1
00:00:10,830 --> 00:00:11,670
SAARIK KALIA: OK.

2
00:00:11,670 --> 00:00:12,170
Hi.

3
00:00:12,170 --> 00:00:13,990
So my name is
Saarik, and I'm going

4
00:00:13,990 --> 00:00:17,050
to be talking today about how
we can use the 21 centimeter

5
00:00:17,050 --> 00:00:20,140
hydrogen line to determine
the galactic rotation

6
00:00:20,140 --> 00:00:24,520
curve and some of the structure
of the Milky Way galaxy.

7
00:00:24,520 --> 00:00:27,370
So first off, why do we care
about galactic rotation curves?

8
00:00:27,370 --> 00:00:30,490
So basically rotation speed
can tell us about mass.

9
00:00:30,490 --> 00:00:32,800
We know this from simple
Newtonian mechanics.

10
00:00:32,800 --> 00:00:35,800
If you have a planet
going around a sun,

11
00:00:35,800 --> 00:00:39,090
then its velocity is given by
this equation, where M here

12
00:00:39,090 --> 00:00:41,320
is the mass of the sun.

13
00:00:41,320 --> 00:00:43,561
In our case, since we're
working with a galaxy,

14
00:00:43,561 --> 00:00:44,560
we have spread out mass.

15
00:00:44,560 --> 00:00:46,143
This M is actually
going to correspond

16
00:00:46,143 --> 00:00:49,310
to basically the mass
contained within the orbit.

17
00:00:49,310 --> 00:00:57,130
So using a formula like this,
given the mass distribution

18
00:00:57,130 --> 00:00:58,660
that we see in the
Milky Way galaxy,

19
00:00:58,660 --> 00:01:00,370
we can guess what
kinds of velocities

20
00:01:00,370 --> 00:01:03,370
we should see various
things rotating at.

21
00:01:03,370 --> 00:01:07,700
And we can plot that and we get
a curve that looks like this.

22
00:01:07,700 --> 00:01:09,850
But we actually,
as we'll see later

23
00:01:09,850 --> 00:01:13,810
when we go ahead and observe
what velocities stars are

24
00:01:13,810 --> 00:01:17,170
really moving at, we'll
actually see a huge discrepancy

25
00:01:17,170 --> 00:01:19,450
between what we would expect
from the visible matter

26
00:01:19,450 --> 00:01:20,490
that we can see.

27
00:01:20,490 --> 00:01:24,070
And basically the way that we
might be able to explain this

28
00:01:24,070 --> 00:01:27,070
is possibly there is matter out
there that we just can't see.

29
00:01:27,070 --> 00:01:31,460
And physicists term this
matter as dark matter.

30
00:01:31,460 --> 00:01:34,930
So what we're going to be
working on in this experiment

31
00:01:34,930 --> 00:01:41,380
is trying to be able to actually
plot this rotation curve.

32
00:01:41,380 --> 00:01:44,710
And in being able to
show these discrepancies,

33
00:01:44,710 --> 00:01:48,280
this will motivate new physics.

34
00:01:48,280 --> 00:01:52,390
So how are we going to
find this rotation curve?

35
00:01:52,390 --> 00:01:54,850
So the way we're
going to be looking

36
00:01:54,850 --> 00:01:56,470
at the velocities
of various stars

37
00:01:56,470 --> 00:01:59,884
is using the Doppler effect.

38
00:01:59,884 --> 00:02:02,050
In our case, this will be
a non-relativistic Doppler

39
00:02:02,050 --> 00:02:02,550
effect.

40
00:02:02,550 --> 00:02:04,360
This is simply
just, as an object

41
00:02:04,360 --> 00:02:06,280
is moving towards
you, the frequencies

42
00:02:06,280 --> 00:02:09,257
that it emits are
slightly higher than if it

43
00:02:09,257 --> 00:02:10,090
were standing still.

44
00:02:12,680 --> 00:02:16,679
So we can look out at the stars.

45
00:02:16,679 --> 00:02:18,220
But looking for
optical light doesn't

46
00:02:18,220 --> 00:02:20,260
work too well because
it suffers absorption

47
00:02:20,260 --> 00:02:24,880
from other stars or
interstellar gas and dust.

