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3/24/13
Primordial Black Hole Dark Ma1er Kim Griest, March 2013 (with Agnieszka Cieplak and Ma1hew Lehner)   For decades we looked to SUSY, Grand Unification, String Theory, etc. for inspiration on the nature of the Dark Matter:   Low energy SUSY explained the hierarchy fine-­‐tuning problem and SUSY WIMPS “naturally” gave us an appropriate relic abundance   However, a Higgs at 126 GeV and no SUSY partners so far at the LHC increases the fine-­‐tuning required for SUSY Dark Matter (DM)   Perhaps we should draw inspiration, not from grand theories, but from remarkable recent experimental results which all seem to implicate the scalar field sector:   Anisotropy of CMB implies inflation probably from scalar fields   Accelerating expansion implies a cosmological constant, Λ, or quintessence type scalar field (even Λ can be thought of as a vacuum expectation value of a scalar field)   The value of the Higgs Boson mass is puzzling   Thus we have several scalar fields each of which forces us to confront non-­‐natural parameter values:   Inflaton field parameter values need to be fine-­‐tuned   Cosmological constant fine tuning problem is so severe that some even invoke anthropic arguments!   Higgs at 126 GeV requires some fine-­‐tuning (few percent) to solve hierarchy problem 1
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  Perhaps the DM problem is also part of the scalar field mystery; if so then Primordial Black Holes (PBHs) may be the answer   There are many ways to create PBHs in the early universe, many of which involve scalar fields, e.g. double inflation models where end of first inflation creates particles that cause PBH creation (Frampton et al, 2011), or where one inflation creates a very “tilted” spectrum that results in PBH formation and the other inflation solves the normal problems (anisotopies, flatness), etc. (Kawasaki, et al. 1998)   DM is observed as a gravitational problem; PBH DM would thus be a gravitational solution to a gravitation problem  Primordial Black Holes (PBHs) may be the answer…   PBH DM is one of the few STANDARD MODEL DM candidates   PBH DM is Cold DM, it evades BBN, CMB, baryon, etc. limits and can make up totality of DM (or a portion of it)   Theory has been a poor guide for physics of inflation, dark energy, and dark matter. But if PBH DM is discovered it probably gives insight into epoch and physics of formation; mass of PBH DM is typically the mass inside the horizon during formation epoch.   Thus all efforts should be made to discover PBH DM 2
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Examples of many ways to form PBH: Only 10% fluctuaOon needed   From Khlopov Review ( 2007): “They could be formed by many different mechanisms, e.g., initial density inhomogeneities [29, 30] and non-­‐linear metric perturbations [31, 32, 33], blue spectra of density fluctuations [34, 35, 36, 37, 38, 39], a softening of the equation of state [40, 34, 35], development of gravitational instability on early dust-­‐like stages of dominance of supermassive particles and scalar fields [41, 42, 43, 44] and evolution of gravitationally bound objects formed at these stages [45, 46], collapse of cosmic strings [47, 48, 49, 50, 51] and necklaces [52], a double inflation scenario [53, 54, 55, 56], first order phase transitions [57, 58, 59, 60, 61], a step in the power spectrum [62, 63], etc”. Mass of PBH typically is given by horizon mass at formaOon epoch   Some formation mechanisms give a wide distribution of masses, but double inflation formation mechanisms tend to give nearly delta function distributions:   MPBH = 0.05 Msun (g*/100)-­‐1/2 (Tform/GeV)-­‐2, so for MPBH=10-­‐8 Msun, Tform ~ 2 TeV   Relic density given by details of scalar field potentials giving rise to inflations (yes it is fine-­‐tuned, like always with scalar fields!) 3
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Experiment has been main guide to Primordial Black Hole Dark Ma1er   Many experiments eliminate most masses, but interesting window left Msun = 2 x 1033 g
Carr et al. 2005 Experiment has been main guide to Primordial Black Hole Dark Ma1er   Many experiments eliminate most masses, but interesting window left Msun = 2 x 1033 g
Carr et al. 2005 4
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Interesting recent limits based existence of neutron stars in Globular Clusters
(Capela, Pshirkov, Tinyakov (2013))
BUT: requires 3000 times normal halo DM density in GCs and very optimistic
capture rate.
