabilities are indeed very small (i.e., Thomas Smid's
scenario seems highly unlikely). And figure 8 in the paper shows
likelihood contours which put the fraction of all objects that are in
the planetary-mass population at between 20 and 85% (95% confidence
interval).
However, the authors don't provide a Bayesian analysis (the word "prior"
doesn't appear anywhere in the paper). Such an analysis would be very
interesting, and I would feel more comfortable if it agreed with the
analyses the authors do give in this paper.
I also found this passage noteworthy [[page 4 of the arxiv version]]:
| The lenses for these short events could be either free-floating
| planets or planets with wide separations of more than about ten
| astronomical units (AU) from their host stars, for which we cannot
| detect the host star in the light curves $^{25}$. However, direct
| imaging, with adaptive optics, of planets orbiting young stars
| places upper limits on planets at wide separations. The Gemini
| Planet Imager has set upper limits $^{9}$ on the number of stars with
| Jupiter-mass planets at semi-major axes of 10-500 AU. From these
| results, we estimate that <0.4 of the 1.8 planetary-mass objects
| per star are likely to be bound to stars at orbital separations of
| <500 AU (see Supplementary Information Section 8). Hence, more than
| 75% of these planetary mass objects are probably unbound to stars
| if their typical mass is a Jupiter-mass or more.
I wonder how solid those adaptive-optics-imaging bounds are?
All in all, an intriguing paper. If their results are true, we should
see lots more confirming evidence in the next few years (the microlensing
searches are rapidly improving).....
--
-- "Jonathan Thornburg [remove -animal to reply]" <jth...@astro.indiana-zebra.edu>
Dept of Astronomy & IUCSS, Indiana University, Bloomington, Indiana, USA
"Washing one's hands of the conflict between the powerful and the
powerless means to side with the powerful, not to be neutral."
-- quote by Freire / poster by Oxfam
Thomas Smid
<jth...@astro.indiana-zebra.edu> wrote:
> Thomas Smid <thomas.s...@gmail.com> wrote:
> > Actually, after having a closer look at the paper in question (
> > for a planetary population at all. The error bars in the plot for the
> > distribution function of the event time scales (Fig.2 in the paper)
> > are just standard error bars, and thus a non-overlap of the latter
> > with the theoretical stellar distribution is statistically not
> > significant (seehttp://www.graphpad.com/articles/errorbars.htm).
> > I have extended the error bars for time scales below 2 days to 2-sigma
> > error bars (indicated by the green delimiters) and now practically all
> > of them cut the theoretical stellar curve (see
> > there is no conclusive evidence for a planetary population.
> The authors claim that their quantitative statistical analysis refutes
> the above interpretation. Quoting from page 3 of the arxiv version of
> the paper:
> | We have evaluated the likelihood distributions for these mass
> | functions both with and without the $t_E < 2$ events, but the inclusion
> | of the events with $t_E < 2$ days makes little difference. The results
> | are shown in Supplementary Table 3 and Supplementary Figs 6 and 7.
> | Fig. 2 indicates that both models match the data well for $t_E \ge 2$
> | days, but at $t_E < 2$ days, the ten observed events are well above
> | the model predictions. The power-law and log-normal models predict
> | 1.5 and 2.5 events with $t_E < 2$ days, respectively, and the corresponding
> | Poisson probabilities for the ten observed events are $4 \times 10^{-6}$
> | and $3 \times $10^{-4}$. Thus, we feel confident in adding a new
> | planetary-mass population.
They say 'the ten observed events are well above the model
predictions'. Well, they aren't. If you look at Fig.3 in the
Supplementary section (where the data are corrected for the detection
efficiency), then the mean values of the data points are only about
one standard deviation above the model predictions, which is
statistically insignificant. For statistical significance one would
need 2 standard deviations, as indicated in my modified figure
http://www.plasmaphysics.org.uk/imgs/planet_microlensing.gif .
So I am not sure what their confidence is based on.