48
00:02:24,880 --> 00:02:27,700
So instead we prefer something
in a slightly lower frequency

49
00:02:27,700 --> 00:02:32,320
range around the
radio emission range.

50
00:02:32,320 --> 00:02:34,240
Luckily for us,
hydrogen actually

51
00:02:34,240 --> 00:02:37,690
exhibits an emission
in this lower frequency

52
00:02:37,690 --> 00:02:43,020
range, particularly, yeah,
at this 21 centimeter line.

53
00:02:43,020 --> 00:02:46,850
And this occurs as
spin flip transition.

54
00:02:46,850 --> 00:02:49,660
So when the proton
and electron go

55
00:02:49,660 --> 00:02:51,460
from being aligned
to anti-aligned,

56
00:02:51,460 --> 00:02:53,550
that's a slightly
lower energy state,

57
00:02:53,550 --> 00:02:55,300
and so it releases a
little bit of energy.

58
00:02:55,300 --> 00:02:58,390
And we can look at that
energy coming from the sky.

59
00:02:58,390 --> 00:03:01,000
And by seeing how
that frequency shifts,

60
00:03:01,000 --> 00:03:03,490
we can deduce the
velocity that the emitter

61
00:03:03,490 --> 00:03:05,800
must have been moving at.

62
00:03:05,800 --> 00:03:07,300
So this is the
apparatus we're going

63
00:03:07,300 --> 00:03:12,700
to be using for detecting
our various emissions.

64
00:03:12,700 --> 00:03:16,120
The actual telescope
itself is a parabolic dish,

65
00:03:16,120 --> 00:03:18,820
which takes an incoming
light, reflects it

66
00:03:18,820 --> 00:03:22,450
onto this feed horn,
and the net signal

67
00:03:22,450 --> 00:03:26,080
is fed into this
fairly complex circuit.

68
00:03:26,080 --> 00:03:29,170
I'll just point out
some important things.

69
00:03:29,170 --> 00:03:31,900
The signal comes in,
it gets amplified,

70
00:03:31,900 --> 00:03:33,160
goes to the bandpass filter.

71
00:03:33,160 --> 00:03:35,451
That's just to get rid of
any frequencies we absolutely

72
00:03:35,451 --> 00:03:36,427
don't care about.

73
00:03:36,427 --> 00:03:38,260
And then one important
point is that it goes

74
00:03:38,260 --> 00:03:40,600
to this image rejection mixer.

75
00:03:40,600 --> 00:03:44,290
And what that does is it
multiplies the incoming signal

76
00:03:44,290 --> 00:03:50,150
by a signal that we manually
put in of 1420.4 megahertz.

77
00:03:50,150 --> 00:03:53,430
That's the frequency of
the 21 centimeter line

78
00:03:53,430 --> 00:03:54,830
that we're looking for.

79
00:03:54,830 --> 00:03:58,390
And as you can see from
this trigonometric formula,

80
00:03:58,390 --> 00:04:00,910
multiplying two
signals is actually

81
00:04:00,910 --> 00:04:04,090
equivalent to just producing
one signal whose frequency is

82
00:04:04,090 --> 00:04:06,040
the sum and one
who's the difference.

83
00:04:06,040 --> 00:04:08,170
And by using the
second bandpass filter,

84
00:04:08,170 --> 00:04:09,880
we can eliminate
the sum and just

85
00:04:09,880 --> 00:04:12,250
be left with this signal,
which is the difference.

86
00:04:12,250 --> 00:04:13,750
And so the reason
we do this is just

87
00:04:13,750 --> 00:04:16,959
to get a very precise
measurement of how

88
00:04:16,959 --> 00:04:20,620
off the signal we're seeing
is from the 21 centimeter line

89
00:04:20,620 --> 00:04:22,420
we would expect from
a still observer.

90
00:04:22,420 --> 00:04:26,890
And using that we can figure
out what velocity the emitter

91
00:04:26,890 --> 00:04:29,500
is moving at.