If true, then only one small window left below MACHO/EROS microlensing limits
  We realized that the 1998 MACHO/EROS limits could probably be improved using current planet microlensing experiments, but then thought of something new:   The Kepler spacecraft in its search for extra-­‐solar planets might be far better than any of the ground-­‐based microlensing searches   We were surprised how much better Kepler analysis could be: Can detect or rule out PBH DM over much of the remaining PBH mass range! 5
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Kepler Mission   1 m aperture telescope with 115 deg2 FOV in an Earth trailing heliocentric orbit   Photometric measurements of ~170,000 stars every 30 min, each with 0.03% precision; for 7.5 years   Goal is to detect small dip in lightcurve caused by a planet transiting in front of its star So far discovered ~2000 extra-­‐solar planets 6
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Kepler has found around 2000 planet candidates Kepler looks for downward bumps; we want upward bumps Data processing needed for PBH microlensing is similar to that needed for planet search! 7
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  Surprise that Kepler is useful because:   Probability of detection is proportional to number of stars monitored, the distance to the stars and the duration of the experiment   LMC microlensing surveys monitored 12 million stars at a distance of 50 kpc for 8 years.   Kepler will monitor 160,000 stars at a distance of 1 kpc for 7.5 years; naively 4000 times less sensitive   Two key new ideas:   extreme precision allows very low magnification microlensing events to be detected; enhances detection rate by factor of 30   Small mass of allowed PBH candidates imply lensing finite source effects enhance detection rates by a factor of 3000   Kepler wins for PBH’s in mass range 5 x 10-­‐10 to 10-­‐6 solar masses, for the first time allowing exploration of almost two orders of magnitude of remaining PBH DM mass range New microlensing theory   Microlensing “occurs” when PBH !enters microlensing “tube” which has Einstein radius rE = 0.0193 x(1 − x)[(Ds /kpc)(m/10−9 )m" )]1/2 R"
  Inside tube, magnification > AT = 1.34, but Kepler allows AT=1.001, which increase the tube volume by a factor of 36.   The rate of events is the rate at which PBHs enter the tube.   For normal mass MACHOs, rE >> Rstar, but for mPBH in the PBH DM window (10-­‐12 < mPBH < 10-­‐7 Solar mass), rE < Rstar, so the effective tube radius becomes the projected radius of the star.   For mPBH=10-­‐9, Ds=1 kpc, x=0.5, we find increase to be u*=xR*/rE ~ 52, giving an event rate ~2700 times larger Star
Einstein ring
8
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  Finite Source => detection rate increases, but shape of microlensing lightcurve also changes (Witt and Mao !
1994). 1 + 4/u2∗
  Maxmimum magnification: Amax =
  New microlensing rate formalism needed CalculaOon of number of expected microlensing events in 8 years of Kepler data to find possible reach of experiment • Used standard DM density, ρ, along the line-­‐of-­‐sight and a Maxwellian velocity distribution, g(v) • Integrated the differential event rate over a relevant range of event durations: x max
dΓ ρ
= DS v c2 ∫ dx β'2 g( β')
dt e m
0
1
g( β') =
∫ dy y
3/2
(1 − y) −1/ 2 e − β ' y
y = v r2 /( β'v c2 )
2
β' = 4rE2 uthresh
/(t e2 v c2 )
0
• Require 4 sequential measurements 3 sigma above avg (at least 2 hr duration) €
€
• Include subtleties such as maximum distance lens, xmax for A to be detectable €
€
D
x = L →1: Amax →1 since u* →∞
DS
€
9
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Potential results of search through 7.5 years of Kepler
data if no events detected
•  Solid line: our predictions; dashed lined previous best results (MACHO/
EROS 1998); Areas above curved ruled out at 95% CL; thin horizontal
line show 100% PBH
Dark Matter
•  Thin horizontal
lines show DM
Halo consisting
entirely of PBH
•  Based upon
157,000 3rd
quarter light
curves
•  Require not a
variable & 4
conseq meas 3sigma above
median
If Microlensing events are detected PBH mass distribuOon can be determined (but probably not distance) Distance likelihood is very wide. It will not be easy to determine the distances to the lens. A. M. Cieplak and KG 2012 3/24/13 BNL For each event, likelihood can be calculated. The product of these likelihood funcOons would give us an esOmate of the PBH DM 20 10
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Can we do be1er than Kepler? •  Better stars can be selected
•  Event rate is strong function of effective temp of star:
•  WFIRST will be better!