Thomas
Jonathan Thornburg [remove -animal to reply]
> They say 'the ten observed events are well above the model
> predictions'. Well, they aren't. If you look at Fig.3 in the
> Supplementary section (where the data are corrected for the detection
> efficiency), then the mean values of the data points are only about
> one standard deviation above the model predictions, which is
> statistically insignificant. For statistical significance one would
> need 2 standard deviations, as indicated in my modified figure
> http://www.plasmaphysics.org.uk/imgs/planet_microlensing.gif .
No, for statistical significance [in the usual frequentist sense]
one would need the probability of obtaining *all* of the data points
being *simultaneously* above the curve by that far, to be less than
some threshold (often taken to be 0.05). Since there are 6 separate
points in the "bump", one can indeed have statistical significance
even if each individual point is only about 1 standard deviation
[actually standard error of the mean] above the model predictions.
To repeat, you don't compute the significance of individual data
points, rather you compute the significance of a whole *set* of
data points.
If you feel that the authors' calculations of this significance are
incorrect, please provide details of your own *quantitative* calculation
of the likelihood of obtaining data at least as far from the model
as the authors' data.
> So I am not sure what their confidence is based on.
The authors have done the computation I just described, with the
following result [quoting from page 3 of the arxiv version of the
paper]:
| We have evaluated the likelihood distributions for these mass
| functions both with and without the $t_E < 2$ events, but the inclusion
| of the events with $t_E < 2$ days makes little difference. The results
| are shown in Supplementary Table 3 and Supplementary Figs 6 and 7.
| Fig. 2 indicates that both models match the data well for $t_E \ge 2$
| days, but at $t_E < 2$ days, the ten observed events are well above
| the model predictions. The power-law and log-normal models predict
| 1.5 and 2.5 events with $t_E < 2$ days, respectively, and the corresponding
| Poisson probabilities for the ten observed events are $4 \times 10^{-6}$
| and $3 \times $10^{-4}$. Thus, we feel confident in adding a new
| planetary-mass population.
--
Thomas Smid
<jth...@astro.indiana-zebra.edu> wrote:
> Thomas Smid <thomas.s...@gmail.com> wrote:
> > They say 'the ten observed events are well above the model
> > predictions'. Well, they aren't. If you look at Fig.3 in the
> > Supplementary section (where the data are corrected for the detection
> > efficiency), then the mean values of the data points are only about
> > one standard deviation above the model predictions, which is
> > statistically insignificant. For statistical significance one would
> > need 2 standard deviations, as indicated in my modified figure
> >http://www.plasmaphysics.org.uk/imgs/planet_microlensing.gif.
>
> No, for statistical significance [in the usual frequentist sense]
> one would need the probability of obtaining *all* of the data points
> being *simultaneously* above the curve by that far, to be less than
> some threshold (often taken to be 0.05). Since there are 6 separate
> points in the "bump", one can indeed have statistical significance
> even if each individual point is only about 1 standard deviation
> [actually standard error of the mean] above the model predictions.
You would have a point here if you had more events in the
corresponding bins and the usual statistical arguments could actually
be applied: if you look at Fig.2 in the paper ( http://arxiv.org/abs/1105.3544
) then you see that the three left-most error bars signify just one
event each, whilst the theoretical stellar curve in this region has a
value of around N=0.1, so effectively zero (as N must be an integer
greater or equal to zero). So naturally, for such low count rates, any
statistical error will only lift them up but not reduce them.
It seems almost that the authors chose a sample just large enough to
have 1 or 2 events in a bin and then make their claim on the basis of
this. Why didn't they choose a much larger sample that would yield a
half-decent statistics in this range? Where they afraid that this
would have invalidated their claim? As it is, this seems be just
another paper that crucially relies on statistical obscurity.
Thomas
Steve Willner
Thomas Smid <thoma...@gmail.com> writes:
> if you look at Fig.2 in the paper ( http://arxiv.org/abs/1105.3544
> ) then you see that the three left-most error bars signify just one
> event each
You can argue about the figure, but the text says they found 10
events of which they expect about 3 to be spurious. That's pretty
good statistical significance.
> Why didn't they choose a much larger sample
As far as I can tell, they published all the data in a particular
time range. I'm guessing that was all the data they had analyzed so
far.
What impressed me was how well the independent OGLE data points
agreed with the light curves derived from only the MOA data.