92
00:04:29,500 --> 00:04:35,720
OK, and so in order to
turn this into temperatures

93
00:04:35,720 --> 00:04:37,697
is what we'll be dealing with.

94
00:04:37,697 --> 00:04:39,280
We're going to first
have to calibrate

95
00:04:39,280 --> 00:04:41,110
this with a noise diode.

96
00:04:41,110 --> 00:04:45,360
What this will do is just
send a signal to the feed horn

97
00:04:45,360 --> 00:04:48,580
that looks like 115
Kelvin blackbody all

98
00:04:48,580 --> 00:04:50,330
throughout the sky.

99
00:04:50,330 --> 00:04:55,330
And so it uses the signal it
sees from this to extrapolate

100
00:04:55,330 --> 00:04:57,460
other signals that it will see.

101
00:04:57,460 --> 00:04:59,770
So basically, if
later on it sees

102
00:04:59,770 --> 00:05:02,170
a signal that's twice as
strong as the signal that's

103
00:05:02,170 --> 00:05:05,170
on its calibration, at some
specific frequency then

104
00:05:05,170 --> 00:05:08,110
it says, oh, there must
be a 230 Kelvin blackbody

105
00:05:08,110 --> 00:05:09,790
at that specific frequency.

106
00:05:09,790 --> 00:05:11,730
So at the end we'll
be getting some sort

107
00:05:11,730 --> 00:05:16,340
of temperature profile as
a function of frequency.

108
00:05:16,340 --> 00:05:18,450
And we're going to be
taking measurements

109
00:05:18,450 --> 00:05:20,820
all across the galaxy.

110
00:05:20,820 --> 00:05:24,990
Essentially, our galaxy is
mostly shaped in a planar disk,

111
00:05:24,990 --> 00:05:28,950
so we'll be just looking
within that disk.

112
00:05:28,950 --> 00:05:31,530
The galaxy has some central
bulge with some spiral

113
00:05:31,530 --> 00:05:33,180
arms coming out of it.

114
00:05:33,180 --> 00:05:35,310
And our sun is
located down here.

115
00:05:35,310 --> 00:05:39,660
We will be sweeping from the
galactic longitude of zero,

116
00:05:39,660 --> 00:05:42,120
which is directed towards
the center of the galaxy,

117
00:05:42,120 --> 00:05:45,320
out to 180, which is
directed away from it,

118
00:05:45,320 --> 00:05:48,110
so we'll be looking at the
first and second quadrants.

119
00:05:48,110 --> 00:05:50,640
As we'll talk about later, these
first quadrant measurements

120
00:05:50,640 --> 00:05:52,920
will be used to determine
the rotation curve

121
00:05:52,920 --> 00:05:55,350
and the second
quadrant measurements

122
00:05:55,350 --> 00:06:01,030
will be used to determine
the structures of the galaxy.

123
00:06:01,030 --> 00:06:07,110
OK, so as we mentioned
before, given a frequency,

124
00:06:07,110 --> 00:06:09,870
we can turn that into a
velocity using our Doppler

125
00:06:09,870 --> 00:06:12,600
shift via this formula.

126
00:06:12,600 --> 00:06:14,016
This 120.

127
00:06:14,016 --> 00:06:20,250
4-- or 1420.4 megahertz is just
the emission, the frequency

128
00:06:20,250 --> 00:06:22,320
of the 21 centimeter line.

129
00:06:22,320 --> 00:06:24,180
This right here is just
the speed of light.

130
00:06:24,180 --> 00:06:25,800
And then we have this VLSR.

131
00:06:25,800 --> 00:06:29,370
This is just our velocity
with respect to the sun

132
00:06:29,370 --> 00:06:30,960
just to factor
out any revolution

133
00:06:30,960 --> 00:06:32,300
that we have around the sun.

134
00:06:32,300 --> 00:06:35,160
So this V observed is actually
the velocity with respect

135
00:06:35,160 --> 00:06:39,010
to the sun, not with respect us.

136
00:06:39,010 --> 00:06:44,820
And so now we can use this
velocity using various trig

137
00:06:44,820 --> 00:06:46,920
formulas, Law of Sines.