Γ ~ Teff12
BNL 21 WFIRST
WFIRST •  Designed to search for Dark Energy and extrasolar planets •  Preliminary specificaOons: 2 x 108 stars monitored towards the galacOc bulge with a cadence of 15 min and a 1 % photometry precision (Benne1 et al. 2010) 3/24/13 BNL Expected number of events •  Solid line: predicOon for WFIRST •  Dashed line: PredicOon for Kepler (A. M. Cieplak and KG 2012) 22 11
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Enough Theory, Let’s look through data! 5th quarter data
Several beautiful
microlensing
events!
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Comet! 294
entries 28 / 28
entries 28 / 28
46
292
44
290
288
42
286
40
284
38
282
460
480
500
520
540
460
480
btime
520
540
Comet C/2206 Q1 (McNaught) entries 28 / 28
46
500
btime
Constant velocity: 16 arcseconds/hour = 3.3 km/s (distance/1AU) Distance 10 AU 44
42
40
38
282
284
286
3/24/13 288
290
ra
BNL 292
294
25 5878249 index=25 lag=0.2973689735 rr=8.431999207 ll=6.749929428 i=25
entries 59 / 59
0.002
0.001
0
313
313.5
314
time
entries 599 / 599
0.002
0.001
0
310
315
320
time
entries 4112 / 4112
0.002
0.001
• But also a large
background of variable
star events that must
be eliminated
• Most importantly
many stellar flare
events are present
• These are actually
discoveries in their
own right since not
seen before on Sunlike stars!
• Can be eliminated as
PBHs by asymmetry
and shape; fast rise
and exponential fall
0
-0.001
260
280
300
320
340
time
13
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Quarter 9 candidate: Comet?
3/24/13 BNL 27 More Comets and…Candidates? 3/24/13 BNL 28 14
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New Limits on PBH DM   Develop selection criteria to distinguish microlensing from background, e.g.   Good fit to microlensing lightcurve   Better fit to microlensing than flare event; not asymmetric   >4 sequential measurements, 3-­‐sigma above median   Various stats to eliminate variable stars   With tight cuts, no candidates found in first two years Kepler data!   Add millions of fake microlensing events into real data to measure efficiency of DM detection as a function of DM mass (use same selection criteria as for real microlensing)   Predict number of microlensing events that should be detected given Kepler data and above efficiencies   Limits on density of PBH DM NEW (PRELIMINARY) RESULTS   Black solid line: 95% CL exclusion (two years data, strict cuts (no candidates found))(KG,Cieplak,Lehner)   Black dashed line: MACHO/EROS limit (Alcock, et al. 1998)   Red dashed line: GRB femtolensing limit (Barnacka, et al, 2012)   Blue dashed line: our theoretical limit from the entire Kepler mission (Cieplak, KG) 15
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Summary   PBHs make an excellent DM candidate   New techniques may allow search over entire remaining parameter space   Microlensing, esp. with Kepler or upcoming satellite missions should be very powerful   Preliminary limits from Kepler are moving into new area of parameter space ApproximaOon for Future Star SelecOon Γ ~ Teff12
4
3
% L ( 6 % R* ( 6 % M ( % 1hr (
1
1
Γ ≈ 2.63 × 10 20 '
* '
*
*' *'
5
& 1kpc ) & R ) & M⊗ ) & t min ) Athresh 2 −1 year
(
3/24/13 €
BNL )
32 16