138
00:06:46,920 --> 00:06:51,330
We can relate the velocity we
observed to the actual velocity

139
00:06:51,330 --> 00:06:57,760
of the star in question.

140
00:06:57,760 --> 00:07:00,570
And note here we have to
use this critical assumption

141
00:07:00,570 --> 00:07:03,450
that the stars move in
circular orbits, which

142
00:07:03,450 --> 00:07:06,840
is fairly close to accurate.

143
00:07:06,840 --> 00:07:08,700
But using this
assumption allows us

144
00:07:08,700 --> 00:07:11,400
to say that the
velocity of this star

145
00:07:11,400 --> 00:07:14,190
is at a right angle
with its radius.

146
00:07:14,190 --> 00:07:18,120
And then if we know the
radius at which the star lies,

147
00:07:18,120 --> 00:07:23,010
then we can use this formula
to relate the velocity we see

148
00:07:23,010 --> 00:07:25,920
with the velocity of the star.

149
00:07:25,920 --> 00:07:28,080
And here we're going to
be taking R naught, which

150
00:07:28,080 --> 00:07:30,420
is the distance from us
to the center of the sun,

151
00:07:30,420 --> 00:07:33,090
to be a 8.5 kiloparsecs
and theta naught,

152
00:07:33,090 --> 00:07:37,980
which is our speed
within the galaxy,

153
00:07:37,980 --> 00:07:40,570
to be 220 kilometers per second.

154
00:07:40,570 --> 00:07:43,950
These numbers are
not too well known,

155
00:07:43,950 --> 00:07:45,817
but these will be the
values we'll be using.

156
00:07:45,817 --> 00:07:47,400
And the literature
will compare again,

157
00:07:47,400 --> 00:07:48,816
so we'll be using
the same values.

158
00:07:51,360 --> 00:07:53,340
Right, and so this formula
is all well and good

159
00:07:53,340 --> 00:07:56,514
if we actually know what
radius this star is at.

160
00:07:56,514 --> 00:07:57,930
But, a priori, we
don't know that.

161
00:07:57,930 --> 00:07:59,820
So the trick we're
going to be using here

162
00:07:59,820 --> 00:08:03,200
is actually just to consider the
maximum velocity that we see.

163
00:08:03,200 --> 00:08:06,990
And the maximum velocity will
occur at the minimum radius.

164
00:08:06,990 --> 00:08:10,510
And that's simply given
by this R naught sine L.

165
00:08:10,510 --> 00:08:14,670
And so if we specifically
consider that minimum radius,

166
00:08:14,670 --> 00:08:17,670
then this formula allows us to
relate that maximum velocity

167
00:08:17,670 --> 00:08:20,010
to the velocity of
the star in question.

168
00:08:20,010 --> 00:08:21,720
Note, however, that
this only works

169
00:08:21,720 --> 00:08:24,787
for longitudes less than 90.

170
00:08:24,787 --> 00:08:27,120
That's in the first quadrant
I was talking about before.

171
00:08:27,120 --> 00:08:29,340
And that's simply
because, if you're

172
00:08:29,340 --> 00:08:31,680
looking at stars
which are further

173
00:08:31,680 --> 00:08:34,518
away from the center
of the galaxy, then

174
00:08:34,518 --> 00:08:36,809
they're all just going to
get further and further away.

175
00:08:36,809 --> 00:08:41,070
There's not going to
be any minimum radius.

176
00:08:41,070 --> 00:08:45,690
Right, so we wanted to determine
this maximum velocity that's

177
00:08:45,690 --> 00:08:48,220
equivalent to determining
a minimum frequency.

178
00:08:48,220 --> 00:08:51,060
So how are we actually going
to get that minimum frequency?

179
00:08:51,060 --> 00:08:55,020
So as we said before, we have
this temperature spectrum

180
00:08:55,020 --> 00:08:56,370
as a function of frequency.

181
00:08:56,370 --> 00:08:58,680
We're going to start off
by trimming off the edges.

182
00:08:58,680 --> 00:09:00,541
There's just a
very quick falloff

183
00:09:00,541 --> 00:09:02,040
just from the
bandpass filter there,

184
00:09:02,040 --> 00:09:04,350
so we have to get rid of those.

185
00:09:04,350 --> 00:09:08,330
And at each given longitude,
we take about 40 trials

186
00:09:08,330 --> 00:09:14,920
and we average that into one
the temperature spectrum.

187
00:09:14,920 --> 00:09:16,650
So this is what our
spectrum looks like.

188
00:09:16,650 --> 00:09:22,050
We're going to fit the first
few bins to a linear background.

189
00:09:22,050 --> 00:09:24,090
And we can see that the
background fit is quite

190
00:09:24,090 --> 00:09:26,670
good for these initial points.

191
00:09:26,670 --> 00:09:29,490
You'll notice here we have
this annoying little peak here.

192
00:09:29,490 --> 00:09:32,410
This actually shows up
in most of our plots.

193
00:09:32,410 --> 00:09:34,920
This is probably because of
just some constant source

194
00:09:34,920 --> 00:09:36,360
that's creating noise.

195
00:09:36,360 --> 00:09:39,300
So when we fit this background,
we just ignore those points

196
00:09:39,300 --> 00:09:40,470
in particular.

197
00:09:40,470 --> 00:09:44,760
But for the rest of the
points, the fit is quite good.

198
00:09:44,760 --> 00:09:48,090
Then we're going to find
the first point, which

199
00:09:48,090 --> 00:09:51,607
exceeds this background by
some fixed amount one Kelvin.

200
00:09:51,607 --> 00:09:53,940
And we say that that is going
to be our minimum emission

201
00:09:53,940 --> 00:09:54,760
frequency.

202
00:09:54,760 --> 00:09:59,550
So in this case, this
is 1420.4494 megahertz.

203
00:09:59,550 --> 00:10:02,160
And we can estimate the
error on this method

204
00:10:02,160 --> 00:10:04,600
by basically fudging
this 35 number,

205
00:10:04,600 --> 00:10:06,360
so see what happens
if we use the first 20

206
00:10:06,360 --> 00:10:12,220
bins versus what happens when
we use the first 50 instead.

207
00:10:12,220 --> 00:10:14,680
And so the number
we get out of it

208
00:10:14,680 --> 00:10:16,680
will shift a little bit
up or a little bit down.

209
00:10:16,680 --> 00:10:20,640
In this case, it shifted one
bin up and two bins down.

210
00:10:20,640 --> 00:10:24,390
And so that gives us an error
on what this kind of method

211
00:10:24,390 --> 00:10:27,210
will give for a minimum
emission frequency.

212
00:10:27,210 --> 00:10:31,290
And by default, if shifting
around this 35 number

213
00:10:31,290 --> 00:10:32,790
doesn't change
anything, then we'll

214
00:10:32,790 --> 00:10:38,190
just say that the error is
just the bin with itself.

215
00:10:38,190 --> 00:10:38,690
Great.

216
00:10:38,690 --> 00:10:41,970
So using that minimum
mission frequency,

217
00:10:41,970 --> 00:10:44,870
we can find a velocity
as per the formulas

218
00:10:44,870 --> 00:10:46,510
I had a few slides ago.

219
00:10:46,510 --> 00:10:49,740
And we can also get
the radius simply

220
00:10:49,740 --> 00:10:52,110
as a function of the
galactic longitude.

221
00:10:52,110 --> 00:10:53,730
And we can plot it out.

222
00:10:53,730 --> 00:10:56,800
And we'll get a curve that
looks something like this.

223
00:10:56,800 --> 00:10:58,830
So this red curve
that I'm plotting here

224
00:10:58,830 --> 00:11:02,760
is a curve I found in the
literature from a paper

225
00:11:02,760 --> 00:11:03,750
by Clemens.

226
00:11:03,750 --> 00:11:09,184
He fit a piecewise polynomial
to his observed data,

227
00:11:09,184 --> 00:11:10,600
and so we're
comparing it to that.

228
00:11:10,600 --> 00:11:16,290
We see actually that the
later values, the higher radii

229
00:11:16,290 --> 00:11:18,840
actually agree quite
well with the literature.

230
00:11:18,840 --> 00:11:20,220
We see a little
more disagreement

231
00:11:20,220 --> 00:11:21,810
with the lower values.

232
00:11:21,810 --> 00:11:24,520
This can be for
possibly a few reasons.

233
00:11:24,520 --> 00:11:28,986
One could be you might have
seen in that plot I had before

234
00:11:28,986 --> 00:11:33,779
that the temperature
starts to rise much slower,

235
00:11:33,779 --> 00:11:35,820
and so it's harder to find
an emission frequency.

236
00:11:35,820 --> 00:11:38,940
For these higher values,
there's a much sharper jump.

237
00:11:38,940 --> 00:11:42,960
Secondly, the actual
frequencies that you

238
00:11:42,960 --> 00:11:46,860
need to move these
points up to this line

239
00:11:46,860 --> 00:11:49,410
tend to be outside of
our frequency window

240
00:11:49,410 --> 00:11:53,030
or where that annoying
little noise was, so that's

241
00:11:53,030 --> 00:11:55,500
just somewhat of a
limitation of the apparatus.

242
00:11:55,500 --> 00:12:01,104
And then the third is the
circular orbit assumption.

243
00:12:01,104 --> 00:12:02,520
For smaller angles
this assumption

244
00:12:02,520 --> 00:12:05,070
becomes more critical, and so
even a small shift in angle

245
00:12:05,070 --> 00:12:08,490
can make a much
bigger difference.

246
00:12:08,490 --> 00:12:11,850
So we see, if we look
just at the later points,

247
00:12:11,850 --> 00:12:18,720
we actually get a pretty
decent chi squared of 13.4.

248
00:12:18,720 --> 00:12:22,290
So, yeah, this agrees fairly
well with the literature.

249
00:12:22,290 --> 00:12:24,210
So then there's one
more thing that we

250
00:12:24,210 --> 00:12:29,264
want to try to look at using
this 21 centimeter line,

251
00:12:29,264 --> 00:12:31,680
and that's going to be the
galactic structure of the Milky

252
00:12:31,680 --> 00:12:32,430
Way.

253
00:12:32,430 --> 00:12:34,312
As we talked about
before, we know

254
00:12:34,312 --> 00:12:35,770
that the Milky Way
has spiral arms,

255
00:12:35,770 --> 00:12:38,103
so we're going to try to see
if we can look out and find

256
00:12:38,103 --> 00:12:41,770
those structures.

257
00:12:41,770 --> 00:12:44,280
So in order to do
this, we specifically

258
00:12:44,280 --> 00:12:46,802
need to assume some sort
of galactic rotation curve,

259
00:12:46,802 --> 00:12:48,510
so we're going to be
working with the one

260
00:12:48,510 --> 00:12:50,550
that we found in Clemens.

261
00:12:50,550 --> 00:12:52,620
And using the
formulas before, we

262
00:12:52,620 --> 00:12:57,060
can use this given curve to
solve for a specific R given

263
00:12:57,060 --> 00:12:58,500
any observed velocity.

264
00:12:58,500 --> 00:13:03,360
So now we can associate
radii with all the velocities

265
00:13:03,360 --> 00:13:05,280
that we see.

266
00:13:05,280 --> 00:13:08,231
And, of course, this
is just the radius

267
00:13:08,231 --> 00:13:09,480
from the center of the galaxy.

268
00:13:09,480 --> 00:13:12,030
What we actually want
is the distance from us

269
00:13:12,030 --> 00:13:13,800
in order to be
able to plot this,

270
00:13:13,800 --> 00:13:18,580
so we can make that
quick change here.

271
00:13:18,580 --> 00:13:21,150
And now note that
this only really works

272
00:13:21,150 --> 00:13:24,330
for galactic longitudes
greater than 90.

273
00:13:24,330 --> 00:13:26,790
Those are things in the
second quadrant simply

274
00:13:26,790 --> 00:13:29,010
because, if we look inwards
to the first quadrant,

275
00:13:29,010 --> 00:13:32,280
there are two
possible solutions.

276
00:13:32,280 --> 00:13:33,780
Along the same line
of sight you can

277
00:13:33,780 --> 00:13:36,930
find two different points
that have the same distance

278
00:13:36,930 --> 00:13:39,660
from the center.

279
00:13:39,660 --> 00:13:45,540
And again, we're going to fit
these to a linear background

280
00:13:45,540 --> 00:13:49,657
now with 25 initial
bins and 10 final bins.

281
00:13:49,657 --> 00:13:51,240
And we're going to
say the temperature

282
00:13:51,240 --> 00:13:55,860
above the background
multiplied by the distance

283
00:13:55,860 --> 00:13:58,560
from us squared,
this is just because

284
00:13:58,560 --> 00:14:01,496
of an inverse square
power law, we're

285
00:14:01,496 --> 00:14:03,870
going to say that that gives
us a relative measure of how

286
00:14:03,870 --> 00:14:09,150
much hydrogen must be there and,
as a result, how much emission

287
00:14:09,150 --> 00:14:10,540
that we're seeing.

288
00:14:10,540 --> 00:14:15,330
So we can use these methods
and plot out of a big plot

289
00:14:15,330 --> 00:14:18,090
of what the second quadrant
of the Milky Way galaxy

290
00:14:18,090 --> 00:14:19,440
looks like.

291
00:14:19,440 --> 00:14:24,120
So you can see here, there are
two spiral arms we can see,

292
00:14:24,120 --> 00:14:28,710
one much closer to us and then
one forming out around here.

293
00:14:28,710 --> 00:14:32,970
Those actually correspond fairly
well with this Perseus arm here

294
00:14:32,970 --> 00:14:35,820
and then the outer
arm further out here.

295
00:14:35,820 --> 00:14:39,760
You might notice that, as we
get up to higher longitudes,

296
00:14:39,760 --> 00:14:41,460
the points start
to become larger.

297
00:14:41,460 --> 00:14:45,900
Here the points denote
the strength, yeah,

298
00:14:45,900 --> 00:14:47,700
the relative amount
of hydrogen that we

299
00:14:47,700 --> 00:14:51,600
would see in a region
out there based

300
00:14:51,600 --> 00:14:54,900
on the temperature
of the background.

301
00:14:54,900 --> 00:14:58,050
And so you might see
here that, as we get out

302
00:14:58,050 --> 00:15:01,620
to higher longitudes, we start
to see it blow up a little bit.

303
00:15:01,620 --> 00:15:06,820
We don't believe that this
is a physical consequence,

304
00:15:06,820 --> 00:15:08,130
that this is actually physical.

305
00:15:08,130 --> 00:15:11,250
This is more just a
limitation of the apparatus.

306
00:15:11,250 --> 00:15:14,190
So in conclusion, we were
able to use this 21 centimeter

307
00:15:14,190 --> 00:15:18,414
technique to derive the
rotation curve of the Milky Way,

308
00:15:18,414 --> 00:15:20,580
and we saw pretty good
agreement with the literature

309
00:15:20,580 --> 00:15:23,640
for large radii.

310
00:15:23,640 --> 00:15:26,880
In particular, we saw there was
a constant velocity function

311
00:15:26,880 --> 00:15:30,600
as we went out to
higher radii, and that

312
00:15:30,600 --> 00:15:32,890
disagrees with the
theoretical prediction.

313
00:15:32,890 --> 00:15:35,310
And so this really
necessitates some sort

314
00:15:35,310 --> 00:15:39,450
of dark matter, which can
compensate for the discrepancy.

315
00:15:39,450 --> 00:15:42,330
We were also able to see some
of the Milky Way structure

316
00:15:42,330 --> 00:15:45,450
by looking at the
exterior points.

317
00:15:45,450 --> 00:15:47,820
And in particular, we
saw two spiral arms

318
00:15:47,820 --> 00:15:50,910
in that second quadrant.

319
00:15:50,910 --> 00:15:53,735
And finally I would like to
thank my partner, Toby, for all

320
00:15:53,735 --> 00:15:55,110
his help throughout
this semester

321
00:15:55,110 --> 00:15:57,900
and on this particular
experiment, some last minute

322
00:15:57,900 --> 00:15:59,900
data collection.

323
00:15:59,900 --> 00:16:03,150
I'd like to thank the 8.13
staff for all their help

324
00:16:03,150 --> 00:16:05,400
throughout and
instruction and then MIT

325
00:16:05,400 --> 00:16:07,381
for offering this course.

326
00:16:07,381 --> 00:16:07,881
OK.

327
00:16:16,330 --> 00:16:17,324
PROFESSOR: Questions?

328
00:16:20,803 --> 00:16:21,619
SAARIK KALIA: Yeah?

329
00:16:21,619 --> 00:16:23,785
AUDIENCE: You mentioned
that you fit your background

330
00:16:23,785 --> 00:16:24,773
to a linear fit.

331
00:16:24,773 --> 00:16:25,773
SAARIK KALIA: All right.

332
00:16:25,773 --> 00:16:27,761
AUDIENCE: Why do you
expect the background

333
00:16:27,761 --> 00:16:29,749
to go up as you go in frequency?

334
00:16:29,749 --> 00:16:31,737
It seems like, at
least [INAUDIBLE],,

335
00:16:31,737 --> 00:16:36,230
it would just stay constant
across all the planes.

336
00:16:36,230 --> 00:16:41,312
SAARIK KALIA: So I think this
is essentially because of the--

337
00:16:41,312 --> 00:16:45,140
you would expect the temperature
that you see from a blackbody

338
00:16:45,140 --> 00:16:51,160
to go like Planck's Law
or his formula, right,

339
00:16:51,160 --> 00:16:53,132
the blackbody spectrum formula.

340
00:16:53,132 --> 00:16:54,590
But essentially
what we're doing is

341
00:16:54,590 --> 00:16:58,070
we're zooming in on a very,
very small part of that,

342
00:16:58,070 --> 00:17:00,200
specifically around
one frequency.

343
00:17:00,200 --> 00:17:02,539
And so in that
region, it's linear.

344
00:17:02,539 --> 00:17:03,080
AUDIENCE: OK.

345
00:17:03,080 --> 00:17:04,220
SAARIK KALIA: So this
is why we're expecting

346
00:17:04,220 --> 00:17:05,349
some sort of linear background.

347
00:17:05,349 --> 00:17:05,890
AUDIENCE: OK.

348
00:17:09,285 --> 00:17:10,761
PROFESSOR: Good questions?

349
00:17:14,210 --> 00:17:15,889
SAARIK KALIA: Yeah.

350
00:17:15,889 --> 00:17:18,545
AUDIENCE: What uncertainty do
you find in your temperature

351
00:17:18,545 --> 00:17:19,270
counts?

352
00:17:23,134 --> 00:17:27,000
Or is there uncertainty?

353
00:17:27,000 --> 00:17:32,890
SAARIK KALIA: So for the
rotation curve, the uncertainty

354
00:17:32,890 --> 00:17:33,390
in the--

355
00:17:33,390 --> 00:17:36,300
I mean, yeah, I guess there
should be some like Poisson

356
00:17:36,300 --> 00:17:38,340
uncertainty in the
temperature counts.

357
00:17:38,340 --> 00:17:39,960
For the rotation
curve, that's not

358
00:17:39,960 --> 00:17:41,370
as important
because what we care

359
00:17:41,370 --> 00:17:46,030
about is the frequency
at which it occurs.

360
00:17:46,030 --> 00:17:49,420
I guess for the
galactic structure,

361
00:17:49,420 --> 00:17:52,060
you really could put
some uncertainty on that

362
00:17:52,060 --> 00:17:56,020
and it would just be squared
of n Poisson uncertainty.

363
00:18:00,220 --> 00:18:00,820
PROFESSOR: OK.

364
00:18:00,820 --> 00:18:02,620
And no other questions?

365
00:18:02,620 --> 00:18:04,770
Thank the speaker again.